/* Generated by Cython 3.1.6 */

/* BEGIN: Cython Metadata
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#ifndef Py_UNREACHABLE
  #define Py_UNREACHABLE()  assert(0); abort()
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#ifdef __cplusplus
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  #define __PYX_NEED_TP_PRINT_SLOT  (PY_VERSION_HEX >= 0x030800b4 && PY_VERSION_HEX < 0x03090000)
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#define __PYX_REINTERPRET_FUNCION(func_pointer, other_pointer) ((func_pointer)(void(*)(void))(other_pointer))

/* CInitCode */
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    #define CYTHON_INLINE __inline__
  #elif defined(_MSC_VER)
    #define CYTHON_INLINE __inline
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    #define CYTHON_INLINE
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/* PythonCompatibility */
#define __PYX_BUILD_PY_SSIZE_T "n"
#define CYTHON_FORMAT_SSIZE_T "z"
#define __Pyx_BUILTIN_MODULE_NAME "builtins"
#define __Pyx_DefaultClassType PyType_Type
#if CYTHON_COMPILING_IN_LIMITED_API
    #ifndef CO_OPTIMIZED
    static int CO_OPTIMIZED;
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    #ifndef CO_NEWLOCALS
    static int CO_NEWLOCALS;
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    #ifndef CO_VARKEYWORDS
    static int CO_VARKEYWORDS;
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    #ifndef CO_ASYNC_GENERATOR
    static int CO_ASYNC_GENERATOR;
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    #ifndef CO_GENERATOR
    static int CO_GENERATOR;
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    #ifndef CO_COROUTINE
    static int CO_COROUTINE;
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#else
    #ifndef CO_COROUTINE
      #define CO_COROUTINE 0x80
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    #ifndef CO_ASYNC_GENERATOR
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static int __Pyx_init_co_variables(void);
#if PY_VERSION_HEX >= 0x030900A4 || defined(Py_IS_TYPE)
  #define __Pyx_IS_TYPE(ob, type) Py_IS_TYPE(ob, type)
#else
  #define __Pyx_IS_TYPE(ob, type) (((const PyObject*)ob)->ob_type == (type))
#endif
#if PY_VERSION_HEX >= 0x030A00B1 || defined(Py_Is)
  #define __Pyx_Py_Is(x, y)  Py_Is(x, y)
#else
  #define __Pyx_Py_Is(x, y) ((x) == (y))
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#if PY_VERSION_HEX >= 0x030A00B1 || defined(Py_IsNone)
  #define __Pyx_Py_IsNone(ob) Py_IsNone(ob)
#else
  #define __Pyx_Py_IsNone(ob) __Pyx_Py_Is((ob), Py_None)
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#if PY_VERSION_HEX >= 0x030A00B1 || defined(Py_IsTrue)
  #define __Pyx_Py_IsTrue(ob) Py_IsTrue(ob)
#else
  #define __Pyx_Py_IsTrue(ob) __Pyx_Py_Is((ob), Py_True)
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#if PY_VERSION_HEX >= 0x030A00B1 || defined(Py_IsFalse)
  #define __Pyx_Py_IsFalse(ob) Py_IsFalse(ob)
#else
  #define __Pyx_Py_IsFalse(ob) __Pyx_Py_Is((ob), Py_False)
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#define __Pyx_NoneAsNull(obj)  (__Pyx_Py_IsNone(obj) ? NULL : (obj))
#if PY_VERSION_HEX >= 0x030900F0 && !CYTHON_COMPILING_IN_PYPY
  #define __Pyx_PyObject_GC_IsFinalized(o) PyObject_GC_IsFinalized(o)
#else
  #define __Pyx_PyObject_GC_IsFinalized(o) _PyGC_FINALIZED(o)
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#ifndef Py_TPFLAGS_CHECKTYPES
  #define Py_TPFLAGS_CHECKTYPES 0
#endif
#ifndef Py_TPFLAGS_HAVE_INDEX
  #define Py_TPFLAGS_HAVE_INDEX 0
#endif
#ifndef Py_TPFLAGS_HAVE_NEWBUFFER
  #define Py_TPFLAGS_HAVE_NEWBUFFER 0
#endif
#ifndef Py_TPFLAGS_HAVE_FINALIZE
  #define Py_TPFLAGS_HAVE_FINALIZE 0
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#ifndef Py_TPFLAGS_SEQUENCE
  #define Py_TPFLAGS_SEQUENCE 0
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#ifndef Py_TPFLAGS_MAPPING
  #define Py_TPFLAGS_MAPPING 0
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#ifndef METH_STACKLESS
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#ifndef METH_FASTCALL
  #ifndef METH_FASTCALL
     #define METH_FASTCALL 0x80
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  typedef PyObject *(*__Pyx_PyCFunctionFast) (PyObject *self, PyObject *const *args, Py_ssize_t nargs);
  typedef PyObject *(*__Pyx_PyCFunctionFastWithKeywords) (PyObject *self, PyObject *const *args,
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#else
  #if PY_VERSION_HEX >= 0x030d00A4
  #  define __Pyx_PyCFunctionFast PyCFunctionFast
  #  define __Pyx_PyCFunctionFastWithKeywords PyCFunctionFastWithKeywords
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  #  define __Pyx_PyCFunctionFast _PyCFunctionFast
  #  define __Pyx_PyCFunctionFastWithKeywords _PyCFunctionFastWithKeywords
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#if CYTHON_METH_FASTCALL
  #define __Pyx_METH_FASTCALL METH_FASTCALL
  #define __Pyx_PyCFunction_FastCall __Pyx_PyCFunctionFast
  #define __Pyx_PyCFunction_FastCallWithKeywords __Pyx_PyCFunctionFastWithKeywords
#else
  #define __Pyx_METH_FASTCALL METH_VARARGS
  #define __Pyx_PyCFunction_FastCall PyCFunction
  #define __Pyx_PyCFunction_FastCallWithKeywords PyCFunctionWithKeywords
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#if CYTHON_VECTORCALL
  #define __pyx_vectorcallfunc vectorcallfunc
  #define __Pyx_PY_VECTORCALL_ARGUMENTS_OFFSET  PY_VECTORCALL_ARGUMENTS_OFFSET
  #define __Pyx_PyVectorcall_NARGS(n)  PyVectorcall_NARGS((size_t)(n))
#elif CYTHON_BACKPORT_VECTORCALL
  typedef PyObject *(*__pyx_vectorcallfunc)(PyObject *callable, PyObject *const *args,
                                            size_t nargsf, PyObject *kwnames);
  #define __Pyx_PY_VECTORCALL_ARGUMENTS_OFFSET  ((size_t)1 << (8 * sizeof(size_t) - 1))
  #define __Pyx_PyVectorcall_NARGS(n)  ((Py_ssize_t)(((size_t)(n)) & ~__Pyx_PY_VECTORCALL_ARGUMENTS_OFFSET))
#else
  #define __Pyx_PY_VECTORCALL_ARGUMENTS_OFFSET  0
  #define __Pyx_PyVectorcall_NARGS(n)  ((Py_ssize_t)(n))
#endif
#if PY_VERSION_HEX >= 0x030900B1
#define __Pyx_PyCFunction_CheckExact(func)  PyCFunction_CheckExact(func)
#else
#define __Pyx_PyCFunction_CheckExact(func)  PyCFunction_Check(func)
#endif
#define __Pyx_CyOrPyCFunction_Check(func)  PyCFunction_Check(func)
#if CYTHON_COMPILING_IN_CPYTHON
#define __Pyx_CyOrPyCFunction_GET_FUNCTION(func)  (((PyCFunctionObject*)(func))->m_ml->ml_meth)
#elif !CYTHON_COMPILING_IN_LIMITED_API
#define __Pyx_CyOrPyCFunction_GET_FUNCTION(func)  PyCFunction_GET_FUNCTION(func)
#endif
#if CYTHON_COMPILING_IN_CPYTHON
#define __Pyx_CyOrPyCFunction_GET_FLAGS(func)  (((PyCFunctionObject*)(func))->m_ml->ml_flags)
static CYTHON_INLINE PyObject* __Pyx_CyOrPyCFunction_GET_SELF(PyObject *func) {
    return (__Pyx_CyOrPyCFunction_GET_FLAGS(func) & METH_STATIC) ? NULL : ((PyCFunctionObject*)func)->m_self;
}
#endif
static CYTHON_INLINE int __Pyx__IsSameCFunction(PyObject *func, void (*cfunc)(void)) {
#if CYTHON_COMPILING_IN_LIMITED_API
    return PyCFunction_Check(func) && PyCFunction_GetFunction(func) == (PyCFunction) cfunc;
#else
    return PyCFunction_Check(func) && PyCFunction_GET_FUNCTION(func) == (PyCFunction) cfunc;
#endif
}
#define __Pyx_IsSameCFunction(func, cfunc)   __Pyx__IsSameCFunction(func, cfunc)
#if __PYX_LIMITED_VERSION_HEX < 0x03090000
  #define __Pyx_PyType_FromModuleAndSpec(m, s, b)  ((void)m, PyType_FromSpecWithBases(s, b))
  typedef PyObject *(*__Pyx_PyCMethod)(PyObject *, PyTypeObject *, PyObject *const *, size_t, PyObject *);
#else
  #define __Pyx_PyType_FromModuleAndSpec(m, s, b)  PyType_FromModuleAndSpec(m, s, b)
  #define __Pyx_PyCMethod  PyCMethod
#endif
#ifndef METH_METHOD
  #define METH_METHOD 0x200
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#if CYTHON_COMPILING_IN_PYPY && !defined(PyObject_Malloc)
  #define PyObject_Malloc(s)   PyMem_Malloc(s)
  #define PyObject_Free(p)     PyMem_Free(p)
  #define PyObject_Realloc(p)  PyMem_Realloc(p)
#endif
#if CYTHON_COMPILING_IN_LIMITED_API
  #define __Pyx_PyFrame_SetLineNumber(frame, lineno)
#elif CYTHON_COMPILING_IN_GRAAL
  #define __Pyx_PyCode_HasFreeVars(co)  (PyCode_GetNumFree(co) > 0)
  #define __Pyx_PyFrame_SetLineNumber(frame, lineno) _PyFrame_SetLineNumber((frame), (lineno))
#else
  #define __Pyx_PyCode_HasFreeVars(co)  (PyCode_GetNumFree(co) > 0)
  #define __Pyx_PyFrame_SetLineNumber(frame, lineno)  (frame)->f_lineno = (lineno)
#endif
#if CYTHON_COMPILING_IN_LIMITED_API
  #define __Pyx_PyThreadState_Current PyThreadState_Get()
#elif !CYTHON_FAST_THREAD_STATE
  #define __Pyx_PyThreadState_Current PyThreadState_GET()
#elif PY_VERSION_HEX >= 0x030d00A1
  #define __Pyx_PyThreadState_Current PyThreadState_GetUnchecked()
#else
  #define __Pyx_PyThreadState_Current _PyThreadState_UncheckedGet()
#endif
#if CYTHON_USE_MODULE_STATE
static CYTHON_INLINE void *__Pyx__PyModule_GetState(PyObject *op)
{
    void *result;
    result = PyModule_GetState(op);
    if (!result)
        Py_FatalError("Couldn't find the module state");
    return result;
}
#define __Pyx_PyModule_GetState(o) (__pyx_mstatetype *)__Pyx__PyModule_GetState(o)
#else
#define __Pyx_PyModule_GetState(op) ((void)op,__pyx_mstate_global)
#endif
#define __Pyx_PyObject_GetSlot(obj, name, func_ctype)  __Pyx_PyType_GetSlot(Py_TYPE((PyObject *) obj), name, func_ctype)
#define __Pyx_PyObject_TryGetSlot(obj, name, func_ctype) __Pyx_PyType_TryGetSlot(Py_TYPE(obj), name, func_ctype)
#define __Pyx_PyObject_GetSubSlot(obj, sub, name, func_ctype) __Pyx_PyType_GetSubSlot(Py_TYPE(obj), sub, name, func_ctype)
#define __Pyx_PyObject_TryGetSubSlot(obj, sub, name, func_ctype) __Pyx_PyType_TryGetSubSlot(Py_TYPE(obj), sub, name, func_ctype)
#if CYTHON_USE_TYPE_SLOTS
  #define __Pyx_PyType_GetSlot(type, name, func_ctype)  ((type)->name)
  #define __Pyx_PyType_TryGetSlot(type, name, func_ctype) __Pyx_PyType_GetSlot(type, name, func_ctype)
  #define __Pyx_PyType_GetSubSlot(type, sub, name, func_ctype) (((type)->sub) ? ((type)->sub->name) : NULL)
  #define __Pyx_PyType_TryGetSubSlot(type, sub, name, func_ctype) __Pyx_PyType_GetSubSlot(type, sub, name, func_ctype)
#else
  #define __Pyx_PyType_GetSlot(type, name, func_ctype)  ((func_ctype) PyType_GetSlot((type), Py_##name))
  #define __Pyx_PyType_TryGetSlot(type, name, func_ctype)\
    ((__PYX_LIMITED_VERSION_HEX >= 0x030A0000 ||\
     (PyType_GetFlags(type) & Py_TPFLAGS_HEAPTYPE) || __Pyx_get_runtime_version() >= 0x030A0000) ?\
     __Pyx_PyType_GetSlot(type, name, func_ctype) : NULL)
  #define __Pyx_PyType_GetSubSlot(obj, sub, name, func_ctype) __Pyx_PyType_GetSlot(obj, name, func_ctype)
  #define __Pyx_PyType_TryGetSubSlot(obj, sub, name, func_ctype) __Pyx_PyType_TryGetSlot(obj, name, func_ctype)
#endif
#if CYTHON_COMPILING_IN_CPYTHON || defined(_PyDict_NewPresized)
#define __Pyx_PyDict_NewPresized(n)  ((n <= 8) ? PyDict_New() : _PyDict_NewPresized(n))
#else
#define __Pyx_PyDict_NewPresized(n)  PyDict_New()
#endif
#define __Pyx_PyNumber_Divide(x,y)         PyNumber_TrueDivide(x,y)
#define __Pyx_PyNumber_InPlaceDivide(x,y)  PyNumber_InPlaceTrueDivide(x,y)
#if CYTHON_COMPILING_IN_CPYTHON && CYTHON_USE_UNICODE_INTERNALS
#define __Pyx_PyDict_GetItemStrWithError(dict, name)  _PyDict_GetItem_KnownHash(dict, name, ((PyASCIIObject *) name)->hash)
static CYTHON_INLINE PyObject * __Pyx_PyDict_GetItemStr(PyObject *dict, PyObject *name) {
    PyObject *res = __Pyx_PyDict_GetItemStrWithError(dict, name);
    if (res == NULL) PyErr_Clear();
    return res;
}
#elif !CYTHON_COMPILING_IN_PYPY || PYPY_VERSION_NUM >= 0x07020000
#define __Pyx_PyDict_GetItemStrWithError  PyDict_GetItemWithError
#define __Pyx_PyDict_GetItemStr           PyDict_GetItem
#else
static CYTHON_INLINE PyObject * __Pyx_PyDict_GetItemStrWithError(PyObject *dict, PyObject *name) {
#if CYTHON_COMPILING_IN_PYPY
    return PyDict_GetItem(dict, name);
#else
    PyDictEntry *ep;
    PyDictObject *mp = (PyDictObject*) dict;
    long hash = ((PyStringObject *) name)->ob_shash;
    assert(hash != -1);
    ep = (mp->ma_lookup)(mp, name, hash);
    if (ep == NULL) {
        return NULL;
    }
    return ep->me_value;
#endif
}
#define __Pyx_PyDict_GetItemStr           PyDict_GetItem
#endif
#if CYTHON_USE_TYPE_SLOTS
  #define __Pyx_PyType_GetFlags(tp)   (((PyTypeObject *)tp)->tp_flags)
  #define __Pyx_PyType_HasFeature(type, feature)  ((__Pyx_PyType_GetFlags(type) & (feature)) != 0)
#else
  #define __Pyx_PyType_GetFlags(tp)   (PyType_GetFlags((PyTypeObject *)tp))
  #define __Pyx_PyType_HasFeature(type, feature)  PyType_HasFeature(type, feature)
#endif
#define __Pyx_PyObject_GetIterNextFunc(iterator)  __Pyx_PyObject_GetSlot(iterator, tp_iternext, iternextfunc)
#if CYTHON_USE_TYPE_SPECS && PY_VERSION_HEX >= 0x03080000
#define __Pyx_PyHeapTypeObject_GC_Del(obj)  {\
    PyTypeObject *type = Py_TYPE((PyObject*)obj);\
    assert(__Pyx_PyType_HasFeature(type, Py_TPFLAGS_HEAPTYPE));\
    PyObject_GC_Del(obj);\
    Py_DECREF(type);\
}
#else
#define __Pyx_PyHeapTypeObject_GC_Del(obj)  PyObject_GC_Del(obj)
#endif
#if CYTHON_COMPILING_IN_LIMITED_API
  #define __Pyx_PyUnicode_READY(op)       (0)
  #define __Pyx_PyUnicode_READ_CHAR(u, i) PyUnicode_ReadChar(u, i)
  #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u)   ((void)u, 1114111U)
  #define __Pyx_PyUnicode_KIND(u)         ((void)u, (0))
  #define __Pyx_PyUnicode_DATA(u)         ((void*)u)
  #define __Pyx_PyUnicode_READ(k, d, i)   ((void)k, PyUnicode_ReadChar((PyObject*)(d), i))
  #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != PyUnicode_GetLength(u))
#else
  #if PY_VERSION_HEX >= 0x030C0000
    #define __Pyx_PyUnicode_READY(op)       (0)
  #else
    #define __Pyx_PyUnicode_READY(op)       (likely(PyUnicode_IS_READY(op)) ?\
                                                0 : _PyUnicode_Ready((PyObject *)(op)))
  #endif
  #define __Pyx_PyUnicode_READ_CHAR(u, i) PyUnicode_READ_CHAR(u, i)
  #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u)   PyUnicode_MAX_CHAR_VALUE(u)
  #define __Pyx_PyUnicode_KIND(u)         ((int)PyUnicode_KIND(u))
  #define __Pyx_PyUnicode_DATA(u)         PyUnicode_DATA(u)
  #define __Pyx_PyUnicode_READ(k, d, i)   PyUnicode_READ(k, d, i)
  #define __Pyx_PyUnicode_WRITE(k, d, i, ch)  PyUnicode_WRITE(k, d, i, (Py_UCS4) ch)
  #if PY_VERSION_HEX >= 0x030C0000
    #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != PyUnicode_GET_LENGTH(u))
  #else
    #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x03090000
    #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != (likely(PyUnicode_IS_READY(u)) ? PyUnicode_GET_LENGTH(u) : ((PyCompactUnicodeObject *)(u))->wstr_length))
    #else
    #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != (likely(PyUnicode_IS_READY(u)) ? PyUnicode_GET_LENGTH(u) : PyUnicode_GET_SIZE(u)))
    #endif
  #endif
#endif
#if CYTHON_COMPILING_IN_PYPY
  #define __Pyx_PyUnicode_Concat(a, b)      PyNumber_Add(a, b)
  #define __Pyx_PyUnicode_ConcatSafe(a, b)  PyNumber_Add(a, b)
#else
  #define __Pyx_PyUnicode_Concat(a, b)      PyUnicode_Concat(a, b)
  #define __Pyx_PyUnicode_ConcatSafe(a, b)  ((unlikely((a) == Py_None) || unlikely((b) == Py_None)) ?\
      PyNumber_Add(a, b) : __Pyx_PyUnicode_Concat(a, b))
#endif
#if CYTHON_COMPILING_IN_PYPY
  #if !defined(PyUnicode_DecodeUnicodeEscape)
    #define PyUnicode_DecodeUnicodeEscape(s, size, errors)  PyUnicode_Decode(s, size, "unicode_escape", errors)
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  #if !defined(PyUnicode_Contains)
    #define PyUnicode_Contains(u, s)  PySequence_Contains(u, s)
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  #if !defined(PyByteArray_Check)
    #define PyByteArray_Check(obj)  PyObject_TypeCheck(obj, &PyByteArray_Type)
  #endif
  #if !defined(PyObject_Format)
    #define PyObject_Format(obj, fmt)  PyObject_CallMethod(obj, "__format__", "O", fmt)
  #endif
#endif
#define __Pyx_PyUnicode_FormatSafe(a, b)  ((unlikely((a) == Py_None || (PyUnicode_Check(b) && !PyUnicode_CheckExact(b)))) ? PyNumber_Remainder(a, b) : PyUnicode_Format(a, b))
#if CYTHON_COMPILING_IN_CPYTHON
  #define __Pyx_PySequence_ListKeepNew(obj)\
    (likely(PyList_CheckExact(obj) && Py_REFCNT(obj) == 1) ? __Pyx_NewRef(obj) : PySequence_List(obj))
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  #define __Pyx_PySequence_ListKeepNew(obj)  PySequence_List(obj)
#endif
#ifndef PySet_CheckExact
  #define PySet_CheckExact(obj)        __Pyx_IS_TYPE(obj, &PySet_Type)
#endif
#if PY_VERSION_HEX >= 0x030900A4
  #define __Pyx_SET_REFCNT(obj, refcnt) Py_SET_REFCNT(obj, refcnt)
  #define __Pyx_SET_SIZE(obj, size) Py_SET_SIZE(obj, size)
#else
  #define __Pyx_SET_REFCNT(obj, refcnt) Py_REFCNT(obj) = (refcnt)
  #define __Pyx_SET_SIZE(obj, size) Py_SIZE(obj) = (size)
#endif
#if CYTHON_AVOID_BORROWED_REFS || CYTHON_AVOID_THREAD_UNSAFE_BORROWED_REFS
  #if __PYX_LIMITED_VERSION_HEX >= 0x030d0000
    #define __Pyx_PyList_GetItemRef(o, i) PyList_GetItemRef(o, i)
  #elif CYTHON_COMPILING_IN_LIMITED_API || !CYTHON_ASSUME_SAFE_MACROS
    #define __Pyx_PyList_GetItemRef(o, i) (likely((i) >= 0) ? PySequence_GetItem(o, i) : (PyErr_SetString(PyExc_IndexError, "list index out of range"), (PyObject*)NULL))
  #else
    #define __Pyx_PyList_GetItemRef(o, i) PySequence_ITEM(o, i)
  #endif
#elif CYTHON_COMPILING_IN_LIMITED_API || !CYTHON_ASSUME_SAFE_MACROS
  #if __PYX_LIMITED_VERSION_HEX >= 0x030d0000
    #define __Pyx_PyList_GetItemRef(o, i) PyList_GetItemRef(o, i)
  #else
    #define __Pyx_PyList_GetItemRef(o, i) __Pyx_XNewRef(PyList_GetItem(o, i))
  #endif
#else
  #define __Pyx_PyList_GetItemRef(o, i) __Pyx_NewRef(PyList_GET_ITEM(o, i))
#endif
#if __PYX_LIMITED_VERSION_HEX >= 0x030d0000
#define __Pyx_PyDict_GetItemRef(dict, key, result) PyDict_GetItemRef(dict, key, result)
#elif CYTHON_AVOID_BORROWED_REFS || CYTHON_AVOID_THREAD_UNSAFE_BORROWED_REFS
static CYTHON_INLINE int __Pyx_PyDict_GetItemRef(PyObject *dict, PyObject *key, PyObject **result) {
  *result = PyObject_GetItem(dict, key);
  if (*result == NULL) {
    if (PyErr_ExceptionMatches(PyExc_KeyError)) {
      PyErr_Clear();
      return 0;
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    return -1;
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  return 1;
}
#else
static CYTHON_INLINE int __Pyx_PyDict_GetItemRef(PyObject *dict, PyObject *key, PyObject **result) {
  *result = PyDict_GetItemWithError(dict, key);
  if (*result == NULL) {
    return PyErr_Occurred() ? -1 : 0;
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  Py_INCREF(*result);
  return 1;
}
#endif
#if defined(CYTHON_DEBUG_VISIT_CONST) && CYTHON_DEBUG_VISIT_CONST
  #define __Pyx_VISIT_CONST(obj)  Py_VISIT(obj)
#else
  #define __Pyx_VISIT_CONST(obj)
#endif
#if CYTHON_ASSUME_SAFE_MACROS
  #define __Pyx_PySequence_ITEM(o, i) PySequence_ITEM(o, i)
  #define __Pyx_PySequence_SIZE(seq)  Py_SIZE(seq)
  #define __Pyx_PyTuple_SET_ITEM(o, i, v) (PyTuple_SET_ITEM(o, i, v), (0))
  #define __Pyx_PyTuple_GET_ITEM(o, i) PyTuple_GET_ITEM(o, i)
  #define __Pyx_PyList_SET_ITEM(o, i, v) (PyList_SET_ITEM(o, i, v), (0))
  #define __Pyx_PyList_GET_ITEM(o, i) PyList_GET_ITEM(o, i)
#else
  #define __Pyx_PySequence_ITEM(o, i) PySequence_GetItem(o, i)
  #define __Pyx_PySequence_SIZE(seq)  PySequence_Size(seq)
  #define __Pyx_PyTuple_SET_ITEM(o, i, v) PyTuple_SetItem(o, i, v)
  #define __Pyx_PyTuple_GET_ITEM(o, i) PyTuple_GetItem(o, i)
  #define __Pyx_PyList_SET_ITEM(o, i, v) PyList_SetItem(o, i, v)
  #define __Pyx_PyList_GET_ITEM(o, i) PyList_GetItem(o, i)
#endif
#if CYTHON_ASSUME_SAFE_SIZE
  #define __Pyx_PyTuple_GET_SIZE(o) PyTuple_GET_SIZE(o)
  #define __Pyx_PyList_GET_SIZE(o) PyList_GET_SIZE(o)
  #define __Pyx_PySet_GET_SIZE(o) PySet_GET_SIZE(o)
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#elif defined(__PYX_EXTERN_C)
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#include "numpy/arrayobject.h"
#include "numpy/ndarrayobject.h"
#include "numpy/ndarraytypes.h"
#include "numpy/arrayscalars.h"
#include "numpy/ufuncobject.h"
#include <math.h>
#include <stdlib.h>
#ifdef _OPENMP
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#if defined(PYREX_WITHOUT_ASSERTIONS) && !defined(CYTHON_WITHOUT_ASSERTIONS)
#define CYTHON_WITHOUT_ASSERTIONS
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#define __PYX_DEFAULT_STRING_ENCODING_IS_ASCII 0
#define __PYX_DEFAULT_STRING_ENCODING_IS_UTF8 0
#define __PYX_DEFAULT_STRING_ENCODING ""
#define __Pyx_PyObject_FromString __Pyx_PyBytes_FromString
#define __Pyx_PyObject_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
#define __Pyx_uchar_cast(c) ((unsigned char)c)
#define __Pyx_long_cast(x) ((long)x)
#define __Pyx_fits_Py_ssize_t(v, type, is_signed)  (\
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static CYTHON_INLINE int __Pyx_is_valid_index(Py_ssize_t i, Py_ssize_t limit) {
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    #define __Pyx_sst_abs(value) labs(value)
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static CYTHON_INLINE Py_ssize_t __Pyx_ssize_strlen(const char *s);
static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject*);
static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject*, Py_ssize_t* length);
static CYTHON_INLINE PyObject* __Pyx_PyByteArray_FromString(const char*);
#define __Pyx_PyByteArray_FromStringAndSize(s, l) PyByteArray_FromStringAndSize((const char*)s, l)
#define __Pyx_PyBytes_FromString        PyBytes_FromString
#define __Pyx_PyBytes_FromStringAndSize PyBytes_FromStringAndSize
static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char*);
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    #define __Pyx_PyBytes_AsWritableUString(s)    ((unsigned char*) PyBytes_AsString(s))
    #define __Pyx_PyBytes_AsString(s)     ((const char*) PyBytes_AsString(s))
    #define __Pyx_PyBytes_AsSString(s)    ((const signed char*) PyBytes_AsString(s))
    #define __Pyx_PyBytes_AsUString(s)    ((const unsigned char*) PyBytes_AsString(s))
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#define __Pyx_PyObject_AsWritableString(s)    ((char*)(__pyx_uintptr_t) __Pyx_PyObject_AsString(s))
#define __Pyx_PyObject_AsWritableSString(s)    ((signed char*)(__pyx_uintptr_t) __Pyx_PyObject_AsString(s))
#define __Pyx_PyObject_AsWritableUString(s)    ((unsigned char*)(__pyx_uintptr_t) __Pyx_PyObject_AsString(s))
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#define __Pyx_PyObject_AsUString(s)    ((const unsigned char*) __Pyx_PyObject_AsString(s))
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#define __Pyx_PyBytes_FromCString(s)   __Pyx_PyBytes_FromString((const char*)s)
#define __Pyx_PyByteArray_FromCString(s)   __Pyx_PyByteArray_FromString((const char*)s)
#define __Pyx_PyUnicode_FromCString(s) __Pyx_PyUnicode_FromString((const char*)s)
#define __Pyx_PyUnicode_FromOrdinal(o)       PyUnicode_FromOrdinal((int)o)
#define __Pyx_PyUnicode_AsUnicode            PyUnicode_AsUnicode
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static CYTHON_INLINE PyObject *__Pyx_XNewRef(PyObject *obj) {
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static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b);
static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*);
static CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject*);
static CYTHON_INLINE PyObject* __Pyx_PyNumber_Long(PyObject* x);
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static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject*);
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#define __Pyx_PyFloat_AsFloat(x) ((float) __Pyx_PyFloat_AsDouble(x))
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/* PretendToInitialize */
#ifdef __cplusplus
#if __cplusplus > 201103L
#include <type_traits>
#endif
template <typename T>
static void __Pyx_pretend_to_initialize(T* ptr) {
#if __cplusplus > 201103L
    if ((std::is_trivially_default_constructible<T>::value))
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        *ptr = T();
    (void)ptr;
}
#else
static CYTHON_INLINE void __Pyx_pretend_to_initialize(void* ptr) { (void)ptr; }
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#if !CYTHON_USE_MODULE_STATE
static PyObject *__pyx_m = NULL;
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static int __pyx_lineno;
static int __pyx_clineno = 0;
static const char * const __pyx_cfilenm = __FILE__;
static const char *__pyx_filename;

/* Header.proto */
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#if CYTHON_CCOMPLEX
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#if CYTHON_CCOMPLEX && !defined(__cplusplus) && defined(__sun__) && defined(__GNUC__)
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/* #### Code section: filename_table ### */

static const char* const __pyx_f[] = {
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  "cpython/contextvars.pxd",
  "array.pxd",
  "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd",
  "pyRing/waveform.pxd",
  "cpython/type.pxd",
  "cpython/bool.pxd",
  "cpython/complex.pxd",
};
/* #### Code section: utility_code_proto_before_types ### */
/* Atomics.proto */
#include <pythread.h>
#ifndef CYTHON_ATOMICS
    #define CYTHON_ATOMICS 1
#endif
#define __PYX_CYTHON_ATOMICS_ENABLED() CYTHON_ATOMICS
#define __PYX_GET_CYTHON_COMPILING_IN_CPYTHON_FREETHREADING() CYTHON_COMPILING_IN_CPYTHON_FREETHREADING
#define __pyx_atomic_int_type int
#define __pyx_nonatomic_int_type int
#if CYTHON_ATOMICS && (defined(__STDC_VERSION__) &&\
                        (__STDC_VERSION__ >= 201112L) &&\
                        !defined(__STDC_NO_ATOMICS__))
    #include <stdatomic.h>
#elif CYTHON_ATOMICS && (defined(__cplusplus) && (\
                    (__cplusplus >= 201103L) ||\
                    (defined(_MSC_VER) && _MSC_VER >= 1700)))
    #include <atomic>
#endif
#if CYTHON_ATOMICS && (defined(__STDC_VERSION__) &&\
                        (__STDC_VERSION__ >= 201112L) &&\
                        !defined(__STDC_NO_ATOMICS__) &&\
                       ATOMIC_INT_LOCK_FREE == 2)
    #undef __pyx_atomic_int_type
    #define __pyx_atomic_int_type atomic_int
    #define __pyx_atomic_ptr_type atomic_uintptr_t
    #define __pyx_nonatomic_ptr_type uintptr_t
    #define __pyx_atomic_incr_relaxed(value) atomic_fetch_add_explicit(value, 1, memory_order_relaxed)
    #define __pyx_atomic_incr_acq_rel(value) atomic_fetch_add_explicit(value, 1, memory_order_acq_rel)
    #define __pyx_atomic_decr_acq_rel(value) atomic_fetch_sub_explicit(value, 1, memory_order_acq_rel)
    #define __pyx_atomic_sub(value, arg) atomic_fetch_sub(value, arg)
    #define __pyx_atomic_int_cmp_exchange(value, expected, desired) atomic_compare_exchange_strong(value, expected, desired)
    #define __pyx_atomic_load(value) atomic_load(value)
    #define __pyx_atomic_store(value, new_value) atomic_store(value, new_value)
    #define __pyx_atomic_pointer_load_relaxed(value) atomic_load_explicit(value, memory_order_relaxed)
    #define __pyx_atomic_pointer_load_acquire(value) atomic_load_explicit(value, memory_order_acquire)
    #define __pyx_atomic_pointer_exchange(value, new_value) atomic_exchange(value, (__pyx_nonatomic_ptr_type)new_value)
    #if defined(__PYX_DEBUG_ATOMICS) && defined(_MSC_VER)
        #pragma message ("Using standard C atomics")
    #elif defined(__PYX_DEBUG_ATOMICS)
        #warning "Using standard C atomics"
    #endif
#elif CYTHON_ATOMICS && (defined(__cplusplus) && (\
                    (__cplusplus >= 201103L) ||\
\
                    (defined(_MSC_VER) && _MSC_VER >= 1700)) &&\
                    ATOMIC_INT_LOCK_FREE == 2)
    #undef __pyx_atomic_int_type
    #define __pyx_atomic_int_type std::atomic_int
    #define __pyx_atomic_ptr_type std::atomic_uintptr_t
    #define __pyx_nonatomic_ptr_type uintptr_t
    #define __pyx_atomic_incr_relaxed(value) std::atomic_fetch_add_explicit(value, 1, std::memory_order_relaxed)
    #define __pyx_atomic_incr_acq_rel(value) std::atomic_fetch_add_explicit(value, 1, std::memory_order_acq_rel)
    #define __pyx_atomic_decr_acq_rel(value) std::atomic_fetch_sub_explicit(value, 1, std::memory_order_acq_rel)
    #define __pyx_atomic_sub(value, arg) std::atomic_fetch_sub(value, arg)
    #define __pyx_atomic_int_cmp_exchange(value, expected, desired) std::atomic_compare_exchange_strong(value, expected, desired)
    #define __pyx_atomic_load(value) std::atomic_load(value)
    #define __pyx_atomic_store(value, new_value) std::atomic_store(value, new_value)
    #define __pyx_atomic_pointer_load_relaxed(value) std::atomic_load_explicit(value, std::memory_order_relaxed)
    #define __pyx_atomic_pointer_load_acquire(value) std::atomic_load_explicit(value, std::memory_order_acquire)
    #define __pyx_atomic_pointer_exchange(value, new_value) std::atomic_exchange(value, (__pyx_nonatomic_ptr_type)new_value)
    #if defined(__PYX_DEBUG_ATOMICS) && defined(_MSC_VER)
        #pragma message ("Using standard C++ atomics")
    #elif defined(__PYX_DEBUG_ATOMICS)
        #warning "Using standard C++ atomics"
    #endif
#elif CYTHON_ATOMICS && (__GNUC__ >= 5 || (__GNUC__ == 4 &&\
                    (__GNUC_MINOR__ > 1 ||\
                    (__GNUC_MINOR__ == 1 && __GNUC_PATCHLEVEL__ >= 2))))
    #define __pyx_atomic_ptr_type void*
    #define __pyx_atomic_incr_relaxed(value) __sync_fetch_and_add(value, 1)
    #define __pyx_atomic_incr_acq_rel(value) __sync_fetch_and_add(value, 1)
    #define __pyx_atomic_decr_acq_rel(value) __sync_fetch_and_sub(value, 1)
    #define __pyx_atomic_sub(value, arg) __sync_fetch_and_sub(value, arg)
    static CYTHON_INLINE int __pyx_atomic_int_cmp_exchange(__pyx_atomic_int_type* value, __pyx_nonatomic_int_type* expected, __pyx_nonatomic_int_type desired) {
        __pyx_nonatomic_int_type old = __sync_val_compare_and_swap(value, *expected, desired);
        int result = old == *expected;
        *expected = old;
        return result;
    }
    #define __pyx_atomic_load(value) __sync_fetch_and_add(value, 0)
    #define __pyx_atomic_store(value, new_value) __sync_lock_test_and_set(value, new_value)
    #define __pyx_atomic_pointer_load_relaxed(value) __sync_fetch_and_add(value, 0)
    #define __pyx_atomic_pointer_load_acquire(value) __sync_fetch_and_add(value, 0)
    #define __pyx_atomic_pointer_exchange(value, new_value) __sync_lock_test_and_set(value, (__pyx_atomic_ptr_type)new_value)
    #ifdef __PYX_DEBUG_ATOMICS
        #warning "Using GNU atomics"
    #endif
#elif CYTHON_ATOMICS && defined(_MSC_VER)
    #include <intrin.h>
    #undef __pyx_atomic_int_type
    #define __pyx_atomic_int_type long
    #define __pyx_atomic_ptr_type void*
    #undef __pyx_nonatomic_int_type
    #define __pyx_nonatomic_int_type long
    #pragma intrinsic (_InterlockedExchangeAdd, _InterlockedExchange, _InterlockedCompareExchange, _InterlockedCompareExchangePointer, _InterlockedExchangePointer)
    #define __pyx_atomic_incr_relaxed(value) _InterlockedExchangeAdd(value, 1)
    #define __pyx_atomic_incr_acq_rel(value) _InterlockedExchangeAdd(value, 1)
    #define __pyx_atomic_decr_acq_rel(value) _InterlockedExchangeAdd(value, -1)
    #define __pyx_atomic_sub(value, arg) _InterlockedExchangeAdd(value, -arg)
    static CYTHON_INLINE int __pyx_atomic_int_cmp_exchange(__pyx_atomic_int_type* value, __pyx_nonatomic_int_type* expected, __pyx_nonatomic_int_type desired) {
        __pyx_nonatomic_int_type old = _InterlockedCompareExchange(value, desired, *expected);
        int result = old == *expected;
        *expected = old;
        return result;
    }
    #define __pyx_atomic_load(value) _InterlockedExchangeAdd(value, 0)
    #define __pyx_atomic_store(value, new_value) _InterlockedExchange(value, new_value)
    #define __pyx_atomic_pointer_load_relaxed(value) *(void * volatile *)value
    #define __pyx_atomic_pointer_load_acquire(value) _InterlockedCompareExchangePointer(value, 0, 0)
    #define __pyx_atomic_pointer_exchange(value, new_value) _InterlockedExchangePointer(value, (__pyx_atomic_ptr_type)new_value)
    #ifdef __PYX_DEBUG_ATOMICS
        #pragma message ("Using MSVC atomics")
    #endif
#else
    #undef CYTHON_ATOMICS
    #define CYTHON_ATOMICS 0
    #ifdef __PYX_DEBUG_ATOMICS
        #warning "Not using atomics"
    #endif
#endif
#if CYTHON_ATOMICS
    #define __pyx_add_acquisition_count(memview)\
             __pyx_atomic_incr_relaxed(__pyx_get_slice_count_pointer(memview))
    #define __pyx_sub_acquisition_count(memview)\
            __pyx_atomic_decr_acq_rel(__pyx_get_slice_count_pointer(memview))
#else
    #define __pyx_add_acquisition_count(memview)\
            __pyx_add_acquisition_count_locked(__pyx_get_slice_count_pointer(memview), memview->lock)
    #define __pyx_sub_acquisition_count(memview)\
            __pyx_sub_acquisition_count_locked(__pyx_get_slice_count_pointer(memview), memview->lock)
#endif

/* ForceInitThreads.proto */
#ifndef __PYX_FORCE_INIT_THREADS
  #define __PYX_FORCE_INIT_THREADS 0
#endif

/* NoFastGil.proto */
#define __Pyx_PyGILState_Ensure PyGILState_Ensure
#define __Pyx_PyGILState_Release PyGILState_Release
#define __Pyx_FastGIL_Remember()
#define __Pyx_FastGIL_Forget()
#define __Pyx_FastGilFuncInit()

/* BufferFormatStructs.proto */
struct __Pyx_StructField_;
#define __PYX_BUF_FLAGS_PACKED_STRUCT (1 << 0)
typedef struct {
  const char* name;
  const struct __Pyx_StructField_* fields;
  size_t size;
  size_t arraysize[8];
  int ndim;
  char typegroup;
  char is_unsigned;
  int flags;
} __Pyx_TypeInfo;
typedef struct __Pyx_StructField_ {
  const __Pyx_TypeInfo* type;
  const char* name;
  size_t offset;
} __Pyx_StructField;
typedef struct {
  const __Pyx_StructField* field;
  size_t parent_offset;
} __Pyx_BufFmt_StackElem;
typedef struct {
  __Pyx_StructField root;
  __Pyx_BufFmt_StackElem* head;
  size_t fmt_offset;
  size_t new_count, enc_count;
  size_t struct_alignment;
  int is_complex;
  char enc_type;
  char new_packmode;
  char enc_packmode;
  char is_valid_array;
} __Pyx_BufFmt_Context;

/* IncludeStructmemberH.proto */
#include <structmember.h>

/* CriticalSections.proto */
#if !CYTHON_COMPILING_IN_CPYTHON_FREETHREADING
#define __Pyx_PyCriticalSection void*
#define __Pyx_PyCriticalSection2 void*
#define __Pyx_PyCriticalSection_Begin1(cs, arg) (void)cs
#define __Pyx_PyCriticalSection_Begin2(cs, arg1, arg2) (void)cs
#define __Pyx_PyCriticalSection_End1(cs)
#define __Pyx_PyCriticalSection_End2(cs)
#else
#define __Pyx_PyCriticalSection PyCriticalSection
#define __Pyx_PyCriticalSection2 PyCriticalSection2
#define __Pyx_PyCriticalSection_Begin1 PyCriticalSection_Begin
#define __Pyx_PyCriticalSection_Begin2 PyCriticalSection2_Begin
#define __Pyx_PyCriticalSection_End1 PyCriticalSection_End
#define __Pyx_PyCriticalSection_End2 PyCriticalSection2_End
#endif
#if PY_VERSION_HEX < 0x030d0000 || CYTHON_COMPILING_IN_LIMITED_API
#define __Pyx_BEGIN_CRITICAL_SECTION(o) {
#define __Pyx_END_CRITICAL_SECTION() }
#else
#define __Pyx_BEGIN_CRITICAL_SECTION Py_BEGIN_CRITICAL_SECTION
#define __Pyx_END_CRITICAL_SECTION Py_END_CRITICAL_SECTION
#endif

/* MemviewSliceStruct.proto */
struct __pyx_memoryview_obj;
typedef struct {
  struct __pyx_memoryview_obj *memview;
  char *data;
  Py_ssize_t shape[8];
  Py_ssize_t strides[8];
  Py_ssize_t suboffsets[8];
} __Pyx_memviewslice;
#define __Pyx_MemoryView_Len(m)  (m.shape[0])

/* #### Code section: numeric_typedefs ### */

/* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":743
 * # in Cython to enable them only on the right systems.
 * 
 * ctypedef npy_int8       int8_t             # <<<<<<<<<<<<<<
 * ctypedef npy_int16      int16_t
 * ctypedef npy_int32      int32_t
*/
typedef npy_int8 __pyx_t_5numpy_int8_t;

/* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":744
 * 
 * ctypedef npy_int8       int8_t
 * ctypedef npy_int16      int16_t             # <<<<<<<<<<<<<<
 * ctypedef npy_int32      int32_t
 * ctypedef npy_int64      int64_t
*/
typedef npy_int16 __pyx_t_5numpy_int16_t;

/* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":745
 * ctypedef npy_int8       int8_t
 * ctypedef npy_int16      int16_t
 * ctypedef npy_int32      int32_t             # <<<<<<<<<<<<<<
 * ctypedef npy_int64      int64_t
 * 
*/
typedef npy_int32 __pyx_t_5numpy_int32_t;

/* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":746
 * ctypedef npy_int16      int16_t
 * ctypedef npy_int32      int32_t
 * ctypedef npy_int64      int64_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_uint8      uint8_t
*/
typedef npy_int64 __pyx_t_5numpy_int64_t;

/* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":748
 * ctypedef npy_int64      int64_t
 * 
 * ctypedef npy_uint8      uint8_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uint16     uint16_t
 * ctypedef npy_uint32     uint32_t
*/
typedef npy_uint8 __pyx_t_5numpy_uint8_t;

/* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":749
 * 
 * ctypedef npy_uint8      uint8_t
 * ctypedef npy_uint16     uint16_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uint32     uint32_t
 * ctypedef npy_uint64     uint64_t
*/
typedef npy_uint16 __pyx_t_5numpy_uint16_t;

/* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":750
 * ctypedef npy_uint8      uint8_t
 * ctypedef npy_uint16     uint16_t
 * ctypedef npy_uint32     uint32_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uint64     uint64_t
 * 
*/
typedef npy_uint32 __pyx_t_5numpy_uint32_t;

/* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":751
 * ctypedef npy_uint16     uint16_t
 * ctypedef npy_uint32     uint32_t
 * ctypedef npy_uint64     uint64_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_float32    float32_t
*/
typedef npy_uint64 __pyx_t_5numpy_uint64_t;

/* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":753
 * ctypedef npy_uint64     uint64_t
 * 
 * ctypedef npy_float32    float32_t             # <<<<<<<<<<<<<<
 * ctypedef npy_float64    float64_t
 * #ctypedef npy_float80    float80_t
*/
typedef npy_float32 __pyx_t_5numpy_float32_t;

/* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":754
 * 
 * ctypedef npy_float32    float32_t
 * ctypedef npy_float64    float64_t             # <<<<<<<<<<<<<<
 * #ctypedef npy_float80    float80_t
 * #ctypedef npy_float128   float128_t
*/
typedef npy_float64 __pyx_t_5numpy_float64_t;

/* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":761
 * ctypedef double complex complex128_t
 * 
 * ctypedef npy_longlong   longlong_t             # <<<<<<<<<<<<<<
 * ctypedef npy_ulonglong  ulonglong_t
 * 
*/
typedef npy_longlong __pyx_t_5numpy_longlong_t;

/* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":762
 * 
 * ctypedef npy_longlong   longlong_t
 * ctypedef npy_ulonglong  ulonglong_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_intp       intp_t
*/
typedef npy_ulonglong __pyx_t_5numpy_ulonglong_t;

/* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":764
 * ctypedef npy_ulonglong  ulonglong_t
 * 
 * ctypedef npy_intp       intp_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uintp      uintp_t
 * 
*/
typedef npy_intp __pyx_t_5numpy_intp_t;

/* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":765
 * 
 * ctypedef npy_intp       intp_t
 * ctypedef npy_uintp      uintp_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_double     float_t
*/
typedef npy_uintp __pyx_t_5numpy_uintp_t;

/* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":767
 * ctypedef npy_uintp      uintp_t
 * 
 * ctypedef npy_double     float_t             # <<<<<<<<<<<<<<
 * ctypedef npy_double     double_t
 * ctypedef npy_longdouble longdouble_t
*/
typedef npy_double __pyx_t_5numpy_float_t;

/* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":768
 * 
 * ctypedef npy_double     float_t
 * ctypedef npy_double     double_t             # <<<<<<<<<<<<<<
 * ctypedef npy_longdouble longdouble_t
 * 
*/
typedef npy_double __pyx_t_5numpy_double_t;

/* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":769
 * ctypedef npy_double     float_t
 * ctypedef npy_double     double_t
 * ctypedef npy_longdouble longdouble_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef float complex       cfloat_t
*/
typedef npy_longdouble __pyx_t_5numpy_longdouble_t;
/* #### Code section: complex_type_declarations ### */
/* Declarations.proto */
#if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus)
  #ifdef __cplusplus
    typedef ::std::complex< double > __pyx_t_double_complex;
  #else
    typedef double _Complex __pyx_t_double_complex;
  #endif
#else
    typedef struct { double real, imag; } __pyx_t_double_complex;
#endif
static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double, double);

/* Declarations.proto */
#if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus)
  #ifdef __cplusplus
    typedef ::std::complex< float > __pyx_t_float_complex;
  #else
    typedef float _Complex __pyx_t_float_complex;
  #endif
#else
    typedef struct { float real, imag; } __pyx_t_float_complex;
#endif
static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float, float);

/* Declarations.proto */
#if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus)
  #ifdef __cplusplus
    typedef ::std::complex< long double > __pyx_t_long_double_complex;
  #else
    typedef long double _Complex __pyx_t_long_double_complex;
  #endif
#else
    typedef struct { long double real, imag; } __pyx_t_long_double_complex;
#endif
static CYTHON_INLINE __pyx_t_long_double_complex __pyx_t_long_double_complex_from_parts(long double, long double);

/* #### Code section: type_declarations ### */

/*--- Type declarations ---*/
#ifndef _ARRAYARRAY_H
struct arrayobject;
typedef struct arrayobject arrayobject;
#endif
struct __pyx_obj_6pyRing_8waveform_QNM;
struct __pyx_obj_6pyRing_8waveform_QNM_fit;
struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec;
struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized;
struct __pyx_obj_6pyRing_8waveform_QNM_braneworld_fit;
struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids;
struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets;
struct __pyx_obj_6pyRing_8waveform_SWSH;
struct __pyx_obj_6pyRing_8waveform_KerrBH;
struct __pyx_obj_6pyRing_8waveform_MMRDNS;
struct __pyx_obj_6pyRing_8waveform_MMRDNP;
struct __pyx_obj_6pyRing_8waveform_KHS_2012;
struct __pyx_obj_6pyRing_8waveform_TEOBPM;
struct __pyx_obj_6pyRing_8waveform_IMR_WF;
struct __pyx_array_obj;
struct __pyx_MemviewEnum_obj;
struct __pyx_memoryview_obj;
struct __pyx_memoryviewslice_obj;
struct __pyx_opt_args_7cpython_11contextvars_get_value;
struct __pyx_opt_args_7cpython_11contextvars_get_value_no_default;

/* "cpython/contextvars.pxd":116
 * 
 * @_cython.c_compile_guard("!CYTHON_COMPILING_IN_LIMITED_API")
 * cdef inline object get_value(var, default_value=None):             # <<<<<<<<<<<<<<
 *     """Return a new reference to the value of the context variable,
 *     or the default value of the context variable,
*/
struct __pyx_opt_args_7cpython_11contextvars_get_value {
  int __pyx_n;
  PyObject *default_value;
};

/* "cpython/contextvars.pxd":134
 * 
 * @_cython.c_compile_guard("!CYTHON_COMPILING_IN_LIMITED_API")
 * cdef inline object get_value_no_default(var, default_value=None):             # <<<<<<<<<<<<<<
 *     """Return a new reference to the value of the context variable,
 *     or the provided default value if no such value was found.
*/
struct __pyx_opt_args_7cpython_11contextvars_get_value_no_default {
  int __pyx_n;
  PyObject *default_value;
};

/* "pyRing/waveform.pxd":10
 * cdef public list Interpolated_ns
 * 
 * cdef class QNM:             # <<<<<<<<<<<<<<
 * 
 *     """
*/
struct __pyx_obj_6pyRing_8waveform_QNM {
  PyObject_HEAD
  struct __pyx_vtabstruct_6pyRing_8waveform_QNM *__pyx_vtab;
  unsigned int s;
  unsigned int l;
  int m;
  unsigned int n;
  unsigned int geom;
  PyObject *omegar_interp;
  PyObject *omegai_interp;
  double prefactor_freq;
  double prefactor_tau;
};


/* "pyRing/waveform.pxd":35
 *     cpdef double tau_BW(self, double M, double a, double beta)
 * 
 * cdef class QNM_fit:             # <<<<<<<<<<<<<<
 * 
 *     """
*/
struct __pyx_obj_6pyRing_8waveform_QNM_fit {
  PyObject_HEAD
  struct __pyx_vtabstruct_6pyRing_8waveform_QNM_fit *__pyx_vtab;
  unsigned int l;
  int m;
  unsigned int n;
  unsigned int charge;
  PyObject *f_coeff;
  PyObject *q_coeff;
  double prefactor_freq;
};


/* "pyRing/waveform.pxd":60
 * 
 * 
 * cdef class QNM_ParSpec:             # <<<<<<<<<<<<<<
 * 
 *     """
*/
struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec {
  PyObject_HEAD
  struct __pyx_vtabstruct_6pyRing_8waveform_QNM_ParSpec *__pyx_vtab;
  unsigned int l;
  int m;
  unsigned int n;
  PyObject *f_coeff;
  PyObject *tau_coeff;
  double prefactor_freq;
  double prefactor_tau;
};


/* "pyRing/waveform.pxd":79
 *     cpdef double tau(self, double M, double a, double gamma, np.ndarray[double, ndim=1] dw_vec)
 * 
 * cdef class QNM_220_area_quantized:             # <<<<<<<<<<<<<<
 * 
 *     """
*/
struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized {
  PyObject_HEAD
  struct __pyx_vtabstruct_6pyRing_8waveform_QNM_220_area_quantized *__pyx_vtab;
  unsigned int l_QA;
  int m_QA;
  unsigned int n_QA;
  PyObject *q_coeff_GR;
};


/* "pyRing/waveform.pxd":96
 *     cpdef double tau_QA(self, double M, double a, double alpha)
 * 
 * cdef class QNM_braneworld_fit:             # <<<<<<<<<<<<<<
 * 
 *     """
*/
struct __pyx_obj_6pyRing_8waveform_QNM_braneworld_fit {
  PyObject_HEAD
  struct __pyx_vtabstruct_6pyRing_8waveform_QNM_braneworld_fit *__pyx_vtab;
  unsigned int l_BW;
  int m_BW;
  unsigned int n_BW;
};


/* "pyRing/waveform.pxd":112
 *     cpdef double tau_BW(self, double M, double a, double beta)
 * 
 * cdef class Damped_sinusoids:             # <<<<<<<<<<<<<<
 * 
 *     """
*/
struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids {
  PyObject_HEAD
  struct __pyx_vtabstruct_6pyRing_8waveform_Damped_sinusoids *__pyx_vtab;
  PyObject *A;
  PyObject *f;
  PyObject *tau;
  PyObject *phi;
  PyObject *t0;
  PyObject *N;
};


/* "pyRing/waveform.pxd":130
 *     cpdef np.ndarray[double, ndim=5] waveform(self,np.ndarray[double, ndim=1] t)
 * 
 * cdef class Morlet_Gabor_wavelets:             # <<<<<<<<<<<<<<
 * 
 *     """
*/
struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets {
  PyObject_HEAD
  struct __pyx_vtabstruct_6pyRing_8waveform_Morlet_Gabor_wavelets *__pyx_vtab;
  PyObject *A;
  PyObject *f;
  PyObject *tau;
  PyObject *phi;
  PyObject *t0;
  PyObject *N;
};


/* "pyRing/waveform.pxd":148
 *     cpdef np.ndarray[double, ndim=5] waveform(self,np.ndarray[double, ndim=1] t)
 * 
 * cdef class SWSH:             # <<<<<<<<<<<<<<
 * 
 *     """
*/
struct __pyx_obj_6pyRing_8waveform_SWSH {
  PyObject_HEAD
  struct __pyx_vtabstruct_6pyRing_8waveform_SWSH *__pyx_vtab;
  int l;
  int m;
  int s;
  double swsh_prefactor;
};


/* "pyRing/waveform.pxd":163
 *     cpdef complex evaluate(self, double theta, double phi)
 * 
 * cdef class KerrBH:             # <<<<<<<<<<<<<<
 * 
 *     """
*/
struct __pyx_obj_6pyRing_8waveform_KerrBH {
  PyObject_HEAD
  struct __pyx_vtabstruct_6pyRing_8waveform_KerrBH *__pyx_vtab;
  double t0;
  double Mf;
  double af;
  PyObject *amps;
  double r;
  double iota;
  double phi;
  double reference_amplitude;
  unsigned int geom;
  unsigned int qnm_fit;
  PyObject *interpolants;
  unsigned int Spheroidal;
  unsigned int amp_non_prec_sym;
  PyObject *tail_parameters;
  PyObject *quadratic_modes;
  unsigned int quad_lin_prop;
  unsigned int neg_quad_freq;
  PyObject *qnm_cached;
  PyObject *TGR_params;
  unsigned int AreaQuantization;
  unsigned int ParSpec;
  unsigned int charge;
  unsigned int braneworld;
  PyObject *qnms;
  PyObject *qnms_ParSpec;
  PyObject *swshs;
};


/* "pyRing/waveform.pxd":206
 *     cpdef np.ndarray[double, ndim=5] waveform(self,np.ndarray[double, ndim=1] times)
 * 
 * cdef class MMRDNS:             # <<<<<<<<<<<<<<
 * 
 *     """
*/
struct __pyx_obj_6pyRing_8waveform_MMRDNS {
  PyObject_HEAD
  struct __pyx_vtabstruct_6pyRing_8waveform_MMRDNS *__pyx_vtab;
  double t0;
  double t_ref;
  double Mf;
  double af;
  double eta;
  double r;
  double iota;
  double phi;
  PyObject *TGR_params;
  int single_l;
  int single_m;
  int single_n;
  unsigned int single_mode;
  unsigned int Spheroidal;
  PyObject *interpolants;
  unsigned int qnm_fit;
  PyObject *multipoles;
};


/* "pyRing/waveform.pxd":235
 *     cpdef np.ndarray[double, ndim=5] waveform(self,np.ndarray[double, ndim=1] times)
 * 
 * cdef class MMRDNP:             # <<<<<<<<<<<<<<
 * 
 *     """
*/
struct __pyx_obj_6pyRing_8waveform_MMRDNP {
  PyObject_HEAD
  struct __pyx_vtabstruct_6pyRing_8waveform_MMRDNP *__pyx_vtab;
  double t0;
  double t_ref;
  double Mf;
  double af;
  double Mi;
  double eta;
  double chi_s;
  double chi_a;
  double r;
  double iota;
  double phi;
  PyObject *TGR_params;
  PyObject *modes;
  unsigned int geom;
  unsigned int qnm_fit;
  PyObject *interpolants;
  PyObject *qnm_cached;
  double delta;
  PyObject *multipoles;
};


/* "pyRing/waveform.pxd":266
 *     cpdef np.ndarray[double, ndim=5] waveform(self,np.ndarray[double, ndim=1] times)
 * 
 * cdef class KHS_2012:             # <<<<<<<<<<<<<<
 * 
 *     """
*/
struct __pyx_obj_6pyRing_8waveform_KHS_2012 {
  PyObject_HEAD
  struct __pyx_vtabstruct_6pyRing_8waveform_KHS_2012 *__pyx_vtab;
  double t0;
  double t_ref;
  double Mf;
  double af;
  double eta;
  double chi_eff;
  double r;
  double iota;
  double phi;
  PyObject *TGR_params;
  int single_l;
  int single_m;
  unsigned int single_mode;
  PyObject *multipoles;
};


/* "pyRing/waveform.pxd":292
 *     cpdef np.ndarray[double, ndim=5] waveform(self,np.ndarray[double, ndim=1] times)
 * 
 * cdef class TEOBPM:             # <<<<<<<<<<<<<<
 * 
 *     """
*/
struct __pyx_obj_6pyRing_8waveform_TEOBPM {
  PyObject_HEAD
  struct __pyx_vtabstruct_6pyRing_8waveform_TEOBPM *__pyx_vtab;
  double t0;
  double m1;
  double m2;
  double chi1;
  double chi2;
  PyObject *phases;
  double M;
  double r;
  double iota;
  double phi;
  PyObject *modes;
  unsigned int full_modes;
  PyObject *TGR_params;
  unsigned int geom;
  PyObject *NR_fit_coeffs;
  PyObject *multipoles;
  PyObject *fit_coefficients;
  double nu;
  double X1;
  double X2;
  double X12;
  double a0;
  double a12;
  double Shat;
  double Sbar;
  double Mf;
  double af;
};


/* "pyRing/waveform.pxd":336
 *     cdef np.ndarray[double, ndim=5] _waveform(self, double[::1] times)
 * 
 * cdef class IMR_WF:             # <<<<<<<<<<<<<<
 * 
 *     """
*/
struct __pyx_obj_6pyRing_8waveform_IMR_WF {
  PyObject_HEAD
  struct __pyx_vtabstruct_6pyRing_8waveform_IMR_WF *__pyx_vtab;
  double m1;
  double m2;
  double s1z;
  double s2z;
  double dist;
  double cosiota;
  double phi;
  double t0;
  double dt;
  double starttime;
  double signal_seglen;
};


/* "View.MemoryView":110
 * 
 * 
 * @cython.collection_type("sequence")             # <<<<<<<<<<<<<<
 * @cname("__pyx_array")
 * cdef class array:
*/
struct __pyx_array_obj {
  PyObject_HEAD
  struct __pyx_vtabstruct_array *__pyx_vtab;
  char *data;
  Py_ssize_t len;
  char *format;
  int ndim;
  Py_ssize_t *_shape;
  Py_ssize_t *_strides;
  Py_ssize_t itemsize;
  PyObject *mode;
  PyObject *_format;
  void (*callback_free_data)(void *);
  int free_data;
  int dtype_is_object;
};


/* "View.MemoryView":299
 * 
 * 
 * @cname('__pyx_MemviewEnum')             # <<<<<<<<<<<<<<
 * cdef class Enum(object):
 *     cdef object name
*/
struct __pyx_MemviewEnum_obj {
  PyObject_HEAD
  PyObject *name;
};


/* "View.MemoryView":334
 * 
 * 
 * @cname('__pyx_memoryview')             # <<<<<<<<<<<<<<
 * cdef class memoryview:
 * 
*/
struct __pyx_memoryview_obj {
  PyObject_HEAD
  struct __pyx_vtabstruct_memoryview *__pyx_vtab;
  PyObject *obj;
  PyObject *_size;
  PyObject *_array_interface;
  PyThread_type_lock lock;
  __pyx_atomic_int_type acquisition_count;
  Py_buffer view;
  int flags;
  int dtype_is_object;
  __Pyx_TypeInfo const *typeinfo;
};


/* "View.MemoryView":950
 * 
 * 
 * @cython.collection_type("sequence")             # <<<<<<<<<<<<<<
 * @cname('__pyx_memoryviewslice')
 * cdef class _memoryviewslice(memoryview):
*/
struct __pyx_memoryviewslice_obj {
  struct __pyx_memoryview_obj __pyx_base;
  __Pyx_memviewslice from_slice;
  PyObject *from_object;
  PyObject *(*to_object_func)(char *);
  int (*to_dtype_func)(char *, PyObject *);
};



/* "pyRing/waveform.pyx":72
 * 
 * 
 * cdef class QNM:             # <<<<<<<<<<<<<<
 * 
 *     """
*/

struct __pyx_vtabstruct_6pyRing_8waveform_QNM {
  double (*f)(struct __pyx_obj_6pyRing_8waveform_QNM *, double, double, int __pyx_skip_dispatch);
  double (*tau)(struct __pyx_obj_6pyRing_8waveform_QNM *, double, double, int __pyx_skip_dispatch);
  double (*f_KN)(struct __pyx_obj_6pyRing_8waveform_QNM *, double, double, double, int __pyx_skip_dispatch);
  double (*tau_KN)(struct __pyx_obj_6pyRing_8waveform_QNM *, double, double, double, int __pyx_skip_dispatch);
  double (*f_BW)(struct __pyx_obj_6pyRing_8waveform_QNM *, double, double, double, int __pyx_skip_dispatch);
  double (*tau_BW)(struct __pyx_obj_6pyRing_8waveform_QNM *, double, double, double, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_6pyRing_8waveform_QNM *__pyx_vtabptr_6pyRing_8waveform_QNM;


/* "pyRing/waveform.pyx":164
 *     cpdef double tau_BW(self, double M, double a, double beta): return -1.0/(self.omegai_interp(a, beta)*self.prefactor_tau*(1.0/M))
 * 
 * cdef class QNM_fit:             # <<<<<<<<<<<<<<
 * 
 *     """
*/

struct __pyx_vtabstruct_6pyRing_8waveform_QNM_fit {
  double (*f)(struct __pyx_obj_6pyRing_8waveform_QNM_fit *, double, double, int __pyx_skip_dispatch);
  double (*q)(struct __pyx_obj_6pyRing_8waveform_QNM_fit *, double, int __pyx_skip_dispatch);
  double (*tau)(struct __pyx_obj_6pyRing_8waveform_QNM_fit *, double, double, int __pyx_skip_dispatch);
  double (*f_KN)(struct __pyx_obj_6pyRing_8waveform_QNM_fit *, double, double, double, int __pyx_skip_dispatch);
  double (*q_KN)(struct __pyx_obj_6pyRing_8waveform_QNM_fit *, double, double, int __pyx_skip_dispatch);
  double (*tau_KN)(struct __pyx_obj_6pyRing_8waveform_QNM_fit *, double, double, double, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_6pyRing_8waveform_QNM_fit *__pyx_vtabptr_6pyRing_8waveform_QNM_fit;


/* "pyRing/waveform.pyx":249
 * 
 * #NO-REVIEW-NEEDED
 * cdef class QNM_ParSpec:             # <<<<<<<<<<<<<<
 * 
 *     """
*/

struct __pyx_vtabstruct_6pyRing_8waveform_QNM_ParSpec {
  double (*f)(struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *, double, double, double, PyArrayObject *, int __pyx_skip_dispatch);
  double (*tau)(struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *, double, double, double, PyArrayObject *, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_6pyRing_8waveform_QNM_ParSpec *__pyx_vtabptr_6pyRing_8waveform_QNM_ParSpec;


/* "pyRing/waveform.pyx":341
 * 
 * #NO-REVIEW-NEEDED
 * cdef class QNM_220_area_quantized:             # <<<<<<<<<<<<<<
 * 
 *     """
*/

struct __pyx_vtabstruct_6pyRing_8waveform_QNM_220_area_quantized {
  double (*f_QA)(struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *, double, double, double, int __pyx_skip_dispatch);
  double (*q_GR)(struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *, double, int __pyx_skip_dispatch);
  double (*tau_QA)(struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *, double, double, double, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_6pyRing_8waveform_QNM_220_area_quantized *__pyx_vtabptr_6pyRing_8waveform_QNM_220_area_quantized;


/* "pyRing/waveform.pyx":406
 * 
 * #NO-REVIEW-NEEDED
 * cdef class QNM_braneworld_fit:             # <<<<<<<<<<<<<<
 * 
 *     """
*/

struct __pyx_vtabstruct_6pyRing_8waveform_QNM_braneworld_fit {
  double (*f_BW)(struct __pyx_obj_6pyRing_8waveform_QNM_braneworld_fit *, double, double, double, int __pyx_skip_dispatch);
  double (*q_BW)(struct __pyx_obj_6pyRing_8waveform_QNM_braneworld_fit *, double, double, int __pyx_skip_dispatch);
  double (*tau_BW)(struct __pyx_obj_6pyRing_8waveform_QNM_braneworld_fit *, double, double, double, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_6pyRing_8waveform_QNM_braneworld_fit *__pyx_vtabptr_6pyRing_8waveform_QNM_braneworld_fit;


/* "pyRing/waveform.pyx":627
 *     return h
 * 
 * cdef class Damped_sinusoids:             # <<<<<<<<<<<<<<
 * 
 *     """
*/

struct __pyx_vtabstruct_6pyRing_8waveform_Damped_sinusoids {
  PyArrayObject *(*waveform)(struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *, PyArrayObject *, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_6pyRing_8waveform_Damped_sinusoids *__pyx_vtabptr_6pyRing_8waveform_Damped_sinusoids;


/* "pyRing/waveform.pyx":740
 *         return np.array([h_s, h_vx, h_vy, h_p, h_c])
 * 
 * cdef class Morlet_Gabor_wavelets:             # <<<<<<<<<<<<<<
 * 
 *     """
*/

struct __pyx_vtabstruct_6pyRing_8waveform_Morlet_Gabor_wavelets {
  PyArrayObject *(*waveform)(struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *, PyArrayObject *, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_6pyRing_8waveform_Morlet_Gabor_wavelets *__pyx_vtabptr_6pyRing_8waveform_Morlet_Gabor_wavelets;


/* "pyRing/waveform.pyx":851
 *         return np.array([h_s, h_vx, h_vy, h_p, h_c])
 * 
 * cdef class SWSH:             # <<<<<<<<<<<<<<
 * 
 *   """
*/

struct __pyx_vtabstruct_6pyRing_8waveform_SWSH {
  __pyx_t_double_complex (*evaluate)(struct __pyx_obj_6pyRing_8waveform_SWSH *, double, double, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_6pyRing_8waveform_SWSH *__pyx_vtabptr_6pyRing_8waveform_SWSH;


/* "pyRing/waveform.pyx":934
 *     return result
 * 
 * cdef class KerrBH:             # <<<<<<<<<<<<<<
 * 
 *   """
*/

struct __pyx_vtabstruct_6pyRing_8waveform_KerrBH {
  PyArrayObject *(*waveform)(struct __pyx_obj_6pyRing_8waveform_KerrBH *, PyArrayObject *, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_6pyRing_8waveform_KerrBH *__pyx_vtabptr_6pyRing_8waveform_KerrBH;


/* "pyRing/waveform.pyx":1310
 * 
 * #NO-REVIEW-NEEDED
 * cdef class MMRDNS:             # <<<<<<<<<<<<<<
 * 
 *   """
*/

struct __pyx_vtabstruct_6pyRing_8waveform_MMRDNS {
  PyArrayObject *(*waveform)(struct __pyx_obj_6pyRing_8waveform_MMRDNS *, PyArrayObject *, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_6pyRing_8waveform_MMRDNS *__pyx_vtabptr_6pyRing_8waveform_MMRDNS;


/* "pyRing/waveform.pyx":1472
 *     return np.array([h_s, h_vx, h_vy, h_p, h_c])
 * 
 * cdef class MMRDNP:             # <<<<<<<<<<<<<<
 * 
 *   """
*/

struct __pyx_vtabstruct_6pyRing_8waveform_MMRDNP {
  PyArrayObject *(*waveform)(struct __pyx_obj_6pyRing_8waveform_MMRDNP *, PyArrayObject *, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_6pyRing_8waveform_MMRDNP *__pyx_vtabptr_6pyRing_8waveform_MMRDNP;


/* "pyRing/waveform.pyx":1650
 * 
 * #NO-REVIEW-NEEDED
 * cdef class KHS_2012:             # <<<<<<<<<<<<<<
 * 
 *   """
*/

struct __pyx_vtabstruct_6pyRing_8waveform_KHS_2012 {
  PyArrayObject *(*waveform)(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *, PyArrayObject *, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_6pyRing_8waveform_KHS_2012 *__pyx_vtabptr_6pyRing_8waveform_KHS_2012;


/* "pyRing/waveform.pyx":1768
 * 
 * #NO-REVIEW-NEEDED
 * cdef class TEOBPM:             # <<<<<<<<<<<<<<
 * 
 *     """
*/

struct __pyx_vtabstruct_6pyRing_8waveform_TEOBPM {
  PyObject *(*_EOBPM_SetupFitCoefficients)(struct __pyx_obj_6pyRing_8waveform_TEOBPM *, int, int, PyObject *);
  double (*_TEOBPM_Amplitude)(struct __pyx_obj_6pyRing_8waveform_TEOBPM *, double, double, double, double, double, double);
  double (*_TEOBPM_Phase)(struct __pyx_obj_6pyRing_8waveform_TEOBPM *, double, double, double, double, double, double, double);
  PyArrayObject *(*_TEOBPM_single_multipole)(struct __pyx_obj_6pyRing_8waveform_TEOBPM *, __Pyx_memviewslice, double, double, int, int, int);
  PyArrayObject *(*_waveform)(struct __pyx_obj_6pyRing_8waveform_TEOBPM *, __Pyx_memviewslice);
};
static struct __pyx_vtabstruct_6pyRing_8waveform_TEOBPM *__pyx_vtabptr_6pyRing_8waveform_TEOBPM;
static double __pyx_f_6pyRing_8waveform_6TEOBPM__TEOBPM_Amplitude(struct __pyx_obj_6pyRing_8waveform_TEOBPM *, double, double, double, double, double, double);
static double __pyx_f_6pyRing_8waveform_6TEOBPM__TEOBPM_Phase(struct __pyx_obj_6pyRing_8waveform_TEOBPM *, double, double, double, double, double, double, double);


/* "pyRing/waveform.pyx":2192
 * 
 * #NO-REVIEW-NEEDED
 * cdef class IMR_WF:             # <<<<<<<<<<<<<<
 * 
 *   """
*/

struct __pyx_vtabstruct_6pyRing_8waveform_IMR_WF {
  PyArrayObject *(*waveform)(struct __pyx_obj_6pyRing_8waveform_IMR_WF *, PyArrayObject *, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_6pyRing_8waveform_IMR_WF *__pyx_vtabptr_6pyRing_8waveform_IMR_WF;


/* "View.MemoryView":110
 * 
 * 
 * @cython.collection_type("sequence")             # <<<<<<<<<<<<<<
 * @cname("__pyx_array")
 * cdef class array:
*/

struct __pyx_vtabstruct_array {
  PyObject *(*get_memview)(struct __pyx_array_obj *);
};
static struct __pyx_vtabstruct_array *__pyx_vtabptr_array;


/* "View.MemoryView":334
 * 
 * 
 * @cname('__pyx_memoryview')             # <<<<<<<<<<<<<<
 * cdef class memoryview:
 * 
*/

struct __pyx_vtabstruct_memoryview {
  char *(*get_item_pointer)(struct __pyx_memoryview_obj *, PyObject *);
  PyObject *(*is_slice)(struct __pyx_memoryview_obj *, PyObject *);
  PyObject *(*setitem_slice_assignment)(struct __pyx_memoryview_obj *, PyObject *, PyObject *);
  PyObject *(*setitem_slice_assign_scalar)(struct __pyx_memoryview_obj *, struct __pyx_memoryview_obj *, PyObject *);
  PyObject *(*setitem_indexed)(struct __pyx_memoryview_obj *, PyObject *, PyObject *);
  PyObject *(*convert_item_to_object)(struct __pyx_memoryview_obj *, char *);
  PyObject *(*assign_item_from_object)(struct __pyx_memoryview_obj *, char *, PyObject *);
  PyObject *(*_get_base)(struct __pyx_memoryview_obj *);
};
static struct __pyx_vtabstruct_memoryview *__pyx_vtabptr_memoryview;


/* "View.MemoryView":950
 * 
 * 
 * @cython.collection_type("sequence")             # <<<<<<<<<<<<<<
 * @cname('__pyx_memoryviewslice')
 * cdef class _memoryviewslice(memoryview):
*/

struct __pyx_vtabstruct__memoryviewslice {
  struct __pyx_vtabstruct_memoryview __pyx_base;
};
static struct __pyx_vtabstruct__memoryviewslice *__pyx_vtabptr__memoryviewslice;
/* #### Code section: utility_code_proto ### */

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  #define __Pyx_GIVEREF(r)
  #define __Pyx_XINCREF(r) Py_XINCREF(r)
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#define __Pyx_Py_XDECREF_SET(r, v) do {\
        PyObject *tmp = (PyObject *) r;\
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#define __Pyx_XCLEAR(r)   do { if((r) != NULL) {PyObject* tmp = ((PyObject*)(r)); r = NULL; __Pyx_DECREF(tmp);}} while(0)

/* PyErrExceptionMatches.proto */
#if CYTHON_FAST_THREAD_STATE
#define __Pyx_PyErr_ExceptionMatches(err) __Pyx_PyErr_ExceptionMatchesInState(__pyx_tstate, err)
static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err);
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#define __Pyx_PyErr_ExceptionMatches(err)  PyErr_ExceptionMatches(err)
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/* PyThreadStateGet.proto */
#if CYTHON_FAST_THREAD_STATE
#define __Pyx_PyThreadState_declare  PyThreadState *__pyx_tstate;
#define __Pyx_PyThreadState_assign  __pyx_tstate = __Pyx_PyThreadState_Current;
#if PY_VERSION_HEX >= 0x030C00A6
#define __Pyx_PyErr_Occurred()  (__pyx_tstate->current_exception != NULL)
#define __Pyx_PyErr_CurrentExceptionType()  (__pyx_tstate->current_exception ? (PyObject*) Py_TYPE(__pyx_tstate->current_exception) : (PyObject*) NULL)
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#define __Pyx_PyErr_Occurred()  (__pyx_tstate->curexc_type != NULL)
#define __Pyx_PyErr_CurrentExceptionType()  (__pyx_tstate->curexc_type)
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#define __Pyx_PyThreadState_declare
#define __Pyx_PyThreadState_assign
#define __Pyx_PyErr_Occurred()  (PyErr_Occurred() != NULL)
#define __Pyx_PyErr_CurrentExceptionType()  PyErr_Occurred()
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/* PyErrFetchRestore.proto */
#if CYTHON_FAST_THREAD_STATE
#define __Pyx_PyErr_Clear() __Pyx_ErrRestore(NULL, NULL, NULL)
#define __Pyx_ErrRestoreWithState(type, value, tb)  __Pyx_ErrRestoreInState(PyThreadState_GET(), type, value, tb)
#define __Pyx_ErrFetchWithState(type, value, tb)    __Pyx_ErrFetchInState(PyThreadState_GET(), type, value, tb)
#define __Pyx_ErrRestore(type, value, tb)  __Pyx_ErrRestoreInState(__pyx_tstate, type, value, tb)
#define __Pyx_ErrFetch(type, value, tb)    __Pyx_ErrFetchInState(__pyx_tstate, type, value, tb)
static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb);
static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX < 0x030C00A6
#define __Pyx_PyErr_SetNone(exc) (Py_INCREF(exc), __Pyx_ErrRestore((exc), NULL, NULL))
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#define __Pyx_PyErr_SetNone(exc) PyErr_SetNone(exc)
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#define __Pyx_PyErr_Clear() PyErr_Clear()
#define __Pyx_PyErr_SetNone(exc) PyErr_SetNone(exc)
#define __Pyx_ErrRestoreWithState(type, value, tb)  PyErr_Restore(type, value, tb)
#define __Pyx_ErrFetchWithState(type, value, tb)  PyErr_Fetch(type, value, tb)
#define __Pyx_ErrRestoreInState(tstate, type, value, tb)  PyErr_Restore(type, value, tb)
#define __Pyx_ErrFetchInState(tstate, type, value, tb)  PyErr_Fetch(type, value, tb)
#define __Pyx_ErrRestore(type, value, tb)  PyErr_Restore(type, value, tb)
#define __Pyx_ErrFetch(type, value, tb)  PyErr_Fetch(type, value, tb)
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/* PyObjectGetAttrStr.proto */
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static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStr(PyObject* obj, PyObject* attr_name);
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#define __Pyx_PyObject_GetAttrStr(o,n) PyObject_GetAttr(o,n)
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/* PyObjectGetAttrStrNoError.proto */
static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStrNoError(PyObject* obj, PyObject* attr_name);

/* GetBuiltinName.proto */
static PyObject *__Pyx_GetBuiltinName(PyObject *name);

/* TupleAndListFromArray.proto */
#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyList_FromArray(PyObject *const *src, Py_ssize_t n);
#endif
#if CYTHON_COMPILING_IN_CPYTHON || CYTHON_METH_FASTCALL
static CYTHON_INLINE PyObject* __Pyx_PyTuple_FromArray(PyObject *const *src, Py_ssize_t n);
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/* IncludeStringH.proto */
#include <string.h>

/* BytesEquals.proto */
static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals);

/* UnicodeEquals.proto */
static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals);

/* fastcall.proto */
#if CYTHON_AVOID_BORROWED_REFS
    #define __Pyx_ArgRef_VARARGS(args, i) __Pyx_PySequence_ITEM(args, i)
#elif CYTHON_ASSUME_SAFE_MACROS
    #define __Pyx_ArgRef_VARARGS(args, i) __Pyx_NewRef(__Pyx_PyTuple_GET_ITEM(args, i))
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    #define __Pyx_ArgRef_VARARGS(args, i) __Pyx_XNewRef(PyTuple_GetItem(args, i))
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#define __Pyx_NumKwargs_VARARGS(kwds) PyDict_Size(kwds)
#define __Pyx_KwValues_VARARGS(args, nargs) NULL
#define __Pyx_GetKwValue_VARARGS(kw, kwvalues, s) __Pyx_PyDict_GetItemStrWithError(kw, s)
#define __Pyx_KwargsAsDict_VARARGS(kw, kwvalues) PyDict_Copy(kw)
#if CYTHON_METH_FASTCALL
    #define __Pyx_ArgRef_FASTCALL(args, i) __Pyx_NewRef(args[i])
    #define __Pyx_NumKwargs_FASTCALL(kwds) __Pyx_PyTuple_GET_SIZE(kwds)
    #define __Pyx_KwValues_FASTCALL(args, nargs) ((args) + (nargs))
    static CYTHON_INLINE PyObject * __Pyx_GetKwValue_FASTCALL(PyObject *kwnames, PyObject *const *kwvalues, PyObject *s);
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    CYTHON_UNUSED static PyObject *__Pyx_KwargsAsDict_FASTCALL(PyObject *kwnames, PyObject *const *kwvalues);
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    #define __Pyx_KwargsAsDict_FASTCALL(kw, kwvalues) _PyStack_AsDict(kwvalues, kw)
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    #define __Pyx_ArgRef_FASTCALL __Pyx_ArgRef_VARARGS
    #define __Pyx_NumKwargs_FASTCALL __Pyx_NumKwargs_VARARGS
    #define __Pyx_KwValues_FASTCALL __Pyx_KwValues_VARARGS
    #define __Pyx_GetKwValue_FASTCALL __Pyx_GetKwValue_VARARGS
    #define __Pyx_KwargsAsDict_FASTCALL __Pyx_KwargsAsDict_VARARGS
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#define __Pyx_ArgsSlice_VARARGS(args, start, stop) PyTuple_GetSlice(args, start, stop)
#if CYTHON_METH_FASTCALL || (CYTHON_COMPILING_IN_CPYTHON && CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS)
#define __Pyx_ArgsSlice_FASTCALL(args, start, stop) __Pyx_PyTuple_FromArray(args + start, stop - start)
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#define __Pyx_ArgsSlice_FASTCALL(args, start, stop) PyTuple_GetSlice(args, start, stop)
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/* RaiseDoubleKeywords.proto */
static void __Pyx_RaiseDoubleKeywordsError(const char* func_name, PyObject* kw_name);

/* ParseKeywords.proto */
static CYTHON_INLINE int __Pyx_ParseKeywords(
    PyObject *kwds, PyObject *const *kwvalues, PyObject ** const argnames[],
    PyObject *kwds2, PyObject *values[],
    Py_ssize_t num_pos_args, Py_ssize_t num_kwargs,
    const char* function_name,
    int ignore_unknown_kwargs
);

/* CallCFunction.proto */
#define __Pyx_CallCFunction(cfunc, self, args)\
    ((PyCFunction)(void(*)(void))(cfunc)->func)(self, args)
#define __Pyx_CallCFunctionWithKeywords(cfunc, self, args, kwargs)\
    ((PyCFunctionWithKeywords)(void(*)(void))(cfunc)->func)(self, args, kwargs)
#define __Pyx_CallCFunctionFast(cfunc, self, args, nargs)\
    ((__Pyx_PyCFunctionFast)(void(*)(void))(PyCFunction)(cfunc)->func)(self, args, nargs)
#define __Pyx_CallCFunctionFastWithKeywords(cfunc, self, args, nargs, kwnames)\
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/* PyFunctionFastCall.proto */
#if CYTHON_FAST_PYCALL
#if !CYTHON_VECTORCALL
#define __Pyx_PyFunction_FastCall(func, args, nargs)\
    __Pyx_PyFunction_FastCallDict((func), (args), (nargs), NULL)
static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject *const *args, Py_ssize_t nargs, PyObject *kwargs);
#endif
#define __Pyx_BUILD_ASSERT_EXPR(cond)\
    (sizeof(char [1 - 2*!(cond)]) - 1)
#ifndef Py_MEMBER_SIZE
#define Py_MEMBER_SIZE(type, member) sizeof(((type *)0)->member)
#endif
#if !CYTHON_VECTORCALL
#if PY_VERSION_HEX >= 0x03080000
  #include "frameobject.h"
  #define __Pxy_PyFrame_Initialize_Offsets()
  #define __Pyx_PyFrame_GetLocalsplus(frame)  ((frame)->f_localsplus)
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  static size_t __pyx_pyframe_localsplus_offset = 0;
  #include "frameobject.h"
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/* PyObjectCall.proto */
#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw);
#else
#define __Pyx_PyObject_Call(func, arg, kw) PyObject_Call(func, arg, kw)
#endif

/* PyObjectCallMethO.proto */
#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg);
#endif

/* PyObjectFastCall.proto */
#define __Pyx_PyObject_FastCall(func, args, nargs)  __Pyx_PyObject_FastCallDict(func, args, (size_t)(nargs), NULL)
static CYTHON_INLINE PyObject* __Pyx_PyObject_FastCallDict(PyObject *func, PyObject * const*args, size_t nargs, PyObject *kwargs);

/* UnpackUnboundCMethod.proto */
typedef struct {
    PyObject *type;
    PyObject **method_name;
#if CYTHON_COMPILING_IN_CPYTHON_FREETHREADING && CYTHON_ATOMICS
    __pyx_atomic_int_type initialized;
#endif
    PyCFunction func;
    PyObject *method;
    int flag;
} __Pyx_CachedCFunction;
#if CYTHON_COMPILING_IN_CPYTHON_FREETHREADING
static CYTHON_INLINE int __Pyx_CachedCFunction_GetAndSetInitializing(__Pyx_CachedCFunction *cfunc) {
#if !CYTHON_ATOMICS
    return 1;
#else
    __pyx_nonatomic_int_type expected = 0;
    if (__pyx_atomic_int_cmp_exchange(&cfunc->initialized, &expected, 1)) {
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    }
    return expected;
#endif
}
static CYTHON_INLINE void __Pyx_CachedCFunction_SetFinishedInitializing(__Pyx_CachedCFunction *cfunc) {
#if CYTHON_ATOMICS
    __pyx_atomic_store(&cfunc->initialized, 2);
#endif
}
#else
#define __Pyx_CachedCFunction_GetAndSetInitializing(cfunc) 2
#define __Pyx_CachedCFunction_SetFinishedInitializing(cfunc)
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/* CallUnboundCMethod2.proto */
CYTHON_UNUSED
static PyObject* __Pyx__CallUnboundCMethod2(__Pyx_CachedCFunction* cfunc, PyObject* self, PyObject* arg1, PyObject* arg2);
#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject *__Pyx_CallUnboundCMethod2(__Pyx_CachedCFunction *cfunc, PyObject *self, PyObject *arg1, PyObject *arg2);
#else
#define __Pyx_CallUnboundCMethod2(cfunc, self, arg1, arg2)  __Pyx__CallUnboundCMethod2(cfunc, self, arg1, arg2)
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/* RaiseArgTupleInvalid.proto */
static void __Pyx_RaiseArgtupleInvalid(const char* func_name, int exact,
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/* ArgTypeTest.proto */
#define __Pyx_ArgTypeTest(obj, type, none_allowed, name, exact)\
    ((likely(__Pyx_IS_TYPE(obj, type) | (none_allowed && (obj == Py_None)))) ? 1 :\
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static int __Pyx__ArgTypeTest(PyObject *obj, PyTypeObject *type, const char *name, int exact);

/* RaiseException.proto */
static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause);

/* PyObjectFastCallMethod.proto */
#if CYTHON_VECTORCALL && PY_VERSION_HEX >= 0x03090000
#define __Pyx_PyObject_FastCallMethod(name, args, nargsf) PyObject_VectorcallMethod(name, args, nargsf, NULL)
#else
static PyObject *__Pyx_PyObject_FastCallMethod(PyObject *name, PyObject *const *args, size_t nargsf);
#endif

/* RaiseUnexpectedTypeError.proto */
static int __Pyx_RaiseUnexpectedTypeError(const char *expected, PyObject *obj);

/* BuildPyUnicode.proto */
static PyObject* __Pyx_PyUnicode_BuildFromAscii(Py_ssize_t ulength, const char* chars, int clength,
                                                int prepend_sign, char padding_char);

/* COrdinalToPyUnicode.proto */
static CYTHON_INLINE int __Pyx_CheckUnicodeValue(int value);
static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromOrdinal_Padded(int value, Py_ssize_t width, char padding_char);

/* GCCDiagnostics.proto */
#if !defined(__INTEL_COMPILER) && defined(__GNUC__) && (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6))
#define __Pyx_HAS_GCC_DIAGNOSTIC
#endif

/* IncludeStdlibH.proto */
#include <stdlib.h>

/* CIntToPyUnicode.proto */
static CYTHON_INLINE PyObject* __Pyx_PyUnicode_From_int(int value, Py_ssize_t width, char padding_char, char format_char);

/* CIntToPyUnicode.proto */
static CYTHON_INLINE PyObject* __Pyx_PyUnicode_From_Py_ssize_t(Py_ssize_t value, Py_ssize_t width, char padding_char, char format_char);

/* JoinPyUnicode.proto */
static PyObject* __Pyx_PyUnicode_Join(PyObject** values, Py_ssize_t value_count, Py_ssize_t result_ulength,
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/* PyObjectFormatSimple.proto */
#if CYTHON_COMPILING_IN_PYPY
    #define __Pyx_PyObject_FormatSimple(s, f) (\
        likely(PyUnicode_CheckExact(s)) ? (Py_INCREF(s), s) :\
        PyObject_Format(s, f))
#elif CYTHON_USE_TYPE_SLOTS
    #define __Pyx_PyObject_FormatSimple(s, f) (\
        likely(PyUnicode_CheckExact(s)) ? (Py_INCREF(s), s) :\
        likely(PyLong_CheckExact(s)) ? PyLong_Type.tp_repr(s) :\
        likely(PyFloat_CheckExact(s)) ? PyFloat_Type.tp_repr(s) :\
        PyObject_Format(s, f))
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    #define __Pyx_PyObject_FormatSimple(s, f) (\
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        PyObject_Format(s, f))
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CYTHON_UNUSED static int __pyx_array_getbuffer(PyObject *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /*proto*/
static PyObject *__pyx_array_get_memview(struct __pyx_array_obj *); /*proto*/
/* GetAttr.proto */
static CYTHON_INLINE PyObject *__Pyx_GetAttr(PyObject *, PyObject *);

/* GetItemInt.proto */
#define __Pyx_GetItemInt(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck, has_gil)\
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#define __Pyx_GetItemInt_List(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck, has_gil)\
    (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\
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static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i,
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#define __Pyx_GetItemInt_Tuple(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck, has_gil)\
    (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\
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static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i,
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static PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j);
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i,
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/* PyObjectCallOneArg.proto */
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg);

/* ObjectGetItem.proto */
#if CYTHON_USE_TYPE_SLOTS
static CYTHON_INLINE PyObject *__Pyx_PyObject_GetItem(PyObject *obj, PyObject *key);
#else
#define __Pyx_PyObject_GetItem(obj, key)  PyObject_GetItem(obj, key)
#endif

/* RejectKeywords.proto */
static void __Pyx_RejectKeywords(const char* function_name, PyObject *kwds);

/* DivInt[Py_ssize_t].proto */
static CYTHON_INLINE Py_ssize_t __Pyx_div_Py_ssize_t(Py_ssize_t, Py_ssize_t, int b_is_constant);

/* UnaryNegOverflows.proto */
#define __Pyx_UNARY_NEG_WOULD_OVERFLOW(x)\
        (((x) < 0) & ((unsigned long)(x) == 0-(unsigned long)(x)))

/* GetAttr3.proto */
static CYTHON_INLINE PyObject *__Pyx_GetAttr3(PyObject *, PyObject *, PyObject *);

/* PyDictVersioning.proto */
#if CYTHON_USE_DICT_VERSIONS && CYTHON_USE_TYPE_SLOTS
#define __PYX_DICT_VERSION_INIT  ((PY_UINT64_T) -1)
#define __PYX_GET_DICT_VERSION(dict)  (((PyDictObject*)(dict))->ma_version_tag)
#define __PYX_UPDATE_DICT_CACHE(dict, value, cache_var, version_var)\
    (version_var) = __PYX_GET_DICT_VERSION(dict);\
    (cache_var) = (value);
#define __PYX_PY_DICT_LOOKUP_IF_MODIFIED(VAR, DICT, LOOKUP) {\
    static PY_UINT64_T __pyx_dict_version = 0;\
    static PyObject *__pyx_dict_cached_value = NULL;\
    if (likely(__PYX_GET_DICT_VERSION(DICT) == __pyx_dict_version)) {\
        (VAR) = __pyx_dict_cached_value;\
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        (VAR) = __pyx_dict_cached_value = (LOOKUP);\
        __pyx_dict_version = __PYX_GET_DICT_VERSION(DICT);\
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static CYTHON_INLINE PY_UINT64_T __Pyx_get_tp_dict_version(PyObject *obj);
static CYTHON_INLINE PY_UINT64_T __Pyx_get_object_dict_version(PyObject *obj);
static CYTHON_INLINE int __Pyx_object_dict_version_matches(PyObject* obj, PY_UINT64_T tp_dict_version, PY_UINT64_T obj_dict_version);
#else
#define __PYX_GET_DICT_VERSION(dict)  (0)
#define __PYX_UPDATE_DICT_CACHE(dict, value, cache_var, version_var)
#define __PYX_PY_DICT_LOOKUP_IF_MODIFIED(VAR, DICT, LOOKUP)  (VAR) = (LOOKUP);
#endif

/* GetModuleGlobalName.proto */
#if CYTHON_USE_DICT_VERSIONS
#define __Pyx_GetModuleGlobalName(var, name)  do {\
    static PY_UINT64_T __pyx_dict_version = 0;\
    static PyObject *__pyx_dict_cached_value = NULL;\
    (var) = (likely(__pyx_dict_version == __PYX_GET_DICT_VERSION(__pyx_mstate_global->__pyx_d))) ?\
        (likely(__pyx_dict_cached_value) ? __Pyx_NewRef(__pyx_dict_cached_value) : __Pyx_GetBuiltinName(name)) :\
        __Pyx__GetModuleGlobalName(name, &__pyx_dict_version, &__pyx_dict_cached_value);\
} while(0)
#define __Pyx_GetModuleGlobalNameUncached(var, name)  do {\
    PY_UINT64_T __pyx_dict_version;\
    PyObject *__pyx_dict_cached_value;\
    (var) = __Pyx__GetModuleGlobalName(name, &__pyx_dict_version, &__pyx_dict_cached_value);\
} while(0)
static PyObject *__Pyx__GetModuleGlobalName(PyObject *name, PY_UINT64_T *dict_version, PyObject **dict_cached_value);
#else
#define __Pyx_GetModuleGlobalName(var, name)  (var) = __Pyx__GetModuleGlobalName(name)
#define __Pyx_GetModuleGlobalNameUncached(var, name)  (var) = __Pyx__GetModuleGlobalName(name)
static CYTHON_INLINE PyObject *__Pyx__GetModuleGlobalName(PyObject *name);
#endif

/* AssertionsEnabled.proto */
#if CYTHON_COMPILING_IN_LIMITED_API  ||  (CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030C0000)
  static int __pyx_assertions_enabled_flag;
  #define __pyx_assertions_enabled() (__pyx_assertions_enabled_flag)
  static int __Pyx_init_assertions_enabled(void) {
    PyObject *builtins, *debug, *debug_str;
    int flag;
    builtins = PyEval_GetBuiltins();
    if (!builtins) goto bad;
    debug_str = PyUnicode_FromStringAndSize("__debug__", 9);
    if (!debug_str) goto bad;
    debug = PyObject_GetItem(builtins, debug_str);
    Py_DECREF(debug_str);
    if (!debug) goto bad;
    flag = PyObject_IsTrue(debug);
    Py_DECREF(debug);
    if (flag == -1) goto bad;
    __pyx_assertions_enabled_flag = flag;
    return 0;
  bad:
    __pyx_assertions_enabled_flag = 1;
    return -1;
  }
#else
  #define __Pyx_init_assertions_enabled()  (0)
  #define __pyx_assertions_enabled()  (!Py_OptimizeFlag)
#endif

/* RaiseTooManyValuesToUnpack.proto */
static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected);

/* RaiseNeedMoreValuesToUnpack.proto */
static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index);

/* RaiseNoneIterError.proto */
static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void);

/* ExtTypeTest.proto */
static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type);

/* GetTopmostException.proto */
#if CYTHON_USE_EXC_INFO_STACK && CYTHON_FAST_THREAD_STATE
static _PyErr_StackItem * __Pyx_PyErr_GetTopmostException(PyThreadState *tstate);
#endif

/* SaveResetException.proto */
#if CYTHON_FAST_THREAD_STATE
#define __Pyx_ExceptionSave(type, value, tb)  __Pyx__ExceptionSave(__pyx_tstate, type, value, tb)
static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
#define __Pyx_ExceptionReset(type, value, tb)  __Pyx__ExceptionReset(__pyx_tstate, type, value, tb)
static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb);
#else
#define __Pyx_ExceptionSave(type, value, tb)   PyErr_GetExcInfo(type, value, tb)
#define __Pyx_ExceptionReset(type, value, tb)  PyErr_SetExcInfo(type, value, tb)
#endif

/* GetException.proto */
#if CYTHON_FAST_THREAD_STATE
#define __Pyx_GetException(type, value, tb)  __Pyx__GetException(__pyx_tstate, type, value, tb)
static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
#else
static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb);
#endif

/* SwapException.proto */
#if CYTHON_FAST_THREAD_STATE
#define __Pyx_ExceptionSwap(type, value, tb)  __Pyx__ExceptionSwap(__pyx_tstate, type, value, tb)
static CYTHON_INLINE void __Pyx__ExceptionSwap(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
#else
static CYTHON_INLINE void __Pyx_ExceptionSwap(PyObject **type, PyObject **value, PyObject **tb);
#endif

/* Import.proto */
static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level);

/* ImportDottedModule.proto */
static PyObject *__Pyx_ImportDottedModule(PyObject *name, PyObject *parts_tuple);
static PyObject *__Pyx_ImportDottedModule_WalkParts(PyObject *module, PyObject *name, PyObject *parts_tuple);

/* FastTypeChecks.proto */
#if CYTHON_COMPILING_IN_CPYTHON
#define __Pyx_TypeCheck(obj, type) __Pyx_IsSubtype(Py_TYPE(obj), (PyTypeObject *)type)
#define __Pyx_TypeCheck2(obj, type1, type2) __Pyx_IsAnySubtype2(Py_TYPE(obj), (PyTypeObject *)type1, (PyTypeObject *)type2)
static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b);
static CYTHON_INLINE int __Pyx_IsAnySubtype2(PyTypeObject *cls, PyTypeObject *a, PyTypeObject *b);
static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject *type);
static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *type1, PyObject *type2);
#else
#define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type)
#define __Pyx_TypeCheck2(obj, type1, type2) (PyObject_TypeCheck(obj, (PyTypeObject *)type1) || PyObject_TypeCheck(obj, (PyTypeObject *)type2))
#define __Pyx_PyErr_GivenExceptionMatches(err, type) PyErr_GivenExceptionMatches(err, type)
static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *type1, PyObject *type2) {
    return PyErr_GivenExceptionMatches(err, type1) || PyErr_GivenExceptionMatches(err, type2);
}
#endif
#define __Pyx_PyErr_ExceptionMatches2(err1, err2)  __Pyx_PyErr_GivenExceptionMatches2(__Pyx_PyErr_CurrentExceptionType(), err1, err2)
#define __Pyx_PyException_Check(obj) __Pyx_TypeCheck(obj, PyExc_Exception)
#ifdef PyExceptionInstance_Check
  #define __Pyx_PyBaseException_Check(obj) PyExceptionInstance_Check(obj)
#else
  #define __Pyx_PyBaseException_Check(obj) __Pyx_TypeCheck(obj, PyExc_BaseException)
#endif

CYTHON_UNUSED static int __pyx_memoryview_getbuffer(PyObject *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /*proto*/
/* ListCompAppend.proto */
#if CYTHON_USE_PYLIST_INTERNALS && CYTHON_ASSUME_SAFE_MACROS
static CYTHON_INLINE int __Pyx_ListComp_Append(PyObject* list, PyObject* x) {
    PyListObject* L = (PyListObject*) list;
    Py_ssize_t len = Py_SIZE(list);
    if (likely(L->allocated > len)) {
        Py_INCREF(x);
        #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030d0000
        L->ob_item[len] = x;
        #else
        PyList_SET_ITEM(list, len, x);
        #endif
        __Pyx_SET_SIZE(list, len + 1);
        return 0;
    }
    return PyList_Append(list, x);
}
#else
#define __Pyx_ListComp_Append(L,x) PyList_Append(L,x)
#endif

/* PySequenceMultiply.proto */
#define __Pyx_PySequence_Multiply_Left(mul, seq)  __Pyx_PySequence_Multiply(seq, mul)
static CYTHON_INLINE PyObject* __Pyx_PySequence_Multiply(PyObject *seq, Py_ssize_t mul);

/* PyObjectFormatAndDecref.proto */
static CYTHON_INLINE PyObject* __Pyx_PyObject_FormatSimpleAndDecref(PyObject* s, PyObject* f);
static CYTHON_INLINE PyObject* __Pyx_PyObject_FormatAndDecref(PyObject* s, PyObject* f);

/* PyObjectFormat.proto */
#if CYTHON_USE_UNICODE_WRITER
static PyObject* __Pyx_PyObject_Format(PyObject* s, PyObject* f);
#else
#define __Pyx_PyObject_Format(s, f) PyObject_Format(s, f)
#endif

/* SetItemInt.proto */
#define __Pyx_SetItemInt(o, i, v, type, is_signed, to_py_func, is_list, wraparound, boundscheck, has_gil)\
    (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\
    __Pyx_SetItemInt_Fast(o, (Py_ssize_t)i, v, is_list, wraparound, boundscheck) :\
    (is_list ? (PyErr_SetString(PyExc_IndexError, "list assignment index out of range"), -1) :\
               __Pyx_SetItemInt_Generic(o, to_py_func(i), v)))
static int __Pyx_SetItemInt_Generic(PyObject *o, PyObject *j, PyObject *v);
static CYTHON_INLINE int __Pyx_SetItemInt_Fast(PyObject *o, Py_ssize_t i, PyObject *v,
                                               int is_list, int wraparound, int boundscheck);

/* RaiseUnboundLocalError.proto */
static void __Pyx_RaiseUnboundLocalError(const char *varname);

/* DivInt[long].proto */
static CYTHON_INLINE long __Pyx_div_long(long, long, int b_is_constant);

/* PySequenceContains.proto */
static CYTHON_INLINE int __Pyx_PySequence_ContainsTF(PyObject* item, PyObject* seq, int eq) {
    int result = PySequence_Contains(seq, item);
    return unlikely(result < 0) ? result : (result == (eq == Py_EQ));
}

/* ImportFrom.proto */
static PyObject* __Pyx_ImportFrom(PyObject* module, PyObject* name);

/* HasAttr.proto */
#if __PYX_LIMITED_VERSION_HEX >= 0x030d0000
#define __Pyx_HasAttr(o, n)  PyObject_HasAttrWithError(o, n)
#else
static CYTHON_INLINE int __Pyx_HasAttr(PyObject *, PyObject *);
#endif

/* DictGetItem.proto */
#if !CYTHON_COMPILING_IN_PYPY
static PyObject *__Pyx_PyDict_GetItem(PyObject *d, PyObject* key);
#define __Pyx_PyObject_Dict_GetItem(obj, name)\
    (likely(PyDict_CheckExact(obj)) ?\
     __Pyx_PyDict_GetItem(obj, name) : PyObject_GetItem(obj, name))
#else
#define __Pyx_PyDict_GetItem(d, key) PyObject_GetItem(d, key)
#define __Pyx_PyObject_Dict_GetItem(obj, name)  PyObject_GetItem(obj, name)
#endif

/* PyFloatBinop.proto */
#if !CYTHON_COMPILING_IN_PYPY
static PyObject* __Pyx_PyFloat_TrueDivideCObj(PyObject *op1, PyObject *op2, double floatval, int inplace, int zerodivision_check);
#else
#define __Pyx_PyFloat_TrueDivideCObj(op1, op2, floatval, inplace, zerodivision_check)\
    (inplace ? PyNumber_InPlaceTrueDivide(op1, op2) : PyNumber_TrueDivide(op1, op2))
#endif

/* PyLongCompare.proto */
static CYTHON_INLINE int __Pyx_PyLong_BoolEqObjC(PyObject *op1, PyObject *op2, long intval, long inplace);

/* IsLittleEndian.proto */
static CYTHON_INLINE int __Pyx_Is_Little_Endian(void);

/* BufferFormatCheck.proto */
static const char* __Pyx_BufFmt_CheckString(__Pyx_BufFmt_Context* ctx, const char* ts);
static void __Pyx_BufFmt_Init(__Pyx_BufFmt_Context* ctx,
                              __Pyx_BufFmt_StackElem* stack,
                              const __Pyx_TypeInfo* type);

/* BufferGetAndValidate.proto */
#define __Pyx_GetBufferAndValidate(buf, obj, dtype, flags, nd, cast, stack)\
    ((obj == Py_None || obj == NULL) ?\
    (__Pyx_ZeroBuffer(buf), 0) :\
    __Pyx__GetBufferAndValidate(buf, obj, dtype, flags, nd, cast, stack))
static int  __Pyx__GetBufferAndValidate(Py_buffer* buf, PyObject* obj,
  const __Pyx_TypeInfo* dtype, int flags, int nd, int cast, __Pyx_BufFmt_StackElem* stack);
static void __Pyx_ZeroBuffer(Py_buffer* buf);
static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info);
static Py_ssize_t __Pyx_minusones[] = { -1, -1, -1, -1, -1, -1, -1, -1 };
static Py_ssize_t __Pyx_zeros[] = { 0, 0, 0, 0, 0, 0, 0, 0 };

/* PyLongBinop.proto */
#if !CYTHON_COMPILING_IN_PYPY
static CYTHON_INLINE PyObject* __Pyx_PyLong_AddCObj(PyObject *op1, PyObject *op2, long intval, int inplace, int zerodivision_check);
#else
#define __Pyx_PyLong_AddCObj(op1, op2, intval, inplace, zerodivision_check)\
    (inplace ? PyNumber_InPlaceAdd(op1, op2) : PyNumber_Add(op1, op2))
#endif

/* PyLongBinop.proto */
#if !CYTHON_COMPILING_IN_PYPY
static CYTHON_INLINE PyObject* __Pyx_PyLong_MultiplyCObj(PyObject *op1, PyObject *op2, long intval, int inplace, int zerodivision_check);
#else
#define __Pyx_PyLong_MultiplyCObj(op1, op2, intval, inplace, zerodivision_check)\
    (inplace ? PyNumber_InPlaceMultiply(op1, op2) : PyNumber_Multiply(op1, op2))
#endif

/* PyObjectVectorCallKwBuilder.proto */
CYTHON_UNUSED static int __Pyx_VectorcallBuilder_AddArg_Check(PyObject *key, PyObject *value, PyObject *builder, PyObject **args, int n);
#if CYTHON_VECTORCALL
#if PY_VERSION_HEX >= 0x03090000
#define __Pyx_Object_Vectorcall_CallFromBuilder PyObject_Vectorcall
#else
#define __Pyx_Object_Vectorcall_CallFromBuilder _PyObject_Vectorcall
#endif
#define __Pyx_MakeVectorcallBuilderKwds(n) PyTuple_New(n)
static int __Pyx_VectorcallBuilder_AddArg(PyObject *key, PyObject *value, PyObject *builder, PyObject **args, int n);
static int __Pyx_VectorcallBuilder_AddArgStr(const char *key, PyObject *value, PyObject *builder, PyObject **args, int n);
#else
#define __Pyx_Object_Vectorcall_CallFromBuilder __Pyx_PyObject_FastCallDict
#define __Pyx_MakeVectorcallBuilderKwds(n) __Pyx_PyDict_NewPresized(n)
#define __Pyx_VectorcallBuilder_AddArg(key, value, builder, args, n) PyDict_SetItem(builder, key, value)
#define __Pyx_VectorcallBuilder_AddArgStr(key, value, builder, args, n) PyDict_SetItemString(builder, key, value)
#endif

/* PyLongBinop.proto */
#if !CYTHON_COMPILING_IN_PYPY
static CYTHON_INLINE PyObject* __Pyx_PyLong_SubtractObjC(PyObject *op1, PyObject *op2, long intval, int inplace, int zerodivision_check);
#else
#define __Pyx_PyLong_SubtractObjC(op1, op2, intval, inplace, zerodivision_check)\
    (inplace ? PyNumber_InPlaceSubtract(op1, op2) : PyNumber_Subtract(op1, op2))
#endif

#define __Pyx_BufPtrStrided1d(type, buf, i0, s0) (type)((char*)buf + i0 * s0)
/* IterFinish.proto */
static CYTHON_INLINE int __Pyx_IterFinish(void);

/* PyObjectCallNoArg.proto */
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func);

/* PyObjectGetMethod.proto */
static int __Pyx_PyObject_GetMethod(PyObject *obj, PyObject *name, PyObject **method);

/* PyObjectCallMethod0.proto */
static PyObject* __Pyx_PyObject_CallMethod0(PyObject* obj, PyObject* method_name);

/* UnpackItemEndCheck.proto */
static int __Pyx_IternextUnpackEndCheck(PyObject *retval, Py_ssize_t expected);

/* UnpackTupleError.proto */
static void __Pyx_UnpackTupleError(PyObject *, Py_ssize_t index);

/* UnpackTuple2.proto */
static CYTHON_INLINE int __Pyx_unpack_tuple2(
    PyObject* tuple, PyObject** value1, PyObject** value2, int is_tuple, int has_known_size, int decref_tuple);
static CYTHON_INLINE int __Pyx_unpack_tuple2_exact(
    PyObject* tuple, PyObject** value1, PyObject** value2, int decref_tuple);
static int __Pyx_unpack_tuple2_generic(
    PyObject* tuple, PyObject** value1, PyObject** value2, int has_known_size, int decref_tuple);

/* dict_iter.proto */
static CYTHON_INLINE PyObject* __Pyx_dict_iterator(PyObject* dict, int is_dict, PyObject* method_name,
                                                   Py_ssize_t* p_orig_length, int* p_is_dict);
static CYTHON_INLINE int __Pyx_dict_iter_next(PyObject* dict_or_iter, Py_ssize_t orig_length, Py_ssize_t* ppos,
                                              PyObject** pkey, PyObject** pvalue, PyObject** pitem, int is_dict);

/* BufferFallbackError.proto */
static void __Pyx_RaiseBufferFallbackError(void);

/* PyLongBinop.proto */
#if !CYTHON_COMPILING_IN_PYPY
static CYTHON_INLINE PyObject* __Pyx_PyLong_AddObjC(PyObject *op1, PyObject *op2, long intval, int inplace, int zerodivision_check);
#else
#define __Pyx_PyLong_AddObjC(op1, op2, intval, inplace, zerodivision_check)\
    (inplace ? PyNumber_InPlaceAdd(op1, op2) : PyNumber_Add(op1, op2))
#endif

/* PyLongBinop.proto */
#if !CYTHON_COMPILING_IN_PYPY
static CYTHON_INLINE PyObject* __Pyx_PyLong_MultiplyObjC(PyObject *op1, PyObject *op2, long intval, int inplace, int zerodivision_check);
#else
#define __Pyx_PyLong_MultiplyObjC(op1, op2, intval, inplace, zerodivision_check)\
    (inplace ? PyNumber_InPlaceMultiply(op1, op2) : PyNumber_Multiply(op1, op2))
#endif

/* ListAppend.proto */
#if CYTHON_USE_PYLIST_INTERNALS && CYTHON_ASSUME_SAFE_MACROS
static CYTHON_INLINE int __Pyx_PyList_Append(PyObject* list, PyObject* x) {
    PyListObject* L = (PyListObject*) list;
    Py_ssize_t len = Py_SIZE(list);
    if (likely(L->allocated > len) & likely(len > (L->allocated >> 1))) {
        Py_INCREF(x);
        #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030d0000
        L->ob_item[len] = x;
        #else
        PyList_SET_ITEM(list, len, x);
        #endif
        __Pyx_SET_SIZE(list, len + 1);
        return 0;
    }
    return PyList_Append(list, x);
}
#else
#define __Pyx_PyList_Append(L,x) PyList_Append(L,x)
#endif

/* py_dict_keys.proto */
static CYTHON_INLINE PyObject* __Pyx_PyDict_Keys(PyObject* d);

/* CallUnboundCMethod0.proto */
CYTHON_UNUSED
static PyObject* __Pyx__CallUnboundCMethod0(__Pyx_CachedCFunction* cfunc, PyObject* self);
#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_CallUnboundCMethod0(__Pyx_CachedCFunction* cfunc, PyObject* self);
#else
#define __Pyx_CallUnboundCMethod0(cfunc, self)  __Pyx__CallUnboundCMethod0(cfunc, self)
#endif

/* PyFloatBinop.proto */
#if !CYTHON_COMPILING_IN_PYPY
static PyObject* __Pyx_PyFloat_AddCObj(PyObject *op1, PyObject *op2, double floatval, int inplace, int zerodivision_check);
#else
#define __Pyx_PyFloat_AddCObj(op1, op2, floatval, inplace, zerodivision_check)\
    (inplace ? PyNumber_InPlaceAdd(op1, op2) : PyNumber_Add(op1, op2))
#endif

/* PyDictContains.proto */
static CYTHON_INLINE int __Pyx_PyDict_ContainsTF(PyObject* item, PyObject* dict, int eq) {
    int result = PyDict_Contains(dict, item);
    return unlikely(result < 0) ? result : (result == (eq == Py_EQ));
}

/* CallTypeTraverse.proto */
#if !CYTHON_USE_TYPE_SPECS || (!CYTHON_COMPILING_IN_LIMITED_API && PY_VERSION_HEX < 0x03090000)
#define __Pyx_call_type_traverse(o, always_call, visit, arg) 0
#else
static int __Pyx_call_type_traverse(PyObject *o, int always_call, visitproc visit, void *arg);
#endif

/* LimitedApiGetTypeDict.proto */
#if CYTHON_COMPILING_IN_LIMITED_API
static PyObject *__Pyx_GetTypeDict(PyTypeObject *tp);
#endif

/* SetItemOnTypeDict.proto */
static int __Pyx__SetItemOnTypeDict(PyTypeObject *tp, PyObject *k, PyObject *v);
#define __Pyx_SetItemOnTypeDict(tp, k, v) __Pyx__SetItemOnTypeDict((PyTypeObject*)tp, k, v)

/* FixUpExtensionType.proto */
static CYTHON_INLINE int __Pyx_fix_up_extension_type_from_spec(PyType_Spec *spec, PyTypeObject *type);

/* ValidateBasesTuple.proto */
#if CYTHON_COMPILING_IN_CPYTHON || CYTHON_COMPILING_IN_LIMITED_API || CYTHON_USE_TYPE_SPECS
static int __Pyx_validate_bases_tuple(const char *type_name, Py_ssize_t dictoffset, PyObject *bases);
#endif

/* PyType_Ready.proto */
CYTHON_UNUSED static int __Pyx_PyType_Ready(PyTypeObject *t);

/* SetVTable.proto */
static int __Pyx_SetVtable(PyTypeObject* typeptr , void* vtable);

/* GetVTable.proto */
static void* __Pyx_GetVtable(PyTypeObject *type);

/* MergeVTables.proto */
static int __Pyx_MergeVtables(PyTypeObject *type);

/* DelItemOnTypeDict.proto */
static int __Pyx__DelItemOnTypeDict(PyTypeObject *tp, PyObject *k);
#define __Pyx_DelItemOnTypeDict(tp, k) __Pyx__DelItemOnTypeDict((PyTypeObject*)tp, k)

/* SetupReduce.proto */
static int __Pyx_setup_reduce(PyObject* type_obj);

/* TypeImport.proto */
#ifndef __PYX_HAVE_RT_ImportType_proto_3_1_6
#define __PYX_HAVE_RT_ImportType_proto_3_1_6
#if defined (__STDC_VERSION__) && __STDC_VERSION__ >= 201112L
#include <stdalign.h>
#endif
#if (defined (__STDC_VERSION__) && __STDC_VERSION__ >= 201112L) || __cplusplus >= 201103L
#define __PYX_GET_STRUCT_ALIGNMENT_3_1_6(s) alignof(s)
#else
#define __PYX_GET_STRUCT_ALIGNMENT_3_1_6(s) sizeof(void*)
#endif
enum __Pyx_ImportType_CheckSize_3_1_6 {
   __Pyx_ImportType_CheckSize_Error_3_1_6 = 0,
   __Pyx_ImportType_CheckSize_Warn_3_1_6 = 1,
   __Pyx_ImportType_CheckSize_Ignore_3_1_6 = 2
};
static PyTypeObject *__Pyx_ImportType_3_1_6(PyObject* module, const char *module_name, const char *class_name, size_t size, size_t alignment, enum __Pyx_ImportType_CheckSize_3_1_6 check_size);
#endif

/* ListPack.proto */
static PyObject *__Pyx_PyList_Pack(Py_ssize_t n, ...);

/* FetchSharedCythonModule.proto */
static PyObject *__Pyx_FetchSharedCythonABIModule(void);

/* dict_setdefault.proto */
static CYTHON_INLINE PyObject *__Pyx_PyDict_SetDefault(PyObject *d, PyObject *key, PyObject *default_value, int is_safe_type);

/* FetchCommonType.proto */
static PyTypeObject* __Pyx_FetchCommonTypeFromSpec(PyTypeObject *metaclass, PyObject *module, PyType_Spec *spec, PyObject *bases);

/* CommonTypesMetaclass.proto */
static int __pyx_CommonTypesMetaclass_init(PyObject *module);
#define __Pyx_CommonTypesMetaclass_USED

/* PyMethodNew.proto */
static PyObject *__Pyx_PyMethod_New(PyObject *func, PyObject *self, PyObject *typ);

/* PyVectorcallFastCallDict.proto */
#if CYTHON_METH_FASTCALL && (CYTHON_VECTORCALL || CYTHON_BACKPORT_VECTORCALL)
static CYTHON_INLINE PyObject *__Pyx_PyVectorcall_FastCallDict(PyObject *func, __pyx_vectorcallfunc vc, PyObject *const *args, size_t nargs, PyObject *kw);
#endif

/* CythonFunctionShared.proto */
#define __Pyx_CyFunction_USED
#define __Pyx_CYFUNCTION_STATICMETHOD  0x01
#define __Pyx_CYFUNCTION_CLASSMETHOD   0x02
#define __Pyx_CYFUNCTION_CCLASS        0x04
#define __Pyx_CYFUNCTION_COROUTINE     0x08
#define __Pyx_CyFunction_GetClosure(f)\
    (((__pyx_CyFunctionObject *) (f))->func_closure)
#if PY_VERSION_HEX < 0x030900B1 || CYTHON_COMPILING_IN_LIMITED_API
  #define __Pyx_CyFunction_GetClassObj(f)\
      (((__pyx_CyFunctionObject *) (f))->func_classobj)
#else
  #define __Pyx_CyFunction_GetClassObj(f)\
      ((PyObject*) ((PyCMethodObject *) (f))->mm_class)
#endif
#define __Pyx_CyFunction_SetClassObj(f, classobj)\
    __Pyx__CyFunction_SetClassObj((__pyx_CyFunctionObject *) (f), (classobj))
#define __Pyx_CyFunction_Defaults(type, f)\
    ((type *)(((__pyx_CyFunctionObject *) (f))->defaults))
#define __Pyx_CyFunction_SetDefaultsGetter(f, g)\
    ((__pyx_CyFunctionObject *) (f))->defaults_getter = (g)
typedef struct {
#if CYTHON_COMPILING_IN_LIMITED_API
    PyObject_HEAD
    PyObject *func;
#elif PY_VERSION_HEX < 0x030900B1
    PyCFunctionObject func;
#else
    PyCMethodObject func;
#endif
#if CYTHON_BACKPORT_VECTORCALL ||\
        (CYTHON_COMPILING_IN_LIMITED_API && CYTHON_METH_FASTCALL)
    __pyx_vectorcallfunc func_vectorcall;
#endif
#if CYTHON_COMPILING_IN_LIMITED_API
    PyObject *func_weakreflist;
#endif
    PyObject *func_dict;
    PyObject *func_name;
    PyObject *func_qualname;
    PyObject *func_doc;
    PyObject *func_globals;
    PyObject *func_code;
    PyObject *func_closure;
#if PY_VERSION_HEX < 0x030900B1 || CYTHON_COMPILING_IN_LIMITED_API
    PyObject *func_classobj;
#endif
    PyObject *defaults;
    int flags;
    PyObject *defaults_tuple;
    PyObject *defaults_kwdict;
    PyObject *(*defaults_getter)(PyObject *);
    PyObject *func_annotations;
    PyObject *func_is_coroutine;
} __pyx_CyFunctionObject;
#undef __Pyx_CyOrPyCFunction_Check
#define __Pyx_CyFunction_Check(obj)  __Pyx_TypeCheck(obj, __pyx_mstate_global->__pyx_CyFunctionType)
#define __Pyx_CyOrPyCFunction_Check(obj)  __Pyx_TypeCheck2(obj, __pyx_mstate_global->__pyx_CyFunctionType, &PyCFunction_Type)
#define __Pyx_CyFunction_CheckExact(obj)  __Pyx_IS_TYPE(obj, __pyx_mstate_global->__pyx_CyFunctionType)
static CYTHON_INLINE int __Pyx__IsSameCyOrCFunction(PyObject *func, void (*cfunc)(void));
#undef __Pyx_IsSameCFunction
#define __Pyx_IsSameCFunction(func, cfunc)   __Pyx__IsSameCyOrCFunction(func, cfunc)
static PyObject *__Pyx_CyFunction_Init(__pyx_CyFunctionObject* op, PyMethodDef *ml,
                                      int flags, PyObject* qualname,
                                      PyObject *closure,
                                      PyObject *module, PyObject *globals,
                                      PyObject* code);
static CYTHON_INLINE void __Pyx__CyFunction_SetClassObj(__pyx_CyFunctionObject* f, PyObject* classobj);
static CYTHON_INLINE PyObject *__Pyx_CyFunction_InitDefaults(PyObject *func,
                                                         PyTypeObject *defaults_type);
static CYTHON_INLINE void __Pyx_CyFunction_SetDefaultsTuple(PyObject *m,
                                                            PyObject *tuple);
static CYTHON_INLINE void __Pyx_CyFunction_SetDefaultsKwDict(PyObject *m,
                                                             PyObject *dict);
static CYTHON_INLINE void __Pyx_CyFunction_SetAnnotationsDict(PyObject *m,
                                                              PyObject *dict);
static int __pyx_CyFunction_init(PyObject *module);
#if CYTHON_METH_FASTCALL
static PyObject * __Pyx_CyFunction_Vectorcall_NOARGS(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames);
static PyObject * __Pyx_CyFunction_Vectorcall_O(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames);
static PyObject * __Pyx_CyFunction_Vectorcall_FASTCALL_KEYWORDS(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames);
static PyObject * __Pyx_CyFunction_Vectorcall_FASTCALL_KEYWORDS_METHOD(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames);
#if CYTHON_BACKPORT_VECTORCALL || CYTHON_COMPILING_IN_LIMITED_API
#define __Pyx_CyFunction_func_vectorcall(f) (((__pyx_CyFunctionObject*)f)->func_vectorcall)
#else
#define __Pyx_CyFunction_func_vectorcall(f) (((PyCFunctionObject*)f)->vectorcall)
#endif
#endif

/* CythonFunction.proto */
static PyObject *__Pyx_CyFunction_New(PyMethodDef *ml,
                                      int flags, PyObject* qualname,
                                      PyObject *closure,
                                      PyObject *module, PyObject *globals,
                                      PyObject* code);

/* CLineInTraceback.proto */
#if CYTHON_CLINE_IN_TRACEBACK && CYTHON_CLINE_IN_TRACEBACK_RUNTIME
static int __Pyx_CLineForTraceback(PyThreadState *tstate, int c_line);
#else
#define __Pyx_CLineForTraceback(tstate, c_line)  (((CYTHON_CLINE_IN_TRACEBACK)) ? c_line : 0)
#endif

/* CodeObjectCache.proto */
#if CYTHON_COMPILING_IN_LIMITED_API
typedef PyObject __Pyx_CachedCodeObjectType;
#else
typedef PyCodeObject __Pyx_CachedCodeObjectType;
#endif
typedef struct {
    __Pyx_CachedCodeObjectType* code_object;
    int code_line;
} __Pyx_CodeObjectCacheEntry;
struct __Pyx_CodeObjectCache {
    int count;
    int max_count;
    __Pyx_CodeObjectCacheEntry* entries;
  #if CYTHON_COMPILING_IN_CPYTHON_FREETHREADING
    __pyx_atomic_int_type accessor_count;
  #endif
};
static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line);
static __Pyx_CachedCodeObjectType *__pyx_find_code_object(int code_line);
static void __pyx_insert_code_object(int code_line, __Pyx_CachedCodeObjectType* code_object);

/* AddTraceback.proto */
static void __Pyx_AddTraceback(const char *funcname, int c_line,
                               int py_line, const char *filename);

/* ArrayAPI.proto */
#ifndef _ARRAYARRAY_H
#define _ARRAYARRAY_H
typedef struct arraydescr {
    int typecode;
    int itemsize;
    PyObject * (*getitem)(struct arrayobject *, Py_ssize_t);
    int (*setitem)(struct arrayobject *, Py_ssize_t, PyObject *);
    char *formats;
} arraydescr;
struct arrayobject {
    PyObject_HEAD
    Py_ssize_t ob_size;
    union {
        char *ob_item;
        float *as_floats;
        double *as_doubles;
        int *as_ints;
        unsigned int *as_uints;
        unsigned char *as_uchars;
        signed char *as_schars;
        char *as_chars;
        unsigned long *as_ulongs;
        long *as_longs;
        unsigned long long *as_ulonglongs;
        long long *as_longlongs;
        short *as_shorts;
        unsigned short *as_ushorts;
        #if PY_VERSION_HEX >= 0x030d0000
        Py_DEPRECATED(3.13)
        #endif
            wchar_t *as_pyunicodes;
        void *as_voidptr;
    } data;
    Py_ssize_t allocated;
    struct arraydescr *ob_descr;
    PyObject *weakreflist;
    int ob_exports;
};
#ifndef NO_NEWARRAY_INLINE
static CYTHON_INLINE PyObject * newarrayobject(PyTypeObject *type, Py_ssize_t size,
    struct arraydescr *descr) {
    arrayobject *op;
    size_t nbytes;
    if (size < 0) {
        PyErr_BadInternalCall();
        return NULL;
    }
    nbytes = size * descr->itemsize;
    if (nbytes / descr->itemsize != (size_t)size) {
        return PyErr_NoMemory();
    }
    op = (arrayobject *) type->tp_alloc(type, 0);
    if (op == NULL) {
        return NULL;
    }
    op->ob_descr = descr;
    op->allocated = size;
    op->weakreflist = NULL;
    __Pyx_SET_SIZE(op, size);
    if (size <= 0) {
        op->data.ob_item = NULL;
    }
    else {
        op->data.ob_item = PyMem_NEW(char, nbytes);
        if (op->data.ob_item == NULL) {
            Py_DECREF(op);
            return PyErr_NoMemory();
        }
    }
    return (PyObject *) op;
}
#else
PyObject* newarrayobject(PyTypeObject *type, Py_ssize_t size,
    struct arraydescr *descr);
#endif
static CYTHON_INLINE int resize(arrayobject *self, Py_ssize_t n) {
    void *items = (void*) self->data.ob_item;
    PyMem_Resize(items, char, (size_t)(n * self->ob_descr->itemsize));
    if (items == NULL) {
        PyErr_NoMemory();
        return -1;
    }
    self->data.ob_item = (char*) items;
    __Pyx_SET_SIZE(self, n);
    self->allocated = n;
    return 0;
}
static CYTHON_INLINE int resize_smart(arrayobject *self, Py_ssize_t n) {
    void *items = (void*) self->data.ob_item;
    Py_ssize_t newsize;
    if (n < self->allocated && n*4 > self->allocated) {
        __Pyx_SET_SIZE(self, n);
        return 0;
    }
    newsize = n + (n / 2) + 1;
    if (newsize <= n) {
        PyErr_NoMemory();
        return -1;
    }
    PyMem_Resize(items, char, (size_t)(newsize * self->ob_descr->itemsize));
    if (items == NULL) {
        PyErr_NoMemory();
        return -1;
    }
    self->data.ob_item = (char*) items;
    __Pyx_SET_SIZE(self, n);
    self->allocated = newsize;
    return 0;
}
#endif

/* RealImag.proto */
#if CYTHON_CCOMPLEX
  #ifdef __cplusplus
    #define __Pyx_CREAL(z) ((z).real())
    #define __Pyx_CIMAG(z) ((z).imag())
  #else
    #define __Pyx_CREAL(z) (__real__(z))
    #define __Pyx_CIMAG(z) (__imag__(z))
  #endif
#else
    #define __Pyx_CREAL(z) ((z).real)
    #define __Pyx_CIMAG(z) ((z).imag)
#endif
#if defined(__cplusplus) && CYTHON_CCOMPLEX\
        && (defined(_WIN32) || defined(__clang__) || (defined(__GNUC__) && (__GNUC__ >= 5 || __GNUC__ == 4 && __GNUC_MINOR__ >= 4 )) || __cplusplus >= 201103)
    #define __Pyx_SET_CREAL(z,x) ((z).real(x))
    #define __Pyx_SET_CIMAG(z,y) ((z).imag(y))
#else
    #define __Pyx_SET_CREAL(z,x) __Pyx_CREAL(z) = (x)
    #define __Pyx_SET_CIMAG(z,y) __Pyx_CIMAG(z) = (y)
#endif

/* Arithmetic.proto */
#if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus)
    #define __Pyx_c_eq_double(a, b)   ((a)==(b))
    #define __Pyx_c_sum_double(a, b)  ((a)+(b))
    #define __Pyx_c_diff_double(a, b) ((a)-(b))
    #define __Pyx_c_prod_double(a, b) ((a)*(b))
    #define __Pyx_c_quot_double(a, b) ((a)/(b))
    #define __Pyx_c_neg_double(a)     (-(a))
  #ifdef __cplusplus
    #define __Pyx_c_is_zero_double(z) ((z)==(double)0)
    #define __Pyx_c_conj_double(z)    (::std::conj(z))
    #if 1
        #define __Pyx_c_abs_double(z)     (::std::abs(z))
        #define __Pyx_c_pow_double(a, b)  (::std::pow(a, b))
    #endif
  #else
    #define __Pyx_c_is_zero_double(z) ((z)==0)
    #define __Pyx_c_conj_double(z)    (conj(z))
    #if 1
        #define __Pyx_c_abs_double(z)     (cabs(z))
        #define __Pyx_c_pow_double(a, b)  (cpow(a, b))
    #endif
 #endif
#else
    static CYTHON_INLINE int __Pyx_c_eq_double(__pyx_t_double_complex, __pyx_t_double_complex);
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum_double(__pyx_t_double_complex, __pyx_t_double_complex);
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff_double(__pyx_t_double_complex, __pyx_t_double_complex);
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod_double(__pyx_t_double_complex, __pyx_t_double_complex);
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex, __pyx_t_double_complex);
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__pyx_t_double_complex);
    static CYTHON_INLINE int __Pyx_c_is_zero_double(__pyx_t_double_complex);
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__pyx_t_double_complex);
    #if 1
        static CYTHON_INLINE double __Pyx_c_abs_double(__pyx_t_double_complex);
        static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow_double(__pyx_t_double_complex, __pyx_t_double_complex);
    #endif
#endif

/* BufferStructDeclare.proto */
typedef struct {
  Py_ssize_t shape, strides, suboffsets;
} __Pyx_Buf_DimInfo;
typedef struct {
  size_t refcount;
  Py_buffer pybuffer;
} __Pyx_Buffer;
typedef struct {
  __Pyx_Buffer *rcbuffer;
  char *data;
  __Pyx_Buf_DimInfo diminfo[8];
} __Pyx_LocalBuf_ND;

/* MemviewSliceIsContig.proto */
static int __pyx_memviewslice_is_contig(const __Pyx_memviewslice mvs, char order, int ndim);

/* OverlappingSlices.proto */
static int __pyx_slices_overlap(__Pyx_memviewslice *slice1,
                                __Pyx_memviewslice *slice2,
                                int ndim, size_t itemsize);

/* ToPy.proto */
#define __pyx_PyComplex_FromComplex(z)\
        PyComplex_FromDoubles((double)__Pyx_CREAL(z),\
                              (double)__Pyx_CIMAG(z))

/* FromPy.proto */
static __pyx_t_double_complex __Pyx_PyComplex_As___pyx_t_double_complex(PyObject*);

/* TypeInfoCompare.proto */
static int __pyx_typeinfo_cmp(const __Pyx_TypeInfo *a, const __Pyx_TypeInfo *b);

/* MemviewSliceValidateAndInit.proto */
static int __Pyx_ValidateAndInit_memviewslice(
                int *axes_specs,
                int c_or_f_flag,
                int buf_flags,
                int ndim,
                const __Pyx_TypeInfo *dtype,
                __Pyx_BufFmt_StackElem stack[],
                __Pyx_memviewslice *memviewslice,
                PyObject *original_obj);

/* ObjectToMemviewSlice.proto */
static CYTHON_INLINE __Pyx_memviewslice __Pyx_PyObject_to_MemoryviewSlice_dc___pyx_t_double_complex(PyObject *, int writable_flag);

/* ObjectToMemviewSlice.proto */
static CYTHON_INLINE __Pyx_memviewslice __Pyx_PyObject_to_MemoryviewSlice_dc_double(PyObject *, int writable_flag);

/* Arithmetic.proto */
#if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus)
    #define __Pyx_c_eq_float(a, b)   ((a)==(b))
    #define __Pyx_c_sum_float(a, b)  ((a)+(b))
    #define __Pyx_c_diff_float(a, b) ((a)-(b))
    #define __Pyx_c_prod_float(a, b) ((a)*(b))
    #define __Pyx_c_quot_float(a, b) ((a)/(b))
    #define __Pyx_c_neg_float(a)     (-(a))
  #ifdef __cplusplus
    #define __Pyx_c_is_zero_float(z) ((z)==(float)0)
    #define __Pyx_c_conj_float(z)    (::std::conj(z))
    #if 1
        #define __Pyx_c_abs_float(z)     (::std::abs(z))
        #define __Pyx_c_pow_float(a, b)  (::std::pow(a, b))
    #endif
  #else
    #define __Pyx_c_is_zero_float(z) ((z)==0)
    #define __Pyx_c_conj_float(z)    (conjf(z))
    #if 1
        #define __Pyx_c_abs_float(z)     (cabsf(z))
        #define __Pyx_c_pow_float(a, b)  (cpowf(a, b))
    #endif
 #endif
#else
    static CYTHON_INLINE int __Pyx_c_eq_float(__pyx_t_float_complex, __pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sum_float(__pyx_t_float_complex, __pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_diff_float(__pyx_t_float_complex, __pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prod_float(__pyx_t_float_complex, __pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex, __pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_neg_float(__pyx_t_float_complex);
    static CYTHON_INLINE int __Pyx_c_is_zero_float(__pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conj_float(__pyx_t_float_complex);
    #if 1
        static CYTHON_INLINE float __Pyx_c_abs_float(__pyx_t_float_complex);
        static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_pow_float(__pyx_t_float_complex, __pyx_t_float_complex);
    #endif
#endif

/* Arithmetic.proto */
#if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus)
    #define __Pyx_c_eq_long__double(a, b)   ((a)==(b))
    #define __Pyx_c_sum_long__double(a, b)  ((a)+(b))
    #define __Pyx_c_diff_long__double(a, b) ((a)-(b))
    #define __Pyx_c_prod_long__double(a, b) ((a)*(b))
    #define __Pyx_c_quot_long__double(a, b) ((a)/(b))
    #define __Pyx_c_neg_long__double(a)     (-(a))
  #ifdef __cplusplus
    #define __Pyx_c_is_zero_long__double(z) ((z)==(long double)0)
    #define __Pyx_c_conj_long__double(z)    (::std::conj(z))
    #if 1
        #define __Pyx_c_abs_long__double(z)     (::std::abs(z))
        #define __Pyx_c_pow_long__double(a, b)  (::std::pow(a, b))
    #endif
  #else
    #define __Pyx_c_is_zero_long__double(z) ((z)==0)
    #define __Pyx_c_conj_long__double(z)    (conjl(z))
    #if 1
        #define __Pyx_c_abs_long__double(z)     (cabsl(z))
        #define __Pyx_c_pow_long__double(a, b)  (cpowl(a, b))
    #endif
 #endif
#else
    static CYTHON_INLINE int __Pyx_c_eq_long__double(__pyx_t_long_double_complex, __pyx_t_long_double_complex);
    static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_sum_long__double(__pyx_t_long_double_complex, __pyx_t_long_double_complex);
    static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_diff_long__double(__pyx_t_long_double_complex, __pyx_t_long_double_complex);
    static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_prod_long__double(__pyx_t_long_double_complex, __pyx_t_long_double_complex);
    static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_quot_long__double(__pyx_t_long_double_complex, __pyx_t_long_double_complex);
    static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_neg_long__double(__pyx_t_long_double_complex);
    static CYTHON_INLINE int __Pyx_c_is_zero_long__double(__pyx_t_long_double_complex);
    static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_conj_long__double(__pyx_t_long_double_complex);
    #if 1
        static CYTHON_INLINE long double __Pyx_c_abs_long__double(__pyx_t_long_double_complex);
        static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_pow_long__double(__pyx_t_long_double_complex, __pyx_t_long_double_complex);
    #endif
#endif

/* MemviewSliceCopyTemplate.proto */
static __Pyx_memviewslice
__pyx_memoryview_copy_new_contig(const __Pyx_memviewslice *from_mvs,
                                 const char *mode, int ndim,
                                 size_t sizeof_dtype, int contig_flag,
                                 int dtype_is_object);

/* MemviewSliceInit.proto */
#include <stdio.h>
#define __Pyx_BUF_MAX_NDIMS %(BUF_MAX_NDIMS)d
#define __Pyx_MEMVIEW_DIRECT   1
#define __Pyx_MEMVIEW_PTR      2
#define __Pyx_MEMVIEW_FULL     4
#define __Pyx_MEMVIEW_CONTIG   8
#define __Pyx_MEMVIEW_STRIDED  16
#define __Pyx_MEMVIEW_FOLLOW   32
#define __Pyx_IS_C_CONTIG 1
#define __Pyx_IS_F_CONTIG 2
static int __Pyx_init_memviewslice(
                struct __pyx_memoryview_obj *memview,
                int ndim,
                __Pyx_memviewslice *memviewslice,
                int memview_is_new_reference);
static CYTHON_INLINE int __pyx_add_acquisition_count_locked(
    __pyx_atomic_int_type *acquisition_count, PyThread_type_lock lock);
static CYTHON_INLINE int __pyx_sub_acquisition_count_locked(
    __pyx_atomic_int_type *acquisition_count, PyThread_type_lock lock);
#define __pyx_get_slice_count_pointer(memview) (&memview->acquisition_count)
#define __PYX_INC_MEMVIEW(slice, have_gil) __Pyx_INC_MEMVIEW(slice, have_gil, __LINE__)
#define __PYX_XCLEAR_MEMVIEW(slice, have_gil) __Pyx_XCLEAR_MEMVIEW(slice, have_gil, __LINE__)
static CYTHON_INLINE void __Pyx_INC_MEMVIEW(__Pyx_memviewslice *, int, int);
static CYTHON_INLINE void __Pyx_XCLEAR_MEMVIEW(__Pyx_memviewslice *, int, int);

/* CIntToPy.proto */
static CYTHON_INLINE PyObject* __Pyx_PyLong_From_int(int value);

/* CIntFromPy.proto */
static CYTHON_INLINE int __Pyx_PyLong_As_int(PyObject *);

/* CIntToPy.proto */
static CYTHON_INLINE PyObject* __Pyx_PyLong_From_long(long value);

/* CIntFromPy.proto */
static CYTHON_INLINE unsigned int __Pyx_PyLong_As_unsigned_int(PyObject *);

/* CIntFromPy.proto */
static CYTHON_INLINE long __Pyx_PyLong_As_long(PyObject *);

/* CIntToPy.proto */
static CYTHON_INLINE PyObject* __Pyx_PyLong_From_unsigned_int(unsigned int value);

/* CIntToPy.proto */
static CYTHON_INLINE PyObject* __Pyx_PyLong_From_npy_intp(npy_intp value);

/* CIntFromPy.proto */
static CYTHON_INLINE char __Pyx_PyLong_As_char(PyObject *);

/* FormatTypeName.proto */
#if CYTHON_COMPILING_IN_LIMITED_API
typedef PyObject *__Pyx_TypeName;
#define __Pyx_FMT_TYPENAME "%U"
#define __Pyx_DECREF_TypeName(obj) Py_XDECREF(obj)
#if __PYX_LIMITED_VERSION_HEX >= 0x030d0000
#define __Pyx_PyType_GetFullyQualifiedName PyType_GetFullyQualifiedName
#else
static __Pyx_TypeName __Pyx_PyType_GetFullyQualifiedName(PyTypeObject* tp);
#endif
#else  // !LIMITED_API
typedef const char *__Pyx_TypeName;
#define __Pyx_FMT_TYPENAME "%.200s"
#define __Pyx_PyType_GetFullyQualifiedName(tp) ((tp)->tp_name)
#define __Pyx_DECREF_TypeName(obj)
#endif

/* GetRuntimeVersion.proto */
static unsigned long __Pyx_get_runtime_version(void);

/* CheckBinaryVersion.proto */
static int __Pyx_check_binary_version(unsigned long ct_version, unsigned long rt_version, int allow_newer);

/* PyObjectDelAttr.proto */
#if CYTHON_COMPILING_IN_LIMITED_API && __PYX_LIMITED_VERSION_HEX < 0x030d0000
#define __Pyx_PyObject_DelAttr(o, n) PyObject_SetAttr(o, n, NULL)
#else
#define __Pyx_PyObject_DelAttr(o, n) PyObject_DelAttr(o, n)
#endif

/* PyObjectSetAttrStr.proto */
#if CYTHON_USE_TYPE_SLOTS
#define __Pyx_PyObject_DelAttrStr(o,n) __Pyx_PyObject_SetAttrStr(o, n, NULL)
static CYTHON_INLINE int __Pyx_PyObject_SetAttrStr(PyObject* obj, PyObject* attr_name, PyObject* value);
#else
#define __Pyx_PyObject_DelAttrStr(o,n)   __Pyx_PyObject_DelAttr(o,n)
#define __Pyx_PyObject_SetAttrStr(o,n,v) PyObject_SetAttr(o,n,v)
#endif

/* VoidPtrExport.proto */
static int __Pyx_ExportVoidPtr(PyObject *name, void *p, const char *sig);

/* FunctionImport.proto */
static int __Pyx_ImportFunction_3_1_6(PyObject *module, const char *funcname, void (**f)(void), const char *sig);

/* MultiPhaseInitModuleState.proto */
#if CYTHON_PEP489_MULTI_PHASE_INIT && CYTHON_USE_MODULE_STATE
static PyObject *__Pyx_State_FindModule(void*);
static int __Pyx_State_AddModule(PyObject* module, void*);
static int __Pyx_State_RemoveModule(void*);
#elif CYTHON_USE_MODULE_STATE
#define __Pyx_State_FindModule PyState_FindModule
#define __Pyx_State_AddModule PyState_AddModule
#define __Pyx_State_RemoveModule PyState_RemoveModule
#endif

/* #### Code section: module_declarations ### */
/* CythonABIVersion.proto */
#if CYTHON_COMPILING_IN_LIMITED_API
    #if CYTHON_METH_FASTCALL
        #define __PYX_FASTCALL_ABI_SUFFIX  "_fastcall"
    #else
        #define __PYX_FASTCALL_ABI_SUFFIX
    #endif
    #define __PYX_LIMITED_ABI_SUFFIX "limited" __PYX_FASTCALL_ABI_SUFFIX __PYX_AM_SEND_ABI_SUFFIX
#else
    #define __PYX_LIMITED_ABI_SUFFIX
#endif
#if __PYX_HAS_PY_AM_SEND == 1
    #define __PYX_AM_SEND_ABI_SUFFIX
#elif __PYX_HAS_PY_AM_SEND == 2
    #define __PYX_AM_SEND_ABI_SUFFIX "amsendbackport"
#else
    #define __PYX_AM_SEND_ABI_SUFFIX "noamsend"
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#ifndef __PYX_MONITORING_ABI_SUFFIX
    #define __PYX_MONITORING_ABI_SUFFIX
#endif
#if CYTHON_USE_TP_FINALIZE
    #define __PYX_TP_FINALIZE_ABI_SUFFIX
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    #define __PYX_TP_FINALIZE_ABI_SUFFIX "nofinalize"
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    #define __PYX_FREELISTS_ABI_SUFFIX
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    #define __PYX_FREELISTS_ABI_SUFFIX "nofreelists"
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#define CYTHON_ABI  __PYX_ABI_VERSION __PYX_LIMITED_ABI_SUFFIX __PYX_MONITORING_ABI_SUFFIX __PYX_TP_FINALIZE_ABI_SUFFIX __PYX_FREELISTS_ABI_SUFFIX __PYX_AM_SEND_ABI_SUFFIX
#define __PYX_ABI_MODULE_NAME "_cython_" CYTHON_ABI
#define __PYX_TYPE_MODULE_PREFIX __PYX_ABI_MODULE_NAME "."

static PyObject *__pyx_array_get_memview(struct __pyx_array_obj *__pyx_v_self); /* proto*/
static char *__pyx_memoryview_get_item_pointer(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_index); /* proto*/
static PyObject *__pyx_memoryview_is_slice(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_obj); /* proto*/
static PyObject *__pyx_memoryview_setitem_slice_assignment(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_dst, PyObject *__pyx_v_src); /* proto*/
static PyObject *__pyx_memoryview_setitem_slice_assign_scalar(struct __pyx_memoryview_obj *__pyx_v_self, struct __pyx_memoryview_obj *__pyx_v_dst, PyObject *__pyx_v_value); /* proto*/
static PyObject *__pyx_memoryview_setitem_indexed(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_index, PyObject *__pyx_v_value); /* proto*/
static PyObject *__pyx_memoryview_convert_item_to_object(struct __pyx_memoryview_obj *__pyx_v_self, char *__pyx_v_itemp); /* proto*/
static PyObject *__pyx_memoryview_assign_item_from_object(struct __pyx_memoryview_obj *__pyx_v_self, char *__pyx_v_itemp, PyObject *__pyx_v_value); /* proto*/
static PyObject *__pyx_memoryview__get_base(struct __pyx_memoryview_obj *__pyx_v_self); /* proto*/
static PyObject *__pyx_memoryviewslice_convert_item_to_object(struct __pyx_memoryviewslice_obj *__pyx_v_self, char *__pyx_v_itemp); /* proto*/
static PyObject *__pyx_memoryviewslice_assign_item_from_object(struct __pyx_memoryviewslice_obj *__pyx_v_self, char *__pyx_v_itemp, PyObject *__pyx_v_value); /* proto*/
static PyObject *__pyx_memoryviewslice__get_base(struct __pyx_memoryviewslice_obj *__pyx_v_self); /* proto*/
#if !CYTHON_COMPILING_IN_LIMITED_API
static CYTHON_INLINE double __pyx_f_7cpython_7complex_7complex_4real_real(PyComplexObject *__pyx_v_self); /* proto*/
#endif
#if !CYTHON_COMPILING_IN_LIMITED_API
static CYTHON_INLINE double __pyx_f_7cpython_7complex_7complex_4imag_imag(PyComplexObject *__pyx_v_self); /* proto*/
#endif
static CYTHON_INLINE npy_intp __pyx_f_5numpy_5dtype_8itemsize_itemsize(PyArray_Descr *__pyx_v_self); /* proto*/
static CYTHON_INLINE npy_intp __pyx_f_5numpy_5dtype_9alignment_alignment(PyArray_Descr *__pyx_v_self); /* proto*/
static CYTHON_INLINE PyObject *__pyx_f_5numpy_5dtype_6fields_fields(PyArray_Descr *__pyx_v_self); /* proto*/
static CYTHON_INLINE PyObject *__pyx_f_5numpy_5dtype_5names_names(PyArray_Descr *__pyx_v_self); /* proto*/
static CYTHON_INLINE PyArray_ArrayDescr *__pyx_f_5numpy_5dtype_8subarray_subarray(PyArray_Descr *__pyx_v_self); /* proto*/
static CYTHON_INLINE npy_uint64 __pyx_f_5numpy_5dtype_5flags_flags(PyArray_Descr *__pyx_v_self); /* proto*/
static CYTHON_INLINE int __pyx_f_5numpy_9broadcast_7numiter_numiter(PyArrayMultiIterObject *__pyx_v_self); /* proto*/
static CYTHON_INLINE npy_intp __pyx_f_5numpy_9broadcast_4size_size(PyArrayMultiIterObject *__pyx_v_self); /* proto*/
static CYTHON_INLINE npy_intp __pyx_f_5numpy_9broadcast_5index_index(PyArrayMultiIterObject *__pyx_v_self); /* proto*/
static CYTHON_INLINE int __pyx_f_5numpy_9broadcast_2nd_nd(PyArrayMultiIterObject *__pyx_v_self); /* proto*/
static CYTHON_INLINE npy_intp *__pyx_f_5numpy_9broadcast_10dimensions_dimensions(PyArrayMultiIterObject *__pyx_v_self); /* proto*/
static CYTHON_INLINE void **__pyx_f_5numpy_9broadcast_5iters_iters(PyArrayMultiIterObject *__pyx_v_self); /* proto*/
static CYTHON_INLINE PyObject *__pyx_f_5numpy_7ndarray_4base_base(PyArrayObject *__pyx_v_self); /* proto*/
static CYTHON_INLINE PyArray_Descr *__pyx_f_5numpy_7ndarray_5descr_descr(PyArrayObject *__pyx_v_self); /* proto*/
static CYTHON_INLINE int __pyx_f_5numpy_7ndarray_4ndim_ndim(PyArrayObject *__pyx_v_self); /* proto*/
static CYTHON_INLINE npy_intp *__pyx_f_5numpy_7ndarray_5shape_shape(PyArrayObject *__pyx_v_self); /* proto*/
static CYTHON_INLINE npy_intp *__pyx_f_5numpy_7ndarray_7strides_strides(PyArrayObject *__pyx_v_self); /* proto*/
static CYTHON_INLINE npy_intp __pyx_f_5numpy_7ndarray_4size_size(PyArrayObject *__pyx_v_self); /* proto*/
static CYTHON_INLINE char *__pyx_f_5numpy_7ndarray_4data_data(PyArrayObject *__pyx_v_self); /* proto*/
static double __pyx_f_6pyRing_8waveform_3QNM_f(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self, double __pyx_v_M, double __pyx_v_a, int __pyx_skip_dispatch); /* proto*/
static double __pyx_f_6pyRing_8waveform_3QNM_f_KN(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self, double __pyx_v_M, double __pyx_v_a, double __pyx_v_Q, int __pyx_skip_dispatch); /* proto*/
static double __pyx_f_6pyRing_8waveform_3QNM_f_BW(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self, double __pyx_v_M, double __pyx_v_a, double __pyx_v_beta, int __pyx_skip_dispatch); /* proto*/
static double __pyx_f_6pyRing_8waveform_3QNM_tau(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self, double __pyx_v_M, double __pyx_v_a, int __pyx_skip_dispatch); /* proto*/
static double __pyx_f_6pyRing_8waveform_3QNM_tau_KN(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self, double __pyx_v_M, double __pyx_v_a, double __pyx_v_Q, int __pyx_skip_dispatch); /* proto*/
static double __pyx_f_6pyRing_8waveform_3QNM_tau_BW(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self, double __pyx_v_M, double __pyx_v_a, double __pyx_v_beta, int __pyx_skip_dispatch); /* proto*/
static double __pyx_f_6pyRing_8waveform_7QNM_fit_f(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self, double __pyx_v_M, double __pyx_v_a, int __pyx_skip_dispatch); /* proto*/
static double __pyx_f_6pyRing_8waveform_7QNM_fit_q(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self, double __pyx_v_a, int __pyx_skip_dispatch); /* proto*/
static double __pyx_f_6pyRing_8waveform_7QNM_fit_tau(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self, double __pyx_v_M, double __pyx_v_a, int __pyx_skip_dispatch); /* proto*/
static double __pyx_f_6pyRing_8waveform_7QNM_fit_f_KN(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self, double __pyx_v_M, double __pyx_v_a, CYTHON_UNUSED double __pyx_v_Q, int __pyx_skip_dispatch); /* proto*/
static double __pyx_f_6pyRing_8waveform_7QNM_fit_q_KN(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self, double __pyx_v_a, CYTHON_UNUSED double __pyx_v_Q, int __pyx_skip_dispatch); /* proto*/
static double __pyx_f_6pyRing_8waveform_7QNM_fit_tau_KN(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self, double __pyx_v_M, double __pyx_v_a, double __pyx_v_Q, int __pyx_skip_dispatch); /* proto*/
static double __pyx_f_6pyRing_8waveform_11QNM_ParSpec_f(struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *__pyx_v_self, double __pyx_v_M, double __pyx_v_a, double __pyx_v_gamma, PyArrayObject *__pyx_v_dw_vec, int __pyx_skip_dispatch); /* proto*/
static double __pyx_f_6pyRing_8waveform_11QNM_ParSpec_tau(struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *__pyx_v_self, double __pyx_v_M, double __pyx_v_a, double __pyx_v_gamma, PyArrayObject *__pyx_v_dt_vec, int __pyx_skip_dispatch); /* proto*/
static double __pyx_f_6pyRing_8waveform_22QNM_220_area_quantized_f_QA(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *__pyx_v_self, double __pyx_v_M, double __pyx_v_a, double __pyx_v_alpha, int __pyx_skip_dispatch); /* proto*/
static double __pyx_f_6pyRing_8waveform_22QNM_220_area_quantized_q_GR(struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *__pyx_v_self, double __pyx_v_a, int __pyx_skip_dispatch); /* proto*/
static double __pyx_f_6pyRing_8waveform_22QNM_220_area_quantized_tau_QA(struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *__pyx_v_self, double __pyx_v_M, double __pyx_v_a, double __pyx_v_alpha, int __pyx_skip_dispatch); /* proto*/
static double __pyx_f_6pyRing_8waveform_18QNM_braneworld_fit_f_BW(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_QNM_braneworld_fit *__pyx_v_self, double __pyx_v_M, double __pyx_v_a, double __pyx_v_beta, int __pyx_skip_dispatch); /* proto*/
static double __pyx_f_6pyRing_8waveform_18QNM_braneworld_fit_q_BW(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_QNM_braneworld_fit *__pyx_v_self, double __pyx_v_a, double __pyx_v_beta, int __pyx_skip_dispatch); /* proto*/
static double __pyx_f_6pyRing_8waveform_18QNM_braneworld_fit_tau_BW(struct __pyx_obj_6pyRing_8waveform_QNM_braneworld_fit *__pyx_v_self, double __pyx_v_M, double __pyx_v_a, double __pyx_v_beta, int __pyx_skip_dispatch); /* proto*/
static PyArrayObject *__pyx_f_6pyRing_8waveform_16Damped_sinusoids_waveform(struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *__pyx_v_self, PyArrayObject *__pyx_v_t, int __pyx_skip_dispatch); /* proto*/
static PyArrayObject *__pyx_f_6pyRing_8waveform_21Morlet_Gabor_wavelets_waveform(struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *__pyx_v_self, PyArrayObject *__pyx_v_t, int __pyx_skip_dispatch); /* proto*/
static __pyx_t_double_complex __pyx_f_6pyRing_8waveform_4SWSH_evaluate(struct __pyx_obj_6pyRing_8waveform_SWSH *__pyx_v_self, double __pyx_v_theta, double __pyx_v_phi, int __pyx_skip_dispatch); /* proto*/
static PyArrayObject *__pyx_f_6pyRing_8waveform_6KerrBH_waveform(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, PyArrayObject *__pyx_v_times, int __pyx_skip_dispatch); /* proto*/
static PyArrayObject *__pyx_f_6pyRing_8waveform_6MMRDNS_waveform(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self, PyArrayObject *__pyx_v_times, int __pyx_skip_dispatch); /* proto*/
static PyArrayObject *__pyx_f_6pyRing_8waveform_6MMRDNP_waveform(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self, PyArrayObject *__pyx_v_times, int __pyx_skip_dispatch); /* proto*/
static PyArrayObject *__pyx_f_6pyRing_8waveform_8KHS_2012_waveform(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self, PyArrayObject *__pyx_v_times, int __pyx_skip_dispatch); /* proto*/
static PyObject *__pyx_f_6pyRing_8waveform_6TEOBPM__EOBPM_SetupFitCoefficients(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, int __pyx_v_l, int __pyx_v_m, PyObject *__pyx_v_NR_fit_coeffs); /* proto*/
static double __pyx_f_6pyRing_8waveform_6TEOBPM__TEOBPM_Amplitude(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, double __pyx_v_tau, double __pyx_v_sigma_real, double __pyx_v_a1, double __pyx_v_a2, double __pyx_v_a3, double __pyx_v_a4); /* proto*/
static double __pyx_f_6pyRing_8waveform_6TEOBPM__TEOBPM_Phase(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, double __pyx_v_tau, double __pyx_v_sigma_imag, double __pyx_v_phi_0, double __pyx_v_p1, double __pyx_v_p2, double __pyx_v_p3, double __pyx_v_p4); /* proto*/
static PyArrayObject *__pyx_f_6pyRing_8waveform_6TEOBPM__TEOBPM_single_multipole(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, __Pyx_memviewslice __pyx_v_time, double __pyx_v_tlm, double __pyx_v_philm, int __pyx_v_l, int __pyx_v_m, int __pyx_v_N); /* proto*/
static PyArrayObject *__pyx_f_6pyRing_8waveform_6TEOBPM__waveform(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, __Pyx_memviewslice __pyx_v_times); /* proto*/
static PyArrayObject *__pyx_f_6pyRing_8waveform_6IMR_WF_waveform(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_IMR_WF *__pyx_v_self, CYTHON_UNUSED PyArrayObject *__pyx_v_times, int __pyx_skip_dispatch); /* proto*/

/* Module declarations from "cpython.version" */

/* Module declarations from "__builtin__" */

/* Module declarations from "cpython.type" */

/* Module declarations from "libc.string" */

/* Module declarations from "libc.stdio" */

/* Module declarations from "cpython.object" */

/* Module declarations from "cpython.ref" */

/* Module declarations from "cpython.exc" */

/* Module declarations from "cpython.module" */

/* Module declarations from "cpython.mem" */

/* Module declarations from "cpython.tuple" */

/* Module declarations from "cpython.list" */

/* Module declarations from "cpython.sequence" */

/* Module declarations from "cpython.mapping" */

/* Module declarations from "cpython.iterator" */

/* Module declarations from "cpython.number" */

/* Module declarations from "__builtin__" */

/* Module declarations from "cpython.bool" */

/* Module declarations from "cpython.long" */

/* Module declarations from "cpython.float" */

/* Module declarations from "cython.view" */

/* Module declarations from "cython.dataclasses" */

/* Module declarations from "cython" */

/* Module declarations from "__builtin__" */

/* Module declarations from "cpython.complex" */

/* Module declarations from "libc.stddef" */

/* Module declarations from "cpython.unicode" */

/* Module declarations from "cpython.pyport" */

/* Module declarations from "cpython.dict" */

/* Module declarations from "cpython.instance" */

/* Module declarations from "cpython.function" */

/* Module declarations from "cpython.method" */

/* Module declarations from "cpython.weakref" */

/* Module declarations from "cpython.getargs" */

/* Module declarations from "cpython.pythread" */

/* Module declarations from "cpython.pystate" */

/* Module declarations from "cpython.set" */

/* Module declarations from "cpython.buffer" */

/* Module declarations from "cpython.bytes" */

/* Module declarations from "cpython.pycapsule" */

/* Module declarations from "cpython.contextvars" */

/* Module declarations from "cpython" */

/* Module declarations from "array" */

/* Module declarations from "cpython.array" */
static CYTHON_INLINE int __pyx_f_7cpython_5array_extend_buffer(arrayobject *, char *, Py_ssize_t); /*proto*/

/* Module declarations from "numpy" */

/* Module declarations from "numpy" */

/* Module declarations from "libc.math" */

/* Module declarations from "pyRing" */

/* Module declarations from "pyRing.eob_utils" */
static double (*__pyx_f_6pyRing_9eob_utils__sym_mass_ratio)(double, double); /*proto*/
static double (*__pyx_f_6pyRing_9eob_utils__X_1)(double, double); /*proto*/
static double (*__pyx_f_6pyRing_9eob_utils__X_2)(double, double); /*proto*/
static double (*__pyx_f_6pyRing_9eob_utils__X_12)(double, double); /*proto*/
static double (*__pyx_f_6pyRing_9eob_utils__a_0)(double, double, double, double); /*proto*/
static double (*__pyx_f_6pyRing_9eob_utils__a_12)(double, double, double, double); /*proto*/
static double (*__pyx_f_6pyRing_9eob_utils__S_hat)(double, double, double); /*proto*/
static double (*__pyx_f_6pyRing_9eob_utils__S_bar)(double, double, double); /*proto*/
static double (*__pyx_f_6pyRing_9eob_utils__alpha1)(double, int, int); /*proto*/
static double (*__pyx_f_6pyRing_9eob_utils__alpha21)(double, int, int); /*proto*/
static double (*__pyx_f_6pyRing_9eob_utils__omega1)(double, int, int); /*proto*/
static double (*__pyx_f_6pyRing_9eob_utils__c3_A)(double, double, double, double, int, int); /*proto*/
static double (*__pyx_f_6pyRing_9eob_utils__c3_phi)(double, double, double, int, int); /*proto*/
static double (*__pyx_f_6pyRing_9eob_utils__c4_phi)(double, double, double, int, int); /*proto*/
static double (*__pyx_f_6pyRing_9eob_utils__dOmega)(double, double, double); /*proto*/
static double (*__pyx_f_6pyRing_9eob_utils__amplitude_peak)(double, double, double, double, double, double, double, int, int); /*proto*/
static double (*__pyx_f_6pyRing_9eob_utils__omega_peak)(double, double, double, double, int, int); /*proto*/
static double (*__pyx_f_6pyRing_9eob_utils__JimenezFortezaRemnantMass)(double, double, double, double, double, double); /*proto*/
static double (*__pyx_f_6pyRing_9eob_utils__JimenezFortezaRemnantSpin)(double, double, double, double, double); /*proto*/
static double (*__pyx_f_6pyRing_9eob_utils__DeltaT)(double, double, double, double, unsigned int, int); /*proto*/
static double (*__pyx_f_6pyRing_9eob_utils__DeltaPhi)(double, double, double, unsigned int, int); /*proto*/

/* Module declarations from "pyRing.waveform" */
__PYX_EXTERN_C DL_EXPORT(PyObject) *__pyx_v_6pyRing_8waveform_interpolate_freqs;
__PYX_EXTERN_C DL_EXPORT(PyObject) *__pyx_v_6pyRing_8waveform_interpolate_taus;
__PYX_EXTERN_C DL_EXPORT(PyObject) *__pyx_v_6pyRing_8waveform_Interpolated_ls;
__PYX_EXTERN_C DL_EXPORT(PyObject) *__pyx_v_6pyRing_8waveform_Interpolated_ms;
__PYX_EXTERN_C DL_EXPORT(PyObject) *__pyx_v_6pyRing_8waveform_Interpolated_ns;
static double __pyx_v_6pyRing_8waveform_MPC_SI;
static double __pyx_v_6pyRing_8waveform_mass_dist_units_conversion;
static double __pyx_v_6pyRing_8waveform_mass_time_units_conversion;
static double __pyx_v_6pyRing_8waveform_MTSUN_SI;
static PyObject *__pyx_v_6pyRing_8waveform_F_fit_coeff = 0;
static PyObject *__pyx_v_6pyRing_8waveform_q_fit_coeff = 0;
static PyObject *__pyx_v_6pyRing_8waveform_F_KN_fit_coeff = 0;
static PyObject *__pyx_v_6pyRing_8waveform_q_KN_fit_coeff = 0;
static PyObject *__pyx_v_6pyRing_8waveform_f_ParSpec_coeff = 0;
static PyObject *__pyx_v_6pyRing_8waveform_tau_ParSpec_coeff = 0;
static PyObject *__pyx_v_6pyRing_8waveform_f_ParSpec_coeff_high_spin = 0;
static PyObject *__pyx_v_6pyRing_8waveform_tau_ParSpec_coeff_high_spin = 0;
static PyObject *__pyx_7genexpr__pyx_v_6pyRing_8waveform_j;
static PyObject *__pyx_8genexpr1__pyx_v_6pyRing_8waveform_j;
static PyObject *__pyx_8genexpr2__pyx_v_6pyRing_8waveform_j;
static PyObject *__pyx_8genexpr3__pyx_v_6pyRing_8waveform_j;
static PyObject *__pyx_collections_abc_Sequence = 0;
static PyObject *generic = 0;
static PyObject *strided = 0;
static PyObject *indirect = 0;
static PyObject *contiguous = 0;
static PyObject *indirect_contiguous = 0;
static int __pyx_memoryview_thread_locks_used;
static PyThread_type_lock __pyx_memoryview_thread_locks[8];
static PyArrayObject *__pyx_f_6pyRing_8waveform_damped_sinusoid(double, double, double, double, double, double, PyArrayObject *, int __pyx_skip_dispatch); /*proto*/
static PyArrayObject *__pyx_f_6pyRing_8waveform_tail_factor(double, double, double, double, double, PyArrayObject *, int __pyx_skip_dispatch); /*proto*/
static PyArrayObject *__pyx_f_6pyRing_8waveform_morlet_gabor_wavelet(double, double, double, double, double, double, PyArrayObject *); /*proto*/
static PyObject *__pyx_f_6pyRing_8waveform___pyx_unpickle_SWSH__set_state(struct __pyx_obj_6pyRing_8waveform_SWSH *, PyObject *); /*proto*/
static int __pyx_array_allocate_buffer(struct __pyx_array_obj *); /*proto*/
static struct __pyx_array_obj *__pyx_array_new(PyObject *, Py_ssize_t, char *, char const *, char *); /*proto*/
static PyObject *__pyx_memoryview_new(PyObject *, int, int, __Pyx_TypeInfo const *); /*proto*/
static CYTHON_INLINE int __pyx_memoryview_check(PyObject *); /*proto*/
static PyObject *_unellipsify(PyObject *, int); /*proto*/
static int assert_direct_dimensions(Py_ssize_t *, int); /*proto*/
static struct __pyx_memoryview_obj *__pyx_memview_slice(struct __pyx_memoryview_obj *, PyObject *); /*proto*/
static int __pyx_memoryview_slice_memviewslice(__Pyx_memviewslice *, Py_ssize_t, Py_ssize_t, Py_ssize_t, int, int, int *, Py_ssize_t, Py_ssize_t, Py_ssize_t, int, int, int, int); /*proto*/
static char *__pyx_pybuffer_index(Py_buffer *, char *, Py_ssize_t, Py_ssize_t); /*proto*/
static int __pyx_memslice_transpose(__Pyx_memviewslice *); /*proto*/
static PyObject *__pyx_memoryview_fromslice(__Pyx_memviewslice, int, PyObject *(*)(char *), int (*)(char *, PyObject *), int); /*proto*/
static __Pyx_memviewslice *__pyx_memoryview_get_slice_from_memoryview(struct __pyx_memoryview_obj *, __Pyx_memviewslice *); /*proto*/
static void __pyx_memoryview_slice_copy(struct __pyx_memoryview_obj *, __Pyx_memviewslice *); /*proto*/
static PyObject *__pyx_memoryview_copy_object(struct __pyx_memoryview_obj *); /*proto*/
static PyObject *__pyx_memoryview_copy_object_from_slice(struct __pyx_memoryview_obj *, __Pyx_memviewslice *); /*proto*/
static Py_ssize_t abs_py_ssize_t(Py_ssize_t); /*proto*/
static char __pyx_get_best_slice_order(__Pyx_memviewslice *, int); /*proto*/
static void _copy_strided_to_strided(char *, Py_ssize_t *, char *, Py_ssize_t *, Py_ssize_t *, Py_ssize_t *, int, size_t); /*proto*/
static void copy_strided_to_strided(__Pyx_memviewslice *, __Pyx_memviewslice *, int, size_t); /*proto*/
static Py_ssize_t __pyx_memoryview_slice_get_size(__Pyx_memviewslice *, int); /*proto*/
static Py_ssize_t __pyx_fill_contig_strides_array(Py_ssize_t *, Py_ssize_t *, Py_ssize_t, int, char); /*proto*/
static void *__pyx_memoryview_copy_data_to_temp(__Pyx_memviewslice *, __Pyx_memviewslice *, char, int); /*proto*/
static int __pyx_memoryview_err_extents(int, Py_ssize_t, Py_ssize_t); /*proto*/
static int __pyx_memoryview_err_dim(PyObject *, PyObject *, int); /*proto*/
static int __pyx_memoryview_err(PyObject *, PyObject *); /*proto*/
static int __pyx_memoryview_err_no_memory(void); /*proto*/
static int __pyx_memoryview_copy_contents(__Pyx_memviewslice, __Pyx_memviewslice, int, int, int); /*proto*/
static void __pyx_memoryview_broadcast_leading(__Pyx_memviewslice *, int, int); /*proto*/
static void __pyx_memoryview_refcount_copying(__Pyx_memviewslice *, int, int, int); /*proto*/
static void __pyx_memoryview_refcount_objects_in_slice_with_gil(char *, Py_ssize_t *, Py_ssize_t *, int, int); /*proto*/
static void __pyx_memoryview_refcount_objects_in_slice(char *, Py_ssize_t *, Py_ssize_t *, int, int); /*proto*/
static void __pyx_memoryview_slice_assign_scalar(__Pyx_memviewslice *, int, size_t, void *, int); /*proto*/
static void __pyx_memoryview__slice_assign_scalar(char *, Py_ssize_t *, Py_ssize_t *, int, size_t, void *); /*proto*/
static PyObject *__pyx_unpickle_Enum__set_state(struct __pyx_MemviewEnum_obj *, PyObject *); /*proto*/
/* #### Code section: typeinfo ### */
static const __Pyx_TypeInfo __Pyx_TypeInfo_double = { "double", NULL, sizeof(double), { 0 }, 0, 'R', 0, 0 };
static const __Pyx_TypeInfo __Pyx_TypeInfo___pyx_t_double_complex = { "double complex", NULL, sizeof(__pyx_t_double_complex), { 0 }, 0, 'C', 0, 0 };
/* #### Code section: before_global_var ### */
#define __Pyx_MODULE_NAME "pyRing.waveform"
extern int __pyx_module_is_main_pyRing__waveform;
int __pyx_module_is_main_pyRing__waveform = 0;

/* Implementation of "pyRing.waveform" */
/* #### Code section: global_var ### */
static PyObject *__pyx_builtin_xrange;
static PyObject *__pyx_builtin_range;
static PyObject *__pyx_builtin_TypeError;
static PyObject *__pyx_builtin_AssertionError;
static PyObject *__pyx_builtin_ValueError;
static PyObject *__pyx_builtin_KeyError;
static PyObject *__pyx_builtin___import__;
static PyObject *__pyx_builtin_MemoryError;
static PyObject *__pyx_builtin_enumerate;
static PyObject *__pyx_builtin_Ellipsis;
static PyObject *__pyx_builtin_id;
static PyObject *__pyx_builtin_IndexError;
static PyObject *__pyx_builtin_ImportError;
/* #### Code section: string_decls ### */
static const char __pyx_k_[] = ": ";
static const char __pyx_k_6[] = "\200\001\330\004\"\240!\2406\250\021";
static const char __pyx_k_A[] = "A";
static const char __pyx_k_M[] = "M";
static const char __pyx_k_O[] = "O";
static const char __pyx_k_Q[] = "Q";
static const char __pyx_k_a[] = "a";
static const char __pyx_k_c[] = "c";
static const char __pyx_k_f[] = "f";
static const char __pyx_k_i[] = "i";
static const char __pyx_k_l[] = "l";
static const char __pyx_k_m[] = "m";
static const char __pyx_k_n[] = "n";
static const char __pyx_k_p[] = "p";
static const char __pyx_k_q[] = "q";
static const char __pyx_k_r[] = "r";
static const char __pyx_k_s[] = "s";
static const char __pyx_k_t[] = "t";
static const char __pyx_k_v[] = "v";
static const char __pyx_k_w[] = "w{}";
static const char __pyx_k_x[] = "x";
static const char __pyx_k_Mf[] = "Mf";
static const char __pyx_k_Mi[] = "Mi";
static const char __pyx_k__2[] = ".";
static const char __pyx_k__3[] = ">";
static const char __pyx_k__4[] = "'";
static const char __pyx_k__5[] = ")";
static const char __pyx_k__7[] = "?";
static const char __pyx_k_a1[] = "a1";
static const char __pyx_k_a2[] = "a2";
static const char __pyx_k_a3[] = "a3";
static const char __pyx_k_a4[] = "a4";
static const char __pyx_k_af[] = "af";
static const char __pyx_k_dt[] = "dt";
static const char __pyx_k_f1[] = "f1";
static const char __pyx_k_f2[] = "f2";
static const char __pyx_k_f3[] = "f3";
static const char __pyx_k_gc[] = "gc";
static const char __pyx_k_id[] = "id";
static const char __pyx_k_m1[] = "m1";
static const char __pyx_k_m2[] = "m2";
static const char __pyx_k_np[] = "np";
static const char __pyx_k_os[] = "os";
static const char __pyx_k_p1[] = "p1";
static const char __pyx_k_p2[] = "p2";
static const char __pyx_k_p3[] = "p3";
static const char __pyx_k_p4[] = "p4";
static const char __pyx_k_pi[] = "pi";
static const char __pyx_k_q1[] = "q1";
static const char __pyx_k_q2[] = "q2";
static const char __pyx_k_q3[] = "q3";
static const char __pyx_k_t0[] = "t0";
static const char __pyx_k_A_1[] = "A_1";
static const char __pyx_k_A_2[] = "A_2";
static const char __pyx_k_QNM[] = "QNM";
static const char __pyx_k_Q_2[] = "\200\001\330\004\n\210+\220Q";
static const char __pyx_k_X_1[] = "X_1";
static const char __pyx_k_X_2[] = "X_2";
static const char __pyx_k_a_0[] = "a_0";
static const char __pyx_k_abc[] = "abc";
static const char __pyx_k_abs[] = "abs";
static const char __pyx_k_and[] = " and ";
static const char __pyx_k_c3A[] = "c3A";
static const char __pyx_k_c3p[] = "c3p";
static const char __pyx_k_c4p[] = "c4p";
static const char __pyx_k_cos[] = "cos";
static const char __pyx_k_eta[] = "eta";
static const char __pyx_k_exp[] = "exp";
static const char __pyx_k_fit[] = "fit";
static const char __pyx_k_got[] = " (got ";
static const char __pyx_k_lal[] = "lal";
static const char __pyx_k_new[] = "__new__";
static const char __pyx_k_obj[] = "obj";
static const char __pyx_k_p_1[] = "p_1";
static const char __pyx_k_p_2[] = "p_2";
static const char __pyx_k_phi[] = "phi";
static const char __pyx_k_pop[] = "pop";
static const char __pyx_k_s1z[] = "s1z";
static const char __pyx_k_s2z[] = "s2z";
static const char __pyx_k_sum[] = "sum";
static const char __pyx_k_t_0[] = "t_0";
static const char __pyx_k_t_2[] = "t{}";
static const char __pyx_k_tau[] = "tau";
static const char __pyx_k_16_1[] = "\200!\360\006\000\005\014\2101\3606\000\005\014\2101";
static const char __pyx_k_A_e1[] = "\200A\330\010\021\220\030\230\021\230(\240$\240e\2501";
static const char __pyx_k_C_SI[] = "C_SI";
static const char __pyx_k_G_SI[] = "G_SI";
static const char __pyx_k_SWSH[] = "SWSH";
static const char __pyx_k_X_12[] = "X_12";
static const char __pyx_k_a_12[] = "a_12";
static const char __pyx_k_amps[] = "amps";
static const char __pyx_k_base[] = "base";
static const char __pyx_k_beta[] = "beta";
static const char __pyx_k_c3_A[] = "c3_A";
static const char __pyx_k_chi1[] = "chi1";
static const char __pyx_k_chi2[] = "chi2";
static const char __pyx_k_conj[] = "conj";
static const char __pyx_k_dict[] = "__dict__";
static const char __pyx_k_diff[] = "diff";
static const char __pyx_k_dist[] = "dist";
static const char __pyx_k_dtau[] = "dtau_{}{}{}";
static const char __pyx_k_f_BW[] = "f_BW";
static const char __pyx_k_f_KN[] = "f_KN";
static const char __pyx_k_f_QA[] = "f_QA";
static const char __pyx_k_fact[] = "fact";
static const char __pyx_k_freq[] = "freq";
static const char __pyx_k_func[] = "__func__";
static const char __pyx_k_geom[] = "geom";
static const char __pyx_k_imag[] = "imag";
static const char __pyx_k_iota[] = "iota";
static const char __pyx_k_keys[] = "keys";
static const char __pyx_k_l_BW[] = "l_BW";
static const char __pyx_k_l_QA[] = "l_QA";
static const char __pyx_k_m_BW[] = "m_BW";
static const char __pyx_k_m_QA[] = "m_QA";
static const char __pyx_k_main[] = "__main__";
static const char __pyx_k_math[] = "math";
static const char __pyx_k_mode[] = "mode";
static const char __pyx_k_n_BW[] = "n_BW";
static const char __pyx_k_n_QA[] = "n_QA";
static const char __pyx_k_name[] = "name";
static const char __pyx_k_ndim[] = "ndim";
static const char __pyx_k_pack[] = "pack";
static const char __pyx_k_q_BW[] = "q_BW";
static const char __pyx_k_q_GR[] = "q_GR";
static const char __pyx_k_q_KN[] = "q_KN";
static const char __pyx_k_real[] = "real";
static const char __pyx_k_self[] = "self";
static const char __pyx_k_size[] = "size";
static const char __pyx_k_spec[] = "__spec__";
static const char __pyx_k_sqrt[] = "sqrt";
static const char __pyx_k_step[] = "step";
static const char __pyx_k_stop[] = "stop";
static const char __pyx_k_test[] = "__test__";
static const char __pyx_k_ASCII[] = "ASCII";
static const char __pyx_k_A_e3a[] = "\200A\330\010\021\220\030\230\021\230$\230e\2403\240a";
static const char __pyx_k_A_e4q[] = "\200A\330\010\021\320\021!\240\021\240$\240e\2504\250q";
static const char __pyx_k_PC_SI[] = "PC_SI";
static const char __pyx_k_QNM_f[] = "QNM.f";
static const char __pyx_k_S_bar[] = "S_bar";
static const char __pyx_k_S_hat[] = "S_hat";
static const char __pyx_k_alpha[] = "alpha";
static const char __pyx_k_array[] = "array";
static const char __pyx_k_at_0x[] = " at 0x";
static const char __pyx_k_chi_a[] = "chi_a";
static const char __pyx_k_chi_s[] = "chi_s";
static const char __pyx_k_class[] = "__class__";
static const char __pyx_k_count[] = "count";
static const char __pyx_k_dtype[] = "dtype";
static const char __pyx_k_error[] = "error";
static const char __pyx_k_flags[] = "flags";
static const char __pyx_k_gamma[] = "gamma";
static const char __pyx_k_index[] = "index";
static const char __pyx_k_items[] = "items";
static const char __pyx_k_modes[] = "modes";
static const char __pyx_k_names[] = "names";
static const char __pyx_k_numpy[] = "numpy";
static const char __pyx_k_phi_0[] = "phi_0";
static const char __pyx_k_phi_1[] = "phi_1";
static const char __pyx_k_phi_2[] = "phi_2";
static const char __pyx_k_range[] = "range";
static const char __pyx_k_scipy[] = "scipy";
static const char __pyx_k_shape[] = "shape";
static const char __pyx_k_start[] = "start";
static const char __pyx_k_state[] = "state";
static const char __pyx_k_t_ref[] = "t_ref";
static const char __pyx_k_theta[] = "theta";
static const char __pyx_k_times[] = "times";
static const char __pyx_k_zeros[] = "zeros";
static const char __pyx_k_A_4uCq[] = "\200A\330\010\021\220\031\230!\2304\230u\240C\240q";
static const char __pyx_k_A_V4uD[] = "\200A\330\010\021\220\027\230\001\230\024\230V\2404\240u\250D\260\001";
static const char __pyx_k_A_t_Qa[] = "\200A\330\010\017\210t\220:\230Q\230a";
static const char __pyx_k_DeltaT[] = "DeltaT";
static const char __pyx_k_IMR_WF[] = "IMR_WF";
static const char __pyx_k_KerrBH[] = "KerrBH";
static const char __pyx_k_MMRDNP[] = "MMRDNP";
static const char __pyx_k_MMRDNS[] = "MMRDNS";
static const char __pyx_k_NR_amp[] = "NR_amp";
static const char __pyx_k_TEOBPM[] = "TEOBPM";
static const char __pyx_k_alpha1[] = "alpha1";
static const char __pyx_k_c3_phi[] = "c3_phi";
static const char __pyx_k_c4_phi[] = "c4_phi";
static const char __pyx_k_charge[] = "charge";
static const char __pyx_k_dOmega[] = "dOmega";
static const char __pyx_k_dict_2[] = "_dict";
static const char __pyx_k_domega[] = "domega_{}{}{}";
static const char __pyx_k_double[] = "double";
static const char __pyx_k_dt_vec[] = "dt_vec";
static const char __pyx_k_dw_vec[] = "dw_vec";
static const char __pyx_k_enable[] = "enable";
static const char __pyx_k_encode[] = "encode";
static const char __pyx_k_format[] = "format";
static const char __pyx_k_import[] = "__import__";
static const char __pyx_k_lalsim[] = "lalsim";
static const char __pyx_k_module[] = "__module__";
static const char __pyx_k_name_2[] = "__name__";
static const char __pyx_k_object[] = " object>";
static const char __pyx_k_omega1[] = "omega1";
static const char __pyx_k_phases[] = "phases";
static const char __pyx_k_pickle[] = "pickle";
static const char __pyx_k_pyRing[] = "pyRing";
static const char __pyx_k_pykerr[] = "pykerr";
static const char __pyx_k_reduce[] = "__reduce__";
static const char __pyx_k_struct[] = "struct";
static const char __pyx_k_tau_AQ[] = "tau_AQ";
static const char __pyx_k_tau_BW[] = "tau_BW";
static const char __pyx_k_tau_KN[] = "tau_KN";
static const char __pyx_k_tau_QA[] = "tau_QA";
static const char __pyx_k_unpack[] = "unpack";
static const char __pyx_k_update[] = "update";
static const char __pyx_k_A_at5_A[] = "\200A\330\010\021\220\025\220a\220t\2305\240\004\240A";
static const char __pyx_k_A_q_E_Q[] = "\200A\330\010\021\220\026\220q\230\004\230E\240\024\240Q";
static const char __pyx_k_A_r_1_q[] = "\200A\330\010\037\230r\240\022\2401\330\010\017\210q";
static const char __pyx_k_Amp_KHS[] = "Amp_KHS";
static const char __pyx_k_MSUN_SI[] = "MSUN_SI";
static const char __pyx_k_ParSpec[] = "ParSpec";
static const char __pyx_k_QNM_fit[] = "QNM_fit";
static const char __pyx_k_QNM_tau[] = "QNM.tau";
static const char __pyx_k_alpha21[] = "alpha21";
static const char __pyx_k_chi_eff[] = "chi_eff";
static const char __pyx_k_complex[] = "complex";
static const char __pyx_k_cosiota[] = "cosiota";
static const char __pyx_k_disable[] = "disable";
static const char __pyx_k_dtau__0[] = "dtau_{}{}0";
static const char __pyx_k_fortran[] = "fortran";
static const char __pyx_k_memview[] = "memview";
static const char __pyx_k_qnm_fit[] = "qnm_fit";
static const char __pyx_k_A_e4vT_1[] = "\200A\330\010\021\220\030\230\021\230$\230e\2404\240v\250T\260\027\270\003\2701";
static const char __pyx_k_A_t_q_3a[] = "\200A\330\010\017\210t\320\023/\250q\260\003\2603\260a";
static const char __pyx_k_DeltaPhi[] = "DeltaPhi";
static const char __pyx_k_Ellipsis[] = "Ellipsis";
static const char __pyx_k_KHS_2012[] = "KHS_2012";
static const char __pyx_k_KeyError[] = "KeyError";
static const char __pyx_k_MTSUN_SI[] = "MTSUN_SI";
static const char __pyx_k_QNM_f_BW[] = "QNM.f_BW";
static const char __pyx_k_QNM_f_KN[] = "QNM.f_KN";
static const char __pyx_k_Sequence[] = "Sequence";
static const char __pyx_k_add_note[] = "add_note";
static const char __pyx_k_evaluate[] = "evaluate";
static const char __pyx_k_fromkeys[] = "fromkeys";
static const char __pyx_k_getstate[] = "__getstate__";
static const char __pyx_k_itemsize[] = "itemsize";
static const char __pyx_k_omg_peak[] = "omg_peak";
static const char __pyx_k_pyx_capi[] = "__pyx_capi__";
static const char __pyx_k_pyx_type[] = "__pyx_type";
static const char __pyx_k_qualname[] = "__qualname__";
static const char __pyx_k_register[] = "register";
static const char __pyx_k_set_name[] = "__set_name__";
static const char __pyx_k_setstate[] = "__setstate__";
static const char __pyx_k_single_l[] = "single_l";
static const char __pyx_k_single_m[] = "single_m";
static const char __pyx_k_single_n[] = "single_n";
static const char __pyx_k_waveform[] = "waveform";
static const char __pyx_k_A_t_7_d_a[] = "\200A\330\010\017\210t\220>\240\021\240%\240|\2607\270$\270d\300$\300a";
static const char __pyx_k_KN_coeffs[] = "KN_coeffs";
static const char __pyx_k_QNM_fit_f[] = "QNM_fit.f";
static const char __pyx_k_QNM_fit_q[] = "QNM_fit.q";
static const char __pyx_k_TypeError[] = "TypeError";
static const char __pyx_k_domega__0[] = "domega_{}{}0";
static const char __pyx_k_enumerate[] = "enumerate";
static const char __pyx_k_factorial[] = "factorial";
static const char __pyx_k_high_spin[] = "high_spin";
static const char __pyx_k_isenabled[] = "isenabled";
static const char __pyx_k_pyx_state[] = "__pyx_state";
static const char __pyx_k_reduce_ex[] = "__reduce_ex__";
static const char __pyx_k_starttime[] = "starttime";
static const char __pyx_k_A_at5_E_WD[] = "\200A\330\010\021\220\025\220a\220t\2305\240\004\240E\250\024\250W\260D\270\001";
static const char __pyx_k_A_e4vT_E_A[] = "\200A\330\010\021\220\030\230\021\230$\230e\2404\240v\250T\260\027\270\004\270E\300\023\300A";
static const char __pyx_k_A_q_E_U_gT[] = "\200A\330\010\021\220\026\220q\230\004\230E\240\024\240U\250$\250g\260T\270\021";
static const char __pyx_k_Amp_MMRDNP[] = "Amp_MMRDNP";
static const char __pyx_k_Amp_MMRDNS[] = "Amp_MMRDNS";
static const char __pyx_k_IndexError[] = "IndexError";
static const char __pyx_k_QNM_tau_BW[] = "QNM.tau_BW";
static const char __pyx_k_QNM_tau_KN[] = "QNM.tau_KN";
static const char __pyx_k_Spheroidal[] = "Spheroidal";
static const char __pyx_k_TEOBPM_X_1[] = "TEOBPM.X_1";
static const char __pyx_k_TEOBPM_X_2[] = "TEOBPM.X_2";
static const char __pyx_k_TEOBPM_a_0[] = "TEOBPM.a_0";
static const char __pyx_k_TGR_params[] = "TGR_params";
static const char __pyx_k_ValueError[] = "ValueError";
static const char __pyx_k_braneworld[] = "braneworld";
static const char __pyx_k_genfromtxt[] = "genfromtxt";
static const char __pyx_k_omega_peak[] = "omega_peak";
static const char __pyx_k_pyx_result[] = "__pyx_result";
static const char __pyx_k_pyx_vtable[] = "__pyx_vtable__";
static const char __pyx_k_qnm_cached[] = "qnm_cached";
static const char __pyx_k_sigma_imag[] = "sigma_imag";
static const char __pyx_k_sigma_real[] = "sigma_real";
static const char __pyx_k_spheroidal[] = "spheroidal";
static const char __pyx_k_A_1D_T_t7_Q[] = "\200A\330\010\021\220\032\2301\230D\240\005\240T\250\026\250t\2607\270#\270Q";
static const char __pyx_k_A_t_Qe_t4t1[] = "\200A\330\010\017\210t\320\023%\240Q\240e\250<\260t\2704\270t\3001";
static const char __pyx_k_ImportError[] = "ImportError";
static const char __pyx_k_MemoryError[] = "MemoryError";
static const char __pyx_k_PickleError[] = "PickleError";
static const char __pyx_k_QNM_ParSpec[] = "QNM_ParSpec";
static const char __pyx_k_QNM_fit_tau[] = "QNM_fit.tau";
static const char __pyx_k_TEOBPM_X_12[] = "TEOBPM.X_12";
static const char __pyx_k_TEOBPM_a_12[] = "TEOBPM.a_12";
static const char __pyx_k_TEOBPM_c3_A[] = "TEOBPM.c3_A";
static const char __pyx_k_single_mode[] = "single_mode";
static const char __pyx_k_tail_factor[] = "tail_factor";
static const char __pyx_k_A_Qd_t6_WD_S[] = "\200A\330\010\021\220\034\230Q\230d\240%\240t\2506\260\024\260W\270D\300\005\300S\310\001";
static const char __pyx_k_A_q_E_V4wd_1[] = "\200A\330\010\021\220\026\220q\230\004\230E\240\024\240V\2504\250w\260d\270&\300\003\3001";
static const char __pyx_k_QNM_fit_f_KN[] = "QNM_fit.f_KN";
static const char __pyx_k_QNM_fit_q_KN[] = "QNM_fit.q_KN";
static const char __pyx_k_TEOBPM_Phase[] = "TEOBPM_Phase";
static const char __pyx_k_TEOBPM_S_bar[] = "TEOBPM.S_bar";
static const char __pyx_k_TEOBPM_S_hat[] = "TEOBPM.S_hat";
static const char __pyx_k_initializing[] = "_initializing";
static const char __pyx_k_interpolants[] = "interpolants";
static const char __pyx_k_is_coroutine[] = "_is_coroutine";
static const char __pyx_k_pyRing_utils[] = "pyRing.utils";
static const char __pyx_k_pyx_checksum[] = "__pyx_checksum";
static const char __pyx_k_stringsource[] = "<stringsource>";
static const char __pyx_k_use_setstate[] = "use_setstate";
static const char __pyx_k_MemoryView_of[] = "<MemoryView of ";
static const char __pyx_k_NR_fit_coeffs[] = "NR_fit_coeffs";
static const char __pyx_k_QNM_ParSpec_f[] = "QNM_ParSpec.f";
static const char __pyx_k_SWSH_evaluate[] = "SWSH.evaluate";
static const char __pyx_k_TEOBPM_DeltaT[] = "TEOBPM.DeltaT";
static const char __pyx_k_TEOBPM_alpha1[] = "TEOBPM.alpha1";
static const char __pyx_k_TEOBPM_c3_phi[] = "TEOBPM.c3_phi";
static const char __pyx_k_TEOBPM_c4_phi[] = "TEOBPM.c4_phi";
static const char __pyx_k_TEOBPM_dOmega[] = "TEOBPM.dOmega";
static const char __pyx_k_TEOBPM_omega1[] = "TEOBPM.omega1";
static const char __pyx_k_WD_2RrQTTUUYY[] = "\320\004=\270W\300D\310\002\310!\3102\310R\310r\320QT\320TU\320UY\320Y[\320[\\\320\\^\320^_";
static const char __pyx_k_class_getitem[] = "__class_getitem__";
static const char __pyx_k_lalsimulation[] = "lalsimulation";
static const char __pyx_k_quad_lin_prop[] = "quad_lin_prop";
static const char __pyx_k_reduce_cython[] = "__reduce_cython__";
static const char __pyx_k_signal_seglen[] = "signal_seglen";
static const char __pyx_k_A_peak_over_nu[] = "A_peak_over_nu";
static const char __pyx_k_AssertionError[] = "AssertionError";
static const char __pyx_k_ParSpec_coeffs[] = "ParSpec_coeffs";
static const char __pyx_k_QNM_fit_tau_KN[] = "QNM_fit.tau_KN";
static const char __pyx_k_TEOBPM_alpha21[] = "TEOBPM.alpha21";
static const char __pyx_k_amplitude_peak[] = "amplitude_peak";
static const char __pyx_k_sym_mass_ratio[] = "sym_mass_ratio";
static const char __pyx_k_A_AT_d_t5_GSWWX[] = "\200A\330\010\021\320\021,\250A\250T\260\025\260d\270%\270t\3005\310\004\310G\320SW\320WX";
static const char __pyx_k_IMR_WF_waveform[] = "IMR_WF.waveform";
static const char __pyx_k_Interpolated_ls[] = "Interpolated_ls";
static const char __pyx_k_Interpolated_ms[] = "Interpolated_ms";
static const char __pyx_k_Interpolated_ns[] = "Interpolated_ns";
static const char __pyx_k_KerrBH_waveform[] = "KerrBH.waveform";
static const char __pyx_k_MMRDNP_waveform[] = "MMRDNP.waveform";
static const char __pyx_k_MMRDNS_waveform[] = "MMRDNS.waveform";
static const char __pyx_k_QNM_ParSpec_tau[] = "QNM_ParSpec.tau";
static const char __pyx_k_TEOBPM_DeltaPhi[] = "TEOBPM.DeltaPhi";
static const char __pyx_k_TEOBPM_waveform[] = "TEOBPM.waveform";
static const char __pyx_k_View_MemoryView[] = "View.MemoryView";
static const char __pyx_k_allocate_buffer[] = "allocate_buffer";
static const char __pyx_k_collections_abc[] = "collections.abc";
static const char __pyx_k_damped_sinusoid[] = "damped_sinusoid";
static const char __pyx_k_dtype_is_object[] = "dtype_is_object";
static const char __pyx_k_pyRing_waveform[] = "pyRing.waveform";
static const char __pyx_k_pyx_PickleError[] = "__pyx_PickleError";
static const char __pyx_k_quadratic_modes[] = "quadratic_modes";
static const char __pyx_k_setstate_cython[] = "__setstate_cython__";
static const char __pyx_k_tail_parameters[] = "tail_parameters";
static const char __pyx_k_A_Kq_4_2Rq_2T_AQ[] = "\200A\330\010\020\220\004\220K\230q\240\002\240!\2404\240{\260!\2602\260R\260q\270\001\270\022\2702\270T\300\033\310A\310Q";
static const char __pyx_k_AreaQuantization[] = "AreaQuantization";
static const char __pyx_k_Damped_sinusoids[] = "Damped_sinusoids";
static const char __pyx_k_TEOBPM_Amplitude[] = "TEOBPM_Amplitude";
static const char __pyx_k_amp_non_prec_sym[] = "amp_non_prec_sym";
static const char __pyx_k_interpolate_taus[] = "interpolate_taus";
static const char __pyx_k_KHS_2012_waveform[] = "KHS_2012.waveform";
static const char __pyx_k_Kerr_Berti_coeffs[] = "Kerr_Berti_coeffs";
static const char __pyx_k_TEOBPM_omega_peak[] = "TEOBPM.omega_peak";
static const char __pyx_k_interpolate_freqs[] = "interpolate_freqs";
static const char __pyx_k_pyx_unpickle_Enum[] = "__pyx_unpickle_Enum";
static const char __pyx_k_pyx_unpickle_SWSH[] = "__pyx_unpickle_SWSH";
static const char __pyx_k_A_AT_d_t5_GSWW_bbc[] = "\200A\330\010\021\320\021,\250A\250T\260\025\260d\270%\270t\3005\310\004\310G\320SW\320W^\320^b\320bc";
static const char __pyx_k_QNM_braneworld_fit[] = "QNM_braneworld_fit";
static const char __pyx_k_asyncio_coroutines[] = "asyncio.coroutines";
static const char __pyx_k_cline_in_traceback[] = "cline_in_traceback";
static const char __pyx_k_resize_time_series[] = "resize_time_series";
static const char __pyx_k_strided_and_direct[] = "<strided and direct>";
static const char __pyx_k_A_t5_Cq_t5_A_xr_3aq[] = "\200A\330\010\037\230t\2405\250\001\250\023\250C\250q\330\010\037\230t\2405\250\001\250\023\250A\330\010\017\210x\220r\230\022\2303\230a\230q";
static const char __pyx_k_QNM___reduce_cython[] = "QNM.__reduce_cython__";
static const char __pyx_k_TEOBPM_TEOBPM_Phase[] = "TEOBPM.TEOBPM_Phase";
static const char __pyx_k_gT_WXX_aaeettvvyyzz[] = "\320\004>\270g\300T\310\036\320WX\320X`\320`a\320ae\320et\320tv\320vy\320yz\320z{";
static const char __pyx_k_pyRing_waveform_pyx[] = "pyRing/waveform.pyx";
static const char __pyx_k_reference_amplitude[] = "reference_amplitude";
static const char __pyx_k_A_4uAS_1_4uAQ_t2Rs_1[] = "\200A\330\010\033\2304\230u\240A\240S\250\003\2501\330\010\033\2304\230u\240A\240Q\330\010\017\210t\2202\220R\220s\230!\2301";
static const char __pyx_k_A_e4vT_F_hVZZ__kknno[] = "\200A\330\010\021\320\021!\240\021\240$\240e\2504\250v\260T\270\027\300\004\300F\310$\310h\320VZ\320Z_\320_k\320kn\320no";
static const char __pyx_k_SWSH___reduce_cython[] = "SWSH.__reduce_cython__";
static const char __pyx_k_import_datafile_path[] = "import_datafile_path";
static const char __pyx_k_strided_and_indirect[] = "<strided and indirect>";
static const char __pyx_k_Invalid_shape_in_axis[] = "Invalid shape in axis ";
static const char __pyx_k_Morlet_Gabor_wavelets[] = "Morlet_Gabor_wavelets";
static const char __pyx_k_QNM___setstate_cython[] = "QNM.__setstate_cython__";
static const char __pyx_k_TEOBPM_amplitude_peak[] = "TEOBPM.amplitude_peak";
static const char __pyx_k_TEOBPM_sym_mass_ratio[] = "TEOBPM.sym_mass_ratio";
static const char __pyx_k_contiguous_and_direct[] = "<contiguous and direct>";
static const char __pyx_k_gT_WXX_aaeettvvyyzz_2[] = "\320\004>\270g\300T\310\036\320WX\320X[\320[`\320`a\320ae\320et\320tv\320vy\320yz\320z{";
static const char __pyx_k_Cannot_index_with_type[] = "Cannot index with type '";
static const char __pyx_k_IMR_WF___reduce_cython[] = "IMR_WF.__reduce_cython__";
static const char __pyx_k_KerrBH___reduce_cython[] = "KerrBH.__reduce_cython__";
static const char __pyx_k_MMRDNP___reduce_cython[] = "MMRDNP.__reduce_cython__";
static const char __pyx_k_MMRDNS___reduce_cython[] = "MMRDNS.__reduce_cython__";
static const char __pyx_k_ParSpec_coeffs_f_order[] = "ParSpec_coeffs_f_order";
static const char __pyx_k_QNM_220_area_quantized[] = "QNM_220_area_quantized";
static const char __pyx_k_SWSH___setstate_cython[] = "SWSH.__setstate_cython__";
static const char __pyx_k_TEOBPM___reduce_cython[] = "TEOBPM.__reduce_cython__";
static const char __pyx_k_QNM_braneworld_fit_f_BW[] = "QNM_braneworld_fit.f_BW";
static const char __pyx_k_QNM_braneworld_fit_q_BW[] = "QNM_braneworld_fit.q_BW";
static const char __pyx_k_QNM_fit___reduce_cython[] = "QNM_fit.__reduce_cython__";
static const char __pyx_k_TEOBPM_TEOBPM_Amplitude[] = "TEOBPM.TEOBPM_Amplitude";
static const char __pyx_k_contiguous_and_indirect[] = "<contiguous and indirect>";
static const char __pyx_k_t2TQ___hhiimm_A_A_B_B_C[] = "\320\004@\300\007\300t\3102\310T\320Q_\320_`\320`h\320hi\320im\320m{\320{}\360\000\000~\001A\002\360\000\000A\002B\002\360\000\000B\002C\002";
static const char __pyx_k_IMR_WF___setstate_cython[] = "IMR_WF.__setstate_cython__";
static const char __pyx_k_KHS_2012___reduce_cython[] = "KHS_2012.__reduce_cython__";
static const char __pyx_k_KerrBH___setstate_cython[] = "KerrBH.__setstate_cython__";
static const char __pyx_k_MMRDNP___setstate_cython[] = "MMRDNP.__setstate_cython__";
static const char __pyx_k_MMRDNS___setstate_cython[] = "MMRDNS.__setstate_cython__";
static const char __pyx_k_ParSpec_coeffs_high_spin[] = "ParSpec_coeffs_high_spin";
static const char __pyx_k_ParSpec_coeffs_tau_order[] = "ParSpec_coeffs_tau_order";
static const char __pyx_k_TEOBPM___setstate_cython[] = "TEOBPM.__setstate_cython__";
static const char __pyx_k_Damped_sinusoids_waveform[] = "Damped_sinusoids.waveform";
static const char __pyx_k_Dimension_d_is_not_direct[] = "Dimension %d is not direct";
static const char __pyx_k_JimenezFortezaRemnantMass[] = "JimenezFortezaRemnantMass";
static const char __pyx_k_JimenezFortezaRemnantSpin[] = "JimenezFortezaRemnantSpin";
static const char __pyx_k_QNM_braneworld_fit_tau_BW[] = "QNM_braneworld_fit.tau_BW";
static const char __pyx_k_QNM_fit___setstate_cython[] = "QNM_fit.__setstate_cython__";
static const char __pyx_k_t2TQ___cchhiimm_A_A_B_B_C[] = "\320\004@\300\007\300t\3102\310T\320Q_\320_`\320`c\320ch\320hi\320im\320m{\320{}\360\000\000~\001A\002\360\000\000A\002B\002\360\000\000B\002C\002";
static const char __pyx_k_EOBPM_SetupFitCoefficients[] = "EOBPM_SetupFitCoefficients";
static const char __pyx_k_Index_out_of_bounds_axis_d[] = "Index out of bounds (axis %d)";
static const char __pyx_k_KHS_2012___setstate_cython[] = "KHS_2012.__setstate_cython__";
static const char __pyx_k_WD_QcQSSUUWWZZ___ddeehhkkl[] = "\320\004=\270W\300D\310\005\310Q\310c\320QS\320SU\320UW\320WZ\320Z[\320[_\320_d\320de\320eh\320hk\320kl";
static const char __pyx_k_QNM_220_area_quantized_f_QA[] = "QNM_220_area_quantized.f_QA";
static const char __pyx_k_QNM_220_area_quantized_q_GR[] = "QNM_220_area_quantized.q_GR";
static const char __pyx_k_QNM_ParSpec___reduce_cython[] = "QNM_ParSpec.__reduce_cython__";
static const char __pyx_k_Step_may_not_be_zero_axis_d[] = "Step may not be zero (axis %d)";
static const char __pyx_k_itemsize_0_for_cython_array[] = "itemsize <= 0 for cython.array";
static const char __pyx_k_QNM_220_area_quantized_tau_QA[] = "QNM_220_area_quantized.tau_QA";
static const char __pyx_k_QNM_ParSpec___setstate_cython[] = "QNM_ParSpec.__setstate_cython__";
static const char __pyx_k_hk_A_1_C_C_E_E_F_4xq_7_awnA_1[] = "\200\001\360\006\000\005\010\200\177\220h\230k\250\033\260A\330\010\r\210^\2301\330\010\016\320\016!\360\000\000\"C\002\360\000\000C\002E\002\360\000\000E\002F\002\330\004\023\2204\220x\230q\240\001\330\004\007\200|\2207\230!\330\010&\240a\240w\250n\270A\330\004\013\2101";
static const char __pyx_k_unable_to_allocate_array_data[] = "unable to allocate array data.";
static const char __pyx_k_Morlet_Gabor_wavelets_waveform[] = "Morlet_Gabor_wavelets.waveform";
static const char __pyx_k_R_6_F_ARs_1_ar_1_U_3aq_1AS_1_r[] = "\200\001\360R\001\000\005*\250\021\250&\260\001\260\021\330\004)\250\022\2506\260\021\260\"\260F\270!\330\004)\250\023\250A\250R\250s\260!\2601\330\004)\250\025\250a\250r\260\021\260!\360\006\000\005\034\2301\330\004\010\210\005\210U\220!\2203\220a\220q\330\010\013\2101\210A\210S\220\003\2201\330\014\017\210r\220\024\220R\220q\230\001\230\022\2301\230F\240#\240R\240t\2502\250Q\250a\250q\260\001\260\022\2601\260H\270N\310!\330<J\310!\3101\310A\330\014\r\360\010\000\005\006\200Q\320\006\026\220a\220q\230\002\230$\230a\230r\240\021\240'\250\022\2501\250A\250]\270!\2706\300\021\300\"\300A\300Q\340\004\013\2101";
static const char __pyx_k_T_T_T_T_G1F_a_vWA_q_q_q_T_G1_T[] = "\200\001\360\010\000\005\016\210T\220\024\220T\230\024\230T\240\024\240T\250\021\330\004\014\210G\2201\220F\230,\240a\330\004\007\200v\210W\220A\330\010\022\220!\330\010\027\220q\340\010\027\220q\330\004\007\200q\330\010\017\320\017%\240T\250\021\250'\260\033\270G\3001\340\010\017\320\017%\240T\250\021\250'\260\033\270A";
static const char __pyx_k_strided_and_direct_or_indirect[] = "<strided and direct or indirect>";
static const char __pyx_k_ARt2Qd_AT_1D_4r_a_U_3b_Bb_Qe1Bc[] = "\200!\360(\000\005\033\230!\340\004\014\210A\210R\210t\2202\220Q\220d\230!\330\004\014\210A\210T\220\022\2201\220D\230\003\2304\230r\240\021\240$\240a\330\004\010\210\005\210U\220!\2203\220b\230\001\230\021\330\006\022\220\"\220B\220b\230\002\230#\230Q\230e\2401\240B\240c\250\021\250!\2501\250A\250T\260\022\2601\260D\270\004\270B\270c\300\021\300%\300q\310\002\310#\310Q\310a\310t\320SU\320UV\320VZ\320Z\\\320\\]\320]a\320ac\320cd\320de\320ef\320fg\330\016\020\220\001\220\022\2204\220q\230\002\230!\2304\230q\240\004\240B\240a\240t\2502\250Q\250b\260\001\260\024\260Q\260d\270\"\270A\270T\300\022\3001\300B\300a\300t\3101\310D\320PR\320RS\320SW\320WY\320YZ\320Z[\340\004\016\210b\220\004\220A\220R\220q\230\004\230B\230a\230t\2401\240D\250\001\340\004\013\2101";
static const char __pyx_k_Angular_selection_rules_require[] = "Angular selection rules require the |m|=|m1|+|m2|, but the values m={},m1={}, m2={} were passed.";
static const char __pyx_k_BfAU_V1_BfAU_V1_BfAU_V1_BfAU_V1[] = 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static const char __pyx_k_Invalid_quadratic_term_selected[] = "Invalid quadratic term selected: {}";
static const char __pyx_k_L_6_F_1_U_3aq_1AS_1_r_Rq_1F_Rt2[] = "\200\001\360L\001\000\005*\250\021\250&\260\001\260\021\330\004)\250\022\2506\260\021\260\"\260F\270!\340\004\033\2301\330\004\010\210\005\210U\220!\2203\220a\220q\330\010\013\2101\210A\210S\220\003\2201\330\014\017\210r\220\024\220R\220q\230\001\230\022\2301\230F\240#\240R\240t\2502\250Q\250a\250q\260\001\260\022\2601\260H\270N\310!\330<J\310!\3101\310A\330\014\r\360\010\000\005\006\200Q\320\006\026\220a\220q\230\002\230$\230a\230r\240\021\240$\240b\250\001\250\021\250-\260q\270\006\270b\300\001\340\004\013\2101";
static const char __pyx_k_MMRDNP_You_have_chosen_at_least[] = "MMRDNP: You have chosen at least one mode not available.";
static const char __pyx_k_QNM_220_area_quantized___reduce[] = "QNM_220_area_quantized.__reduce_cython__";
static const char __pyx_k_Q_6_fD_6_Q_Bb_b_as_86_war_2Rs_e[] = "\200!\360\014\000\005\036\230Q\360\006\000\005\014\2106\220\030\230\021\230$\230f\240D\250\001\340\004\t\210\022\2106\220\024\220Q\330\010\024\220B\220b\230\006\230b\240\006\240a\240s\250!\2508\2606\270\021\330\010\017\210w\220a\220r\230\022\2302\230R\230s\240$\240e\2504\250q\330\010\017\210w\220a\220r\230\022\2302\230T\240\021\240$\240e\2504\250q\330\010\020\220\010\230\004\230K\240q\250\017\260w\270a\270r\300\022\3001\330\020\030\230\001\330\010\020\220\010\230\004\230K\240q\250\r\260W\270A\270R\270r\300\021\330\020\030\230\001\340\010\021\220\024\220Q\220c\230\023\230B\230a\230t\2407\250%\250t\2602\260R\260r\270\022\2704\270q\300\003\3003\300a\300r\310\021\310$\310g\320UV\330\010\021\220\024\220Q\220c\230\023\230B\230a\230t\2407\250%\250t\2602\260R\260r\270\022\2704\270q\300\003\3003\300a\300r\310\021\310$\310g\320UV\330\010\021\220\024\220U\230\"\230B\230a\340\010\024\220B\220b\230\001\330\014\023\2202\220R\220u\230A\230_\250A\250S\260\004\260B\260c\270\021\270(\300#\300R\300s\310!\3107\320RS\320ST\320TU\320UY\320Y_\320_c\320ch\320hl\320lt\360\000\000u\001L\002\360\000\000L\002M\002\330\014\023\2202\220R\220u\230A\230_\250A\250S\260\004\260B\260c\270\021\270(\300#\300R\300s\310!\3107\320RS\320ST\320TU\320UY\320Y_\320_c\320ch\320hl\320lt\320t|\320|~\320~\177\360\006\000\005\016\210R\210v\220Q\220c\230\021\230(\240&\250\001\340\004\r\210R\210v\220Q\220e\2306\240\021\240$\240f\250A\330\004\r\210R\210v\220Q\220e\2306\240\021\240$\240f\250A\330\004\r\210R\210v\220Q\220e\2306\240\021\240$\240f\250A\330\004\r\210R\210v\220Q\220e\2306\240\021\240$\240f\250A\330\004\r\210R\210v\220Q\220e\2306\240\021\240$\240f\250A\340\004\010\210\004\210A\330\010\021\220\034\230R\230t\240;\250d\260!\340\010\r\210R\210v\220T\230\021\330\014\026\220l\240\"\240B\240a\330\004\014\210D\220\004\220B\220c\230\030\240\022\2403\240f\250C\250t\2603\260b\270\007\270r\300\023\300E\310\022\3101\360\006\000\005\r\210B\210e\2201\220A\330\004\013\2101\210B\210e\2201\220A\340\004\013\2102\210V\2201\220A""\220U\230&\240\006\240e\2501";
static const char __pyx_k_Q_k_fD_HD_6_Q_Bb_b_as_86_YivT_B[] = "\200!\360\022\000\005\036\230Q\340\004\020\220\006\220k\240\021\240$\240f\250D\260\010\270\004\270H\300D\310\001\360\006\000\005\n\210\022\2106\220\024\220[\240\005\240Q\330\010\024\220B\220b\230\006\230b\240\006\240a\240s\250!\2508\2606\270\021\360\006\000\t\016\210Y\220i\230v\240T\250\033\260B\260b\270\001\360\006\000\r\020\210t\2204\220r\230\021\330\020\032\230!\2301\330\020\024\220F\230!\2304\230q\330\014\017\210t\220<\230s\240!\330\020\023\2204\220q\330\024\033\2307\240!\2409\250I\260S\270\005\270T\300\026\300r\310\023\310D\320PU\320UY\320YZ\330\024\033\2307\240!\2409\250I\260S\270\005\270T\300\026\300t\3101\310D\320PU\320UY\320YZ\340\024\033\2304\230t\240=\260\002\260'\270\021\330\024\033\2303\230a\230r\240\031\250)\2603\260d\270.\310\002\310#\310T\320QV\320VZ\320Z[\330\024\033\2303\230a\230r\240\031\250)\2603\260d\270.\310\004\310A\310T\320QV\320VZ\320Z[\340\020\027\220t\230;\240b\250\002\250)\2609\270C\270q\300\001\330\020\027\220t\230;\240b\250\002\250)\2609\270C\270q\300\001\340\014\024\220H\230D\240\013\2501\250O\2707\300!\3009\310I\320UV\330\024\034\230A\330\014\024\220H\230D\240\013\2501\250M\270\027\300\003\3009\310I\320UV\330\024\034\230A\340\014\017\210t\2201\330\020\034\230B\230b\240\001\330\024\035\230U\240\"\240B\240c\250\021\250)\2602\260T\270\021\270*\320D}\320}~\330\024#\2401\240F\250$\250b\260\003\2601\260H\270C\270r\300\023\300A\300W\310C\310t\320SX\320X\\\320\\d\320de\340\020\034\230B\230b\240\001\330\024\030\230\001\230\023\230C\230r\240\021\240$\240f\250D\260\007\260r\270\031\300%\300r\310\022\3103\310a\310y\320XZ\320Z^\320^_\320_i\320i}\320}~\330\024#\2401\240F\250$\250b\260\003\2601\260H\270C\270r\300\023\300A\300W\310C\310t\320SX\320X\\\320\\d\320dk\320kl\330\024\030\230\001\230\023\230C\230q\240\002\240!\2404\240v\250T\260\026\260r\270\022\2705\300\001\300\031\310%\310r\320QS\320SV\320VW\320W`\320`b\320bf\320fg\320gq\320qt\320tw\320wy\320y{\320{}\320}~\330\024#\2401\240E\250\021\250$\250b\260\003\2601\260H\270C\270r\300\023\300A\300W""\310C\310t\320SX\320X\\\320\\d\320de\360\010\000\005\016\210R\210v\220Q\220e\2306\240\021\240$\240f\250A\330\004\r\210R\210v\220Q\220e\2306\240\021\240$\240f\250A\330\004\r\210R\210v\220Q\220e\2306\240\021\240$\240f\250A\330\004\r\210R\210v\220Q\220e\2306\240\021\240$\240f\250A\330\004\r\210R\210v\220Q\220e\2306\240\021\240$\240f\250A\330\004\r\210R\210v\220Q\220c\230\021\230(\240&\250\001\330\004\t\210\022\2106\220\024\220[\240\005\240Q\330\014\026\220l\240\"\240B\240a\340\004\007\200t\2104\210x\220x\230t\2404\240r\250\023\250H\260B\260c\270\026\270s\300$\300c\310\022\3107\320RT\320TW\320W\\\320\\^\320^_\330\027 \240\003\2401\240D\250\003\2501\250B\250d\260!\2602\260Q\260d\270!\340\004\014\210B\210e\2201\220A\330\004\013\2101\210B\210e\2201\220A\340\004\013\2102\210V\2201\220A\220U\230&\240\006\240e\2501";
static const char __pyx_k_RvQe6_fA_RvQe6_fA_RvQe6_fA_RvQe[] = "\200!\360\026\000\005\016\210R\210v\220Q\220e\2306\240\021\240$\240f\250A\330\004\r\210R\210v\220Q\220e\2306\240\021\240$\240f\250A\330\004\r\210R\210v\220Q\220e\2306\240\021\240$\240f\250A\330\004\r\210R\210v\220Q\220e\2306\240\021\240$\240f\250A\330\004\r\210R\210v\220Q\220e\2306\240\021\240$\240f\250A\330\004\r\210R\210v\220Q\220c\230\021\230(\240&\250\001\360\n\000\005\021\220\006\220k\240\021\240$\240a\330\004\026\220a\330\004\010\210\004\210A\340\010\013\2104\210q\330\014\022\220'\230\021\230$\230j\250\004\250J\260d\270!\340\014\023\2204\220t\230=\250\002\250'\260\021\330\014\022\220#\220Q\220c\230\024\230[\250\004\250K\260t\270;\300d\310!\340\010\020\220\010\230\004\230K\240q\250\017\260w\270a\270t\300;\310d\320R]\320]a\320ab\330\020\030\230\001\330\010\020\220\010\230\004\230K\240q\250\r\260W\270A\270T\300\033\310D\320P[\320[_\320_`\330\020\030\230\001\330\010\017\210s\220\"\220A\220T\230\025\230d\240!\330\010\017\210s\220$\220a\220t\2305\240\004\240A\340\010\014\210D\220\016\230g\240V\250;\260a\260t\2707\300$\300e\3104\310|\320[_\320_j\320jn\320ny\320y}\360\000\000~\001B\002\360\000\000B\002C\002\330\036%\240T\250\021\250\"\250D\260\n\270$\270j\310\001\310\024\310W\320TX\320XY\330\010\r\210R\210t\220:\230T\240\032\2504\250~\270Q\340\010\022\220%\220r\230\024\230[\250\004\250J\260d\270,\300b\310\t\320QV\320VX\320X\\\320\\f\320fj\320jt\320tx\360\000\000y\001E\002\360\000\000E\002G\002\360\000\000G\002V\002\360\000\000V\002W\002\360\000\000W\002]\002\360\000\000]\002a\002\360\000\000a\002c\002\360\000\000c\002f\002\360\000\000f\002g\002\360\000\000g\002o\002\360\000\000o\002r\002\360\000\000r\002t\002\360\000\000t\002w\002\360\000\000w\002x\002\360\000\000x\002\177\002\360\000\000\177\002B\003\360\000\000B\003F\003\360\000\000F\003K\003\360\000\000K\003O\003\360\000\000O\003W\003\360\000\000W\003^\003\360\000\000^\003_\003\330\022\027\220r\230\024\230Z\240q\250\004\250J\260d\270,\300b\310\002\310%\310q\320PY\320Y^\320^`\320`d\320dn\320nr\320r|\360\000\000}""\001A\002\360\000\000A\002M\002\360\000\000M\002P\002\360\000\000P\002R\002\360\000\000R\002T\002\360\000\000T\002X\002\360\000\000X\002b\002\360\000\000b\002d\002\360\000\000d\002s\002\360\000\000s\002t\002\360\000\000t\002y\002\360\000\000y\002z\002\360\000\000z\002~\002\360\000\000~\002@\003\360\000\000@\003C\003\360\000\000C\003D\003\360\000\000D\003L\003\360\000\000L\003O\003\360\000\000O\003Q\003\360\000\000Q\003T\003\360\000\000T\003U\003\360\000\000U\003\\\003\360\000\000\\\003_\003\360\000\000_\003c\003\360\000\000c\003h\003\360\000\000h\003l\003\360\000\000l\003t\003\360\000\000t\003u\003\340\010\r\210R\210r\220\026\220t\2301\340\014\017\210t\2201\330\020\026\220g\230Q\230b\240\002\240!\340\020\027\220t\2304\230}\250B\250g\260Q\330\020\026\220c\230\021\230\"\230B\230b\240\002\240$\240a\340\014\024\220H\230D\240\013\2501\250O\2707\300!\3003\300c\310\021\330\024\034\230A\330\014\024\220H\230D\240\013\2501\250M\270\027\300\001\300\023\300C\300q\330\024\034\230A\330\014\023\2203\220b\230\001\230\024\230U\240$\240a\330\014\023\2203\220d\230!\2304\230u\240D\250\001\340\014\020\220\004\220A\330\020\031\230\026\230{\250!\2504\250w\260d\270%\270t\3003\300c\310\024\310T\320QR\330\020\031\230\026\230{\250!\2504\250w\260d\270%\270s\300!\3003\300c\310\024\310T\320QR\340\020\031\230\024\230Q\230b\240\003\2402\240Q\240d\250'\260\024\260Q\330\020\031\230\024\230Q\230b\240\002\240!\2402\240Q\240d\250'\260\024\260Q\340\014\021\220\022\2203\220b\230\006\230a\330\014\021\220\022\2202\220Q\220b\230\006\230a\340\014\026\220e\2302\230S\240\002\240$\240b\250\t\260\025\260b\270\002\270\"\320<Q\320QS\320Sb\320bc\320ci\320im\320mo\320or\320rs\320s{\320{~\360\000\000\177\001A\002\360\000\000A\002D\002\360\000\000D\002E\002\360\000\000E\002L\002\360\000\000L\002O\002\360\000\000O\002S\002\360\000\000S\002X\002\360\000\000X\002\\\002\360\000\000\\\002d\002\360\000\000d\002k\002\360\000\000k\002l\002\330\026\033\2302\230R\230q\240\002\240$\240b\250\002\250%\250q\260\t\270\025\270b\300""\002\300\"\300D\310\003\3102\310R\310r\320QS\320Sb\320bc\320ch\320hi\320im\320mo\320or\320rs\320s{\320{~\360\000\000\177\001A\002\360\000\000A\002D\002\360\000\000D\002E\002\360\000\000E\002L\002\360\000\000L\002O\002\360\000\000O\002S\002\360\000\000S\002X\002\360\000\000X\002\\\002\360\000\000\\\002d\002\360\000\000d\002e\002\360\006\000\005\016\210Q\210b\220\005\220Q\220a\330\004\014\210D\220\004\220B\220c\230\030\240\022\2403\240f\250C\250t\2603\260b\270\007\270r\300\023\300E\310\022\3101\360\006\000\005\r\210B\210e\2201\220A\330\004\013\2101\210B\210e\2201\220A\340\004\013\2102\210V\2201\220A\220U\230&\240\006\240e\2501";
static const char __pyx_k_TEOBPM_You_have_chosen_at_least[] = "TEOBPM: You have chosen at least one mode not available.";
static const char __pyx_k_XT_QRRTTUUYYaabbddffgghhjjllppx[] = "\320\004=\270X\300T\310\030\320QR\320RT\320TU\320UY\320Ya\320ab\320bd\320df\320fg\320gh\320hj\320jl\320lp\320px\320xy\320y|\320|}\360\000\000~\001B\002\360\000\000B\002Q\002\360\000\000Q\002S\002\360\000\000S\002V\002\360\000\000V\002W\002\360\000\000W\002X\002";
static const char __pyx_k_data_NR_data_berti_qnm_fits_txt[] = "data/NR_data/berti_qnm_fits.txt";
static const char __pyx_k_A_1F_1_1_6_F_r_q_6_r_q_6_r_q_6_r[] = "\200A\360,\000\t$\2401\240F\250!\2501\330\0101\260\022\2606\270\021\270\"\270F\300!\340\010\017\210r\220\026\220q\230\003\2306\240\021\330\010\017\210r\220\026\220q\230\003\2306\240\021\330\010\017\210r\220\026\220q\230\003\2306\240\021\330\010\017\210r\220\026\220q\230\003\2306\240\021\330\010\017\210r\220\026\220q\230\003\2306\240\021\340\010\014\210G\2204\220r\230\025\230a\330\014\020\220\005\220U\230!\2304\230r\240\021\240!\330\020\031\230\037\250\001\250\024\250R\250q\260\004\260A\260Q\330)-\250R\250q\260\004\260A\260Q\330)-\250T\260\021\260$\260a\260q\330)-\250T\260\021\260$\260a\260q\330)-\250S\260\001\260\024\260Q\260a\330)-\250S\260\001\260\024\260Q\260a\330)*\330\014\017\210s\220\"\220A\330\020\031\230\022\2305\240\001\240\021\330\021\024\220B\220a\330\020\031\230\022\2305\240\001\240\021\330\020\030\230\001\230\022\2305\240\001\240\021\330\021\024\220B\220a\330\020\031\230\022\2305\240\001\240\021\330\020\030\230\001\230\022\2305\240\001\240\021\330\014\024\220B\220f\230A\230S\240\006\240a\340\010\017\210r\220\026\220q\230\001\230\025\230f\240F\250%\250q";
static const char __pyx_k_A_AT_AQ_1_E_aq_r_7_ar_2T_S_FRTTZ[] = "\200A\340\010\031\230\023\230A\230T\240\021\330\010\031\230\023\230A\230Q\340\010\033\2301\330\010\014\210E\220\025\220a\220q\340\014\017\210r\220\022\2207\320\032.\250a\250r\260\022\2602\260T\270\030\300\021\300#\300S\310\002\310\"\310F\320RT\320TZ\320Z[\320[\\\330\032.\250a\250r\260\022\2602\260T\270\030\300\021\300!\340\010\020\220\003\2201\220B\220a\220t\230?\250!\2501";
static const char __pyx_k_A_AT_AQ_E_aq_r_7_Qb_D_3c_2VSUU_Q[] = "\200A\340\010\031\230\023\230A\230T\240\021\330\010\031\230\023\230A\230Q\340\010\032\230!\330\010\014\210E\220\025\220a\220q\340\014\017\210r\220\022\2207\320\032-\250Q\250b\260\002\260\"\260D\270\n\300!\3003\300c\310\022\3102\310V\320SU\320U[\320[\\\320\\]\330\032-\250Q\250b\260\002\260\"\260D\270\n\300!\3001\340\010\017\210s\220#\220S\230\001\230\022\2301\230D\320 0\260\002\260!";
static const char __pyx_k_A_c_as_q_5_ARs_3eSTTUUVVYYZ_RuAU[] = "\200A\330\010&\240c\250\025\250a\250s\260%\260q\270\003\2705\300\002\300\"\300A\300R\300s\310!\3103\310e\320ST\320TU\320UV\320VY\320YZ\330\010 \240\001\330\010 \240\001\330\010\017\210~\230R\230u\240A\240U\250!\2502\250U\260!\2601\260A\260Q\260a\260r\270\021\270!\2701\270B\270c\300\021\300!\3001\300G\3102\310R\310q\320PR\320RU\320UW\320WX\320XY\320Y[\320[`\320`a\320ab\320bc\320cd\320de\320ef";
static const char __pyx_k_A_c_as_q_5_ARs_3eSTTUUVVYYZ_q_2R[] = "\200A\330\010&\240c\250\025\250a\250s\260%\260q\270\003\2705\300\002\300\"\300A\300R\300s\310!\3103\310e\320ST\320TU\320UV\320VY\320YZ\330\010\037\230q\240\001\240\022\2402\240R\240r\250\021\330\010\017\210~\230Q\230a";
static const char __pyx_k_All_dimensions_preceding_dimensi[] = "All dimensions preceding dimension %d must be indexed and not sliced";
static const char __pyx_k_Berti_fits_are_not_available_for[] = "Berti fits are not available for n>2. Please unselect the 'qnm-fit' option in order to obtain a direct interpolation from NR data.";
static const char __pyx_k_Braneworld_QNMs_still_do_not_sup[] = "Braneworld QNMs still do not support fits. Please set qnm-fit=0 inside the config file.";
static const char __pyx_k_Buffer_view_does_not_expose_stri[] = "Buffer view does not expose strides";
static const char __pyx_k_Can_only_create_a_buffer_that_is[] = "Can only create a buffer that is contiguous in memory.";
static const char __pyx_k_Cannot_assign_to_read_only_memor[] = "Cannot assign to read-only memoryview";
static const char __pyx_k_Cannot_create_writable_memory_vi[] = "Cannot create writable memory view from read-only memoryview";
static const char __pyx_k_Cannot_transpose_memoryview_with[] = "Cannot transpose memoryview with indirect dimensions";
static const char __pyx_k_Damped_sinusoids___reduce_cython[] = "Damped_sinusoids.__reduce_cython__";
static const char __pyx_k_Damped_sinusoids___setstate_cyth[] = "Damped_sinusoids.__setstate_cython__";
static const char __pyx_k_Empty_shape_tuple_for_cython_arr[] = "Empty shape tuple for cython.array";
static const char __pyx_k_If_quantization_of_the_horizon_a[] = "If quantization of the horizon area is invoked, the alpha parameter must be passed.";
static const char __pyx_k_Incompatible_checksums_0x_x_vs_0[] = "Incompatible checksums (0x%x vs (0x82a3537, 0x6ae9995, 0xb068931) = (name))";
static const char __pyx_k_Indirect_dimensions_not_supporte[] = "Indirect dimensions not supported";
static const char __pyx_k_Invalid_mode_expected_c_or_fortr[] = "Invalid mode, expected 'c' or 'fortran', got ";
static const char __pyx_k_KHS_2012_Distance_be_negative_or[] = "KHS_2012: Distance be negative or 0.";
static const char __pyx_k_KHS_2012_Eta_cannot_be_smaller_t[] = "KHS_2012: Eta cannot be smaller than 0 or greater than 0.25.";
static const char __pyx_k_KHS_2012_Mass_cannot_be_negative[] = "KHS_2012: Mass cannot be negative or 0. No tachyons around here, not yet at least.";
static const char __pyx_k_KHS_2012_Spin_cannot_be_grater_t[] = "KHS_2012: |Spin| cannot be grater than 1. You shall not break CCC, not on my watch.";
static const char __pyx_k_KN_QNMs_still_do_not_support_fit[] = "KN QNMs still do not support fits. Please set the qnm-fit=0";
static const char __pyx_k_MMRDNP_Distance_cannot_be_negati[] = "MMRDNP: Distance cannot be negative or 0.";
static const char __pyx_k_MMRDNP_Eta_cannot_be_smaller_tha[] = "MMRDNP: Eta cannot be smaller than 0 or greater than 0.25.";
static const char __pyx_k_MMRDNP_Mass_cannot_be_negative_o[] = "MMRDNP: Mass cannot be negative or 0. No tachyons around here, not yet at least.";
static const char __pyx_k_MMRDNP_Spin_cannot_be_grater_tha[] = "MMRDNP: |Spin| cannot be grater than 1. You shall not break CCC, not on my watch.";
static const char __pyx_k_MMRDNP_The_modes_list_contains_r[] = "MMRDNP: The modes list contains repeated elements.";
static const char __pyx_k_MMRDNS_Distance_be_negative_or_0[] = "MMRDNS: Distance be negative or 0.";
static const char __pyx_k_MMRDNS_Eta_cannot_be_smaller_tha[] = "MMRDNS: Eta cannot be smaller than 0 or greater than 0.25.";
static const char __pyx_k_MMRDNS_Mass_cannot_be_negative_o[] = "MMRDNS: Mass cannot be negative or 0. No tachyons around here, not yet al least.";
static const char __pyx_k_MMRDNS_Spin_cannot_be_grater_tha[] = "MMRDNS: |Spin| cannot be grater than 1. You shall not break causality, not on my watch.";
static const char __pyx_k_Morlet_Gabor_wavelets___reduce_c[] = "Morlet_Gabor_wavelets.__reduce_cython__";
static const char __pyx_k_Morlet_Gabor_wavelets___setstate[] = "Morlet_Gabor_wavelets.__setstate_cython__";
static const char __pyx_k_Non_tensorial_modes_s_was_select[] = "Non-tensorial modes (s={} was selected) are incompatible with using either a fit for QNM or the area quantization proposal or a BH charge or braneworld corrections.";
static const char __pyx_k_Note_that_Cython_is_deliberately[] = "Note that Cython is deliberately stricter than PEP-484 and rejects subclasses of builtin types. If you need to pass subclasses then set the 'annotation_typing' directive to False.";
static const char __pyx_k_Out_of_bounds_on_buffer_access_a[] = "Out of bounds on buffer access (axis ";
static const char __pyx_k_ParSpec_coeffs_f_order_high_spin[] = "ParSpec_coeffs_f_order_high_spin";
static const char __pyx_k_ParSpec_coeffs_tau_order_high_sp[] = "ParSpec_coeffs_tau_order_high_spin";
static const char __pyx_k_QNM_220_area_quantized___setstat[] = "QNM_220_area_quantized.__setstate_cython__";
static const char __pyx_k_QNM_braneworld_fit___reduce_cyth[] = "QNM_braneworld_fit.__reduce_cython__";
static const char __pyx_k_QNM_braneworld_fit___setstate_cy[] = "QNM_braneworld_fit.__setstate_cython__";
static const char __pyx_k_QNM_m_cannot_be_greater_than_l_i[] = "QNM: m cannot be greater than l in modulus.";
static const char __pyx_k_TEOBPM_Distance_cannot_be_negati[] = "TEOBPM: Distance cannot be negative or 0.";
static const char __pyx_k_TEOBPM_EOBPM_SetupFitCoefficient[] = "TEOBPM.EOBPM_SetupFitCoefficients";
static const char __pyx_k_TEOBPM_JimenezFortezaRemnantMass[] = "TEOBPM.JimenezFortezaRemnantMass";
static const char __pyx_k_TEOBPM_JimenezFortezaRemnantSpin[] = "TEOBPM.JimenezFortezaRemnantSpin";
static const char __pyx_k_TEOBPM_Masses_cannot_be_negative[] = "TEOBPM: Masses cannot be negative.";
static const char __pyx_k_TEOBPM_Please_do_not_invoke_a_na[] = "TEOBPM: Please do not invoke a naked singularity.";
static const char __pyx_k_TEOBPM_The_modes_list_contains_r[] = "TEOBPM: The modes list contains repeated elements.";
static const char __pyx_k_The_QNM_coming_from_quantized_ar[] = "The QNM coming from quantized are valid only for the 220 mode.";
static const char __pyx_k_Unable_to_convert_item_to_object[] = "Unable to convert item to object";
static const char __pyx_k_When_fixing_the_quadratic_amplit[] = "When fixing the quadratic amplitudes in terms of the linear ones, the linear modes have to contain the corresponding quadratic parent modes.";
static const char __pyx_k_You_deselected_qnm_fit_without_p[] = "You deselected qnm-fit without providing any interpolant.";
static const char __pyx_k_data_NR_data_ParSpec_coefficient[] = "data/NR_data/ParSpec_coefficients.txt";
static const char __pyx_k_got_differing_extents_in_dimensi[] = "got differing extents in dimension ";
static const char __pyx_k_no_default___reduce___due_to_non[] = "no default __reduce__ due to non-trivial __cinit__";
static const char __pyx_k_numpy__core_multiarray_failed_to[] = "numpy._core.multiarray failed to import";
static const char __pyx_k_numpy__core_umath_failed_to_impo[] = "numpy._core.umath failed to import";
static const char __pyx_k_unable_to_allocate_shape_and_str[] = "unable to allocate shape and strides.";
static const char __pyx_k_Angular_selection_rules_require_2[] = "Angular selection rules require the l1-l2 <= l <= l1+l2, but the values l={},l1={}, l2={} were passed.";
static const char __pyx_k_XT_QRRTTUUYYaabbddffgghhjjllppx_2[] = "\320\004=\270X\300T\310\030\320QR\320RT\320TU\320UY\320Ya\320ab\320bd\320df\320fg\320gh\320hj\320jl\320lp\320px\320xy\320yz";
static const char __pyx_k_A_1F_1_1_6_F_r_q_6_r_q_6_r_q_6_r_2[] = "\200A\360*\000\t$\2401\240F\250!\2501\330\0101\260\022\2606\270\021\270\"\270F\300!\340\010\017\210r\220\026\220q\230\003\2306\240\021\330\010\017\210r\220\026\220q\230\003\2306\240\021\330\010\017\210r\220\026\220q\230\003\2306\240\021\330\010\017\210r\220\026\220q\230\003\2306\240\021\330\010\017\210r\220\026\220q\230\003\2306\240\021\340\010\014\210G\2204\220r\230\025\230a\330\014\020\220\005\220U\230!\2304\230r\240\021\240!\330\020\031\320\031-\250Q\250d\260\"\260A\260T\270\021\270!\330.2\260\"\260A\260T\270\021\270!\330.2\260$\260a\260t\2701\270A\330.2\260$\260a\260t\2701\270A\330.2\260#\260Q\260d\270!\2701\330.2\260#\260Q\260d\270!\2701\330./\330\014\017\210s\220\"\220A\330\020\031\230\022\2305\240\001\240\021\330\021\024\220B\220a\330\020\031\230\022\2305\240\001\240\021\330\020\030\230\001\230\022\2305\240\001\240\021\330\021\024\220B\220a\330\020\031\230\022\2305\240\001\240\021\330\020\030\230\001\230\022\2305\240\001\240\021\330\014\024\220B\220f\230A\230S\240\006\240a\340\010\017\210r\220\026\220q\230\001\230\025\230f\240F\250%\250q";
static const char __pyx_k_Incompatible_checksums_0x_x_vs_0_2[] = "Incompatible checksums (0x%x vs (0x761e8a1, 0x110c922, 0x6adc97b) = (l, m, s, swsh_prefactor))";
static const char __pyx_k_KN_QNMs_still_do_not_support_fit_2[] = "KN QNMs still do not support fits. Please set qnm-fit=0 inside the config file.";
static const char __pyx_k_data_NR_data_ParSpec_coefficient_2[] = "data/NR_data/ParSpec_coefficients_high_spin.txt";
/* #### Code section: decls ### */
static int __pyx_array___pyx_pf_15View_dot_MemoryView_5array___cinit__(struct __pyx_array_obj *__pyx_v_self, PyObject *__pyx_v_shape, Py_ssize_t __pyx_v_itemsize, PyObject *__pyx_v_format, PyObject *__pyx_v_mode, int __pyx_v_allocate_buffer); /* proto */
static int __pyx_array___pyx_pf_15View_dot_MemoryView_5array_2__getbuffer__(struct __pyx_array_obj *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /* proto */
static void __pyx_array___pyx_pf_15View_dot_MemoryView_5array_4__dealloc__(struct __pyx_array_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_15View_dot_MemoryView_5array_7memview___get__(struct __pyx_array_obj *__pyx_v_self); /* proto */
static Py_ssize_t __pyx_array___pyx_pf_15View_dot_MemoryView_5array_6__len__(struct __pyx_array_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_array___pyx_pf_15View_dot_MemoryView_5array_8__getattr__(struct __pyx_array_obj *__pyx_v_self, PyObject *__pyx_v_attr); /* proto */
static PyObject *__pyx_array___pyx_pf_15View_dot_MemoryView_5array_10__getitem__(struct __pyx_array_obj *__pyx_v_self, PyObject *__pyx_v_item); /* proto */
static int __pyx_array___pyx_pf_15View_dot_MemoryView_5array_12__setitem__(struct __pyx_array_obj *__pyx_v_self, PyObject *__pyx_v_item, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf___pyx_array___reduce_cython__(CYTHON_UNUSED struct __pyx_array_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_pf___pyx_array_2__setstate_cython__(CYTHON_UNUSED struct __pyx_array_obj *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* proto */
static int __pyx_MemviewEnum___pyx_pf_15View_dot_MemoryView_4Enum___init__(struct __pyx_MemviewEnum_obj *__pyx_v_self, PyObject *__pyx_v_name); /* proto */
static PyObject *__pyx_MemviewEnum___pyx_pf_15View_dot_MemoryView_4Enum_2__repr__(struct __pyx_MemviewEnum_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_pf___pyx_MemviewEnum___reduce_cython__(struct __pyx_MemviewEnum_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_pf___pyx_MemviewEnum_2__setstate_cython__(struct __pyx_MemviewEnum_obj *__pyx_v_self, PyObject *__pyx_v___pyx_state); /* proto */
static int __pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview___cinit__(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_obj, int __pyx_v_flags, int __pyx_v_dtype_is_object); /* proto */
static void __pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_2__dealloc__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_4__getitem__(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_index); /* proto */
static int __pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_6__setitem__(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_index, PyObject *__pyx_v_value); /* proto */
static int __pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_8__getbuffer__(struct __pyx_memoryview_obj *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /* proto */
static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_1T___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_4base___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_5shape___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_7strides___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_10suboffsets___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_4ndim___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_8itemsize___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_6nbytes___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_4size___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static Py_ssize_t __pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_10__len__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_12__repr__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_14__str__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_16is_c_contig(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_18is_f_contig(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_20copy(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_22copy_fortran(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_pf___pyx_memoryview___reduce_cython__(CYTHON_UNUSED struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_pf___pyx_memoryview_2__setstate_cython__(CYTHON_UNUSED struct __pyx_memoryview_obj *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* proto */
static void __pyx_memoryviewslice___pyx_pf_15View_dot_MemoryView_16_memoryviewslice___dealloc__(struct __pyx_memoryviewslice_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_pf___pyx_memoryviewslice___reduce_cython__(CYTHON_UNUSED struct __pyx_memoryviewslice_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_pf___pyx_memoryviewslice_2__setstate_cython__(CYTHON_UNUSED struct __pyx_memoryviewslice_obj *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* proto */
static PyObject *__pyx_pf_15View_dot_MemoryView___pyx_unpickle_Enum(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v___pyx_type, long __pyx_v___pyx_checksum, PyObject *__pyx_v___pyx_state); /* proto */
static int __pyx_pf_7cpython_5array_5array___getbuffer__(arrayobject *__pyx_v_self, Py_buffer *__pyx_v_info, CYTHON_UNUSED int __pyx_v_flags); /* proto */
static void __pyx_pf_7cpython_5array_5array_2__releasebuffer__(CYTHON_UNUSED arrayobject *__pyx_v_self, Py_buffer *__pyx_v_info); /* proto */
static int __pyx_pf_6pyRing_8waveform_3QNM___cinit__(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self, unsigned int __pyx_v_s, unsigned int __pyx_v_l, int __pyx_v_m, unsigned int __pyx_v_n, PyObject *__pyx_v_interpolants, unsigned int __pyx_v_geom); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_3QNM_2f(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self, double __pyx_v_M, double __pyx_v_a); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_3QNM_4f_KN(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self, double __pyx_v_M, double __pyx_v_a, double __pyx_v_Q); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_3QNM_6f_BW(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self, double __pyx_v_M, double __pyx_v_a, double __pyx_v_beta); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_3QNM_8tau(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self, double __pyx_v_M, double __pyx_v_a); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_3QNM_10tau_KN(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self, double __pyx_v_M, double __pyx_v_a, double __pyx_v_Q); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_3QNM_12tau_BW(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self, double __pyx_v_M, double __pyx_v_a, double __pyx_v_beta); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_3QNM_1s___get__(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_3QNM_1s_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_3QNM_1l___get__(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_3QNM_1l_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_3QNM_1m___get__(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_3QNM_1m_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_3QNM_1n___get__(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_3QNM_1n_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_3QNM_4geom___get__(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_3QNM_4geom_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_3QNM_13omegar_interp___get__(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_3QNM_13omegar_interp_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_3QNM_13omegar_interp_4__del__(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_3QNM_13omegai_interp___get__(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_3QNM_13omegai_interp_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_3QNM_13omegai_interp_4__del__(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_3QNM_14prefactor_freq___get__(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_3QNM_14prefactor_freq_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_3QNM_13prefactor_tau___get__(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_3QNM_13prefactor_tau_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_3QNM_14__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_3QNM_16__setstate_cython__(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_QNM *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* proto */
static int __pyx_pf_6pyRing_8waveform_7QNM_fit___cinit__(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self, unsigned int __pyx_v_l, int __pyx_v_m, unsigned int __pyx_v_n, unsigned int __pyx_v_charge, PyObject *__pyx_v_geom); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_7QNM_fit_2f(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self, double __pyx_v_M, double __pyx_v_a); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_7QNM_fit_4q(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self, double __pyx_v_a); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_7QNM_fit_6tau(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self, double __pyx_v_M, double __pyx_v_a); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_7QNM_fit_8f_KN(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self, double __pyx_v_M, double __pyx_v_a, double __pyx_v_Q); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_7QNM_fit_10q_KN(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self, double __pyx_v_a, double __pyx_v_Q); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_7QNM_fit_12tau_KN(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self, double __pyx_v_M, double __pyx_v_a, double __pyx_v_Q); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_7QNM_fit_1l___get__(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_7QNM_fit_1l_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_7QNM_fit_1m___get__(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_7QNM_fit_1m_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_7QNM_fit_1n___get__(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_7QNM_fit_1n_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_7QNM_fit_6charge___get__(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_7QNM_fit_6charge_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_7QNM_fit_7f_coeff___get__(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_7QNM_fit_7f_coeff_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_7QNM_fit_7f_coeff_4__del__(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_7QNM_fit_7q_coeff___get__(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_7QNM_fit_7q_coeff_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_7QNM_fit_7q_coeff_4__del__(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_7QNM_fit_14prefactor_freq___get__(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_7QNM_fit_14prefactor_freq_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_7QNM_fit_14__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_7QNM_fit_16__setstate_cython__(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_QNM_fit *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* proto */
static int __pyx_pf_6pyRing_8waveform_11QNM_ParSpec___cinit__(struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *__pyx_v_self, unsigned int __pyx_v_l, int __pyx_v_m, unsigned int __pyx_v_n, PyObject *__pyx_v_fit, PyObject *__pyx_v_geom); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_11QNM_ParSpec_2f(struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *__pyx_v_self, double __pyx_v_M, double __pyx_v_a, double __pyx_v_gamma, PyArrayObject *__pyx_v_dw_vec); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_11QNM_ParSpec_4tau(struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *__pyx_v_self, double __pyx_v_M, double __pyx_v_a, double __pyx_v_gamma, PyArrayObject *__pyx_v_dt_vec); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_11QNM_ParSpec_1l___get__(struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_11QNM_ParSpec_1l_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_11QNM_ParSpec_1m___get__(struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_11QNM_ParSpec_1m_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_11QNM_ParSpec_1n___get__(struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_11QNM_ParSpec_1n_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_11QNM_ParSpec_7f_coeff___get__(struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_11QNM_ParSpec_7f_coeff_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_11QNM_ParSpec_7f_coeff_4__del__(struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_11QNM_ParSpec_9tau_coeff___get__(struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_11QNM_ParSpec_9tau_coeff_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_11QNM_ParSpec_9tau_coeff_4__del__(struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_11QNM_ParSpec_14prefactor_freq___get__(struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_11QNM_ParSpec_14prefactor_freq_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_11QNM_ParSpec_13prefactor_tau___get__(struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_11QNM_ParSpec_13prefactor_tau_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_11QNM_ParSpec_6__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_11QNM_ParSpec_8__setstate_cython__(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* proto */
static int __pyx_pf_6pyRing_8waveform_22QNM_220_area_quantized___cinit__(struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *__pyx_v_self, unsigned int __pyx_v_l_QA, int __pyx_v_m_QA, unsigned int __pyx_v_n_QA); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_22QNM_220_area_quantized_2f_QA(struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *__pyx_v_self, double __pyx_v_M, double __pyx_v_a, double __pyx_v_alpha); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_22QNM_220_area_quantized_4q_GR(struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *__pyx_v_self, double __pyx_v_a); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_22QNM_220_area_quantized_6tau_QA(struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *__pyx_v_self, double __pyx_v_M, double __pyx_v_a, double __pyx_v_alpha); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_22QNM_220_area_quantized_4l_QA___get__(struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_22QNM_220_area_quantized_4l_QA_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_22QNM_220_area_quantized_4m_QA___get__(struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_22QNM_220_area_quantized_4m_QA_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_22QNM_220_area_quantized_4n_QA___get__(struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_22QNM_220_area_quantized_4n_QA_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_22QNM_220_area_quantized_10q_coeff_GR___get__(struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_22QNM_220_area_quantized_10q_coeff_GR_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_22QNM_220_area_quantized_10q_coeff_GR_4__del__(struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_22QNM_220_area_quantized_8__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_22QNM_220_area_quantized_10__setstate_cython__(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* proto */
static int __pyx_pf_6pyRing_8waveform_18QNM_braneworld_fit___cinit__(struct __pyx_obj_6pyRing_8waveform_QNM_braneworld_fit *__pyx_v_self, unsigned int __pyx_v_l_BW, int __pyx_v_m_BW, unsigned int __pyx_v_n_BW); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_18QNM_braneworld_fit_2f_BW(struct __pyx_obj_6pyRing_8waveform_QNM_braneworld_fit *__pyx_v_self, double __pyx_v_M, double __pyx_v_a, double __pyx_v_beta); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_18QNM_braneworld_fit_4q_BW(struct __pyx_obj_6pyRing_8waveform_QNM_braneworld_fit *__pyx_v_self, double __pyx_v_a, double __pyx_v_beta); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_18QNM_braneworld_fit_6tau_BW(struct __pyx_obj_6pyRing_8waveform_QNM_braneworld_fit *__pyx_v_self, double __pyx_v_M, double __pyx_v_a, double __pyx_v_beta); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_18QNM_braneworld_fit_4l_BW___get__(struct __pyx_obj_6pyRing_8waveform_QNM_braneworld_fit *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_18QNM_braneworld_fit_4l_BW_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM_braneworld_fit *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_18QNM_braneworld_fit_4m_BW___get__(struct __pyx_obj_6pyRing_8waveform_QNM_braneworld_fit *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_18QNM_braneworld_fit_4m_BW_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM_braneworld_fit *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_18QNM_braneworld_fit_4n_BW___get__(struct __pyx_obj_6pyRing_8waveform_QNM_braneworld_fit *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_18QNM_braneworld_fit_4n_BW_2__set__(struct __pyx_obj_6pyRing_8waveform_QNM_braneworld_fit *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_18QNM_braneworld_fit_8__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_QNM_braneworld_fit *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_18QNM_braneworld_fit_10__setstate_cython__(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_QNM_braneworld_fit *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_damped_sinusoid(CYTHON_UNUSED PyObject *__pyx_self, double __pyx_v_A, double __pyx_v_f, double __pyx_v_tau, double __pyx_v_phi, double __pyx_v_t_0, double __pyx_v_t_ref, PyArrayObject *__pyx_v_t); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_2tail_factor(CYTHON_UNUSED PyObject *__pyx_self, double __pyx_v_A, double __pyx_v_phi, double __pyx_v_p, double __pyx_v_t_0, double __pyx_v_t_ref, PyArrayObject *__pyx_v_t); /* proto */
static int __pyx_pf_6pyRing_8waveform_16Damped_sinusoids___cinit__(struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *__pyx_v_self, PyObject *__pyx_v_A, PyObject *__pyx_v_f, PyObject *__pyx_v_tau, PyObject *__pyx_v_phi, PyObject *__pyx_v_t0); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_16Damped_sinusoids_2waveform(struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *__pyx_v_self, PyArrayObject *__pyx_v_t); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_16Damped_sinusoids_1A___get__(struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_16Damped_sinusoids_1A_2__set__(struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_16Damped_sinusoids_1A_4__del__(struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_16Damped_sinusoids_1f___get__(struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_16Damped_sinusoids_1f_2__set__(struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_16Damped_sinusoids_1f_4__del__(struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_16Damped_sinusoids_3tau___get__(struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_16Damped_sinusoids_3tau_2__set__(struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_16Damped_sinusoids_3tau_4__del__(struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_16Damped_sinusoids_3phi___get__(struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_16Damped_sinusoids_3phi_2__set__(struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_16Damped_sinusoids_3phi_4__del__(struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_16Damped_sinusoids_2t0___get__(struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_16Damped_sinusoids_2t0_2__set__(struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_16Damped_sinusoids_2t0_4__del__(struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_16Damped_sinusoids_1N___get__(struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_16Damped_sinusoids_1N_2__set__(struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_16Damped_sinusoids_1N_4__del__(struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_16Damped_sinusoids_4__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_16Damped_sinusoids_6__setstate_cython__(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* proto */
static int __pyx_pf_6pyRing_8waveform_21Morlet_Gabor_wavelets___cinit__(struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *__pyx_v_self, PyObject *__pyx_v_A, PyObject *__pyx_v_f, PyObject *__pyx_v_tau, PyObject *__pyx_v_phi, PyObject *__pyx_v_t0); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_21Morlet_Gabor_wavelets_2waveform(struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *__pyx_v_self, PyArrayObject *__pyx_v_t); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_21Morlet_Gabor_wavelets_1A___get__(struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_21Morlet_Gabor_wavelets_1A_2__set__(struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_21Morlet_Gabor_wavelets_1A_4__del__(struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_21Morlet_Gabor_wavelets_1f___get__(struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_21Morlet_Gabor_wavelets_1f_2__set__(struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_21Morlet_Gabor_wavelets_1f_4__del__(struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_21Morlet_Gabor_wavelets_3tau___get__(struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_21Morlet_Gabor_wavelets_3tau_2__set__(struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_21Morlet_Gabor_wavelets_3tau_4__del__(struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_21Morlet_Gabor_wavelets_3phi___get__(struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_21Morlet_Gabor_wavelets_3phi_2__set__(struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_21Morlet_Gabor_wavelets_3phi_4__del__(struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_21Morlet_Gabor_wavelets_2t0___get__(struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_21Morlet_Gabor_wavelets_2t0_2__set__(struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_21Morlet_Gabor_wavelets_2t0_4__del__(struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_21Morlet_Gabor_wavelets_1N___get__(struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_21Morlet_Gabor_wavelets_1N_2__set__(struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_21Morlet_Gabor_wavelets_1N_4__del__(struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_21Morlet_Gabor_wavelets_4__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_21Morlet_Gabor_wavelets_6__setstate_cython__(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* proto */
static int __pyx_pf_6pyRing_8waveform_4SWSH___init__(struct __pyx_obj_6pyRing_8waveform_SWSH *__pyx_v_self, int __pyx_v_s, int __pyx_v_l, int __pyx_v_m); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_4SWSH_2__call__(struct __pyx_obj_6pyRing_8waveform_SWSH *__pyx_v_self, double __pyx_v_theta, double __pyx_v_phi); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_4SWSH_4evaluate(struct __pyx_obj_6pyRing_8waveform_SWSH *__pyx_v_self, double __pyx_v_theta, double __pyx_v_phi); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_4SWSH_1l___get__(struct __pyx_obj_6pyRing_8waveform_SWSH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_4SWSH_1l_2__set__(struct __pyx_obj_6pyRing_8waveform_SWSH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_4SWSH_1m___get__(struct __pyx_obj_6pyRing_8waveform_SWSH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_4SWSH_1m_2__set__(struct __pyx_obj_6pyRing_8waveform_SWSH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_4SWSH_1s___get__(struct __pyx_obj_6pyRing_8waveform_SWSH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_4SWSH_1s_2__set__(struct __pyx_obj_6pyRing_8waveform_SWSH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_4SWSH_14swsh_prefactor___get__(struct __pyx_obj_6pyRing_8waveform_SWSH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_4SWSH_14swsh_prefactor_2__set__(struct __pyx_obj_6pyRing_8waveform_SWSH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_4SWSH_6__reduce_cython__(struct __pyx_obj_6pyRing_8waveform_SWSH *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_4SWSH_8__setstate_cython__(struct __pyx_obj_6pyRing_8waveform_SWSH *__pyx_v_self, PyObject *__pyx_v___pyx_state); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH___cinit__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, double __pyx_v_t0, double __pyx_v_Mf, double __pyx_v_af, PyObject *__pyx_v_amps, double __pyx_v_r, double __pyx_v_iota, double __pyx_v_phi, double __pyx_v_reference_amplitude, unsigned int __pyx_v_geom, unsigned int __pyx_v_qnm_fit, PyObject *__pyx_v_interpolants, unsigned int __pyx_v_Spheroidal, unsigned int __pyx_v_amp_non_prec_sym, PyObject *__pyx_v_tail_parameters, PyObject *__pyx_v_quadratic_modes, unsigned int __pyx_v_quad_lin_prop, PyObject *__pyx_v_qnm_cached, PyObject *__pyx_v_TGR_params, unsigned int __pyx_v_AreaQuantization, unsigned int __pyx_v_ParSpec, unsigned int __pyx_v_charge, unsigned int __pyx_v_braneworld); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_2waveform(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, PyArrayObject *__pyx_v_times); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_2t0___get__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_2t0_2__set__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_2Mf___get__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_2Mf_2__set__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_2af___get__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_2af_2__set__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_4amps___get__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_4amps_2__set__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_4amps_4__del__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_1r___get__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_1r_2__set__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_4iota___get__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_4iota_2__set__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_3phi___get__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_3phi_2__set__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_19reference_amplitude___get__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_19reference_amplitude_2__set__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_4geom___get__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_4geom_2__set__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_7qnm_fit___get__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_7qnm_fit_2__set__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_12interpolants___get__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_12interpolants_2__set__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_12interpolants_4__del__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_10Spheroidal___get__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_10Spheroidal_2__set__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_16amp_non_prec_sym___get__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_16amp_non_prec_sym_2__set__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_15tail_parameters___get__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_15tail_parameters_2__set__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_15tail_parameters_4__del__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_15quadratic_modes___get__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_15quadratic_modes_2__set__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_15quadratic_modes_4__del__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_13quad_lin_prop___get__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_13quad_lin_prop_2__set__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_13neg_quad_freq___get__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_13neg_quad_freq_2__set__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_10qnm_cached___get__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_10qnm_cached_2__set__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_10qnm_cached_4__del__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_10TGR_params___get__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_10TGR_params_2__set__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_10TGR_params_4__del__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_16AreaQuantization___get__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_16AreaQuantization_2__set__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_7ParSpec___get__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_7ParSpec_2__set__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_6charge___get__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_6charge_2__set__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_10braneworld___get__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_10braneworld_2__set__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_4qnms___get__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_4qnms_2__set__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_4qnms_4__del__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_12qnms_ParSpec___get__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_12qnms_ParSpec_2__set__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_12qnms_ParSpec_4__del__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_5swshs___get__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_5swshs_2__set__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_6KerrBH_5swshs_4__del__(struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_4__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6KerrBH_6__setstate_cython__(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_KerrBH *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNS___cinit__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self, double __pyx_v_t0, double __pyx_v_t_ref, double __pyx_v_Mf, double __pyx_v_af, double __pyx_v_eta, double __pyx_v_r, double __pyx_v_iota, double __pyx_v_phi, PyObject *__pyx_v_TGR_params, int __pyx_v_single_l, int __pyx_v_single_m, int __pyx_v_single_n, unsigned int __pyx_v_single_mode, unsigned int __pyx_v_Spheroidal, PyObject *__pyx_v_interpolants, unsigned int __pyx_v_qnm_fit); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNS_2waveform(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self, PyArrayObject *__pyx_v_times); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNS_2t0___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNS_2t0_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNS_5t_ref___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNS_5t_ref_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNS_2Mf___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNS_2Mf_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNS_2af___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNS_2af_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNS_3eta___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNS_3eta_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNS_1r___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNS_1r_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNS_4iota___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNS_4iota_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNS_3phi___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNS_3phi_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNS_10TGR_params___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNS_10TGR_params_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNS_10TGR_params_4__del__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNS_8single_l___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNS_8single_l_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNS_8single_m___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNS_8single_m_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNS_8single_n___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNS_8single_n_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNS_11single_mode___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNS_11single_mode_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNS_10Spheroidal___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNS_10Spheroidal_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNS_12interpolants___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNS_12interpolants_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNS_12interpolants_4__del__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNS_7qnm_fit___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNS_7qnm_fit_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNS_10multipoles___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNS_10multipoles_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNS_10multipoles_4__del__(struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNS_4__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNS_6__setstate_cython__(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_MMRDNS *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNP___cinit__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self, double __pyx_v_t0, double __pyx_v_t_ref, double __pyx_v_Mf, double __pyx_v_af, double __pyx_v_Mi, double __pyx_v_eta, double __pyx_v_chi_s, double __pyx_v_chi_a, double __pyx_v_r, double __pyx_v_iota, double __pyx_v_phi, PyObject *__pyx_v_TGR_params, PyObject *__pyx_v_modes, unsigned int __pyx_v_geom, unsigned int __pyx_v_qnm_fit, PyObject *__pyx_v_qnm_cached, PyObject *__pyx_v_interpolants); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNP_2waveform(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self, PyArrayObject *__pyx_v_times); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNP_2t0___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNP_2t0_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNP_5t_ref___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNP_5t_ref_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNP_2Mf___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNP_2Mf_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNP_2af___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNP_2af_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNP_2Mi___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNP_2Mi_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNP_3eta___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNP_3eta_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNP_5chi_s___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNP_5chi_s_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNP_5chi_a___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNP_5chi_a_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNP_1r___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNP_1r_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNP_4iota___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNP_4iota_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNP_3phi___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNP_3phi_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNP_10TGR_params___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNP_10TGR_params_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNP_10TGR_params_4__del__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNP_5modes___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNP_5modes_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNP_5modes_4__del__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNP_4geom___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNP_4geom_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNP_7qnm_fit___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNP_7qnm_fit_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNP_12interpolants___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNP_12interpolants_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNP_12interpolants_4__del__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNP_10qnm_cached___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNP_10qnm_cached_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNP_10qnm_cached_4__del__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNP_5delta___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNP_5delta_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNP_10multipoles___get__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNP_10multipoles_2__set__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_6MMRDNP_10multipoles_4__del__(struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNP_4__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6MMRDNP_6__setstate_cython__(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_MMRDNP *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* proto */
static int __pyx_pf_6pyRing_8waveform_8KHS_2012___cinit__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self, double __pyx_v_t0, double __pyx_v_t_ref, double __pyx_v_Mf, double __pyx_v_af, double __pyx_v_eta, double __pyx_v_chi_eff, double __pyx_v_r, double __pyx_v_iota, double __pyx_v_phi, PyObject *__pyx_v_TGR_params, int __pyx_v_single_l, int __pyx_v_single_m, unsigned int __pyx_v_single_mode); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_8KHS_2012_2waveform(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self, PyArrayObject *__pyx_v_times); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_8KHS_2012_2t0___get__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_8KHS_2012_2t0_2__set__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_8KHS_2012_5t_ref___get__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_8KHS_2012_5t_ref_2__set__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_8KHS_2012_2Mf___get__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_8KHS_2012_2Mf_2__set__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_8KHS_2012_2af___get__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_8KHS_2012_2af_2__set__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_8KHS_2012_3eta___get__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_8KHS_2012_3eta_2__set__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_8KHS_2012_7chi_eff___get__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_8KHS_2012_7chi_eff_2__set__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_8KHS_2012_1r___get__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_8KHS_2012_1r_2__set__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_8KHS_2012_4iota___get__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_8KHS_2012_4iota_2__set__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_8KHS_2012_3phi___get__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_8KHS_2012_3phi_2__set__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_8KHS_2012_10TGR_params___get__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_8KHS_2012_10TGR_params_2__set__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_8KHS_2012_10TGR_params_4__del__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_8KHS_2012_8single_l___get__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_8KHS_2012_8single_l_2__set__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_8KHS_2012_8single_m___get__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_8KHS_2012_8single_m_2__set__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_8KHS_2012_11single_mode___get__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_8KHS_2012_11single_mode_2__set__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_8KHS_2012_10multipoles___get__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_8KHS_2012_10multipoles_2__set__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_8KHS_2012_10multipoles_4__del__(struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_8KHS_2012_4__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_8KHS_2012_6__setstate_cython__(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_KHS_2012 *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM___cinit__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, double __pyx_v_t0, double __pyx_v_m1, double __pyx_v_m2, double __pyx_v_chi1, double __pyx_v_chi2, PyObject *__pyx_v_phases, double __pyx_v_r, double __pyx_v_iota, double __pyx_v_phi, PyObject *__pyx_v_modes, PyObject *__pyx_v_TGR_params, unsigned int __pyx_v_geom, PyObject *__pyx_v_NR_fit_coeffs); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_2EOBPM_SetupFitCoefficients(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, int __pyx_v_l, int __pyx_v_m, PyObject *__pyx_v_NR_fit_coeffs); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_4TEOBPM_Amplitude(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, double __pyx_v_tau, double __pyx_v_sigma_real, double __pyx_v_a1, double __pyx_v_a2, double __pyx_v_a3, double __pyx_v_a4); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_6TEOBPM_Phase(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, double __pyx_v_tau, double __pyx_v_sigma_imag, double __pyx_v_phi_0, double __pyx_v_p1, double __pyx_v_p2, double __pyx_v_p3, double __pyx_v_p4); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_8waveform(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, PyArrayObject *__pyx_v_times); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_10sym_mass_ratio(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_12X_1(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_14X_2(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_16X_12(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_18a_0(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_20a_12(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_22S_hat(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_24S_bar(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_26alpha1(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, int __pyx_v_l, int __pyx_v_m); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_28alpha21(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, int __pyx_v_l, int __pyx_v_m); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_30omega1(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, int __pyx_v_l, int __pyx_v_m); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_32c3_A(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, int __pyx_v_l, int __pyx_v_m); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_34c3_phi(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, int __pyx_v_l, int __pyx_v_m); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_36c4_phi(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, int __pyx_v_l, int __pyx_v_m); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_38dOmega(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, double __pyx_v_omega1, double __pyx_v_omega_peak); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_40amplitude_peak(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, double __pyx_v_omega_peak, int __pyx_v_l, int __pyx_v_m); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_42omega_peak(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, int __pyx_v_l, int __pyx_v_m); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_44JimenezFortezaRemnantMass(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_46JimenezFortezaRemnantSpin(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_48DeltaT(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, int __pyx_v_l, int __pyx_v_m); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_50DeltaPhi(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, int __pyx_v_l, int __pyx_v_m); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_2t0___get__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_2t0_2__set__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_2m1___get__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_2m1_2__set__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_2m2___get__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_2m2_2__set__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_4chi1___get__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_4chi1_2__set__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_4chi2___get__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_4chi2_2__set__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_6phases___get__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_6phases_2__set__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_6phases_4__del__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_1M___get__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_1M_2__set__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_1r___get__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_1r_2__set__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_4iota___get__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_4iota_2__set__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_3phi___get__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_3phi_2__set__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_5modes___get__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_5modes_2__set__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_5modes_4__del__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_10full_modes___get__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_10full_modes_2__set__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_10TGR_params___get__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_10TGR_params_2__set__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_10TGR_params_4__del__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_4geom___get__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_4geom_2__set__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_13NR_fit_coeffs___get__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_13NR_fit_coeffs_2__set__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_13NR_fit_coeffs_4__del__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_10multipoles___get__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_10multipoles_2__set__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_10multipoles_4__del__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_16fit_coefficients___get__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_16fit_coefficients_2__set__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_16fit_coefficients_4__del__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_2nu___get__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_2nu_2__set__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_2X1___get__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_2X1_2__set__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_2X2___get__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_2X2_2__set__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_3X12___get__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_3X12_2__set__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_2a0___get__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_2a0_2__set__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_3a12___get__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_3a12_2__set__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_4Shat___get__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_4Shat_2__set__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_4Sbar___get__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_4Sbar_2__set__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_2Mf___get__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_2Mf_2__set__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_2af___get__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6TEOBPM_2af_2__set__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_52__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6TEOBPM_54__setstate_cython__(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* proto */
static int __pyx_pf_6pyRing_8waveform_6IMR_WF___cinit__(struct __pyx_obj_6pyRing_8waveform_IMR_WF *__pyx_v_self, double __pyx_v_m1, double __pyx_v_m2, double __pyx_v_s1z, double __pyx_v_s2z, double __pyx_v_dist, double __pyx_v_cosiota, double __pyx_v_phi, double __pyx_v_t0, double __pyx_v_dt, double __pyx_v_starttime, double __pyx_v_signal_seglen); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6IMR_WF_2waveform(struct __pyx_obj_6pyRing_8waveform_IMR_WF *__pyx_v_self, PyArrayObject *__pyx_v_times); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6IMR_WF_2m1___get__(struct __pyx_obj_6pyRing_8waveform_IMR_WF *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6IMR_WF_2m1_2__set__(struct __pyx_obj_6pyRing_8waveform_IMR_WF *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6IMR_WF_2m2___get__(struct __pyx_obj_6pyRing_8waveform_IMR_WF *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6IMR_WF_2m2_2__set__(struct __pyx_obj_6pyRing_8waveform_IMR_WF *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6IMR_WF_3s1z___get__(struct __pyx_obj_6pyRing_8waveform_IMR_WF *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6IMR_WF_3s1z_2__set__(struct __pyx_obj_6pyRing_8waveform_IMR_WF *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6IMR_WF_3s2z___get__(struct __pyx_obj_6pyRing_8waveform_IMR_WF *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6IMR_WF_3s2z_2__set__(struct __pyx_obj_6pyRing_8waveform_IMR_WF *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6IMR_WF_4dist___get__(struct __pyx_obj_6pyRing_8waveform_IMR_WF *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6IMR_WF_4dist_2__set__(struct __pyx_obj_6pyRing_8waveform_IMR_WF *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6IMR_WF_7cosiota___get__(struct __pyx_obj_6pyRing_8waveform_IMR_WF *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6IMR_WF_7cosiota_2__set__(struct __pyx_obj_6pyRing_8waveform_IMR_WF *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6IMR_WF_3phi___get__(struct __pyx_obj_6pyRing_8waveform_IMR_WF *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6IMR_WF_3phi_2__set__(struct __pyx_obj_6pyRing_8waveform_IMR_WF *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6IMR_WF_2t0___get__(struct __pyx_obj_6pyRing_8waveform_IMR_WF *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6IMR_WF_2t0_2__set__(struct __pyx_obj_6pyRing_8waveform_IMR_WF *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6IMR_WF_2dt___get__(struct __pyx_obj_6pyRing_8waveform_IMR_WF *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6IMR_WF_2dt_2__set__(struct __pyx_obj_6pyRing_8waveform_IMR_WF *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6IMR_WF_9starttime___get__(struct __pyx_obj_6pyRing_8waveform_IMR_WF *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6IMR_WF_9starttime_2__set__(struct __pyx_obj_6pyRing_8waveform_IMR_WF *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6IMR_WF_13signal_seglen___get__(struct __pyx_obj_6pyRing_8waveform_IMR_WF *__pyx_v_self); /* proto */
static int __pyx_pf_6pyRing_8waveform_6IMR_WF_13signal_seglen_2__set__(struct __pyx_obj_6pyRing_8waveform_IMR_WF *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6IMR_WF_4__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_IMR_WF *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_6IMR_WF_6__setstate_cython__(CYTHON_UNUSED struct __pyx_obj_6pyRing_8waveform_IMR_WF *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* proto */
static PyObject *__pyx_pf_6pyRing_8waveform_4__pyx_unpickle_SWSH(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v___pyx_type, long __pyx_v___pyx_checksum, PyObject *__pyx_v___pyx_state); /* proto */
static PyObject *__pyx_tp_new_6pyRing_8waveform_QNM(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_6pyRing_8waveform_QNM_fit(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_6pyRing_8waveform_QNM_ParSpec(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_6pyRing_8waveform_QNM_220_area_quantized(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_6pyRing_8waveform_QNM_braneworld_fit(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_6pyRing_8waveform_Damped_sinusoids(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_6pyRing_8waveform_Morlet_Gabor_wavelets(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_6pyRing_8waveform_SWSH(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_6pyRing_8waveform_KerrBH(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_6pyRing_8waveform_MMRDNS(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_6pyRing_8waveform_MMRDNP(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_6pyRing_8waveform_KHS_2012(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_6pyRing_8waveform_TEOBPM(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_6pyRing_8waveform_IMR_WF(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_array(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_Enum(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_memoryview(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new__memoryviewslice(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
/* #### Code section: late_includes ### */
/* #### Code section: module_state ### */
/* SmallCodeConfig */
#ifndef CYTHON_SMALL_CODE
#if defined(__clang__)
    #define CYTHON_SMALL_CODE
#elif defined(__GNUC__) && (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 3))
    #define CYTHON_SMALL_CODE __attribute__((cold))
#else
    #define CYTHON_SMALL_CODE
#endif
#endif

typedef struct {
  PyObject *__pyx_d;
  PyObject *__pyx_b;
  PyObject *__pyx_cython_runtime;
  PyObject *__pyx_empty_tuple;
  PyObject *__pyx_empty_bytes;
  PyObject *__pyx_empty_unicode;
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#define __pyx_n_u_Amp_MMRDNP __pyx_string_tab[8]
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#define __pyx_kp_u_Cannot_index_with_type __pyx_string_tab[21]
#define __pyx_kp_u_Cannot_transpose_memoryview_with __pyx_string_tab[22]
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#define __pyx_n_u_Damped_sinusoids_waveform __pyx_string_tab[26]
#define __pyx_n_u_DeltaPhi __pyx_string_tab[27]
#define __pyx_n_u_DeltaT __pyx_string_tab[28]
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#define __pyx_n_u_IMR_WF___reduce_cython __pyx_string_tab[35]
#define __pyx_n_u_IMR_WF___setstate_cython __pyx_string_tab[36]
#define __pyx_n_u_IMR_WF_waveform __pyx_string_tab[37]
#define __pyx_kp_u_If_quantization_of_the_horizon_a __pyx_string_tab[38]
#define __pyx_n_u_ImportError __pyx_string_tab[39]
#define __pyx_kp_u_Incompatible_checksums_0x_x_vs_0 __pyx_string_tab[40]
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#define __pyx_kp_u_Invalid_quadratic_term_selected __pyx_string_tab[49]
#define __pyx_kp_u_Invalid_shape_in_axis __pyx_string_tab[50]
#define __pyx_n_u_JimenezFortezaRemnantMass __pyx_string_tab[51]
#define __pyx_n_u_JimenezFortezaRemnantSpin __pyx_string_tab[52]
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#define __pyx_n_u_KerrBH___reduce_cython __pyx_string_tab[65]
#define __pyx_n_u_KerrBH___setstate_cython __pyx_string_tab[66]
#define __pyx_n_u_KerrBH_waveform __pyx_string_tab[67]
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#define __pyx_kp_u_MMRDNS_Mass_cannot_be_negative_o __pyx_string_tab[84]
#define __pyx_kp_u_MMRDNS_Spin_cannot_be_grater_tha __pyx_string_tab[85]
#define __pyx_n_u_MMRDNS___reduce_cython __pyx_string_tab[86]
#define __pyx_n_u_MMRDNS___setstate_cython __pyx_string_tab[87]
#define __pyx_n_u_MMRDNS_waveform __pyx_string_tab[88]
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#define __pyx_n_u_MTSUN_SI __pyx_string_tab[90]
#define __pyx_n_u_MemoryError __pyx_string_tab[91]
#define __pyx_kp_u_MemoryView_of __pyx_string_tab[92]
#define __pyx_n_u_Mf __pyx_string_tab[93]
#define __pyx_n_u_Mi __pyx_string_tab[94]
#define __pyx_n_u_Morlet_Gabor_wavelets __pyx_string_tab[95]
#define __pyx_n_u_Morlet_Gabor_wavelets___reduce_c __pyx_string_tab[96]
#define __pyx_n_u_Morlet_Gabor_wavelets___setstate __pyx_string_tab[97]
#define __pyx_n_u_Morlet_Gabor_wavelets_waveform __pyx_string_tab[98]
#define __pyx_n_u_NR_amp __pyx_string_tab[99]
#define __pyx_n_u_NR_fit_coeffs __pyx_string_tab[100]
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#define __pyx_n_u_ParSpec_coeffs_tau_order_high_sp __pyx_string_tab[112]
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#define __pyx_n_u_Q __pyx_string_tab[114]
#define __pyx_n_u_QNM __pyx_string_tab[115]
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#define __pyx_n_u_QNM_220_area_quantized_tau_QA __pyx_string_tab[121]
#define __pyx_n_u_QNM_ParSpec __pyx_string_tab[122]
#define __pyx_n_u_QNM_ParSpec___reduce_cython __pyx_string_tab[123]
#define __pyx_n_u_QNM_ParSpec___setstate_cython __pyx_string_tab[124]
#define __pyx_n_u_QNM_ParSpec_f __pyx_string_tab[125]
#define __pyx_n_u_QNM_ParSpec_tau __pyx_string_tab[126]
#define __pyx_n_u_QNM___reduce_cython __pyx_string_tab[127]
#define __pyx_n_u_QNM___setstate_cython __pyx_string_tab[128]
#define __pyx_n_u_QNM_braneworld_fit __pyx_string_tab[129]
#define __pyx_n_u_QNM_braneworld_fit___reduce_cyth __pyx_string_tab[130]
#define __pyx_n_u_QNM_braneworld_fit___setstate_cy __pyx_string_tab[131]
#define __pyx_n_u_QNM_braneworld_fit_f_BW __pyx_string_tab[132]
#define __pyx_n_u_QNM_braneworld_fit_q_BW __pyx_string_tab[133]
#define __pyx_n_u_QNM_braneworld_fit_tau_BW __pyx_string_tab[134]
#define __pyx_n_u_QNM_f __pyx_string_tab[135]
#define __pyx_n_u_QNM_f_BW __pyx_string_tab[136]
#define __pyx_n_u_QNM_f_KN __pyx_string_tab[137]
#define __pyx_n_u_QNM_fit __pyx_string_tab[138]
#define __pyx_n_u_QNM_fit___reduce_cython __pyx_string_tab[139]
#define __pyx_n_u_QNM_fit___setstate_cython __pyx_string_tab[140]
#define __pyx_n_u_QNM_fit_f __pyx_string_tab[141]
#define __pyx_n_u_QNM_fit_f_KN __pyx_string_tab[142]
#define __pyx_n_u_QNM_fit_q __pyx_string_tab[143]
#define __pyx_n_u_QNM_fit_q_KN __pyx_string_tab[144]
#define __pyx_n_u_QNM_fit_tau __pyx_string_tab[145]
#define __pyx_n_u_QNM_fit_tau_KN __pyx_string_tab[146]
#define __pyx_kp_u_QNM_m_cannot_be_greater_than_l_i __pyx_string_tab[147]
#define __pyx_n_u_QNM_tau __pyx_string_tab[148]
#define __pyx_n_u_QNM_tau_BW __pyx_string_tab[149]
#define __pyx_n_u_QNM_tau_KN __pyx_string_tab[150]
#define __pyx_n_u_SWSH __pyx_string_tab[151]
#define __pyx_n_u_SWSH___reduce_cython __pyx_string_tab[152]
#define __pyx_n_u_SWSH___setstate_cython __pyx_string_tab[153]
#define __pyx_n_u_SWSH_evaluate __pyx_string_tab[154]
#define __pyx_n_u_S_bar __pyx_string_tab[155]
#define __pyx_n_u_S_hat __pyx_string_tab[156]
#define __pyx_n_u_Sequence __pyx_string_tab[157]
#define __pyx_n_u_Spheroidal __pyx_string_tab[158]
#define __pyx_kp_u_Step_may_not_be_zero_axis_d __pyx_string_tab[159]
#define __pyx_n_u_TEOBPM __pyx_string_tab[160]
#define __pyx_n_u_TEOBPM_Amplitude __pyx_string_tab[161]
#define __pyx_n_u_TEOBPM_DeltaPhi __pyx_string_tab[162]
#define __pyx_n_u_TEOBPM_DeltaT __pyx_string_tab[163]
#define __pyx_kp_u_TEOBPM_Distance_cannot_be_negati __pyx_string_tab[164]
#define __pyx_n_u_TEOBPM_EOBPM_SetupFitCoefficient __pyx_string_tab[165]
#define __pyx_n_u_TEOBPM_JimenezFortezaRemnantMass __pyx_string_tab[166]
#define __pyx_n_u_TEOBPM_JimenezFortezaRemnantSpin __pyx_string_tab[167]
#define __pyx_kp_u_TEOBPM_Masses_cannot_be_negative __pyx_string_tab[168]
#define __pyx_n_u_TEOBPM_Phase __pyx_string_tab[169]
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#define __pyx_n_u_TEOBPM_S_bar __pyx_string_tab[171]
#define __pyx_n_u_TEOBPM_S_hat __pyx_string_tab[172]
#define __pyx_n_u_TEOBPM_TEOBPM_Amplitude __pyx_string_tab[173]
#define __pyx_n_u_TEOBPM_TEOBPM_Phase __pyx_string_tab[174]
#define __pyx_kp_u_TEOBPM_The_modes_list_contains_r __pyx_string_tab[175]
#define __pyx_n_u_TEOBPM_X_1 __pyx_string_tab[176]
#define __pyx_n_u_TEOBPM_X_12 __pyx_string_tab[177]
#define __pyx_n_u_TEOBPM_X_2 __pyx_string_tab[178]
#define __pyx_kp_u_TEOBPM_You_have_chosen_at_least __pyx_string_tab[179]
#define __pyx_n_u_TEOBPM___reduce_cython __pyx_string_tab[180]
#define __pyx_n_u_TEOBPM___setstate_cython __pyx_string_tab[181]
#define __pyx_n_u_TEOBPM_a_0 __pyx_string_tab[182]
#define __pyx_n_u_TEOBPM_a_12 __pyx_string_tab[183]
#define __pyx_n_u_TEOBPM_alpha1 __pyx_string_tab[184]
#define __pyx_n_u_TEOBPM_alpha21 __pyx_string_tab[185]
#define __pyx_n_u_TEOBPM_amplitude_peak __pyx_string_tab[186]
#define __pyx_n_u_TEOBPM_c3_A __pyx_string_tab[187]
#define __pyx_n_u_TEOBPM_c3_phi __pyx_string_tab[188]
#define __pyx_n_u_TEOBPM_c4_phi __pyx_string_tab[189]
#define __pyx_n_u_TEOBPM_dOmega __pyx_string_tab[190]
#define __pyx_n_u_TEOBPM_omega1 __pyx_string_tab[191]
#define __pyx_n_u_TEOBPM_omega_peak __pyx_string_tab[192]
#define __pyx_n_u_TEOBPM_sym_mass_ratio __pyx_string_tab[193]
#define __pyx_n_u_TEOBPM_waveform __pyx_string_tab[194]
#define __pyx_n_u_TGR_params __pyx_string_tab[195]
#define __pyx_kp_u_The_QNM_coming_from_quantized_ar __pyx_string_tab[196]
#define __pyx_n_u_TypeError __pyx_string_tab[197]
#define __pyx_kp_u_Unable_to_convert_item_to_object __pyx_string_tab[198]
#define __pyx_n_u_ValueError __pyx_string_tab[199]
#define __pyx_n_u_View_MemoryView __pyx_string_tab[200]
#define __pyx_kp_u_When_fixing_the_quadratic_amplit __pyx_string_tab[201]
#define __pyx_n_u_X_1 __pyx_string_tab[202]
#define __pyx_n_u_X_12 __pyx_string_tab[203]
#define __pyx_n_u_X_2 __pyx_string_tab[204]
#define __pyx_kp_u_You_deselected_qnm_fit_without_p __pyx_string_tab[205]
#define __pyx_kp_u__2 __pyx_string_tab[206]
#define __pyx_kp_u__3 __pyx_string_tab[207]
#define __pyx_kp_u__4 __pyx_string_tab[208]
#define __pyx_kp_u__5 __pyx_string_tab[209]
#define __pyx_kp_u__7 __pyx_string_tab[210]
#define __pyx_n_u_a __pyx_string_tab[211]
#define __pyx_n_u_a1 __pyx_string_tab[212]
#define __pyx_n_u_a2 __pyx_string_tab[213]
#define __pyx_n_u_a3 __pyx_string_tab[214]
#define __pyx_n_u_a4 __pyx_string_tab[215]
#define __pyx_n_u_a_0 __pyx_string_tab[216]
#define __pyx_n_u_a_12 __pyx_string_tab[217]
#define __pyx_n_u_abc __pyx_string_tab[218]
#define __pyx_n_u_abs __pyx_string_tab[219]
#define __pyx_kp_u_add_note __pyx_string_tab[220]
#define __pyx_n_u_af __pyx_string_tab[221]
#define __pyx_n_u_allocate_buffer __pyx_string_tab[222]
#define __pyx_n_u_alpha __pyx_string_tab[223]
#define __pyx_n_u_alpha1 __pyx_string_tab[224]
#define __pyx_n_u_alpha21 __pyx_string_tab[225]
#define __pyx_n_u_amp_non_prec_sym __pyx_string_tab[226]
#define __pyx_n_u_amplitude_peak __pyx_string_tab[227]
#define __pyx_n_u_amps __pyx_string_tab[228]
#define __pyx_kp_u_and __pyx_string_tab[229]
#define __pyx_n_u_array __pyx_string_tab[230]
#define __pyx_n_u_asyncio_coroutines __pyx_string_tab[231]
#define __pyx_kp_u_at_0x __pyx_string_tab[232]
#define __pyx_n_u_base __pyx_string_tab[233]
#define __pyx_n_u_beta __pyx_string_tab[234]
#define __pyx_n_u_braneworld __pyx_string_tab[235]
#define __pyx_n_u_c __pyx_string_tab[236]
#define __pyx_n_u_c3A __pyx_string_tab[237]
#define __pyx_n_u_c3_A __pyx_string_tab[238]
#define __pyx_n_u_c3_phi __pyx_string_tab[239]
#define __pyx_n_u_c3p __pyx_string_tab[240]
#define __pyx_n_u_c4_phi __pyx_string_tab[241]
#define __pyx_n_u_c4p __pyx_string_tab[242]
#define __pyx_n_u_charge __pyx_string_tab[243]
#define __pyx_n_u_chi1 __pyx_string_tab[244]
#define __pyx_n_u_chi2 __pyx_string_tab[245]
#define __pyx_n_u_chi_a __pyx_string_tab[246]
#define __pyx_n_u_chi_eff __pyx_string_tab[247]
#define __pyx_n_u_chi_s __pyx_string_tab[248]
#define __pyx_n_u_class __pyx_string_tab[249]
#define __pyx_n_u_class_getitem __pyx_string_tab[250]
#define __pyx_n_u_cline_in_traceback __pyx_string_tab[251]
#define __pyx_kp_u_collections_abc __pyx_string_tab[252]
#define __pyx_n_u_complex __pyx_string_tab[253]
#define __pyx_n_u_conj __pyx_string_tab[254]
#define __pyx_kp_u_contiguous_and_direct __pyx_string_tab[255]
#define __pyx_kp_u_contiguous_and_indirect __pyx_string_tab[256]
#define __pyx_n_u_cos __pyx_string_tab[257]
#define __pyx_n_u_cosiota __pyx_string_tab[258]
#define __pyx_n_u_count __pyx_string_tab[259]
#define __pyx_n_u_dOmega __pyx_string_tab[260]
#define __pyx_n_u_damped_sinusoid __pyx_string_tab[261]
#define __pyx_kp_u_data_NR_data_ParSpec_coefficient __pyx_string_tab[262]
#define __pyx_kp_u_data_NR_data_ParSpec_coefficient_2 __pyx_string_tab[263]
#define __pyx_kp_u_data_NR_data_berti_qnm_fits_txt __pyx_string_tab[264]
#define __pyx_n_u_dict __pyx_string_tab[265]
#define __pyx_n_u_dict_2 __pyx_string_tab[266]
#define __pyx_n_u_diff __pyx_string_tab[267]
#define __pyx_kp_u_disable __pyx_string_tab[268]
#define __pyx_n_u_dist __pyx_string_tab[269]
#define __pyx_kp_u_domega __pyx_string_tab[270]
#define __pyx_kp_u_domega__0 __pyx_string_tab[271]
#define __pyx_n_u_double __pyx_string_tab[272]
#define __pyx_n_u_dt __pyx_string_tab[273]
#define __pyx_n_u_dt_vec __pyx_string_tab[274]
#define __pyx_kp_u_dtau __pyx_string_tab[275]
#define __pyx_kp_u_dtau__0 __pyx_string_tab[276]
#define __pyx_n_u_dtype __pyx_string_tab[277]
#define __pyx_n_u_dtype_is_object __pyx_string_tab[278]
#define __pyx_n_u_dw_vec __pyx_string_tab[279]
#define __pyx_kp_u_enable __pyx_string_tab[280]
#define __pyx_n_u_encode __pyx_string_tab[281]
#define __pyx_n_u_enumerate __pyx_string_tab[282]
#define __pyx_n_u_error __pyx_string_tab[283]
#define __pyx_n_u_eta __pyx_string_tab[284]
#define __pyx_n_u_evaluate __pyx_string_tab[285]
#define __pyx_n_u_exp __pyx_string_tab[286]
#define __pyx_n_u_f __pyx_string_tab[287]
#define __pyx_n_u_f1 __pyx_string_tab[288]
#define __pyx_n_u_f2 __pyx_string_tab[289]
#define __pyx_n_u_f3 __pyx_string_tab[290]
#define __pyx_n_u_f_BW __pyx_string_tab[291]
#define __pyx_n_u_f_KN __pyx_string_tab[292]
#define __pyx_n_u_f_QA __pyx_string_tab[293]
#define __pyx_n_u_fact __pyx_string_tab[294]
#define __pyx_n_u_factorial __pyx_string_tab[295]
#define __pyx_n_u_fit __pyx_string_tab[296]
#define __pyx_n_u_flags __pyx_string_tab[297]
#define __pyx_n_u_format __pyx_string_tab[298]
#define __pyx_n_u_fortran __pyx_string_tab[299]
#define __pyx_n_u_freq __pyx_string_tab[300]
#define __pyx_n_u_fromkeys __pyx_string_tab[301]
#define __pyx_n_u_func __pyx_string_tab[302]
#define __pyx_n_u_gamma __pyx_string_tab[303]
#define __pyx_kp_u_gc __pyx_string_tab[304]
#define __pyx_n_u_genfromtxt __pyx_string_tab[305]
#define __pyx_n_u_geom __pyx_string_tab[306]
#define __pyx_n_u_getstate __pyx_string_tab[307]
#define __pyx_kp_u_got __pyx_string_tab[308]
#define __pyx_kp_u_got_differing_extents_in_dimensi __pyx_string_tab[309]
#define __pyx_n_u_high_spin __pyx_string_tab[310]
#define __pyx_n_u_i __pyx_string_tab[311]
#define __pyx_n_u_id __pyx_string_tab[312]
#define __pyx_n_u_imag __pyx_string_tab[313]
#define __pyx_n_u_import __pyx_string_tab[314]
#define __pyx_n_u_import_datafile_path __pyx_string_tab[315]
#define __pyx_n_u_index __pyx_string_tab[316]
#define __pyx_n_u_initializing __pyx_string_tab[317]
#define __pyx_n_u_interpolants __pyx_string_tab[318]
#define __pyx_n_u_interpolate_freqs __pyx_string_tab[319]
#define __pyx_n_u_interpolate_taus __pyx_string_tab[320]
#define __pyx_n_u_iota __pyx_string_tab[321]
#define __pyx_n_u_is_coroutine __pyx_string_tab[322]
#define __pyx_kp_u_isenabled __pyx_string_tab[323]
#define __pyx_n_u_items __pyx_string_tab[324]
#define __pyx_n_u_itemsize __pyx_string_tab[325]
#define __pyx_kp_u_itemsize_0_for_cython_array __pyx_string_tab[326]
#define __pyx_n_u_keys __pyx_string_tab[327]
#define __pyx_n_u_l __pyx_string_tab[328]
#define __pyx_n_u_l_BW __pyx_string_tab[329]
#define __pyx_n_u_l_QA __pyx_string_tab[330]
#define __pyx_n_u_lal __pyx_string_tab[331]
#define __pyx_n_u_lalsim __pyx_string_tab[332]
#define __pyx_n_u_lalsimulation __pyx_string_tab[333]
#define __pyx_n_u_m __pyx_string_tab[334]
#define __pyx_n_u_m1 __pyx_string_tab[335]
#define __pyx_n_u_m2 __pyx_string_tab[336]
#define __pyx_n_u_m_BW __pyx_string_tab[337]
#define __pyx_n_u_m_QA __pyx_string_tab[338]
#define __pyx_n_u_main __pyx_string_tab[339]
#define __pyx_n_u_math __pyx_string_tab[340]
#define __pyx_n_u_memview __pyx_string_tab[341]
#define __pyx_n_u_mode __pyx_string_tab[342]
#define __pyx_n_u_modes __pyx_string_tab[343]
#define __pyx_n_u_module __pyx_string_tab[344]
#define __pyx_n_u_n __pyx_string_tab[345]
#define __pyx_n_u_n_BW __pyx_string_tab[346]
#define __pyx_n_u_n_QA __pyx_string_tab[347]
#define __pyx_n_u_name __pyx_string_tab[348]
#define __pyx_n_u_name_2 __pyx_string_tab[349]
#define __pyx_n_u_names __pyx_string_tab[350]
#define __pyx_n_u_ndim __pyx_string_tab[351]
#define __pyx_n_u_new __pyx_string_tab[352]
#define __pyx_kp_u_no_default___reduce___due_to_non __pyx_string_tab[353]
#define __pyx_n_u_np __pyx_string_tab[354]
#define __pyx_n_u_numpy __pyx_string_tab[355]
#define __pyx_kp_u_numpy__core_multiarray_failed_to __pyx_string_tab[356]
#define __pyx_kp_u_numpy__core_umath_failed_to_impo __pyx_string_tab[357]
#define __pyx_n_u_obj __pyx_string_tab[358]
#define __pyx_kp_u_object __pyx_string_tab[359]
#define __pyx_n_u_omega1 __pyx_string_tab[360]
#define __pyx_n_u_omega_peak __pyx_string_tab[361]
#define __pyx_n_u_omg_peak __pyx_string_tab[362]
#define __pyx_n_u_os __pyx_string_tab[363]
#define __pyx_n_u_p __pyx_string_tab[364]
#define __pyx_n_u_p1 __pyx_string_tab[365]
#define __pyx_n_u_p2 __pyx_string_tab[366]
#define __pyx_n_u_p3 __pyx_string_tab[367]
#define __pyx_n_u_p4 __pyx_string_tab[368]
#define __pyx_n_u_p_1 __pyx_string_tab[369]
#define __pyx_n_u_p_2 __pyx_string_tab[370]
#define __pyx_n_u_pack __pyx_string_tab[371]
#define __pyx_n_u_phases __pyx_string_tab[372]
#define __pyx_n_u_phi __pyx_string_tab[373]
#define __pyx_n_u_phi_0 __pyx_string_tab[374]
#define __pyx_n_u_phi_1 __pyx_string_tab[375]
#define __pyx_n_u_phi_2 __pyx_string_tab[376]
#define __pyx_n_u_pi __pyx_string_tab[377]
#define __pyx_n_u_pickle __pyx_string_tab[378]
#define __pyx_n_u_pop __pyx_string_tab[379]
#define __pyx_n_u_pyRing __pyx_string_tab[380]
#define __pyx_n_u_pyRing_utils __pyx_string_tab[381]
#define __pyx_n_u_pyRing_waveform __pyx_string_tab[382]
#define __pyx_kp_u_pyRing_waveform_pyx __pyx_string_tab[383]
#define __pyx_n_u_pykerr __pyx_string_tab[384]
#define __pyx_n_u_pyx_PickleError __pyx_string_tab[385]
#define __pyx_n_u_pyx_capi __pyx_string_tab[386]
#define __pyx_n_u_pyx_checksum __pyx_string_tab[387]
#define __pyx_n_u_pyx_result __pyx_string_tab[388]
#define __pyx_n_u_pyx_state __pyx_string_tab[389]
#define __pyx_n_u_pyx_type __pyx_string_tab[390]
#define __pyx_n_u_pyx_unpickle_Enum __pyx_string_tab[391]
#define __pyx_n_u_pyx_unpickle_SWSH __pyx_string_tab[392]
#define __pyx_n_u_pyx_vtable __pyx_string_tab[393]
#define __pyx_n_u_q __pyx_string_tab[394]
#define __pyx_n_u_q1 __pyx_string_tab[395]
#define __pyx_n_u_q2 __pyx_string_tab[396]
#define __pyx_n_u_q3 __pyx_string_tab[397]
#define __pyx_n_u_q_BW __pyx_string_tab[398]
#define __pyx_n_u_q_GR __pyx_string_tab[399]
#define __pyx_n_u_q_KN __pyx_string_tab[400]
#define __pyx_n_u_qnm_cached __pyx_string_tab[401]
#define __pyx_n_u_qnm_fit __pyx_string_tab[402]
#define __pyx_n_u_quad_lin_prop __pyx_string_tab[403]
#define __pyx_n_u_quadratic_modes __pyx_string_tab[404]
#define __pyx_n_u_qualname __pyx_string_tab[405]
#define __pyx_n_u_r __pyx_string_tab[406]
#define __pyx_n_u_range __pyx_string_tab[407]
#define __pyx_n_u_real __pyx_string_tab[408]
#define __pyx_n_u_reduce __pyx_string_tab[409]
#define __pyx_n_u_reduce_cython __pyx_string_tab[410]
#define __pyx_n_u_reduce_ex __pyx_string_tab[411]
#define __pyx_n_u_reference_amplitude __pyx_string_tab[412]
#define __pyx_n_u_register __pyx_string_tab[413]
#define __pyx_n_u_resize_time_series __pyx_string_tab[414]
#define __pyx_n_u_s __pyx_string_tab[415]
#define __pyx_n_u_s1z __pyx_string_tab[416]
#define __pyx_n_u_s2z __pyx_string_tab[417]
#define __pyx_n_u_scipy __pyx_string_tab[418]
#define __pyx_n_u_self __pyx_string_tab[419]
#define __pyx_n_u_set_name __pyx_string_tab[420]
#define __pyx_n_u_setstate __pyx_string_tab[421]
#define __pyx_n_u_setstate_cython __pyx_string_tab[422]
#define __pyx_n_u_shape __pyx_string_tab[423]
#define __pyx_n_u_sigma_imag __pyx_string_tab[424]
#define __pyx_n_u_sigma_real __pyx_string_tab[425]
#define __pyx_n_u_signal_seglen __pyx_string_tab[426]
#define __pyx_n_u_single_l __pyx_string_tab[427]
#define __pyx_n_u_single_m __pyx_string_tab[428]
#define __pyx_n_u_single_mode __pyx_string_tab[429]
#define __pyx_n_u_single_n __pyx_string_tab[430]
#define __pyx_n_u_size __pyx_string_tab[431]
#define __pyx_n_u_spec __pyx_string_tab[432]
#define __pyx_n_u_spheroidal __pyx_string_tab[433]
#define __pyx_n_u_sqrt __pyx_string_tab[434]
#define __pyx_n_u_start __pyx_string_tab[435]
#define __pyx_n_u_starttime __pyx_string_tab[436]
#define __pyx_n_u_state __pyx_string_tab[437]
#define __pyx_n_u_step __pyx_string_tab[438]
#define __pyx_n_u_stop __pyx_string_tab[439]
#define __pyx_kp_u_strided_and_direct __pyx_string_tab[440]
#define __pyx_kp_u_strided_and_direct_or_indirect __pyx_string_tab[441]
#define __pyx_kp_u_strided_and_indirect __pyx_string_tab[442]
#define __pyx_kp_u_stringsource __pyx_string_tab[443]
#define __pyx_n_u_struct __pyx_string_tab[444]
#define __pyx_n_u_sum __pyx_string_tab[445]
#define __pyx_n_u_sym_mass_ratio __pyx_string_tab[446]
#define __pyx_n_u_t __pyx_string_tab[447]
#define __pyx_n_u_t0 __pyx_string_tab[448]
#define __pyx_n_u_t_0 __pyx_string_tab[449]
#define __pyx_kp_u_t_2 __pyx_string_tab[450]
#define __pyx_n_u_t_ref __pyx_string_tab[451]
#define __pyx_n_u_tail_factor __pyx_string_tab[452]
#define __pyx_n_u_tail_parameters __pyx_string_tab[453]
#define __pyx_n_u_tau __pyx_string_tab[454]
#define __pyx_n_u_tau_AQ __pyx_string_tab[455]
#define __pyx_n_u_tau_BW __pyx_string_tab[456]
#define __pyx_n_u_tau_KN __pyx_string_tab[457]
#define __pyx_n_u_tau_QA __pyx_string_tab[458]
#define __pyx_n_u_test __pyx_string_tab[459]
#define __pyx_n_u_theta __pyx_string_tab[460]
#define __pyx_n_u_times __pyx_string_tab[461]
#define __pyx_kp_u_unable_to_allocate_array_data __pyx_string_tab[462]
#define __pyx_kp_u_unable_to_allocate_shape_and_str __pyx_string_tab[463]
#define __pyx_n_u_unpack __pyx_string_tab[464]
#define __pyx_n_u_update __pyx_string_tab[465]
#define __pyx_n_u_use_setstate __pyx_string_tab[466]
#define __pyx_n_u_v __pyx_string_tab[467]
#define __pyx_kp_u_w __pyx_string_tab[468]
#define __pyx_n_u_waveform __pyx_string_tab[469]
#define __pyx_n_u_x __pyx_string_tab[470]
#define __pyx_n_u_zeros __pyx_string_tab[471]
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 *         if have_step:
 *             negative_step = step < 0
 *             if step == 0:             # <<<<<<<<<<<<<<
 *                 _err_dim(PyExc_ValueError, "Step may not be zero (axis %d)", dim)
 *         else:
*/
      __pyx_t_2 = (__pyx_v_step == 0);
      if (__pyx_t_2) {

        /* "View.MemoryView":824
 *             negative_step = step < 0
 *             if step == 0:
 *                 _err_dim(PyExc_ValueError, "Step may not be zero (axis %d)", dim)             # <<<<<<<<<<<<<<
 *         else:
 *             negative_step = False
*/
        __pyx_t_3 = __pyx_memoryview_err_dim(PyExc_ValueError, __pyx_mstate_global->__pyx_kp_u_Step_may_not_be_zero_axis_d, __pyx_v_dim); if (unlikely(__pyx_t_3 == ((int)-1))) __PYX_ERR(1, 824, __pyx_L1_error)

        /* "View.MemoryView":823
 *         if have_step:
 *             negative_step = step < 0
 *             if step == 0:             # <<<<<<<<<<<<<<
 *                 _err_dim(PyExc_ValueError, "Step may not be zero (axis %d)", dim)
 *         else:
*/
      }

      /* "View.MemoryView":821
 *     else:
 * 
 *         if have_step:             # <<<<<<<<<<<<<<
 *             negative_step = step < 0
 *             if step == 0:
*/
      goto __pyx_L6;
    }

    /* "View.MemoryView":826
 *                 _err_dim(PyExc_ValueError, "Step may not be zero (axis %d)", dim)
 *         else:
 *             negative_step = False             # <<<<<<<<<<<<<<
 *             step = 1
 * 
*/
    /*else*/ {
      __pyx_v_negative_step = 0;

      /* "View.MemoryView":827
 *         else:
 *             negative_step = False
 *             step = 1             # <<<<<<<<<<<<<<
 * 
 * 
*/
      __pyx_v_step = 1;
    }
    __pyx_L6:;

    /* "View.MemoryView":830
 * 
 * 
 *         if have_start:             # <<<<<<<<<<<<<<
 *             if start < 0:
 *                 start += shape
*/
    __pyx_t_2 = (__pyx_v_have_start != 0);
    if (__pyx_t_2) {

      /* "View.MemoryView":831
 * 
 *         if have_start:
 *             if start < 0:             # <<<<<<<<<<<<<<
 *                 start += shape
 *                 if start < 0:
*/
      __pyx_t_2 = (__pyx_v_start < 0);
      if (__pyx_t_2) {

        /* "View.MemoryView":832
 *         if have_start:
 *             if start < 0:
 *                 start += shape             # <<<<<<<<<<<<<<
 *                 if start < 0:
 *                     start = 0
*/
        __pyx_v_start = (__pyx_v_start + __pyx_v_shape);

        /* "View.MemoryView":833
 *             if start < 0:
 *                 start += shape
 *                 if start < 0:             # <<<<<<<<<<<<<<
 *                     start = 0
 *             elif start >= shape:
*/
        __pyx_t_2 = (__pyx_v_start < 0);
        if (__pyx_t_2) {

          /* "View.MemoryView":834
 *                 start += shape
 *                 if start < 0:
 *                     start = 0             # <<<<<<<<<<<<<<
 *             elif start >= shape:
 *                 if negative_step:
*/
          __pyx_v_start = 0;

          /* "View.MemoryView":833
 *             if start < 0:
 *                 start += shape
 *                 if start < 0:             # <<<<<<<<<<<<<<
 *                     start = 0
 *             elif start >= shape:
*/
        }

        /* "View.MemoryView":831
 * 
 *         if have_start:
 *             if start < 0:             # <<<<<<<<<<<<<<
 *                 start += shape
 *                 if start < 0:
*/
        goto __pyx_L9;
      }

      /* "View.MemoryView":835
 *                 if start < 0:
 *                     start = 0
 *             elif start >= shape:             # <<<<<<<<<<<<<<
 *                 if negative_step:
 *                     start = shape - 1
*/
      __pyx_t_2 = (__pyx_v_start >= __pyx_v_shape);
      if (__pyx_t_2) {

        /* "View.MemoryView":836
 *                     start = 0
 *             elif start >= shape:
 *                 if negative_step:             # <<<<<<<<<<<<<<
 *                     start = shape - 1
 *                 else:
*/
        if (__pyx_v_negative_step) {

          /* "View.MemoryView":837
 *             elif start >= shape:
 *                 if negative_step:
 *                     start = shape - 1             # <<<<<<<<<<<<<<
 *                 else:
 *                     start = shape
*/
          __pyx_v_start = (__pyx_v_shape - 1);

          /* "View.MemoryView":836
 *                     start = 0
 *             elif start >= shape:
 *                 if negative_step:             # <<<<<<<<<<<<<<
 *                     start = shape - 1
 *                 else:
*/
          goto __pyx_L11;
        }

        /* "View.MemoryView":839
 *                     start = shape - 1
 *                 else:
 *                     start = shape             # <<<<<<<<<<<<<<
 *         else:
 *             if negative_step:
*/
        /*else*/ {
          __pyx_v_start = __pyx_v_shape;
        }
        __pyx_L11:;

        /* "View.MemoryView":835
 *                 if start < 0:
 *                     start = 0
 *             elif start >= shape:             # <<<<<<<<<<<<<<
 *                 if negative_step:
 *                     start = shape - 1
*/
      }
      __pyx_L9:;

      /* "View.MemoryView":830
 * 
 * 
 *         if have_start:             # <<<<<<<<<<<<<<
 *             if start < 0:
 *                 start += shape
*/
      goto __pyx_L8;
    }

    /* "View.MemoryView":841
 *                     start = shape
 *         else:
 *             if negative_step:             # <<<<<<<<<<<<<<
 *                 start = shape - 1
 *             else:
*/
    /*else*/ {
      if (__pyx_v_negative_step) {

        /* "View.MemoryView":842
 *         else:
 *             if negative_step:
 *                 start = shape - 1             # <<<<<<<<<<<<<<
 *             else:
 *                 start = 0
*/
        __pyx_v_start = (__pyx_v_shape - 1);

        /* "View.MemoryView":841
 *                     start = shape
 *         else:
 *             if negative_step:             # <<<<<<<<<<<<<<
 *                 start = shape - 1
 *             else:
*/
        goto __pyx_L12;
      }

      /* "View.MemoryView":844
 *                 start = shape - 1
 *             else:
 *                 start = 0             # <<<<<<<<<<<<<<
 * 
 *         if have_stop:
*/
      /*else*/ {
        __pyx_v_start = 0;
      }
      __pyx_L12:;
    }
    __pyx_L8:;

    /* "View.MemoryView":846
 *                 start = 0
 * 
 *         if have_stop:             # <<<<<<<<<<<<<<
 *             if stop < 0:
 *                 stop += shape
*/
    __pyx_t_2 = (__pyx_v_have_stop != 0);
    if (__pyx_t_2) {

      /* "View.MemoryView":847
 * 
 *         if have_stop:
 *             if stop < 0:             # <<<<<<<<<<<<<<
 *                 stop += shape
 *                 if stop < 0:
*/
      __pyx_t_2 = (__pyx_v_stop < 0);
      if (__pyx_t_2) {

        /* "View.MemoryView":848
 *         if have_stop:
 *             if stop < 0:
 *                 stop += shape             # <<<<<<<<<<<<<<
 *                 if stop < 0:
 *                     stop = 0
*/
        __pyx_v_stop = (__pyx_v_stop + __pyx_v_shape);

        /* "View.MemoryView":849
 *             if stop < 0:
 *                 stop += shape
 *                 if stop < 0:             # <<<<<<<<<<<<<<
 *                     stop = 0
 *             elif stop > shape:
*/
        __pyx_t_2 = (__pyx_v_stop < 0);
        if (__pyx_t_2) {

          /* "View.MemoryView":850
 *                 stop += shape
 *                 if stop < 0:
 *                     stop = 0             # <<<<<<<<<<<<<<
 *             elif stop > shape:
 *                 stop = shape
*/
          __pyx_v_stop = 0;

          /* "View.MemoryView":849
 *             if stop < 0:
 *                 stop += shape
 *                 if stop < 0:             # <<<<<<<<<<<<<<
 *                     stop = 0
 *             elif stop > shape:
*/
        }

        /* "View.MemoryView":847
 * 
 *         if have_stop:
 *             if stop < 0:             # <<<<<<<<<<<<<<
 *                 stop += shape
 *                 if stop < 0:
*/
        goto __pyx_L14;
      }

      /* "View.MemoryView":851
 *                 if stop < 0:
 *                     stop = 0
 *             elif stop > shape:             # <<<<<<<<<<<<<<
 *                 stop = shape
 *         else:
*/
      __pyx_t_2 = (__pyx_v_stop > __pyx_v_shape);
      if (__pyx_t_2) {

        /* "View.MemoryView":852
 *                     stop = 0
 *             elif stop > shape:
 *                 stop = shape             # <<<<<<<<<<<<<<
 *         else:
 *             if negative_step:
*/
        __pyx_v_stop = __pyx_v_shape;

        /* "View.MemoryView":851
 *                 if stop < 0:
 *                     stop = 0
 *             elif stop > shape:             # <<<<<<<<<<<<<<
 *                 stop = shape
 *         else:
*/
      }
      __pyx_L14:;

      /* "View.MemoryView":846
 *                 start = 0
 * 
 *         if have_stop:             # <<<<<<<<<<<<<<
 *             if stop < 0:
 *                 stop += shape
*/
      goto __pyx_L13;
    }

    /* "View.MemoryView":854
 *                 stop = shape
 *         else:
 *             if negative_step:             # <<<<<<<<<<<<<<
 *                 stop = -1
 *             else:
*/
    /*else*/ {
      if (__pyx_v_negative_step) {

        /* "View.MemoryView":855
 *         else:
 *             if negative_step:
 *                 stop = -1             # <<<<<<<<<<<<<<
 *             else:
 *                 stop = shape
*/
        __pyx_v_stop = -1L;

        /* "View.MemoryView":854
 *                 stop = shape
 *         else:
 *             if negative_step:             # <<<<<<<<<<<<<<
 *                 stop = -1
 *             else:
*/
        goto __pyx_L16;
      }

      /* "View.MemoryView":857
 *                 stop = -1
 *             else:
 *                 stop = shape             # <<<<<<<<<<<<<<
 * 
 * 
*/
      /*else*/ {
        __pyx_v_stop = __pyx_v_shape;
      }
      __pyx_L16:;
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    __pyx_L13:;

    /* "View.MemoryView":861
 * 
 *         with cython.cdivision(True):
 *             new_shape = (stop - start) // step             # <<<<<<<<<<<<<<
 * 
 *             if (stop - start) - step * new_shape:
*/
    __pyx_v_new_shape = ((__pyx_v_stop - __pyx_v_start) / __pyx_v_step);

    /* "View.MemoryView":863
 *             new_shape = (stop - start) // step
 * 
 *             if (stop - start) - step * new_shape:             # <<<<<<<<<<<<<<
 *                 new_shape += 1
 * 
*/
    __pyx_t_2 = (((__pyx_v_stop - __pyx_v_start) - (__pyx_v_step * __pyx_v_new_shape)) != 0);
    if (__pyx_t_2) {

      /* "View.MemoryView":864
 * 
 *             if (stop - start) - step * new_shape:
 *                 new_shape += 1             # <<<<<<<<<<<<<<
 * 
 *         if new_shape < 0:
*/
      __pyx_v_new_shape = (__pyx_v_new_shape + 1);

      /* "View.MemoryView":863
 *             new_shape = (stop - start) // step
 * 
 *             if (stop - start) - step * new_shape:             # <<<<<<<<<<<<<<
 *                 new_shape += 1
 * 
*/
    }

    /* "View.MemoryView":866
 *                 new_shape += 1
 * 
 *         if new_shape < 0:             # <<<<<<<<<<<<<<
 *             new_shape = 0
 * 
*/
    __pyx_t_2 = (__pyx_v_new_shape < 0);
    if (__pyx_t_2) {

      /* "View.MemoryView":867
 * 
 *         if new_shape < 0:
 *             new_shape = 0             # <<<<<<<<<<<<<<
 * 
 * 
*/
      __pyx_v_new_shape = 0;

      /* "View.MemoryView":866
 *                 new_shape += 1
 * 
 *         if new_shape < 0:             # <<<<<<<<<<<<<<
 *             new_shape = 0
 * 
*/
    }

    /* "View.MemoryView":870
 * 
 * 
 *         dst.strides[new_ndim] = stride * step             # <<<<<<<<<<<<<<
 *         dst.shape[new_ndim] = new_shape
 *         dst.suboffsets[new_ndim] = suboffset
*/
    (__pyx_v_dst->strides[__pyx_v_new_ndim]) = (__pyx_v_stride * __pyx_v_step);

    /* "View.MemoryView":871
 * 
 *         dst.strides[new_ndim] = stride * step
 *         dst.shape[new_ndim] = new_shape             # <<<<<<<<<<<<<<
 *         dst.suboffsets[new_ndim] = suboffset
 * 
*/
    (__pyx_v_dst->shape[__pyx_v_new_ndim]) = __pyx_v_new_shape;

    /* "View.MemoryView":872
 *         dst.strides[new_ndim] = stride * step
 *         dst.shape[new_ndim] = new_shape
 *         dst.suboffsets[new_ndim] = suboffset             # <<<<<<<<<<<<<<
 * 
 * 
*/
    (__pyx_v_dst->suboffsets[__pyx_v_new_ndim]) = __pyx_v_suboffset;
  }
  __pyx_L3:;

  /* "View.MemoryView":875
 * 
 * 
 *     if suboffset_dim[0] < 0:             # <<<<<<<<<<<<<<
 *         dst.data += start * stride
 *     else:
*/
  __pyx_t_2 = ((__pyx_v_suboffset_dim[0]) < 0);
  if (__pyx_t_2) {

    /* "View.MemoryView":876
 * 
 *     if suboffset_dim[0] < 0:
 *         dst.data += start * stride             # <<<<<<<<<<<<<<
 *     else:
 *         dst.suboffsets[suboffset_dim[0]] += start * stride
*/
    __pyx_v_dst->data = (__pyx_v_dst->data + (__pyx_v_start * __pyx_v_stride));

    /* "View.MemoryView":875
 * 
 * 
 *     if suboffset_dim[0] < 0:             # <<<<<<<<<<<<<<
 *         dst.data += start * stride
 *     else:
*/
    goto __pyx_L19;
  }

  /* "View.MemoryView":878
 *         dst.data += start * stride
 *     else:
 *         dst.suboffsets[suboffset_dim[0]] += start * stride             # <<<<<<<<<<<<<<
 * 
 *     if suboffset >= 0:
*/
  /*else*/ {
    __pyx_t_3 = (__pyx_v_suboffset_dim[0]);
    (__pyx_v_dst->suboffsets[__pyx_t_3]) = ((__pyx_v_dst->suboffsets[__pyx_t_3]) + (__pyx_v_start * __pyx_v_stride));
  }
  __pyx_L19:;

  /* "View.MemoryView":880
 *         dst.suboffsets[suboffset_dim[0]] += start * stride
 * 
 *     if suboffset >= 0:             # <<<<<<<<<<<<<<
 *         if not is_slice:
 *             if new_ndim == 0:
*/
  __pyx_t_2 = (__pyx_v_suboffset >= 0);
  if (__pyx_t_2) {

    /* "View.MemoryView":881
 * 
 *     if suboffset >= 0:
 *         if not is_slice:             # <<<<<<<<<<<<<<
 *             if new_ndim == 0:
 *                 dst.data = (<char **> dst.data)[0] + suboffset
*/
    __pyx_t_2 = (!__pyx_v_is_slice);
    if (__pyx_t_2) {

      /* "View.MemoryView":882
 *     if suboffset >= 0:
 *         if not is_slice:
 *             if new_ndim == 0:             # <<<<<<<<<<<<<<
 *                 dst.data = (<char **> dst.data)[0] + suboffset
 *             else:
*/
      __pyx_t_2 = (__pyx_v_new_ndim == 0);
      if (__pyx_t_2) {

        /* "View.MemoryView":883
 *         if not is_slice:
 *             if new_ndim == 0:
 *                 dst.data = (<char **> dst.data)[0] + suboffset             # <<<<<<<<<<<<<<
 *             else:
 *                 _err_dim(PyExc_IndexError, "All dimensions preceding dimension %d "
*/
        __pyx_v_dst->data = ((((char **)__pyx_v_dst->data)[0]) + __pyx_v_suboffset);

        /* "View.MemoryView":882
 *     if suboffset >= 0:
 *         if not is_slice:
 *             if new_ndim == 0:             # <<<<<<<<<<<<<<
 *                 dst.data = (<char **> dst.data)[0] + suboffset
 *             else:
*/
        goto __pyx_L22;
      }

      /* "View.MemoryView":885
 *                 dst.data = (<char **> dst.data)[0] + suboffset
 *             else:
 *                 _err_dim(PyExc_IndexError, "All dimensions preceding dimension %d "             # <<<<<<<<<<<<<<
 *                                      "must be indexed and not sliced", dim)
 *         else:
*/
      /*else*/ {

        /* "View.MemoryView":886
 *             else:
 *                 _err_dim(PyExc_IndexError, "All dimensions preceding dimension %d "
 *                                      "must be indexed and not sliced", dim)             # <<<<<<<<<<<<<<
 *         else:
 *             suboffset_dim[0] = new_ndim
*/
        __pyx_t_3 = __pyx_memoryview_err_dim(PyExc_IndexError, __pyx_mstate_global->__pyx_kp_u_All_dimensions_preceding_dimensi, __pyx_v_dim); if (unlikely(__pyx_t_3 == ((int)-1))) __PYX_ERR(1, 885, __pyx_L1_error)
      }
      __pyx_L22:;

      /* "View.MemoryView":881
 * 
 *     if suboffset >= 0:
 *         if not is_slice:             # <<<<<<<<<<<<<<
 *             if new_ndim == 0:
 *                 dst.data = (<char **> dst.data)[0] + suboffset
*/
      goto __pyx_L21;
    }

    /* "View.MemoryView":888
 *                                      "must be indexed and not sliced", dim)
 *         else:
 *             suboffset_dim[0] = new_ndim             # <<<<<<<<<<<<<<
 * 
 *     return 0
*/
    /*else*/ {
      (__pyx_v_suboffset_dim[0]) = __pyx_v_new_ndim;
    }
    __pyx_L21:;

    /* "View.MemoryView":880
 *         dst.suboffsets[suboffset_dim[0]] += start * stride
 * 
 *     if suboffset >= 0:             # <<<<<<<<<<<<<<
 *         if not is_slice:
 *             if new_ndim == 0:
*/
  }

  /* "View.MemoryView":890
 *             suboffset_dim[0] = new_ndim
 * 
 *     return 0             # <<<<<<<<<<<<<<
 * 
 * 
*/
  __pyx_r = 0;
  goto __pyx_L0;

  /* "View.MemoryView":792
 * 
 * 
 * @cname('__pyx_memoryview_slice_memviewslice')             # <<<<<<<<<<<<<<
 * cdef int slice_memviewslice(
 *         __Pyx_memviewslice *dst,
*/

  /* function exit code */
  __pyx_L1_error:;
  __pyx_gilstate_save = __Pyx_PyGILState_Ensure();
  __Pyx_AddTraceback("View.MemoryView.slice_memviewslice", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = -1;
  __Pyx_PyGILState_Release(__pyx_gilstate_save);
  __pyx_L0:;
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}

/* "View.MemoryView":895
 * 
 * 
 * @cname('__pyx_pybuffer_index')             # <<<<<<<<<<<<<<
 * cdef char *pybuffer_index(Py_buffer *view, char *bufp, Py_ssize_t index,
 *                           Py_ssize_t dim) except NULL:
*/

static char *__pyx_pybuffer_index(Py_buffer *__pyx_v_view, char *__pyx_v_bufp, Py_ssize_t __pyx_v_index, Py_ssize_t __pyx_v_dim) {
  Py_ssize_t __pyx_v_shape;
  Py_ssize_t __pyx_v_stride;
  Py_ssize_t __pyx_v_suboffset;
  Py_ssize_t __pyx_v_itemsize;
  char *__pyx_v_resultp;
  char *__pyx_r;
  __Pyx_RefNannyDeclarations
  Py_ssize_t __pyx_t_1;
  int __pyx_t_2;
  PyObject *__pyx_t_3 = NULL;
  PyObject *__pyx_t_4[3];
  PyObject *__pyx_t_5 = NULL;
  int __pyx_lineno = 0;
  const char *__pyx_filename = NULL;
  int __pyx_clineno = 0;
  __Pyx_RefNannySetupContext("pybuffer_index", 0);

  /* "View.MemoryView":898
 * cdef char *pybuffer_index(Py_buffer *view, char *bufp, Py_ssize_t index,
 *                           Py_ssize_t dim) except NULL:
 *     cdef Py_ssize_t shape, stride, suboffset = -1             # <<<<<<<<<<<<<<
 *     cdef Py_ssize_t itemsize = view.itemsize
 *     cdef char *resultp
*/
  __pyx_v_suboffset = -1L;

  /* "View.MemoryView":899
 *                           Py_ssize_t dim) except NULL:
 *     cdef Py_ssize_t shape, stride, suboffset = -1
 *     cdef Py_ssize_t itemsize = view.itemsize             # <<<<<<<<<<<<<<
 *     cdef char *resultp
 * 
*/
  __pyx_t_1 = __pyx_v_view->itemsize;
  __pyx_v_itemsize = __pyx_t_1;

  /* "View.MemoryView":902
 *     cdef char *resultp
 * 
 *     if view.ndim == 0:             # <<<<<<<<<<<<<<
 *         shape = view.len // itemsize
 *         stride = itemsize
*/
  __pyx_t_2 = (__pyx_v_view->ndim == 0);
  if (__pyx_t_2) {

    /* "View.MemoryView":903
 * 
 *     if view.ndim == 0:
 *         shape = view.len // itemsize             # <<<<<<<<<<<<<<
 *         stride = itemsize
 *     else:
*/
    if (unlikely(__pyx_v_itemsize == 0)) {
      PyErr_SetString(PyExc_ZeroDivisionError, "integer division or modulo by zero");
      __PYX_ERR(1, 903, __pyx_L1_error)
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    else if (sizeof(Py_ssize_t) == sizeof(long) && (!(((Py_ssize_t)-1) > 0)) && unlikely(__pyx_v_itemsize == (Py_ssize_t)-1)  && unlikely(__Pyx_UNARY_NEG_WOULD_OVERFLOW(__pyx_v_view->len))) {
      PyErr_SetString(PyExc_OverflowError, "value too large to perform division");
      __PYX_ERR(1, 903, __pyx_L1_error)
    }
    __pyx_v_shape = __Pyx_div_Py_ssize_t(__pyx_v_view->len, __pyx_v_itemsize, 0);

    /* "View.MemoryView":904
 *     if view.ndim == 0:
 *         shape = view.len // itemsize
 *         stride = itemsize             # <<<<<<<<<<<<<<
 *     else:
 *         shape = view.shape[dim]
*/
    __pyx_v_stride = __pyx_v_itemsize;

    /* "View.MemoryView":902
 *     cdef char *resultp
 * 
 *     if view.ndim == 0:             # <<<<<<<<<<<<<<
 *         shape = view.len // itemsize
 *         stride = itemsize
*/
    goto __pyx_L3;
  }

  /* "View.MemoryView":906
 *         stride = itemsize
 *     else:
 *         shape = view.shape[dim]             # <<<<<<<<<<<<<<
 *         stride = view.strides[dim]
 *         if view.suboffsets != NULL:
*/
  /*else*/ {
    __pyx_v_shape = (__pyx_v_view->shape[__pyx_v_dim]);

    /* "View.MemoryView":907
 *     else:
 *         shape = view.shape[dim]
 *         stride = view.strides[dim]             # <<<<<<<<<<<<<<
 *         if view.suboffsets != NULL:
 *             suboffset = view.suboffsets[dim]
*/
    __pyx_v_stride = (__pyx_v_view->strides[__pyx_v_dim]);

    /* "View.MemoryView":908
 *         shape = view.shape[dim]
 *         stride = view.strides[dim]
 *         if view.suboffsets != NULL:             # <<<<<<<<<<<<<<
 *             suboffset = view.suboffsets[dim]
 * 
*/
    __pyx_t_2 = (__pyx_v_view->suboffsets != NULL);
    if (__pyx_t_2) {

      /* "View.MemoryView":909
 *         stride = view.strides[dim]
 *         if view.suboffsets != NULL:
 *             suboffset = view.suboffsets[dim]             # <<<<<<<<<<<<<<
 * 
 *     if index < 0:
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  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "View.MemoryView":1112
 *     return -arg if arg < 0 else arg
 * 
 * @cname('__pyx_get_best_slice_order')             # <<<<<<<<<<<<<<
 * cdef char get_best_order(__Pyx_memviewslice *mslice, int ndim) noexcept nogil:
 *     """
*/

static char __pyx_get_best_slice_order(__Pyx_memviewslice *__pyx_v_mslice, int __pyx_v_ndim) {
  int __pyx_v_i;
  Py_ssize_t __pyx_v_c_stride;
  Py_ssize_t __pyx_v_f_stride;
  char __pyx_r;
  int __pyx_t_1;
  int __pyx_t_2;
  int __pyx_t_3;
  int __pyx_t_4;

  /* "View.MemoryView":1118
 *     """
 *     cdef int i
 *     cdef Py_ssize_t c_stride = 0             # <<<<<<<<<<<<<<
 *     cdef Py_ssize_t f_stride = 0
 * 
*/
  __pyx_v_c_stride = 0;

  /* "View.MemoryView":1119
 *     cdef int i
 *     cdef Py_ssize_t c_stride = 0
 *     cdef Py_ssize_t f_stride = 0             # <<<<<<<<<<<<<<
 * 
 *     for i in range(ndim - 1, -1, -1):
*/
  __pyx_v_f_stride = 0;

  /* "View.MemoryView":1121
 *     cdef Py_ssize_t f_stride = 0
 * 
 *     for i in range(ndim - 1, -1, -1):             # <<<<<<<<<<<<<<
 *         if mslice.shape[i] > 1:
 *             c_stride = mslice.strides[i]
*/
  for (__pyx_t_1 = (__pyx_v_ndim - 1); __pyx_t_1 > -1; __pyx_t_1-=1) {
    __pyx_v_i = __pyx_t_1;

    /* "View.MemoryView":1122
 * 
 *     for i in range(ndim - 1, -1, -1):
 *         if mslice.shape[i] > 1:             # <<<<<<<<<<<<<<
 *             c_stride = mslice.strides[i]
 *             break
*/
    __pyx_t_2 = ((__pyx_v_mslice->shape[__pyx_v_i]) > 1);
    if (__pyx_t_2) {

      /* "View.MemoryView":1123
 *     for i in range(ndim - 1, -1, -1):
 *         if mslice.shape[i] > 1:
 *             c_stride = mslice.strides[i]             # <<<<<<<<<<<<<<
 *             break
 * 
*/
      __pyx_v_c_stride = (__pyx_v_mslice->strides[__pyx_v_i]);

      /* "View.MemoryView":1124
 *         if mslice.shape[i] > 1:
 *             c_stride = mslice.strides[i]
 *             break             # <<<<<<<<<<<<<<
 * 
 *     for i in range(ndim):
*/
      goto __pyx_L4_break;

      /* "View.MemoryView":1122
 * 
 *     for i in range(ndim - 1, -1, -1):
 *         if mslice.shape[i] > 1:             # <<<<<<<<<<<<<<
 *             c_stride = mslice.strides[i]
 *             break
*/
    }
  }
  __pyx_L4_break:;

  /* "View.MemoryView":1126
 *             break
 * 
 *     for i in range(ndim):             # <<<<<<<<<<<<<<
 *         if mslice.shape[i] > 1:
 *             f_stride = mslice.strides[i]
*/
  __pyx_t_1 = __pyx_v_ndim;
  __pyx_t_3 = __pyx_t_1;
  for (__pyx_t_4 = 0; __pyx_t_4 < __pyx_t_3; __pyx_t_4+=1) {
    __pyx_v_i = __pyx_t_4;

    /* "View.MemoryView":1127
 * 
 *     for i in range(ndim):
 *         if mslice.shape[i] > 1:             # <<<<<<<<<<<<<<
 *             f_stride = mslice.strides[i]
 *             break
*/
    __pyx_t_2 = ((__pyx_v_mslice->shape[__pyx_v_i]) > 1);
    if (__pyx_t_2) {

      /* "View.MemoryView":1128
 *     for i in range(ndim):
 *         if mslice.shape[i] > 1:
 *             f_stride = mslice.strides[i]             # <<<<<<<<<<<<<<
 *             break
 * 
*/
      __pyx_v_f_stride = (__pyx_v_mslice->strides[__pyx_v_i]);

      /* "View.MemoryView":1129
 *         if mslice.shape[i] > 1:
 *             f_stride = mslice.strides[i]
 *             break             # <<<<<<<<<<<<<<
 * 
 *     if abs_py_ssize_t(c_stride) <= abs_py_ssize_t(f_stride):
*/
      goto __pyx_L7_break;

      /* "View.MemoryView":1127
 * 
 *     for i in range(ndim):
 *         if mslice.shape[i] > 1:             # <<<<<<<<<<<<<<
 *             f_stride = mslice.strides[i]
 *             break
*/
    }
  }
  __pyx_L7_break:;

  /* "View.MemoryView":1131
 *             break
 * 
 *     if abs_py_ssize_t(c_stride) <= abs_py_ssize_t(f_stride):             # <<<<<<<<<<<<<<
 *         return 'C'
 *     else:
*/
  __pyx_t_2 = (abs_py_ssize_t(__pyx_v_c_stride) <= abs_py_ssize_t(__pyx_v_f_stride));
  if (__pyx_t_2) {

    /* "View.MemoryView":1132
 * 
 *     if abs_py_ssize_t(c_stride) <= abs_py_ssize_t(f_stride):
 *         return 'C'             # <<<<<<<<<<<<<<
 *     else:
 *         return 'F'
*/
    __pyx_r = 'C';
    goto __pyx_L0;

    /* "View.MemoryView":1131
 *             break
 * 
 *     if abs_py_ssize_t(c_stride) <= abs_py_ssize_t(f_stride):             # <<<<<<<<<<<<<<
 *         return 'C'
 *     else:
*/
  }

  /* "View.MemoryView":1134
 *         return 'C'
 *     else:
 *         return 'F'             # <<<<<<<<<<<<<<
 * 
 * @cython.cdivision(True)
*/
  /*else*/ {
    __pyx_r = 'F';
    goto __pyx_L0;
  }

  /* "View.MemoryView":1112
 *     return -arg if arg < 0 else arg
 * 
 * @cname('__pyx_get_best_slice_order')             # <<<<<<<<<<<<<<
 * cdef char get_best_order(__Pyx_memviewslice *mslice, int ndim) noexcept nogil:
 *     """
*/

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "View.MemoryView":1136
 *         return 'F'
 * 
 * @cython.cdivision(True)             # <<<<<<<<<<<<<<
 * cdef void _copy_strided_to_strided(char *src_data, Py_ssize_t *src_strides,
 *                                    char *dst_data, Py_ssize_t *dst_strides,
*/

static void _copy_strided_to_strided(char *__pyx_v_src_data, Py_ssize_t *__pyx_v_src_strides, char *__pyx_v_dst_data, Py_ssize_t *__pyx_v_dst_strides, Py_ssize_t *__pyx_v_src_shape, Py_ssize_t *__pyx_v_dst_shape, int __pyx_v_ndim, size_t __pyx_v_itemsize) {
  CYTHON_UNUSED Py_ssize_t __pyx_v_i;
  CYTHON_UNUSED Py_ssize_t __pyx_v_src_extent;
  Py_ssize_t __pyx_v_dst_extent;
  Py_ssize_t __pyx_v_src_stride;
  Py_ssize_t __pyx_v_dst_stride;
  int __pyx_t_1;
  int __pyx_t_2;
  Py_ssize_t __pyx_t_3;
  Py_ssize_t __pyx_t_4;
  Py_ssize_t __pyx_t_5;

  /* "View.MemoryView":1144
 * 
 *     cdef Py_ssize_t i
 *     cdef Py_ssize_t src_extent = src_shape[0]             # <<<<<<<<<<<<<<
 *     cdef Py_ssize_t dst_extent = dst_shape[0]
 *     cdef Py_ssize_t src_stride = src_strides[0]
*/
  __pyx_v_src_extent = (__pyx_v_src_shape[0]);

  /* "View.MemoryView":1145
 *     cdef Py_ssize_t i
 *     cdef Py_ssize_t src_extent = src_shape[0]
 *     cdef Py_ssize_t dst_extent = dst_shape[0]             # <<<<<<<<<<<<<<
 *     cdef Py_ssize_t src_stride = src_strides[0]
 *     cdef Py_ssize_t dst_stride = dst_strides[0]
*/
  __pyx_v_dst_extent = (__pyx_v_dst_shape[0]);

  /* "View.MemoryView":1146
 *     cdef Py_ssize_t src_extent = src_shape[0]
 *     cdef Py_ssize_t dst_extent = dst_shape[0]
 *     cdef Py_ssize_t src_stride = src_strides[0]             # <<<<<<<<<<<<<<
 *     cdef Py_ssize_t dst_stride = dst_strides[0]
 * 
*/
  __pyx_v_src_stride = (__pyx_v_src_strides[0]);

  /* "View.MemoryView":1147
 *     cdef Py_ssize_t dst_extent = dst_shape[0]
 *     cdef Py_ssize_t src_stride = src_strides[0]
 *     cdef Py_ssize_t dst_stride = dst_strides[0]             # <<<<<<<<<<<<<<
 * 
 *     if ndim == 1:
*/
  __pyx_v_dst_stride = (__pyx_v_dst_strides[0]);

  /* "View.MemoryView":1149
 *     cdef Py_ssize_t dst_stride = dst_strides[0]
 * 
 *     if ndim == 1:             # <<<<<<<<<<<<<<
 *         if (src_stride > 0 and dst_stride > 0 and
 *             <size_t> src_stride == itemsize == <size_t> dst_stride):
*/
  __pyx_t_1 = (__pyx_v_ndim == 1);
  if (__pyx_t_1) {

    /* "View.MemoryView":1150
 * 
 *     if ndim == 1:
 *         if (src_stride > 0 and dst_stride > 0 and             # <<<<<<<<<<<<<<
 *             <size_t> src_stride == itemsize == <size_t> dst_stride):
 *             memcpy(dst_data, src_data, itemsize * dst_extent)
*/
    __pyx_t_2 = (__pyx_v_src_stride > 0);
    if (__pyx_t_2) {
    } else {
      __pyx_t_1 = __pyx_t_2;
      goto __pyx_L5_bool_binop_done;
    }
    __pyx_t_2 = (__pyx_v_dst_stride > 0);
    if (__pyx_t_2) {
    } else {
      __pyx_t_1 = __pyx_t_2;
      goto __pyx_L5_bool_binop_done;
    }

    /* "View.MemoryView":1151
 *     if ndim == 1:
 *         if (src_stride > 0 and dst_stride > 0 and
 *             <size_t> src_stride == itemsize == <size_t> dst_stride):             # <<<<<<<<<<<<<<
 *             memcpy(dst_data, src_data, itemsize * dst_extent)
 *         else:
*/
    __pyx_t_2 = (((size_t)__pyx_v_src_stride) == __pyx_v_itemsize);
    if (__pyx_t_2) {
      __pyx_t_2 = (__pyx_v_itemsize == ((size_t)__pyx_v_dst_stride));
    }
    __pyx_t_1 = __pyx_t_2;
    __pyx_L5_bool_binop_done:;

    /* "View.MemoryView":1150
 * 
 *     if ndim == 1:
 *         if (src_stride > 0 and dst_stride > 0 and             # <<<<<<<<<<<<<<
 *             <size_t> src_stride == itemsize == <size_t> dst_stride):
 *             memcpy(dst_data, src_data, itemsize * dst_extent)
*/
    if (__pyx_t_1) {

      /* "View.MemoryView":1152
 *         if (src_stride > 0 and dst_stride > 0 and
 *             <size_t> src_stride == itemsize == <size_t> dst_stride):
 *             memcpy(dst_data, src_data, itemsize * dst_extent)             # <<<<<<<<<<<<<<
 *         else:
 *             for i in range(dst_extent):
*/
      (void)(memcpy(__pyx_v_dst_data, __pyx_v_src_data, (__pyx_v_itemsize * __pyx_v_dst_extent)));

      /* "View.MemoryView":1150
 * 
 *     if ndim == 1:
 *         if (src_stride > 0 and dst_stride > 0 and             # <<<<<<<<<<<<<<
 *             <size_t> src_stride == itemsize == <size_t> dst_stride):
 *             memcpy(dst_data, src_data, itemsize * dst_extent)
*/
      goto __pyx_L4;
    }

    /* "View.MemoryView":1154
 *             memcpy(dst_data, src_data, itemsize * dst_extent)
 *         else:
 *             for i in range(dst_extent):             # <<<<<<<<<<<<<<
 *                 memcpy(dst_data, src_data, itemsize)
 *                 src_data += src_stride
*/
    /*else*/ {
      __pyx_t_3 = __pyx_v_dst_extent;
      __pyx_t_4 = __pyx_t_3;
      for (__pyx_t_5 = 0; __pyx_t_5 < __pyx_t_4; __pyx_t_5+=1) {
        __pyx_v_i = __pyx_t_5;

        /* "View.MemoryView":1155
 *         else:
 *             for i in range(dst_extent):
 *                 memcpy(dst_data, src_data, itemsize)             # <<<<<<<<<<<<<<
 *                 src_data += src_stride
 *                 dst_data += dst_stride
*/
        (void)(memcpy(__pyx_v_dst_data, __pyx_v_src_data, __pyx_v_itemsize));

        /* "View.MemoryView":1156
 *             for i in range(dst_extent):
 *                 memcpy(dst_data, src_data, itemsize)
 *                 src_data += src_stride             # <<<<<<<<<<<<<<
 *                 dst_data += dst_stride
 *     else:
*/
        __pyx_v_src_data = (__pyx_v_src_data + __pyx_v_src_stride);

        /* "View.MemoryView":1157
 *                 memcpy(dst_data, src_data, itemsize)
 *                 src_data += src_stride
 *                 dst_data += dst_stride             # <<<<<<<<<<<<<<
 *     else:
 *         for i in range(dst_extent):
*/
        __pyx_v_dst_data = (__pyx_v_dst_data + __pyx_v_dst_stride);
      }
    }
    __pyx_L4:;

    /* "View.MemoryView":1149
 *     cdef Py_ssize_t dst_stride = dst_strides[0]
 * 
 *     if ndim == 1:             # <<<<<<<<<<<<<<
 *         if (src_stride > 0 and dst_stride > 0 and
 *             <size_t> src_stride == itemsize == <size_t> dst_stride):
*/
    goto __pyx_L3;
  }

  /* "View.MemoryView":1159
 *                 dst_data += dst_stride
 *     else:
 *         for i in range(dst_extent):             # <<<<<<<<<<<<<<
 *             _copy_strided_to_strided(src_data, src_strides + 1,
 *                                      dst_data, dst_strides + 1,
*/
  /*else*/ {
    __pyx_t_3 = __pyx_v_dst_extent;
    __pyx_t_4 = __pyx_t_3;
    for (__pyx_t_5 = 0; __pyx_t_5 < __pyx_t_4; __pyx_t_5+=1) {
      __pyx_v_i = __pyx_t_5;

      /* "View.MemoryView":1160
 *     else:
 *         for i in range(dst_extent):
 *             _copy_strided_to_strided(src_data, src_strides + 1,             # <<<<<<<<<<<<<<
 *                                      dst_data, dst_strides + 1,
 *                                      src_shape + 1, dst_shape + 1,
*/
      _copy_strided_to_strided(__pyx_v_src_data, (__pyx_v_src_strides + 1), __pyx_v_dst_data, (__pyx_v_dst_strides + 1), (__pyx_v_src_shape + 1), (__pyx_v_dst_shape + 1), (__pyx_v_ndim - 1), __pyx_v_itemsize);

      /* "View.MemoryView":1164
 *                                      src_shape + 1, dst_shape + 1,
 *                                      ndim - 1, itemsize)
 *             src_data += src_stride             # <<<<<<<<<<<<<<
 *             dst_data += dst_stride
 * 
*/
      __pyx_v_src_data = (__pyx_v_src_data + __pyx_v_src_stride);

      /* "View.MemoryView":1165
 *                                      ndim - 1, itemsize)
 *             src_data += src_stride
 *             dst_data += dst_stride             # <<<<<<<<<<<<<<
 * 
 * cdef void copy_strided_to_strided(__Pyx_memviewslice *src,
*/
      __pyx_v_dst_data = (__pyx_v_dst_data + __pyx_v_dst_stride);
    }
  }
  __pyx_L3:;

  /* "View.MemoryView":1136
 *         return 'F'
 * 
 * @cython.cdivision(True)             # <<<<<<<<<<<<<<
 * cdef void _copy_strided_to_strided(char *src_data, Py_ssize_t *src_strides,
 *                                    char *dst_data, Py_ssize_t *dst_strides,
*/

  /* function exit code */
}

/* "View.MemoryView":1167
 *             dst_data += dst_stride
 * 
 * cdef void copy_strided_to_strided(__Pyx_memviewslice *src,             # <<<<<<<<<<<<<<
 *                                   __Pyx_memviewslice *dst,
 *                                   int ndim, size_t itemsize) noexcept nogil:
*/

static void copy_strided_to_strided(__Pyx_memviewslice *__pyx_v_src, __Pyx_memviewslice *__pyx_v_dst, int __pyx_v_ndim, size_t __pyx_v_itemsize) {

  /* "View.MemoryView":1170
 *                                   __Pyx_memviewslice *dst,
 *                                   int ndim, size_t itemsize) noexcept nogil:
 *     _copy_strided_to_strided(src.data, src.strides, dst.data, dst.strides,             # <<<<<<<<<<<<<<
 *                              src.shape, dst.shape, ndim, itemsize)
 * 
*/
  _copy_strided_to_strided(__pyx_v_src->data, __pyx_v_src->strides, __pyx_v_dst->data, __pyx_v_dst->strides, __pyx_v_src->shape, __pyx_v_dst->shape, __pyx_v_ndim, __pyx_v_itemsize);

  /* "View.MemoryView":1167
 *             dst_data += dst_stride
 * 
 * cdef void copy_strided_to_strided(__Pyx_memviewslice *src,             # <<<<<<<<<<<<<<
 *                                   __Pyx_memviewslice *dst,
 *                                   int ndim, size_t itemsize) noexcept nogil:
*/

  /* function exit code */
}

/* "View.MemoryView":1173
 *                              src.shape, dst.shape, ndim, itemsize)
 * 
 * @cname('__pyx_memoryview_slice_get_size')             # <<<<<<<<<<<<<<
 * cdef Py_ssize_t slice_get_size(__Pyx_memviewslice *src, int ndim) noexcept nogil:
 *     "Return the size of the memory occupied by the slice in number of bytes"
*/

static Py_ssize_t __pyx_memoryview_slice_get_size(__Pyx_memviewslice *__pyx_v_src, int __pyx_v_ndim) {
  Py_ssize_t __pyx_v_shape;
  Py_ssize_t __pyx_v_size;
  Py_ssize_t __pyx_r;
  Py_ssize_t __pyx_t_1;
  Py_ssize_t *__pyx_t_2;
  Py_ssize_t *__pyx_t_3;
  Py_ssize_t *__pyx_t_4;

  /* "View.MemoryView":1176
 * cdef Py_ssize_t slice_get_size(__Pyx_memviewslice *src, int ndim) noexcept nogil:
 *     "Return the size of the memory occupied by the slice in number of bytes"
 *     cdef Py_ssize_t shape, size = src.memview.view.itemsize             # <<<<<<<<<<<<<<
 * 
 *     for shape in src.shape[:ndim]:
*/
  __pyx_t_1 = __pyx_v_src->memview->view.itemsize;
  __pyx_v_size = __pyx_t_1;

  /* "View.MemoryView":1178
 *     cdef Py_ssize_t shape, size = src.memview.view.itemsize
 * 
 *     for shape in src.shape[:ndim]:             # <<<<<<<<<<<<<<
 *         size *= shape
 * 
*/
  __pyx_t_3 = (__pyx_v_src->shape + __pyx_v_ndim);
  for (__pyx_t_4 = __pyx_v_src->shape; __pyx_t_4 < __pyx_t_3; __pyx_t_4++) {
    __pyx_t_2 = __pyx_t_4;
    __pyx_v_shape = (__pyx_t_2[0]);

    /* "View.MemoryView":1179
 * 
 *     for shape in src.shape[:ndim]:
 *         size *= shape             # <<<<<<<<<<<<<<
 * 
 *     return size
*/
    __pyx_v_size = (__pyx_v_size * __pyx_v_shape);
  }

  /* "View.MemoryView":1181
 *         size *= shape
 * 
 *     return size             # <<<<<<<<<<<<<<
 * 
 * @cname('__pyx_fill_contig_strides_array')
*/
  __pyx_r = __pyx_v_size;
  goto __pyx_L0;

  /* "View.MemoryView":1173
 *                              src.shape, dst.shape, ndim, itemsize)
 * 
 * @cname('__pyx_memoryview_slice_get_size')             # <<<<<<<<<<<<<<
 * cdef Py_ssize_t slice_get_size(__Pyx_memviewslice *src, int ndim) noexcept nogil:
 *     "Return the size of the memory occupied by the slice in number of bytes"
*/

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "View.MemoryView":1183
 *     return size
 * 
 * @cname('__pyx_fill_contig_strides_array')             # <<<<<<<<<<<<<<
 * cdef Py_ssize_t fill_contig_strides_array(
 *                 Py_ssize_t *shape, Py_ssize_t *strides, Py_ssize_t stride,
*/

static Py_ssize_t __pyx_fill_contig_strides_array(Py_ssize_t *__pyx_v_shape, Py_ssize_t *__pyx_v_strides, Py_ssize_t __pyx_v_stride, int __pyx_v_ndim, char __pyx_v_order) {
  int __pyx_v_idx;
  Py_ssize_t __pyx_r;
  int __pyx_t_1;
  int __pyx_t_2;
  int __pyx_t_3;
  int __pyx_t_4;

  /* "View.MemoryView":1193
 *     cdef int idx
 * 
 *     if order == 'F':             # <<<<<<<<<<<<<<
 *         for idx in range(ndim):
 *             strides[idx] = stride
*/
  __pyx_t_1 = (__pyx_v_order == 'F');
  if (__pyx_t_1) {

    /* "View.MemoryView":1194
 * 
 *     if order == 'F':
 *         for idx in range(ndim):             # <<<<<<<<<<<<<<
 *             strides[idx] = stride
 *             stride *= shape[idx]
*/
    __pyx_t_2 = __pyx_v_ndim;
    __pyx_t_3 = __pyx_t_2;
    for (__pyx_t_4 = 0; __pyx_t_4 < __pyx_t_3; __pyx_t_4+=1) {
      __pyx_v_idx = __pyx_t_4;

      /* "View.MemoryView":1195
 *     if order == 'F':
 *         for idx in range(ndim):
 *             strides[idx] = stride             # <<<<<<<<<<<<<<
 *             stride *= shape[idx]
 *     else:
*/
      (__pyx_v_strides[__pyx_v_idx]) = __pyx_v_stride;

      /* "View.MemoryView":1196
 *         for idx in range(ndim):
 *             strides[idx] = stride
 *             stride *= shape[idx]             # <<<<<<<<<<<<<<
 *     else:
 *         for idx in range(ndim - 1, -1, -1):
*/
      __pyx_v_stride = (__pyx_v_stride * (__pyx_v_shape[__pyx_v_idx]));
    }

    /* "View.MemoryView":1193
 *     cdef int idx
 * 
 *     if order == 'F':             # <<<<<<<<<<<<<<
 *         for idx in range(ndim):
 *             strides[idx] = stride
*/
    goto __pyx_L3;
  }

  /* "View.MemoryView":1198
 *             stride *= shape[idx]
 *     else:
 *         for idx in range(ndim - 1, -1, -1):             # <<<<<<<<<<<<<<
 *             strides[idx] = stride
 *             stride *= shape[idx]
*/
  /*else*/ {
    for (__pyx_t_2 = (__pyx_v_ndim - 1); __pyx_t_2 > -1; __pyx_t_2-=1) {
      __pyx_v_idx = __pyx_t_2;

      /* "View.MemoryView":1199
 *     else:
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 *     cdef size_t itemsize = src.memview.view.itemsize
 *     cdef int i
 *     cdef char order = get_best_order(&src, src_ndim)             # <<<<<<<<<<<<<<
 *     cdef bint broadcasting = False
 *     cdef bint direct_copy = False
*/
  __pyx_v_order = __pyx_get_best_slice_order((&__pyx_v_src), __pyx_v_src_ndim);

  /* "View.MemoryView":1277
 *     cdef int i
 *     cdef char order = get_best_order(&src, src_ndim)
 *     cdef bint broadcasting = False             # <<<<<<<<<<<<<<
 *     cdef bint direct_copy = False
 *     cdef __Pyx_memviewslice tmp
*/
  __pyx_v_broadcasting = 0;

  /* "View.MemoryView":1278
 *     cdef char order = get_best_order(&src, src_ndim)
 *     cdef bint broadcasting = False
 *     cdef bint direct_copy = False             # <<<<<<<<<<<<<<
 *     cdef __Pyx_memviewslice tmp
 * 
*/
  __pyx_v_direct_copy = 0;

  /* "View.MemoryView":1281
 *     cdef __Pyx_memviewslice tmp
 * 
 *     if src_ndim < dst_ndim:             # <<<<<<<<<<<<<<
 *         broadcast_leading(&src, src_ndim, dst_ndim)
 *     elif dst_ndim < src_ndim:
*/
  __pyx_t_2 = (__pyx_v_src_ndim < __pyx_v_dst_ndim);
  if (__pyx_t_2) {

    /* "View.MemoryView":1282
 * 
 *     if src_ndim < dst_ndim:
 *         broadcast_leading(&src, src_ndim, dst_ndim)             # <<<<<<<<<<<<<<
 *     elif dst_ndim < src_ndim:
 *         broadcast_leading(&dst, dst_ndim, src_ndim)
*/
    __pyx_memoryview_broadcast_leading((&__pyx_v_src), __pyx_v_src_ndim, __pyx_v_dst_ndim);

    /* "View.MemoryView":1281
 *     cdef __Pyx_memviewslice tmp
 * 
 *     if src_ndim < dst_ndim:             # <<<<<<<<<<<<<<
 *         broadcast_leading(&src, src_ndim, dst_ndim)
 *     elif dst_ndim < src_ndim:
*/
    goto __pyx_L3;
  }

  /* "View.MemoryView":1283
 *     if src_ndim < dst_ndim:
 *         broadcast_leading(&src, src_ndim, dst_ndim)
 *     elif dst_ndim < src_ndim:             # <<<<<<<<<<<<<<
 *         broadcast_leading(&dst, dst_ndim, src_ndim)
 * 
*/
  __pyx_t_2 = (__pyx_v_dst_ndim < __pyx_v_src_ndim);
  if (__pyx_t_2) {

    /* "View.MemoryView":1284
 *         broadcast_leading(&src, src_ndim, dst_ndim)
 *     elif dst_ndim < src_ndim:
 *         broadcast_leading(&dst, dst_ndim, src_ndim)             # <<<<<<<<<<<<<<
 * 
 *     cdef int ndim = max(src_ndim, dst_ndim)
*/
    __pyx_memoryview_broadcast_leading((&__pyx_v_dst), __pyx_v_dst_ndim, __pyx_v_src_ndim);

    /* "View.MemoryView":1283
 *     if src_ndim < dst_ndim:
 *         broadcast_leading(&src, src_ndim, dst_ndim)
 *     elif dst_ndim < src_ndim:             # <<<<<<<<<<<<<<
 *         broadcast_leading(&dst, dst_ndim, src_ndim)
 * 
*/
  }
  __pyx_L3:;

  /* "View.MemoryView":1286
 *         broadcast_leading(&dst, dst_ndim, src_ndim)
 * 
 *     cdef int ndim = max(src_ndim, dst_ndim)             # <<<<<<<<<<<<<<
 * 
 *     for i in range(ndim):
*/
  __pyx_t_3 = __pyx_v_dst_ndim;
  __pyx_t_4 = __pyx_v_src_ndim;
  __pyx_t_2 = (__pyx_t_3 > __pyx_t_4);
  if (__pyx_t_2) {
    __pyx_t_5 = __pyx_t_3;
  } else {
    __pyx_t_5 = __pyx_t_4;
  }
  __pyx_v_ndim = __pyx_t_5;

  /* "View.MemoryView":1288
 *     cdef int ndim = max(src_ndim, dst_ndim)
 * 
 *     for i in range(ndim):             # <<<<<<<<<<<<<<
 *         if src.shape[i] != dst.shape[i]:
 *             if src.shape[i] == 1:
*/
  __pyx_t_5 = __pyx_v_ndim;
  __pyx_t_3 = __pyx_t_5;
  for (__pyx_t_4 = 0; __pyx_t_4 < __pyx_t_3; __pyx_t_4+=1) {
    __pyx_v_i = __pyx_t_4;

    /* "View.MemoryView":1289
 * 
 *     for i in range(ndim):
 *         if src.shape[i] != dst.shape[i]:             # <<<<<<<<<<<<<<
 *             if src.shape[i] == 1:
 *                 broadcasting = True
*/
    __pyx_t_2 = ((__pyx_v_src.shape[__pyx_v_i]) != (__pyx_v_dst.shape[__pyx_v_i]));
    if (__pyx_t_2) {

      /* "View.MemoryView":1290
 *     for i in range(ndim):
 *         if src.shape[i] != dst.shape[i]:
 *             if src.shape[i] == 1:             # <<<<<<<<<<<<<<
 *                 broadcasting = True
 *                 src.strides[i] = 0
*/
      __pyx_t_2 = ((__pyx_v_src.shape[__pyx_v_i]) == 1);
      if (__pyx_t_2) {

        /* "View.MemoryView":1291
 *         if src.shape[i] != dst.shape[i]:
 *             if src.shape[i] == 1:
 *                 broadcasting = True             # <<<<<<<<<<<<<<
 *                 src.strides[i] = 0
 *             else:
*/
        __pyx_v_broadcasting = 1;

        /* "View.MemoryView":1292
 *             if src.shape[i] == 1:
 *                 broadcasting = True
 *                 src.strides[i] = 0             # <<<<<<<<<<<<<<
 *             else:
 *                 _err_extents(i, dst.shape[i], src.shape[i])
*/
        (__pyx_v_src.strides[__pyx_v_i]) = 0;

        /* "View.MemoryView":1290
 *     for i in range(ndim):
 *         if src.shape[i] != dst.shape[i]:
 *             if src.shape[i] == 1:             # <<<<<<<<<<<<<<
 *                 broadcasting = True
 *                 src.strides[i] = 0
*/
        goto __pyx_L7;
      }

      /* "View.MemoryView":1294
 *                 src.strides[i] = 0
 *             else:
 *                 _err_extents(i, dst.shape[i], src.shape[i])             # <<<<<<<<<<<<<<
 * 
 *         if src.suboffsets[i] >= 0:
*/
      /*else*/ {
        __pyx_t_6 = __pyx_memoryview_err_extents(__pyx_v_i, (__pyx_v_dst.shape[__pyx_v_i]), (__pyx_v_src.shape[__pyx_v_i])); if (unlikely(__pyx_t_6 == ((int)-1))) __PYX_ERR(1, 1294, __pyx_L1_error)
      }
      __pyx_L7:;

      /* "View.MemoryView":1289
 * 
 *     for i in range(ndim):
 *         if src.shape[i] != dst.shape[i]:             # <<<<<<<<<<<<<<
 *             if src.shape[i] == 1:
 *                 broadcasting = True
*/
    }

    /* "View.MemoryView":1296
 *                 _err_extents(i, dst.shape[i], src.shape[i])
 * 
 *         if src.suboffsets[i] >= 0:             # <<<<<<<<<<<<<<
 *             _err_dim(PyExc_ValueError, "Dimension %d is not direct", i)
 * 
*/
    __pyx_t_2 = ((__pyx_v_src.suboffsets[__pyx_v_i]) >= 0);
    if (__pyx_t_2) {

      /* "View.MemoryView":1297
 * 
 *         if src.suboffsets[i] >= 0:
 *             _err_dim(PyExc_ValueError, "Dimension %d is not direct", i)             # <<<<<<<<<<<<<<
 * 
 *     if slices_overlap(&src, &dst, ndim, itemsize):
*/
      __pyx_t_6 = __pyx_memoryview_err_dim(PyExc_ValueError, __pyx_mstate_global->__pyx_kp_u_Dimension_d_is_not_direct, __pyx_v_i); if (unlikely(__pyx_t_6 == ((int)-1))) __PYX_ERR(1, 1297, __pyx_L1_error)

      /* "View.MemoryView":1296
 *                 _err_extents(i, dst.shape[i], src.shape[i])
 * 
 *         if src.suboffsets[i] >= 0:             # <<<<<<<<<<<<<<
 *             _err_dim(PyExc_ValueError, "Dimension %d is not direct", i)
 * 
*/
    }
  }

  /* "View.MemoryView":1299
 *             _err_dim(PyExc_ValueError, "Dimension %d is not direct", i)
 * 
 *     if slices_overlap(&src, &dst, ndim, itemsize):             # <<<<<<<<<<<<<<
 * 
 *         if not slice_is_contig(src, order, ndim):
*/
  __pyx_t_2 = __pyx_slices_overlap((&__pyx_v_src), (&__pyx_v_dst), __pyx_v_ndim, __pyx_v_itemsize);
  if (__pyx_t_2) {

    /* "View.MemoryView":1301
 *     if slices_overlap(&src, &dst, ndim, itemsize):
 * 
 *         if not slice_is_contig(src, order, ndim):             # <<<<<<<<<<<<<<
 *             order = get_best_order(&dst, ndim)
 * 
*/
    __pyx_t_2 = (!__pyx_memviewslice_is_contig(__pyx_v_src, __pyx_v_order, __pyx_v_ndim));
    if (__pyx_t_2) {

      /* "View.MemoryView":1302
 * 
 *         if not slice_is_contig(src, order, ndim):
 *             order = get_best_order(&dst, ndim)             # <<<<<<<<<<<<<<
 * 
 *         tmpdata = copy_data_to_temp(&src, &tmp, order, ndim)
*/
      __pyx_v_order = __pyx_get_best_slice_order((&__pyx_v_dst), __pyx_v_ndim);

      /* "View.MemoryView":1301
 *     if slices_overlap(&src, &dst, ndim, itemsize):
 * 
 *         if not slice_is_contig(src, order, ndim):             # <<<<<<<<<<<<<<
 *             order = get_best_order(&dst, ndim)
 * 
*/
    }

    /* "View.MemoryView":1304
 *             order = get_best_order(&dst, ndim)
 * 
 *         tmpdata = copy_data_to_temp(&src, &tmp, order, ndim)             # <<<<<<<<<<<<<<
 *         src = tmp
 * 
*/
    __pyx_t_7 = __pyx_memoryview_copy_data_to_temp((&__pyx_v_src), (&__pyx_v_tmp), __pyx_v_order, __pyx_v_ndim); if (unlikely(__pyx_t_7 == ((void *)0))) __PYX_ERR(1, 1304, __pyx_L1_error)
    __pyx_v_tmpdata = __pyx_t_7;

    /* "View.MemoryView":1305
 * 
 *         tmpdata = copy_data_to_temp(&src, &tmp, order, ndim)
 *         src = tmp             # <<<<<<<<<<<<<<
 * 
 *     if not broadcasting:
*/
    __pyx_v_src = __pyx_v_tmp;

    /* "View.MemoryView":1299
 *             _err_dim(PyExc_ValueError, "Dimension %d is not direct", i)
 * 
 *     if slices_overlap(&src, &dst, ndim, itemsize):             # <<<<<<<<<<<<<<
 * 
 *         if not slice_is_contig(src, order, ndim):
*/
  }

  /* "View.MemoryView":1307
 *         src = tmp
 * 
 *     if not broadcasting:             # <<<<<<<<<<<<<<
 * 
 * 
*/
  __pyx_t_2 = (!__pyx_v_broadcasting);
  if (__pyx_t_2) {

    /* "View.MemoryView":1310
 * 
 * 
 *         if slice_is_contig(src, 'C', ndim):             # <<<<<<<<<<<<<<
 *             direct_copy = slice_is_contig(dst, 'C', ndim)
 *         elif slice_is_contig(src, 'F', ndim):
*/
    __pyx_t_2 = __pyx_memviewslice_is_contig(__pyx_v_src, 'C', __pyx_v_ndim);
    if (__pyx_t_2) {

      /* "View.MemoryView":1311
 * 
 *         if slice_is_contig(src, 'C', ndim):
 *             direct_copy = slice_is_contig(dst, 'C', ndim)             # <<<<<<<<<<<<<<
 *         elif slice_is_contig(src, 'F', ndim):
 *             direct_copy = slice_is_contig(dst, 'F', ndim)
*/
      __pyx_v_direct_copy = __pyx_memviewslice_is_contig(__pyx_v_dst, 'C', __pyx_v_ndim);

      /* "View.MemoryView":1310
 * 
 * 
 *         if slice_is_contig(src, 'C', ndim):             # <<<<<<<<<<<<<<
 *             direct_copy = slice_is_contig(dst, 'C', ndim)
 *         elif slice_is_contig(src, 'F', ndim):
*/
      goto __pyx_L12;
    }

    /* "View.MemoryView":1312
 *         if slice_is_contig(src, 'C', ndim):
 *             direct_copy = slice_is_contig(dst, 'C', ndim)
 *         elif slice_is_contig(src, 'F', ndim):             # <<<<<<<<<<<<<<
 *             direct_copy = slice_is_contig(dst, 'F', ndim)
 * 
*/
    __pyx_t_2 = __pyx_memviewslice_is_contig(__pyx_v_src, 'F', __pyx_v_ndim);
    if (__pyx_t_2) {

      /* "View.MemoryView":1313
 *             direct_copy = slice_is_contig(dst, 'C', ndim)
 *         elif slice_is_contig(src, 'F', ndim):
 *             direct_copy = slice_is_contig(dst, 'F', ndim)             # <<<<<<<<<<<<<<
 * 
 *         if direct_copy:
*/
      __pyx_v_direct_copy = __pyx_memviewslice_is_contig(__pyx_v_dst, 'F', __pyx_v_ndim);

      /* "View.MemoryView":1312
 *         if slice_is_contig(src, 'C', ndim):
 *             direct_copy = slice_is_contig(dst, 'C', ndim)
 *         elif slice_is_contig(src, 'F', ndim):             # <<<<<<<<<<<<<<
 *             direct_copy = slice_is_contig(dst, 'F', ndim)
 * 
*/
    }
    __pyx_L12:;

    /* "View.MemoryView":1315
 *             direct_copy = slice_is_contig(dst, 'F', ndim)
 * 
 *         if direct_copy:             # <<<<<<<<<<<<<<
 * 
 *             refcount_copying(&dst, dtype_is_object, ndim, inc=False)
*/
    if (__pyx_v_direct_copy) {

      /* "View.MemoryView":1317
 *         if direct_copy:
 * 
 *             refcount_copying(&dst, dtype_is_object, ndim, inc=False)             # <<<<<<<<<<<<<<
 *             memcpy(dst.data, src.data, slice_get_size(&src, ndim))
 *             refcount_copying(&dst, dtype_is_object, ndim, inc=True)
*/
      __pyx_memoryview_refcount_copying((&__pyx_v_dst), __pyx_v_dtype_is_object, __pyx_v_ndim, 0);

      /* "View.MemoryView":1318
 * 
 *             refcount_copying(&dst, dtype_is_object, ndim, inc=False)
 *             memcpy(dst.data, src.data, slice_get_size(&src, ndim))             # <<<<<<<<<<<<<<
 *             refcount_copying(&dst, dtype_is_object, ndim, inc=True)
 *             free(tmpdata)
*/
      (void)(memcpy(__pyx_v_dst.data, __pyx_v_src.data, __pyx_memoryview_slice_get_size((&__pyx_v_src), __pyx_v_ndim)));

      /* "View.MemoryView":1319
 *             refcount_copying(&dst, dtype_is_object, ndim, inc=False)
 *             memcpy(dst.data, src.data, slice_get_size(&src, ndim))
 *             refcount_copying(&dst, dtype_is_object, ndim, inc=True)             # <<<<<<<<<<<<<<
 *             free(tmpdata)
 *             return 0
*/
      __pyx_memoryview_refcount_copying((&__pyx_v_dst), __pyx_v_dtype_is_object, __pyx_v_ndim, 1);

      /* "View.MemoryView":1320
 *             memcpy(dst.data, src.data, slice_get_size(&src, ndim))
 *             refcount_copying(&dst, dtype_is_object, ndim, inc=True)
 *             free(tmpdata)             # <<<<<<<<<<<<<<
 *             return 0
 * 
*/
      free(__pyx_v_tmpdata);

      /* "View.MemoryView":1321
 *             refcount_copying(&dst, dtype_is_object, ndim, inc=True)
 *             free(tmpdata)
 *             return 0             # <<<<<<<<<<<<<<
 * 
 *     if order == 'F' == get_best_order(&dst, ndim):
*/
      __pyx_r = 0;
      goto __pyx_L0;

      /* "View.MemoryView":1315
 *             direct_copy = slice_is_contig(dst, 'F', ndim)
 * 
 *         if direct_copy:             # <<<<<<<<<<<<<<
 * 
 *             refcount_copying(&dst, dtype_is_object, ndim, inc=False)
*/
    }

    /* "View.MemoryView":1307
 *         src = tmp
 * 
 *     if not broadcasting:             # <<<<<<<<<<<<<<
 * 
 * 
*/
  }

  /* "View.MemoryView":1323
 *             return 0
 * 
 *     if order == 'F' == get_best_order(&dst, ndim):             # <<<<<<<<<<<<<<
 * 
 * 
*/
  __pyx_t_2 = (__pyx_v_order == 'F');
  if (__pyx_t_2) {
    __pyx_t_2 = ('F' == __pyx_get_best_slice_order((&__pyx_v_dst), __pyx_v_ndim));
  }
  if (__pyx_t_2) {

    /* "View.MemoryView":1326
 * 
 * 
 *         transpose_memslice(&src)             # <<<<<<<<<<<<<<
 *         transpose_memslice(&dst)
 * 
*/
    __pyx_t_5 = __pyx_memslice_transpose((&__pyx_v_src)); if (unlikely(__pyx_t_5 == ((int)-1))) __PYX_ERR(1, 1326, __pyx_L1_error)

    /* "View.MemoryView":1327
 * 
 *         transpose_memslice(&src)
 *         transpose_memslice(&dst)             # <<<<<<<<<<<<<<
 * 
 *     refcount_copying(&dst, dtype_is_object, ndim, inc=False)
*/
    __pyx_t_5 = __pyx_memslice_transpose((&__pyx_v_dst)); if (unlikely(__pyx_t_5 == ((int)-1))) __PYX_ERR(1, 1327, __pyx_L1_error)

    /* "View.MemoryView":1323
 *             return 0
 * 
 *     if order == 'F' == get_best_order(&dst, ndim):             # <<<<<<<<<<<<<<
 * 
 * 
*/
  }

  /* "View.MemoryView":1329
 *         transpose_memslice(&dst)
 * 
 *     refcount_copying(&dst, dtype_is_object, ndim, inc=False)             # <<<<<<<<<<<<<<
 *     copy_strided_to_strided(&src, &dst, ndim, itemsize)
 *     refcount_copying(&dst, dtype_is_object, ndim, inc=True)
*/
  __pyx_memoryview_refcount_copying((&__pyx_v_dst), __pyx_v_dtype_is_object, __pyx_v_ndim, 0);

  /* "View.MemoryView":1330
 * 
 *     refcount_copying(&dst, dtype_is_object, ndim, inc=False)
 *     copy_strided_to_strided(&src, &dst, ndim, itemsize)             # <<<<<<<<<<<<<<
 *     refcount_copying(&dst, dtype_is_object, ndim, inc=True)
 * 
*/
  copy_strided_to_strided((&__pyx_v_src), (&__pyx_v_dst), __pyx_v_ndim, __pyx_v_itemsize);

  /* "View.MemoryView":1331
 *     refcount_copying(&dst, dtype_is_object, ndim, inc=False)
 *     copy_strided_to_strided(&src, &dst, ndim, itemsize)
 *     refcount_copying(&dst, dtype_is_object, ndim, inc=True)             # <<<<<<<<<<<<<<
 * 
 *     free(tmpdata)
*/
  __pyx_memoryview_refcount_copying((&__pyx_v_dst), __pyx_v_dtype_is_object, __pyx_v_ndim, 1);

  /* "View.MemoryView":1333
 *     refcount_copying(&dst, dtype_is_object, ndim, inc=True)
 * 
 *     free(tmpdata)             # <<<<<<<<<<<<<<
 *     return 0
 * 
*/
  free(__pyx_v_tmpdata);

  /* "View.MemoryView":1334
 * 
 *     free(tmpdata)
 *     return 0             # <<<<<<<<<<<<<<
 * 
 * @cname('__pyx_memoryview_broadcast_leading')
*/
  __pyx_r = 0;
  goto __pyx_L0;

  /* "View.MemoryView":1264
 * 
 * 
 * @cname('__pyx_memoryview_copy_contents')             # <<<<<<<<<<<<<<
 * cdef int memoryview_copy_contents(__Pyx_memviewslice src,
 *                                   __Pyx_memviewslice dst,
*/

  /* function exit code */
  __pyx_L1_error:;
  __pyx_gilstate_save = __Pyx_PyGILState_Ensure();
  __Pyx_AddTraceback("View.MemoryView.memoryview_copy_contents", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = -1;
  __Pyx_PyGILState_Release(__pyx_gilstate_save);
  __pyx_L0:;
  return __pyx_r;
}

/* "View.MemoryView":1336
 *     return 0
 * 
 * @cname('__pyx_memoryview_broadcast_leading')             # <<<<<<<<<<<<<<
 * cdef void broadcast_leading(__Pyx_memviewslice *mslice,
 *                             int ndim,
*/

static void __pyx_memoryview_broadcast_leading(__Pyx_memviewslice *__pyx_v_mslice, int __pyx_v_ndim, int __pyx_v_ndim_other) {
  int __pyx_v_i;
  int __pyx_v_offset;
  int __pyx_t_1;
  int __pyx_t_2;
  int __pyx_t_3;

  /* "View.MemoryView":1341
 *                             int ndim_other) noexcept nogil:
 *     cdef int i
 *     cdef int offset = ndim_other - ndim             # <<<<<<<<<<<<<<
 * 
 *     for i in range(ndim - 1, -1, -1):
*/
  __pyx_v_offset = (__pyx_v_ndim_other - __pyx_v_ndim);

  /* "View.MemoryView":1343
 *     cdef int offset = ndim_other - ndim
 * 
 *     for i in range(ndim - 1, -1, -1):             # <<<<<<<<<<<<<<
 *         mslice.shape[i + offset] = mslice.shape[i]
 *         mslice.strides[i + offset] = mslice.strides[i]
*/
  for (__pyx_t_1 = (__pyx_v_ndim - 1); __pyx_t_1 > -1; __pyx_t_1-=1) {
    __pyx_v_i = __pyx_t_1;

    /* "View.MemoryView":1344
 * 
 *     for i in range(ndim - 1, -1, -1):
 *         mslice.shape[i + offset] = mslice.shape[i]             # <<<<<<<<<<<<<<
 *         mslice.strides[i + offset] = mslice.strides[i]
 *         mslice.suboffsets[i + offset] = mslice.suboffsets[i]
*/
    (__pyx_v_mslice->shape[(__pyx_v_i + __pyx_v_offset)]) = (__pyx_v_mslice->shape[__pyx_v_i]);

    /* "View.MemoryView":1345
 *     for i in range(ndim - 1, -1, -1):
 *         mslice.shape[i + offset] = mslice.shape[i]
 *         mslice.strides[i + offset] = mslice.strides[i]             # <<<<<<<<<<<<<<
 *         mslice.suboffsets[i + offset] = mslice.suboffsets[i]
 * 
*/
    (__pyx_v_mslice->strides[(__pyx_v_i + __pyx_v_offset)]) = (__pyx_v_mslice->strides[__pyx_v_i]);

    /* "View.MemoryView":1346
 *         mslice.shape[i + offset] = mslice.shape[i]
 *         mslice.strides[i + offset] = mslice.strides[i]
 *         mslice.suboffsets[i + offset] = mslice.suboffsets[i]             # <<<<<<<<<<<<<<
 * 
 *     for i in range(offset):
*/
    (__pyx_v_mslice->suboffsets[(__pyx_v_i + __pyx_v_offset)]) = (__pyx_v_mslice->suboffsets[__pyx_v_i]);
  }

  /* "View.MemoryView":1348
 *         mslice.suboffsets[i + offset] = mslice.suboffsets[i]
 * 
 *     for i in range(offset):             # <<<<<<<<<<<<<<
 *         mslice.shape[i] = 1
 *         mslice.strides[i] = mslice.strides[0]
*/
  __pyx_t_1 = __pyx_v_offset;
  __pyx_t_2 = __pyx_t_1;
  for (__pyx_t_3 = 0; __pyx_t_3 < __pyx_t_2; __pyx_t_3+=1) {
    __pyx_v_i = __pyx_t_3;

    /* "View.MemoryView":1349
 * 
 *     for i in range(offset):
 *         mslice.shape[i] = 1             # <<<<<<<<<<<<<<
 *         mslice.strides[i] = mslice.strides[0]
 *         mslice.suboffsets[i] = -1
*/
    (__pyx_v_mslice->shape[__pyx_v_i]) = 1;

    /* "View.MemoryView":1350
 *     for i in range(offset):
 *         mslice.shape[i] = 1
 *         mslice.strides[i] = mslice.strides[0]             # <<<<<<<<<<<<<<
 *         mslice.suboffsets[i] = -1
 * 
*/
    (__pyx_v_mslice->strides[__pyx_v_i]) = (__pyx_v_mslice->strides[0]);

    /* "View.MemoryView":1351
 *         mslice.shape[i] = 1
 *         mslice.strides[i] = mslice.strides[0]
 *         mslice.suboffsets[i] = -1             # <<<<<<<<<<<<<<
 * 
 * 
*/
    (__pyx_v_mslice->suboffsets[__pyx_v_i]) = -1L;
  }

  /* "View.MemoryView":1336
 *     return 0
 * 
 * @cname('__pyx_memoryview_broadcast_leading')             # <<<<<<<<<<<<<<
 * cdef void broadcast_leading(__Pyx_memviewslice *mslice,
 *                             int ndim,
*/

  /* function exit code */
}

/* "View.MemoryView":1358
 * 
 * 
 * @cname('__pyx_memoryview_refcount_copying')             # <<<<<<<<<<<<<<
 * cdef void refcount_copying(__Pyx_memviewslice *dst, bint dtype_is_object, int ndim, bint inc) noexcept nogil:
 * 
*/

static void __pyx_memoryview_refcount_copying(__Pyx_memviewslice *__pyx_v_dst, int __pyx_v_dtype_is_object, int __pyx_v_ndim, int __pyx_v_inc) {

  /* "View.MemoryView":1361
 * cdef void refcount_copying(__Pyx_memviewslice *dst, bint dtype_is_object, int ndim, bint inc) noexcept nogil:
 * 
 *     if dtype_is_object:             # <<<<<<<<<<<<<<
 *         refcount_objects_in_slice_with_gil(dst.data, dst.shape, dst.strides, ndim, inc)
 * 
*/
  if (__pyx_v_dtype_is_object) {

    /* "View.MemoryView":1362
 * 
 *     if dtype_is_object:
 *         refcount_objects_in_slice_with_gil(dst.data, dst.shape, dst.strides, ndim, inc)             # <<<<<<<<<<<<<<
 * 
 * @cname('__pyx_memoryview_refcount_objects_in_slice_with_gil')
*/
    __pyx_memoryview_refcount_objects_in_slice_with_gil(__pyx_v_dst->data, __pyx_v_dst->shape, __pyx_v_dst->strides, __pyx_v_ndim, __pyx_v_inc);

    /* "View.MemoryView":1361
 * cdef void refcount_copying(__Pyx_memviewslice *dst, bint dtype_is_object, int ndim, bint inc) noexcept nogil:
 * 
 *     if dtype_is_object:             # <<<<<<<<<<<<<<
 *         refcount_objects_in_slice_with_gil(dst.data, dst.shape, dst.strides, ndim, inc)
 * 
*/
  }

  /* "View.MemoryView":1358
 * 
 * 
 * @cname('__pyx_memoryview_refcount_copying')             # <<<<<<<<<<<<<<
 * cdef void refcount_copying(__Pyx_memviewslice *dst, bint dtype_is_object, int ndim, bint inc) noexcept nogil:
 * 
*/

  /* function exit code */
}

/* "View.MemoryView":1364
 *         refcount_objects_in_slice_with_gil(dst.data, dst.shape, dst.strides, ndim, inc)
 * 
 * @cname('__pyx_memoryview_refcount_objects_in_slice_with_gil')             # <<<<<<<<<<<<<<
 * cdef void refcount_objects_in_slice_with_gil(char *data, Py_ssize_t *shape,
 *                                              Py_ssize_t *strides, int ndim,
*/

static void __pyx_memoryview_refcount_objects_in_slice_with_gil(char *__pyx_v_data, Py_ssize_t *__pyx_v_shape, Py_ssize_t *__pyx_v_strides, int __pyx_v_ndim, int __pyx_v_inc) {
  PyGILState_STATE __pyx_gilstate_save = __Pyx_PyGILState_Ensure();

  /* "View.MemoryView":1368
 *                                              Py_ssize_t *strides, int ndim,
 *                                              bint inc) noexcept with gil:
 *     refcount_objects_in_slice(data, shape, strides, ndim, inc)             # <<<<<<<<<<<<<<
 * 
 * @cname('__pyx_memoryview_refcount_objects_in_slice')
*/
  __pyx_memoryview_refcount_objects_in_slice(__pyx_v_data, __pyx_v_shape, __pyx_v_strides, __pyx_v_ndim, __pyx_v_inc);

  /* "View.MemoryView":1364
 *         refcount_objects_in_slice_with_gil(dst.data, dst.shape, dst.strides, ndim, inc)
 * 
 * @cname('__pyx_memoryview_refcount_objects_in_slice_with_gil')             # <<<<<<<<<<<<<<
 * cdef void refcount_objects_in_slice_with_gil(char *data, Py_ssize_t *shape,
 *                                              Py_ssize_t *strides, int ndim,
*/

  /* function exit code */
  __Pyx_PyGILState_Release(__pyx_gilstate_save);
}

/* "View.MemoryView":1370
 *     refcount_objects_in_slice(data, shape, strides, ndim, inc)
 * 
 * @cname('__pyx_memoryview_refcount_objects_in_slice')             # <<<<<<<<<<<<<<
 * cdef void refcount_objects_in_slice(char *data, Py_ssize_t *shape,
 *                                     Py_ssize_t *strides, int ndim, bint inc) noexcept:
*/

static void __pyx_memoryview_refcount_objects_in_slice(char *__pyx_v_data, Py_ssize_t *__pyx_v_shape, Py_ssize_t *__pyx_v_strides, int __pyx_v_ndim, int __pyx_v_inc) {
  CYTHON_UNUSED Py_ssize_t __pyx_v_i;
  Py_ssize_t __pyx_v_stride;
  Py_ssize_t __pyx_t_1;
  Py_ssize_t __pyx_t_2;
  Py_ssize_t __pyx_t_3;
  int __pyx_t_4;

  /* "View.MemoryView":1374
 *                                     Py_ssize_t *strides, int ndim, bint inc) noexcept:
 *     cdef Py_ssize_t i
 *     cdef Py_ssize_t stride = strides[0]             # <<<<<<<<<<<<<<
 * 
 *     for i in range(shape[0]):
*/
  __pyx_v_stride = (__pyx_v_strides[0]);

  /* "View.MemoryView":1376
 *     cdef Py_ssize_t stride = strides[0]
 * 
 *     for i in range(shape[0]):             # <<<<<<<<<<<<<<
 *         if ndim == 1:
 *             if inc:
*/
  __pyx_t_1 = (__pyx_v_shape[0]);
  __pyx_t_2 = __pyx_t_1;
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    /* "View.MemoryView":1377
 * 
 *     for i in range(shape[0]):
 *         if ndim == 1:             # <<<<<<<<<<<<<<
 *             if inc:
 *                 Py_INCREF((<PyObject **> data)[0])
*/
    __pyx_t_4 = (__pyx_v_ndim == 1);
    if (__pyx_t_4) {

      /* "View.MemoryView":1378
 *     for i in range(shape[0]):
 *         if ndim == 1:
 *             if inc:             # <<<<<<<<<<<<<<
 *                 Py_INCREF((<PyObject **> data)[0])
 *             else:
*/
      if (__pyx_v_inc) {

        /* "View.MemoryView":1379
 *         if ndim == 1:
 *             if inc:
 *                 Py_INCREF((<PyObject **> data)[0])             # <<<<<<<<<<<<<<
 *             else:
 *                 Py_DECREF((<PyObject **> data)[0])
*/
        Py_INCREF((((PyObject **)__pyx_v_data)[0]));

        /* "View.MemoryView":1378
 *     for i in range(shape[0]):
 *         if ndim == 1:
 *             if inc:             # <<<<<<<<<<<<<<
 *                 Py_INCREF((<PyObject **> data)[0])
 *             else:
*/
        goto __pyx_L6;
      }

      /* "View.MemoryView":1381
 *                 Py_INCREF((<PyObject **> data)[0])
 *             else:
 *                 Py_DECREF((<PyObject **> data)[0])             # <<<<<<<<<<<<<<
 *         else:
 *             refcount_objects_in_slice(data, shape + 1, strides + 1, ndim - 1, inc)
*/
      /*else*/ {
        Py_DECREF((((PyObject **)__pyx_v_data)[0]));
      }
      __pyx_L6:;

      /* "View.MemoryView":1377
 * 
 *     for i in range(shape[0]):
 *         if ndim == 1:             # <<<<<<<<<<<<<<
 *             if inc:
 *                 Py_INCREF((<PyObject **> data)[0])
*/
      goto __pyx_L5;
    }

    /* "View.MemoryView":1383
 *                 Py_DECREF((<PyObject **> data)[0])
 *         else:
 *             refcount_objects_in_slice(data, shape + 1, strides + 1, ndim - 1, inc)             # <<<<<<<<<<<<<<
 * 
 *         data += stride
*/
    /*else*/ {
      __pyx_memoryview_refcount_objects_in_slice(__pyx_v_data, (__pyx_v_shape + 1), (__pyx_v_strides + 1), (__pyx_v_ndim - 1), __pyx_v_inc);
    }
    __pyx_L5:;

    /* "View.MemoryView":1385
 *             refcount_objects_in_slice(data, shape + 1, strides + 1, ndim - 1, inc)
 * 
 *         data += stride             # <<<<<<<<<<<<<<
 * 
 * 
*/
    __pyx_v_data = (__pyx_v_data + __pyx_v_stride);
  }

  /* "View.MemoryView":1370
 *     refcount_objects_in_slice(data, shape, strides, ndim, inc)
 * 
 * @cname('__pyx_memoryview_refcount_objects_in_slice')             # <<<<<<<<<<<<<<
 * cdef void refcount_objects_in_slice(char *data, Py_ssize_t *shape,
 *                                     Py_ssize_t *strides, int ndim, bint inc) noexcept:
*/

  /* function exit code */
}

/* "View.MemoryView":1390
 * 
 * 
 * @cname('__pyx_memoryview_slice_assign_scalar')             # <<<<<<<<<<<<<<
 * cdef void slice_assign_scalar(__Pyx_memviewslice *dst, int ndim,
 *                               size_t itemsize, void *item,
*/

static void __pyx_memoryview_slice_assign_scalar(__Pyx_memviewslice *__pyx_v_dst, int __pyx_v_ndim, size_t __pyx_v_itemsize, void *__pyx_v_item, int __pyx_v_dtype_is_object) {

  /* "View.MemoryView":1394
 *                               size_t itemsize, void *item,
 *                               bint dtype_is_object) noexcept nogil:
 *     refcount_copying(dst, dtype_is_object, ndim, inc=False)             # <<<<<<<<<<<<<<
 *     _slice_assign_scalar(dst.data, dst.shape, dst.strides, ndim, itemsize, item)
 *     refcount_copying(dst, dtype_is_object, ndim, inc=True)
*/
  __pyx_memoryview_refcount_copying(__pyx_v_dst, __pyx_v_dtype_is_object, __pyx_v_ndim, 0);

  /* "View.MemoryView":1395
 *                               bint dtype_is_object) noexcept nogil:
 *     refcount_copying(dst, dtype_is_object, ndim, inc=False)
 *     _slice_assign_scalar(dst.data, dst.shape, dst.strides, ndim, itemsize, item)             # <<<<<<<<<<<<<<
 *     refcount_copying(dst, dtype_is_object, ndim, inc=True)
 * 
*/
  __pyx_memoryview__slice_assign_scalar(__pyx_v_dst->data, __pyx_v_dst->shape, __pyx_v_dst->strides, __pyx_v_ndim, __pyx_v_itemsize, __pyx_v_item);

  /* "View.MemoryView":1396
 *     refcount_copying(dst, dtype_is_object, ndim, inc=False)
 *     _slice_assign_scalar(dst.data, dst.shape, dst.strides, ndim, itemsize, item)
 *     refcount_copying(dst, dtype_is_object, ndim, inc=True)             # <<<<<<<<<<<<<<
 * 
 * 
*/
  __pyx_memoryview_refcount_copying(__pyx_v_dst, __pyx_v_dtype_is_object, __pyx_v_ndim, 1);

  /* "View.MemoryView":1390
 * 
 * 
 * @cname('__pyx_memoryview_slice_assign_scalar')             # <<<<<<<<<<<<<<
 * cdef void slice_assign_scalar(__Pyx_memviewslice *dst, int ndim,
 *                               size_t itemsize, void *item,
*/

  /* function exit code */
}

/* "View.MemoryView":1399
 * 
 * 
 * @cname('__pyx_memoryview__slice_assign_scalar')             # <<<<<<<<<<<<<<
 * cdef void _slice_assign_scalar(char *data, Py_ssize_t *shape,
 *                               Py_ssize_t *strides, int ndim,
*/

static void __pyx_memoryview__slice_assign_scalar(char *__pyx_v_data, Py_ssize_t *__pyx_v_shape, Py_ssize_t *__pyx_v_strides, int __pyx_v_ndim, size_t __pyx_v_itemsize, void *__pyx_v_item) {
  CYTHON_UNUSED Py_ssize_t __pyx_v_i;
  Py_ssize_t __pyx_v_stride;
  Py_ssize_t __pyx_v_extent;
  int __pyx_t_1;
  Py_ssize_t __pyx_t_2;
  Py_ssize_t __pyx_t_3;
  Py_ssize_t __pyx_t_4;

  /* "View.MemoryView":1404
 *                               size_t itemsize, void *item) noexcept nogil:
 *     cdef Py_ssize_t i
 *     cdef Py_ssize_t stride = strides[0]             # <<<<<<<<<<<<<<
 *     cdef Py_ssize_t extent = shape[0]
 * 
*/
  __pyx_v_stride = (__pyx_v_strides[0]);

  /* "View.MemoryView":1405
 *     cdef Py_ssize_t i
 *     cdef Py_ssize_t stride = strides[0]
 *     cdef Py_ssize_t extent = shape[0]             # <<<<<<<<<<<<<<
 * 
 *     if ndim == 1:
*/
  __pyx_v_extent = (__pyx_v_shape[0]);

  /* "View.MemoryView":1407
 *     cdef Py_ssize_t extent = shape[0]
 * 
 *     if ndim == 1:             # <<<<<<<<<<<<<<
 *         for i in range(extent):
 *             memcpy(data, item, itemsize)
*/
  __pyx_t_1 = (__pyx_v_ndim == 1);
  if (__pyx_t_1) {

    /* "View.MemoryView":1408
 * 
 *     if ndim == 1:
 *         for i in range(extent):             # <<<<<<<<<<<<<<
 *             memcpy(data, item, itemsize)
 *             data += stride
*/
    __pyx_t_2 = __pyx_v_extent;
    __pyx_t_3 = __pyx_t_2;
    for (__pyx_t_4 = 0; __pyx_t_4 < __pyx_t_3; __pyx_t_4+=1) {
      __pyx_v_i = __pyx_t_4;

      /* "View.MemoryView":1409
 *     if ndim == 1:
 *         for i in range(extent):
 *             memcpy(data, item, itemsize)             # <<<<<<<<<<<<<<
 *             data += stride
 *     else:
*/
      (void)(memcpy(__pyx_v_data, __pyx_v_item, __pyx_v_itemsize));

      /* "View.MemoryView":1410
 *         for i in range(extent):
 *             memcpy(data, item, itemsize)
 *             data += stride             # <<<<<<<<<<<<<<
 *     else:
 *         for i in range(extent):
*/
      __pyx_v_data = (__pyx_v_data + __pyx_v_stride);
    }

    /* "View.MemoryView":1407
 *     cdef Py_ssize_t extent = shape[0]
 * 
 *     if ndim == 1:             # <<<<<<<<<<<<<<
 *         for i in range(extent):
 *             memcpy(data, item, itemsize)
*/
    goto __pyx_L3;
  }

  /* "View.MemoryView":1412
 *             data += stride
 *     else:
 *         for i in range(extent):             # <<<<<<<<<<<<<<
 *             _slice_assign_scalar(data, shape + 1, strides + 1, ndim - 1, itemsize, item)
 *             data += stride
*/
  /*else*/ {
    __pyx_t_2 = __pyx_v_extent;
    __pyx_t_3 = __pyx_t_2;
    for (__pyx_t_4 = 0; __pyx_t_4 < __pyx_t_3; __pyx_t_4+=1) {
      __pyx_v_i = __pyx_t_4;

      /* "View.MemoryView":1413
 *     else:
 *         for i in range(extent):
 *             _slice_assign_scalar(data, shape + 1, strides + 1, ndim - 1, itemsize, item)             # <<<<<<<<<<<<<<
 *             data += stride
 * 
*/
      __pyx_memoryview__slice_assign_scalar(__pyx_v_data, (__pyx_v_shape + 1), (__pyx_v_strides + 1), (__pyx_v_ndim - 1), __pyx_v_itemsize, __pyx_v_item);

      /* "View.MemoryView":1414
 *         for i in range(extent):
 *             _slice_assign_scalar(data, shape + 1, strides + 1, ndim - 1, itemsize, item)
 *             data += stride             # <<<<<<<<<<<<<<
 * 
 * 
*/
      __pyx_v_data = (__pyx_v_data + __pyx_v_stride);
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  /* "View.MemoryView":1399
 * 
 * 
 * @cname('__pyx_memoryview__slice_assign_scalar')             # <<<<<<<<<<<<<<
 * cdef void _slice_assign_scalar(char *data, Py_ssize_t *shape,
 *                               Py_ssize_t *strides, int ndim,
*/

  /* function exit code */
}

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/* Python wrapper */
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PyObject *const *__pyx_args, Py_ssize_t __pyx_nargs, PyObject *__pyx_kwds
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PyObject *__pyx_args, PyObject *__pyx_kwds
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#if CYTHON_METH_FASTCALL
PyObject *const *__pyx_args, Py_ssize_t __pyx_nargs, PyObject *__pyx_kwds
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  CYTHON_UNUSED PyObject *const *__pyx_kwvalues;
  PyObject* values[3] = {0,0,0};
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 *             """The number of arrays that need to be broadcast to the same shape."""
*/

static CYTHON_INLINE int __pyx_f_5numpy_9broadcast_7numiter_numiter(PyArrayMultiIterObject *__pyx_v_self) {
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  /* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":282
 *         cdef inline int numiter(self) noexcept nogil:
 *             """The number of arrays that need to be broadcast to the same shape."""
 *             return PyArray_MultiIter_NUMITER(self)             # <<<<<<<<<<<<<<
 * 
 *         @property
*/
  __pyx_r = PyArray_MultiIter_NUMITER(__pyx_v_self);
  goto __pyx_L0;

  /* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":279
 *     ctypedef class numpy.broadcast [object PyArrayMultiIterObject, check_size ignore]:
 * 
 *         @property             # <<<<<<<<<<<<<<
 *         cdef inline int numiter(self) noexcept nogil:
 *             """The number of arrays that need to be broadcast to the same shape."""
*/

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":284
 *             return PyArray_MultiIter_NUMITER(self)
 * 
 *         @property             # <<<<<<<<<<<<<<
 *         cdef inline npy_intp size(self) noexcept nogil:
 *             """The total broadcasted size."""
*/

static CYTHON_INLINE npy_intp __pyx_f_5numpy_9broadcast_4size_size(PyArrayMultiIterObject *__pyx_v_self) {
  npy_intp __pyx_r;

  /* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":287
 *         cdef inline npy_intp size(self) noexcept nogil:
 *             """The total broadcasted size."""
 *             return PyArray_MultiIter_SIZE(self)             # <<<<<<<<<<<<<<
 * 
 *         @property
*/
  __pyx_r = PyArray_MultiIter_SIZE(__pyx_v_self);
  goto __pyx_L0;

  /* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":284
 *             return PyArray_MultiIter_NUMITER(self)
 * 
 *         @property             # <<<<<<<<<<<<<<
 *         cdef inline npy_intp size(self) noexcept nogil:
 *             """The total broadcasted size."""
*/

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":289
 *             return PyArray_MultiIter_SIZE(self)
 * 
 *         @property             # <<<<<<<<<<<<<<
 *         cdef inline npy_intp index(self) noexcept nogil:
 *             """The current (1-d) index into the broadcasted result."""
*/

static CYTHON_INLINE npy_intp __pyx_f_5numpy_9broadcast_5index_index(PyArrayMultiIterObject *__pyx_v_self) {
  npy_intp __pyx_r;

  /* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":292
 *         cdef inline npy_intp index(self) noexcept nogil:
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 *             return PyArray_MultiIter_INDEX(self)             # <<<<<<<<<<<<<<
 * 
 *         @property
*/
  __pyx_r = PyArray_MultiIter_INDEX(__pyx_v_self);
  goto __pyx_L0;

  /* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":289
 *             return PyArray_MultiIter_SIZE(self)
 * 
 *         @property             # <<<<<<<<<<<<<<
 *         cdef inline npy_intp index(self) noexcept nogil:
 *             """The current (1-d) index into the broadcasted result."""
*/

  /* function exit code */
  __pyx_L0:;
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/* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":294
 *             return PyArray_MultiIter_INDEX(self)
 * 
 *         @property             # <<<<<<<<<<<<<<
 *         cdef inline int nd(self) noexcept nogil:
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*/

static CYTHON_INLINE int __pyx_f_5numpy_9broadcast_2nd_nd(PyArrayMultiIterObject *__pyx_v_self) {
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  /* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":297
 *         cdef inline int nd(self) noexcept nogil:
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 *             return PyArray_MultiIter_NDIM(self)             # <<<<<<<<<<<<<<
 * 
 *         @property
*/
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  /* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":294
 *             return PyArray_MultiIter_INDEX(self)
 * 
 *         @property             # <<<<<<<<<<<<<<
 *         cdef inline int nd(self) noexcept nogil:
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*/

  /* function exit code */
  __pyx_L0:;
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/* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":299
 *             return PyArray_MultiIter_NDIM(self)
 * 
 *         @property             # <<<<<<<<<<<<<<
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static CYTHON_INLINE npy_intp *__pyx_f_5numpy_9broadcast_10dimensions_dimensions(PyArrayMultiIterObject *__pyx_v_self) {
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  /* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":302
 *         cdef inline npy_intp* dimensions(self) noexcept nogil:
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 * 
 *         @property
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  /* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":299
 *             return PyArray_MultiIter_NDIM(self)
 * 
 *         @property             # <<<<<<<<<<<<<<
 *         cdef inline npy_intp* dimensions(self) noexcept nogil:
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*/

  /* function exit code */
  __pyx_L0:;
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/* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":304
 *             return PyArray_MultiIter_DIMS(self)
 * 
 *         @property             # <<<<<<<<<<<<<<
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static CYTHON_INLINE void **__pyx_f_5numpy_9broadcast_5iters_iters(PyArrayMultiIterObject *__pyx_v_self) {
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  /* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":308
 *             """An array of iterator objects that holds the iterators for the arrays to be broadcast together.
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 * 
 * 
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  /* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":304
 *             return PyArray_MultiIter_DIMS(self)
 * 
 *         @property             # <<<<<<<<<<<<<<
 *         cdef inline void** iters(self) noexcept nogil:
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*/

  /* function exit code */
  __pyx_L0:;
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/* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":322
 *         # Instead, we use properties that map to the corresponding C-API functions.
 * 
 *         @property             # <<<<<<<<<<<<<<
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static CYTHON_INLINE PyObject *__pyx_f_5numpy_7ndarray_4base_base(PyArrayObject *__pyx_v_self) {
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 *         @property
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  /* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":322
 *         # Instead, we use properties that map to the corresponding C-API functions.
 * 
 *         @property             # <<<<<<<<<<<<<<
 *         cdef inline PyObject* base(self) noexcept nogil:
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  /* function exit code */
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/* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":328
 *             return PyArray_BASE(self)
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 *         @property             # <<<<<<<<<<<<<<
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static CYTHON_INLINE PyArray_Descr *__pyx_f_5numpy_7ndarray_5descr_descr(PyArrayObject *__pyx_v_self) {
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 *             """Returns an owned reference to the dtype of the array.
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 *             return <dtype>PyArray_DESCR(self)             # <<<<<<<<<<<<<<
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 *         @property
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  /* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":328
 *             return PyArray_BASE(self)
 * 
 *         @property             # <<<<<<<<<<<<<<
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/* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":334
 *             return <dtype>PyArray_DESCR(self)
 * 
 *         @property             # <<<<<<<<<<<<<<
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static CYTHON_INLINE int __pyx_f_5numpy_7ndarray_4ndim_ndim(PyArrayObject *__pyx_v_self) {
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  /* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":338
 *             """Returns the number of dimensions in the array.
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 * 
 *         @property
*/
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  /* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":334
 *             return <dtype>PyArray_DESCR(self)
 * 
 *         @property             # <<<<<<<<<<<<<<
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  /* function exit code */
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/* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":340
 *             return PyArray_NDIM(self)
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 *         @property             # <<<<<<<<<<<<<<
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static CYTHON_INLINE npy_intp *__pyx_f_5numpy_7ndarray_5shape_shape(PyArrayObject *__pyx_v_self) {
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  /* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":346
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 * 
 *         @property
*/
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  /* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":340
 *             return PyArray_NDIM(self)
 * 
 *         @property             # <<<<<<<<<<<<<<
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/* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":348
 *             return PyArray_DIMS(self)
 * 
 *         @property             # <<<<<<<<<<<<<<
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static CYTHON_INLINE npy_intp *__pyx_f_5numpy_7ndarray_7strides_strides(PyArrayObject *__pyx_v_self) {
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  /* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":353
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 * 
 *         @property
*/
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  /* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":348
 *             return PyArray_DIMS(self)
 * 
 *         @property             # <<<<<<<<<<<<<<
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  /* function exit code */
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/* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":355
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 *         @property
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  /* "../../../../private/var/folders/dr/cck4_3v12q38ttcrstf8rlp80000gr/T/build-env-_kma84j2/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd":355
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 *         @property             # <<<<<<<<<<<<<<
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 *             return PyArray_SIZE(self)
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static int __pyx_pf_6pyRing_8waveform_6TEOBPM___cinit__(struct __pyx_obj_6pyRing_8waveform_TEOBPM *__pyx_v_self, double __pyx_v_t0, double __pyx_v_m1, double __pyx_v_m2, double __pyx_v_chi1, double __pyx_v_chi2, PyObject *__pyx_v_phases, double __pyx_v_r, double __pyx_v_iota, double __pyx_v_phi, PyObject *__pyx_v_modes, PyObject *__pyx_v_TGR_params, unsigned int __pyx_v_geom, PyObject *__pyx_v_NR_fit_coeffs) {
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 * 
 *         # Sanity checks
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    /* "pyRing/waveform.pyx":1927
 *         cdef double coshc3A # auxiliary variable
 * 
 *         if(NR_fit_coeffs is not None):             # <<<<<<<<<<<<<<
 *             omg_peak = NR_fit_coeffs[(l,m)]['omg_peak']
 *             A_peak   = NR_fit_coeffs[(l,m)]['A_peak_over_nu']
*/
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  }

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 *             A_peak   = NR_fit_coeffs[(l,m)]['A_peak_over_nu']
 *         else:
 *             omg_peak = eu._omega_peak(    self.nu, self.X12, self.Shat,                      self.a0,           l, m)             # <<<<<<<<<<<<<<
 *             A_peak   = eu._amplitude_peak(self.nu, self.X12, self.Shat, self.a12, self.Sbar, self.a0, omg_peak, l, m)     # [A/nu]
 * 
*/
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    /* "pyRing/waveform.pyx":1932
 *         else:
 *             omg_peak = eu._omega_peak(    self.nu, self.X12, self.Shat,                      self.a0,           l, m)
 *             A_peak   = eu._amplitude_peak(self.nu, self.X12, self.Shat, self.a12, self.Sbar, self.a0, omg_peak, l, m)     # [A/nu]             # <<<<<<<<<<<<<<
 * 
 *         Domg = eu._dOmega(omg1, self.Mf/self.M, omg_peak)
*/
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 *             A_peak   = eu._amplitude_peak(self.nu, self.X12, self.Shat, self.a12, self.Sbar, self.a0, omg_peak, l, m)     # [A/nu]
 * 
 *         Domg = eu._dOmega(omg1, self.Mf/self.M, omg_peak)             # <<<<<<<<<<<<<<
 * 
 *         ''' The parameters c3A, c3phi, c4phi are implemented in eob_utils.pyx, section 3.
*/
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 *         they enter in eqs. 5.4-5.10 of arXiv:1904.09550v2. '''
 * 
 *         if(NR_fit_coeffs is not None):             # <<<<<<<<<<<<<<
 *             c3A = NR_fit_coeffs[(l,m)]['c3A']
 *             c3p = NR_fit_coeffs[(l,m)]['c3p']
*/
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 * 
 *         if(NR_fit_coeffs is not None):
 *             c3A = NR_fit_coeffs[(l,m)]['c3A']             # <<<<<<<<<<<<<<
 *             c3p = NR_fit_coeffs[(l,m)]['c3p']
 *             c4p = NR_fit_coeffs[(l,m)]['c4p']
*/
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 *             c3p = NR_fit_coeffs[(l,m)]['c3p']             # <<<<<<<<<<<<<<
 *             c4p = NR_fit_coeffs[(l,m)]['c4p']
 *         else:
*/
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 *         else:
 *             c3A = eu._c3_A(  self.nu, self.X12, self.Shat, self.a12, l, m)
*/
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    /* "pyRing/waveform.pyx":1940
 *         they enter in eqs. 5.4-5.10 of arXiv:1904.09550v2. '''
 * 
 *         if(NR_fit_coeffs is not None):             # <<<<<<<<<<<<<<
 *             c3A = NR_fit_coeffs[(l,m)]['c3A']
 *             c3p = NR_fit_coeffs[(l,m)]['c3p']
*/
    goto __pyx_L20;
  }

  /* "pyRing/waveform.pyx":1945
 *             c4p = NR_fit_coeffs[(l,m)]['c4p']
 *         else:
 *             c3A = eu._c3_A(  self.nu, self.X12, self.Shat, self.a12, l, m)             # <<<<<<<<<<<<<<
 *             c3p = eu._c3_phi(self.nu, self.X12, self.Shat,           l, m)
 *             c4p = eu._c4_phi(self.nu, self.X12, self.Shat,           l, m)
*/
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    /* "pyRing/waveform.pyx":1946
 *         else:
 *             c3A = eu._c3_A(  self.nu, self.X12, self.Shat, self.a12, l, m)
 *             c3p = eu._c3_phi(self.nu, self.X12, self.Shat,           l, m)             # <<<<<<<<<<<<<<
 *             c4p = eu._c4_phi(self.nu, self.X12, self.Shat,           l, m)
 * 
*/
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 *             c3A = eu._c3_A(  self.nu, self.X12, self.Shat, self.a12, l, m)
 *             c3p = eu._c3_phi(self.nu, self.X12, self.Shat,           l, m)
 *             c4p = eu._c4_phi(self.nu, self.X12, self.Shat,           l, m)             # <<<<<<<<<<<<<<
 * 
 *         c2A     = 0.5 * alph21                                 # eq. 5.6 of arXiv:1904.09550v2
*/
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 *             c4p = eu._c4_phi(self.nu, self.X12, self.Shat,           l, m)
 * 
 *         c2A     = 0.5 * alph21                                 # eq. 5.6 of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 *         coshc3A = cosh(c3A)
 *         c1A     = A_peak * alph1 * (coshc3A*coshc3A) / c2A     # eq. 5.8 of arXiv:1904.09550v2
*/
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 * 
 *         c2A     = 0.5 * alph21                                 # eq. 5.6 of arXiv:1904.09550v2
 *         coshc3A = cosh(c3A)             # <<<<<<<<<<<<<<
 *         c1A     = A_peak * alph1 * (coshc3A*coshc3A) / c2A     # eq. 5.8 of arXiv:1904.09550v2
 *         c4A     = A_peak - c1A * tanh(c3A)                     # eq. 5.7 of arXiv:1904.09550v2
*/
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 *         c2A     = 0.5 * alph21                                 # eq. 5.6 of arXiv:1904.09550v2
 *         coshc3A = cosh(c3A)
 *         c1A     = A_peak * alph1 * (coshc3A*coshc3A) / c2A     # eq. 5.8 of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 *         c4A     = A_peak - c1A * tanh(c3A)                     # eq. 5.7 of arXiv:1904.09550v2
 * 
*/
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 *         coshc3A = cosh(c3A)
 *         c1A     = A_peak * alph1 * (coshc3A*coshc3A) / c2A     # eq. 5.8 of arXiv:1904.09550v2
 *         c4A     = A_peak - c1A * tanh(c3A)                     # eq. 5.7 of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 * 
 *         c2p     = alph21                                       # eq. 5.10 of arXiv:1904.09550v2
*/
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 *         c4A     = A_peak - c1A * tanh(c3A)                     # eq. 5.7 of arXiv:1904.09550v2
 * 
 *         c2p     = alph21                                       # eq. 5.10 of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 *         c1p     = Domg * (1.0+c3p+c4p) / (c2p * (c3p+2.0*c4p)) # eq. 5.9 of arXiv:1904.09550v2
 * 
*/
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 * 
 *         c2p     = alph21                                       # eq. 5.10 of arXiv:1904.09550v2
 *         c1p     = Domg * (1.0+c3p+c4p) / (c2p * (c3p+2.0*c4p)) # eq. 5.9 of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 * 
 *         cdef dict single_mode_fit_coefficients = {}
*/
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 * 
 *         cdef dict single_mode_fit_coefficients = {}             # <<<<<<<<<<<<<<
 * 
 *         single_mode_fit_coefficients['a1']     = c1A
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 * 
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 *         single_mode_fit_coefficients['a2']     = c2A
 *         single_mode_fit_coefficients['a3']     = c3A
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 * 
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 *         single_mode_fit_coefficients['a2']     = c2A             # <<<<<<<<<<<<<<
 *         single_mode_fit_coefficients['a3']     = c3A
 *         single_mode_fit_coefficients['a4']     = c4A
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 *         single_mode_fit_coefficients['a1']     = c1A
 *         single_mode_fit_coefficients['a2']     = c2A
 *         single_mode_fit_coefficients['a3']     = c3A             # <<<<<<<<<<<<<<
 *         single_mode_fit_coefficients['a4']     = c4A
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/* "pyRing/waveform.pyx":1975
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/* "pyRing/waveform.pyx":1980
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/* "pyRing/waveform.pyx":1983
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}

static PyMethodDef __pyx_methods_6pyRing_8waveform_QNM[] = {
  {"__reduce_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_3QNM_15__reduce_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_3QNM_14__reduce_cython__},
  {"__setstate_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_3QNM_17__setstate_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_3QNM_16__setstate_cython__},
  {0, 0, 0, 0}
};

static struct PyGetSetDef __pyx_getsets_6pyRing_8waveform_QNM[] = {
  {"s", __pyx_getprop_6pyRing_8waveform_3QNM_s, __pyx_setprop_6pyRing_8waveform_3QNM_s, PyDoc_STR("s: 'unsigned int'"), 0},
  {"l", __pyx_getprop_6pyRing_8waveform_3QNM_l, __pyx_setprop_6pyRing_8waveform_3QNM_l, PyDoc_STR("l: 'unsigned int'"), 0},
  {"m", __pyx_getprop_6pyRing_8waveform_3QNM_m, __pyx_setprop_6pyRing_8waveform_3QNM_m, PyDoc_STR("m: 'int'"), 0},
  {"n", __pyx_getprop_6pyRing_8waveform_3QNM_n, __pyx_setprop_6pyRing_8waveform_3QNM_n, PyDoc_STR("n: 'unsigned int'"), 0},
  {"geom", __pyx_getprop_6pyRing_8waveform_3QNM_geom, __pyx_setprop_6pyRing_8waveform_3QNM_geom, PyDoc_STR("geom: 'unsigned int'"), 0},
  {"omegar_interp", __pyx_getprop_6pyRing_8waveform_3QNM_omegar_interp, __pyx_setprop_6pyRing_8waveform_3QNM_omegar_interp, PyDoc_STR("omegar_interp: object"), 0},
  {"omegai_interp", __pyx_getprop_6pyRing_8waveform_3QNM_omegai_interp, __pyx_setprop_6pyRing_8waveform_3QNM_omegai_interp, PyDoc_STR("omegai_interp: object"), 0},
  {"prefactor_freq", __pyx_getprop_6pyRing_8waveform_3QNM_prefactor_freq, __pyx_setprop_6pyRing_8waveform_3QNM_prefactor_freq, PyDoc_STR("prefactor_freq: 'double'"), 0},
  {"prefactor_tau", __pyx_getprop_6pyRing_8waveform_3QNM_prefactor_tau, __pyx_setprop_6pyRing_8waveform_3QNM_prefactor_tau, PyDoc_STR("prefactor_tau: 'double'"), 0},
  {0, 0, 0, 0, 0}
};
#if CYTHON_USE_TYPE_SPECS
static PyType_Slot __pyx_type_6pyRing_8waveform_QNM_slots[] = {
  {Py_tp_dealloc, (void *)__pyx_tp_dealloc_6pyRing_8waveform_QNM},
  {Py_tp_doc, (void *)PyDoc_STR("\n\n    Class to compute the complex frequency and damping time of a QNM.\n\n    Parameters\n    ----------\n\n    s : int\n        Spin-weight of the QNM.\n\n    l : int\n        Orbital angular number of the QNM.\n\n    m : int\n        Azimuthal number of the QNM.\n\n    n : int\n        Radial (overtone) number of the QNM.\n\n    interpolants : dict\n        Dictionary of interpolants for the QNM frequencies and damping times.\n\n    geom : int, optional\n        Geometric units flag. If 1, the QNM frequencies are returned in geometric units, otherwise they are returned in standard units.\n\n    Attributes\n    ----------\n\n    s : int\n        Spin-weight of the QNM.\n    l : int\n        Orbital angular number of the QNM.\n    m : int\n        Azimuthal number of the QNM.\n    n : int\n        Radial (overtone) number of the QNM.\n    geom : int\n        Geometric units flag. If 1, the QNM frequencies are returned in geometric units, otherwise they are returned in standard units.\n    omegar_interp : scipy.interpolate.interp1d\n        Interpolant for the real part of the QNM frequency.\n    omegai_interp : scipy.interpolate.interp1d\n        Interpolant for the imaginary part of the QNM frequency.\n    prefactor_freq : float\n        Prefactor for the QNM frequency.\n    prefactor_tau : float\n        Prefactor for the QNM damping time.\n    \n    Functions\n    ---------\n\n    f : float\n        Returns the real part of the QNM frequency.\n    tau : float\n        Returns the imaginary part of the QNM frequency.\n    f_KN : float\n        Returns the real part of the QNM frequency for the Kerr-Newman metric.\n    tau_KN : float\n        Returns the imaginary part of the QNM frequency for the Kerr-Newman metric.\n    f_BW : float\n        Returns the real part of the QNM frequency for the braneworld model.\n    tau_BW : float\n        Returns the imaginary part of the QNM frequency for the braneworld model.\n\n    ")},
  {Py_tp_traverse, (void *)__pyx_tp_traverse_6pyRing_8waveform_QNM},
  {Py_tp_clear, (void *)__pyx_tp_clear_6pyRing_8waveform_QNM},
  {Py_tp_methods, (void *)__pyx_methods_6pyRing_8waveform_QNM},
  {Py_tp_getset, (void *)__pyx_getsets_6pyRing_8waveform_QNM},
  {Py_tp_new, (void *)__pyx_tp_new_6pyRing_8waveform_QNM},
  {0, 0},
};
static PyType_Spec __pyx_type_6pyRing_8waveform_QNM_spec = {
  "pyRing.waveform.QNM",
  sizeof(struct __pyx_obj_6pyRing_8waveform_QNM),
  0,
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC,
  __pyx_type_6pyRing_8waveform_QNM_slots,
};
#else

static PyTypeObject __pyx_type_6pyRing_8waveform_QNM = {
  PyVarObject_HEAD_INIT(0, 0)
  "pyRing.waveform.""QNM", /*tp_name*/
  sizeof(struct __pyx_obj_6pyRing_8waveform_QNM), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc_6pyRing_8waveform_QNM, /*tp_dealloc*/
  #if PY_VERSION_HEX < 0x030800b4
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b4
  0, /*tp_vectorcall_offset*/
  #endif
  0, /*tp_getattr*/
  0, /*tp_setattr*/
  0, /*tp_as_async*/
  0, /*tp_repr*/
  0, /*tp_as_number*/
  0, /*tp_as_sequence*/
  0, /*tp_as_mapping*/
  0, /*tp_hash*/
  0, /*tp_call*/
  0, /*tp_str*/
  0, /*tp_getattro*/
  0, /*tp_setattro*/
  0, /*tp_as_buffer*/
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC, /*tp_flags*/
  PyDoc_STR("\n\n    Class to compute the complex frequency and damping time of a QNM.\n\n    Parameters\n    ----------\n\n    s : int\n        Spin-weight of the QNM.\n\n    l : int\n        Orbital angular number of the QNM.\n\n    m : int\n        Azimuthal number of the QNM.\n\n    n : int\n        Radial (overtone) number of the QNM.\n\n    interpolants : dict\n        Dictionary of interpolants for the QNM frequencies and damping times.\n\n    geom : int, optional\n        Geometric units flag. If 1, the QNM frequencies are returned in geometric units, otherwise they are returned in standard units.\n\n    Attributes\n    ----------\n\n    s : int\n        Spin-weight of the QNM.\n    l : int\n        Orbital angular number of the QNM.\n    m : int\n        Azimuthal number of the QNM.\n    n : int\n        Radial (overtone) number of the QNM.\n    geom : int\n        Geometric units flag. If 1, the QNM frequencies are returned in geometric units, otherwise they are returned in standard units.\n    omegar_interp : scipy.interpolate.interp1d\n        Interpolant for the real part of the QNM frequency.\n    omegai_interp : scipy.interpolate.interp1d\n        Interpolant for the imaginary part of the QNM frequency.\n    prefactor_freq : float\n        Prefactor for the QNM frequency.\n    prefactor_tau : float\n        Prefactor for the QNM damping time.\n    \n    Functions\n    ---------\n\n    f : float\n        Returns the real part of the QNM frequency.\n    tau : float\n        Returns the imaginary part of the QNM frequency.\n    f_KN : float\n        Returns the real part of the QNM frequency for the Kerr-Newman metric.\n    tau_KN : float\n        Returns the imaginary part of the QNM frequency for the Kerr-Newman metric.\n    f_BW : float\n        Returns the real part of the QNM frequency for the braneworld model.\n    tau_BW : float\n        Returns the imaginary part of the QNM frequency for the braneworld model.\n\n    "), /*tp_doc*/
  __pyx_tp_traverse_6pyRing_8waveform_QNM, /*tp_traverse*/
  __pyx_tp_clear_6pyRing_8waveform_QNM, /*tp_clear*/
  0, /*tp_richcompare*/
  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
  0, /*tp_iternext*/
  __pyx_methods_6pyRing_8waveform_QNM, /*tp_methods*/
  0, /*tp_members*/
  __pyx_getsets_6pyRing_8waveform_QNM, /*tp_getset*/
  0, /*tp_base*/
  0, /*tp_dict*/
  0, /*tp_descr_get*/
  0, /*tp_descr_set*/
  #if !CYTHON_USE_TYPE_SPECS
  0, /*tp_dictoffset*/
  #endif
  0, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_6pyRing_8waveform_QNM, /*tp_new*/
  0, /*tp_free*/
  0, /*tp_is_gc*/
  0, /*tp_bases*/
  0, /*tp_mro*/
  0, /*tp_cache*/
  0, /*tp_subclasses*/
  0, /*tp_weaklist*/
  0, /*tp_del*/
  0, /*tp_version_tag*/
  #if CYTHON_USE_TP_FINALIZE
  0, /*tp_finalize*/
  #else
  NULL, /*tp_finalize*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b1 && (!CYTHON_COMPILING_IN_PYPY || PYPY_VERSION_NUM >= 0x07030800)
  0, /*tp_vectorcall*/
  #endif
  #if __PYX_NEED_TP_PRINT_SLOT == 1
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030C0000
  0, /*tp_watched*/
  #endif
  #if PY_VERSION_HEX >= 0x030d00A4
  0, /*tp_versions_used*/
  #endif
  #if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX >= 0x03090000 && PY_VERSION_HEX < 0x030a0000
  0, /*tp_pypy_flags*/
  #endif
};
#endif
static struct __pyx_vtabstruct_6pyRing_8waveform_QNM_fit __pyx_vtable_6pyRing_8waveform_QNM_fit;

static PyObject *__pyx_tp_new_6pyRing_8waveform_QNM_fit(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_6pyRing_8waveform_QNM_fit *p;
  PyObject *o;
  #if CYTHON_COMPILING_IN_LIMITED_API
  allocfunc alloc_func = (allocfunc)PyType_GetSlot(t, Py_tp_alloc);
  o = alloc_func(t, 0);
  #else
  if (likely(!__Pyx_PyType_HasFeature(t, Py_TPFLAGS_IS_ABSTRACT))) {
    o = (*t->tp_alloc)(t, 0);
  } else {
    o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_mstate_global->__pyx_empty_tuple, 0);
  }
  if (unlikely(!o)) return 0;
  #endif
  p = ((struct __pyx_obj_6pyRing_8waveform_QNM_fit *)o);
  p->__pyx_vtab = __pyx_vtabptr_6pyRing_8waveform_QNM_fit;
  p->f_coeff = Py_None; Py_INCREF(Py_None);
  p->q_coeff = Py_None; Py_INCREF(Py_None);
  if (unlikely(__pyx_pw_6pyRing_8waveform_7QNM_fit_1__cinit__(o, a, k) < 0)) goto bad;
  return o;
  bad:
  Py_DECREF(o); o = 0;
  return NULL;
}

static void __pyx_tp_dealloc_6pyRing_8waveform_QNM_fit(PyObject *o) {
  struct __pyx_obj_6pyRing_8waveform_QNM_fit *p = (struct __pyx_obj_6pyRing_8waveform_QNM_fit *)o;
  #if CYTHON_USE_TP_FINALIZE
  if (unlikely((PY_VERSION_HEX >= 0x03080000 || __Pyx_PyType_HasFeature(Py_TYPE(o), Py_TPFLAGS_HAVE_FINALIZE)) && __Pyx_PyObject_GetSlot(o, tp_finalize, destructor)) && !__Pyx_PyObject_GC_IsFinalized(o)) {
    if (__Pyx_PyObject_GetSlot(o, tp_dealloc, destructor) == __pyx_tp_dealloc_6pyRing_8waveform_QNM_fit) {
      if (PyObject_CallFinalizerFromDealloc(o)) return;
    }
  }
  #endif
  PyObject_GC_UnTrack(o);
  Py_CLEAR(p->f_coeff);
  Py_CLEAR(p->q_coeff);
  #if CYTHON_USE_TYPE_SLOTS
  (*Py_TYPE(o)->tp_free)(o);
  #else
  {
    freefunc tp_free = (freefunc)PyType_GetSlot(Py_TYPE(o), Py_tp_free);
    if (tp_free) tp_free(o);
  }
  #endif
}

static int __pyx_tp_traverse_6pyRing_8waveform_QNM_fit(PyObject *o, visitproc v, void *a) {
  int e;
  struct __pyx_obj_6pyRing_8waveform_QNM_fit *p = (struct __pyx_obj_6pyRing_8waveform_QNM_fit *)o;
  {
    e = __Pyx_call_type_traverse(o, 1, v, a);
    if (e) return e;
  }
  if (p->f_coeff) {
    e = (*v)(p->f_coeff, a); if (e) return e;
  }
  if (p->q_coeff) {
    e = (*v)(p->q_coeff, a); if (e) return e;
  }
  return 0;
}

static int __pyx_tp_clear_6pyRing_8waveform_QNM_fit(PyObject *o) {
  PyObject* tmp;
  struct __pyx_obj_6pyRing_8waveform_QNM_fit *p = (struct __pyx_obj_6pyRing_8waveform_QNM_fit *)o;
  tmp = ((PyObject*)p->f_coeff);
  p->f_coeff = Py_None; Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->q_coeff);
  p->q_coeff = Py_None; Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  return 0;
}

static PyObject *__pyx_getprop_6pyRing_8waveform_7QNM_fit_l(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_7QNM_fit_1l_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_7QNM_fit_l(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_7QNM_fit_1l_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_7QNM_fit_m(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_7QNM_fit_1m_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_7QNM_fit_m(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_7QNM_fit_1m_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_7QNM_fit_n(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_7QNM_fit_1n_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_7QNM_fit_n(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_7QNM_fit_1n_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_7QNM_fit_charge(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_7QNM_fit_6charge_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_7QNM_fit_charge(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_7QNM_fit_6charge_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_7QNM_fit_f_coeff(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_7QNM_fit_7f_coeff_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_7QNM_fit_f_coeff(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_7QNM_fit_7f_coeff_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_7QNM_fit_7f_coeff_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_7QNM_fit_q_coeff(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_7QNM_fit_7q_coeff_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_7QNM_fit_q_coeff(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_7QNM_fit_7q_coeff_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_7QNM_fit_7q_coeff_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_7QNM_fit_prefactor_freq(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_7QNM_fit_14prefactor_freq_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_7QNM_fit_prefactor_freq(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_7QNM_fit_14prefactor_freq_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyMethodDef __pyx_methods_6pyRing_8waveform_QNM_fit[] = {
  {"__reduce_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_7QNM_fit_15__reduce_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_7QNM_fit_14__reduce_cython__},
  {"__setstate_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_7QNM_fit_17__setstate_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_7QNM_fit_16__setstate_cython__},
  {0, 0, 0, 0}
};

static struct PyGetSetDef __pyx_getsets_6pyRing_8waveform_QNM_fit[] = {
  {"l", __pyx_getprop_6pyRing_8waveform_7QNM_fit_l, __pyx_setprop_6pyRing_8waveform_7QNM_fit_l, PyDoc_STR("l: 'unsigned int'"), 0},
  {"m", __pyx_getprop_6pyRing_8waveform_7QNM_fit_m, __pyx_setprop_6pyRing_8waveform_7QNM_fit_m, PyDoc_STR("m: 'int'"), 0},
  {"n", __pyx_getprop_6pyRing_8waveform_7QNM_fit_n, __pyx_setprop_6pyRing_8waveform_7QNM_fit_n, PyDoc_STR("n: 'unsigned int'"), 0},
  {"charge", __pyx_getprop_6pyRing_8waveform_7QNM_fit_charge, __pyx_setprop_6pyRing_8waveform_7QNM_fit_charge, PyDoc_STR("charge: 'unsigned int'"), 0},
  {"f_coeff", __pyx_getprop_6pyRing_8waveform_7QNM_fit_f_coeff, __pyx_setprop_6pyRing_8waveform_7QNM_fit_f_coeff, PyDoc_STR("f_coeff: object"), 0},
  {"q_coeff", __pyx_getprop_6pyRing_8waveform_7QNM_fit_q_coeff, __pyx_setprop_6pyRing_8waveform_7QNM_fit_q_coeff, PyDoc_STR("q_coeff: object"), 0},
  {"prefactor_freq", __pyx_getprop_6pyRing_8waveform_7QNM_fit_prefactor_freq, __pyx_setprop_6pyRing_8waveform_7QNM_fit_prefactor_freq, PyDoc_STR("prefactor_freq: 'double'"), 0},
  {0, 0, 0, 0, 0}
};
#if CYTHON_USE_TYPE_SPECS
static PyType_Slot __pyx_type_6pyRing_8waveform_QNM_fit_slots[] = {
  {Py_tp_dealloc, (void *)__pyx_tp_dealloc_6pyRing_8waveform_QNM_fit},
  {Py_tp_doc, (void *)PyDoc_STR("\n    \n    Class to compute the complex frequency and damping time of a QNM using fits to the Berti et al. (2015) fits.\n\n    Parameters\n    ----------\n\n    l : int\n        Orbital angular number of the QNM.  \n    m : int\n        Azimuthal number of the QNM.\n    n : int\n        Radial (overtone) number of the QNM.\n    charge : int, optional\n        Charge flag. If not 0, compute the QNM for a charged BH.\n    geom : int, optional\n        Geometric units flag. If 1, the QNM frequencies are returned in geometric units, otherwise they are returned in the International System of Units. Default is 0.\n    \n    Attributes\n    ----------\n\n    l : int\n        Orbital angular number of the QNM.\n    m : int\n        Azimuthal number of the QNM.\n    n : int \n        Radial (overtone) number of the QNM.\n    charge : int\n        Charge flag. If not 0, compute the QNM for a charged BH.\n    f_coeff : list\n        List of coefficients for the real part of the complex QNM frequency.\n    q_coeff : list\n        List of coefficients for the quality factor of the complex QNM frequency.\n    \n    Functions\n    ---------\n\n    f : float\n        Returns the real part of the QNM frequency.\n    q : float\n        Returns the quality factor of the QNM frequency.\n    tau : float\n        Returns the imaginary part of the QNM frequency.\n    f_KN : float\n        Returns the real part of the QNM frequency for the Kerr-Newman metric.\n    tau_KN : float\n        Returns the imaginary part of the QNM frequency for the Kerr-Newman metric.\n    q_KN : float\n        Returns the quality factor of the QNM frequency for the Kerr-Newman metric.\n\n    ")},
  {Py_tp_traverse, (void *)__pyx_tp_traverse_6pyRing_8waveform_QNM_fit},
  {Py_tp_clear, (void *)__pyx_tp_clear_6pyRing_8waveform_QNM_fit},
  {Py_tp_methods, (void *)__pyx_methods_6pyRing_8waveform_QNM_fit},
  {Py_tp_getset, (void *)__pyx_getsets_6pyRing_8waveform_QNM_fit},
  {Py_tp_new, (void *)__pyx_tp_new_6pyRing_8waveform_QNM_fit},
  {0, 0},
};
static PyType_Spec __pyx_type_6pyRing_8waveform_QNM_fit_spec = {
  "pyRing.waveform.QNM_fit",
  sizeof(struct __pyx_obj_6pyRing_8waveform_QNM_fit),
  0,
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC,
  __pyx_type_6pyRing_8waveform_QNM_fit_slots,
};
#else

static PyTypeObject __pyx_type_6pyRing_8waveform_QNM_fit = {
  PyVarObject_HEAD_INIT(0, 0)
  "pyRing.waveform.""QNM_fit", /*tp_name*/
  sizeof(struct __pyx_obj_6pyRing_8waveform_QNM_fit), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc_6pyRing_8waveform_QNM_fit, /*tp_dealloc*/
  #if PY_VERSION_HEX < 0x030800b4
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b4
  0, /*tp_vectorcall_offset*/
  #endif
  0, /*tp_getattr*/
  0, /*tp_setattr*/
  0, /*tp_as_async*/
  0, /*tp_repr*/
  0, /*tp_as_number*/
  0, /*tp_as_sequence*/
  0, /*tp_as_mapping*/
  0, /*tp_hash*/
  0, /*tp_call*/
  0, /*tp_str*/
  0, /*tp_getattro*/
  0, /*tp_setattro*/
  0, /*tp_as_buffer*/
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC, /*tp_flags*/
  PyDoc_STR("\n    \n    Class to compute the complex frequency and damping time of a QNM using fits to the Berti et al. (2015) fits.\n\n    Parameters\n    ----------\n\n    l : int\n        Orbital angular number of the QNM.  \n    m : int\n        Azimuthal number of the QNM.\n    n : int\n        Radial (overtone) number of the QNM.\n    charge : int, optional\n        Charge flag. If not 0, compute the QNM for a charged BH.\n    geom : int, optional\n        Geometric units flag. If 1, the QNM frequencies are returned in geometric units, otherwise they are returned in the International System of Units. Default is 0.\n    \n    Attributes\n    ----------\n\n    l : int\n        Orbital angular number of the QNM.\n    m : int\n        Azimuthal number of the QNM.\n    n : int \n        Radial (overtone) number of the QNM.\n    charge : int\n        Charge flag. If not 0, compute the QNM for a charged BH.\n    f_coeff : list\n        List of coefficients for the real part of the complex QNM frequency.\n    q_coeff : list\n        List of coefficients for the quality factor of the complex QNM frequency.\n    \n    Functions\n    ---------\n\n    f : float\n        Returns the real part of the QNM frequency.\n    q : float\n        Returns the quality factor of the QNM frequency.\n    tau : float\n        Returns the imaginary part of the QNM frequency.\n    f_KN : float\n        Returns the real part of the QNM frequency for the Kerr-Newman metric.\n    tau_KN : float\n        Returns the imaginary part of the QNM frequency for the Kerr-Newman metric.\n    q_KN : float\n        Returns the quality factor of the QNM frequency for the Kerr-Newman metric.\n\n    "), /*tp_doc*/
  __pyx_tp_traverse_6pyRing_8waveform_QNM_fit, /*tp_traverse*/
  __pyx_tp_clear_6pyRing_8waveform_QNM_fit, /*tp_clear*/
  0, /*tp_richcompare*/
  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
  0, /*tp_iternext*/
  __pyx_methods_6pyRing_8waveform_QNM_fit, /*tp_methods*/
  0, /*tp_members*/
  __pyx_getsets_6pyRing_8waveform_QNM_fit, /*tp_getset*/
  0, /*tp_base*/
  0, /*tp_dict*/
  0, /*tp_descr_get*/
  0, /*tp_descr_set*/
  #if !CYTHON_USE_TYPE_SPECS
  0, /*tp_dictoffset*/
  #endif
  0, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_6pyRing_8waveform_QNM_fit, /*tp_new*/
  0, /*tp_free*/
  0, /*tp_is_gc*/
  0, /*tp_bases*/
  0, /*tp_mro*/
  0, /*tp_cache*/
  0, /*tp_subclasses*/
  0, /*tp_weaklist*/
  0, /*tp_del*/
  0, /*tp_version_tag*/
  #if CYTHON_USE_TP_FINALIZE
  0, /*tp_finalize*/
  #else
  NULL, /*tp_finalize*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b1 && (!CYTHON_COMPILING_IN_PYPY || PYPY_VERSION_NUM >= 0x07030800)
  0, /*tp_vectorcall*/
  #endif
  #if __PYX_NEED_TP_PRINT_SLOT == 1
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030C0000
  0, /*tp_watched*/
  #endif
  #if PY_VERSION_HEX >= 0x030d00A4
  0, /*tp_versions_used*/
  #endif
  #if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX >= 0x03090000 && PY_VERSION_HEX < 0x030a0000
  0, /*tp_pypy_flags*/
  #endif
};
#endif
static struct __pyx_vtabstruct_6pyRing_8waveform_QNM_ParSpec __pyx_vtable_6pyRing_8waveform_QNM_ParSpec;

static PyObject *__pyx_tp_new_6pyRing_8waveform_QNM_ParSpec(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *p;
  PyObject *o;
  #if CYTHON_COMPILING_IN_LIMITED_API
  allocfunc alloc_func = (allocfunc)PyType_GetSlot(t, Py_tp_alloc);
  o = alloc_func(t, 0);
  #else
  if (likely(!__Pyx_PyType_HasFeature(t, Py_TPFLAGS_IS_ABSTRACT))) {
    o = (*t->tp_alloc)(t, 0);
  } else {
    o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_mstate_global->__pyx_empty_tuple, 0);
  }
  if (unlikely(!o)) return 0;
  #endif
  p = ((struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *)o);
  p->__pyx_vtab = __pyx_vtabptr_6pyRing_8waveform_QNM_ParSpec;
  p->f_coeff = Py_None; Py_INCREF(Py_None);
  p->tau_coeff = Py_None; Py_INCREF(Py_None);
  if (unlikely(__pyx_pw_6pyRing_8waveform_11QNM_ParSpec_1__cinit__(o, a, k) < 0)) goto bad;
  return o;
  bad:
  Py_DECREF(o); o = 0;
  return NULL;
}

static void __pyx_tp_dealloc_6pyRing_8waveform_QNM_ParSpec(PyObject *o) {
  struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *p = (struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *)o;
  #if CYTHON_USE_TP_FINALIZE
  if (unlikely((PY_VERSION_HEX >= 0x03080000 || __Pyx_PyType_HasFeature(Py_TYPE(o), Py_TPFLAGS_HAVE_FINALIZE)) && __Pyx_PyObject_GetSlot(o, tp_finalize, destructor)) && !__Pyx_PyObject_GC_IsFinalized(o)) {
    if (__Pyx_PyObject_GetSlot(o, tp_dealloc, destructor) == __pyx_tp_dealloc_6pyRing_8waveform_QNM_ParSpec) {
      if (PyObject_CallFinalizerFromDealloc(o)) return;
    }
  }
  #endif
  PyObject_GC_UnTrack(o);
  Py_CLEAR(p->f_coeff);
  Py_CLEAR(p->tau_coeff);
  #if CYTHON_USE_TYPE_SLOTS
  (*Py_TYPE(o)->tp_free)(o);
  #else
  {
    freefunc tp_free = (freefunc)PyType_GetSlot(Py_TYPE(o), Py_tp_free);
    if (tp_free) tp_free(o);
  }
  #endif
}

static int __pyx_tp_traverse_6pyRing_8waveform_QNM_ParSpec(PyObject *o, visitproc v, void *a) {
  int e;
  struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *p = (struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *)o;
  {
    e = __Pyx_call_type_traverse(o, 1, v, a);
    if (e) return e;
  }
  if (p->f_coeff) {
    e = (*v)(p->f_coeff, a); if (e) return e;
  }
  if (p->tau_coeff) {
    e = (*v)(p->tau_coeff, a); if (e) return e;
  }
  return 0;
}

static int __pyx_tp_clear_6pyRing_8waveform_QNM_ParSpec(PyObject *o) {
  PyObject* tmp;
  struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *p = (struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec *)o;
  tmp = ((PyObject*)p->f_coeff);
  p->f_coeff = Py_None; Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->tau_coeff);
  p->tau_coeff = Py_None; Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  return 0;
}

static PyObject *__pyx_getprop_6pyRing_8waveform_11QNM_ParSpec_l(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_11QNM_ParSpec_1l_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_11QNM_ParSpec_l(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_11QNM_ParSpec_1l_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_11QNM_ParSpec_m(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_11QNM_ParSpec_1m_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_11QNM_ParSpec_m(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_11QNM_ParSpec_1m_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_11QNM_ParSpec_n(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_11QNM_ParSpec_1n_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_11QNM_ParSpec_n(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_11QNM_ParSpec_1n_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_11QNM_ParSpec_f_coeff(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_11QNM_ParSpec_7f_coeff_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_11QNM_ParSpec_f_coeff(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_11QNM_ParSpec_7f_coeff_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_11QNM_ParSpec_7f_coeff_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_11QNM_ParSpec_tau_coeff(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_11QNM_ParSpec_9tau_coeff_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_11QNM_ParSpec_tau_coeff(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_11QNM_ParSpec_9tau_coeff_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_11QNM_ParSpec_9tau_coeff_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_11QNM_ParSpec_prefactor_freq(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_11QNM_ParSpec_14prefactor_freq_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_11QNM_ParSpec_prefactor_freq(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_11QNM_ParSpec_14prefactor_freq_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_11QNM_ParSpec_prefactor_tau(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_11QNM_ParSpec_13prefactor_tau_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_11QNM_ParSpec_prefactor_tau(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_11QNM_ParSpec_13prefactor_tau_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyMethodDef __pyx_methods_6pyRing_8waveform_QNM_ParSpec[] = {
  {"__reduce_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_11QNM_ParSpec_7__reduce_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_11QNM_ParSpec_6__reduce_cython__},
  {"__setstate_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_11QNM_ParSpec_9__setstate_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_11QNM_ParSpec_8__setstate_cython__},
  {0, 0, 0, 0}
};

static struct PyGetSetDef __pyx_getsets_6pyRing_8waveform_QNM_ParSpec[] = {
  {"l", __pyx_getprop_6pyRing_8waveform_11QNM_ParSpec_l, __pyx_setprop_6pyRing_8waveform_11QNM_ParSpec_l, PyDoc_STR("l: 'unsigned int'"), 0},
  {"m", __pyx_getprop_6pyRing_8waveform_11QNM_ParSpec_m, __pyx_setprop_6pyRing_8waveform_11QNM_ParSpec_m, PyDoc_STR("m: 'int'"), 0},
  {"n", __pyx_getprop_6pyRing_8waveform_11QNM_ParSpec_n, __pyx_setprop_6pyRing_8waveform_11QNM_ParSpec_n, PyDoc_STR("n: 'unsigned int'"), 0},
  {"f_coeff", __pyx_getprop_6pyRing_8waveform_11QNM_ParSpec_f_coeff, __pyx_setprop_6pyRing_8waveform_11QNM_ParSpec_f_coeff, PyDoc_STR("f_coeff: object"), 0},
  {"tau_coeff", __pyx_getprop_6pyRing_8waveform_11QNM_ParSpec_tau_coeff, __pyx_setprop_6pyRing_8waveform_11QNM_ParSpec_tau_coeff, PyDoc_STR("tau_coeff: object"), 0},
  {"prefactor_freq", __pyx_getprop_6pyRing_8waveform_11QNM_ParSpec_prefactor_freq, __pyx_setprop_6pyRing_8waveform_11QNM_ParSpec_prefactor_freq, PyDoc_STR("prefactor_freq: 'double'"), 0},
  {"prefactor_tau", __pyx_getprop_6pyRing_8waveform_11QNM_ParSpec_prefactor_tau, __pyx_setprop_6pyRing_8waveform_11QNM_ParSpec_prefactor_tau, PyDoc_STR("prefactor_tau: 'double'"), 0},
  {0, 0, 0, 0, 0}
};
#if CYTHON_USE_TYPE_SPECS
static PyType_Slot __pyx_type_6pyRing_8waveform_QNM_ParSpec_slots[] = {
  {Py_tp_dealloc, (void *)__pyx_tp_dealloc_6pyRing_8waveform_QNM_ParSpec},
  {Py_tp_doc, (void *)PyDoc_STR("\n\n    Class to compute the complex frequency and damping time of a QNM using the ParSpec fits.\n\n    Parameters\n    ----------\n\n    l : int\n        Orbital angular number of the QNM.\n    m : int\n        Azimuthal number of the QNM.\n    n : int\n        Radial (overtone) number of the QNM.\n    fit : str, optional\n        Fit to use. Either 'high_spin' or 'low_spin'. Default is 'high_spin'.\n    geom : int, optional\n        Geometric units flag. If 1, the QNM frequencies are returned in geometric units, otherwise they are returned in the International System of Units. Default is 0.\n    \n    Attributes\n    ----------\n\n    l : int\n        Orbital angular number of the QNM.\n    m : int\n        Azimuthal number of the QNM.\n    n : int\n        Radial (overtone) number of the QNM.\n    f_coeff : list\n        List of coefficients for the real part of the complex QNM frequency.\n    tau_coeff : list\n        List of coefficients for the imaginary part of the complex QNM frequency.\n\n    Functions\n    ---------\n\n    f : float\n        Returns the real part of the QNM frequency.\n    tau : float\n        Returns the imaginary part of the QNM frequency.\n    \n    ")},
  {Py_tp_traverse, (void *)__pyx_tp_traverse_6pyRing_8waveform_QNM_ParSpec},
  {Py_tp_clear, (void *)__pyx_tp_clear_6pyRing_8waveform_QNM_ParSpec},
  {Py_tp_methods, (void *)__pyx_methods_6pyRing_8waveform_QNM_ParSpec},
  {Py_tp_getset, (void *)__pyx_getsets_6pyRing_8waveform_QNM_ParSpec},
  {Py_tp_new, (void *)__pyx_tp_new_6pyRing_8waveform_QNM_ParSpec},
  {0, 0},
};
static PyType_Spec __pyx_type_6pyRing_8waveform_QNM_ParSpec_spec = {
  "pyRing.waveform.QNM_ParSpec",
  sizeof(struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec),
  0,
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC,
  __pyx_type_6pyRing_8waveform_QNM_ParSpec_slots,
};
#else

static PyTypeObject __pyx_type_6pyRing_8waveform_QNM_ParSpec = {
  PyVarObject_HEAD_INIT(0, 0)
  "pyRing.waveform.""QNM_ParSpec", /*tp_name*/
  sizeof(struct __pyx_obj_6pyRing_8waveform_QNM_ParSpec), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc_6pyRing_8waveform_QNM_ParSpec, /*tp_dealloc*/
  #if PY_VERSION_HEX < 0x030800b4
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b4
  0, /*tp_vectorcall_offset*/
  #endif
  0, /*tp_getattr*/
  0, /*tp_setattr*/
  0, /*tp_as_async*/
  0, /*tp_repr*/
  0, /*tp_as_number*/
  0, /*tp_as_sequence*/
  0, /*tp_as_mapping*/
  0, /*tp_hash*/
  0, /*tp_call*/
  0, /*tp_str*/
  0, /*tp_getattro*/
  0, /*tp_setattro*/
  0, /*tp_as_buffer*/
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC, /*tp_flags*/
  PyDoc_STR("\n\n    Class to compute the complex frequency and damping time of a QNM using the ParSpec fits.\n\n    Parameters\n    ----------\n\n    l : int\n        Orbital angular number of the QNM.\n    m : int\n        Azimuthal number of the QNM.\n    n : int\n        Radial (overtone) number of the QNM.\n    fit : str, optional\n        Fit to use. Either 'high_spin' or 'low_spin'. Default is 'high_spin'.\n    geom : int, optional\n        Geometric units flag. If 1, the QNM frequencies are returned in geometric units, otherwise they are returned in the International System of Units. Default is 0.\n    \n    Attributes\n    ----------\n\n    l : int\n        Orbital angular number of the QNM.\n    m : int\n        Azimuthal number of the QNM.\n    n : int\n        Radial (overtone) number of the QNM.\n    f_coeff : list\n        List of coefficients for the real part of the complex QNM frequency.\n    tau_coeff : list\n        List of coefficients for the imaginary part of the complex QNM frequency.\n\n    Functions\n    ---------\n\n    f : float\n        Returns the real part of the QNM frequency.\n    tau : float\n        Returns the imaginary part of the QNM frequency.\n    \n    "), /*tp_doc*/
  __pyx_tp_traverse_6pyRing_8waveform_QNM_ParSpec, /*tp_traverse*/
  __pyx_tp_clear_6pyRing_8waveform_QNM_ParSpec, /*tp_clear*/
  0, /*tp_richcompare*/
  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
  0, /*tp_iternext*/
  __pyx_methods_6pyRing_8waveform_QNM_ParSpec, /*tp_methods*/
  0, /*tp_members*/
  __pyx_getsets_6pyRing_8waveform_QNM_ParSpec, /*tp_getset*/
  0, /*tp_base*/
  0, /*tp_dict*/
  0, /*tp_descr_get*/
  0, /*tp_descr_set*/
  #if !CYTHON_USE_TYPE_SPECS
  0, /*tp_dictoffset*/
  #endif
  0, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_6pyRing_8waveform_QNM_ParSpec, /*tp_new*/
  0, /*tp_free*/
  0, /*tp_is_gc*/
  0, /*tp_bases*/
  0, /*tp_mro*/
  0, /*tp_cache*/
  0, /*tp_subclasses*/
  0, /*tp_weaklist*/
  0, /*tp_del*/
  0, /*tp_version_tag*/
  #if CYTHON_USE_TP_FINALIZE
  0, /*tp_finalize*/
  #else
  NULL, /*tp_finalize*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b1 && (!CYTHON_COMPILING_IN_PYPY || PYPY_VERSION_NUM >= 0x07030800)
  0, /*tp_vectorcall*/
  #endif
  #if __PYX_NEED_TP_PRINT_SLOT == 1
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030C0000
  0, /*tp_watched*/
  #endif
  #if PY_VERSION_HEX >= 0x030d00A4
  0, /*tp_versions_used*/
  #endif
  #if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX >= 0x03090000 && PY_VERSION_HEX < 0x030a0000
  0, /*tp_pypy_flags*/
  #endif
};
#endif
static struct __pyx_vtabstruct_6pyRing_8waveform_QNM_220_area_quantized __pyx_vtable_6pyRing_8waveform_QNM_220_area_quantized;

static PyObject *__pyx_tp_new_6pyRing_8waveform_QNM_220_area_quantized(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *p;
  PyObject *o;
  #if CYTHON_COMPILING_IN_LIMITED_API
  allocfunc alloc_func = (allocfunc)PyType_GetSlot(t, Py_tp_alloc);
  o = alloc_func(t, 0);
  #else
  if (likely(!__Pyx_PyType_HasFeature(t, Py_TPFLAGS_IS_ABSTRACT))) {
    o = (*t->tp_alloc)(t, 0);
  } else {
    o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_mstate_global->__pyx_empty_tuple, 0);
  }
  if (unlikely(!o)) return 0;
  #endif
  p = ((struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *)o);
  p->__pyx_vtab = __pyx_vtabptr_6pyRing_8waveform_QNM_220_area_quantized;
  p->q_coeff_GR = Py_None; Py_INCREF(Py_None);
  if (unlikely(__pyx_pw_6pyRing_8waveform_22QNM_220_area_quantized_1__cinit__(o, a, k) < 0)) goto bad;
  return o;
  bad:
  Py_DECREF(o); o = 0;
  return NULL;
}

static void __pyx_tp_dealloc_6pyRing_8waveform_QNM_220_area_quantized(PyObject *o) {
  struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *p = (struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *)o;
  #if CYTHON_USE_TP_FINALIZE
  if (unlikely((PY_VERSION_HEX >= 0x03080000 || __Pyx_PyType_HasFeature(Py_TYPE(o), Py_TPFLAGS_HAVE_FINALIZE)) && __Pyx_PyObject_GetSlot(o, tp_finalize, destructor)) && !__Pyx_PyObject_GC_IsFinalized(o)) {
    if (__Pyx_PyObject_GetSlot(o, tp_dealloc, destructor) == __pyx_tp_dealloc_6pyRing_8waveform_QNM_220_area_quantized) {
      if (PyObject_CallFinalizerFromDealloc(o)) return;
    }
  }
  #endif
  PyObject_GC_UnTrack(o);
  Py_CLEAR(p->q_coeff_GR);
  #if CYTHON_USE_TYPE_SLOTS
  (*Py_TYPE(o)->tp_free)(o);
  #else
  {
    freefunc tp_free = (freefunc)PyType_GetSlot(Py_TYPE(o), Py_tp_free);
    if (tp_free) tp_free(o);
  }
  #endif
}

static int __pyx_tp_traverse_6pyRing_8waveform_QNM_220_area_quantized(PyObject *o, visitproc v, void *a) {
  int e;
  struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *p = (struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *)o;
  {
    e = __Pyx_call_type_traverse(o, 1, v, a);
    if (e) return e;
  }
  if (p->q_coeff_GR) {
    e = (*v)(p->q_coeff_GR, a); if (e) return e;
  }
  return 0;
}

static int __pyx_tp_clear_6pyRing_8waveform_QNM_220_area_quantized(PyObject *o) {
  PyObject* tmp;
  struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *p = (struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized *)o;
  tmp = ((PyObject*)p->q_coeff_GR);
  p->q_coeff_GR = Py_None; Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  return 0;
}

static PyObject *__pyx_getprop_6pyRing_8waveform_22QNM_220_area_quantized_l_QA(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_22QNM_220_area_quantized_4l_QA_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_22QNM_220_area_quantized_l_QA(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_22QNM_220_area_quantized_4l_QA_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_22QNM_220_area_quantized_m_QA(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_22QNM_220_area_quantized_4m_QA_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_22QNM_220_area_quantized_m_QA(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_22QNM_220_area_quantized_4m_QA_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_22QNM_220_area_quantized_n_QA(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_22QNM_220_area_quantized_4n_QA_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_22QNM_220_area_quantized_n_QA(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_22QNM_220_area_quantized_4n_QA_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_22QNM_220_area_quantized_q_coeff_GR(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_22QNM_220_area_quantized_10q_coeff_GR_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_22QNM_220_area_quantized_q_coeff_GR(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_22QNM_220_area_quantized_10q_coeff_GR_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_22QNM_220_area_quantized_10q_coeff_GR_5__del__(o);
  }
}

static PyMethodDef __pyx_methods_6pyRing_8waveform_QNM_220_area_quantized[] = {
  {"__reduce_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_22QNM_220_area_quantized_9__reduce_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_22QNM_220_area_quantized_8__reduce_cython__},
  {"__setstate_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_22QNM_220_area_quantized_11__setstate_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_22QNM_220_area_quantized_10__setstate_cython__},
  {0, 0, 0, 0}
};

static struct PyGetSetDef __pyx_getsets_6pyRing_8waveform_QNM_220_area_quantized[] = {
  {"l_QA", __pyx_getprop_6pyRing_8waveform_22QNM_220_area_quantized_l_QA, __pyx_setprop_6pyRing_8waveform_22QNM_220_area_quantized_l_QA, PyDoc_STR("l_QA: 'unsigned int'"), 0},
  {"m_QA", __pyx_getprop_6pyRing_8waveform_22QNM_220_area_quantized_m_QA, __pyx_setprop_6pyRing_8waveform_22QNM_220_area_quantized_m_QA, PyDoc_STR("m_QA: 'int'"), 0},
  {"n_QA", __pyx_getprop_6pyRing_8waveform_22QNM_220_area_quantized_n_QA, __pyx_setprop_6pyRing_8waveform_22QNM_220_area_quantized_n_QA, PyDoc_STR("n_QA: 'unsigned int'"), 0},
  {"q_coeff_GR", __pyx_getprop_6pyRing_8waveform_22QNM_220_area_quantized_q_coeff_GR, __pyx_setprop_6pyRing_8waveform_22QNM_220_area_quantized_q_coeff_GR, PyDoc_STR("q_coeff_GR: object"), 0},
  {0, 0, 0, 0, 0}
};
#if CYTHON_USE_TYPE_SPECS
static PyType_Slot __pyx_type_6pyRing_8waveform_QNM_220_area_quantized_slots[] = {
  {Py_tp_dealloc, (void *)__pyx_tp_dealloc_6pyRing_8waveform_QNM_220_area_quantized},
  {Py_tp_doc, (void *)PyDoc_STR("\n\n    Class to compute the complex frequency and damping time of the 220 QNM coming from quantized area presciption.\n\n    Parameters\n    ----------\n\n    l_QA : int\n        Orbital angular number of the QNM.\n    m_QA : int\n        Azimuthal number of the QNM.\n    n_QA : int\n        Radial (overtone) number of the QNM.\n    \n    Attributes\n    ----------\n\n    l_QA : int\n        Orbital angular number of the QNM.\n    m_QA : int\n        Azimuthal number of the QNM.\n    n_QA : int\n        Radial (overtone) number of the QNM.\n    q_coeff_GR : list\n        List of coefficients for the quality factor QNM frequency.\n\n    Functions\n    ---------\n\n    f_QA : float\n        Returns the real part of the QNM frequency.\n    q_QA : float\n        Returns the quality factor of the QNM frequency.\n    tau_QA : float\n        Returns the imaginary part of the QNM frequency.\n\n    ")},
  {Py_tp_traverse, (void *)__pyx_tp_traverse_6pyRing_8waveform_QNM_220_area_quantized},
  {Py_tp_clear, (void *)__pyx_tp_clear_6pyRing_8waveform_QNM_220_area_quantized},
  {Py_tp_methods, (void *)__pyx_methods_6pyRing_8waveform_QNM_220_area_quantized},
  {Py_tp_getset, (void *)__pyx_getsets_6pyRing_8waveform_QNM_220_area_quantized},
  {Py_tp_new, (void *)__pyx_tp_new_6pyRing_8waveform_QNM_220_area_quantized},
  {0, 0},
};
static PyType_Spec __pyx_type_6pyRing_8waveform_QNM_220_area_quantized_spec = {
  "pyRing.waveform.QNM_220_area_quantized",
  sizeof(struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized),
  0,
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC,
  __pyx_type_6pyRing_8waveform_QNM_220_area_quantized_slots,
};
#else

static PyTypeObject __pyx_type_6pyRing_8waveform_QNM_220_area_quantized = {
  PyVarObject_HEAD_INIT(0, 0)
  "pyRing.waveform.""QNM_220_area_quantized", /*tp_name*/
  sizeof(struct __pyx_obj_6pyRing_8waveform_QNM_220_area_quantized), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc_6pyRing_8waveform_QNM_220_area_quantized, /*tp_dealloc*/
  #if PY_VERSION_HEX < 0x030800b4
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b4
  0, /*tp_vectorcall_offset*/
  #endif
  0, /*tp_getattr*/
  0, /*tp_setattr*/
  0, /*tp_as_async*/
  0, /*tp_repr*/
  0, /*tp_as_number*/
  0, /*tp_as_sequence*/
  0, /*tp_as_mapping*/
  0, /*tp_hash*/
  0, /*tp_call*/
  0, /*tp_str*/
  0, /*tp_getattro*/
  0, /*tp_setattro*/
  0, /*tp_as_buffer*/
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC, /*tp_flags*/
  PyDoc_STR("\n\n    Class to compute the complex frequency and damping time of the 220 QNM coming from quantized area presciption.\n\n    Parameters\n    ----------\n\n    l_QA : int\n        Orbital angular number of the QNM.\n    m_QA : int\n        Azimuthal number of the QNM.\n    n_QA : int\n        Radial (overtone) number of the QNM.\n    \n    Attributes\n    ----------\n\n    l_QA : int\n        Orbital angular number of the QNM.\n    m_QA : int\n        Azimuthal number of the QNM.\n    n_QA : int\n        Radial (overtone) number of the QNM.\n    q_coeff_GR : list\n        List of coefficients for the quality factor QNM frequency.\n\n    Functions\n    ---------\n\n    f_QA : float\n        Returns the real part of the QNM frequency.\n    q_QA : float\n        Returns the quality factor of the QNM frequency.\n    tau_QA : float\n        Returns the imaginary part of the QNM frequency.\n\n    "), /*tp_doc*/
  __pyx_tp_traverse_6pyRing_8waveform_QNM_220_area_quantized, /*tp_traverse*/
  __pyx_tp_clear_6pyRing_8waveform_QNM_220_area_quantized, /*tp_clear*/
  0, /*tp_richcompare*/
  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
  0, /*tp_iternext*/
  __pyx_methods_6pyRing_8waveform_QNM_220_area_quantized, /*tp_methods*/
  0, /*tp_members*/
  __pyx_getsets_6pyRing_8waveform_QNM_220_area_quantized, /*tp_getset*/
  0, /*tp_base*/
  0, /*tp_dict*/
  0, /*tp_descr_get*/
  0, /*tp_descr_set*/
  #if !CYTHON_USE_TYPE_SPECS
  0, /*tp_dictoffset*/
  #endif
  0, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_6pyRing_8waveform_QNM_220_area_quantized, /*tp_new*/
  0, /*tp_free*/
  0, /*tp_is_gc*/
  0, /*tp_bases*/
  0, /*tp_mro*/
  0, /*tp_cache*/
  0, /*tp_subclasses*/
  0, /*tp_weaklist*/
  0, /*tp_del*/
  0, /*tp_version_tag*/
  #if CYTHON_USE_TP_FINALIZE
  0, /*tp_finalize*/
  #else
  NULL, /*tp_finalize*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b1 && (!CYTHON_COMPILING_IN_PYPY || PYPY_VERSION_NUM >= 0x07030800)
  0, /*tp_vectorcall*/
  #endif
  #if __PYX_NEED_TP_PRINT_SLOT == 1
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030C0000
  0, /*tp_watched*/
  #endif
  #if PY_VERSION_HEX >= 0x030d00A4
  0, /*tp_versions_used*/
  #endif
  #if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX >= 0x03090000 && PY_VERSION_HEX < 0x030a0000
  0, /*tp_pypy_flags*/
  #endif
};
#endif
static struct __pyx_vtabstruct_6pyRing_8waveform_QNM_braneworld_fit __pyx_vtable_6pyRing_8waveform_QNM_braneworld_fit;

static PyObject *__pyx_tp_new_6pyRing_8waveform_QNM_braneworld_fit(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_6pyRing_8waveform_QNM_braneworld_fit *p;
  PyObject *o;
  #if CYTHON_COMPILING_IN_LIMITED_API
  allocfunc alloc_func = (allocfunc)PyType_GetSlot(t, Py_tp_alloc);
  o = alloc_func(t, 0);
  #else
  if (likely(!__Pyx_PyType_HasFeature(t, Py_TPFLAGS_IS_ABSTRACT))) {
    o = (*t->tp_alloc)(t, 0);
  } else {
    o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_mstate_global->__pyx_empty_tuple, 0);
  }
  if (unlikely(!o)) return 0;
  #endif
  p = ((struct __pyx_obj_6pyRing_8waveform_QNM_braneworld_fit *)o);
  p->__pyx_vtab = __pyx_vtabptr_6pyRing_8waveform_QNM_braneworld_fit;
  if (unlikely(__pyx_pw_6pyRing_8waveform_18QNM_braneworld_fit_1__cinit__(o, a, k) < 0)) goto bad;
  return o;
  bad:
  Py_DECREF(o); o = 0;
  return NULL;
}

static void __pyx_tp_dealloc_6pyRing_8waveform_QNM_braneworld_fit(PyObject *o) {
  #if CYTHON_USE_TP_FINALIZE
  if (unlikely((PY_VERSION_HEX >= 0x03080000 || __Pyx_PyType_HasFeature(Py_TYPE(o), Py_TPFLAGS_HAVE_FINALIZE)) && __Pyx_PyObject_GetSlot(o, tp_finalize, destructor)) && (!PyType_IS_GC(Py_TYPE(o)) || !__Pyx_PyObject_GC_IsFinalized(o))) {
    if (__Pyx_PyObject_GetSlot(o, tp_dealloc, destructor) == __pyx_tp_dealloc_6pyRing_8waveform_QNM_braneworld_fit) {
      if (PyObject_CallFinalizerFromDealloc(o)) return;
    }
  }
  #endif
  #if CYTHON_USE_TYPE_SLOTS
  (*Py_TYPE(o)->tp_free)(o);
  #else
  {
    freefunc tp_free = (freefunc)PyType_GetSlot(Py_TYPE(o), Py_tp_free);
    if (tp_free) tp_free(o);
  }
  #endif
}

static PyObject *__pyx_getprop_6pyRing_8waveform_18QNM_braneworld_fit_l_BW(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_18QNM_braneworld_fit_4l_BW_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_18QNM_braneworld_fit_l_BW(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_18QNM_braneworld_fit_4l_BW_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_18QNM_braneworld_fit_m_BW(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_18QNM_braneworld_fit_4m_BW_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_18QNM_braneworld_fit_m_BW(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_18QNM_braneworld_fit_4m_BW_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_18QNM_braneworld_fit_n_BW(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_18QNM_braneworld_fit_4n_BW_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_18QNM_braneworld_fit_n_BW(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_18QNM_braneworld_fit_4n_BW_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyMethodDef __pyx_methods_6pyRing_8waveform_QNM_braneworld_fit[] = {
  {"__reduce_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_18QNM_braneworld_fit_9__reduce_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_18QNM_braneworld_fit_8__reduce_cython__},
  {"__setstate_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_18QNM_braneworld_fit_11__setstate_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_18QNM_braneworld_fit_10__setstate_cython__},
  {0, 0, 0, 0}
};

static struct PyGetSetDef __pyx_getsets_6pyRing_8waveform_QNM_braneworld_fit[] = {
  {"l_BW", __pyx_getprop_6pyRing_8waveform_18QNM_braneworld_fit_l_BW, __pyx_setprop_6pyRing_8waveform_18QNM_braneworld_fit_l_BW, PyDoc_STR("l_BW: 'unsigned int'"), 0},
  {"m_BW", __pyx_getprop_6pyRing_8waveform_18QNM_braneworld_fit_m_BW, __pyx_setprop_6pyRing_8waveform_18QNM_braneworld_fit_m_BW, PyDoc_STR("m_BW: 'int'"), 0},
  {"n_BW", __pyx_getprop_6pyRing_8waveform_18QNM_braneworld_fit_n_BW, __pyx_setprop_6pyRing_8waveform_18QNM_braneworld_fit_n_BW, PyDoc_STR("n_BW: 'unsigned int'"), 0},
  {0, 0, 0, 0, 0}
};
#if CYTHON_USE_TYPE_SPECS
static PyType_Slot __pyx_type_6pyRing_8waveform_QNM_braneworld_fit_slots[] = {
  {Py_tp_dealloc, (void *)__pyx_tp_dealloc_6pyRing_8waveform_QNM_braneworld_fit},
  {Py_tp_doc, (void *)PyDoc_STR("\n\n    Class to compute the complex frequency and damping time of the QNM coming from braneworld fit.\n\n    Parameters\n    ----------\n\n    l_BW : int\n        Orbital angular number of the QNM.\n    m_BW : int\n        Azimuthal number of the QNM.\n    n_BW : int\n        Radial (overtone) number of the QNM.\n    \n    Attributes\n    ----------\n\n    l_BW : int\n        Orbital angular number of the QNM.  \n    m_BW : int\n        Azimuthal number of the QNM.\n    n_BW : int\n        Radial (overtone) number of the QNM.\n\n    Functions\n    ---------\n\n    f_BW : float\n        Returns the real part of the QNM frequency.\n    q_BW : float\n        Returns the quality factor of the QNM frequency.\n    tau_BW : float\n        Returns the imaginary part of the QNM frequency.\n    \n    ")},
  {Py_tp_methods, (void *)__pyx_methods_6pyRing_8waveform_QNM_braneworld_fit},
  {Py_tp_getset, (void *)__pyx_getsets_6pyRing_8waveform_QNM_braneworld_fit},
  {Py_tp_new, (void *)__pyx_tp_new_6pyRing_8waveform_QNM_braneworld_fit},
  {0, 0},
};
static PyType_Spec __pyx_type_6pyRing_8waveform_QNM_braneworld_fit_spec = {
  "pyRing.waveform.QNM_braneworld_fit",
  sizeof(struct __pyx_obj_6pyRing_8waveform_QNM_braneworld_fit),
  0,
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE,
  __pyx_type_6pyRing_8waveform_QNM_braneworld_fit_slots,
};
#else

static PyTypeObject __pyx_type_6pyRing_8waveform_QNM_braneworld_fit = {
  PyVarObject_HEAD_INIT(0, 0)
  "pyRing.waveform.""QNM_braneworld_fit", /*tp_name*/
  sizeof(struct __pyx_obj_6pyRing_8waveform_QNM_braneworld_fit), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc_6pyRing_8waveform_QNM_braneworld_fit, /*tp_dealloc*/
  #if PY_VERSION_HEX < 0x030800b4
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b4
  0, /*tp_vectorcall_offset*/
  #endif
  0, /*tp_getattr*/
  0, /*tp_setattr*/
  0, /*tp_as_async*/
  0, /*tp_repr*/
  0, /*tp_as_number*/
  0, /*tp_as_sequence*/
  0, /*tp_as_mapping*/
  0, /*tp_hash*/
  0, /*tp_call*/
  0, /*tp_str*/
  0, /*tp_getattro*/
  0, /*tp_setattro*/
  0, /*tp_as_buffer*/
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE, /*tp_flags*/
  PyDoc_STR("\n\n    Class to compute the complex frequency and damping time of the QNM coming from braneworld fit.\n\n    Parameters\n    ----------\n\n    l_BW : int\n        Orbital angular number of the QNM.\n    m_BW : int\n        Azimuthal number of the QNM.\n    n_BW : int\n        Radial (overtone) number of the QNM.\n    \n    Attributes\n    ----------\n\n    l_BW : int\n        Orbital angular number of the QNM.  \n    m_BW : int\n        Azimuthal number of the QNM.\n    n_BW : int\n        Radial (overtone) number of the QNM.\n\n    Functions\n    ---------\n\n    f_BW : float\n        Returns the real part of the QNM frequency.\n    q_BW : float\n        Returns the quality factor of the QNM frequency.\n    tau_BW : float\n        Returns the imaginary part of the QNM frequency.\n    \n    "), /*tp_doc*/
  0, /*tp_traverse*/
  0, /*tp_clear*/
  0, /*tp_richcompare*/
  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
  0, /*tp_iternext*/
  __pyx_methods_6pyRing_8waveform_QNM_braneworld_fit, /*tp_methods*/
  0, /*tp_members*/
  __pyx_getsets_6pyRing_8waveform_QNM_braneworld_fit, /*tp_getset*/
  0, /*tp_base*/
  0, /*tp_dict*/
  0, /*tp_descr_get*/
  0, /*tp_descr_set*/
  #if !CYTHON_USE_TYPE_SPECS
  0, /*tp_dictoffset*/
  #endif
  0, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_6pyRing_8waveform_QNM_braneworld_fit, /*tp_new*/
  0, /*tp_free*/
  0, /*tp_is_gc*/
  0, /*tp_bases*/
  0, /*tp_mro*/
  0, /*tp_cache*/
  0, /*tp_subclasses*/
  0, /*tp_weaklist*/
  0, /*tp_del*/
  0, /*tp_version_tag*/
  #if CYTHON_USE_TP_FINALIZE
  0, /*tp_finalize*/
  #else
  NULL, /*tp_finalize*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b1 && (!CYTHON_COMPILING_IN_PYPY || PYPY_VERSION_NUM >= 0x07030800)
  0, /*tp_vectorcall*/
  #endif
  #if __PYX_NEED_TP_PRINT_SLOT == 1
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030C0000
  0, /*tp_watched*/
  #endif
  #if PY_VERSION_HEX >= 0x030d00A4
  0, /*tp_versions_used*/
  #endif
  #if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX >= 0x03090000 && PY_VERSION_HEX < 0x030a0000
  0, /*tp_pypy_flags*/
  #endif
};
#endif
static struct __pyx_vtabstruct_6pyRing_8waveform_Damped_sinusoids __pyx_vtable_6pyRing_8waveform_Damped_sinusoids;

static PyObject *__pyx_tp_new_6pyRing_8waveform_Damped_sinusoids(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *p;
  PyObject *o;
  #if CYTHON_COMPILING_IN_LIMITED_API
  allocfunc alloc_func = (allocfunc)PyType_GetSlot(t, Py_tp_alloc);
  o = alloc_func(t, 0);
  #else
  if (likely(!__Pyx_PyType_HasFeature(t, Py_TPFLAGS_IS_ABSTRACT))) {
    o = (*t->tp_alloc)(t, 0);
  } else {
    o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_mstate_global->__pyx_empty_tuple, 0);
  }
  if (unlikely(!o)) return 0;
  #endif
  p = ((struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *)o);
  p->__pyx_vtab = __pyx_vtabptr_6pyRing_8waveform_Damped_sinusoids;
  p->A = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->f = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->tau = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->phi = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->t0 = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->N = ((PyObject*)Py_None); Py_INCREF(Py_None);
  if (unlikely(__pyx_pw_6pyRing_8waveform_16Damped_sinusoids_1__cinit__(o, a, k) < 0)) goto bad;
  return o;
  bad:
  Py_DECREF(o); o = 0;
  return NULL;
}

static void __pyx_tp_dealloc_6pyRing_8waveform_Damped_sinusoids(PyObject *o) {
  struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *p = (struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *)o;
  #if CYTHON_USE_TP_FINALIZE
  if (unlikely((PY_VERSION_HEX >= 0x03080000 || __Pyx_PyType_HasFeature(Py_TYPE(o), Py_TPFLAGS_HAVE_FINALIZE)) && __Pyx_PyObject_GetSlot(o, tp_finalize, destructor)) && !__Pyx_PyObject_GC_IsFinalized(o)) {
    if (__Pyx_PyObject_GetSlot(o, tp_dealloc, destructor) == __pyx_tp_dealloc_6pyRing_8waveform_Damped_sinusoids) {
      if (PyObject_CallFinalizerFromDealloc(o)) return;
    }
  }
  #endif
  PyObject_GC_UnTrack(o);
  Py_CLEAR(p->A);
  Py_CLEAR(p->f);
  Py_CLEAR(p->tau);
  Py_CLEAR(p->phi);
  Py_CLEAR(p->t0);
  Py_CLEAR(p->N);
  #if CYTHON_USE_TYPE_SLOTS
  (*Py_TYPE(o)->tp_free)(o);
  #else
  {
    freefunc tp_free = (freefunc)PyType_GetSlot(Py_TYPE(o), Py_tp_free);
    if (tp_free) tp_free(o);
  }
  #endif
}

static int __pyx_tp_traverse_6pyRing_8waveform_Damped_sinusoids(PyObject *o, visitproc v, void *a) {
  int e;
  struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *p = (struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *)o;
  {
    e = __Pyx_call_type_traverse(o, 1, v, a);
    if (e) return e;
  }
  if (p->A) {
    e = (*v)(p->A, a); if (e) return e;
  }
  if (p->f) {
    e = (*v)(p->f, a); if (e) return e;
  }
  if (p->tau) {
    e = (*v)(p->tau, a); if (e) return e;
  }
  if (p->phi) {
    e = (*v)(p->phi, a); if (e) return e;
  }
  if (p->t0) {
    e = (*v)(p->t0, a); if (e) return e;
  }
  if (p->N) {
    e = (*v)(p->N, a); if (e) return e;
  }
  return 0;
}

static int __pyx_tp_clear_6pyRing_8waveform_Damped_sinusoids(PyObject *o) {
  PyObject* tmp;
  struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *p = (struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids *)o;
  tmp = ((PyObject*)p->A);
  p->A = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->f);
  p->f = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->tau);
  p->tau = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->phi);
  p->phi = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->t0);
  p->t0 = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->N);
  p->N = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  return 0;
}

static PyObject *__pyx_getprop_6pyRing_8waveform_16Damped_sinusoids_A(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_16Damped_sinusoids_1A_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_16Damped_sinusoids_A(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_16Damped_sinusoids_1A_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_16Damped_sinusoids_1A_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_16Damped_sinusoids_f(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_16Damped_sinusoids_1f_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_16Damped_sinusoids_f(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_16Damped_sinusoids_1f_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_16Damped_sinusoids_1f_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_16Damped_sinusoids_tau(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_16Damped_sinusoids_3tau_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_16Damped_sinusoids_tau(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_16Damped_sinusoids_3tau_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_16Damped_sinusoids_3tau_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_16Damped_sinusoids_phi(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_16Damped_sinusoids_3phi_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_16Damped_sinusoids_phi(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_16Damped_sinusoids_3phi_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_16Damped_sinusoids_3phi_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_16Damped_sinusoids_t0(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_16Damped_sinusoids_2t0_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_16Damped_sinusoids_t0(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_16Damped_sinusoids_2t0_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_16Damped_sinusoids_2t0_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_16Damped_sinusoids_N(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_16Damped_sinusoids_1N_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_16Damped_sinusoids_N(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_16Damped_sinusoids_1N_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_16Damped_sinusoids_1N_5__del__(o);
  }
}

static PyMethodDef __pyx_methods_6pyRing_8waveform_Damped_sinusoids[] = {
  {"__reduce_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_16Damped_sinusoids_5__reduce_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_16Damped_sinusoids_4__reduce_cython__},
  {"__setstate_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_16Damped_sinusoids_7__setstate_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_16Damped_sinusoids_6__setstate_cython__},
  {0, 0, 0, 0}
};

static struct PyGetSetDef __pyx_getsets_6pyRing_8waveform_Damped_sinusoids[] = {
  {"A", __pyx_getprop_6pyRing_8waveform_16Damped_sinusoids_A, __pyx_setprop_6pyRing_8waveform_16Damped_sinusoids_A, PyDoc_STR("A: dict"), 0},
  {"f", __pyx_getprop_6pyRing_8waveform_16Damped_sinusoids_f, __pyx_setprop_6pyRing_8waveform_16Damped_sinusoids_f, PyDoc_STR("f: dict"), 0},
  {"tau", __pyx_getprop_6pyRing_8waveform_16Damped_sinusoids_tau, __pyx_setprop_6pyRing_8waveform_16Damped_sinusoids_tau, PyDoc_STR("tau: dict"), 0},
  {"phi", __pyx_getprop_6pyRing_8waveform_16Damped_sinusoids_phi, __pyx_setprop_6pyRing_8waveform_16Damped_sinusoids_phi, PyDoc_STR("phi: dict"), 0},
  {"t0", __pyx_getprop_6pyRing_8waveform_16Damped_sinusoids_t0, __pyx_setprop_6pyRing_8waveform_16Damped_sinusoids_t0, PyDoc_STR("t0: dict"), 0},
  {"N", __pyx_getprop_6pyRing_8waveform_16Damped_sinusoids_N, __pyx_setprop_6pyRing_8waveform_16Damped_sinusoids_N, PyDoc_STR("N: dict"), 0},
  {0, 0, 0, 0, 0}
};
#if CYTHON_USE_TYPE_SPECS
static PyType_Slot __pyx_type_6pyRing_8waveform_Damped_sinusoids_slots[] = {
  {Py_tp_dealloc, (void *)__pyx_tp_dealloc_6pyRing_8waveform_Damped_sinusoids},
  {Py_tp_doc, (void *)PyDoc_STR("\n    Class implementing a superposition of Damped Sinusoids of arbitrary polarisation.\n\n    Parameters\n    ----------\n\n    A : dict\n        Dictionary of amplitudes of the damped sinusoids.\n    f : dict\n        Dictionary of frequencies of the damped sinusoids.\n    tau : dict\n        Dictionary of damping times of the damped sinusoids.\n    phi : dict\n        Dictionary of phases of the damped sinusoids.\n    t0 : dict\n        Dictionary of start times of the damped sinusoids.\n\n    Attributes\n    ----------\n\n    A : dict\n        Dictionary of amplitudes of the damped sinusoids.\n    f : dict\n        Dictionary of frequencies of the damped sinusoids.\n    tau : dict\n        Dictionary of damping times of the damped sinusoids.\n    phi : dict\n        Dictionary of phases of the damped sinusoids.\n    t0 : dict\n        Dictionary of start times of the damped sinusoids.\n    N : dict\n        Dictionary of number of damped sinusoids for each polarisation.\n\n    Functions\n    ---------\n\n    waveform(t)\n        Returns the waveform model.\n\n    ")},
  {Py_tp_traverse, (void *)__pyx_tp_traverse_6pyRing_8waveform_Damped_sinusoids},
  {Py_tp_clear, (void *)__pyx_tp_clear_6pyRing_8waveform_Damped_sinusoids},
  {Py_tp_methods, (void *)__pyx_methods_6pyRing_8waveform_Damped_sinusoids},
  {Py_tp_getset, (void *)__pyx_getsets_6pyRing_8waveform_Damped_sinusoids},
  {Py_tp_new, (void *)__pyx_tp_new_6pyRing_8waveform_Damped_sinusoids},
  {0, 0},
};
static PyType_Spec __pyx_type_6pyRing_8waveform_Damped_sinusoids_spec = {
  "pyRing.waveform.Damped_sinusoids",
  sizeof(struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids),
  0,
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC,
  __pyx_type_6pyRing_8waveform_Damped_sinusoids_slots,
};
#else

static PyTypeObject __pyx_type_6pyRing_8waveform_Damped_sinusoids = {
  PyVarObject_HEAD_INIT(0, 0)
  "pyRing.waveform.""Damped_sinusoids", /*tp_name*/
  sizeof(struct __pyx_obj_6pyRing_8waveform_Damped_sinusoids), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc_6pyRing_8waveform_Damped_sinusoids, /*tp_dealloc*/
  #if PY_VERSION_HEX < 0x030800b4
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b4
  0, /*tp_vectorcall_offset*/
  #endif
  0, /*tp_getattr*/
  0, /*tp_setattr*/
  0, /*tp_as_async*/
  0, /*tp_repr*/
  0, /*tp_as_number*/
  0, /*tp_as_sequence*/
  0, /*tp_as_mapping*/
  0, /*tp_hash*/
  0, /*tp_call*/
  0, /*tp_str*/
  0, /*tp_getattro*/
  0, /*tp_setattro*/
  0, /*tp_as_buffer*/
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC, /*tp_flags*/
  PyDoc_STR("\n    Class implementing a superposition of Damped Sinusoids of arbitrary polarisation.\n\n    Parameters\n    ----------\n\n    A : dict\n        Dictionary of amplitudes of the damped sinusoids.\n    f : dict\n        Dictionary of frequencies of the damped sinusoids.\n    tau : dict\n        Dictionary of damping times of the damped sinusoids.\n    phi : dict\n        Dictionary of phases of the damped sinusoids.\n    t0 : dict\n        Dictionary of start times of the damped sinusoids.\n\n    Attributes\n    ----------\n\n    A : dict\n        Dictionary of amplitudes of the damped sinusoids.\n    f : dict\n        Dictionary of frequencies of the damped sinusoids.\n    tau : dict\n        Dictionary of damping times of the damped sinusoids.\n    phi : dict\n        Dictionary of phases of the damped sinusoids.\n    t0 : dict\n        Dictionary of start times of the damped sinusoids.\n    N : dict\n        Dictionary of number of damped sinusoids for each polarisation.\n\n    Functions\n    ---------\n\n    waveform(t)\n        Returns the waveform model.\n\n    "), /*tp_doc*/
  __pyx_tp_traverse_6pyRing_8waveform_Damped_sinusoids, /*tp_traverse*/
  __pyx_tp_clear_6pyRing_8waveform_Damped_sinusoids, /*tp_clear*/
  0, /*tp_richcompare*/
  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
  0, /*tp_iternext*/
  __pyx_methods_6pyRing_8waveform_Damped_sinusoids, /*tp_methods*/
  0, /*tp_members*/
  __pyx_getsets_6pyRing_8waveform_Damped_sinusoids, /*tp_getset*/
  0, /*tp_base*/
  0, /*tp_dict*/
  0, /*tp_descr_get*/
  0, /*tp_descr_set*/
  #if !CYTHON_USE_TYPE_SPECS
  0, /*tp_dictoffset*/
  #endif
  0, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_6pyRing_8waveform_Damped_sinusoids, /*tp_new*/
  0, /*tp_free*/
  0, /*tp_is_gc*/
  0, /*tp_bases*/
  0, /*tp_mro*/
  0, /*tp_cache*/
  0, /*tp_subclasses*/
  0, /*tp_weaklist*/
  0, /*tp_del*/
  0, /*tp_version_tag*/
  #if CYTHON_USE_TP_FINALIZE
  0, /*tp_finalize*/
  #else
  NULL, /*tp_finalize*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b1 && (!CYTHON_COMPILING_IN_PYPY || PYPY_VERSION_NUM >= 0x07030800)
  0, /*tp_vectorcall*/
  #endif
  #if __PYX_NEED_TP_PRINT_SLOT == 1
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030C0000
  0, /*tp_watched*/
  #endif
  #if PY_VERSION_HEX >= 0x030d00A4
  0, /*tp_versions_used*/
  #endif
  #if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX >= 0x03090000 && PY_VERSION_HEX < 0x030a0000
  0, /*tp_pypy_flags*/
  #endif
};
#endif
static struct __pyx_vtabstruct_6pyRing_8waveform_Morlet_Gabor_wavelets __pyx_vtable_6pyRing_8waveform_Morlet_Gabor_wavelets;

static PyObject *__pyx_tp_new_6pyRing_8waveform_Morlet_Gabor_wavelets(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *p;
  PyObject *o;
  #if CYTHON_COMPILING_IN_LIMITED_API
  allocfunc alloc_func = (allocfunc)PyType_GetSlot(t, Py_tp_alloc);
  o = alloc_func(t, 0);
  #else
  if (likely(!__Pyx_PyType_HasFeature(t, Py_TPFLAGS_IS_ABSTRACT))) {
    o = (*t->tp_alloc)(t, 0);
  } else {
    o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_mstate_global->__pyx_empty_tuple, 0);
  }
  if (unlikely(!o)) return 0;
  #endif
  p = ((struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *)o);
  p->__pyx_vtab = __pyx_vtabptr_6pyRing_8waveform_Morlet_Gabor_wavelets;
  p->A = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->f = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->tau = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->phi = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->t0 = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->N = ((PyObject*)Py_None); Py_INCREF(Py_None);
  if (unlikely(__pyx_pw_6pyRing_8waveform_21Morlet_Gabor_wavelets_1__cinit__(o, a, k) < 0)) goto bad;
  return o;
  bad:
  Py_DECREF(o); o = 0;
  return NULL;
}

static void __pyx_tp_dealloc_6pyRing_8waveform_Morlet_Gabor_wavelets(PyObject *o) {
  struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *p = (struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *)o;
  #if CYTHON_USE_TP_FINALIZE
  if (unlikely((PY_VERSION_HEX >= 0x03080000 || __Pyx_PyType_HasFeature(Py_TYPE(o), Py_TPFLAGS_HAVE_FINALIZE)) && __Pyx_PyObject_GetSlot(o, tp_finalize, destructor)) && !__Pyx_PyObject_GC_IsFinalized(o)) {
    if (__Pyx_PyObject_GetSlot(o, tp_dealloc, destructor) == __pyx_tp_dealloc_6pyRing_8waveform_Morlet_Gabor_wavelets) {
      if (PyObject_CallFinalizerFromDealloc(o)) return;
    }
  }
  #endif
  PyObject_GC_UnTrack(o);
  Py_CLEAR(p->A);
  Py_CLEAR(p->f);
  Py_CLEAR(p->tau);
  Py_CLEAR(p->phi);
  Py_CLEAR(p->t0);
  Py_CLEAR(p->N);
  #if CYTHON_USE_TYPE_SLOTS
  (*Py_TYPE(o)->tp_free)(o);
  #else
  {
    freefunc tp_free = (freefunc)PyType_GetSlot(Py_TYPE(o), Py_tp_free);
    if (tp_free) tp_free(o);
  }
  #endif
}

static int __pyx_tp_traverse_6pyRing_8waveform_Morlet_Gabor_wavelets(PyObject *o, visitproc v, void *a) {
  int e;
  struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *p = (struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *)o;
  {
    e = __Pyx_call_type_traverse(o, 1, v, a);
    if (e) return e;
  }
  if (p->A) {
    e = (*v)(p->A, a); if (e) return e;
  }
  if (p->f) {
    e = (*v)(p->f, a); if (e) return e;
  }
  if (p->tau) {
    e = (*v)(p->tau, a); if (e) return e;
  }
  if (p->phi) {
    e = (*v)(p->phi, a); if (e) return e;
  }
  if (p->t0) {
    e = (*v)(p->t0, a); if (e) return e;
  }
  if (p->N) {
    e = (*v)(p->N, a); if (e) return e;
  }
  return 0;
}

static int __pyx_tp_clear_6pyRing_8waveform_Morlet_Gabor_wavelets(PyObject *o) {
  PyObject* tmp;
  struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *p = (struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets *)o;
  tmp = ((PyObject*)p->A);
  p->A = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->f);
  p->f = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->tau);
  p->tau = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->phi);
  p->phi = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->t0);
  p->t0 = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->N);
  p->N = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  return 0;
}

static PyObject *__pyx_getprop_6pyRing_8waveform_21Morlet_Gabor_wavelets_A(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_21Morlet_Gabor_wavelets_1A_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_21Morlet_Gabor_wavelets_A(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_21Morlet_Gabor_wavelets_1A_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_21Morlet_Gabor_wavelets_1A_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_21Morlet_Gabor_wavelets_f(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_21Morlet_Gabor_wavelets_1f_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_21Morlet_Gabor_wavelets_f(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_21Morlet_Gabor_wavelets_1f_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_21Morlet_Gabor_wavelets_1f_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_21Morlet_Gabor_wavelets_tau(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_21Morlet_Gabor_wavelets_3tau_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_21Morlet_Gabor_wavelets_tau(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_21Morlet_Gabor_wavelets_3tau_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_21Morlet_Gabor_wavelets_3tau_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_21Morlet_Gabor_wavelets_phi(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_21Morlet_Gabor_wavelets_3phi_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_21Morlet_Gabor_wavelets_phi(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_21Morlet_Gabor_wavelets_3phi_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_21Morlet_Gabor_wavelets_3phi_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_21Morlet_Gabor_wavelets_t0(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_21Morlet_Gabor_wavelets_2t0_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_21Morlet_Gabor_wavelets_t0(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_21Morlet_Gabor_wavelets_2t0_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_21Morlet_Gabor_wavelets_2t0_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_21Morlet_Gabor_wavelets_N(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_21Morlet_Gabor_wavelets_1N_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_21Morlet_Gabor_wavelets_N(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_21Morlet_Gabor_wavelets_1N_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_21Morlet_Gabor_wavelets_1N_5__del__(o);
  }
}

static PyMethodDef __pyx_methods_6pyRing_8waveform_Morlet_Gabor_wavelets[] = {
  {"__reduce_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_21Morlet_Gabor_wavelets_5__reduce_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_21Morlet_Gabor_wavelets_4__reduce_cython__},
  {"__setstate_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_21Morlet_Gabor_wavelets_7__setstate_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_21Morlet_Gabor_wavelets_6__setstate_cython__},
  {0, 0, 0, 0}
};

static struct PyGetSetDef __pyx_getsets_6pyRing_8waveform_Morlet_Gabor_wavelets[] = {
  {"A", __pyx_getprop_6pyRing_8waveform_21Morlet_Gabor_wavelets_A, __pyx_setprop_6pyRing_8waveform_21Morlet_Gabor_wavelets_A, PyDoc_STR("A: dict"), 0},
  {"f", __pyx_getprop_6pyRing_8waveform_21Morlet_Gabor_wavelets_f, __pyx_setprop_6pyRing_8waveform_21Morlet_Gabor_wavelets_f, PyDoc_STR("f: dict"), 0},
  {"tau", __pyx_getprop_6pyRing_8waveform_21Morlet_Gabor_wavelets_tau, __pyx_setprop_6pyRing_8waveform_21Morlet_Gabor_wavelets_tau, PyDoc_STR("tau: dict"), 0},
  {"phi", __pyx_getprop_6pyRing_8waveform_21Morlet_Gabor_wavelets_phi, __pyx_setprop_6pyRing_8waveform_21Morlet_Gabor_wavelets_phi, PyDoc_STR("phi: dict"), 0},
  {"t0", __pyx_getprop_6pyRing_8waveform_21Morlet_Gabor_wavelets_t0, __pyx_setprop_6pyRing_8waveform_21Morlet_Gabor_wavelets_t0, PyDoc_STR("t0: dict"), 0},
  {"N", __pyx_getprop_6pyRing_8waveform_21Morlet_Gabor_wavelets_N, __pyx_setprop_6pyRing_8waveform_21Morlet_Gabor_wavelets_N, PyDoc_STR("N: dict"), 0},
  {0, 0, 0, 0, 0}
};
#if CYTHON_USE_TYPE_SPECS
static PyType_Slot __pyx_type_6pyRing_8waveform_Morlet_Gabor_wavelets_slots[] = {
  {Py_tp_dealloc, (void *)__pyx_tp_dealloc_6pyRing_8waveform_Morlet_Gabor_wavelets},
  {Py_tp_doc, (void *)PyDoc_STR("\n\n    Class implementing a superposition of Morlet-Gabor wavelets of arbitrary polarisation.\n\n    Parameters\n    ----------\n\n    A : dict\n        Dictionary of amplitudes of the Morlet-Gabor wavelets.\n    f : dict\n        Dictionary of frequencies of the Morlet-Gabor wavelets.\n    tau : dict\n        Dictionary of damping times of the Morlet-Gabor wavelets.\n    phi : dict\n        Dictionary of phases of the Morlet-Gabor wavelets.\n    t0 : dict\n        Dictionary of start times of the Morlet-Gabor wavelets.\n    \n    Attributes\n    ----------\n\n    A : dict\n        Dictionary of amplitudes of the Morlet-Gabor wavelets.\n    f : dict\n        Dictionary of frequencies of the Morlet-Gabor wavelets.\n    tau : dict\n        Dictionary of damping times of the Morlet-Gabor wavelets.\n    phi : dict\n        Dictionary of phases of the Morlet-Gabor wavelets.\n    t0 : dict\n        Dictionary of start times of the Morlet-Gabor wavelets.\n    N : dict\n        Dictionary of number of Morlet-Gabor wavelets for each polarisation.\n    \n    Functions\n    ---------\n\n    waveform(t)\n        Returns the waveform model.\n\n    ")},
  {Py_tp_traverse, (void *)__pyx_tp_traverse_6pyRing_8waveform_Morlet_Gabor_wavelets},
  {Py_tp_clear, (void *)__pyx_tp_clear_6pyRing_8waveform_Morlet_Gabor_wavelets},
  {Py_tp_methods, (void *)__pyx_methods_6pyRing_8waveform_Morlet_Gabor_wavelets},
  {Py_tp_getset, (void *)__pyx_getsets_6pyRing_8waveform_Morlet_Gabor_wavelets},
  {Py_tp_new, (void *)__pyx_tp_new_6pyRing_8waveform_Morlet_Gabor_wavelets},
  {0, 0},
};
static PyType_Spec __pyx_type_6pyRing_8waveform_Morlet_Gabor_wavelets_spec = {
  "pyRing.waveform.Morlet_Gabor_wavelets",
  sizeof(struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets),
  0,
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC,
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};
#else

static PyTypeObject __pyx_type_6pyRing_8waveform_Morlet_Gabor_wavelets = {
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  "pyRing.waveform.""Morlet_Gabor_wavelets", /*tp_name*/
  sizeof(struct __pyx_obj_6pyRing_8waveform_Morlet_Gabor_wavelets), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc_6pyRing_8waveform_Morlet_Gabor_wavelets, /*tp_dealloc*/
  #if PY_VERSION_HEX < 0x030800b4
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b4
  0, /*tp_vectorcall_offset*/
  #endif
  0, /*tp_getattr*/
  0, /*tp_setattr*/
  0, /*tp_as_async*/
  0, /*tp_repr*/
  0, /*tp_as_number*/
  0, /*tp_as_sequence*/
  0, /*tp_as_mapping*/
  0, /*tp_hash*/
  0, /*tp_call*/
  0, /*tp_str*/
  0, /*tp_getattro*/
  0, /*tp_setattro*/
  0, /*tp_as_buffer*/
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC, /*tp_flags*/
  PyDoc_STR("\n\n    Class implementing a superposition of Morlet-Gabor wavelets of arbitrary polarisation.\n\n    Parameters\n    ----------\n\n    A : dict\n        Dictionary of amplitudes of the Morlet-Gabor wavelets.\n    f : dict\n        Dictionary of frequencies of the Morlet-Gabor wavelets.\n    tau : dict\n        Dictionary of damping times of the Morlet-Gabor wavelets.\n    phi : dict\n        Dictionary of phases of the Morlet-Gabor wavelets.\n    t0 : dict\n        Dictionary of start times of the Morlet-Gabor wavelets.\n    \n    Attributes\n    ----------\n\n    A : dict\n        Dictionary of amplitudes of the Morlet-Gabor wavelets.\n    f : dict\n        Dictionary of frequencies of the Morlet-Gabor wavelets.\n    tau : dict\n        Dictionary of damping times of the Morlet-Gabor wavelets.\n    phi : dict\n        Dictionary of phases of the Morlet-Gabor wavelets.\n    t0 : dict\n        Dictionary of start times of the Morlet-Gabor wavelets.\n    N : dict\n        Dictionary of number of Morlet-Gabor wavelets for each polarisation.\n    \n    Functions\n    ---------\n\n    waveform(t)\n        Returns the waveform model.\n\n    "), /*tp_doc*/
  __pyx_tp_traverse_6pyRing_8waveform_Morlet_Gabor_wavelets, /*tp_traverse*/
  __pyx_tp_clear_6pyRing_8waveform_Morlet_Gabor_wavelets, /*tp_clear*/
  0, /*tp_richcompare*/
  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
  0, /*tp_iternext*/
  __pyx_methods_6pyRing_8waveform_Morlet_Gabor_wavelets, /*tp_methods*/
  0, /*tp_members*/
  __pyx_getsets_6pyRing_8waveform_Morlet_Gabor_wavelets, /*tp_getset*/
  0, /*tp_base*/
  0, /*tp_dict*/
  0, /*tp_descr_get*/
  0, /*tp_descr_set*/
  #if !CYTHON_USE_TYPE_SPECS
  0, /*tp_dictoffset*/
  #endif
  0, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_6pyRing_8waveform_Morlet_Gabor_wavelets, /*tp_new*/
  0, /*tp_free*/
  0, /*tp_is_gc*/
  0, /*tp_bases*/
  0, /*tp_mro*/
  0, /*tp_cache*/
  0, /*tp_subclasses*/
  0, /*tp_weaklist*/
  0, /*tp_del*/
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  #if CYTHON_USE_TP_FINALIZE
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  #else
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  #if PY_VERSION_HEX >= 0x030800b1 && (!CYTHON_COMPILING_IN_PYPY || PYPY_VERSION_NUM >= 0x07030800)
  0, /*tp_vectorcall*/
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  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030C0000
  0, /*tp_watched*/
  #endif
  #if PY_VERSION_HEX >= 0x030d00A4
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  #endif
  #if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX >= 0x03090000 && PY_VERSION_HEX < 0x030a0000
  0, /*tp_pypy_flags*/
  #endif
};
#endif
static struct __pyx_vtabstruct_6pyRing_8waveform_SWSH __pyx_vtable_6pyRing_8waveform_SWSH;

static PyObject *__pyx_tp_new_6pyRing_8waveform_SWSH(PyTypeObject *t, CYTHON_UNUSED PyObject *a, CYTHON_UNUSED PyObject *k) {
  struct __pyx_obj_6pyRing_8waveform_SWSH *p;
  PyObject *o;
  #if CYTHON_COMPILING_IN_LIMITED_API
  allocfunc alloc_func = (allocfunc)PyType_GetSlot(t, Py_tp_alloc);
  o = alloc_func(t, 0);
  #else
  if (likely(!__Pyx_PyType_HasFeature(t, Py_TPFLAGS_IS_ABSTRACT))) {
    o = (*t->tp_alloc)(t, 0);
  } else {
    o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_mstate_global->__pyx_empty_tuple, 0);
  }
  if (unlikely(!o)) return 0;
  #endif
  p = ((struct __pyx_obj_6pyRing_8waveform_SWSH *)o);
  p->__pyx_vtab = __pyx_vtabptr_6pyRing_8waveform_SWSH;
  return o;
}

static void __pyx_tp_dealloc_6pyRing_8waveform_SWSH(PyObject *o) {
  #if CYTHON_USE_TP_FINALIZE
  if (unlikely((PY_VERSION_HEX >= 0x03080000 || __Pyx_PyType_HasFeature(Py_TYPE(o), Py_TPFLAGS_HAVE_FINALIZE)) && __Pyx_PyObject_GetSlot(o, tp_finalize, destructor)) && (!PyType_IS_GC(Py_TYPE(o)) || !__Pyx_PyObject_GC_IsFinalized(o))) {
    if (__Pyx_PyObject_GetSlot(o, tp_dealloc, destructor) == __pyx_tp_dealloc_6pyRing_8waveform_SWSH) {
      if (PyObject_CallFinalizerFromDealloc(o)) return;
    }
  }
  #endif
  #if CYTHON_USE_TYPE_SLOTS
  (*Py_TYPE(o)->tp_free)(o);
  #else
  {
    freefunc tp_free = (freefunc)PyType_GetSlot(Py_TYPE(o), Py_tp_free);
    if (tp_free) tp_free(o);
  }
  #endif
}

static PyObject *__pyx_getprop_6pyRing_8waveform_4SWSH_l(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_4SWSH_1l_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_4SWSH_l(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_4SWSH_1l_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_4SWSH_m(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_4SWSH_1m_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_4SWSH_m(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_4SWSH_1m_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_4SWSH_s(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_4SWSH_1s_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_4SWSH_s(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_4SWSH_1s_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_4SWSH_swsh_prefactor(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_4SWSH_14swsh_prefactor_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_4SWSH_swsh_prefactor(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_4SWSH_14swsh_prefactor_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyMethodDef __pyx_methods_6pyRing_8waveform_SWSH[] = {
  {"__reduce_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_4SWSH_7__reduce_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_4SWSH_6__reduce_cython__},
  {"__setstate_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_4SWSH_9__setstate_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_4SWSH_8__setstate_cython__},
  {0, 0, 0, 0}
};

static struct PyGetSetDef __pyx_getsets_6pyRing_8waveform_SWSH[] = {
  {"l", __pyx_getprop_6pyRing_8waveform_4SWSH_l, __pyx_setprop_6pyRing_8waveform_4SWSH_l, PyDoc_STR("l: 'int'"), 0},
  {"m", __pyx_getprop_6pyRing_8waveform_4SWSH_m, __pyx_setprop_6pyRing_8waveform_4SWSH_m, PyDoc_STR("m: 'int'"), 0},
  {"s", __pyx_getprop_6pyRing_8waveform_4SWSH_s, __pyx_setprop_6pyRing_8waveform_4SWSH_s, PyDoc_STR("s: 'int'"), 0},
  {"swsh_prefactor", __pyx_getprop_6pyRing_8waveform_4SWSH_swsh_prefactor, __pyx_setprop_6pyRing_8waveform_4SWSH_swsh_prefactor, PyDoc_STR("swsh_prefactor: 'double'"), 0},
  {0, 0, 0, 0, 0}
};
#if CYTHON_USE_TYPE_SPECS
static PyType_Slot __pyx_type_6pyRing_8waveform_SWSH_slots[] = {
  {Py_tp_dealloc, (void *)__pyx_tp_dealloc_6pyRing_8waveform_SWSH},
  {Py_tp_call, (void *)__pyx_pw_6pyRing_8waveform_4SWSH_3__call__},
  {Py_tp_doc, (void *)PyDoc_STR("SWSH(int s, int l, int m)\n\nSpin weighted spherical harmonics\n-s_Y_{lm}\nDefined in Kidder (https://arxiv.org/pdf/0710.0614.pdf) Eq.s (4, 5).\nNote that this function returns -s_Y_{l,m} as defined by Kidder.\nThus, for gravitational perturbation s=2 must be passed.\n\nParameters\n----------\n\ns : int\n    Spin of the spherical harmonic.\nl : int\n    Orbital angular number of the spherical harmonic.\nm : int\n    Azimuthal angular number of the spherical harmonic.\n\nAttributes\n----------\n\ns : int\n    Spin of the spherical harmonic.\nl : int\n    Orbital angular number of the spherical harmonic.\nm : int\n    Azimuthal angular number of the spherical harmonic.\nswsh_prefactor : double\n    Prefactor of the spherical harmonic.\n\nFunctions\n---------\n\nevaluate(theta, phi)\n    Returns the value of the spherical harmonic for the given angles.")},
  {Py_tp_methods, (void *)__pyx_methods_6pyRing_8waveform_SWSH},
  {Py_tp_getset, (void *)__pyx_getsets_6pyRing_8waveform_SWSH},
  {Py_tp_init, (void *)__pyx_pw_6pyRing_8waveform_4SWSH_1__init__},
  {Py_tp_new, (void *)__pyx_tp_new_6pyRing_8waveform_SWSH},
  {0, 0},
};
static PyType_Spec __pyx_type_6pyRing_8waveform_SWSH_spec = {
  "pyRing.waveform.SWSH",
  sizeof(struct __pyx_obj_6pyRing_8waveform_SWSH),
  0,
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE,
  __pyx_type_6pyRing_8waveform_SWSH_slots,
};
#else

static PyTypeObject __pyx_type_6pyRing_8waveform_SWSH = {
  PyVarObject_HEAD_INIT(0, 0)
  "pyRing.waveform.""SWSH", /*tp_name*/
  sizeof(struct __pyx_obj_6pyRing_8waveform_SWSH), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc_6pyRing_8waveform_SWSH, /*tp_dealloc*/
  #if PY_VERSION_HEX < 0x030800b4
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b4
  0, /*tp_vectorcall_offset*/
  #endif
  0, /*tp_getattr*/
  0, /*tp_setattr*/
  0, /*tp_as_async*/
  0, /*tp_repr*/
  0, /*tp_as_number*/
  0, /*tp_as_sequence*/
  0, /*tp_as_mapping*/
  0, /*tp_hash*/
  __pyx_pw_6pyRing_8waveform_4SWSH_3__call__, /*tp_call*/
  0, /*tp_str*/
  0, /*tp_getattro*/
  0, /*tp_setattro*/
  0, /*tp_as_buffer*/
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE, /*tp_flags*/
  PyDoc_STR("SWSH(int s, int l, int m)\n\nSpin weighted spherical harmonics\n-s_Y_{lm}\nDefined in Kidder (https://arxiv.org/pdf/0710.0614.pdf) Eq.s (4, 5).\nNote that this function returns -s_Y_{l,m} as defined by Kidder.\nThus, for gravitational perturbation s=2 must be passed.\n\nParameters\n----------\n\ns : int\n    Spin of the spherical harmonic.\nl : int\n    Orbital angular number of the spherical harmonic.\nm : int\n    Azimuthal angular number of the spherical harmonic.\n\nAttributes\n----------\n\ns : int\n    Spin of the spherical harmonic.\nl : int\n    Orbital angular number of the spherical harmonic.\nm : int\n    Azimuthal angular number of the spherical harmonic.\nswsh_prefactor : double\n    Prefactor of the spherical harmonic.\n\nFunctions\n---------\n\nevaluate(theta, phi)\n    Returns the value of the spherical harmonic for the given angles."), /*tp_doc*/
  0, /*tp_traverse*/
  0, /*tp_clear*/
  0, /*tp_richcompare*/
  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
  0, /*tp_iternext*/
  __pyx_methods_6pyRing_8waveform_SWSH, /*tp_methods*/
  0, /*tp_members*/
  __pyx_getsets_6pyRing_8waveform_SWSH, /*tp_getset*/
  0, /*tp_base*/
  0, /*tp_dict*/
  0, /*tp_descr_get*/
  0, /*tp_descr_set*/
  #if !CYTHON_USE_TYPE_SPECS
  0, /*tp_dictoffset*/
  #endif
  __pyx_pw_6pyRing_8waveform_4SWSH_1__init__, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_6pyRing_8waveform_SWSH, /*tp_new*/
  0, /*tp_free*/
  0, /*tp_is_gc*/
  0, /*tp_bases*/
  0, /*tp_mro*/
  0, /*tp_cache*/
  0, /*tp_subclasses*/
  0, /*tp_weaklist*/
  0, /*tp_del*/
  0, /*tp_version_tag*/
  #if CYTHON_USE_TP_FINALIZE
  0, /*tp_finalize*/
  #else
  NULL, /*tp_finalize*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b1 && (!CYTHON_COMPILING_IN_PYPY || PYPY_VERSION_NUM >= 0x07030800)
  0, /*tp_vectorcall*/
  #endif
  #if __PYX_NEED_TP_PRINT_SLOT == 1
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030C0000
  0, /*tp_watched*/
  #endif
  #if PY_VERSION_HEX >= 0x030d00A4
  0, /*tp_versions_used*/
  #endif
  #if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX >= 0x03090000 && PY_VERSION_HEX < 0x030a0000
  0, /*tp_pypy_flags*/
  #endif
};
#endif
static struct __pyx_vtabstruct_6pyRing_8waveform_KerrBH __pyx_vtable_6pyRing_8waveform_KerrBH;

static PyObject *__pyx_tp_new_6pyRing_8waveform_KerrBH(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_6pyRing_8waveform_KerrBH *p;
  PyObject *o;
  #if CYTHON_COMPILING_IN_LIMITED_API
  allocfunc alloc_func = (allocfunc)PyType_GetSlot(t, Py_tp_alloc);
  o = alloc_func(t, 0);
  #else
  if (likely(!__Pyx_PyType_HasFeature(t, Py_TPFLAGS_IS_ABSTRACT))) {
    o = (*t->tp_alloc)(t, 0);
  } else {
    o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_mstate_global->__pyx_empty_tuple, 0);
  }
  if (unlikely(!o)) return 0;
  #endif
  p = ((struct __pyx_obj_6pyRing_8waveform_KerrBH *)o);
  p->__pyx_vtab = __pyx_vtabptr_6pyRing_8waveform_KerrBH;
  p->amps = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->interpolants = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->tail_parameters = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->quadratic_modes = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->qnm_cached = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->TGR_params = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->qnms = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->qnms_ParSpec = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->swshs = ((PyObject*)Py_None); Py_INCREF(Py_None);
  if (unlikely(__pyx_pw_6pyRing_8waveform_6KerrBH_1__cinit__(o, a, k) < 0)) goto bad;
  return o;
  bad:
  Py_DECREF(o); o = 0;
  return NULL;
}

static void __pyx_tp_dealloc_6pyRing_8waveform_KerrBH(PyObject *o) {
  struct __pyx_obj_6pyRing_8waveform_KerrBH *p = (struct __pyx_obj_6pyRing_8waveform_KerrBH *)o;
  #if CYTHON_USE_TP_FINALIZE
  if (unlikely((PY_VERSION_HEX >= 0x03080000 || __Pyx_PyType_HasFeature(Py_TYPE(o), Py_TPFLAGS_HAVE_FINALIZE)) && __Pyx_PyObject_GetSlot(o, tp_finalize, destructor)) && !__Pyx_PyObject_GC_IsFinalized(o)) {
    if (__Pyx_PyObject_GetSlot(o, tp_dealloc, destructor) == __pyx_tp_dealloc_6pyRing_8waveform_KerrBH) {
      if (PyObject_CallFinalizerFromDealloc(o)) return;
    }
  }
  #endif
  PyObject_GC_UnTrack(o);
  Py_CLEAR(p->amps);
  Py_CLEAR(p->interpolants);
  Py_CLEAR(p->tail_parameters);
  Py_CLEAR(p->quadratic_modes);
  Py_CLEAR(p->qnm_cached);
  Py_CLEAR(p->TGR_params);
  Py_CLEAR(p->qnms);
  Py_CLEAR(p->qnms_ParSpec);
  Py_CLEAR(p->swshs);
  #if CYTHON_USE_TYPE_SLOTS
  (*Py_TYPE(o)->tp_free)(o);
  #else
  {
    freefunc tp_free = (freefunc)PyType_GetSlot(Py_TYPE(o), Py_tp_free);
    if (tp_free) tp_free(o);
  }
  #endif
}

static int __pyx_tp_traverse_6pyRing_8waveform_KerrBH(PyObject *o, visitproc v, void *a) {
  int e;
  struct __pyx_obj_6pyRing_8waveform_KerrBH *p = (struct __pyx_obj_6pyRing_8waveform_KerrBH *)o;
  {
    e = __Pyx_call_type_traverse(o, 1, v, a);
    if (e) return e;
  }
  if (p->amps) {
    e = (*v)(p->amps, a); if (e) return e;
  }
  if (p->interpolants) {
    e = (*v)(p->interpolants, a); if (e) return e;
  }
  if (p->tail_parameters) {
    e = (*v)(p->tail_parameters, a); if (e) return e;
  }
  if (p->quadratic_modes) {
    e = (*v)(p->quadratic_modes, a); if (e) return e;
  }
  if (p->qnm_cached) {
    e = (*v)(p->qnm_cached, a); if (e) return e;
  }
  if (p->TGR_params) {
    e = (*v)(p->TGR_params, a); if (e) return e;
  }
  if (p->qnms) {
    e = (*v)(p->qnms, a); if (e) return e;
  }
  if (p->qnms_ParSpec) {
    e = (*v)(p->qnms_ParSpec, a); if (e) return e;
  }
  if (p->swshs) {
    e = (*v)(p->swshs, a); if (e) return e;
  }
  return 0;
}

static int __pyx_tp_clear_6pyRing_8waveform_KerrBH(PyObject *o) {
  PyObject* tmp;
  struct __pyx_obj_6pyRing_8waveform_KerrBH *p = (struct __pyx_obj_6pyRing_8waveform_KerrBH *)o;
  tmp = ((PyObject*)p->amps);
  p->amps = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->interpolants);
  p->interpolants = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->tail_parameters);
  p->tail_parameters = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->quadratic_modes);
  p->quadratic_modes = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->qnm_cached);
  p->qnm_cached = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->TGR_params);
  p->TGR_params = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->qnms);
  p->qnms = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->qnms_ParSpec);
  p->qnms_ParSpec = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->swshs);
  p->swshs = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  return 0;
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6KerrBH_t0(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6KerrBH_2t0_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6KerrBH_t0(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_2t0_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6KerrBH_Mf(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6KerrBH_2Mf_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6KerrBH_Mf(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_2Mf_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6KerrBH_af(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6KerrBH_2af_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6KerrBH_af(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_2af_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6KerrBH_amps(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6KerrBH_4amps_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6KerrBH_amps(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_4amps_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_4amps_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6KerrBH_r(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6KerrBH_1r_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6KerrBH_r(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_1r_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6KerrBH_iota(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6KerrBH_4iota_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6KerrBH_iota(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_4iota_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6KerrBH_phi(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6KerrBH_3phi_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6KerrBH_phi(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_3phi_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6KerrBH_reference_amplitude(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6KerrBH_19reference_amplitude_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6KerrBH_reference_amplitude(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_19reference_amplitude_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6KerrBH_geom(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6KerrBH_4geom_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6KerrBH_geom(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_4geom_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6KerrBH_qnm_fit(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6KerrBH_7qnm_fit_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6KerrBH_qnm_fit(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_7qnm_fit_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6KerrBH_interpolants(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6KerrBH_12interpolants_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6KerrBH_interpolants(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_12interpolants_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_12interpolants_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6KerrBH_Spheroidal(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6KerrBH_10Spheroidal_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6KerrBH_Spheroidal(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_10Spheroidal_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6KerrBH_amp_non_prec_sym(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6KerrBH_16amp_non_prec_sym_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6KerrBH_amp_non_prec_sym(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_16amp_non_prec_sym_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6KerrBH_tail_parameters(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6KerrBH_15tail_parameters_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6KerrBH_tail_parameters(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_15tail_parameters_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_15tail_parameters_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6KerrBH_quadratic_modes(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6KerrBH_15quadratic_modes_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6KerrBH_quadratic_modes(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_15quadratic_modes_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_15quadratic_modes_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6KerrBH_quad_lin_prop(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6KerrBH_13quad_lin_prop_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6KerrBH_quad_lin_prop(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_13quad_lin_prop_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6KerrBH_neg_quad_freq(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6KerrBH_13neg_quad_freq_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6KerrBH_neg_quad_freq(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_13neg_quad_freq_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6KerrBH_qnm_cached(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6KerrBH_10qnm_cached_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6KerrBH_qnm_cached(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_10qnm_cached_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_10qnm_cached_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6KerrBH_TGR_params(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6KerrBH_10TGR_params_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6KerrBH_TGR_params(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_10TGR_params_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_10TGR_params_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6KerrBH_AreaQuantization(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6KerrBH_16AreaQuantization_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6KerrBH_AreaQuantization(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_16AreaQuantization_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6KerrBH_ParSpec(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6KerrBH_7ParSpec_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6KerrBH_ParSpec(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_7ParSpec_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6KerrBH_charge(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6KerrBH_6charge_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6KerrBH_charge(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_6charge_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6KerrBH_braneworld(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6KerrBH_10braneworld_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6KerrBH_braneworld(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_10braneworld_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6KerrBH_qnms(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6KerrBH_4qnms_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6KerrBH_qnms(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_4qnms_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_4qnms_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6KerrBH_qnms_ParSpec(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6KerrBH_12qnms_ParSpec_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6KerrBH_qnms_ParSpec(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_12qnms_ParSpec_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_12qnms_ParSpec_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6KerrBH_swshs(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6KerrBH_5swshs_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6KerrBH_swshs(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_5swshs_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_6KerrBH_5swshs_5__del__(o);
  }
}

static PyMethodDef __pyx_methods_6pyRing_8waveform_KerrBH[] = {
  {"__reduce_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6KerrBH_5__reduce_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6KerrBH_4__reduce_cython__},
  {"__setstate_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6KerrBH_7__setstate_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6KerrBH_6__setstate_cython__},
  {0, 0, 0, 0}
};

static struct PyGetSetDef __pyx_getsets_6pyRing_8waveform_KerrBH[] = {
  {"t0", __pyx_getprop_6pyRing_8waveform_6KerrBH_t0, __pyx_setprop_6pyRing_8waveform_6KerrBH_t0, PyDoc_STR("t0: 'double'"), 0},
  {"Mf", __pyx_getprop_6pyRing_8waveform_6KerrBH_Mf, __pyx_setprop_6pyRing_8waveform_6KerrBH_Mf, PyDoc_STR("Mf: 'double'"), 0},
  {"af", __pyx_getprop_6pyRing_8waveform_6KerrBH_af, __pyx_setprop_6pyRing_8waveform_6KerrBH_af, PyDoc_STR("af: 'double'"), 0},
  {"amps", __pyx_getprop_6pyRing_8waveform_6KerrBH_amps, __pyx_setprop_6pyRing_8waveform_6KerrBH_amps, PyDoc_STR("amps: dict"), 0},
  {"r", __pyx_getprop_6pyRing_8waveform_6KerrBH_r, __pyx_setprop_6pyRing_8waveform_6KerrBH_r, PyDoc_STR("r: 'double'"), 0},
  {"iota", __pyx_getprop_6pyRing_8waveform_6KerrBH_iota, __pyx_setprop_6pyRing_8waveform_6KerrBH_iota, PyDoc_STR("iota: 'double'"), 0},
  {"phi", __pyx_getprop_6pyRing_8waveform_6KerrBH_phi, __pyx_setprop_6pyRing_8waveform_6KerrBH_phi, PyDoc_STR("phi: 'double'"), 0},
  {"reference_amplitude", __pyx_getprop_6pyRing_8waveform_6KerrBH_reference_amplitude, __pyx_setprop_6pyRing_8waveform_6KerrBH_reference_amplitude, PyDoc_STR("reference_amplitude: 'double'"), 0},
  {"geom", __pyx_getprop_6pyRing_8waveform_6KerrBH_geom, __pyx_setprop_6pyRing_8waveform_6KerrBH_geom, PyDoc_STR("geom: 'unsigned int'"), 0},
  {"qnm_fit", __pyx_getprop_6pyRing_8waveform_6KerrBH_qnm_fit, __pyx_setprop_6pyRing_8waveform_6KerrBH_qnm_fit, PyDoc_STR("qnm_fit: 'unsigned int'"), 0},
  {"interpolants", __pyx_getprop_6pyRing_8waveform_6KerrBH_interpolants, __pyx_setprop_6pyRing_8waveform_6KerrBH_interpolants, PyDoc_STR("interpolants: dict"), 0},
  {"Spheroidal", __pyx_getprop_6pyRing_8waveform_6KerrBH_Spheroidal, __pyx_setprop_6pyRing_8waveform_6KerrBH_Spheroidal, PyDoc_STR("Spheroidal: 'unsigned int'"), 0},
  {"amp_non_prec_sym", __pyx_getprop_6pyRing_8waveform_6KerrBH_amp_non_prec_sym, __pyx_setprop_6pyRing_8waveform_6KerrBH_amp_non_prec_sym, PyDoc_STR("amp_non_prec_sym: 'unsigned int'"), 0},
  {"tail_parameters", __pyx_getprop_6pyRing_8waveform_6KerrBH_tail_parameters, __pyx_setprop_6pyRing_8waveform_6KerrBH_tail_parameters, PyDoc_STR("tail_parameters: dict"), 0},
  {"quadratic_modes", __pyx_getprop_6pyRing_8waveform_6KerrBH_quadratic_modes, __pyx_setprop_6pyRing_8waveform_6KerrBH_quadratic_modes, PyDoc_STR("quadratic_modes: dict"), 0},
  {"quad_lin_prop", __pyx_getprop_6pyRing_8waveform_6KerrBH_quad_lin_prop, __pyx_setprop_6pyRing_8waveform_6KerrBH_quad_lin_prop, PyDoc_STR("quad_lin_prop: 'unsigned int'"), 0},
  {"neg_quad_freq", __pyx_getprop_6pyRing_8waveform_6KerrBH_neg_quad_freq, __pyx_setprop_6pyRing_8waveform_6KerrBH_neg_quad_freq, PyDoc_STR("neg_quad_freq: 'unsigned int'"), 0},
  {"qnm_cached", __pyx_getprop_6pyRing_8waveform_6KerrBH_qnm_cached, __pyx_setprop_6pyRing_8waveform_6KerrBH_qnm_cached, PyDoc_STR("qnm_cached: dict"), 0},
  {"TGR_params", __pyx_getprop_6pyRing_8waveform_6KerrBH_TGR_params, __pyx_setprop_6pyRing_8waveform_6KerrBH_TGR_params, PyDoc_STR("TGR_params: dict"), 0},
  {"AreaQuantization", __pyx_getprop_6pyRing_8waveform_6KerrBH_AreaQuantization, __pyx_setprop_6pyRing_8waveform_6KerrBH_AreaQuantization, PyDoc_STR("AreaQuantization: 'unsigned int'"), 0},
  {"ParSpec", __pyx_getprop_6pyRing_8waveform_6KerrBH_ParSpec, __pyx_setprop_6pyRing_8waveform_6KerrBH_ParSpec, PyDoc_STR("ParSpec: 'unsigned int'"), 0},
  {"charge", __pyx_getprop_6pyRing_8waveform_6KerrBH_charge, __pyx_setprop_6pyRing_8waveform_6KerrBH_charge, PyDoc_STR("charge: 'unsigned int'"), 0},
  {"braneworld", __pyx_getprop_6pyRing_8waveform_6KerrBH_braneworld, __pyx_setprop_6pyRing_8waveform_6KerrBH_braneworld, PyDoc_STR("braneworld: 'unsigned int'"), 0},
  {"qnms", __pyx_getprop_6pyRing_8waveform_6KerrBH_qnms, __pyx_setprop_6pyRing_8waveform_6KerrBH_qnms, PyDoc_STR("qnms: dict"), 0},
  {"qnms_ParSpec", __pyx_getprop_6pyRing_8waveform_6KerrBH_qnms_ParSpec, __pyx_setprop_6pyRing_8waveform_6KerrBH_qnms_ParSpec, PyDoc_STR("qnms_ParSpec: dict"), 0},
  {"swshs", __pyx_getprop_6pyRing_8waveform_6KerrBH_swshs, __pyx_setprop_6pyRing_8waveform_6KerrBH_swshs, PyDoc_STR("swshs: dict"), 0},
  {0, 0, 0, 0, 0}
};
#if CYTHON_USE_TYPE_SPECS
static PyType_Slot __pyx_type_6pyRing_8waveform_KerrBH_slots[] = {
  {Py_tp_dealloc, (void *)__pyx_tp_dealloc_6pyRing_8waveform_KerrBH},
  {Py_tp_doc, (void *)PyDoc_STR("\n    | Multi mode ringdown model for a Kerr black hole using predictions of the frequencies and damping times as function of mass and spin, as predicted by perturbation theory.\n    |\n    | [Input parameters]\n    |\n    | t0    : Start time of the analysis (s), and reference time of the amplitudes, currently common for all modes. #IMPROVEME: allow for a different start time for each mode.\n    | Mf    : Final mass in solar masses.\n    | af    : Dimensionless final spin.\n    | amps  : Amplitudes of the (s,l,m,n) modes. Expected syntax: amps[(s,l,m,n)] = `value`. The keys of this dictionary set the modes used in the waveform.\n    | r     : Distance in Mpc.\n    | iota  : Inclination in radians.\n    | phi   : Azimuthal angle in radians.\n    |\n    | [Optional parameters]\n    |\n    | [[Units and spectrum]]\n    |\n    | reference_amplitude : If non-zero, value with which to replace the Mf/r prefactor. Default: 0.0.\n    | geom                : Flag to compute only the h_{l,m} modes, without spherical harmonics. Default: 0.\n    | qnm_fit             : Flag to request the use of an interpolation for QNM complex frequency, instead of analytical fits (not available for s!=2 or n>2). Default: 1.\n    | interpolants        : QNM complex frequencies interpolants, only used if `qnm_fit=0`. Default: None.\n    |\n    | [[Additional Kerr]]\n    |   \n    | Spheroidal          : Flag to activate the use of spheroidal harmonics instead of spherical. Relies on the pykerr package. Default: 0.\n    | amp_non_prec_sym    : Flag to enforce non-precessing symmetry on the amplitudes. Default: 0.\n    | tail_parameters     : Dictionary of tail modes. Default: None.\n    | quadratic_modes     : Amplitudes of the quadratic contributions (both sum and difference of parent frequencies) to the (s,l,m,n) mode generated by (s1,l1,m1,n1)x(s2,l2,m2,n2). If `quad_lin_prop=1`, instead of the amplitude values, contains the proportionality constant (\007lpha) wrt the product of linear terms."" Expected syntax: quad_amps[term][((s,l,m,n), (s1,l1,m1,n1), (s2,l2,m2,n2))] = `value`, with term=['sum','diff']. Default: None.\n    | quad_lin_prop       : Flag to fix the quadratic amplitudes as \007lpha A_1 * A_2, with (A_1, A_2) the corresponding linear amplitudes. Default: 0.\n    | qnm_cached          : Dictionary containing cached values of the QNM frequencies for specific values of Mf,af. Expected syntax: qnm_cached[(2, l, m, n)] = {'f': freq, 'tau': tau}. Default: None.\n\n    |\n    | [[Beyond Kerr]]\n    |   \n    | TGR_params          : Additional non-GR parameters to be sampled. Default: None.\n    | AreaQuantization    : Flag to use a prescription to impose QNM frequencies derived from the area quantisation proposal. Default: 0.\n    | ParSpec             : Flag to use the ParSpec parametrisation of beyond-GR modifications to QNMs. Default: 0.\n    | charge              : Flag to include the effect of charge. Default: 0.\n    | braneworld          : Flag to include the effect of charge in the braneworld scenario. Default: 0.\n\n  ")},
  {Py_tp_traverse, (void *)__pyx_tp_traverse_6pyRing_8waveform_KerrBH},
  {Py_tp_clear, (void *)__pyx_tp_clear_6pyRing_8waveform_KerrBH},
  {Py_tp_methods, (void *)__pyx_methods_6pyRing_8waveform_KerrBH},
  {Py_tp_getset, (void *)__pyx_getsets_6pyRing_8waveform_KerrBH},
  {Py_tp_new, (void *)__pyx_tp_new_6pyRing_8waveform_KerrBH},
  {0, 0},
};
static PyType_Spec __pyx_type_6pyRing_8waveform_KerrBH_spec = {
  "pyRing.waveform.KerrBH",
  sizeof(struct __pyx_obj_6pyRing_8waveform_KerrBH),
  0,
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC,
  __pyx_type_6pyRing_8waveform_KerrBH_slots,
};
#else

static PyTypeObject __pyx_type_6pyRing_8waveform_KerrBH = {
  PyVarObject_HEAD_INIT(0, 0)
  "pyRing.waveform.""KerrBH", /*tp_name*/
  sizeof(struct __pyx_obj_6pyRing_8waveform_KerrBH), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc_6pyRing_8waveform_KerrBH, /*tp_dealloc*/
  #if PY_VERSION_HEX < 0x030800b4
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b4
  0, /*tp_vectorcall_offset*/
  #endif
  0, /*tp_getattr*/
  0, /*tp_setattr*/
  0, /*tp_as_async*/
  0, /*tp_repr*/
  0, /*tp_as_number*/
  0, /*tp_as_sequence*/
  0, /*tp_as_mapping*/
  0, /*tp_hash*/
  0, /*tp_call*/
  0, /*tp_str*/
  0, /*tp_getattro*/
  0, /*tp_setattro*/
  0, /*tp_as_buffer*/
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC, /*tp_flags*/
  PyDoc_STR("\n    | Multi mode ringdown model for a Kerr black hole using predictions of the frequencies and damping times as function of mass and spin, as predicted by perturbation theory.\n    |\n    | [Input parameters]\n    |\n    | t0    : Start time of the analysis (s), and reference time of the amplitudes, currently common for all modes. #IMPROVEME: allow for a different start time for each mode.\n    | Mf    : Final mass in solar masses.\n    | af    : Dimensionless final spin.\n    | amps  : Amplitudes of the (s,l,m,n) modes. Expected syntax: amps[(s,l,m,n)] = `value`. The keys of this dictionary set the modes used in the waveform.\n    | r     : Distance in Mpc.\n    | iota  : Inclination in radians.\n    | phi   : Azimuthal angle in radians.\n    |\n    | [Optional parameters]\n    |\n    | [[Units and spectrum]]\n    |\n    | reference_amplitude : If non-zero, value with which to replace the Mf/r prefactor. Default: 0.0.\n    | geom                : Flag to compute only the h_{l,m} modes, without spherical harmonics. Default: 0.\n    | qnm_fit             : Flag to request the use of an interpolation for QNM complex frequency, instead of analytical fits (not available for s!=2 or n>2). Default: 1.\n    | interpolants        : QNM complex frequencies interpolants, only used if `qnm_fit=0`. Default: None.\n    |\n    | [[Additional Kerr]]\n    |   \n    | Spheroidal          : Flag to activate the use of spheroidal harmonics instead of spherical. Relies on the pykerr package. Default: 0.\n    | amp_non_prec_sym    : Flag to enforce non-precessing symmetry on the amplitudes. Default: 0.\n    | tail_parameters     : Dictionary of tail modes. Default: None.\n    | quadratic_modes     : Amplitudes of the quadratic contributions (both sum and difference of parent frequencies) to the (s,l,m,n) mode generated by (s1,l1,m1,n1)x(s2,l2,m2,n2). If `quad_lin_prop=1`, instead of the amplitude values, contains the proportionality constant (\007lpha) wrt the product of linear terms."" Expected syntax: quad_amps[term][((s,l,m,n), (s1,l1,m1,n1), (s2,l2,m2,n2))] = `value`, with term=['sum','diff']. Default: None.\n    | quad_lin_prop       : Flag to fix the quadratic amplitudes as \007lpha A_1 * A_2, with (A_1, A_2) the corresponding linear amplitudes. Default: 0.\n    | qnm_cached          : Dictionary containing cached values of the QNM frequencies for specific values of Mf,af. Expected syntax: qnm_cached[(2, l, m, n)] = {'f': freq, 'tau': tau}. Default: None.\n\n    |\n    | [[Beyond Kerr]]\n    |   \n    | TGR_params          : Additional non-GR parameters to be sampled. Default: None.\n    | AreaQuantization    : Flag to use a prescription to impose QNM frequencies derived from the area quantisation proposal. Default: 0.\n    | ParSpec             : Flag to use the ParSpec parametrisation of beyond-GR modifications to QNMs. Default: 0.\n    | charge              : Flag to include the effect of charge. Default: 0.\n    | braneworld          : Flag to include the effect of charge in the braneworld scenario. Default: 0.\n\n  "), /*tp_doc*/
  __pyx_tp_traverse_6pyRing_8waveform_KerrBH, /*tp_traverse*/
  __pyx_tp_clear_6pyRing_8waveform_KerrBH, /*tp_clear*/
  0, /*tp_richcompare*/
  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
  0, /*tp_iternext*/
  __pyx_methods_6pyRing_8waveform_KerrBH, /*tp_methods*/
  0, /*tp_members*/
  __pyx_getsets_6pyRing_8waveform_KerrBH, /*tp_getset*/
  0, /*tp_base*/
  0, /*tp_dict*/
  0, /*tp_descr_get*/
  0, /*tp_descr_set*/
  #if !CYTHON_USE_TYPE_SPECS
  0, /*tp_dictoffset*/
  #endif
  0, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_6pyRing_8waveform_KerrBH, /*tp_new*/
  0, /*tp_free*/
  0, /*tp_is_gc*/
  0, /*tp_bases*/
  0, /*tp_mro*/
  0, /*tp_cache*/
  0, /*tp_subclasses*/
  0, /*tp_weaklist*/
  0, /*tp_del*/
  0, /*tp_version_tag*/
  #if CYTHON_USE_TP_FINALIZE
  0, /*tp_finalize*/
  #else
  NULL, /*tp_finalize*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b1 && (!CYTHON_COMPILING_IN_PYPY || PYPY_VERSION_NUM >= 0x07030800)
  0, /*tp_vectorcall*/
  #endif
  #if __PYX_NEED_TP_PRINT_SLOT == 1
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030C0000
  0, /*tp_watched*/
  #endif
  #if PY_VERSION_HEX >= 0x030d00A4
  0, /*tp_versions_used*/
  #endif
  #if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX >= 0x03090000 && PY_VERSION_HEX < 0x030a0000
  0, /*tp_pypy_flags*/
  #endif
};
#endif
static struct __pyx_vtabstruct_6pyRing_8waveform_MMRDNS __pyx_vtable_6pyRing_8waveform_MMRDNS;

static PyObject *__pyx_tp_new_6pyRing_8waveform_MMRDNS(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_6pyRing_8waveform_MMRDNS *p;
  PyObject *o;
  #if CYTHON_COMPILING_IN_LIMITED_API
  allocfunc alloc_func = (allocfunc)PyType_GetSlot(t, Py_tp_alloc);
  o = alloc_func(t, 0);
  #else
  if (likely(!__Pyx_PyType_HasFeature(t, Py_TPFLAGS_IS_ABSTRACT))) {
    o = (*t->tp_alloc)(t, 0);
  } else {
    o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_mstate_global->__pyx_empty_tuple, 0);
  }
  if (unlikely(!o)) return 0;
  #endif
  p = ((struct __pyx_obj_6pyRing_8waveform_MMRDNS *)o);
  p->__pyx_vtab = __pyx_vtabptr_6pyRing_8waveform_MMRDNS;
  p->TGR_params = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->interpolants = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->multipoles = ((PyObject*)Py_None); Py_INCREF(Py_None);
  if (unlikely(__pyx_pw_6pyRing_8waveform_6MMRDNS_1__cinit__(o, a, k) < 0)) goto bad;
  return o;
  bad:
  Py_DECREF(o); o = 0;
  return NULL;
}

static void __pyx_tp_dealloc_6pyRing_8waveform_MMRDNS(PyObject *o) {
  struct __pyx_obj_6pyRing_8waveform_MMRDNS *p = (struct __pyx_obj_6pyRing_8waveform_MMRDNS *)o;
  #if CYTHON_USE_TP_FINALIZE
  if (unlikely((PY_VERSION_HEX >= 0x03080000 || __Pyx_PyType_HasFeature(Py_TYPE(o), Py_TPFLAGS_HAVE_FINALIZE)) && __Pyx_PyObject_GetSlot(o, tp_finalize, destructor)) && !__Pyx_PyObject_GC_IsFinalized(o)) {
    if (__Pyx_PyObject_GetSlot(o, tp_dealloc, destructor) == __pyx_tp_dealloc_6pyRing_8waveform_MMRDNS) {
      if (PyObject_CallFinalizerFromDealloc(o)) return;
    }
  }
  #endif
  PyObject_GC_UnTrack(o);
  Py_CLEAR(p->TGR_params);
  Py_CLEAR(p->interpolants);
  Py_CLEAR(p->multipoles);
  #if CYTHON_USE_TYPE_SLOTS
  (*Py_TYPE(o)->tp_free)(o);
  #else
  {
    freefunc tp_free = (freefunc)PyType_GetSlot(Py_TYPE(o), Py_tp_free);
    if (tp_free) tp_free(o);
  }
  #endif
}

static int __pyx_tp_traverse_6pyRing_8waveform_MMRDNS(PyObject *o, visitproc v, void *a) {
  int e;
  struct __pyx_obj_6pyRing_8waveform_MMRDNS *p = (struct __pyx_obj_6pyRing_8waveform_MMRDNS *)o;
  {
    e = __Pyx_call_type_traverse(o, 1, v, a);
    if (e) return e;
  }
  if (p->TGR_params) {
    e = (*v)(p->TGR_params, a); if (e) return e;
  }
  if (p->interpolants) {
    e = (*v)(p->interpolants, a); if (e) return e;
  }
  if (p->multipoles) {
    e = (*v)(p->multipoles, a); if (e) return e;
  }
  return 0;
}

static int __pyx_tp_clear_6pyRing_8waveform_MMRDNS(PyObject *o) {
  PyObject* tmp;
  struct __pyx_obj_6pyRing_8waveform_MMRDNS *p = (struct __pyx_obj_6pyRing_8waveform_MMRDNS *)o;
  tmp = ((PyObject*)p->TGR_params);
  p->TGR_params = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->interpolants);
  p->interpolants = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->multipoles);
  p->multipoles = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  return 0;
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNS_t0(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNS_2t0_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNS_t0(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNS_2t0_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNS_t_ref(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNS_5t_ref_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNS_t_ref(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNS_5t_ref_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNS_Mf(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNS_2Mf_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNS_Mf(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNS_2Mf_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNS_af(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNS_2af_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNS_af(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNS_2af_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNS_eta(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNS_3eta_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNS_eta(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNS_3eta_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNS_r(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNS_1r_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNS_r(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNS_1r_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNS_iota(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNS_4iota_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNS_iota(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNS_4iota_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNS_phi(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNS_3phi_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNS_phi(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNS_3phi_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNS_TGR_params(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNS_10TGR_params_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNS_TGR_params(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNS_10TGR_params_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_6MMRDNS_10TGR_params_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNS_single_l(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNS_8single_l_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNS_single_l(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNS_8single_l_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNS_single_m(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNS_8single_m_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNS_single_m(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNS_8single_m_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNS_single_n(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNS_8single_n_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNS_single_n(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNS_8single_n_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNS_single_mode(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNS_11single_mode_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNS_single_mode(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNS_11single_mode_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNS_Spheroidal(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNS_10Spheroidal_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNS_Spheroidal(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNS_10Spheroidal_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNS_interpolants(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNS_12interpolants_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNS_interpolants(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNS_12interpolants_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_6MMRDNS_12interpolants_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNS_qnm_fit(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNS_7qnm_fit_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNS_qnm_fit(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNS_7qnm_fit_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNS_multipoles(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNS_10multipoles_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNS_multipoles(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNS_10multipoles_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_6MMRDNS_10multipoles_5__del__(o);
  }
}

static PyMethodDef __pyx_methods_6pyRing_8waveform_MMRDNS[] = {
  {"__reduce_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6MMRDNS_5__reduce_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6MMRDNS_4__reduce_cython__},
  {"__setstate_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6MMRDNS_7__setstate_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6MMRDNS_6__setstate_cython__},
  {0, 0, 0, 0}
};

static struct PyGetSetDef __pyx_getsets_6pyRing_8waveform_MMRDNS[] = {
  {"t0", __pyx_getprop_6pyRing_8waveform_6MMRDNS_t0, __pyx_setprop_6pyRing_8waveform_6MMRDNS_t0, PyDoc_STR("t0: 'double'"), 0},
  {"t_ref", __pyx_getprop_6pyRing_8waveform_6MMRDNS_t_ref, __pyx_setprop_6pyRing_8waveform_6MMRDNS_t_ref, PyDoc_STR("t_ref: 'double'"), 0},
  {"Mf", __pyx_getprop_6pyRing_8waveform_6MMRDNS_Mf, __pyx_setprop_6pyRing_8waveform_6MMRDNS_Mf, PyDoc_STR("Mf: 'double'"), 0},
  {"af", __pyx_getprop_6pyRing_8waveform_6MMRDNS_af, __pyx_setprop_6pyRing_8waveform_6MMRDNS_af, PyDoc_STR("af: 'double'"), 0},
  {"eta", __pyx_getprop_6pyRing_8waveform_6MMRDNS_eta, __pyx_setprop_6pyRing_8waveform_6MMRDNS_eta, PyDoc_STR("eta: 'double'"), 0},
  {"r", __pyx_getprop_6pyRing_8waveform_6MMRDNS_r, __pyx_setprop_6pyRing_8waveform_6MMRDNS_r, PyDoc_STR("r: 'double'"), 0},
  {"iota", __pyx_getprop_6pyRing_8waveform_6MMRDNS_iota, __pyx_setprop_6pyRing_8waveform_6MMRDNS_iota, PyDoc_STR("iota: 'double'"), 0},
  {"phi", __pyx_getprop_6pyRing_8waveform_6MMRDNS_phi, __pyx_setprop_6pyRing_8waveform_6MMRDNS_phi, PyDoc_STR("phi: 'double'"), 0},
  {"TGR_params", __pyx_getprop_6pyRing_8waveform_6MMRDNS_TGR_params, __pyx_setprop_6pyRing_8waveform_6MMRDNS_TGR_params, PyDoc_STR("TGR_params: dict"), 0},
  {"single_l", __pyx_getprop_6pyRing_8waveform_6MMRDNS_single_l, __pyx_setprop_6pyRing_8waveform_6MMRDNS_single_l, PyDoc_STR("single_l: 'int'"), 0},
  {"single_m", __pyx_getprop_6pyRing_8waveform_6MMRDNS_single_m, __pyx_setprop_6pyRing_8waveform_6MMRDNS_single_m, PyDoc_STR("single_m: 'int'"), 0},
  {"single_n", __pyx_getprop_6pyRing_8waveform_6MMRDNS_single_n, __pyx_setprop_6pyRing_8waveform_6MMRDNS_single_n, PyDoc_STR("single_n: 'int'"), 0},
  {"single_mode", __pyx_getprop_6pyRing_8waveform_6MMRDNS_single_mode, __pyx_setprop_6pyRing_8waveform_6MMRDNS_single_mode, PyDoc_STR("single_mode: 'unsigned int'"), 0},
  {"Spheroidal", __pyx_getprop_6pyRing_8waveform_6MMRDNS_Spheroidal, __pyx_setprop_6pyRing_8waveform_6MMRDNS_Spheroidal, PyDoc_STR("Spheroidal: 'unsigned int'"), 0},
  {"interpolants", __pyx_getprop_6pyRing_8waveform_6MMRDNS_interpolants, __pyx_setprop_6pyRing_8waveform_6MMRDNS_interpolants, PyDoc_STR("interpolants: dict"), 0},
  {"qnm_fit", __pyx_getprop_6pyRing_8waveform_6MMRDNS_qnm_fit, __pyx_setprop_6pyRing_8waveform_6MMRDNS_qnm_fit, PyDoc_STR("qnm_fit: 'unsigned int'"), 0},
  {"multipoles", __pyx_getprop_6pyRing_8waveform_6MMRDNS_multipoles, __pyx_setprop_6pyRing_8waveform_6MMRDNS_multipoles, PyDoc_STR("multipoles: list"), 0},
  {0, 0, 0, 0, 0}
};
#if CYTHON_USE_TYPE_SPECS
static PyType_Slot __pyx_type_6pyRing_8waveform_MMRDNS_slots[] = {
  {Py_tp_dealloc, (void *)__pyx_tp_dealloc_6pyRing_8waveform_MMRDNS},
  {Py_tp_doc, (void *)PyDoc_STR("\n    | Multi mode ringdown model from non-spinning progenitors.\n    | Reference: https://arxiv.org/pdf/1404.3197.pdf\n    |\n    | Input parameters:\n    | t0    : Start time of the analysis (s).\n    | t_ref : Reference time of the ringdown, i.e. the time at which amplitudes and phases are defined. h(t=t_ref) = sum_{lmn} A_{lmn} e^{i phi_{lmn}} S_{lmn}(theta,\\phi).\n    | Mf    : Final mass in solar masses.\n    | af    : Dimensionless final spin.\n    | eta   : Symmetric mass ratio of the progenitors.\n    | r     : Distance in Mpc.\n    | iota  : Inclination in radians.\n    | phi   : Azimuthal angle in radians.\n    |\n    | Optional parameters:\n    | TGR_params                   : Additional non-GR parameters to be sampled.\n    | single_mode                  : Flag to request a single specific mode.\n    | single_l, single_m, single_n : Indices of the specific mode to be selected. Requires single_mode = True in order to be read.\n    | Spheroidal                   : Flag to activate the use of spheroidal harmonics instead of spherical. Relies on the pykerr package.\n    | qnm_fit                      : Flag to request the use of an interpolation for QNM complex frequency, instead of analytical fits (not available for n>2)\n    | interpolants                 : QNM complex frequencies interpolants.\n\n    Returns\n    -------\n\n    h_s, h_vx, h_vy, h_p, h_c : 5 numpy arrays containing the waveform.\n\n    Each array is decomposed as: h(t) = sum_{lmn} S_{lmn}(theta, phi) A_{lmn} e^{i phi_{lmn}} e^{i omega_{lmn} t} e^{-t/tau_{lmn}}\n\n  ")},
  {Py_tp_traverse, (void *)__pyx_tp_traverse_6pyRing_8waveform_MMRDNS},
  {Py_tp_clear, (void *)__pyx_tp_clear_6pyRing_8waveform_MMRDNS},
  {Py_tp_methods, (void *)__pyx_methods_6pyRing_8waveform_MMRDNS},
  {Py_tp_getset, (void *)__pyx_getsets_6pyRing_8waveform_MMRDNS},
  {Py_tp_new, (void *)__pyx_tp_new_6pyRing_8waveform_MMRDNS},
  {0, 0},
};
static PyType_Spec __pyx_type_6pyRing_8waveform_MMRDNS_spec = {
  "pyRing.waveform.MMRDNS",
  sizeof(struct __pyx_obj_6pyRing_8waveform_MMRDNS),
  0,
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC,
  __pyx_type_6pyRing_8waveform_MMRDNS_slots,
};
#else

static PyTypeObject __pyx_type_6pyRing_8waveform_MMRDNS = {
  PyVarObject_HEAD_INIT(0, 0)
  "pyRing.waveform.""MMRDNS", /*tp_name*/
  sizeof(struct __pyx_obj_6pyRing_8waveform_MMRDNS), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc_6pyRing_8waveform_MMRDNS, /*tp_dealloc*/
  #if PY_VERSION_HEX < 0x030800b4
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b4
  0, /*tp_vectorcall_offset*/
  #endif
  0, /*tp_getattr*/
  0, /*tp_setattr*/
  0, /*tp_as_async*/
  0, /*tp_repr*/
  0, /*tp_as_number*/
  0, /*tp_as_sequence*/
  0, /*tp_as_mapping*/
  0, /*tp_hash*/
  0, /*tp_call*/
  0, /*tp_str*/
  0, /*tp_getattro*/
  0, /*tp_setattro*/
  0, /*tp_as_buffer*/
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC, /*tp_flags*/
  PyDoc_STR("\n    | Multi mode ringdown model from non-spinning progenitors.\n    | Reference: https://arxiv.org/pdf/1404.3197.pdf\n    |\n    | Input parameters:\n    | t0    : Start time of the analysis (s).\n    | t_ref : Reference time of the ringdown, i.e. the time at which amplitudes and phases are defined. h(t=t_ref) = sum_{lmn} A_{lmn} e^{i phi_{lmn}} S_{lmn}(theta,\\phi).\n    | Mf    : Final mass in solar masses.\n    | af    : Dimensionless final spin.\n    | eta   : Symmetric mass ratio of the progenitors.\n    | r     : Distance in Mpc.\n    | iota  : Inclination in radians.\n    | phi   : Azimuthal angle in radians.\n    |\n    | Optional parameters:\n    | TGR_params                   : Additional non-GR parameters to be sampled.\n    | single_mode                  : Flag to request a single specific mode.\n    | single_l, single_m, single_n : Indices of the specific mode to be selected. Requires single_mode = True in order to be read.\n    | Spheroidal                   : Flag to activate the use of spheroidal harmonics instead of spherical. Relies on the pykerr package.\n    | qnm_fit                      : Flag to request the use of an interpolation for QNM complex frequency, instead of analytical fits (not available for n>2)\n    | interpolants                 : QNM complex frequencies interpolants.\n\n    Returns\n    -------\n\n    h_s, h_vx, h_vy, h_p, h_c : 5 numpy arrays containing the waveform.\n\n    Each array is decomposed as: h(t) = sum_{lmn} S_{lmn}(theta, phi) A_{lmn} e^{i phi_{lmn}} e^{i omega_{lmn} t} e^{-t/tau_{lmn}}\n\n  "), /*tp_doc*/
  __pyx_tp_traverse_6pyRing_8waveform_MMRDNS, /*tp_traverse*/
  __pyx_tp_clear_6pyRing_8waveform_MMRDNS, /*tp_clear*/
  0, /*tp_richcompare*/
  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
  0, /*tp_iternext*/
  __pyx_methods_6pyRing_8waveform_MMRDNS, /*tp_methods*/
  0, /*tp_members*/
  __pyx_getsets_6pyRing_8waveform_MMRDNS, /*tp_getset*/
  0, /*tp_base*/
  0, /*tp_dict*/
  0, /*tp_descr_get*/
  0, /*tp_descr_set*/
  #if !CYTHON_USE_TYPE_SPECS
  0, /*tp_dictoffset*/
  #endif
  0, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_6pyRing_8waveform_MMRDNS, /*tp_new*/
  0, /*tp_free*/
  0, /*tp_is_gc*/
  0, /*tp_bases*/
  0, /*tp_mro*/
  0, /*tp_cache*/
  0, /*tp_subclasses*/
  0, /*tp_weaklist*/
  0, /*tp_del*/
  0, /*tp_version_tag*/
  #if CYTHON_USE_TP_FINALIZE
  0, /*tp_finalize*/
  #else
  NULL, /*tp_finalize*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b1 && (!CYTHON_COMPILING_IN_PYPY || PYPY_VERSION_NUM >= 0x07030800)
  0, /*tp_vectorcall*/
  #endif
  #if __PYX_NEED_TP_PRINT_SLOT == 1
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030C0000
  0, /*tp_watched*/
  #endif
  #if PY_VERSION_HEX >= 0x030d00A4
  0, /*tp_versions_used*/
  #endif
  #if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX >= 0x03090000 && PY_VERSION_HEX < 0x030a0000
  0, /*tp_pypy_flags*/
  #endif
};
#endif
static struct __pyx_vtabstruct_6pyRing_8waveform_MMRDNP __pyx_vtable_6pyRing_8waveform_MMRDNP;

static PyObject *__pyx_tp_new_6pyRing_8waveform_MMRDNP(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_6pyRing_8waveform_MMRDNP *p;
  PyObject *o;
  #if CYTHON_COMPILING_IN_LIMITED_API
  allocfunc alloc_func = (allocfunc)PyType_GetSlot(t, Py_tp_alloc);
  o = alloc_func(t, 0);
  #else
  if (likely(!__Pyx_PyType_HasFeature(t, Py_TPFLAGS_IS_ABSTRACT))) {
    o = (*t->tp_alloc)(t, 0);
  } else {
    o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_mstate_global->__pyx_empty_tuple, 0);
  }
  if (unlikely(!o)) return 0;
  #endif
  p = ((struct __pyx_obj_6pyRing_8waveform_MMRDNP *)o);
  p->__pyx_vtab = __pyx_vtabptr_6pyRing_8waveform_MMRDNP;
  p->TGR_params = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->modes = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->interpolants = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->qnm_cached = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->multipoles = ((PyObject*)Py_None); Py_INCREF(Py_None);
  if (unlikely(__pyx_pw_6pyRing_8waveform_6MMRDNP_1__cinit__(o, a, k) < 0)) goto bad;
  return o;
  bad:
  Py_DECREF(o); o = 0;
  return NULL;
}

static void __pyx_tp_dealloc_6pyRing_8waveform_MMRDNP(PyObject *o) {
  struct __pyx_obj_6pyRing_8waveform_MMRDNP *p = (struct __pyx_obj_6pyRing_8waveform_MMRDNP *)o;
  #if CYTHON_USE_TP_FINALIZE
  if (unlikely((PY_VERSION_HEX >= 0x03080000 || __Pyx_PyType_HasFeature(Py_TYPE(o), Py_TPFLAGS_HAVE_FINALIZE)) && __Pyx_PyObject_GetSlot(o, tp_finalize, destructor)) && !__Pyx_PyObject_GC_IsFinalized(o)) {
    if (__Pyx_PyObject_GetSlot(o, tp_dealloc, destructor) == __pyx_tp_dealloc_6pyRing_8waveform_MMRDNP) {
      if (PyObject_CallFinalizerFromDealloc(o)) return;
    }
  }
  #endif
  PyObject_GC_UnTrack(o);
  Py_CLEAR(p->TGR_params);
  Py_CLEAR(p->modes);
  Py_CLEAR(p->interpolants);
  Py_CLEAR(p->qnm_cached);
  Py_CLEAR(p->multipoles);
  #if CYTHON_USE_TYPE_SLOTS
  (*Py_TYPE(o)->tp_free)(o);
  #else
  {
    freefunc tp_free = (freefunc)PyType_GetSlot(Py_TYPE(o), Py_tp_free);
    if (tp_free) tp_free(o);
  }
  #endif
}

static int __pyx_tp_traverse_6pyRing_8waveform_MMRDNP(PyObject *o, visitproc v, void *a) {
  int e;
  struct __pyx_obj_6pyRing_8waveform_MMRDNP *p = (struct __pyx_obj_6pyRing_8waveform_MMRDNP *)o;
  {
    e = __Pyx_call_type_traverse(o, 1, v, a);
    if (e) return e;
  }
  if (p->TGR_params) {
    e = (*v)(p->TGR_params, a); if (e) return e;
  }
  if (p->modes) {
    e = (*v)(p->modes, a); if (e) return e;
  }
  if (p->interpolants) {
    e = (*v)(p->interpolants, a); if (e) return e;
  }
  if (p->qnm_cached) {
    e = (*v)(p->qnm_cached, a); if (e) return e;
  }
  if (p->multipoles) {
    e = (*v)(p->multipoles, a); if (e) return e;
  }
  return 0;
}

static int __pyx_tp_clear_6pyRing_8waveform_MMRDNP(PyObject *o) {
  PyObject* tmp;
  struct __pyx_obj_6pyRing_8waveform_MMRDNP *p = (struct __pyx_obj_6pyRing_8waveform_MMRDNP *)o;
  tmp = ((PyObject*)p->TGR_params);
  p->TGR_params = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->modes);
  p->modes = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->interpolants);
  p->interpolants = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->qnm_cached);
  p->qnm_cached = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->multipoles);
  p->multipoles = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  return 0;
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNP_t0(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNP_2t0_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNP_t0(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNP_2t0_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNP_t_ref(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNP_5t_ref_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNP_t_ref(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNP_5t_ref_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNP_Mf(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNP_2Mf_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNP_Mf(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNP_2Mf_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNP_af(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNP_2af_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNP_af(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNP_2af_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNP_Mi(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNP_2Mi_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNP_Mi(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNP_2Mi_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNP_eta(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNP_3eta_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNP_eta(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNP_3eta_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNP_chi_s(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNP_5chi_s_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNP_chi_s(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNP_5chi_s_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNP_chi_a(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNP_5chi_a_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNP_chi_a(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNP_5chi_a_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNP_r(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNP_1r_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNP_r(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNP_1r_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNP_iota(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNP_4iota_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNP_iota(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNP_4iota_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNP_phi(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNP_3phi_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNP_phi(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNP_3phi_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNP_TGR_params(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNP_10TGR_params_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNP_TGR_params(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNP_10TGR_params_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_6MMRDNP_10TGR_params_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNP_modes(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNP_5modes_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNP_modes(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNP_5modes_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_6MMRDNP_5modes_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNP_geom(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNP_4geom_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNP_geom(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNP_4geom_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNP_qnm_fit(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNP_7qnm_fit_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNP_qnm_fit(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNP_7qnm_fit_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNP_interpolants(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNP_12interpolants_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNP_interpolants(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNP_12interpolants_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_6MMRDNP_12interpolants_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNP_qnm_cached(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNP_10qnm_cached_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNP_qnm_cached(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNP_10qnm_cached_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_6MMRDNP_10qnm_cached_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNP_delta(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNP_5delta_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNP_delta(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNP_5delta_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6MMRDNP_multipoles(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6MMRDNP_10multipoles_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6MMRDNP_multipoles(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6MMRDNP_10multipoles_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_6MMRDNP_10multipoles_5__del__(o);
  }
}

static PyMethodDef __pyx_methods_6pyRing_8waveform_MMRDNP[] = {
  {"__reduce_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6MMRDNP_5__reduce_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6MMRDNP_4__reduce_cython__},
  {"__setstate_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6MMRDNP_7__setstate_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6MMRDNP_6__setstate_cython__},
  {0, 0, 0, 0}
};

static struct PyGetSetDef __pyx_getsets_6pyRing_8waveform_MMRDNP[] = {
  {"t0", __pyx_getprop_6pyRing_8waveform_6MMRDNP_t0, __pyx_setprop_6pyRing_8waveform_6MMRDNP_t0, PyDoc_STR("t0: 'double'"), 0},
  {"t_ref", __pyx_getprop_6pyRing_8waveform_6MMRDNP_t_ref, __pyx_setprop_6pyRing_8waveform_6MMRDNP_t_ref, PyDoc_STR("t_ref: 'double'"), 0},
  {"Mf", __pyx_getprop_6pyRing_8waveform_6MMRDNP_Mf, __pyx_setprop_6pyRing_8waveform_6MMRDNP_Mf, PyDoc_STR("Mf: 'double'"), 0},
  {"af", __pyx_getprop_6pyRing_8waveform_6MMRDNP_af, __pyx_setprop_6pyRing_8waveform_6MMRDNP_af, PyDoc_STR("af: 'double'"), 0},
  {"Mi", __pyx_getprop_6pyRing_8waveform_6MMRDNP_Mi, __pyx_setprop_6pyRing_8waveform_6MMRDNP_Mi, PyDoc_STR("Mi: 'double'"), 0},
  {"eta", __pyx_getprop_6pyRing_8waveform_6MMRDNP_eta, __pyx_setprop_6pyRing_8waveform_6MMRDNP_eta, PyDoc_STR("eta: 'double'"), 0},
  {"chi_s", __pyx_getprop_6pyRing_8waveform_6MMRDNP_chi_s, __pyx_setprop_6pyRing_8waveform_6MMRDNP_chi_s, PyDoc_STR("chi_s: 'double'"), 0},
  {"chi_a", __pyx_getprop_6pyRing_8waveform_6MMRDNP_chi_a, __pyx_setprop_6pyRing_8waveform_6MMRDNP_chi_a, PyDoc_STR("chi_a: 'double'"), 0},
  {"r", __pyx_getprop_6pyRing_8waveform_6MMRDNP_r, __pyx_setprop_6pyRing_8waveform_6MMRDNP_r, PyDoc_STR("r: 'double'"), 0},
  {"iota", __pyx_getprop_6pyRing_8waveform_6MMRDNP_iota, __pyx_setprop_6pyRing_8waveform_6MMRDNP_iota, PyDoc_STR("iota: 'double'"), 0},
  {"phi", __pyx_getprop_6pyRing_8waveform_6MMRDNP_phi, __pyx_setprop_6pyRing_8waveform_6MMRDNP_phi, PyDoc_STR("phi: 'double'"), 0},
  {"TGR_params", __pyx_getprop_6pyRing_8waveform_6MMRDNP_TGR_params, __pyx_setprop_6pyRing_8waveform_6MMRDNP_TGR_params, PyDoc_STR("TGR_params: dict"), 0},
  {"modes", __pyx_getprop_6pyRing_8waveform_6MMRDNP_modes, __pyx_setprop_6pyRing_8waveform_6MMRDNP_modes, PyDoc_STR("modes: list"), 0},
  {"geom", __pyx_getprop_6pyRing_8waveform_6MMRDNP_geom, __pyx_setprop_6pyRing_8waveform_6MMRDNP_geom, PyDoc_STR("geom: 'unsigned int'"), 0},
  {"qnm_fit", __pyx_getprop_6pyRing_8waveform_6MMRDNP_qnm_fit, __pyx_setprop_6pyRing_8waveform_6MMRDNP_qnm_fit, PyDoc_STR("qnm_fit: 'unsigned int'"), 0},
  {"interpolants", __pyx_getprop_6pyRing_8waveform_6MMRDNP_interpolants, __pyx_setprop_6pyRing_8waveform_6MMRDNP_interpolants, PyDoc_STR("interpolants: dict"), 0},
  {"qnm_cached", __pyx_getprop_6pyRing_8waveform_6MMRDNP_qnm_cached, __pyx_setprop_6pyRing_8waveform_6MMRDNP_qnm_cached, PyDoc_STR("qnm_cached: dict"), 0},
  {"delta", __pyx_getprop_6pyRing_8waveform_6MMRDNP_delta, __pyx_setprop_6pyRing_8waveform_6MMRDNP_delta, PyDoc_STR("delta: 'double'"), 0},
  {"multipoles", __pyx_getprop_6pyRing_8waveform_6MMRDNP_multipoles, __pyx_setprop_6pyRing_8waveform_6MMRDNP_multipoles, PyDoc_STR("multipoles: dict"), 0},
  {0, 0, 0, 0, 0}
};
#if CYTHON_USE_TYPE_SPECS
static PyType_Slot __pyx_type_6pyRing_8waveform_MMRDNP_slots[] = {
  {Py_tp_dealloc, (void *)__pyx_tp_dealloc_6pyRing_8waveform_MMRDNP},
  {Py_tp_doc, (void *)PyDoc_STR("\n    | Multi mode ringdown non-precessing model.\n    | Reference: https://arxiv.org/pdf/1801.08208.pdf\n    | Mi is the initial total mass of the binary, m_i the single masses, chi_i the single spins.\n    | The model was calibrated such that t=0 corresponds to 20M after |\\dot{h}_22| peak.\n    |\n    | Input parameters:\n    | t0    : Start time of the analysis (s).\n    | t_ref : Reference time of the ringdown, i.e. the time at which amplitudes and phases are defined. h(t=t_ref) = sum_{lm} sum_{l'm'n} A_{lml'm'n} e^{i phi_{lml'm'n}} sY_{lm}(theta,phi) * e^{i omega_{l'm'n} t} * e^{-t/tau_{l'm'n}}.\n    |    \n    | Mf    : Final mass in solar masses.\n    | af    : Dimensionless final spin.\n    |\n    | Mi    : Initial mass in solar masses.\n    | eta   : Symmetric mass ratio of the progenitors.\n    | chi_s : (m_1*chi_1 + m_2*chi_2)/M_tot\n    | chi_a : (m_1*chi_1 - m_2*chi_2)/M_tot\n    |\n    | r     : Distance in Mpc.\n    | iota  : Inclination in radians.\n    | phi   : Azimuthal angle in radians.\n    |\n    | TGR_params         : Additional non-GR parameters to be sampled.\n    |    \n    | Optional parameters:\n    | modes              : list of modes to be used [(l,m,n)]\n    | geom               : Flag to compute only the h_{l,m} modes, without spherical harmonics.\n    | qnm_fit            : Flag to switch between analytical fits (qnm_fit=1), not available for s!=2 or n>2) and interpolants for QNM complex frequencies (qnm_fit=0). Default: 1.\n    | interpolants       : QNM complex frequencies interpolants, only used if `qnm_fit=0`. Default: None.\n    | qnm_cached         : Dictionary containing cached values of the QNM frequencies for specific values of Mf,af. Expected syntax: qnm_cached[(2, l, m, n)] = {'f': freq, 'tau': tau}. Default: None.\n\n    Returns\n    -------\n\n    h_s, h_vx, h_vy, h_p, h_c : np.array\n\n    Each h is decomposed as: h(t) = sum_{lm} sum_{l'm'n} A_{lml'm'n} e^{i phi_{lml'm'n}} sY_{lm}(theta,phi) * exp(i omega t) where omeg""a = f - i/tau.\n\n  ")},
  {Py_tp_traverse, (void *)__pyx_tp_traverse_6pyRing_8waveform_MMRDNP},
  {Py_tp_clear, (void *)__pyx_tp_clear_6pyRing_8waveform_MMRDNP},
  {Py_tp_methods, (void *)__pyx_methods_6pyRing_8waveform_MMRDNP},
  {Py_tp_getset, (void *)__pyx_getsets_6pyRing_8waveform_MMRDNP},
  {Py_tp_new, (void *)__pyx_tp_new_6pyRing_8waveform_MMRDNP},
  {0, 0},
};
static PyType_Spec __pyx_type_6pyRing_8waveform_MMRDNP_spec = {
  "pyRing.waveform.MMRDNP",
  sizeof(struct __pyx_obj_6pyRing_8waveform_MMRDNP),
  0,
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC,
  __pyx_type_6pyRing_8waveform_MMRDNP_slots,
};
#else

static PyTypeObject __pyx_type_6pyRing_8waveform_MMRDNP = {
  PyVarObject_HEAD_INIT(0, 0)
  "pyRing.waveform.""MMRDNP", /*tp_name*/
  sizeof(struct __pyx_obj_6pyRing_8waveform_MMRDNP), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc_6pyRing_8waveform_MMRDNP, /*tp_dealloc*/
  #if PY_VERSION_HEX < 0x030800b4
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b4
  0, /*tp_vectorcall_offset*/
  #endif
  0, /*tp_getattr*/
  0, /*tp_setattr*/
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  0, /*tp_as_number*/
  0, /*tp_as_sequence*/
  0, /*tp_as_mapping*/
  0, /*tp_hash*/
  0, /*tp_call*/
  0, /*tp_str*/
  0, /*tp_getattro*/
  0, /*tp_setattro*/
  0, /*tp_as_buffer*/
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC, /*tp_flags*/
  PyDoc_STR("\n    | Multi mode ringdown non-precessing model.\n    | Reference: https://arxiv.org/pdf/1801.08208.pdf\n    | Mi is the initial total mass of the binary, m_i the single masses, chi_i the single spins.\n    | The model was calibrated such that t=0 corresponds to 20M after |\\dot{h}_22| peak.\n    |\n    | Input parameters:\n    | t0    : Start time of the analysis (s).\n    | t_ref : Reference time of the ringdown, i.e. the time at which amplitudes and phases are defined. h(t=t_ref) = sum_{lm} sum_{l'm'n} A_{lml'm'n} e^{i phi_{lml'm'n}} sY_{lm}(theta,phi) * e^{i omega_{l'm'n} t} * e^{-t/tau_{l'm'n}}.\n    |    \n    | Mf    : Final mass in solar masses.\n    | af    : Dimensionless final spin.\n    |\n    | Mi    : Initial mass in solar masses.\n    | eta   : Symmetric mass ratio of the progenitors.\n    | chi_s : (m_1*chi_1 + m_2*chi_2)/M_tot\n    | chi_a : (m_1*chi_1 - m_2*chi_2)/M_tot\n    |\n    | r     : Distance in Mpc.\n    | iota  : Inclination in radians.\n    | phi   : Azimuthal angle in radians.\n    |\n    | TGR_params         : Additional non-GR parameters to be sampled.\n    |    \n    | Optional parameters:\n    | modes              : list of modes to be used [(l,m,n)]\n    | geom               : Flag to compute only the h_{l,m} modes, without spherical harmonics.\n    | qnm_fit            : Flag to switch between analytical fits (qnm_fit=1), not available for s!=2 or n>2) and interpolants for QNM complex frequencies (qnm_fit=0). Default: 1.\n    | interpolants       : QNM complex frequencies interpolants, only used if `qnm_fit=0`. Default: None.\n    | qnm_cached         : Dictionary containing cached values of the QNM frequencies for specific values of Mf,af. Expected syntax: qnm_cached[(2, l, m, n)] = {'f': freq, 'tau': tau}. Default: None.\n\n    Returns\n    -------\n\n    h_s, h_vx, h_vy, h_p, h_c : np.array\n\n    Each h is decomposed as: h(t) = sum_{lm} sum_{l'm'n} A_{lml'm'n} e^{i phi_{lml'm'n}} sY_{lm}(theta,phi) * exp(i omega t) where omeg""a = f - i/tau.\n\n  "), /*tp_doc*/
  __pyx_tp_traverse_6pyRing_8waveform_MMRDNP, /*tp_traverse*/
  __pyx_tp_clear_6pyRing_8waveform_MMRDNP, /*tp_clear*/
  0, /*tp_richcompare*/
  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
  0, /*tp_iternext*/
  __pyx_methods_6pyRing_8waveform_MMRDNP, /*tp_methods*/
  0, /*tp_members*/
  __pyx_getsets_6pyRing_8waveform_MMRDNP, /*tp_getset*/
  0, /*tp_base*/
  0, /*tp_dict*/
  0, /*tp_descr_get*/
  0, /*tp_descr_set*/
  #if !CYTHON_USE_TYPE_SPECS
  0, /*tp_dictoffset*/
  #endif
  0, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_6pyRing_8waveform_MMRDNP, /*tp_new*/
  0, /*tp_free*/
  0, /*tp_is_gc*/
  0, /*tp_bases*/
  0, /*tp_mro*/
  0, /*tp_cache*/
  0, /*tp_subclasses*/
  0, /*tp_weaklist*/
  0, /*tp_del*/
  0, /*tp_version_tag*/
  #if CYTHON_USE_TP_FINALIZE
  0, /*tp_finalize*/
  #else
  NULL, /*tp_finalize*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b1 && (!CYTHON_COMPILING_IN_PYPY || PYPY_VERSION_NUM >= 0x07030800)
  0, /*tp_vectorcall*/
  #endif
  #if __PYX_NEED_TP_PRINT_SLOT == 1
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030C0000
  0, /*tp_watched*/
  #endif
  #if PY_VERSION_HEX >= 0x030d00A4
  0, /*tp_versions_used*/
  #endif
  #if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX >= 0x03090000 && PY_VERSION_HEX < 0x030a0000
  0, /*tp_pypy_flags*/
  #endif
};
#endif
static struct __pyx_vtabstruct_6pyRing_8waveform_KHS_2012 __pyx_vtable_6pyRing_8waveform_KHS_2012;

static PyObject *__pyx_tp_new_6pyRing_8waveform_KHS_2012(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_6pyRing_8waveform_KHS_2012 *p;
  PyObject *o;
  #if CYTHON_COMPILING_IN_LIMITED_API
  allocfunc alloc_func = (allocfunc)PyType_GetSlot(t, Py_tp_alloc);
  o = alloc_func(t, 0);
  #else
  if (likely(!__Pyx_PyType_HasFeature(t, Py_TPFLAGS_IS_ABSTRACT))) {
    o = (*t->tp_alloc)(t, 0);
  } else {
    o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_mstate_global->__pyx_empty_tuple, 0);
  }
  if (unlikely(!o)) return 0;
  #endif
  p = ((struct __pyx_obj_6pyRing_8waveform_KHS_2012 *)o);
  p->__pyx_vtab = __pyx_vtabptr_6pyRing_8waveform_KHS_2012;
  p->TGR_params = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->multipoles = ((PyObject*)Py_None); Py_INCREF(Py_None);
  if (unlikely(__pyx_pw_6pyRing_8waveform_8KHS_2012_1__cinit__(o, a, k) < 0)) goto bad;
  return o;
  bad:
  Py_DECREF(o); o = 0;
  return NULL;
}

static void __pyx_tp_dealloc_6pyRing_8waveform_KHS_2012(PyObject *o) {
  struct __pyx_obj_6pyRing_8waveform_KHS_2012 *p = (struct __pyx_obj_6pyRing_8waveform_KHS_2012 *)o;
  #if CYTHON_USE_TP_FINALIZE
  if (unlikely((PY_VERSION_HEX >= 0x03080000 || __Pyx_PyType_HasFeature(Py_TYPE(o), Py_TPFLAGS_HAVE_FINALIZE)) && __Pyx_PyObject_GetSlot(o, tp_finalize, destructor)) && !__Pyx_PyObject_GC_IsFinalized(o)) {
    if (__Pyx_PyObject_GetSlot(o, tp_dealloc, destructor) == __pyx_tp_dealloc_6pyRing_8waveform_KHS_2012) {
      if (PyObject_CallFinalizerFromDealloc(o)) return;
    }
  }
  #endif
  PyObject_GC_UnTrack(o);
  Py_CLEAR(p->TGR_params);
  Py_CLEAR(p->multipoles);
  #if CYTHON_USE_TYPE_SLOTS
  (*Py_TYPE(o)->tp_free)(o);
  #else
  {
    freefunc tp_free = (freefunc)PyType_GetSlot(Py_TYPE(o), Py_tp_free);
    if (tp_free) tp_free(o);
  }
  #endif
}

static int __pyx_tp_traverse_6pyRing_8waveform_KHS_2012(PyObject *o, visitproc v, void *a) {
  int e;
  struct __pyx_obj_6pyRing_8waveform_KHS_2012 *p = (struct __pyx_obj_6pyRing_8waveform_KHS_2012 *)o;
  {
    e = __Pyx_call_type_traverse(o, 1, v, a);
    if (e) return e;
  }
  if (p->TGR_params) {
    e = (*v)(p->TGR_params, a); if (e) return e;
  }
  if (p->multipoles) {
    e = (*v)(p->multipoles, a); if (e) return e;
  }
  return 0;
}

static int __pyx_tp_clear_6pyRing_8waveform_KHS_2012(PyObject *o) {
  PyObject* tmp;
  struct __pyx_obj_6pyRing_8waveform_KHS_2012 *p = (struct __pyx_obj_6pyRing_8waveform_KHS_2012 *)o;
  tmp = ((PyObject*)p->TGR_params);
  p->TGR_params = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->multipoles);
  p->multipoles = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  return 0;
}

static PyObject *__pyx_getprop_6pyRing_8waveform_8KHS_2012_t0(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_8KHS_2012_2t0_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_8KHS_2012_t0(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_8KHS_2012_2t0_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_8KHS_2012_t_ref(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_8KHS_2012_5t_ref_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_8KHS_2012_t_ref(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_8KHS_2012_5t_ref_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_8KHS_2012_Mf(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_8KHS_2012_2Mf_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_8KHS_2012_Mf(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_8KHS_2012_2Mf_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_8KHS_2012_af(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_8KHS_2012_2af_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_8KHS_2012_af(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_8KHS_2012_2af_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_8KHS_2012_eta(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_8KHS_2012_3eta_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_8KHS_2012_eta(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_8KHS_2012_3eta_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_8KHS_2012_chi_eff(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_8KHS_2012_7chi_eff_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_8KHS_2012_chi_eff(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_8KHS_2012_7chi_eff_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_8KHS_2012_r(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_8KHS_2012_1r_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_8KHS_2012_r(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_8KHS_2012_1r_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_8KHS_2012_iota(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_8KHS_2012_4iota_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_8KHS_2012_iota(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_8KHS_2012_4iota_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_8KHS_2012_phi(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_8KHS_2012_3phi_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_8KHS_2012_phi(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_8KHS_2012_3phi_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_8KHS_2012_TGR_params(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_8KHS_2012_10TGR_params_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_8KHS_2012_TGR_params(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_8KHS_2012_10TGR_params_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_8KHS_2012_10TGR_params_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_8KHS_2012_single_l(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_8KHS_2012_8single_l_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_8KHS_2012_single_l(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_8KHS_2012_8single_l_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_8KHS_2012_single_m(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_8KHS_2012_8single_m_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_8KHS_2012_single_m(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_8KHS_2012_8single_m_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_8KHS_2012_single_mode(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_8KHS_2012_11single_mode_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_8KHS_2012_single_mode(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_8KHS_2012_11single_mode_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_8KHS_2012_multipoles(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_8KHS_2012_10multipoles_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_8KHS_2012_multipoles(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_8KHS_2012_10multipoles_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_8KHS_2012_10multipoles_5__del__(o);
  }
}

static PyMethodDef __pyx_methods_6pyRing_8waveform_KHS_2012[] = {
  {"__reduce_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_8KHS_2012_5__reduce_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_8KHS_2012_4__reduce_cython__},
  {"__setstate_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_8KHS_2012_7__setstate_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_8KHS_2012_6__setstate_cython__},
  {0, 0, 0, 0}
};

static struct PyGetSetDef __pyx_getsets_6pyRing_8waveform_KHS_2012[] = {
  {"t0", __pyx_getprop_6pyRing_8waveform_8KHS_2012_t0, __pyx_setprop_6pyRing_8waveform_8KHS_2012_t0, PyDoc_STR("t0: 'double'"), 0},
  {"t_ref", __pyx_getprop_6pyRing_8waveform_8KHS_2012_t_ref, __pyx_setprop_6pyRing_8waveform_8KHS_2012_t_ref, PyDoc_STR("t_ref: 'double'"), 0},
  {"Mf", __pyx_getprop_6pyRing_8waveform_8KHS_2012_Mf, __pyx_setprop_6pyRing_8waveform_8KHS_2012_Mf, PyDoc_STR("Mf: 'double'"), 0},
  {"af", __pyx_getprop_6pyRing_8waveform_8KHS_2012_af, __pyx_setprop_6pyRing_8waveform_8KHS_2012_af, PyDoc_STR("af: 'double'"), 0},
  {"eta", __pyx_getprop_6pyRing_8waveform_8KHS_2012_eta, __pyx_setprop_6pyRing_8waveform_8KHS_2012_eta, PyDoc_STR("eta: 'double'"), 0},
  {"chi_eff", __pyx_getprop_6pyRing_8waveform_8KHS_2012_chi_eff, __pyx_setprop_6pyRing_8waveform_8KHS_2012_chi_eff, PyDoc_STR("chi_eff: 'double'"), 0},
  {"r", __pyx_getprop_6pyRing_8waveform_8KHS_2012_r, __pyx_setprop_6pyRing_8waveform_8KHS_2012_r, PyDoc_STR("r: 'double'"), 0},
  {"iota", __pyx_getprop_6pyRing_8waveform_8KHS_2012_iota, __pyx_setprop_6pyRing_8waveform_8KHS_2012_iota, PyDoc_STR("iota: 'double'"), 0},
  {"phi", __pyx_getprop_6pyRing_8waveform_8KHS_2012_phi, __pyx_setprop_6pyRing_8waveform_8KHS_2012_phi, PyDoc_STR("phi: 'double'"), 0},
  {"TGR_params", __pyx_getprop_6pyRing_8waveform_8KHS_2012_TGR_params, __pyx_setprop_6pyRing_8waveform_8KHS_2012_TGR_params, PyDoc_STR("TGR_params: dict"), 0},
  {"single_l", __pyx_getprop_6pyRing_8waveform_8KHS_2012_single_l, __pyx_setprop_6pyRing_8waveform_8KHS_2012_single_l, PyDoc_STR("single_l: 'int'"), 0},
  {"single_m", __pyx_getprop_6pyRing_8waveform_8KHS_2012_single_m, __pyx_setprop_6pyRing_8waveform_8KHS_2012_single_m, PyDoc_STR("single_m: 'int'"), 0},
  {"single_mode", __pyx_getprop_6pyRing_8waveform_8KHS_2012_single_mode, __pyx_setprop_6pyRing_8waveform_8KHS_2012_single_mode, PyDoc_STR("single_mode: 'unsigned int'"), 0},
  {"multipoles", __pyx_getprop_6pyRing_8waveform_8KHS_2012_multipoles, __pyx_setprop_6pyRing_8waveform_8KHS_2012_multipoles, PyDoc_STR("multipoles: list"), 0},
  {0, 0, 0, 0, 0}
};
#if CYTHON_USE_TYPE_SPECS
static PyType_Slot __pyx_type_6pyRing_8waveform_KHS_2012_slots[] = {
  {Py_tp_dealloc, (void *)__pyx_tp_dealloc_6pyRing_8waveform_KHS_2012},
  {Py_tp_doc, (void *)PyDoc_STR("\n\n    | Multi mode ringdown non-precessing model.\n    | References: https://arxiv.org/abs/1207.0399, https://arxiv.org/abs/1406.3201\n    | M_tot is the initial total mass of the binary, m_i the single mass, chi_i the single spin.\n    | In this model t=0 corresponds to 20M after the merger.\n    |\n    | Input parameters:\n    | t0         : start time of the analysis (s).\n    | t_ref      : reference time of the ringdown, i.e. the time at which amplitudes and phases are defined. h(t=t_ref) = sum_{lm} A_{lm} e^{i phi_{lm}} sY_{lm}(theta,phi)\n    | Mf         : final mass in solar masses\n    | af         : dimensionless final spin\n    | eta        : symmetric mass ratio of the progenitors\n    | chi_eff    : symmetric spin of the progenitors (defined as: 1/2*(sqrt(1-4*nu) chi1 + (m1*chi1 - m2*chi2)/(m1+m2)))\n    | r          : distance in Mpc\n    | iota       : inclination in radians\n    | phi        : azimuthal angle in radians\n    | TGR_params : additional non-GR parameters to be sampled\n    |\n    | Optional parameters:\n    | single_l, single_n : select a specific mode\n    | single_mode        : flag to request only a specific mode\n\n  ")},
  {Py_tp_traverse, (void *)__pyx_tp_traverse_6pyRing_8waveform_KHS_2012},
  {Py_tp_clear, (void *)__pyx_tp_clear_6pyRing_8waveform_KHS_2012},
  {Py_tp_methods, (void *)__pyx_methods_6pyRing_8waveform_KHS_2012},
  {Py_tp_getset, (void *)__pyx_getsets_6pyRing_8waveform_KHS_2012},
  {Py_tp_new, (void *)__pyx_tp_new_6pyRing_8waveform_KHS_2012},
  {0, 0},
};
static PyType_Spec __pyx_type_6pyRing_8waveform_KHS_2012_spec = {
  "pyRing.waveform.KHS_2012",
  sizeof(struct __pyx_obj_6pyRing_8waveform_KHS_2012),
  0,
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC,
  __pyx_type_6pyRing_8waveform_KHS_2012_slots,
};
#else

static PyTypeObject __pyx_type_6pyRing_8waveform_KHS_2012 = {
  PyVarObject_HEAD_INIT(0, 0)
  "pyRing.waveform.""KHS_2012", /*tp_name*/
  sizeof(struct __pyx_obj_6pyRing_8waveform_KHS_2012), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc_6pyRing_8waveform_KHS_2012, /*tp_dealloc*/
  #if PY_VERSION_HEX < 0x030800b4
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b4
  0, /*tp_vectorcall_offset*/
  #endif
  0, /*tp_getattr*/
  0, /*tp_setattr*/
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  0, /*tp_repr*/
  0, /*tp_as_number*/
  0, /*tp_as_sequence*/
  0, /*tp_as_mapping*/
  0, /*tp_hash*/
  0, /*tp_call*/
  0, /*tp_str*/
  0, /*tp_getattro*/
  0, /*tp_setattro*/
  0, /*tp_as_buffer*/
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC, /*tp_flags*/
  PyDoc_STR("\n\n    | Multi mode ringdown non-precessing model.\n    | References: https://arxiv.org/abs/1207.0399, https://arxiv.org/abs/1406.3201\n    | M_tot is the initial total mass of the binary, m_i the single mass, chi_i the single spin.\n    | In this model t=0 corresponds to 20M after the merger.\n    |\n    | Input parameters:\n    | t0         : start time of the analysis (s).\n    | t_ref      : reference time of the ringdown, i.e. the time at which amplitudes and phases are defined. h(t=t_ref) = sum_{lm} A_{lm} e^{i phi_{lm}} sY_{lm}(theta,phi)\n    | Mf         : final mass in solar masses\n    | af         : dimensionless final spin\n    | eta        : symmetric mass ratio of the progenitors\n    | chi_eff    : symmetric spin of the progenitors (defined as: 1/2*(sqrt(1-4*nu) chi1 + (m1*chi1 - m2*chi2)/(m1+m2)))\n    | r          : distance in Mpc\n    | iota       : inclination in radians\n    | phi        : azimuthal angle in radians\n    | TGR_params : additional non-GR parameters to be sampled\n    |\n    | Optional parameters:\n    | single_l, single_n : select a specific mode\n    | single_mode        : flag to request only a specific mode\n\n  "), /*tp_doc*/
  __pyx_tp_traverse_6pyRing_8waveform_KHS_2012, /*tp_traverse*/
  __pyx_tp_clear_6pyRing_8waveform_KHS_2012, /*tp_clear*/
  0, /*tp_richcompare*/
  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
  0, /*tp_iternext*/
  __pyx_methods_6pyRing_8waveform_KHS_2012, /*tp_methods*/
  0, /*tp_members*/
  __pyx_getsets_6pyRing_8waveform_KHS_2012, /*tp_getset*/
  0, /*tp_base*/
  0, /*tp_dict*/
  0, /*tp_descr_get*/
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  #if !CYTHON_USE_TYPE_SPECS
  0, /*tp_dictoffset*/
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  0, /*tp_init*/
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  __pyx_tp_new_6pyRing_8waveform_KHS_2012, /*tp_new*/
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  #if CYTHON_USE_TP_FINALIZE
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  0, /*tp_vectorcall*/
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  0, /*tp_print*/
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  0, /*tp_watched*/
  #endif
  #if PY_VERSION_HEX >= 0x030d00A4
  0, /*tp_versions_used*/
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  #if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX >= 0x03090000 && PY_VERSION_HEX < 0x030a0000
  0, /*tp_pypy_flags*/
  #endif
};
#endif
static struct __pyx_vtabstruct_6pyRing_8waveform_TEOBPM __pyx_vtable_6pyRing_8waveform_TEOBPM;

static PyObject *__pyx_tp_new_6pyRing_8waveform_TEOBPM(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_6pyRing_8waveform_TEOBPM *p;
  PyObject *o;
  #if CYTHON_COMPILING_IN_LIMITED_API
  allocfunc alloc_func = (allocfunc)PyType_GetSlot(t, Py_tp_alloc);
  o = alloc_func(t, 0);
  #else
  if (likely(!__Pyx_PyType_HasFeature(t, Py_TPFLAGS_IS_ABSTRACT))) {
    o = (*t->tp_alloc)(t, 0);
  } else {
    o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_mstate_global->__pyx_empty_tuple, 0);
  }
  if (unlikely(!o)) return 0;
  #endif
  p = ((struct __pyx_obj_6pyRing_8waveform_TEOBPM *)o);
  p->__pyx_vtab = __pyx_vtabptr_6pyRing_8waveform_TEOBPM;
  p->phases = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->modes = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->TGR_params = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->NR_fit_coeffs = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->multipoles = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->fit_coefficients = ((PyObject*)Py_None); Py_INCREF(Py_None);
  if (unlikely(__pyx_pw_6pyRing_8waveform_6TEOBPM_1__cinit__(o, a, k) < 0)) goto bad;
  return o;
  bad:
  Py_DECREF(o); o = 0;
  return NULL;
}

static void __pyx_tp_dealloc_6pyRing_8waveform_TEOBPM(PyObject *o) {
  struct __pyx_obj_6pyRing_8waveform_TEOBPM *p = (struct __pyx_obj_6pyRing_8waveform_TEOBPM *)o;
  #if CYTHON_USE_TP_FINALIZE
  if (unlikely((PY_VERSION_HEX >= 0x03080000 || __Pyx_PyType_HasFeature(Py_TYPE(o), Py_TPFLAGS_HAVE_FINALIZE)) && __Pyx_PyObject_GetSlot(o, tp_finalize, destructor)) && !__Pyx_PyObject_GC_IsFinalized(o)) {
    if (__Pyx_PyObject_GetSlot(o, tp_dealloc, destructor) == __pyx_tp_dealloc_6pyRing_8waveform_TEOBPM) {
      if (PyObject_CallFinalizerFromDealloc(o)) return;
    }
  }
  #endif
  PyObject_GC_UnTrack(o);
  Py_CLEAR(p->phases);
  Py_CLEAR(p->modes);
  Py_CLEAR(p->TGR_params);
  Py_CLEAR(p->NR_fit_coeffs);
  Py_CLEAR(p->multipoles);
  Py_CLEAR(p->fit_coefficients);
  #if CYTHON_USE_TYPE_SLOTS
  (*Py_TYPE(o)->tp_free)(o);
  #else
  {
    freefunc tp_free = (freefunc)PyType_GetSlot(Py_TYPE(o), Py_tp_free);
    if (tp_free) tp_free(o);
  }
  #endif
}

static int __pyx_tp_traverse_6pyRing_8waveform_TEOBPM(PyObject *o, visitproc v, void *a) {
  int e;
  struct __pyx_obj_6pyRing_8waveform_TEOBPM *p = (struct __pyx_obj_6pyRing_8waveform_TEOBPM *)o;
  {
    e = __Pyx_call_type_traverse(o, 1, v, a);
    if (e) return e;
  }
  if (p->phases) {
    e = (*v)(p->phases, a); if (e) return e;
  }
  if (p->modes) {
    e = (*v)(p->modes, a); if (e) return e;
  }
  if (p->TGR_params) {
    e = (*v)(p->TGR_params, a); if (e) return e;
  }
  if (p->NR_fit_coeffs) {
    e = (*v)(p->NR_fit_coeffs, a); if (e) return e;
  }
  if (p->multipoles) {
    e = (*v)(p->multipoles, a); if (e) return e;
  }
  if (p->fit_coefficients) {
    e = (*v)(p->fit_coefficients, a); if (e) return e;
  }
  return 0;
}

static int __pyx_tp_clear_6pyRing_8waveform_TEOBPM(PyObject *o) {
  PyObject* tmp;
  struct __pyx_obj_6pyRing_8waveform_TEOBPM *p = (struct __pyx_obj_6pyRing_8waveform_TEOBPM *)o;
  tmp = ((PyObject*)p->phases);
  p->phases = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->modes);
  p->modes = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->TGR_params);
  p->TGR_params = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->NR_fit_coeffs);
  p->NR_fit_coeffs = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->multipoles);
  p->multipoles = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->fit_coefficients);
  p->fit_coefficients = ((PyObject*)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  return 0;
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6TEOBPM_t0(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6TEOBPM_2t0_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6TEOBPM_t0(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_2t0_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6TEOBPM_m1(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6TEOBPM_2m1_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6TEOBPM_m1(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_2m1_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6TEOBPM_m2(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6TEOBPM_2m2_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6TEOBPM_m2(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_2m2_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6TEOBPM_chi1(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6TEOBPM_4chi1_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6TEOBPM_chi1(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_4chi1_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6TEOBPM_chi2(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6TEOBPM_4chi2_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6TEOBPM_chi2(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_4chi2_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6TEOBPM_phases(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6TEOBPM_6phases_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6TEOBPM_phases(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_6phases_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_6phases_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6TEOBPM_M(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6TEOBPM_1M_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6TEOBPM_M(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_1M_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6TEOBPM_r(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6TEOBPM_1r_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6TEOBPM_r(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_1r_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6TEOBPM_iota(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6TEOBPM_4iota_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6TEOBPM_iota(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_4iota_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6TEOBPM_phi(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6TEOBPM_3phi_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6TEOBPM_phi(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_3phi_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6TEOBPM_modes(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6TEOBPM_5modes_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6TEOBPM_modes(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_5modes_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_5modes_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6TEOBPM_full_modes(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6TEOBPM_10full_modes_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6TEOBPM_full_modes(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_10full_modes_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6TEOBPM_TGR_params(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6TEOBPM_10TGR_params_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6TEOBPM_TGR_params(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_10TGR_params_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_10TGR_params_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6TEOBPM_geom(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6TEOBPM_4geom_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6TEOBPM_geom(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_4geom_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6TEOBPM_NR_fit_coeffs(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6TEOBPM_13NR_fit_coeffs_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6TEOBPM_NR_fit_coeffs(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_13NR_fit_coeffs_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_13NR_fit_coeffs_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6TEOBPM_multipoles(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6TEOBPM_10multipoles_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6TEOBPM_multipoles(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_10multipoles_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_10multipoles_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6TEOBPM_fit_coefficients(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6TEOBPM_16fit_coefficients_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6TEOBPM_fit_coefficients(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_16fit_coefficients_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_16fit_coefficients_5__del__(o);
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6TEOBPM_nu(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6TEOBPM_2nu_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6TEOBPM_nu(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_2nu_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6TEOBPM_X1(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6TEOBPM_2X1_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6TEOBPM_X1(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_2X1_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6TEOBPM_X2(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6TEOBPM_2X2_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6TEOBPM_X2(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_2X2_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6TEOBPM_X12(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6TEOBPM_3X12_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6TEOBPM_X12(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_3X12_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6TEOBPM_a0(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6TEOBPM_2a0_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6TEOBPM_a0(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_2a0_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6TEOBPM_a12(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6TEOBPM_3a12_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6TEOBPM_a12(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_3a12_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6TEOBPM_Shat(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6TEOBPM_4Shat_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6TEOBPM_Shat(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_4Shat_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6TEOBPM_Sbar(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6TEOBPM_4Sbar_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6TEOBPM_Sbar(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_4Sbar_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6TEOBPM_Mf(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6TEOBPM_2Mf_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6TEOBPM_Mf(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_2Mf_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6TEOBPM_af(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6TEOBPM_2af_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6TEOBPM_af(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6TEOBPM_2af_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyMethodDef __pyx_methods_6pyRing_8waveform_TEOBPM[] = {
  {"EOBPM_SetupFitCoefficients", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6TEOBPM_3EOBPM_SetupFitCoefficients, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6TEOBPM_2EOBPM_SetupFitCoefficients},
  {"TEOBPM_Amplitude", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6TEOBPM_5TEOBPM_Amplitude, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6TEOBPM_4TEOBPM_Amplitude},
  {"TEOBPM_Phase", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6TEOBPM_7TEOBPM_Phase, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6TEOBPM_6TEOBPM_Phase},
  {"waveform", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6TEOBPM_9waveform, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6TEOBPM_8waveform},
  {"sym_mass_ratio", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6TEOBPM_11sym_mass_ratio, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6TEOBPM_10sym_mass_ratio},
  {"X_1", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6TEOBPM_13X_1, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6TEOBPM_12X_1},
  {"X_2", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6TEOBPM_15X_2, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6TEOBPM_14X_2},
  {"X_12", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6TEOBPM_17X_12, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6TEOBPM_16X_12},
  {"a_0", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6TEOBPM_19a_0, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6TEOBPM_18a_0},
  {"a_12", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6TEOBPM_21a_12, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6TEOBPM_20a_12},
  {"S_hat", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6TEOBPM_23S_hat, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6TEOBPM_22S_hat},
  {"S_bar", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6TEOBPM_25S_bar, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6TEOBPM_24S_bar},
  {"alpha1", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6TEOBPM_27alpha1, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6TEOBPM_26alpha1},
  {"alpha21", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6TEOBPM_29alpha21, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6TEOBPM_28alpha21},
  {"omega1", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6TEOBPM_31omega1, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6TEOBPM_30omega1},
  {"c3_A", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6TEOBPM_33c3_A, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6TEOBPM_32c3_A},
  {"c3_phi", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6TEOBPM_35c3_phi, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6TEOBPM_34c3_phi},
  {"c4_phi", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6TEOBPM_37c4_phi, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6TEOBPM_36c4_phi},
  {"dOmega", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6TEOBPM_39dOmega, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6TEOBPM_38dOmega},
  {"amplitude_peak", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6TEOBPM_41amplitude_peak, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6TEOBPM_40amplitude_peak},
  {"omega_peak", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6TEOBPM_43omega_peak, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6TEOBPM_42omega_peak},
  {"JimenezFortezaRemnantMass", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6TEOBPM_45JimenezFortezaRemnantMass, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6TEOBPM_44JimenezFortezaRemnantMass},
  {"JimenezFortezaRemnantSpin", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6TEOBPM_47JimenezFortezaRemnantSpin, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6TEOBPM_46JimenezFortezaRemnantSpin},
  {"DeltaT", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6TEOBPM_49DeltaT, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6TEOBPM_48DeltaT},
  {"DeltaPhi", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6TEOBPM_51DeltaPhi, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6TEOBPM_50DeltaPhi},
  {"__reduce_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6TEOBPM_53__reduce_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6TEOBPM_52__reduce_cython__},
  {"__setstate_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6TEOBPM_55__setstate_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6TEOBPM_54__setstate_cython__},
  {0, 0, 0, 0}
};

static struct PyGetSetDef __pyx_getsets_6pyRing_8waveform_TEOBPM[] = {
  {"t0", __pyx_getprop_6pyRing_8waveform_6TEOBPM_t0, __pyx_setprop_6pyRing_8waveform_6TEOBPM_t0, PyDoc_STR("t0: 'double'"), 0},
  {"m1", __pyx_getprop_6pyRing_8waveform_6TEOBPM_m1, __pyx_setprop_6pyRing_8waveform_6TEOBPM_m1, PyDoc_STR("m1: 'double'"), 0},
  {"m2", __pyx_getprop_6pyRing_8waveform_6TEOBPM_m2, __pyx_setprop_6pyRing_8waveform_6TEOBPM_m2, PyDoc_STR("m2: 'double'"), 0},
  {"chi1", __pyx_getprop_6pyRing_8waveform_6TEOBPM_chi1, __pyx_setprop_6pyRing_8waveform_6TEOBPM_chi1, PyDoc_STR("chi1: 'double'"), 0},
  {"chi2", __pyx_getprop_6pyRing_8waveform_6TEOBPM_chi2, __pyx_setprop_6pyRing_8waveform_6TEOBPM_chi2, PyDoc_STR("chi2: 'double'"), 0},
  {"phases", __pyx_getprop_6pyRing_8waveform_6TEOBPM_phases, __pyx_setprop_6pyRing_8waveform_6TEOBPM_phases, PyDoc_STR("phases: dict"), 0},
  {"M", __pyx_getprop_6pyRing_8waveform_6TEOBPM_M, __pyx_setprop_6pyRing_8waveform_6TEOBPM_M, PyDoc_STR("M: 'double'"), 0},
  {"r", __pyx_getprop_6pyRing_8waveform_6TEOBPM_r, __pyx_setprop_6pyRing_8waveform_6TEOBPM_r, PyDoc_STR("r: 'double'"), 0},
  {"iota", __pyx_getprop_6pyRing_8waveform_6TEOBPM_iota, __pyx_setprop_6pyRing_8waveform_6TEOBPM_iota, PyDoc_STR("iota: 'double'"), 0},
  {"phi", __pyx_getprop_6pyRing_8waveform_6TEOBPM_phi, __pyx_setprop_6pyRing_8waveform_6TEOBPM_phi, PyDoc_STR("phi: 'double'"), 0},
  {"modes", __pyx_getprop_6pyRing_8waveform_6TEOBPM_modes, __pyx_setprop_6pyRing_8waveform_6TEOBPM_modes, PyDoc_STR("modes: list"), 0},
  {"full_modes", __pyx_getprop_6pyRing_8waveform_6TEOBPM_full_modes, __pyx_setprop_6pyRing_8waveform_6TEOBPM_full_modes, PyDoc_STR("full_modes: 'unsigned int'"), 0},
  {"TGR_params", __pyx_getprop_6pyRing_8waveform_6TEOBPM_TGR_params, __pyx_setprop_6pyRing_8waveform_6TEOBPM_TGR_params, PyDoc_STR("TGR_params: dict"), 0},
  {"geom", __pyx_getprop_6pyRing_8waveform_6TEOBPM_geom, __pyx_setprop_6pyRing_8waveform_6TEOBPM_geom, PyDoc_STR("geom: 'unsigned int'"), 0},
  {"NR_fit_coeffs", __pyx_getprop_6pyRing_8waveform_6TEOBPM_NR_fit_coeffs, __pyx_setprop_6pyRing_8waveform_6TEOBPM_NR_fit_coeffs, PyDoc_STR("NR_fit_coeffs: dict"), 0},
  {"multipoles", __pyx_getprop_6pyRing_8waveform_6TEOBPM_multipoles, __pyx_setprop_6pyRing_8waveform_6TEOBPM_multipoles, PyDoc_STR("multipoles: list"), 0},
  {"fit_coefficients", __pyx_getprop_6pyRing_8waveform_6TEOBPM_fit_coefficients, __pyx_setprop_6pyRing_8waveform_6TEOBPM_fit_coefficients, PyDoc_STR("fit_coefficients: dict"), 0},
  {"nu", __pyx_getprop_6pyRing_8waveform_6TEOBPM_nu, __pyx_setprop_6pyRing_8waveform_6TEOBPM_nu, PyDoc_STR("nu: 'double'"), 0},
  {"X1", __pyx_getprop_6pyRing_8waveform_6TEOBPM_X1, __pyx_setprop_6pyRing_8waveform_6TEOBPM_X1, PyDoc_STR("X1: 'double'"), 0},
  {"X2", __pyx_getprop_6pyRing_8waveform_6TEOBPM_X2, __pyx_setprop_6pyRing_8waveform_6TEOBPM_X2, PyDoc_STR("X2: 'double'"), 0},
  {"X12", __pyx_getprop_6pyRing_8waveform_6TEOBPM_X12, __pyx_setprop_6pyRing_8waveform_6TEOBPM_X12, PyDoc_STR("X12: 'double'"), 0},
  {"a0", __pyx_getprop_6pyRing_8waveform_6TEOBPM_a0, __pyx_setprop_6pyRing_8waveform_6TEOBPM_a0, PyDoc_STR("a0: 'double'"), 0},
  {"a12", __pyx_getprop_6pyRing_8waveform_6TEOBPM_a12, __pyx_setprop_6pyRing_8waveform_6TEOBPM_a12, PyDoc_STR("a12: 'double'"), 0},
  {"Shat", __pyx_getprop_6pyRing_8waveform_6TEOBPM_Shat, __pyx_setprop_6pyRing_8waveform_6TEOBPM_Shat, PyDoc_STR("Shat: 'double'"), 0},
  {"Sbar", __pyx_getprop_6pyRing_8waveform_6TEOBPM_Sbar, __pyx_setprop_6pyRing_8waveform_6TEOBPM_Sbar, PyDoc_STR("Sbar: 'double'"), 0},
  {"Mf", __pyx_getprop_6pyRing_8waveform_6TEOBPM_Mf, __pyx_setprop_6pyRing_8waveform_6TEOBPM_Mf, PyDoc_STR("Mf: 'double'"), 0},
  {"af", __pyx_getprop_6pyRing_8waveform_6TEOBPM_af, __pyx_setprop_6pyRing_8waveform_6TEOBPM_af, PyDoc_STR("af: 'double'"), 0},
  {0, 0, 0, 0, 0}
};
#if CYTHON_USE_TYPE_SPECS
static PyType_Slot __pyx_type_6pyRing_8waveform_TEOBPM_slots[] = {
  {Py_tp_dealloc, (void *)__pyx_tp_dealloc_6pyRing_8waveform_TEOBPM},
  {Py_tp_doc, (void *)PyDoc_STR("\n    | Post-merger EOB model\n    | References: arxiv.1406.0401, arXiv:1606.03952, arXiv:2001.09082.\n    | C implementation available here: https://bitbucket.org/eob_ihes/teobresums/src/master/C/src/\n    |\n    | Input parameters:\n    | t0            : start time of the analysis, and reference time for NR-calibrated quantities (s)\n    | m1            : heavier BH mass (solar masses)\n    | m2            : lighter BH mass (solar masses)\n    | chi1          : heavier BH spin (adimensional)\n    | chi2          : lighter BH spin (adimensional)\n    | phases        : phases of modes at peak (rad)\n    | r             : distance (Mpc)\n    | iota          : inclination (rad)\n    | phi           : azimuthal angle (rad)\n    | modes         : list of modes to be used [(l,m)]\n    | TGR_params    : Additional non-GR parameters to be sampled.\n    |\n    | Optional parameters:\n    | geom          : Flag to compute only the h_{l,m} modes, without spherical harmonics.\n    | NR_fit_coeffs : Dictionary containing NR-calibrated quantities and fit coefficients for the model. If not None, overwrites the default values. Structure: dict{'Mf':, 'af':, (l,m): {'omg_peak':,'A_peak_over_nu':, 'c3A':, 'c3p':, 'c4p':}}. Default: None.\n    ")},
  {Py_tp_traverse, (void *)__pyx_tp_traverse_6pyRing_8waveform_TEOBPM},
  {Py_tp_clear, (void *)__pyx_tp_clear_6pyRing_8waveform_TEOBPM},
  {Py_tp_methods, (void *)__pyx_methods_6pyRing_8waveform_TEOBPM},
  {Py_tp_getset, (void *)__pyx_getsets_6pyRing_8waveform_TEOBPM},
  {Py_tp_new, (void *)__pyx_tp_new_6pyRing_8waveform_TEOBPM},
  {0, 0},
};
static PyType_Spec __pyx_type_6pyRing_8waveform_TEOBPM_spec = {
  "pyRing.waveform.TEOBPM",
  sizeof(struct __pyx_obj_6pyRing_8waveform_TEOBPM),
  0,
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC,
  __pyx_type_6pyRing_8waveform_TEOBPM_slots,
};
#else

static PyTypeObject __pyx_type_6pyRing_8waveform_TEOBPM = {
  PyVarObject_HEAD_INIT(0, 0)
  "pyRing.waveform.""TEOBPM", /*tp_name*/
  sizeof(struct __pyx_obj_6pyRing_8waveform_TEOBPM), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc_6pyRing_8waveform_TEOBPM, /*tp_dealloc*/
  #if PY_VERSION_HEX < 0x030800b4
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b4
  0, /*tp_vectorcall_offset*/
  #endif
  0, /*tp_getattr*/
  0, /*tp_setattr*/
  0, /*tp_as_async*/
  0, /*tp_repr*/
  0, /*tp_as_number*/
  0, /*tp_as_sequence*/
  0, /*tp_as_mapping*/
  0, /*tp_hash*/
  0, /*tp_call*/
  0, /*tp_str*/
  0, /*tp_getattro*/
  0, /*tp_setattro*/
  0, /*tp_as_buffer*/
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC, /*tp_flags*/
  PyDoc_STR("\n    | Post-merger EOB model\n    | References: arxiv.1406.0401, arXiv:1606.03952, arXiv:2001.09082.\n    | C implementation available here: https://bitbucket.org/eob_ihes/teobresums/src/master/C/src/\n    |\n    | Input parameters:\n    | t0            : start time of the analysis, and reference time for NR-calibrated quantities (s)\n    | m1            : heavier BH mass (solar masses)\n    | m2            : lighter BH mass (solar masses)\n    | chi1          : heavier BH spin (adimensional)\n    | chi2          : lighter BH spin (adimensional)\n    | phases        : phases of modes at peak (rad)\n    | r             : distance (Mpc)\n    | iota          : inclination (rad)\n    | phi           : azimuthal angle (rad)\n    | modes         : list of modes to be used [(l,m)]\n    | TGR_params    : Additional non-GR parameters to be sampled.\n    |\n    | Optional parameters:\n    | geom          : Flag to compute only the h_{l,m} modes, without spherical harmonics.\n    | NR_fit_coeffs : Dictionary containing NR-calibrated quantities and fit coefficients for the model. If not None, overwrites the default values. Structure: dict{'Mf':, 'af':, (l,m): {'omg_peak':,'A_peak_over_nu':, 'c3A':, 'c3p':, 'c4p':}}. Default: None.\n    "), /*tp_doc*/
  __pyx_tp_traverse_6pyRing_8waveform_TEOBPM, /*tp_traverse*/
  __pyx_tp_clear_6pyRing_8waveform_TEOBPM, /*tp_clear*/
  0, /*tp_richcompare*/
  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
  0, /*tp_iternext*/
  __pyx_methods_6pyRing_8waveform_TEOBPM, /*tp_methods*/
  0, /*tp_members*/
  __pyx_getsets_6pyRing_8waveform_TEOBPM, /*tp_getset*/
  0, /*tp_base*/
  0, /*tp_dict*/
  0, /*tp_descr_get*/
  0, /*tp_descr_set*/
  #if !CYTHON_USE_TYPE_SPECS
  0, /*tp_dictoffset*/
  #endif
  0, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_6pyRing_8waveform_TEOBPM, /*tp_new*/
  0, /*tp_free*/
  0, /*tp_is_gc*/
  0, /*tp_bases*/
  0, /*tp_mro*/
  0, /*tp_cache*/
  0, /*tp_subclasses*/
  0, /*tp_weaklist*/
  0, /*tp_del*/
  0, /*tp_version_tag*/
  #if CYTHON_USE_TP_FINALIZE
  0, /*tp_finalize*/
  #else
  NULL, /*tp_finalize*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b1 && (!CYTHON_COMPILING_IN_PYPY || PYPY_VERSION_NUM >= 0x07030800)
  0, /*tp_vectorcall*/
  #endif
  #if __PYX_NEED_TP_PRINT_SLOT == 1
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030C0000
  0, /*tp_watched*/
  #endif
  #if PY_VERSION_HEX >= 0x030d00A4
  0, /*tp_versions_used*/
  #endif
  #if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX >= 0x03090000 && PY_VERSION_HEX < 0x030a0000
  0, /*tp_pypy_flags*/
  #endif
};
#endif
static struct __pyx_vtabstruct_6pyRing_8waveform_IMR_WF __pyx_vtable_6pyRing_8waveform_IMR_WF;

static PyObject *__pyx_tp_new_6pyRing_8waveform_IMR_WF(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_6pyRing_8waveform_IMR_WF *p;
  PyObject *o;
  #if CYTHON_COMPILING_IN_LIMITED_API
  allocfunc alloc_func = (allocfunc)PyType_GetSlot(t, Py_tp_alloc);
  o = alloc_func(t, 0);
  #else
  if (likely(!__Pyx_PyType_HasFeature(t, Py_TPFLAGS_IS_ABSTRACT))) {
    o = (*t->tp_alloc)(t, 0);
  } else {
    o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_mstate_global->__pyx_empty_tuple, 0);
  }
  if (unlikely(!o)) return 0;
  #endif
  p = ((struct __pyx_obj_6pyRing_8waveform_IMR_WF *)o);
  p->__pyx_vtab = __pyx_vtabptr_6pyRing_8waveform_IMR_WF;
  if (unlikely(__pyx_pw_6pyRing_8waveform_6IMR_WF_1__cinit__(o, a, k) < 0)) goto bad;
  return o;
  bad:
  Py_DECREF(o); o = 0;
  return NULL;
}

static void __pyx_tp_dealloc_6pyRing_8waveform_IMR_WF(PyObject *o) {
  #if CYTHON_USE_TP_FINALIZE
  if (unlikely((PY_VERSION_HEX >= 0x03080000 || __Pyx_PyType_HasFeature(Py_TYPE(o), Py_TPFLAGS_HAVE_FINALIZE)) && __Pyx_PyObject_GetSlot(o, tp_finalize, destructor)) && (!PyType_IS_GC(Py_TYPE(o)) || !__Pyx_PyObject_GC_IsFinalized(o))) {
    if (__Pyx_PyObject_GetSlot(o, tp_dealloc, destructor) == __pyx_tp_dealloc_6pyRing_8waveform_IMR_WF) {
      if (PyObject_CallFinalizerFromDealloc(o)) return;
    }
  }
  #endif
  #if CYTHON_USE_TYPE_SLOTS
  (*Py_TYPE(o)->tp_free)(o);
  #else
  {
    freefunc tp_free = (freefunc)PyType_GetSlot(Py_TYPE(o), Py_tp_free);
    if (tp_free) tp_free(o);
  }
  #endif
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6IMR_WF_m1(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6IMR_WF_2m1_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6IMR_WF_m1(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6IMR_WF_2m1_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6IMR_WF_m2(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6IMR_WF_2m2_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6IMR_WF_m2(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6IMR_WF_2m2_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6IMR_WF_s1z(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6IMR_WF_3s1z_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6IMR_WF_s1z(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6IMR_WF_3s1z_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6IMR_WF_s2z(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6IMR_WF_3s2z_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6IMR_WF_s2z(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6IMR_WF_3s2z_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6IMR_WF_dist(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6IMR_WF_4dist_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6IMR_WF_dist(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6IMR_WF_4dist_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6IMR_WF_cosiota(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6IMR_WF_7cosiota_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6IMR_WF_cosiota(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6IMR_WF_7cosiota_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6IMR_WF_phi(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6IMR_WF_3phi_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6IMR_WF_phi(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6IMR_WF_3phi_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6IMR_WF_t0(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6IMR_WF_2t0_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6IMR_WF_t0(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6IMR_WF_2t0_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6IMR_WF_dt(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6IMR_WF_2dt_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6IMR_WF_dt(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6IMR_WF_2dt_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6IMR_WF_starttime(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6IMR_WF_9starttime_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6IMR_WF_starttime(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6IMR_WF_9starttime_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pyRing_8waveform_6IMR_WF_signal_seglen(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pyRing_8waveform_6IMR_WF_13signal_seglen_1__get__(o);
}

static int __pyx_setprop_6pyRing_8waveform_6IMR_WF_signal_seglen(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pyRing_8waveform_6IMR_WF_13signal_seglen_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyMethodDef __pyx_methods_6pyRing_8waveform_IMR_WF[] = {
  {"__reduce_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6IMR_WF_5__reduce_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6IMR_WF_4__reduce_cython__},
  {"__setstate_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_6pyRing_8waveform_6IMR_WF_7__setstate_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, __pyx_doc_6pyRing_8waveform_6IMR_WF_6__setstate_cython__},
  {0, 0, 0, 0}
};

static struct PyGetSetDef __pyx_getsets_6pyRing_8waveform_IMR_WF[] = {
  {"m1", __pyx_getprop_6pyRing_8waveform_6IMR_WF_m1, __pyx_setprop_6pyRing_8waveform_6IMR_WF_m1, PyDoc_STR("m1: 'double'"), 0},
  {"m2", __pyx_getprop_6pyRing_8waveform_6IMR_WF_m2, __pyx_setprop_6pyRing_8waveform_6IMR_WF_m2, PyDoc_STR("m2: 'double'"), 0},
  {"s1z", __pyx_getprop_6pyRing_8waveform_6IMR_WF_s1z, __pyx_setprop_6pyRing_8waveform_6IMR_WF_s1z, PyDoc_STR("s1z: 'double'"), 0},
  {"s2z", __pyx_getprop_6pyRing_8waveform_6IMR_WF_s2z, __pyx_setprop_6pyRing_8waveform_6IMR_WF_s2z, PyDoc_STR("s2z: 'double'"), 0},
  {"dist", __pyx_getprop_6pyRing_8waveform_6IMR_WF_dist, __pyx_setprop_6pyRing_8waveform_6IMR_WF_dist, PyDoc_STR("dist: 'double'"), 0},
  {"cosiota", __pyx_getprop_6pyRing_8waveform_6IMR_WF_cosiota, __pyx_setprop_6pyRing_8waveform_6IMR_WF_cosiota, PyDoc_STR("cosiota: 'double'"), 0},
  {"phi", __pyx_getprop_6pyRing_8waveform_6IMR_WF_phi, __pyx_setprop_6pyRing_8waveform_6IMR_WF_phi, PyDoc_STR("phi: 'double'"), 0},
  {"t0", __pyx_getprop_6pyRing_8waveform_6IMR_WF_t0, __pyx_setprop_6pyRing_8waveform_6IMR_WF_t0, PyDoc_STR("t0: 'double'"), 0},
  {"dt", __pyx_getprop_6pyRing_8waveform_6IMR_WF_dt, __pyx_setprop_6pyRing_8waveform_6IMR_WF_dt, PyDoc_STR("dt: 'double'"), 0},
  {"starttime", __pyx_getprop_6pyRing_8waveform_6IMR_WF_starttime, __pyx_setprop_6pyRing_8waveform_6IMR_WF_starttime, PyDoc_STR("starttime: 'double'"), 0},
  {"signal_seglen", __pyx_getprop_6pyRing_8waveform_6IMR_WF_signal_seglen, __pyx_setprop_6pyRing_8waveform_6IMR_WF_signal_seglen, PyDoc_STR("signal_seglen: 'double'"), 0},
  {0, 0, 0, 0, 0}
};
#if CYTHON_USE_TYPE_SPECS
static PyType_Slot __pyx_type_6pyRing_8waveform_IMR_WF_slots[] = {
  {Py_tp_dealloc, (void *)__pyx_tp_dealloc_6pyRing_8waveform_IMR_WF},
  {Py_tp_doc, (void *)PyDoc_STR("\n    Call an IMR waveform from LAL\n  ")},
  {Py_tp_methods, (void *)__pyx_methods_6pyRing_8waveform_IMR_WF},
  {Py_tp_getset, (void *)__pyx_getsets_6pyRing_8waveform_IMR_WF},
  {Py_tp_new, (void *)__pyx_tp_new_6pyRing_8waveform_IMR_WF},
  {0, 0},
};
static PyType_Spec __pyx_type_6pyRing_8waveform_IMR_WF_spec = {
  "pyRing.waveform.IMR_WF",
  sizeof(struct __pyx_obj_6pyRing_8waveform_IMR_WF),
  0,
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE,
  __pyx_type_6pyRing_8waveform_IMR_WF_slots,
};
#else

static PyTypeObject __pyx_type_6pyRing_8waveform_IMR_WF = {
  PyVarObject_HEAD_INIT(0, 0)
  "pyRing.waveform.""IMR_WF", /*tp_name*/
  sizeof(struct __pyx_obj_6pyRing_8waveform_IMR_WF), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc_6pyRing_8waveform_IMR_WF, /*tp_dealloc*/
  #if PY_VERSION_HEX < 0x030800b4
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b4
  0, /*tp_vectorcall_offset*/
  #endif
  0, /*tp_getattr*/
  0, /*tp_setattr*/
  0, /*tp_as_async*/
  0, /*tp_repr*/
  0, /*tp_as_number*/
  0, /*tp_as_sequence*/
  0, /*tp_as_mapping*/
  0, /*tp_hash*/
  0, /*tp_call*/
  0, /*tp_str*/
  0, /*tp_getattro*/
  0, /*tp_setattro*/
  0, /*tp_as_buffer*/
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE, /*tp_flags*/
  PyDoc_STR("\n    Call an IMR waveform from LAL\n  "), /*tp_doc*/
  0, /*tp_traverse*/
  0, /*tp_clear*/
  0, /*tp_richcompare*/
  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
  0, /*tp_iternext*/
  __pyx_methods_6pyRing_8waveform_IMR_WF, /*tp_methods*/
  0, /*tp_members*/
  __pyx_getsets_6pyRing_8waveform_IMR_WF, /*tp_getset*/
  0, /*tp_base*/
  0, /*tp_dict*/
  0, /*tp_descr_get*/
  0, /*tp_descr_set*/
  #if !CYTHON_USE_TYPE_SPECS
  0, /*tp_dictoffset*/
  #endif
  0, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_6pyRing_8waveform_IMR_WF, /*tp_new*/
  0, /*tp_free*/
  0, /*tp_is_gc*/
  0, /*tp_bases*/
  0, /*tp_mro*/
  0, /*tp_cache*/
  0, /*tp_subclasses*/
  0, /*tp_weaklist*/
  0, /*tp_del*/
  0, /*tp_version_tag*/
  #if CYTHON_USE_TP_FINALIZE
  0, /*tp_finalize*/
  #else
  NULL, /*tp_finalize*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b1 && (!CYTHON_COMPILING_IN_PYPY || PYPY_VERSION_NUM >= 0x07030800)
  0, /*tp_vectorcall*/
  #endif
  #if __PYX_NEED_TP_PRINT_SLOT == 1
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030C0000
  0, /*tp_watched*/
  #endif
  #if PY_VERSION_HEX >= 0x030d00A4
  0, /*tp_versions_used*/
  #endif
  #if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX >= 0x03090000 && PY_VERSION_HEX < 0x030a0000
  0, /*tp_pypy_flags*/
  #endif
};
#endif
static struct __pyx_vtabstruct_array __pyx_vtable_array;

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  PyObject *o;
  #if CYTHON_COMPILING_IN_LIMITED_API
  allocfunc alloc_func = (allocfunc)PyType_GetSlot(t, Py_tp_alloc);
  o = alloc_func(t, 0);
  #else
  if (likely(!__Pyx_PyType_HasFeature(t, Py_TPFLAGS_IS_ABSTRACT))) {
    o = (*t->tp_alloc)(t, 0);
  } else {
    o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_mstate_global->__pyx_empty_tuple, 0);
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  if (unlikely(!o)) return 0;
  #endif
  p = ((struct __pyx_array_obj *)o);
  p->__pyx_vtab = __pyx_vtabptr_array;
  p->mode = ((PyObject*)Py_None); Py_INCREF(Py_None);
  p->_format = ((PyObject*)Py_None); Py_INCREF(Py_None);
  if (unlikely(__pyx_array___cinit__(o, a, k) < 0)) goto bad;
  return o;
  bad:
  Py_DECREF(o); o = 0;
  return NULL;
}

static void __pyx_tp_dealloc_array(PyObject *o) {
  struct __pyx_array_obj *p = (struct __pyx_array_obj *)o;
  #if CYTHON_USE_TP_FINALIZE
  if (unlikely((PY_VERSION_HEX >= 0x03080000 || __Pyx_PyType_HasFeature(Py_TYPE(o), Py_TPFLAGS_HAVE_FINALIZE)) && __Pyx_PyObject_GetSlot(o, tp_finalize, destructor)) && (!PyType_IS_GC(Py_TYPE(o)) || !__Pyx_PyObject_GC_IsFinalized(o))) {
    if (__Pyx_PyObject_GetSlot(o, tp_dealloc, destructor) == __pyx_tp_dealloc_array) {
      if (PyObject_CallFinalizerFromDealloc(o)) return;
    }
  }
  #endif
  {
    PyObject *etype, *eval, *etb;
    PyErr_Fetch(&etype, &eval, &etb);
    __Pyx_SET_REFCNT(o, Py_REFCNT(o) + 1);
    __pyx_array___dealloc__(o);
    __Pyx_SET_REFCNT(o, Py_REFCNT(o) - 1);
    PyErr_Restore(etype, eval, etb);
  }
  Py_CLEAR(p->mode);
  Py_CLEAR(p->_format);
  #if CYTHON_USE_TYPE_SLOTS
  (*Py_TYPE(o)->tp_free)(o);
  #else
  {
    freefunc tp_free = (freefunc)PyType_GetSlot(Py_TYPE(o), Py_tp_free);
    if (tp_free) tp_free(o);
  }
  #endif
}

static PyObject *__pyx_sq_item_array(PyObject *o, Py_ssize_t i) {
  PyObject *r;
  PyObject *x = PyLong_FromSsize_t(i); if(!x) return 0;
  #if CYTHON_USE_TYPE_SLOTS || (!CYTHON_USE_TYPE_SPECS && __PYX_LIMITED_VERSION_HEX < 0x030A0000)
  r = Py_TYPE(o)->tp_as_mapping->mp_subscript(o, x);
  #else
  r = ((binaryfunc)PyType_GetSlot(Py_TYPE(o), Py_mp_subscript))(o, x);
  #endif
  Py_DECREF(x);
  return r;
}

static int __pyx_mp_ass_subscript_array(PyObject *o, PyObject *i, PyObject *v) {
  if (v) {
    return __pyx_array___setitem__(o, i, v);
  }
  else {
    __Pyx_TypeName o_type_name;
    o_type_name = __Pyx_PyType_GetFullyQualifiedName(Py_TYPE(o));
    PyErr_Format(PyExc_NotImplementedError,
      "Subscript deletion not supported by " __Pyx_FMT_TYPENAME, o_type_name);
    __Pyx_DECREF_TypeName(o_type_name);
    return -1;
  }
}

static PyObject *__pyx_tp_getattro_array(PyObject *o, PyObject *n) {
  PyObject *v = PyObject_GenericGetAttr(o, n);
  if (!v && PyErr_ExceptionMatches(PyExc_AttributeError)) {
    PyErr_Clear();
    v = __pyx_array___getattr__(o, n);
  }
  return v;
}

static PyObject *__pyx_getprop___pyx_array_memview(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_15View_dot_MemoryView_5array_7memview_1__get__(o);
}

static PyMethodDef __pyx_methods_array[] = {
  {"__getattr__", (PyCFunction)__pyx_array___getattr__, METH_O|METH_COEXIST, 0},
  {"__reduce_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw___pyx_array_1__reduce_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, 0},
  {"__setstate_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw___pyx_array_3__setstate_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, 0},
  {0, 0, 0, 0}
};

static struct PyGetSetDef __pyx_getsets_array[] = {
  {"memview", __pyx_getprop___pyx_array_memview, 0, 0, 0},
  {0, 0, 0, 0, 0}
};
#if CYTHON_USE_TYPE_SPECS
#if !CYTHON_COMPILING_IN_LIMITED_API

static PyBufferProcs __pyx_tp_as_buffer_array = {
  __pyx_array_getbuffer, /*bf_getbuffer*/
  0, /*bf_releasebuffer*/
};
#endif
static PyType_Slot __pyx_type___pyx_array_slots[] = {
  {Py_tp_dealloc, (void *)__pyx_tp_dealloc_array},
  {Py_sq_length, (void *)__pyx_array___len__},
  {Py_sq_item, (void *)__pyx_sq_item_array},
  {Py_mp_length, (void *)__pyx_array___len__},
  {Py_mp_subscript, (void *)__pyx_array___getitem__},
  {Py_mp_ass_subscript, (void *)__pyx_mp_ass_subscript_array},
  {Py_tp_getattro, (void *)__pyx_tp_getattro_array},
  #if defined(Py_bf_getbuffer)
  {Py_bf_getbuffer, (void *)__pyx_array_getbuffer},
  #endif
  {Py_tp_methods, (void *)__pyx_methods_array},
  {Py_tp_getset, (void *)__pyx_getsets_array},
  {Py_tp_new, (void *)__pyx_tp_new_array},
  {0, 0},
};
static PyType_Spec __pyx_type___pyx_array_spec = {
  "pyRing.waveform.array",
  sizeof(struct __pyx_array_obj),
  0,
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_SEQUENCE,
  __pyx_type___pyx_array_slots,
};
#else

static PySequenceMethods __pyx_tp_as_sequence_array = {
  __pyx_array___len__, /*sq_length*/
  0, /*sq_concat*/
  0, /*sq_repeat*/
  __pyx_sq_item_array, /*sq_item*/
  0, /*sq_slice*/
  0, /*sq_ass_item*/
  0, /*sq_ass_slice*/
  0, /*sq_contains*/
  0, /*sq_inplace_concat*/
  0, /*sq_inplace_repeat*/
};

static PyMappingMethods __pyx_tp_as_mapping_array = {
  __pyx_array___len__, /*mp_length*/
  __pyx_array___getitem__, /*mp_subscript*/
  __pyx_mp_ass_subscript_array, /*mp_ass_subscript*/
};

static PyBufferProcs __pyx_tp_as_buffer_array = {
  __pyx_array_getbuffer, /*bf_getbuffer*/
  0, /*bf_releasebuffer*/
};

static PyTypeObject __pyx_type___pyx_array = {
  PyVarObject_HEAD_INIT(0, 0)
  "pyRing.waveform.""array", /*tp_name*/
  sizeof(struct __pyx_array_obj), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc_array, /*tp_dealloc*/
  #if PY_VERSION_HEX < 0x030800b4
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b4
  0, /*tp_vectorcall_offset*/
  #endif
  0, /*tp_getattr*/
  0, /*tp_setattr*/
  0, /*tp_as_async*/
  0, /*tp_repr*/
  0, /*tp_as_number*/
  &__pyx_tp_as_sequence_array, /*tp_as_sequence*/
  &__pyx_tp_as_mapping_array, /*tp_as_mapping*/
  0, /*tp_hash*/
  0, /*tp_call*/
  0, /*tp_str*/
  __pyx_tp_getattro_array, /*tp_getattro*/
  0, /*tp_setattro*/
  &__pyx_tp_as_buffer_array, /*tp_as_buffer*/
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_SEQUENCE, /*tp_flags*/
  0, /*tp_doc*/
  0, /*tp_traverse*/
  0, /*tp_clear*/
  0, /*tp_richcompare*/
  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
  0, /*tp_iternext*/
  __pyx_methods_array, /*tp_methods*/
  0, /*tp_members*/
  __pyx_getsets_array, /*tp_getset*/
  0, /*tp_base*/
  0, /*tp_dict*/
  0, /*tp_descr_get*/
  0, /*tp_descr_set*/
  #if !CYTHON_USE_TYPE_SPECS
  0, /*tp_dictoffset*/
  #endif
  0, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_array, /*tp_new*/
  0, /*tp_free*/
  0, /*tp_is_gc*/
  0, /*tp_bases*/
  0, /*tp_mro*/
  0, /*tp_cache*/
  0, /*tp_subclasses*/
  0, /*tp_weaklist*/
  0, /*tp_del*/
  0, /*tp_version_tag*/
  #if CYTHON_USE_TP_FINALIZE
  0, /*tp_finalize*/
  #else
  NULL, /*tp_finalize*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b1 && (!CYTHON_COMPILING_IN_PYPY || PYPY_VERSION_NUM >= 0x07030800)
  0, /*tp_vectorcall*/
  #endif
  #if __PYX_NEED_TP_PRINT_SLOT == 1
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030C0000
  0, /*tp_watched*/
  #endif
  #if PY_VERSION_HEX >= 0x030d00A4
  0, /*tp_versions_used*/
  #endif
  #if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX >= 0x03090000 && PY_VERSION_HEX < 0x030a0000
  0, /*tp_pypy_flags*/
  #endif
};
#endif

static PyObject *__pyx_tp_new_Enum(PyTypeObject *t, CYTHON_UNUSED PyObject *a, CYTHON_UNUSED PyObject *k) {
  struct __pyx_MemviewEnum_obj *p;
  PyObject *o;
  #if CYTHON_COMPILING_IN_LIMITED_API
  allocfunc alloc_func = (allocfunc)PyType_GetSlot(t, Py_tp_alloc);
  o = alloc_func(t, 0);
  #else
  if (likely(!__Pyx_PyType_HasFeature(t, Py_TPFLAGS_IS_ABSTRACT))) {
    o = (*t->tp_alloc)(t, 0);
  } else {
    o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_mstate_global->__pyx_empty_tuple, 0);
  }
  if (unlikely(!o)) return 0;
  #endif
  p = ((struct __pyx_MemviewEnum_obj *)o);
  p->name = Py_None; Py_INCREF(Py_None);
  return o;
}

static void __pyx_tp_dealloc_Enum(PyObject *o) {
  struct __pyx_MemviewEnum_obj *p = (struct __pyx_MemviewEnum_obj *)o;
  #if CYTHON_USE_TP_FINALIZE
  if (unlikely((PY_VERSION_HEX >= 0x03080000 || __Pyx_PyType_HasFeature(Py_TYPE(o), Py_TPFLAGS_HAVE_FINALIZE)) && __Pyx_PyObject_GetSlot(o, tp_finalize, destructor)) && !__Pyx_PyObject_GC_IsFinalized(o)) {
    if (__Pyx_PyObject_GetSlot(o, tp_dealloc, destructor) == __pyx_tp_dealloc_Enum) {
      if (PyObject_CallFinalizerFromDealloc(o)) return;
    }
  }
  #endif
  PyObject_GC_UnTrack(o);
  Py_CLEAR(p->name);
  #if CYTHON_USE_TYPE_SLOTS
  (*Py_TYPE(o)->tp_free)(o);
  #else
  {
    freefunc tp_free = (freefunc)PyType_GetSlot(Py_TYPE(o), Py_tp_free);
    if (tp_free) tp_free(o);
  }
  #endif
}

static int __pyx_tp_traverse_Enum(PyObject *o, visitproc v, void *a) {
  int e;
  struct __pyx_MemviewEnum_obj *p = (struct __pyx_MemviewEnum_obj *)o;
  {
    e = __Pyx_call_type_traverse(o, 1, v, a);
    if (e) return e;
  }
  if (p->name) {
    e = (*v)(p->name, a); if (e) return e;
  }
  return 0;
}

static int __pyx_tp_clear_Enum(PyObject *o) {
  PyObject* tmp;
  struct __pyx_MemviewEnum_obj *p = (struct __pyx_MemviewEnum_obj *)o;
  tmp = ((PyObject*)p->name);
  p->name = Py_None; Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  return 0;
}

static PyMethodDef __pyx_methods_Enum[] = {
  {"__reduce_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw___pyx_MemviewEnum_1__reduce_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, 0},
  {"__setstate_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw___pyx_MemviewEnum_3__setstate_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, 0},
  {0, 0, 0, 0}
};
#if CYTHON_USE_TYPE_SPECS
static PyType_Slot __pyx_type___pyx_MemviewEnum_slots[] = {
  {Py_tp_dealloc, (void *)__pyx_tp_dealloc_Enum},
  {Py_tp_repr, (void *)__pyx_MemviewEnum___repr__},
  {Py_tp_traverse, (void *)__pyx_tp_traverse_Enum},
  {Py_tp_clear, (void *)__pyx_tp_clear_Enum},
  {Py_tp_methods, (void *)__pyx_methods_Enum},
  {Py_tp_init, (void *)__pyx_MemviewEnum___init__},
  {Py_tp_new, (void *)__pyx_tp_new_Enum},
  {0, 0},
};
static PyType_Spec __pyx_type___pyx_MemviewEnum_spec = {
  "pyRing.waveform.Enum",
  sizeof(struct __pyx_MemviewEnum_obj),
  0,
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC,
  __pyx_type___pyx_MemviewEnum_slots,
};
#else

static PyTypeObject __pyx_type___pyx_MemviewEnum = {
  PyVarObject_HEAD_INIT(0, 0)
  "pyRing.waveform.""Enum", /*tp_name*/
  sizeof(struct __pyx_MemviewEnum_obj), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc_Enum, /*tp_dealloc*/
  #if PY_VERSION_HEX < 0x030800b4
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b4
  0, /*tp_vectorcall_offset*/
  #endif
  0, /*tp_getattr*/
  0, /*tp_setattr*/
  0, /*tp_as_async*/
  __pyx_MemviewEnum___repr__, /*tp_repr*/
  0, /*tp_as_number*/
  0, /*tp_as_sequence*/
  0, /*tp_as_mapping*/
  0, /*tp_hash*/
  0, /*tp_call*/
  0, /*tp_str*/
  0, /*tp_getattro*/
  0, /*tp_setattro*/
  0, /*tp_as_buffer*/
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC, /*tp_flags*/
  0, /*tp_doc*/
  __pyx_tp_traverse_Enum, /*tp_traverse*/
  __pyx_tp_clear_Enum, /*tp_clear*/
  0, /*tp_richcompare*/
  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
  0, /*tp_iternext*/
  __pyx_methods_Enum, /*tp_methods*/
  0, /*tp_members*/
  0, /*tp_getset*/
  0, /*tp_base*/
  0, /*tp_dict*/
  0, /*tp_descr_get*/
  0, /*tp_descr_set*/
  #if !CYTHON_USE_TYPE_SPECS
  0, /*tp_dictoffset*/
  #endif
  __pyx_MemviewEnum___init__, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_Enum, /*tp_new*/
  0, /*tp_free*/
  0, /*tp_is_gc*/
  0, /*tp_bases*/
  0, /*tp_mro*/
  0, /*tp_cache*/
  0, /*tp_subclasses*/
  0, /*tp_weaklist*/
  0, /*tp_del*/
  0, /*tp_version_tag*/
  #if CYTHON_USE_TP_FINALIZE
  0, /*tp_finalize*/
  #else
  NULL, /*tp_finalize*/
  #endif
  #if PY_VERSION_HEX >= 0x030800b1 && (!CYTHON_COMPILING_IN_PYPY || PYPY_VERSION_NUM >= 0x07030800)
  0, /*tp_vectorcall*/
  #endif
  #if __PYX_NEED_TP_PRINT_SLOT == 1
  0, /*tp_print*/
  #endif
  #if PY_VERSION_HEX >= 0x030C0000
  0, /*tp_watched*/
  #endif
  #if PY_VERSION_HEX >= 0x030d00A4
  0, /*tp_versions_used*/
  #endif
  #if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX >= 0x03090000 && PY_VERSION_HEX < 0x030a0000
  0, /*tp_pypy_flags*/
  #endif
};
#endif
static struct __pyx_vtabstruct_memoryview __pyx_vtable_memoryview;

static PyObject *__pyx_tp_new_memoryview(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_memoryview_obj *p;
  PyObject *o;
  #if CYTHON_COMPILING_IN_LIMITED_API
  allocfunc alloc_func = (allocfunc)PyType_GetSlot(t, Py_tp_alloc);
  o = alloc_func(t, 0);
  #else
  if (likely(!__Pyx_PyType_HasFeature(t, Py_TPFLAGS_IS_ABSTRACT))) {
    o = (*t->tp_alloc)(t, 0);
  } else {
    o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_mstate_global->__pyx_empty_tuple, 0);
  }
  if (unlikely(!o)) return 0;
  #endif
  p = ((struct __pyx_memoryview_obj *)o);
  p->__pyx_vtab = __pyx_vtabptr_memoryview;
  p->obj = Py_None; Py_INCREF(Py_None);
  p->_size = Py_None; Py_INCREF(Py_None);
  p->_array_interface = Py_None; Py_INCREF(Py_None);
  p->view.obj = NULL;
  if (unlikely(__pyx_memoryview___cinit__(o, a, k) < 0)) goto bad;
  return o;
  bad:
  Py_DECREF(o); o = 0;
  return NULL;
}

static void __pyx_tp_dealloc_memoryview(PyObject *o) {
  struct __pyx_memoryview_obj *p = (struct __pyx_memoryview_obj *)o;
  #if CYTHON_USE_TP_FINALIZE
  if (unlikely((PY_VERSION_HEX >= 0x03080000 || __Pyx_PyType_HasFeature(Py_TYPE(o), Py_TPFLAGS_HAVE_FINALIZE)) && __Pyx_PyObject_GetSlot(o, tp_finalize, destructor)) && !__Pyx_PyObject_GC_IsFinalized(o)) {
    if (__Pyx_PyObject_GetSlot(o, tp_dealloc, destructor) == __pyx_tp_dealloc_memoryview) {
      if (PyObject_CallFinalizerFromDealloc(o)) return;
    }
  }
  #endif
  PyObject_GC_UnTrack(o);
  {
    PyObject *etype, *eval, *etb;
    PyErr_Fetch(&etype, &eval, &etb);
    __Pyx_SET_REFCNT(o, Py_REFCNT(o) + 1);
    __pyx_memoryview___dealloc__(o);
    __Pyx_SET_REFCNT(o, Py_REFCNT(o) - 1);
    PyErr_Restore(etype, eval, etb);
  }
  Py_CLEAR(p->obj);
  Py_CLEAR(p->_size);
  Py_CLEAR(p->_array_interface);
  #if CYTHON_USE_TYPE_SLOTS
  (*Py_TYPE(o)->tp_free)(o);
  #else
  {
    freefunc tp_free = (freefunc)PyType_GetSlot(Py_TYPE(o), Py_tp_free);
    if (tp_free) tp_free(o);
  }
  #endif
}

static int __pyx_tp_traverse_memoryview(PyObject *o, visitproc v, void *a) {
  int e;
  struct __pyx_memoryview_obj *p = (struct __pyx_memoryview_obj *)o;
  {
    e = __Pyx_call_type_traverse(o, 1, v, a);
    if (e) return e;
  }
  if (p->obj) {
    e = (*v)(p->obj, a); if (e) return e;
  }
  if (p->_size) {
    e = (*v)(p->_size, a); if (e) return e;
  }
  if (p->_array_interface) {
    e = (*v)(p->_array_interface, a); if (e) return e;
  }
  if (p->view.obj) {
    e = (*v)(p->view.obj, a); if (e) return e;
  }
  return 0;
}

static int __pyx_tp_clear_memoryview(PyObject *o) {
  PyObject* tmp;
  struct __pyx_memoryview_obj *p = (struct __pyx_memoryview_obj *)o;
  tmp = ((PyObject*)p->obj);
  p->obj = Py_None; Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->_size);
  p->_size = Py_None; Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->_array_interface);
  p->_array_interface = Py_None; Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  Py_CLEAR(p->view.obj);
  return 0;
}

static PyObject *__pyx_sq_item_memoryview(PyObject *o, Py_ssize_t i) {
  PyObject *r;
  PyObject *x = PyLong_FromSsize_t(i); if(!x) return 0;
  #if CYTHON_USE_TYPE_SLOTS || (!CYTHON_USE_TYPE_SPECS && __PYX_LIMITED_VERSION_HEX < 0x030A0000)
  r = Py_TYPE(o)->tp_as_mapping->mp_subscript(o, x);
  #else
  r = ((binaryfunc)PyType_GetSlot(Py_TYPE(o), Py_mp_subscript))(o, x);
  #endif
  Py_DECREF(x);
  return r;
}

static int __pyx_mp_ass_subscript_memoryview(PyObject *o, PyObject *i, PyObject *v) {
  if (v) {
    return __pyx_memoryview___setitem__(o, i, v);
  }
  else {
    __Pyx_TypeName o_type_name;
    o_type_name = __Pyx_PyType_GetFullyQualifiedName(Py_TYPE(o));
    PyErr_Format(PyExc_NotImplementedError,
      "Subscript deletion not supported by " __Pyx_FMT_TYPENAME, o_type_name);
    __Pyx_DECREF_TypeName(o_type_name);
    return -1;
  }
}

static PyObject *__pyx_getprop___pyx_memoryview_T(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_15View_dot_MemoryView_10memoryview_1T_1__get__(o);
}

static PyObject *__pyx_getprop___pyx_memoryview_base(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_15View_dot_MemoryView_10memoryview_4base_1__get__(o);
}

static PyObject *__pyx_getprop___pyx_memoryview_shape(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_15View_dot_MemoryView_10memoryview_5shape_1__get__(o);
}

static PyObject *__pyx_getprop___pyx_memoryview_strides(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_15View_dot_MemoryView_10memoryview_7strides_1__get__(o);
}

static PyObject *__pyx_getprop___pyx_memoryview_suboffsets(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_15View_dot_MemoryView_10memoryview_10suboffsets_1__get__(o);
}

static PyObject *__pyx_getprop___pyx_memoryview_ndim(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_15View_dot_MemoryView_10memoryview_4ndim_1__get__(o);
}

static PyObject *__pyx_getprop___pyx_memoryview_itemsize(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_15View_dot_MemoryView_10memoryview_8itemsize_1__get__(o);
}

static PyObject *__pyx_getprop___pyx_memoryview_nbytes(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_15View_dot_MemoryView_10memoryview_6nbytes_1__get__(o);
}

static PyObject *__pyx_getprop___pyx_memoryview_size(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_15View_dot_MemoryView_10memoryview_4size_1__get__(o);
}

static PyMethodDef __pyx_methods_memoryview[] = {
  {"is_c_contig", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_memoryview_is_c_contig, __Pyx_METH_FASTCALL|METH_KEYWORDS, 0},
  {"is_f_contig", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_memoryview_is_f_contig, __Pyx_METH_FASTCALL|METH_KEYWORDS, 0},
  {"copy", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_memoryview_copy, __Pyx_METH_FASTCALL|METH_KEYWORDS, 0},
  {"copy_fortran", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_memoryview_copy_fortran, __Pyx_METH_FASTCALL|METH_KEYWORDS, 0},
  {"__reduce_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw___pyx_memoryview_1__reduce_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, 0},
  {"__setstate_cython__", (PyCFunction)(void(*)(void))(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw___pyx_memoryview_3__setstate_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, 0},
  {0, 0, 0, 0}
};

static struct PyGetSetDef __pyx_getsets_memoryview[] = {
  {"T", __pyx_getprop___pyx_memoryview_T, 0, 0, 0},
  {"base", __pyx_getprop___pyx_memoryview_base, 0, 0, 0},
  {"shape", __pyx_getprop___pyx_memoryview_shape, 0, 0, 0},
  {"strides", __pyx_getprop___pyx_memoryview_strides, 0, 0, 0},
  {"suboffsets", __pyx_getprop___pyx_memoryview_suboffsets, 0, 0, 0},
  {"ndim", __pyx_getprop___pyx_memoryview_ndim, 0, 0, 0},
  {"itemsize", __pyx_getprop___pyx_memoryview_itemsize, 0, 0, 0},
  {"nbytes", __pyx_getprop___pyx_memoryview_nbytes, 0, 0, 0},
  {"size", __pyx_getprop___pyx_memoryview_size, 0, 0, 0},
  {0, 0, 0, 0, 0}
};
#if CYTHON_USE_TYPE_SPECS
#if !CYTHON_COMPILING_IN_LIMITED_API

static PyBufferProcs __pyx_tp_as_buffer_memoryview = {
  __pyx_memoryview_getbuffer, /*bf_getbuffer*/
  0, /*bf_releasebuffer*/
};
#endif
static PyType_Slot __pyx_type___pyx_memoryview_slots[] = {
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  {Py_sq_length, (void *)__pyx_memoryview___len__},
  {Py_sq_item, (void *)__pyx_sq_item_memoryview},
  {Py_mp_length, (void *)__pyx_memoryview___len__},
  {Py_mp_subscript, (void *)__pyx_memoryview___getitem__},
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  {Py_tp_str, (void *)__pyx_memoryview___str__},
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};
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};
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  0, /*sq_slice*/
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  0, /*sq_contains*/
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};

static PyMappingMethods __pyx_tp_as_mapping_memoryview = {
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};

static PyBufferProcs __pyx_tp_as_buffer_memoryview = {
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  0, /*tp_print*/
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  0, /*tp_hash*/
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  0, /*tp_getattro*/
  0, /*tp_setattro*/
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  0, /*tp_doc*/
  __pyx_tp_traverse_memoryview, /*tp_traverse*/
  __pyx_tp_clear_memoryview, /*tp_clear*/
  0, /*tp_richcompare*/
  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
  0, /*tp_iternext*/
  __pyx_methods_memoryview, /*tp_methods*/
  0, /*tp_members*/
  __pyx_getsets_memoryview, /*tp_getset*/
  0, /*tp_base*/
  0, /*tp_dict*/
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  0, /*tp_dictoffset*/
  #endif
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  0, /*tp_alloc*/
  __pyx_tp_new_memoryview, /*tp_new*/
  0, /*tp_free*/
  0, /*tp_is_gc*/
  0, /*tp_bases*/
  0, /*tp_mro*/
  0, /*tp_cache*/
  0, /*tp_subclasses*/
  0, /*tp_weaklist*/
  0, /*tp_del*/
  0, /*tp_version_tag*/
  #if CYTHON_USE_TP_FINALIZE
  0, /*tp_finalize*/
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  0, /*tp_vectorcall*/
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  0, /*tp_print*/
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  #if PY_VERSION_HEX >= 0x030C0000
  0, /*tp_watched*/
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  #endif
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  0, /*tp_pypy_flags*/
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static struct __pyx_vtabstruct__memoryviewslice __pyx_vtable__memoryviewslice;

static PyObject *__pyx_tp_new__memoryviewslice(PyTypeObject *t, PyObject *a, PyObject *k) {
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static void __pyx_tp_dealloc__memoryviewslice(PyObject *o) {
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  PyObject_GC_UnTrack(o);
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    __Pyx_SET_REFCNT(o, Py_REFCNT(o) - 1);
    PyErr_Restore(etype, eval, etb);
  }
  Py_CLEAR(p->from_object);
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  __pyx_tp_dealloc_memoryview(o);
}

static int __pyx_tp_traverse__memoryviewslice(PyObject *o, visitproc v, void *a) {
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}

static int __pyx_tp_clear__memoryviewslice(PyObject *o) {
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  p->from_object = Py_None; Py_INCREF(Py_None);
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  __PYX_XCLEAR_MEMVIEW(&p->from_slice, 1);
  return 0;
}

static PyMethodDef __pyx_methods__memoryviewslice[] = {
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  {0, 0, 0, 0}
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  {Py_tp_traverse, (void *)__pyx_tp_traverse__memoryviewslice},
  {Py_tp_clear, (void *)__pyx_tp_clear__memoryviewslice},
  {Py_tp_methods, (void *)__pyx_methods__memoryviewslice},
  {Py_tp_new, (void *)__pyx_tp_new__memoryviewslice},
  {0, 0},
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static PyType_Spec __pyx_type___pyx_memoryviewslice_spec = {
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  __pyx_methods__memoryviewslice, /*tp_methods*/
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    __pyx_mstate_global->__pyx_codeobj_tab[0] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_f, __pyx_k_gT_WXX_aaeettvvyyzz, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[0])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {4, 0, 0, 4, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 157, 39};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_M, __pyx_mstate->__pyx_n_u_a, __pyx_mstate->__pyx_n_u_Q};
    __pyx_mstate_global->__pyx_codeobj_tab[1] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_f_KN, __pyx_k_gT_WXX_aaeettvvyyzz_2, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[1])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {4, 0, 0, 4, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 158, 39};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_M, __pyx_mstate->__pyx_n_u_a, __pyx_mstate->__pyx_n_u_beta};
    __pyx_mstate_global->__pyx_codeobj_tab[2] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_f_BW, __pyx_k_gT_WXX_aaeettvvyyzz_2, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[2])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {3, 0, 0, 3, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 160, 53};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_M, __pyx_mstate->__pyx_n_u_a};
    __pyx_mstate_global->__pyx_codeobj_tab[3] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_tau, __pyx_k_t2TQ___hhiimm_A_A_B_B_C, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[3])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {4, 0, 0, 4, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 161, 56};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_M, __pyx_mstate->__pyx_n_u_a, __pyx_mstate->__pyx_n_u_Q};
    __pyx_mstate_global->__pyx_codeobj_tab[4] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_tau_KN, __pyx_k_t2TQ___cchhiimm_A_A_B_B_C, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[4])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {4, 0, 0, 4, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 162, 56};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_M, __pyx_mstate->__pyx_n_u_a, __pyx_mstate->__pyx_n_u_beta};
    __pyx_mstate_global->__pyx_codeobj_tab[5] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_tau_BW, __pyx_k_t2TQ___cchhiimm_A_A_B_B_C, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[5])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {1, 0, 0, 1, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 1, 9};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self};
    __pyx_mstate_global->__pyx_codeobj_tab[6] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_stringsource, __pyx_mstate->__pyx_n_u_reduce_cython, __pyx_k_Q_2, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[6])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {2, 0, 0, 2, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 3, 9};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_pyx_state};
    __pyx_mstate_global->__pyx_codeobj_tab[7] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_stringsource, __pyx_mstate->__pyx_n_u_setstate_cython, __pyx_k_Q_2, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[7])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {3, 0, 0, 3, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 240, 102};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_M, __pyx_mstate->__pyx_n_u_a};
    __pyx_mstate_global->__pyx_codeobj_tab[8] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_f, __pyx_k_XT_QRRTTUUYYaabbddffgghhjjllppx, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[8])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {2, 0, 0, 2, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 241, 57};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_a};
    __pyx_mstate_global->__pyx_codeobj_tab[9] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_q, __pyx_k_XT_QRRTTUUYYaabbddffgghhjjllppx_2, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[9])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {3, 0, 0, 3, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 242, 38};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_M, __pyx_mstate->__pyx_n_u_a};
    __pyx_mstate_global->__pyx_codeobj_tab[10] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_tau, __pyx_k_WD_2RrQTTUUYY, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[10])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {4, 0, 0, 4, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 244, 102};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_M, __pyx_mstate->__pyx_n_u_a, __pyx_mstate->__pyx_n_u_Q};
    __pyx_mstate_global->__pyx_codeobj_tab[11] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_f_KN, __pyx_k_XT_QRRTTUUYYaabbddffgghhjjllppx, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[11])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {3, 0, 0, 3, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 245, 57};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_a, __pyx_mstate->__pyx_n_u_Q};
    __pyx_mstate_global->__pyx_codeobj_tab[12] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_q_KN, __pyx_k_XT_QRRTTUUYYaabbddffgghhjjllppx_2, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[12])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {4, 0, 0, 4, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 246, 46};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_M, __pyx_mstate->__pyx_n_u_a, __pyx_mstate->__pyx_n_u_Q};
    __pyx_mstate_global->__pyx_codeobj_tab[13] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_tau_KN, __pyx_k_WD_QcQSSUUWWZZ___ddeehhkkl, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[13])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {1, 0, 0, 1, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 1, 9};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self};
    __pyx_mstate_global->__pyx_codeobj_tab[14] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_stringsource, __pyx_mstate->__pyx_n_u_reduce_cython, __pyx_k_Q_2, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[14])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {2, 0, 0, 2, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 3, 9};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_pyx_state};
    __pyx_mstate_global->__pyx_codeobj_tab[15] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_stringsource, __pyx_mstate->__pyx_n_u_setstate_cython, __pyx_k_Q_2, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[15])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {5, 0, 0, 5, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 314, 124};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_M, __pyx_mstate->__pyx_n_u_a, __pyx_mstate->__pyx_n_u_gamma, __pyx_mstate->__pyx_n_u_dw_vec};
    __pyx_mstate_global->__pyx_codeobj_tab[16] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_f, __pyx_k_A_AT_AQ_1_E_aq_r_7_ar_2T_S_FRTTZ, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[16])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {5, 0, 0, 5, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 327, 129};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_M, __pyx_mstate->__pyx_n_u_a, __pyx_mstate->__pyx_n_u_gamma, __pyx_mstate->__pyx_n_u_dt_vec};
    __pyx_mstate_global->__pyx_codeobj_tab[17] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_tau, __pyx_k_A_AT_AQ_E_aq_r_7_Qb_D_3c_2VSUU_Q, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[17])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {1, 0, 0, 1, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 1, 9};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self};
    __pyx_mstate_global->__pyx_codeobj_tab[18] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_stringsource, __pyx_mstate->__pyx_n_u_reduce_cython, __pyx_k_Q_2, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[18])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {2, 0, 0, 2, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 3, 9};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_pyx_state};
    __pyx_mstate_global->__pyx_codeobj_tab[19] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_stringsource, __pyx_mstate->__pyx_n_u_setstate_cython, __pyx_k_Q_2, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[19])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {4, 0, 0, 4, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 391, 156};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_M, __pyx_mstate->__pyx_n_u_a, __pyx_mstate->__pyx_n_u_alpha};
    __pyx_mstate_global->__pyx_codeobj_tab[20] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_f_QA, __pyx_k_A_c_as_q_5_ARs_3eSTTUUVVYYZ_RuAU, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[20])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {2, 0, 0, 2, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 397, 41};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_a};
    __pyx_mstate_global->__pyx_codeobj_tab[21] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_q_GR, __pyx_k_A_Kq_4_2Rq_2T_AQ, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[21])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {4, 0, 0, 4, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 400, 43};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_M, __pyx_mstate->__pyx_n_u_a, __pyx_mstate->__pyx_n_u_alpha};
    __pyx_mstate_global->__pyx_codeobj_tab[22] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_tau_QA, __pyx_k_A_4uAS_1_4uAQ_t2Rs_1, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[22])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {1, 0, 0, 1, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 1, 9};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self};
    __pyx_mstate_global->__pyx_codeobj_tab[23] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_stringsource, __pyx_mstate->__pyx_n_u_reduce_cython, __pyx_k_Q_2, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[23])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {2, 0, 0, 2, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 3, 9};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_pyx_state};
    __pyx_mstate_global->__pyx_codeobj_tab[24] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_stringsource, __pyx_mstate->__pyx_n_u_setstate_cython, __pyx_k_Q_2, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[24])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {4, 0, 0, 4, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 450, 78};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_M, __pyx_mstate->__pyx_n_u_a, __pyx_mstate->__pyx_n_u_beta};
    __pyx_mstate_global->__pyx_codeobj_tab[25] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_f_BW, __pyx_k_A_c_as_q_5_ARs_3eSTTUUVVYYZ_q_2R, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[25])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {3, 0, 0, 3, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 455, 16};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_a, __pyx_mstate->__pyx_n_u_beta};
    __pyx_mstate_global->__pyx_codeobj_tab[26] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_q_BW, __pyx_k_A_r_1_q, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[26])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {4, 0, 0, 4, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 459, 45};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_M, __pyx_mstate->__pyx_n_u_a, __pyx_mstate->__pyx_n_u_beta};
    __pyx_mstate_global->__pyx_codeobj_tab[27] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_tau_BW, __pyx_k_A_t5_Cq_t5_A_xr_3aq, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[27])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {1, 0, 0, 1, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 1, 9};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self};
    __pyx_mstate_global->__pyx_codeobj_tab[28] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_stringsource, __pyx_mstate->__pyx_n_u_reduce_cython, __pyx_k_Q_2, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[28])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {2, 0, 0, 2, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 3, 9};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_pyx_state};
    __pyx_mstate_global->__pyx_codeobj_tab[29] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_stringsource, __pyx_mstate->__pyx_n_u_setstate_cython, __pyx_k_Q_2, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[29])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {7, 0, 0, 7, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 464, 202};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_A, __pyx_mstate->__pyx_n_u_f, __pyx_mstate->__pyx_n_u_tau, __pyx_mstate->__pyx_n_u_phi, __pyx_mstate->__pyx_n_u_t_0, __pyx_mstate->__pyx_n_u_t_ref, __pyx_mstate->__pyx_n_u_t};
    __pyx_mstate_global->__pyx_codeobj_tab[30] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_damped_sinusoid, __pyx_k_R_6_F_ARs_1_ar_1_U_3aq_1AS_1_r, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[30])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {6, 0, 0, 6, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 524, 168};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_A, __pyx_mstate->__pyx_n_u_phi, __pyx_mstate->__pyx_n_u_p, __pyx_mstate->__pyx_n_u_t_0, __pyx_mstate->__pyx_n_u_t_ref, __pyx_mstate->__pyx_n_u_t};
    __pyx_mstate_global->__pyx_codeobj_tab[31] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_tail_factor, __pyx_k_L_6_F_1_U_3aq_1AS_1_r_Rq_1F_Rt2, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[31])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {2, 0, 0, 2, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 688, 340};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_t};
    __pyx_mstate_global->__pyx_codeobj_tab[32] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_waveform, __pyx_k_A_1F_1_1_6_F_r_q_6_r_q_6_r_q_6_r, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[32])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {1, 0, 0, 1, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 1, 9};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self};
    __pyx_mstate_global->__pyx_codeobj_tab[33] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_stringsource, __pyx_mstate->__pyx_n_u_reduce_cython, __pyx_k_Q_2, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[33])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {2, 0, 0, 2, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 3, 9};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_pyx_state};
    __pyx_mstate_global->__pyx_codeobj_tab[34] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_stringsource, __pyx_mstate->__pyx_n_u_setstate_cython, __pyx_k_Q_2, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[34])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {2, 0, 0, 2, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 800, 341};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_t};
    __pyx_mstate_global->__pyx_codeobj_tab[35] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_waveform, __pyx_k_A_1F_1_1_6_F_r_q_6_r_q_6_r_q_6_r_2, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[35])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {1, 0, 0, 1, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 1, 9};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self};
    __pyx_mstate_global->__pyx_codeobj_tab[36] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_stringsource, __pyx_mstate->__pyx_n_u_reduce_cython, __pyx_k_Q_2, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[36])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {2, 0, 0, 2, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 3, 9};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_pyx_state};
    __pyx_mstate_global->__pyx_codeobj_tab[37] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_stringsource, __pyx_mstate->__pyx_n_u_setstate_cython, __pyx_k_Q_2, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[37])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {3, 0, 0, 3, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 902, 273};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_theta, __pyx_mstate->__pyx_n_u_phi};
    __pyx_mstate_global->__pyx_codeobj_tab[38] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_evaluate, __pyx_k_ARt2Qd_AT_1D_4r_a_U_3b_Bb_Qe1Bc, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[38])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {1, 0, 0, 4, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 1, 99};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_state, __pyx_mstate->__pyx_n_u_dict_2, __pyx_mstate->__pyx_n_u_use_setstate};
    __pyx_mstate_global->__pyx_codeobj_tab[39] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_stringsource, __pyx_mstate->__pyx_n_u_reduce_cython, __pyx_k_T_T_T_T_G1F_a_vWA_q_q_q_T_G1_T, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[39])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {2, 0, 0, 2, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 16, 11};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_pyx_state};
    __pyx_mstate_global->__pyx_codeobj_tab[40] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_stringsource, __pyx_mstate->__pyx_n_u_setstate_cython, __pyx_k_6, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[40])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {2, 0, 0, 2, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 1094, 2886};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_times};
    __pyx_mstate_global->__pyx_codeobj_tab[41] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_waveform, __pyx_k_BfAU_V1_BfAU_V1_BfAU_V1_BfAU_V1, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[41])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {1, 0, 0, 1, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 1, 9};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self};
    __pyx_mstate_global->__pyx_codeobj_tab[42] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_stringsource, __pyx_mstate->__pyx_n_u_reduce_cython, __pyx_k_Q_2, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[42])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {2, 0, 0, 2, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 3, 9};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_pyx_state};
    __pyx_mstate_global->__pyx_codeobj_tab[43] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_stringsource, __pyx_mstate->__pyx_n_u_setstate_cython, __pyx_k_Q_2, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[43])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {2, 0, 0, 2, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 1389, 1557};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_times};
    __pyx_mstate_global->__pyx_codeobj_tab[44] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_waveform, __pyx_k_RvQe6_fA_RvQe6_fA_RvQe6_fA_RvQe, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[44])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {1, 0, 0, 1, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 1, 9};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self};
    __pyx_mstate_global->__pyx_codeobj_tab[45] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_stringsource, __pyx_mstate->__pyx_n_u_reduce_cython, __pyx_k_Q_2, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[45])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {2, 0, 0, 2, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 3, 9};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_pyx_state};
    __pyx_mstate_global->__pyx_codeobj_tab[46] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_stringsource, __pyx_mstate->__pyx_n_u_setstate_cython, __pyx_k_Q_2, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[46])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {2, 0, 0, 2, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 1578, 995};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_times};
    __pyx_mstate_global->__pyx_codeobj_tab[47] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_waveform, __pyx_k_Q_k_fD_HD_6_Q_Bb_b_as_86_YivT_B, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[47])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {1, 0, 0, 1, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 1, 9};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self};
    __pyx_mstate_global->__pyx_codeobj_tab[48] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_stringsource, __pyx_mstate->__pyx_n_u_reduce_cython, __pyx_k_Q_2, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[48])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {2, 0, 0, 2, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 3, 9};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_pyx_state};
    __pyx_mstate_global->__pyx_codeobj_tab[49] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_stringsource, __pyx_mstate->__pyx_n_u_setstate_cython, __pyx_k_Q_2, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[49])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {2, 0, 0, 2, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 1716, 703};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_times};
    __pyx_mstate_global->__pyx_codeobj_tab[50] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_waveform, __pyx_k_Q_6_fD_6_Q_Bb_b_as_86_war_2Rs_e, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[50])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {1, 0, 0, 1, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 1, 9};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self};
    __pyx_mstate_global->__pyx_codeobj_tab[51] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_stringsource, __pyx_mstate->__pyx_n_u_reduce_cython, __pyx_k_Q_2, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[51])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {2, 0, 0, 2, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 3, 9};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_pyx_state};
    __pyx_mstate_global->__pyx_codeobj_tab[52] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_stringsource, __pyx_mstate->__pyx_n_u_setstate_cython, __pyx_k_Q_2, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[52])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {4, 0, 0, 4, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 1873, 18};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_l, __pyx_mstate->__pyx_n_u_m, __pyx_mstate->__pyx_n_u_NR_fit_coeffs};
    __pyx_mstate_global->__pyx_codeobj_tab[53] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_EOBPM_SetupFitCoefficients, __pyx_k_A_t_q_3a, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[53])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {7, 0, 0, 7, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 1972, 24};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_tau, __pyx_mstate->__pyx_n_u_sigma_real, __pyx_mstate->__pyx_n_u_a1, __pyx_mstate->__pyx_n_u_a2, __pyx_mstate->__pyx_n_u_a3, __pyx_mstate->__pyx_n_u_a4};
    __pyx_mstate_global->__pyx_codeobj_tab[54] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_TEOBPM_Amplitude, __pyx_k_A_t_Qe_t4t1, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[54])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {8, 0, 0, 8, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 1980, 25};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_tau, __pyx_mstate->__pyx_n_u_sigma_imag, __pyx_mstate->__pyx_n_u_phi_0, __pyx_mstate->__pyx_n_u_p1, __pyx_mstate->__pyx_n_u_p2, __pyx_mstate->__pyx_n_u_p3, __pyx_mstate->__pyx_n_u_p4};
    __pyx_mstate_global->__pyx_codeobj_tab[55] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_TEOBPM_Phase, __pyx_k_A_t_7_d_a, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[55])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {2, 0, 0, 2, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 2029, 13};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_times};
    __pyx_mstate_global->__pyx_codeobj_tab[56] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_waveform, __pyx_k_A_t_Qa, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[56])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {1, 0, 0, 1, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 2097, 18};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self};
    __pyx_mstate_global->__pyx_codeobj_tab[57] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_sym_mass_ratio, __pyx_k_A_e4q, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[57])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {1, 0, 0, 1, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 2100, 17};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self};
    __pyx_mstate_global->__pyx_codeobj_tab[58] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_X_1, __pyx_k_A_at5_A, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[58])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {1, 0, 0, 1, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 2103, 17};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self};
    __pyx_mstate_global->__pyx_codeobj_tab[59] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_X_2, __pyx_k_A_at5_A, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[59])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {1, 0, 0, 1, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 2106, 17};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self};
    __pyx_mstate_global->__pyx_codeobj_tab[60] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_X_12, __pyx_k_A_q_E_Q, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[60])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {1, 0, 0, 1, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 2109, 25};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self};
    __pyx_mstate_global->__pyx_codeobj_tab[61] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_a_0, __pyx_k_A_at5_E_WD, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[61])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {1, 0, 0, 1, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 2112, 25};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self};
    __pyx_mstate_global->__pyx_codeobj_tab[62] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_a_12, __pyx_k_A_q_E_U_gT, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[62])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {1, 0, 0, 1, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 2115, 21};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self};
    __pyx_mstate_global->__pyx_codeobj_tab[63] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_S_hat, __pyx_k_A_V4uD, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[63])) goto bad;
  }
  {
    const __Pyx_PyCode_New_function_description descr = {1, 0, 0, 1, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 2118, 21};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self};
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  {
    const __Pyx_PyCode_New_function_description descr = {3, 0, 0, 3, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 2131, 17};
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  {
    const __Pyx_PyCode_New_function_description descr = {3, 0, 0, 3, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 2138, 29};
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  {
    const __Pyx_PyCode_New_function_description descr = {3, 0, 0, 3, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 2141, 25};
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  {
    const __Pyx_PyCode_New_function_description descr = {3, 0, 0, 3, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 2144, 25};
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  {
    const __Pyx_PyCode_New_function_description descr = {3, 0, 0, 3, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 2151, 17};
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  {
    const __Pyx_PyCode_New_function_description descr = {4, 0, 0, 4, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 2154, 45};
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  {
    const __Pyx_PyCode_New_function_description descr = {3, 0, 0, 3, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 2157, 29};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_self, __pyx_mstate->__pyx_n_u_l, __pyx_mstate->__pyx_n_u_m};
    __pyx_mstate_global->__pyx_codeobj_tab[73] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_waveform_pyx, __pyx_mstate->__pyx_n_u_omega_peak, __pyx_k_A_Qd_t6_WD_S, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[73])) goto bad;
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  {
    const __Pyx_PyCode_New_function_description descr = {1, 0, 0, 1, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 2164, 38};
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  {
    const __Pyx_PyCode_New_function_description descr = {1, 0, 0, 1, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 2167, 32};
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  {
    const __Pyx_PyCode_New_function_description descr = {3, 0, 0, 3, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 2174, 29};
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  {
    const __Pyx_PyCode_New_function_description descr = {3, 0, 0, 3, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 2178, 25};
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    const __Pyx_PyCode_New_function_description descr = {2, 0, 0, 2, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 3, 9};
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    const __Pyx_PyCode_New_function_description descr = {2, 0, 0, 2, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 2212, 16};
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static CYTHON_INLINE void __Pyx_copy_object_array(PyObject *const *CYTHON_RESTRICT src, PyObject** CYTHON_RESTRICT dest, Py_ssize_t length) {
    PyObject *v;
    Py_ssize_t i;
    for (i = 0; i < length; i++) {
        v = dest[i] = src[i];
        Py_INCREF(v);
    }
}
static CYTHON_INLINE PyObject *
__Pyx_PyTuple_FromArray(PyObject *const *src, Py_ssize_t n)
{
    PyObject *res;
    if (n <= 0) {
        return __Pyx_NewRef(__pyx_mstate_global->__pyx_empty_tuple);
    }
    res = PyTuple_New(n);
    if (unlikely(res == NULL)) return NULL;
    __Pyx_copy_object_array(src, ((PyTupleObject*)res)->ob_item, n);
    return res;
}
static CYTHON_INLINE PyObject *
__Pyx_PyList_FromArray(PyObject *const *src, Py_ssize_t n)
{
    PyObject *res;
    if (n <= 0) {
        return PyList_New(0);
    }
    res = PyList_New(n);
    if (unlikely(res == NULL)) return NULL;
    __Pyx_copy_object_array(src, ((PyListObject*)res)->ob_item, n);
    return res;
}
#endif

/* BytesEquals */
static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals) {
#if CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_LIMITED_API || CYTHON_COMPILING_IN_GRAAL ||\
        !(CYTHON_ASSUME_SAFE_SIZE && CYTHON_ASSUME_SAFE_MACROS)
    return PyObject_RichCompareBool(s1, s2, equals);
#else
    if (s1 == s2) {
        return (equals == Py_EQ);
    } else if (PyBytes_CheckExact(s1) & PyBytes_CheckExact(s2)) {
        const char *ps1, *ps2;
        Py_ssize_t length = PyBytes_GET_SIZE(s1);
        if (length != PyBytes_GET_SIZE(s2))
            return (equals == Py_NE);
        ps1 = PyBytes_AS_STRING(s1);
        ps2 = PyBytes_AS_STRING(s2);
        if (ps1[0] != ps2[0]) {
            return (equals == Py_NE);
        } else if (length == 1) {
            return (equals == Py_EQ);
        } else {
            int result;
#if CYTHON_USE_UNICODE_INTERNALS && (PY_VERSION_HEX < 0x030B0000)
            Py_hash_t hash1, hash2;
            hash1 = ((PyBytesObject*)s1)->ob_shash;
            hash2 = ((PyBytesObject*)s2)->ob_shash;
            if (hash1 != hash2 && hash1 != -1 && hash2 != -1) {
                return (equals == Py_NE);
            }
#endif
            result = memcmp(ps1, ps2, (size_t)length);
            return (equals == Py_EQ) ? (result == 0) : (result != 0);
        }
    } else if ((s1 == Py_None) & PyBytes_CheckExact(s2)) {
        return (equals == Py_NE);
    } else if ((s2 == Py_None) & PyBytes_CheckExact(s1)) {
        return (equals == Py_NE);
    } else {
        int result;
        PyObject* py_result = PyObject_RichCompare(s1, s2, equals);
        if (!py_result)
            return -1;
        result = __Pyx_PyObject_IsTrue(py_result);
        Py_DECREF(py_result);
        return result;
    }
#endif
}

/* UnicodeEquals */
static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals) {
#if CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_LIMITED_API || CYTHON_COMPILING_IN_GRAAL
    return PyObject_RichCompareBool(s1, s2, equals);
#else
    int s1_is_unicode, s2_is_unicode;
    if (s1 == s2) {
        goto return_eq;
    }
    s1_is_unicode = PyUnicode_CheckExact(s1);
    s2_is_unicode = PyUnicode_CheckExact(s2);
    if (s1_is_unicode & s2_is_unicode) {
        Py_ssize_t length, length2;
        int kind;
        void *data1, *data2;
        #if !CYTHON_COMPILING_IN_LIMITED_API
        if (unlikely(__Pyx_PyUnicode_READY(s1) < 0) || unlikely(__Pyx_PyUnicode_READY(s2) < 0))
            return -1;
        #endif
        length = __Pyx_PyUnicode_GET_LENGTH(s1);
        #if !CYTHON_ASSUME_SAFE_SIZE
        if (unlikely(length < 0)) return -1;
        #endif
        length2 = __Pyx_PyUnicode_GET_LENGTH(s2);
        #if !CYTHON_ASSUME_SAFE_SIZE
        if (unlikely(length2 < 0)) return -1;
        #endif
        if (length != length2) {
            goto return_ne;
        }
#if CYTHON_USE_UNICODE_INTERNALS
        {
            Py_hash_t hash1, hash2;
            hash1 = ((PyASCIIObject*)s1)->hash;
            hash2 = ((PyASCIIObject*)s2)->hash;
            if (hash1 != hash2 && hash1 != -1 && hash2 != -1) {
                goto return_ne;
            }
        }
#endif
        kind = __Pyx_PyUnicode_KIND(s1);
        if (kind != __Pyx_PyUnicode_KIND(s2)) {
            goto return_ne;
        }
        data1 = __Pyx_PyUnicode_DATA(s1);
        data2 = __Pyx_PyUnicode_DATA(s2);
        if (__Pyx_PyUnicode_READ(kind, data1, 0) != __Pyx_PyUnicode_READ(kind, data2, 0)) {
            goto return_ne;
        } else if (length == 1) {
            goto return_eq;
        } else {
            int result = memcmp(data1, data2, (size_t)(length * kind));
            return (equals == Py_EQ) ? (result == 0) : (result != 0);
        }
    } else if ((s1 == Py_None) & s2_is_unicode) {
        goto return_ne;
    } else if ((s2 == Py_None) & s1_is_unicode) {
        goto return_ne;
    } else {
        int result;
        PyObject* py_result = PyObject_RichCompare(s1, s2, equals);
        if (!py_result)
            return -1;
        result = __Pyx_PyObject_IsTrue(py_result);
        Py_DECREF(py_result);
        return result;
    }
return_eq:
    return (equals == Py_EQ);
return_ne:
    return (equals == Py_NE);
#endif
}

/* fastcall */
#if CYTHON_METH_FASTCALL
static CYTHON_INLINE PyObject * __Pyx_GetKwValue_FASTCALL(PyObject *kwnames, PyObject *const *kwvalues, PyObject *s)
{
    Py_ssize_t i, n = __Pyx_PyTuple_GET_SIZE(kwnames);
    #if !CYTHON_ASSUME_SAFE_SIZE
    if (unlikely(n == -1)) return NULL;
    #endif
    for (i = 0; i < n; i++)
    {
        PyObject *namei = __Pyx_PyTuple_GET_ITEM(kwnames, i);
        #if !CYTHON_ASSUME_SAFE_MACROS
        if (unlikely(!namei)) return NULL;
        #endif
        if (s == namei) return kwvalues[i];
    }
    for (i = 0; i < n; i++)
    {
        PyObject *namei = __Pyx_PyTuple_GET_ITEM(kwnames, i);
        #if !CYTHON_ASSUME_SAFE_MACROS
        if (unlikely(!namei)) return NULL;
        #endif
        int eq = __Pyx_PyUnicode_Equals(s, namei, Py_EQ);
        if (unlikely(eq != 0)) {
            if (unlikely(eq < 0)) return NULL;
            return kwvalues[i];
        }
    }
    return NULL;
}
#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030d0000 || CYTHON_COMPILING_IN_LIMITED_API
CYTHON_UNUSED static PyObject *__Pyx_KwargsAsDict_FASTCALL(PyObject *kwnames, PyObject *const *kwvalues) {
    Py_ssize_t i, nkwargs;
    PyObject *dict;
#if !CYTHON_ASSUME_SAFE_SIZE
    nkwargs = PyTuple_Size(kwnames);
    if (unlikely(nkwargs < 0)) return NULL;
#else
    nkwargs = PyTuple_GET_SIZE(kwnames);
#endif
    dict = PyDict_New();
    if (unlikely(!dict))
        return NULL;
    for (i=0; i<nkwargs; i++) {
#if !CYTHON_ASSUME_SAFE_MACROS
        PyObject *key = PyTuple_GetItem(kwnames, i);
        if (!key) goto bad;
#else
        PyObject *key = PyTuple_GET_ITEM(kwnames, i);
#endif
        if (unlikely(PyDict_SetItem(dict, key, kwvalues[i]) < 0))
            goto bad;
    }
    return dict;
bad:
    Py_DECREF(dict);
    return NULL;
}
#endif
#endif

/* RaiseDoubleKeywords */
static void __Pyx_RaiseDoubleKeywordsError(
    const char* func_name,
    PyObject* kw_name)
{
    PyErr_Format(PyExc_TypeError,
        "%s() got multiple values for keyword argument '%U'", func_name, kw_name);
}

/* PyFunctionFastCall */
#if CYTHON_FAST_PYCALL && !CYTHON_VECTORCALL
static PyObject* __Pyx_PyFunction_FastCallNoKw(PyCodeObject *co, PyObject *const *args, Py_ssize_t na,
                                               PyObject *globals) {
    PyFrameObject *f;
    PyThreadState *tstate = __Pyx_PyThreadState_Current;
    PyObject **fastlocals;
    Py_ssize_t i;
    PyObject *result;
    assert(globals != NULL);
    /* XXX Perhaps we should create a specialized
       PyFrame_New() that doesn't take locals, but does
       take builtins without sanity checking them.
       */
    assert(tstate != NULL);
    f = PyFrame_New(tstate, co, globals, NULL);
    if (f == NULL) {
        return NULL;
    }
    fastlocals = __Pyx_PyFrame_GetLocalsplus(f);
    for (i = 0; i < na; i++) {
        Py_INCREF(*args);
        fastlocals[i] = *args++;
    }
    result = PyEval_EvalFrameEx(f,0);
    ++tstate->recursion_depth;
    Py_DECREF(f);
    --tstate->recursion_depth;
    return result;
}
static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject *const *args, Py_ssize_t nargs, PyObject *kwargs) {
    PyCodeObject *co = (PyCodeObject *)PyFunction_GET_CODE(func);
    PyObject *globals = PyFunction_GET_GLOBALS(func);
    PyObject *argdefs = PyFunction_GET_DEFAULTS(func);
    PyObject *closure;
    PyObject *kwdefs;
    PyObject *kwtuple, **k;
    PyObject **d;
    Py_ssize_t nd;
    Py_ssize_t nk;
    PyObject *result;
    assert(kwargs == NULL || PyDict_Check(kwargs));
    nk = kwargs ? PyDict_Size(kwargs) : 0;
    if (unlikely(Py_EnterRecursiveCall(" while calling a Python object"))) {
        return NULL;
    }
    if (
            co->co_kwonlyargcount == 0 &&
            likely(kwargs == NULL || nk == 0) &&
            co->co_flags == (CO_OPTIMIZED | CO_NEWLOCALS | CO_NOFREE)) {
        if (argdefs == NULL && co->co_argcount == nargs) {
            result = __Pyx_PyFunction_FastCallNoKw(co, args, nargs, globals);
            goto done;
        }
        else if (nargs == 0 && argdefs != NULL
                 && co->co_argcount == Py_SIZE(argdefs)) {
            /* function called with no arguments, but all parameters have
               a default value: use default values as arguments .*/
            args = &PyTuple_GET_ITEM(argdefs, 0);
            result =__Pyx_PyFunction_FastCallNoKw(co, args, Py_SIZE(argdefs), globals);
            goto done;
        }
    }
    if (kwargs != NULL) {
        Py_ssize_t pos, i;
        kwtuple = PyTuple_New(2 * nk);
        if (kwtuple == NULL) {
            result = NULL;
            goto done;
        }
        k = &PyTuple_GET_ITEM(kwtuple, 0);
        pos = i = 0;
        while (PyDict_Next(kwargs, &pos, &k[i], &k[i+1])) {
            Py_INCREF(k[i]);
            Py_INCREF(k[i+1]);
            i += 2;
        }
        nk = i / 2;
    }
    else {
        kwtuple = NULL;
        k = NULL;
    }
    closure = PyFunction_GET_CLOSURE(func);
    kwdefs = PyFunction_GET_KW_DEFAULTS(func);
    if (argdefs != NULL) {
        d = &PyTuple_GET_ITEM(argdefs, 0);
        nd = Py_SIZE(argdefs);
    }
    else {
        d = NULL;
        nd = 0;
    }
    result = PyEval_EvalCodeEx((PyObject*)co, globals, (PyObject *)NULL,
                               args, (int)nargs,
                               k, (int)nk,
                               d, (int)nd, kwdefs, closure);
    Py_XDECREF(kwtuple);
done:
    Py_LeaveRecursiveCall();
    return result;
}
#endif

/* PyObjectCall */
#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw) {
    PyObject *result;
    ternaryfunc call = Py_TYPE(func)->tp_call;
    if (unlikely(!call))
        return PyObject_Call(func, arg, kw);
    if (unlikely(Py_EnterRecursiveCall(" while calling a Python object")))
        return NULL;
    result = (*call)(func, arg, kw);
    Py_LeaveRecursiveCall();
    if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
        PyErr_SetString(
            PyExc_SystemError,
            "NULL result without error in PyObject_Call");
    }
    return result;
}
#endif

/* PyObjectCallMethO */
#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg) {
    PyObject *self, *result;
    PyCFunction cfunc;
    cfunc = __Pyx_CyOrPyCFunction_GET_FUNCTION(func);
    self = __Pyx_CyOrPyCFunction_GET_SELF(func);
    if (unlikely(Py_EnterRecursiveCall(" while calling a Python object")))
        return NULL;
    result = cfunc(self, arg);
    Py_LeaveRecursiveCall();
    if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
        PyErr_SetString(
            PyExc_SystemError,
            "NULL result without error in PyObject_Call");
    }
    return result;
}
#endif

/* PyObjectFastCall */
#if PY_VERSION_HEX < 0x03090000 || CYTHON_COMPILING_IN_LIMITED_API
static PyObject* __Pyx_PyObject_FastCall_fallback(PyObject *func, PyObject * const*args, size_t nargs, PyObject *kwargs) {
    PyObject *argstuple;
    PyObject *result = 0;
    size_t i;
    argstuple = PyTuple_New((Py_ssize_t)nargs);
    if (unlikely(!argstuple)) return NULL;
    for (i = 0; i < nargs; i++) {
        Py_INCREF(args[i]);
        if (__Pyx_PyTuple_SET_ITEM(argstuple, (Py_ssize_t)i, args[i]) != (0)) goto bad;
    }
    result = __Pyx_PyObject_Call(func, argstuple, kwargs);
  bad:
    Py_DECREF(argstuple);
    return result;
}
#endif
#if CYTHON_VECTORCALL && !CYTHON_COMPILING_IN_LIMITED_API
  #if PY_VERSION_HEX < 0x03090000
    #define __Pyx_PyVectorcall_Function(callable) _PyVectorcall_Function(callable)
  #elif CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE vectorcallfunc __Pyx_PyVectorcall_Function(PyObject *callable) {
    PyTypeObject *tp = Py_TYPE(callable);
    #if defined(__Pyx_CyFunction_USED)
    if (__Pyx_CyFunction_CheckExact(callable)) {
        return __Pyx_CyFunction_func_vectorcall(callable);
    }
    #endif
    if (!PyType_HasFeature(tp, Py_TPFLAGS_HAVE_VECTORCALL)) {
        return NULL;
    }
    assert(PyCallable_Check(callable));
    Py_ssize_t offset = tp->tp_vectorcall_offset;
    assert(offset > 0);
    vectorcallfunc ptr;
    memcpy(&ptr, (char *) callable + offset, sizeof(ptr));
    return ptr;
}
  #else
    #define __Pyx_PyVectorcall_Function(callable) PyVectorcall_Function(callable)
  #endif
#endif
static CYTHON_INLINE PyObject* __Pyx_PyObject_FastCallDict(PyObject *func, PyObject *const *args, size_t _nargs, PyObject *kwargs) {
    Py_ssize_t nargs = __Pyx_PyVectorcall_NARGS(_nargs);
#if CYTHON_COMPILING_IN_CPYTHON
    if (nargs == 0 && kwargs == NULL) {
        if (__Pyx_CyOrPyCFunction_Check(func) && likely( __Pyx_CyOrPyCFunction_GET_FLAGS(func) & METH_NOARGS))
            return __Pyx_PyObject_CallMethO(func, NULL);
    }
    else if (nargs == 1 && kwargs == NULL) {
        if (__Pyx_CyOrPyCFunction_Check(func) && likely( __Pyx_CyOrPyCFunction_GET_FLAGS(func) & METH_O))
            return __Pyx_PyObject_CallMethO(func, args[0]);
    }
#endif
    #if PY_VERSION_HEX < 0x030800B1
    #if CYTHON_FAST_PYCCALL
    if (PyCFunction_Check(func)) {
        if (kwargs) {
            return _PyCFunction_FastCallDict(func, args, nargs, kwargs);
        } else {
            return _PyCFunction_FastCallKeywords(func, args, nargs, NULL);
        }
    }
    if (!kwargs && __Pyx_IS_TYPE(func, &PyMethodDescr_Type)) {
        return _PyMethodDescr_FastCallKeywords(func, args, nargs, NULL);
    }
    #endif
    #if CYTHON_FAST_PYCALL
    if (PyFunction_Check(func)) {
        return __Pyx_PyFunction_FastCallDict(func, args, nargs, kwargs);
    }
    #endif
    #endif
    if (kwargs == NULL) {
        #if CYTHON_VECTORCALL && !CYTHON_COMPILING_IN_LIMITED_API
        vectorcallfunc f = __Pyx_PyVectorcall_Function(func);
        if (f) {
            return f(func, args, _nargs, NULL);
        }
        #elif defined(__Pyx_CyFunction_USED) && CYTHON_BACKPORT_VECTORCALL
        if (__Pyx_CyFunction_CheckExact(func)) {
            __pyx_vectorcallfunc f = __Pyx_CyFunction_func_vectorcall(func);
            if (f) return f(func, args, _nargs, NULL);
        }
        #elif CYTHON_COMPILING_IN_LIMITED_API && CYTHON_VECTORCALL
        return PyObject_Vectorcall(func, args, _nargs, NULL);
        #endif
    }
    if (nargs == 0) {
        return __Pyx_PyObject_Call(func, __pyx_mstate_global->__pyx_empty_tuple, kwargs);
    }
    #if PY_VERSION_HEX >= 0x03090000 && !CYTHON_COMPILING_IN_LIMITED_API
    return PyObject_VectorcallDict(func, args, (size_t)nargs, kwargs);
    #else
    return __Pyx_PyObject_FastCall_fallback(func, args, (size_t)nargs, kwargs);
    #endif
}

/* UnpackUnboundCMethod */
#if CYTHON_COMPILING_IN_LIMITED_API && __PYX_LIMITED_VERSION_HEX < 0x030C0000
static PyObject *__Pyx_SelflessCall(PyObject *method, PyObject *args, PyObject *kwargs) {
    PyObject *result;
    PyObject *selfless_args = PyTuple_GetSlice(args, 1, PyTuple_Size(args));
    if (unlikely(!selfless_args)) return NULL;
    result = PyObject_Call(method, selfless_args, kwargs);
    Py_DECREF(selfless_args);
    return result;
}
#elif CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03090000
static PyObject *__Pyx_SelflessCall(PyObject *method, PyObject **args, Py_ssize_t nargs, PyObject *kwnames) {
        return _PyObject_Vectorcall
            (method, args ? args+1 : NULL, nargs ? nargs-1 : 0, kwnames);
}
#else
static PyObject *__Pyx_SelflessCall(PyObject *method, PyObject *const *args, Py_ssize_t nargs, PyObject *kwnames) {
    return
#if PY_VERSION_HEX < 0x03090000
    _PyObject_Vectorcall
#else
    PyObject_Vectorcall
#endif
        (method, args ? args+1 : NULL, nargs ? (size_t) nargs-1 : 0, kwnames);
}
#endif
static PyMethodDef __Pyx_UnboundCMethod_Def = {
     "CythonUnboundCMethod",
     __PYX_REINTERPRET_FUNCION(PyCFunction, __Pyx_SelflessCall),
#if CYTHON_COMPILING_IN_LIMITED_API && __PYX_LIMITED_VERSION_HEX < 0x030C0000
     METH_VARARGS | METH_KEYWORDS,
#else
     METH_FASTCALL | METH_KEYWORDS,
#endif
     NULL
};
static int __Pyx_TryUnpackUnboundCMethod(__Pyx_CachedCFunction* target) {
    PyObject *method, *result=NULL;
    method = __Pyx_PyObject_GetAttrStr(target->type, *target->method_name);
    if (unlikely(!method))
        return -1;
    result = method;
#if CYTHON_COMPILING_IN_CPYTHON
    if (likely(__Pyx_TypeCheck(method, &PyMethodDescr_Type)))
    {
        PyMethodDescrObject *descr = (PyMethodDescrObject*) method;
        target->func = descr->d_method->ml_meth;
        target->flag = descr->d_method->ml_flags & ~(METH_CLASS | METH_STATIC | METH_COEXIST | METH_STACKLESS);
    } else
#endif
#if CYTHON_COMPILING_IN_PYPY
#else
    if (PyCFunction_Check(method))
#endif
    {
        PyObject *self;
        int self_found;
#if CYTHON_COMPILING_IN_LIMITED_API || CYTHON_COMPILING_IN_PYPY
        self = PyObject_GetAttrString(method, "__self__");
        if (!self) {
            PyErr_Clear();
        }
#else
        self = PyCFunction_GET_SELF(method);
#endif
        self_found = (self && self != Py_None);
#if CYTHON_COMPILING_IN_LIMITED_API || CYTHON_COMPILING_IN_PYPY
        Py_XDECREF(self);
#endif
        if (self_found) {
            PyObject *unbound_method = PyCFunction_New(&__Pyx_UnboundCMethod_Def, method);
            if (unlikely(!unbound_method)) return -1;
            Py_DECREF(method);
            result = unbound_method;
        }
    }
#if !CYTHON_COMPILING_IN_CPYTHON_FREETHREADING
    if (unlikely(target->method)) {
        Py_DECREF(result);
    } else
#endif
    target->method = result;
    return 0;
}

/* CallUnboundCMethod2 */
#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject *__Pyx_CallUnboundCMethod2(__Pyx_CachedCFunction *cfunc, PyObject *self, PyObject *arg1, PyObject *arg2) {
    int was_initialized = __Pyx_CachedCFunction_GetAndSetInitializing(cfunc);
    if (likely(was_initialized == 2 && cfunc->func)) {
        PyObject *args[2] = {arg1, arg2};
        if (cfunc->flag == METH_FASTCALL) {
            return __Pyx_CallCFunctionFast(cfunc, self, args, 2);
        }
        if (cfunc->flag == (METH_FASTCALL | METH_KEYWORDS))
            return __Pyx_CallCFunctionFastWithKeywords(cfunc, self, args, 2, NULL);
    }
#if CYTHON_COMPILING_IN_CPYTHON_FREETHREADING
    else if (unlikely(was_initialized == 1)) {
        __Pyx_CachedCFunction tmp_cfunc = {
#ifndef __cplusplus
            0
#endif
        };
        tmp_cfunc.type = cfunc->type;
        tmp_cfunc.method_name = cfunc->method_name;
        return __Pyx__CallUnboundCMethod2(&tmp_cfunc, self, arg1, arg2);
    }
#endif
    PyObject *result = __Pyx__CallUnboundCMethod2(cfunc, self, arg1, arg2);
    __Pyx_CachedCFunction_SetFinishedInitializing(cfunc);
    return result;
}
#endif
static PyObject* __Pyx__CallUnboundCMethod2(__Pyx_CachedCFunction* cfunc, PyObject* self, PyObject* arg1, PyObject* arg2){
    if (unlikely(!cfunc->func && !cfunc->method) && unlikely(__Pyx_TryUnpackUnboundCMethod(cfunc) < 0)) return NULL;
#if CYTHON_COMPILING_IN_CPYTHON
    if (cfunc->func && (cfunc->flag & METH_VARARGS)) {
        PyObject *result = NULL;
        PyObject *args = PyTuple_New(2);
        if (unlikely(!args)) return NULL;
        Py_INCREF(arg1);
        PyTuple_SET_ITEM(args, 0, arg1);
        Py_INCREF(arg2);
        PyTuple_SET_ITEM(args, 1, arg2);
        if (cfunc->flag & METH_KEYWORDS)
            result = __Pyx_CallCFunctionWithKeywords(cfunc, self, args, NULL);
        else
            result = __Pyx_CallCFunction(cfunc, self, args);
        Py_DECREF(args);
        return result;
    }
#endif
    {
        PyObject *args[4] = {NULL, self, arg1, arg2};
        return __Pyx_PyObject_FastCall(cfunc->method, args+1, 3 | __Pyx_PY_VECTORCALL_ARGUMENTS_OFFSET);
    }
}

/* ParseKeywords */
static int __Pyx_ValidateDuplicatePosArgs(
    PyObject *kwds,
    PyObject ** const argnames[],
    PyObject ** const *first_kw_arg,
    const char* function_name)
{
    PyObject ** const *name = argnames;
    while (name != first_kw_arg) {
        PyObject *key = **name;
        int found = PyDict_Contains(kwds, key);
        if (unlikely(found)) {
            if (found == 1) __Pyx_RaiseDoubleKeywordsError(function_name, key);
            goto bad;
        }
        name++;
    }
    return 0;
bad:
    return -1;
}
#if CYTHON_USE_UNICODE_INTERNALS
static CYTHON_INLINE int __Pyx_UnicodeKeywordsEqual(PyObject *s1, PyObject *s2) {
    int kind;
    Py_ssize_t len = PyUnicode_GET_LENGTH(s1);
    if (len != PyUnicode_GET_LENGTH(s2)) return 0;
    kind = PyUnicode_KIND(s1);
    if (kind != PyUnicode_KIND(s2)) return 0;
    const void *data1 = PyUnicode_DATA(s1);
    const void *data2 = PyUnicode_DATA(s2);
    return (memcmp(data1, data2, (size_t) len * (size_t) kind) == 0);
}
#endif
static int __Pyx_MatchKeywordArg_str(
    PyObject *key,
    PyObject ** const argnames[],
    PyObject ** const *first_kw_arg,
    size_t *index_found,
    const char *function_name)
{
    PyObject ** const *name;
    #if CYTHON_USE_UNICODE_INTERNALS
    Py_hash_t key_hash = ((PyASCIIObject*)key)->hash;
    if (unlikely(key_hash == -1)) {
        key_hash = PyObject_Hash(key);
        if (unlikely(key_hash == -1))
            goto bad;
    }
    #endif
    name = first_kw_arg;
    while (*name) {
        PyObject *name_str = **name;
        #if CYTHON_USE_UNICODE_INTERNALS
        if (key_hash == ((PyASCIIObject*)name_str)->hash && __Pyx_UnicodeKeywordsEqual(name_str, key)) {
            *index_found = (size_t) (name - argnames);
            return 1;
        }
        #else
        #if CYTHON_ASSUME_SAFE_SIZE
        if (PyUnicode_GET_LENGTH(name_str) == PyUnicode_GET_LENGTH(key))
        #endif
        {
            int cmp = PyUnicode_Compare(name_str, key);
            if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
            if (cmp == 0) {
                *index_found = (size_t) (name - argnames);
                return 1;
            }
        }
        #endif
        name++;
    }
    name = argnames;
    while (name != first_kw_arg) {
        PyObject *name_str = **name;
        #if CYTHON_USE_UNICODE_INTERNALS
        if (unlikely(key_hash == ((PyASCIIObject*)name_str)->hash)) {
            if (__Pyx_UnicodeKeywordsEqual(name_str, key))
                goto arg_passed_twice;
        }
        #else
        #if CYTHON_ASSUME_SAFE_SIZE
        if (PyUnicode_GET_LENGTH(name_str) == PyUnicode_GET_LENGTH(key))
        #endif
        {
            if (unlikely(name_str == key)) goto arg_passed_twice;
            int cmp = PyUnicode_Compare(name_str, key);
            if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
            if (cmp == 0) goto arg_passed_twice;
        }
        #endif
        name++;
    }
    return 0;
arg_passed_twice:
    __Pyx_RaiseDoubleKeywordsError(function_name, key);
    goto bad;
bad:
    return -1;
}
static int __Pyx_MatchKeywordArg_nostr(
    PyObject *key,
    PyObject ** const argnames[],
    PyObject ** const *first_kw_arg,
    size_t *index_found,
    const char *function_name)
{
    PyObject ** const *name;
    if (unlikely(!PyUnicode_Check(key))) goto invalid_keyword_type;
    name = first_kw_arg;
    while (*name) {
        int cmp = PyObject_RichCompareBool(**name, key, Py_EQ);
        if (cmp == 1) {
            *index_found = (size_t) (name - argnames);
            return 1;
        }
        if (unlikely(cmp == -1)) goto bad;
        name++;
    }
    name = argnames;
    while (name != first_kw_arg) {
        int cmp = PyObject_RichCompareBool(**name, key, Py_EQ);
        if (unlikely(cmp != 0)) {
            if (cmp == 1) goto arg_passed_twice;
            else goto bad;
        }
        name++;
    }
    return 0;
arg_passed_twice:
    __Pyx_RaiseDoubleKeywordsError(function_name, key);
    goto bad;
invalid_keyword_type:
    PyErr_Format(PyExc_TypeError,
        "%.200s() keywords must be strings", function_name);
    goto bad;
bad:
    return -1;
}
static CYTHON_INLINE int __Pyx_MatchKeywordArg(
    PyObject *key,
    PyObject ** const argnames[],
    PyObject ** const *first_kw_arg,
    size_t *index_found,
    const char *function_name)
{
    return likely(PyUnicode_CheckExact(key)) ?
        __Pyx_MatchKeywordArg_str(key, argnames, first_kw_arg, index_found, function_name) :
        __Pyx_MatchKeywordArg_nostr(key, argnames, first_kw_arg, index_found, function_name);
}
static void __Pyx_RejectUnknownKeyword(
    PyObject *kwds,
    PyObject ** const argnames[],
    PyObject ** const *first_kw_arg,
    const char *function_name)
{
    Py_ssize_t pos = 0;
    PyObject *key = NULL;
    __Pyx_BEGIN_CRITICAL_SECTION(kwds);
    while (PyDict_Next(kwds, &pos, &key, NULL)) {
        PyObject** const *name = first_kw_arg;
        while (*name && (**name != key)) name++;
        if (!*name) {
            #if CYTHON_AVOID_BORROWED_REFS
            Py_INCREF(key);
            #endif
            size_t index_found = 0;
            int cmp = __Pyx_MatchKeywordArg(key, argnames, first_kw_arg, &index_found, function_name);
            if (cmp != 1) {
                if (cmp == 0) {
                    PyErr_Format(PyExc_TypeError,
                        "%s() got an unexpected keyword argument '%U'",
                        function_name, key);
                }
                #if CYTHON_AVOID_BORROWED_REFS
                Py_DECREF(key);
                #endif
                break;
            }
            #if CYTHON_AVOID_BORROWED_REFS
            Py_DECREF(key);
            #endif
        }
    }
    __Pyx_END_CRITICAL_SECTION();
    assert(PyErr_Occurred());
}
static int __Pyx_ParseKeywordDict(
    PyObject *kwds,
    PyObject ** const argnames[],
    PyObject *values[],
    Py_ssize_t num_pos_args,
    Py_ssize_t num_kwargs,
    const char* function_name,
    int ignore_unknown_kwargs)
{
    PyObject** const *name;
    PyObject** const *first_kw_arg = argnames + num_pos_args;
    Py_ssize_t extracted = 0;
#if !CYTHON_COMPILING_IN_PYPY || defined(PyArg_ValidateKeywordArguments)
    if (unlikely(!PyArg_ValidateKeywordArguments(kwds))) return -1;
#endif
    name = first_kw_arg;
    while (*name && num_kwargs > extracted) {
        PyObject * key = **name;
        PyObject *value;
        int found = 0;
        #if __PYX_LIMITED_VERSION_HEX >= 0x030d0000
        found = PyDict_GetItemRef(kwds, key, &value);
        #else
        value = PyDict_GetItemWithError(kwds, key);
        if (value) {
            Py_INCREF(value);
            found = 1;
        } else {
            if (unlikely(PyErr_Occurred())) goto bad;
        }
        #endif
        if (found) {
            if (unlikely(found < 0)) goto bad;
            values[name-argnames] = value;
            extracted++;
        }
        name++;
    }
    if (num_kwargs > extracted) {
        if (ignore_unknown_kwargs) {
            if (unlikely(__Pyx_ValidateDuplicatePosArgs(kwds, argnames, first_kw_arg, function_name) == -1))
                goto bad;
        } else {
            __Pyx_RejectUnknownKeyword(kwds, argnames, first_kw_arg, function_name);
            goto bad;
        }
    }
    return 0;
bad:
    return -1;
}
static int __Pyx_ParseKeywordDictToDict(
    PyObject *kwds,
    PyObject ** const argnames[],
    PyObject *kwds2,
    PyObject *values[],
    Py_ssize_t num_pos_args,
    const char* function_name)
{
    PyObject** const *name;
    PyObject** const *first_kw_arg = argnames + num_pos_args;
    Py_ssize_t len;
#if !CYTHON_COMPILING_IN_PYPY || defined(PyArg_ValidateKeywordArguments)
    if (unlikely(!PyArg_ValidateKeywordArguments(kwds))) return -1;
#endif
    if (PyDict_Update(kwds2, kwds) < 0) goto bad;
    name = first_kw_arg;
    while (*name) {
        PyObject *key = **name;
        PyObject *value;
#if !CYTHON_COMPILING_IN_LIMITED_API && (PY_VERSION_HEX >= 0x030d00A2 || defined(PyDict_Pop))
        int found = PyDict_Pop(kwds2, key, &value);
        if (found) {
            if (unlikely(found < 0)) goto bad;
            values[name-argnames] = value;
        }
#elif __PYX_LIMITED_VERSION_HEX >= 0x030d0000
        int found = PyDict_GetItemRef(kwds2, key, &value);
        if (found) {
            if (unlikely(found < 0)) goto bad;
            values[name-argnames] = value;
            if (unlikely(PyDict_DelItem(kwds2, key) < 0)) goto bad;
        }
#else
    #if CYTHON_COMPILING_IN_CPYTHON
        value = _PyDict_Pop(kwds2, key, kwds2);
    #else
        value = __Pyx_CallUnboundCMethod2(&__pyx_mstate_global->__pyx_umethod_PyDict_Type_pop, kwds2, key, kwds2);
    #endif
        if (value == kwds2) {
            Py_DECREF(value);
        } else {
            if (unlikely(!value)) goto bad;
            values[name-argnames] = value;
        }
#endif
        name++;
    }
    len = PyDict_Size(kwds2);
    if (len > 0) {
        return __Pyx_ValidateDuplicatePosArgs(kwds, argnames, first_kw_arg, function_name);
    } else if (unlikely(len == -1)) {
        goto bad;
    }
    return 0;
bad:
    return -1;
}
static int __Pyx_ParseKeywordsTuple(
    PyObject *kwds,
    PyObject * const *kwvalues,
    PyObject ** const argnames[],
    PyObject *kwds2,
    PyObject *values[],
    Py_ssize_t num_pos_args,
    Py_ssize_t num_kwargs,
    const char* function_name,
    int ignore_unknown_kwargs)
{
    PyObject *key = NULL;
    PyObject** const * name;
    PyObject** const *first_kw_arg = argnames + num_pos_args;
    for (Py_ssize_t pos = 0; pos < num_kwargs; pos++) {
#if CYTHON_AVOID_BORROWED_REFS
        key = __Pyx_PySequence_ITEM(kwds, pos);
#else
        key = __Pyx_PyTuple_GET_ITEM(kwds, pos);
#endif
#if !CYTHON_ASSUME_SAFE_MACROS
        if (unlikely(!key)) goto bad;
#endif
        name = first_kw_arg;
        while (*name && (**name != key)) name++;
        if (*name) {
            PyObject *value = kwvalues[pos];
            values[name-argnames] = __Pyx_NewRef(value);
        } else {
            size_t index_found = 0;
            int cmp = __Pyx_MatchKeywordArg(key, argnames, first_kw_arg, &index_found, function_name);
            if (cmp == 1) {
                PyObject *value = kwvalues[pos];
                values[index_found] = __Pyx_NewRef(value);
            } else {
                if (unlikely(cmp == -1)) goto bad;
                if (kwds2) {
                    PyObject *value = kwvalues[pos];
                    if (unlikely(PyDict_SetItem(kwds2, key, value))) goto bad;
                } else if (!ignore_unknown_kwargs) {
                    goto invalid_keyword;
                }
            }
        }
        #if CYTHON_AVOID_BORROWED_REFS
        Py_DECREF(key);
        key = NULL;
        #endif
    }
    return 0;
invalid_keyword:
    PyErr_Format(PyExc_TypeError,
        "%s() got an unexpected keyword argument '%U'",
        function_name, key);
    goto bad;
bad:
    #if CYTHON_AVOID_BORROWED_REFS
    Py_XDECREF(key);
    #endif
    return -1;
}
static int __Pyx_ParseKeywords(
    PyObject *kwds,
    PyObject * const *kwvalues,
    PyObject ** const argnames[],
    PyObject *kwds2,
    PyObject *values[],
    Py_ssize_t num_pos_args,
    Py_ssize_t num_kwargs,
    const char* function_name,
    int ignore_unknown_kwargs)
{
    if (CYTHON_METH_FASTCALL && likely(PyTuple_Check(kwds)))
        return __Pyx_ParseKeywordsTuple(kwds, kwvalues, argnames, kwds2, values, num_pos_args, num_kwargs, function_name, ignore_unknown_kwargs);
    else if (kwds2)
        return __Pyx_ParseKeywordDictToDict(kwds, argnames, kwds2, values, num_pos_args, function_name);
    else
        return __Pyx_ParseKeywordDict(kwds, argnames, values, num_pos_args, num_kwargs, function_name, ignore_unknown_kwargs);
}

/* RaiseArgTupleInvalid */
static void __Pyx_RaiseArgtupleInvalid(
    const char* func_name,
    int exact,
    Py_ssize_t num_min,
    Py_ssize_t num_max,
    Py_ssize_t num_found)
{
    Py_ssize_t num_expected;
    const char *more_or_less;
    if (num_found < num_min) {
        num_expected = num_min;
        more_or_less = "at least";
    } else {
        num_expected = num_max;
        more_or_less = "at most";
    }
    if (exact) {
        more_or_less = "exactly";
    }
    PyErr_Format(PyExc_TypeError,
                 "%.200s() takes %.8s %" CYTHON_FORMAT_SSIZE_T "d positional argument%.1s (%" CYTHON_FORMAT_SSIZE_T "d given)",
                 func_name, more_or_less, num_expected,
                 (num_expected == 1) ? "" : "s", num_found);
}

/* ArgTypeTest */
static int __Pyx__ArgTypeTest(PyObject *obj, PyTypeObject *type, const char *name, int exact)
{
    __Pyx_TypeName type_name;
    __Pyx_TypeName obj_type_name;
    PyObject *extra_info = __pyx_mstate_global->__pyx_empty_unicode;
    int from_annotation_subclass = 0;
    if (unlikely(!type)) {
        PyErr_SetString(PyExc_SystemError, "Missing type object");
        return 0;
    }
    else if (!exact) {
        if (likely(__Pyx_TypeCheck(obj, type))) return 1;
    } else if (exact == 2) {
        if (__Pyx_TypeCheck(obj, type)) {
            from_annotation_subclass = 1;
            extra_info = __pyx_mstate_global->__pyx_kp_u_Note_that_Cython_is_deliberately;
        }
    }
    type_name = __Pyx_PyType_GetFullyQualifiedName(type);
    obj_type_name = __Pyx_PyType_GetFullyQualifiedName(Py_TYPE(obj));
    PyErr_Format(PyExc_TypeError,
        "Argument '%.200s' has incorrect type (expected " __Pyx_FMT_TYPENAME
        ", got " __Pyx_FMT_TYPENAME ")"
#if __PYX_LIMITED_VERSION_HEX < 0x030C0000
        "%s%U"
#endif
        , name, type_name, obj_type_name
#if __PYX_LIMITED_VERSION_HEX < 0x030C0000
        , (from_annotation_subclass ? ". " : ""), extra_info
#endif
        );
#if __PYX_LIMITED_VERSION_HEX >= 0x030C0000
    if (exact == 2 && from_annotation_subclass) {
        PyObject *res;
        PyObject *vargs[2];
        vargs[0] = PyErr_GetRaisedException();
        vargs[1] = extra_info;
        res = PyObject_VectorcallMethod(__pyx_mstate_global->__pyx_kp_u_add_note, vargs, 2, NULL);
        Py_XDECREF(res);
        PyErr_SetRaisedException(vargs[0]);
    }
#endif
    __Pyx_DECREF_TypeName(type_name);
    __Pyx_DECREF_TypeName(obj_type_name);
    return 0;
}

/* RaiseException */
static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause) {
    PyObject* owned_instance = NULL;
    if (tb == Py_None) {
        tb = 0;
    } else if (tb && !PyTraceBack_Check(tb)) {
        PyErr_SetString(PyExc_TypeError,
            "raise: arg 3 must be a traceback or None");
        goto bad;
    }
    if (value == Py_None)
        value = 0;
    if (PyExceptionInstance_Check(type)) {
        if (value) {
            PyErr_SetString(PyExc_TypeError,
                "instance exception may not have a separate value");
            goto bad;
        }
        value = type;
        type = (PyObject*) Py_TYPE(value);
    } else if (PyExceptionClass_Check(type)) {
        PyObject *instance_class = NULL;
        if (value && PyExceptionInstance_Check(value)) {
            instance_class = (PyObject*) Py_TYPE(value);
            if (instance_class != type) {
                int is_subclass = PyObject_IsSubclass(instance_class, type);
                if (!is_subclass) {
                    instance_class = NULL;
                } else if (unlikely(is_subclass == -1)) {
                    goto bad;
                } else {
                    type = instance_class;
                }
            }
        }
        if (!instance_class) {
            PyObject *args;
            if (!value)
                args = PyTuple_New(0);
            else if (PyTuple_Check(value)) {
                Py_INCREF(value);
                args = value;
            } else
                args = PyTuple_Pack(1, value);
            if (!args)
                goto bad;
            owned_instance = PyObject_Call(type, args, NULL);
            Py_DECREF(args);
            if (!owned_instance)
                goto bad;
            value = owned_instance;
            if (!PyExceptionInstance_Check(value)) {
                PyErr_Format(PyExc_TypeError,
                             "calling %R should have returned an instance of "
                             "BaseException, not %R",
                             type, Py_TYPE(value));
                goto bad;
            }
        }
    } else {
        PyErr_SetString(PyExc_TypeError,
            "raise: exception class must be a subclass of BaseException");
        goto bad;
    }
    if (cause) {
        PyObject *fixed_cause;
        if (cause == Py_None) {
            fixed_cause = NULL;
        } else if (PyExceptionClass_Check(cause)) {
            fixed_cause = PyObject_CallObject(cause, NULL);
            if (fixed_cause == NULL)
                goto bad;
        } else if (PyExceptionInstance_Check(cause)) {
            fixed_cause = cause;
            Py_INCREF(fixed_cause);
        } else {
            PyErr_SetString(PyExc_TypeError,
                            "exception causes must derive from "
                            "BaseException");
            goto bad;
        }
        PyException_SetCause(value, fixed_cause);
    }
    PyErr_SetObject(type, value);
    if (tb) {
#if PY_VERSION_HEX >= 0x030C00A6
        PyException_SetTraceback(value, tb);
#elif CYTHON_FAST_THREAD_STATE
        PyThreadState *tstate = __Pyx_PyThreadState_Current;
        PyObject* tmp_tb = tstate->curexc_traceback;
        if (tb != tmp_tb) {
            Py_INCREF(tb);
            tstate->curexc_traceback = tb;
            Py_XDECREF(tmp_tb);
        }
#else
        PyObject *tmp_type, *tmp_value, *tmp_tb;
        PyErr_Fetch(&tmp_type, &tmp_value, &tmp_tb);
        Py_INCREF(tb);
        PyErr_Restore(tmp_type, tmp_value, tb);
        Py_XDECREF(tmp_tb);
#endif
    }
bad:
    Py_XDECREF(owned_instance);
    return;
}

/* PyObjectFastCallMethod */
#if !CYTHON_VECTORCALL || PY_VERSION_HEX < 0x03090000
static PyObject *__Pyx_PyObject_FastCallMethod(PyObject *name, PyObject *const *args, size_t nargsf) {
    PyObject *result;
    PyObject *attr = PyObject_GetAttr(args[0], name);
    if (unlikely(!attr))
        return NULL;
    result = __Pyx_PyObject_FastCall(attr, args+1, nargsf - 1);
    Py_DECREF(attr);
    return result;
}
#endif

/* RaiseUnexpectedTypeError */
static int
__Pyx_RaiseUnexpectedTypeError(const char *expected, PyObject *obj)
{
    __Pyx_TypeName obj_type_name = __Pyx_PyType_GetFullyQualifiedName(Py_TYPE(obj));
    PyErr_Format(PyExc_TypeError, "Expected %s, got " __Pyx_FMT_TYPENAME,
                 expected, obj_type_name);
    __Pyx_DECREF_TypeName(obj_type_name);
    return 0;
}

/* CIntToDigits */
static const char DIGIT_PAIRS_10[2*10*10+1] = {
    "00010203040506070809"
    "10111213141516171819"
    "20212223242526272829"
    "30313233343536373839"
    "40414243444546474849"
    "50515253545556575859"
    "60616263646566676869"
    "70717273747576777879"
    "80818283848586878889"
    "90919293949596979899"
};
static const char DIGIT_PAIRS_8[2*8*8+1] = {
    "0001020304050607"
    "1011121314151617"
    "2021222324252627"
    "3031323334353637"
    "4041424344454647"
    "5051525354555657"
    "6061626364656667"
    "7071727374757677"
};
static const char DIGITS_HEX[2*16+1] = {
    "0123456789abcdef"
    "0123456789ABCDEF"
};

/* BuildPyUnicode */
static PyObject* __Pyx_PyUnicode_BuildFromAscii(Py_ssize_t ulength, const char* chars, int clength,
                                                int prepend_sign, char padding_char) {
    PyObject *uval;
    Py_ssize_t uoffset = ulength - clength;
#if CYTHON_USE_UNICODE_INTERNALS
    Py_ssize_t i;
    void *udata;
    uval = PyUnicode_New(ulength, 127);
    if (unlikely(!uval)) return NULL;
    udata = PyUnicode_DATA(uval);
    if (uoffset > 0) {
        i = 0;
        if (prepend_sign) {
            __Pyx_PyUnicode_WRITE(PyUnicode_1BYTE_KIND, udata, 0, '-');
            i++;
        }
        for (; i < uoffset; i++) {
            __Pyx_PyUnicode_WRITE(PyUnicode_1BYTE_KIND, udata, i, padding_char);
        }
    }
    for (i=0; i < clength; i++) {
        __Pyx_PyUnicode_WRITE(PyUnicode_1BYTE_KIND, udata, uoffset+i, chars[i]);
    }
#else
    {
        PyObject *sign = NULL, *padding = NULL;
        uval = NULL;
        if (uoffset > 0) {
            prepend_sign = !!prepend_sign;
            if (uoffset > prepend_sign) {
                padding = PyUnicode_FromOrdinal(padding_char);
                if (likely(padding) && uoffset > prepend_sign + 1) {
                    PyObject *tmp = PySequence_Repeat(padding, uoffset - prepend_sign);
                    Py_DECREF(padding);
                    padding = tmp;
                }
                if (unlikely(!padding)) goto done_or_error;
            }
            if (prepend_sign) {
                sign = PyUnicode_FromOrdinal('-');
                if (unlikely(!sign)) goto done_or_error;
            }
        }
        uval = PyUnicode_DecodeASCII(chars, clength, NULL);
        if (likely(uval) && padding) {
            PyObject *tmp = PyUnicode_Concat(padding, uval);
            Py_DECREF(uval);
            uval = tmp;
        }
        if (likely(uval) && sign) {
            PyObject *tmp = PyUnicode_Concat(sign, uval);
            Py_DECREF(uval);
            uval = tmp;
        }
done_or_error:
        Py_XDECREF(padding);
        Py_XDECREF(sign);
    }
#endif
    return uval;
}

/* COrdinalToPyUnicode */
static CYTHON_INLINE int __Pyx_CheckUnicodeValue(int value) {
    return value <= 1114111;
}
static PyObject* __Pyx_PyUnicode_FromOrdinal_Padded(int value, Py_ssize_t ulength, char padding_char) {
    if (likely(ulength <= 250)) {
        char chars[256];
        if (value <= 255) {
            memset(chars, padding_char, (size_t) (ulength - 1));
            chars[ulength-1] = (char) value;
            return PyUnicode_DecodeLatin1(chars, ulength, NULL);
        }
        char *cpos = chars + sizeof(chars);
        if (value < 0x800) {
            *--cpos = (char) (0x80 | (value & 0x3f));
            value >>= 6;
            *--cpos = (char) (0xc0 | (value & 0x1f));
        } else if (value < 0x10000) {
            *--cpos = (char) (0x80 | (value & 0x3f));
            value >>= 6;
            *--cpos = (char) (0x80 | (value & 0x3f));
            value >>= 6;
            *--cpos = (char) (0xe0 | (value & 0x0f));
        } else {
            *--cpos = (char) (0x80 | (value & 0x3f));
            value >>= 6;
            *--cpos = (char) (0x80 | (value & 0x3f));
            value >>= 6;
            *--cpos = (char) (0x80 | (value & 0x3f));
            value >>= 6;
            *--cpos = (char) (0xf0 | (value & 0x07));
        }
        cpos -= ulength;
        memset(cpos, padding_char, (size_t) (ulength - 1));
        return PyUnicode_DecodeUTF8(cpos, chars + sizeof(chars) - cpos, NULL);
    }
    if (value <= 127 && CYTHON_USE_UNICODE_INTERNALS) {
        const char chars[1] = {(char) value};
        return __Pyx_PyUnicode_BuildFromAscii(ulength, chars, 1, 0, padding_char);
    }
    {
        PyObject *uchar, *padding_uchar, *padding, *result;
        padding_uchar = PyUnicode_FromOrdinal(padding_char);
        if (unlikely(!padding_uchar)) return NULL;
        padding = PySequence_Repeat(padding_uchar, ulength - 1);
        Py_DECREF(padding_uchar);
        if (unlikely(!padding)) return NULL;
        uchar = PyUnicode_FromOrdinal(value);
        if (unlikely(!uchar)) {
            Py_DECREF(padding);
            return NULL;
        }
        result = PyUnicode_Concat(padding, uchar);
        Py_DECREF(padding);
        Py_DECREF(uchar);
        return result;
    }
}

/* CIntToPyUnicode */
static CYTHON_INLINE PyObject* __Pyx_PyUnicode_From_int(int value, Py_ssize_t width, char padding_char, char format_char) {
    char digits[sizeof(int)*3+2];
    char *dpos, *end = digits + sizeof(int)*3+2;
    const char *hex_digits = DIGITS_HEX;
    Py_ssize_t length, ulength;
    int prepend_sign, last_one_off;
    int remaining;
#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wconversion"
#endif
    const int neg_one = (int) -1, const_zero = (int) 0;
#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
#pragma GCC diagnostic pop
#endif
    const int is_unsigned = neg_one > const_zero;
    if (format_char == 'c') {
        if (unlikely(!(is_unsigned || value == 0 || value > 0) ||
                     !(sizeof(value) <= 2 || value & ~ (int) 0x01fffff || __Pyx_CheckUnicodeValue((int) value)))) {
            PyErr_SetString(PyExc_OverflowError, "%c arg not in range(0x110000)");
            return NULL;
        }
        if (width <= 1) {
            return PyUnicode_FromOrdinal((int) value);
        }
        return __Pyx_PyUnicode_FromOrdinal_Padded((int) value, width, padding_char);
    }
    if (format_char == 'X') {
        hex_digits += 16;
        format_char = 'x';
    }
    remaining = value;
    last_one_off = 0;
    dpos = end;
    do {
        int digit_pos;
        switch (format_char) {
        case 'o':
            digit_pos = abs((int)(remaining % (8*8)));
            remaining = (int) (remaining / (8*8));
            dpos -= 2;
            memcpy(dpos, DIGIT_PAIRS_8 + digit_pos * 2, 2);
            last_one_off = (digit_pos < 8);
            break;
        case 'd':
            digit_pos = abs((int)(remaining % (10*10)));
            remaining = (int) (remaining / (10*10));
            dpos -= 2;
            memcpy(dpos, DIGIT_PAIRS_10 + digit_pos * 2, 2);
            last_one_off = (digit_pos < 10);
            break;
        case 'x':
            *(--dpos) = hex_digits[abs((int)(remaining % 16))];
            remaining = (int) (remaining / 16);
            break;
        default:
            assert(0);
            break;
        }
    } while (unlikely(remaining != 0));
    assert(!last_one_off || *dpos == '0');
    dpos += last_one_off;
    length = end - dpos;
    ulength = length;
    prepend_sign = 0;
    if (!is_unsigned && value <= neg_one) {
        if (padding_char == ' ' || width <= length + 1) {
            *(--dpos) = '-';
            ++length;
        } else {
            prepend_sign = 1;
        }
        ++ulength;
    }
    if (width > ulength) {
        ulength = width;
    }
    if (ulength == 1) {
        return PyUnicode_FromOrdinal(*dpos);
    }
    return __Pyx_PyUnicode_BuildFromAscii(ulength, dpos, (int) length, prepend_sign, padding_char);
}

/* CIntToPyUnicode */
static CYTHON_INLINE PyObject* __Pyx_PyUnicode_From_Py_ssize_t(Py_ssize_t value, Py_ssize_t width, char padding_char, char format_char) {
    char digits[sizeof(Py_ssize_t)*3+2];
    char *dpos, *end = digits + sizeof(Py_ssize_t)*3+2;
    const char *hex_digits = DIGITS_HEX;
    Py_ssize_t length, ulength;
    int prepend_sign, last_one_off;
    Py_ssize_t remaining;
#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wconversion"
#endif
    const Py_ssize_t neg_one = (Py_ssize_t) -1, const_zero = (Py_ssize_t) 0;
#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
#pragma GCC diagnostic pop
#endif
    const int is_unsigned = neg_one > const_zero;
    if (format_char == 'c') {
        if (unlikely(!(is_unsigned || value == 0 || value > 0) ||
                     !(sizeof(value) <= 2 || value & ~ (Py_ssize_t) 0x01fffff || __Pyx_CheckUnicodeValue((int) value)))) {
            PyErr_SetString(PyExc_OverflowError, "%c arg not in range(0x110000)");
            return NULL;
        }
        if (width <= 1) {
            return PyUnicode_FromOrdinal((int) value);
        }
        return __Pyx_PyUnicode_FromOrdinal_Padded((int) value, width, padding_char);
    }
    if (format_char == 'X') {
        hex_digits += 16;
        format_char = 'x';
    }
    remaining = value;
    last_one_off = 0;
    dpos = end;
    do {
        int digit_pos;
        switch (format_char) {
        case 'o':
            digit_pos = abs((int)(remaining % (8*8)));
            remaining = (Py_ssize_t) (remaining / (8*8));
            dpos -= 2;
            memcpy(dpos, DIGIT_PAIRS_8 + digit_pos * 2, 2);
            last_one_off = (digit_pos < 8);
            break;
        case 'd':
            digit_pos = abs((int)(remaining % (10*10)));
            remaining = (Py_ssize_t) (remaining / (10*10));
            dpos -= 2;
            memcpy(dpos, DIGIT_PAIRS_10 + digit_pos * 2, 2);
            last_one_off = (digit_pos < 10);
            break;
        case 'x':
            *(--dpos) = hex_digits[abs((int)(remaining % 16))];
            remaining = (Py_ssize_t) (remaining / 16);
            break;
        default:
            assert(0);
            break;
        }
    } while (unlikely(remaining != 0));
    assert(!last_one_off || *dpos == '0');
    dpos += last_one_off;
    length = end - dpos;
    ulength = length;
    prepend_sign = 0;
    if (!is_unsigned && value <= neg_one) {
        if (padding_char == ' ' || width <= length + 1) {
            *(--dpos) = '-';
            ++length;
        } else {
            prepend_sign = 1;
        }
        ++ulength;
    }
    if (width > ulength) {
        ulength = width;
    }
    if (ulength == 1) {
        return PyUnicode_FromOrdinal(*dpos);
    }
    return __Pyx_PyUnicode_BuildFromAscii(ulength, dpos, (int) length, prepend_sign, padding_char);
}

/* JoinPyUnicode */
static PyObject* __Pyx_PyUnicode_Join(PyObject** values, Py_ssize_t value_count, Py_ssize_t result_ulength,
                                      Py_UCS4 max_char) {
#if CYTHON_USE_UNICODE_INTERNALS && CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
    PyObject *result_uval;
    int result_ukind, kind_shift;
    Py_ssize_t i, char_pos;
    void *result_udata;
    if (max_char > 1114111) max_char = 1114111;
    result_uval = PyUnicode_New(result_ulength, max_char);
    if (unlikely(!result_uval)) return NULL;
    result_ukind = (max_char <= 255) ? PyUnicode_1BYTE_KIND : (max_char <= 65535) ? PyUnicode_2BYTE_KIND : PyUnicode_4BYTE_KIND;
    kind_shift = (result_ukind == PyUnicode_4BYTE_KIND) ? 2 : result_ukind - 1;
    result_udata = PyUnicode_DATA(result_uval);
    assert(kind_shift == 2 || kind_shift == 1 || kind_shift == 0);
    if (unlikely((PY_SSIZE_T_MAX >> kind_shift) - result_ulength < 0))
        goto overflow;
    char_pos = 0;
    for (i=0; i < value_count; i++) {
        int ukind;
        Py_ssize_t ulength;
        void *udata;
        PyObject *uval = values[i];
        #if !CYTHON_COMPILING_IN_LIMITED_API
        if (__Pyx_PyUnicode_READY(uval) == (-1))
            goto bad;
        #endif
        ulength = __Pyx_PyUnicode_GET_LENGTH(uval);
        #if !CYTHON_ASSUME_SAFE_SIZE
        if (unlikely(ulength < 0)) goto bad;
        #endif
        if (unlikely(!ulength))
            continue;
        if (unlikely((PY_SSIZE_T_MAX >> kind_shift) - ulength < char_pos))
            goto overflow;
        ukind = __Pyx_PyUnicode_KIND(uval);
        udata = __Pyx_PyUnicode_DATA(uval);
        if (ukind == result_ukind) {
            memcpy((char *)result_udata + (char_pos << kind_shift), udata, (size_t) (ulength << kind_shift));
        } else {
            #if PY_VERSION_HEX >= 0x030d0000
            if (unlikely(PyUnicode_CopyCharacters(result_uval, char_pos, uval, 0, ulength) < 0)) goto bad;
            #elif CYTHON_COMPILING_IN_CPYTHON || defined(_PyUnicode_FastCopyCharacters)
            _PyUnicode_FastCopyCharacters(result_uval, char_pos, uval, 0, ulength);
            #else
            Py_ssize_t j;
            for (j=0; j < ulength; j++) {
                Py_UCS4 uchar = __Pyx_PyUnicode_READ(ukind, udata, j);
                __Pyx_PyUnicode_WRITE(result_ukind, result_udata, char_pos+j, uchar);
            }
            #endif
        }
        char_pos += ulength;
    }
    return result_uval;
overflow:
    PyErr_SetString(PyExc_OverflowError, "join() result is too long for a Python string");
bad:
    Py_DECREF(result_uval);
    return NULL;
#else
    Py_ssize_t i;
    PyObject *result = NULL;
    PyObject *value_tuple = PyTuple_New(value_count);
    if (unlikely(!value_tuple)) return NULL;
    CYTHON_UNUSED_VAR(max_char);
    CYTHON_UNUSED_VAR(result_ulength);
    for (i=0; i<value_count; i++) {
        if (__Pyx_PyTuple_SET_ITEM(value_tuple, i, values[i]) != (0)) goto bad;
        Py_INCREF(values[i]);
    }
    result = PyUnicode_Join(__pyx_mstate_global->__pyx_empty_unicode, value_tuple);
bad:
    Py_DECREF(value_tuple);
    return result;
#endif
}

/* GetAttr */
static CYTHON_INLINE PyObject *__Pyx_GetAttr(PyObject *o, PyObject *n) {
#if CYTHON_USE_TYPE_SLOTS
    if (likely(PyUnicode_Check(n)))
        return __Pyx_PyObject_GetAttrStr(o, n);
#endif
    return PyObject_GetAttr(o, n);
}

/* GetItemInt */
static PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j) {
    PyObject *r;
    if (unlikely(!j)) return NULL;
    r = PyObject_GetItem(o, j);
    Py_DECREF(j);
    return r;
}
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i,
                                                              CYTHON_NCP_UNUSED int wraparound,
                                                              CYTHON_NCP_UNUSED int boundscheck) {
#if CYTHON_ASSUME_SAFE_MACROS && CYTHON_ASSUME_SAFE_SIZE && !CYTHON_AVOID_BORROWED_REFS && !CYTHON_AVOID_THREAD_UNSAFE_BORROWED_REFS
    Py_ssize_t wrapped_i = i;
    if (wraparound & unlikely(i < 0)) {
        wrapped_i += PyList_GET_SIZE(o);
    }
    if ((!boundscheck) || likely(__Pyx_is_valid_index(wrapped_i, PyList_GET_SIZE(o)))) {
        PyObject *r = PyList_GET_ITEM(o, wrapped_i);
        Py_INCREF(r);
        return r;
    }
    return __Pyx_GetItemInt_Generic(o, PyLong_FromSsize_t(i));
#else
    return PySequence_GetItem(o, i);
#endif
}
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i,
                                                              CYTHON_NCP_UNUSED int wraparound,
                                                              CYTHON_NCP_UNUSED int boundscheck) {
#if CYTHON_ASSUME_SAFE_MACROS && CYTHON_ASSUME_SAFE_SIZE && !CYTHON_AVOID_BORROWED_REFS
    Py_ssize_t wrapped_i = i;
    if (wraparound & unlikely(i < 0)) {
        wrapped_i += PyTuple_GET_SIZE(o);
    }
    if ((!boundscheck) || likely(__Pyx_is_valid_index(wrapped_i, PyTuple_GET_SIZE(o)))) {
        PyObject *r = PyTuple_GET_ITEM(o, wrapped_i);
        Py_INCREF(r);
        return r;
    }
    return __Pyx_GetItemInt_Generic(o, PyLong_FromSsize_t(i));
#else
    return PySequence_GetItem(o, i);
#endif
}
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i, int is_list,
                                                     CYTHON_NCP_UNUSED int wraparound,
                                                     CYTHON_NCP_UNUSED int boundscheck) {
#if CYTHON_ASSUME_SAFE_MACROS && CYTHON_ASSUME_SAFE_SIZE && !CYTHON_AVOID_BORROWED_REFS && CYTHON_USE_TYPE_SLOTS
    if (is_list || PyList_CheckExact(o)) {
        Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyList_GET_SIZE(o);
        if ((!boundscheck) || (likely(__Pyx_is_valid_index(n, PyList_GET_SIZE(o))))) {
            return __Pyx_PyList_GetItemRef(o, n);
        }
    }
    else if (PyTuple_CheckExact(o)) {
        Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyTuple_GET_SIZE(o);
        if ((!boundscheck) || likely(__Pyx_is_valid_index(n, PyTuple_GET_SIZE(o)))) {
            PyObject *r = PyTuple_GET_ITEM(o, n);
            Py_INCREF(r);
            return r;
        }
    } else {
        PyMappingMethods *mm = Py_TYPE(o)->tp_as_mapping;
        PySequenceMethods *sm = Py_TYPE(o)->tp_as_sequence;
        if (mm && mm->mp_subscript) {
            PyObject *r, *key = PyLong_FromSsize_t(i);
            if (unlikely(!key)) return NULL;
            r = mm->mp_subscript(o, key);
            Py_DECREF(key);
            return r;
        }
        if (likely(sm && sm->sq_item)) {
            if (wraparound && unlikely(i < 0) && likely(sm->sq_length)) {
                Py_ssize_t l = sm->sq_length(o);
                if (likely(l >= 0)) {
                    i += l;
                } else {
                    if (!PyErr_ExceptionMatches(PyExc_OverflowError))
                        return NULL;
                    PyErr_Clear();
                }
            }
            return sm->sq_item(o, i);
        }
    }
#else
    if (is_list || !PyMapping_Check(o)) {
        return PySequence_GetItem(o, i);
    }
#endif
    return __Pyx_GetItemInt_Generic(o, PyLong_FromSsize_t(i));
}

/* PyObjectCallOneArg */
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
    PyObject *args[2] = {NULL, arg};
    return __Pyx_PyObject_FastCall(func, args+1, 1 | __Pyx_PY_VECTORCALL_ARGUMENTS_OFFSET);
}

/* ObjectGetItem */
#if CYTHON_USE_TYPE_SLOTS
static PyObject *__Pyx_PyObject_GetIndex(PyObject *obj, PyObject *index) {
    PyObject *runerr = NULL;
    Py_ssize_t key_value;
    key_value = __Pyx_PyIndex_AsSsize_t(index);
    if (likely(key_value != -1 || !(runerr = PyErr_Occurred()))) {
        return __Pyx_GetItemInt_Fast(obj, key_value, 0, 1, 1);
    }
    if (PyErr_GivenExceptionMatches(runerr, PyExc_OverflowError)) {
        __Pyx_TypeName index_type_name = __Pyx_PyType_GetFullyQualifiedName(Py_TYPE(index));
        PyErr_Clear();
        PyErr_Format(PyExc_IndexError,
            "cannot fit '" __Pyx_FMT_TYPENAME "' into an index-sized integer", index_type_name);
        __Pyx_DECREF_TypeName(index_type_name);
    }
    return NULL;
}
static PyObject *__Pyx_PyObject_GetItem_Slow(PyObject *obj, PyObject *key) {
    __Pyx_TypeName obj_type_name;
    if (likely(PyType_Check(obj))) {
        PyObject *meth = __Pyx_PyObject_GetAttrStrNoError(obj, __pyx_mstate_global->__pyx_n_u_class_getitem);
        if (!meth) {
            PyErr_Clear();
        } else {
            PyObject *result = __Pyx_PyObject_CallOneArg(meth, key);
            Py_DECREF(meth);
            return result;
        }
    }
    obj_type_name = __Pyx_PyType_GetFullyQualifiedName(Py_TYPE(obj));
    PyErr_Format(PyExc_TypeError,
        "'" __Pyx_FMT_TYPENAME "' object is not subscriptable", obj_type_name);
    __Pyx_DECREF_TypeName(obj_type_name);
    return NULL;
}
static PyObject *__Pyx_PyObject_GetItem(PyObject *obj, PyObject *key) {
    PyTypeObject *tp = Py_TYPE(obj);
    PyMappingMethods *mm = tp->tp_as_mapping;
    PySequenceMethods *sm = tp->tp_as_sequence;
    if (likely(mm && mm->mp_subscript)) {
        return mm->mp_subscript(obj, key);
    }
    if (likely(sm && sm->sq_item)) {
        return __Pyx_PyObject_GetIndex(obj, key);
    }
    return __Pyx_PyObject_GetItem_Slow(obj, key);
}
#endif

/* RejectKeywords */
static void __Pyx_RejectKeywords(const char* function_name, PyObject *kwds) {
    PyObject *key = NULL;
    if (CYTHON_METH_FASTCALL && likely(PyTuple_Check(kwds))) {
        key = __Pyx_PySequence_ITEM(kwds, 0);
    } else {
        Py_ssize_t pos = 0;
#if !CYTHON_COMPILING_IN_PYPY || defined(PyArg_ValidateKeywordArguments)
        if (unlikely(!PyArg_ValidateKeywordArguments(kwds))) return;
#endif
        PyDict_Next(kwds, &pos, &key, NULL);
        Py_INCREF(key);
    }
    if (likely(key)) {
        PyErr_Format(PyExc_TypeError,
            "%s() got an unexpected keyword argument '%U'",
            function_name, key);
        Py_DECREF(key);
    }
}

/* DivInt[Py_ssize_t] */
static CYTHON_INLINE Py_ssize_t __Pyx_div_Py_ssize_t(Py_ssize_t a, Py_ssize_t b, int b_is_constant) {
    Py_ssize_t q = a / b;
    Py_ssize_t r = a - q*b;
    Py_ssize_t adapt_python = (b_is_constant ?
        ((r != 0) & ((r < 0) ^ (b < 0))) :
        ((r != 0) & ((r ^ b) < 0))
    );
    return q - adapt_python;
}

/* GetAttr3 */
#if __PYX_LIMITED_VERSION_HEX < 0x030d0000
static PyObject *__Pyx_GetAttr3Default(PyObject *d) {
    __Pyx_PyThreadState_declare
    __Pyx_PyThreadState_assign
    if (unlikely(!__Pyx_PyErr_ExceptionMatches(PyExc_AttributeError)))
        return NULL;
    __Pyx_PyErr_Clear();
    Py_INCREF(d);
    return d;
}
#endif
static CYTHON_INLINE PyObject *__Pyx_GetAttr3(PyObject *o, PyObject *n, PyObject *d) {
    PyObject *r;
#if __PYX_LIMITED_VERSION_HEX >= 0x030d0000
    int res = PyObject_GetOptionalAttr(o, n, &r);
    return (res != 0) ? r : __Pyx_NewRef(d);
#else
  #if CYTHON_USE_TYPE_SLOTS
    if (likely(PyUnicode_Check(n))) {
        r = __Pyx_PyObject_GetAttrStrNoError(o, n);
        if (unlikely(!r) && likely(!PyErr_Occurred())) {
            r = __Pyx_NewRef(d);
        }
        return r;
    }
  #endif
    r = PyObject_GetAttr(o, n);
    return (likely(r)) ? r : __Pyx_GetAttr3Default(d);
#endif
}

/* PyDictVersioning */
#if CYTHON_USE_DICT_VERSIONS && CYTHON_USE_TYPE_SLOTS
static CYTHON_INLINE PY_UINT64_T __Pyx_get_tp_dict_version(PyObject *obj) {
    PyObject *dict = Py_TYPE(obj)->tp_dict;
    return likely(dict) ? __PYX_GET_DICT_VERSION(dict) : 0;
}
static CYTHON_INLINE PY_UINT64_T __Pyx_get_object_dict_version(PyObject *obj) {
    PyObject **dictptr = NULL;
    Py_ssize_t offset = Py_TYPE(obj)->tp_dictoffset;
    if (offset) {
#if CYTHON_COMPILING_IN_CPYTHON
        dictptr = (likely(offset > 0)) ? (PyObject **) ((char *)obj + offset) : _PyObject_GetDictPtr(obj);
#else
        dictptr = _PyObject_GetDictPtr(obj);
#endif
    }
    return (dictptr && *dictptr) ? __PYX_GET_DICT_VERSION(*dictptr) : 0;
}
static CYTHON_INLINE int __Pyx_object_dict_version_matches(PyObject* obj, PY_UINT64_T tp_dict_version, PY_UINT64_T obj_dict_version) {
    PyObject *dict = Py_TYPE(obj)->tp_dict;
    if (unlikely(!dict) || unlikely(tp_dict_version != __PYX_GET_DICT_VERSION(dict)))
        return 0;
    return obj_dict_version == __Pyx_get_object_dict_version(obj);
}
#endif

/* GetModuleGlobalName */
#if CYTHON_USE_DICT_VERSIONS
static PyObject *__Pyx__GetModuleGlobalName(PyObject *name, PY_UINT64_T *dict_version, PyObject **dict_cached_value)
#else
static CYTHON_INLINE PyObject *__Pyx__GetModuleGlobalName(PyObject *name)
#endif
{
    PyObject *result;
#if CYTHON_COMPILING_IN_LIMITED_API
    if (unlikely(!__pyx_m)) {
        if (!PyErr_Occurred())
            PyErr_SetNone(PyExc_NameError);
        return NULL;
    }
    result = PyObject_GetAttr(__pyx_m, name);
    if (likely(result)) {
        return result;
    }
    PyErr_Clear();
#elif CYTHON_AVOID_BORROWED_REFS || CYTHON_AVOID_THREAD_UNSAFE_BORROWED_REFS
    if (unlikely(__Pyx_PyDict_GetItemRef(__pyx_mstate_global->__pyx_d, name, &result) == -1)) PyErr_Clear();
    __PYX_UPDATE_DICT_CACHE(__pyx_mstate_global->__pyx_d, result, *dict_cached_value, *dict_version)
    if (likely(result)) {
        return result;
    }
#else
    result = _PyDict_GetItem_KnownHash(__pyx_mstate_global->__pyx_d, name, ((PyASCIIObject *) name)->hash);
    __PYX_UPDATE_DICT_CACHE(__pyx_mstate_global->__pyx_d, result, *dict_cached_value, *dict_version)
    if (likely(result)) {
        return __Pyx_NewRef(result);
    }
    PyErr_Clear();
#endif
    return __Pyx_GetBuiltinName(name);
}

/* RaiseTooManyValuesToUnpack */
static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected) {
    PyErr_Format(PyExc_ValueError,
                 "too many values to unpack (expected %" CYTHON_FORMAT_SSIZE_T "d)", expected);
}

/* RaiseNeedMoreValuesToUnpack */
static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index) {
    PyErr_Format(PyExc_ValueError,
                 "need more than %" CYTHON_FORMAT_SSIZE_T "d value%.1s to unpack",
                 index, (index == 1) ? "" : "s");
}

/* RaiseNoneIterError */
static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void) {
    PyErr_SetString(PyExc_TypeError, "'NoneType' object is not iterable");
}

/* ExtTypeTest */
static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type) {
    __Pyx_TypeName obj_type_name;
    __Pyx_TypeName type_name;
    if (unlikely(!type)) {
        PyErr_SetString(PyExc_SystemError, "Missing type object");
        return 0;
    }
    if (likely(__Pyx_TypeCheck(obj, type)))
        return 1;
    obj_type_name = __Pyx_PyType_GetFullyQualifiedName(Py_TYPE(obj));
    type_name = __Pyx_PyType_GetFullyQualifiedName(type);
    PyErr_Format(PyExc_TypeError,
                 "Cannot convert " __Pyx_FMT_TYPENAME " to " __Pyx_FMT_TYPENAME,
                 obj_type_name, type_name);
    __Pyx_DECREF_TypeName(obj_type_name);
    __Pyx_DECREF_TypeName(type_name);
    return 0;
}

/* GetTopmostException */
#if CYTHON_USE_EXC_INFO_STACK && CYTHON_FAST_THREAD_STATE
static _PyErr_StackItem *
__Pyx_PyErr_GetTopmostException(PyThreadState *tstate)
{
    _PyErr_StackItem *exc_info = tstate->exc_info;
    while ((exc_info->exc_value == NULL || exc_info->exc_value == Py_None) &&
           exc_info->previous_item != NULL)
    {
        exc_info = exc_info->previous_item;
    }
    return exc_info;
}
#endif

/* SaveResetException */
#if CYTHON_FAST_THREAD_STATE
static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
  #if CYTHON_USE_EXC_INFO_STACK && PY_VERSION_HEX >= 0x030B00a4
    _PyErr_StackItem *exc_info = __Pyx_PyErr_GetTopmostException(tstate);
    PyObject *exc_value = exc_info->exc_value;
    if (exc_value == NULL || exc_value == Py_None) {
        *value = NULL;
        *type = NULL;
        *tb = NULL;
    } else {
        *value = exc_value;
        Py_INCREF(*value);
        *type = (PyObject*) Py_TYPE(exc_value);
        Py_INCREF(*type);
        *tb = PyException_GetTraceback(exc_value);
    }
  #elif CYTHON_USE_EXC_INFO_STACK
    _PyErr_StackItem *exc_info = __Pyx_PyErr_GetTopmostException(tstate);
    *type = exc_info->exc_type;
    *value = exc_info->exc_value;
    *tb = exc_info->exc_traceback;
    Py_XINCREF(*type);
    Py_XINCREF(*value);
    Py_XINCREF(*tb);
  #else
    *type = tstate->exc_type;
    *value = tstate->exc_value;
    *tb = tstate->exc_traceback;
    Py_XINCREF(*type);
    Py_XINCREF(*value);
    Py_XINCREF(*tb);
  #endif
}
static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {
  #if CYTHON_USE_EXC_INFO_STACK && PY_VERSION_HEX >= 0x030B00a4
    _PyErr_StackItem *exc_info = tstate->exc_info;
    PyObject *tmp_value = exc_info->exc_value;
    exc_info->exc_value = value;
    Py_XDECREF(tmp_value);
    Py_XDECREF(type);
    Py_XDECREF(tb);
  #else
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    #if CYTHON_USE_EXC_INFO_STACK
    _PyErr_StackItem *exc_info = tstate->exc_info;
    tmp_type = exc_info->exc_type;
    tmp_value = exc_info->exc_value;
    tmp_tb = exc_info->exc_traceback;
    exc_info->exc_type = type;
    exc_info->exc_value = value;
    exc_info->exc_traceback = tb;
    #else
    tmp_type = tstate->exc_type;
    tmp_value = tstate->exc_value;
    tmp_tb = tstate->exc_traceback;
    tstate->exc_type = type;
    tstate->exc_value = value;
    tstate->exc_traceback = tb;
    #endif
    Py_XDECREF(tmp_type);
    Py_XDECREF(tmp_value);
    Py_XDECREF(tmp_tb);
  #endif
}
#endif

/* GetException */
#if CYTHON_FAST_THREAD_STATE
static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb)
#else
static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb)
#endif
{
    PyObject *local_type = NULL, *local_value, *local_tb = NULL;
#if CYTHON_FAST_THREAD_STATE
    PyObject *tmp_type, *tmp_value, *tmp_tb;
  #if PY_VERSION_HEX >= 0x030C0000
    local_value = tstate->current_exception;
    tstate->current_exception = 0;
  #else
    local_type = tstate->curexc_type;
    local_value = tstate->curexc_value;
    local_tb = tstate->curexc_traceback;
    tstate->curexc_type = 0;
    tstate->curexc_value = 0;
    tstate->curexc_traceback = 0;
  #endif
#elif __PYX_LIMITED_VERSION_HEX > 0x030C0000
    local_value = PyErr_GetRaisedException();
#else
    PyErr_Fetch(&local_type, &local_value, &local_tb);
#endif
#if __PYX_LIMITED_VERSION_HEX > 0x030C0000
    if (likely(local_value)) {
        local_type = (PyObject*) Py_TYPE(local_value);
        Py_INCREF(local_type);
        local_tb = PyException_GetTraceback(local_value);
    }
#else
    PyErr_NormalizeException(&local_type, &local_value, &local_tb);
#if CYTHON_FAST_THREAD_STATE
    if (unlikely(tstate->curexc_type))
#else
    if (unlikely(PyErr_Occurred()))
#endif
        goto bad;
    if (local_tb) {
        if (unlikely(PyException_SetTraceback(local_value, local_tb) < 0))
            goto bad;
    }
#endif // __PYX_LIMITED_VERSION_HEX > 0x030C0000
    Py_XINCREF(local_tb);
    Py_XINCREF(local_type);
    Py_XINCREF(local_value);
    *type = local_type;
    *value = local_value;
    *tb = local_tb;
#if CYTHON_FAST_THREAD_STATE
    #if CYTHON_USE_EXC_INFO_STACK
    {
        _PyErr_StackItem *exc_info = tstate->exc_info;
      #if PY_VERSION_HEX >= 0x030B00a4
        tmp_value = exc_info->exc_value;
        exc_info->exc_value = local_value;
        tmp_type = NULL;
        tmp_tb = NULL;
        Py_XDECREF(local_type);
        Py_XDECREF(local_tb);
      #else
        tmp_type = exc_info->exc_type;
        tmp_value = exc_info->exc_value;
        tmp_tb = exc_info->exc_traceback;
        exc_info->exc_type = local_type;
        exc_info->exc_value = local_value;
        exc_info->exc_traceback = local_tb;
      #endif
    }
    #else
    tmp_type = tstate->exc_type;
    tmp_value = tstate->exc_value;
    tmp_tb = tstate->exc_traceback;
    tstate->exc_type = local_type;
    tstate->exc_value = local_value;
    tstate->exc_traceback = local_tb;
    #endif
    Py_XDECREF(tmp_type);
    Py_XDECREF(tmp_value);
    Py_XDECREF(tmp_tb);
#elif __PYX_LIMITED_VERSION_HEX >= 0x030b0000
    PyErr_SetHandledException(local_value);
    Py_XDECREF(local_value);
    Py_XDECREF(local_type);
    Py_XDECREF(local_tb);
#else
    PyErr_SetExcInfo(local_type, local_value, local_tb);
#endif
    return 0;
#if __PYX_LIMITED_VERSION_HEX <= 0x030C0000
bad:
    *type = 0;
    *value = 0;
    *tb = 0;
    Py_XDECREF(local_type);
    Py_XDECREF(local_value);
    Py_XDECREF(local_tb);
    return -1;
#endif
}

/* SwapException */
#if CYTHON_FAST_THREAD_STATE
static CYTHON_INLINE void __Pyx__ExceptionSwap(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
    PyObject *tmp_type, *tmp_value, *tmp_tb;
  #if CYTHON_USE_EXC_INFO_STACK && PY_VERSION_HEX >= 0x030B00a4
    _PyErr_StackItem *exc_info = tstate->exc_info;
    tmp_value = exc_info->exc_value;
    exc_info->exc_value = *value;
    if (tmp_value == NULL || tmp_value == Py_None) {
        Py_XDECREF(tmp_value);
        tmp_value = NULL;
        tmp_type = NULL;
        tmp_tb = NULL;
    } else {
        tmp_type = (PyObject*) Py_TYPE(tmp_value);
        Py_INCREF(tmp_type);
        #if CYTHON_COMPILING_IN_CPYTHON
        tmp_tb = ((PyBaseExceptionObject*) tmp_value)->traceback;
        Py_XINCREF(tmp_tb);
        #else
        tmp_tb = PyException_GetTraceback(tmp_value);
        #endif
    }
  #elif CYTHON_USE_EXC_INFO_STACK
    _PyErr_StackItem *exc_info = tstate->exc_info;
    tmp_type = exc_info->exc_type;
    tmp_value = exc_info->exc_value;
    tmp_tb = exc_info->exc_traceback;
    exc_info->exc_type = *type;
    exc_info->exc_value = *value;
    exc_info->exc_traceback = *tb;
  #else
    tmp_type = tstate->exc_type;
    tmp_value = tstate->exc_value;
    tmp_tb = tstate->exc_traceback;
    tstate->exc_type = *type;
    tstate->exc_value = *value;
    tstate->exc_traceback = *tb;
  #endif
    *type = tmp_type;
    *value = tmp_value;
    *tb = tmp_tb;
}
#else
static CYTHON_INLINE void __Pyx_ExceptionSwap(PyObject **type, PyObject **value, PyObject **tb) {
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    PyErr_GetExcInfo(&tmp_type, &tmp_value, &tmp_tb);
    PyErr_SetExcInfo(*type, *value, *tb);
    *type = tmp_type;
    *value = tmp_value;
    *tb = tmp_tb;
}
#endif

/* Import */
static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level) {
    PyObject *module = 0;
    PyObject *empty_dict = 0;
    PyObject *empty_list = 0;
    empty_dict = PyDict_New();
    if (unlikely(!empty_dict))
        goto bad;
    if (level == -1) {
        const char* package_sep = strchr(__Pyx_MODULE_NAME, '.');
        if (package_sep != (0)) {
            module = PyImport_ImportModuleLevelObject(
                name, __pyx_mstate_global->__pyx_d, empty_dict, from_list, 1);
            if (unlikely(!module)) {
                if (unlikely(!PyErr_ExceptionMatches(PyExc_ImportError)))
                    goto bad;
                PyErr_Clear();
            }
        }
        level = 0;
    }
    if (!module) {
        module = PyImport_ImportModuleLevelObject(
            name, __pyx_mstate_global->__pyx_d, empty_dict, from_list, level);
    }
bad:
    Py_XDECREF(empty_dict);
    Py_XDECREF(empty_list);
    return module;
}

/* ImportDottedModule */
static PyObject *__Pyx__ImportDottedModule_Error(PyObject *name, PyObject *parts_tuple, Py_ssize_t count) {
    PyObject *partial_name = NULL, *slice = NULL, *sep = NULL;
    Py_ssize_t size;
    if (unlikely(PyErr_Occurred())) {
        PyErr_Clear();
    }
#if CYTHON_ASSUME_SAFE_SIZE
    size = PyTuple_GET_SIZE(parts_tuple);
#else
    size = PyTuple_Size(parts_tuple);
    if (size < 0) goto bad;
#endif
    if (likely(size == count)) {
        partial_name = name;
    } else {
        slice = PySequence_GetSlice(parts_tuple, 0, count);
        if (unlikely(!slice))
            goto bad;
        sep = PyUnicode_FromStringAndSize(".", 1);
        if (unlikely(!sep))
            goto bad;
        partial_name = PyUnicode_Join(sep, slice);
    }
    PyErr_Format(
        PyExc_ModuleNotFoundError,
        "No module named '%U'", partial_name);
bad:
    Py_XDECREF(sep);
    Py_XDECREF(slice);
    Py_XDECREF(partial_name);
    return NULL;
}
static PyObject *__Pyx__ImportDottedModule_Lookup(PyObject *name) {
    PyObject *imported_module;
#if (CYTHON_COMPILING_IN_PYPY && PYPY_VERSION_NUM  < 0x07030400) ||\
        CYTHON_COMPILING_IN_GRAAL
    PyObject *modules = PyImport_GetModuleDict();
    if (unlikely(!modules))
        return NULL;
    imported_module = __Pyx_PyDict_GetItemStr(modules, name);
    Py_XINCREF(imported_module);
#else
    imported_module = PyImport_GetModule(name);
#endif
    return imported_module;
}
static PyObject *__Pyx_ImportDottedModule_WalkParts(PyObject *module, PyObject *name, PyObject *parts_tuple) {
    Py_ssize_t i, nparts;
#if CYTHON_ASSUME_SAFE_SIZE
    nparts = PyTuple_GET_SIZE(parts_tuple);
#else
    nparts = PyTuple_Size(parts_tuple);
    if (nparts < 0) return NULL;
#endif
    for (i=1; i < nparts && module; i++) {
        PyObject *part, *submodule;
#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
        part = PyTuple_GET_ITEM(parts_tuple, i);
#else
        part = __Pyx_PySequence_ITEM(parts_tuple, i);
        if (!part) return NULL;
#endif
        submodule = __Pyx_PyObject_GetAttrStrNoError(module, part);
#if !(CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS)
        Py_DECREF(part);
#endif
        Py_DECREF(module);
        module = submodule;
    }
    if (unlikely(!module)) {
        return __Pyx__ImportDottedModule_Error(name, parts_tuple, i);
    }
    return module;
}
static PyObject *__Pyx__ImportDottedModule(PyObject *name, PyObject *parts_tuple) {
    PyObject *imported_module;
    PyObject *module = __Pyx_Import(name, NULL, 0);
    if (!parts_tuple || unlikely(!module))
        return module;
    imported_module = __Pyx__ImportDottedModule_Lookup(name);
    if (likely(imported_module)) {
        Py_DECREF(module);
        return imported_module;
    }
    PyErr_Clear();
    return __Pyx_ImportDottedModule_WalkParts(module, name, parts_tuple);
}
static PyObject *__Pyx_ImportDottedModule(PyObject *name, PyObject *parts_tuple) {
#if CYTHON_COMPILING_IN_CPYTHON
    PyObject *module = __Pyx__ImportDottedModule_Lookup(name);
    if (likely(module)) {
        PyObject *spec = __Pyx_PyObject_GetAttrStrNoError(module, __pyx_mstate_global->__pyx_n_u_spec);
        if (likely(spec)) {
            PyObject *unsafe = __Pyx_PyObject_GetAttrStrNoError(spec, __pyx_mstate_global->__pyx_n_u_initializing);
            if (likely(!unsafe || !__Pyx_PyObject_IsTrue(unsafe))) {
                Py_DECREF(spec);
                spec = NULL;
            }
            Py_XDECREF(unsafe);
        }
        if (likely(!spec)) {
            PyErr_Clear();
            return module;
        }
        Py_DECREF(spec);
        Py_DECREF(module);
    } else if (PyErr_Occurred()) {
        PyErr_Clear();
    }
#endif
    return __Pyx__ImportDottedModule(name, parts_tuple);
}

/* FastTypeChecks */
#if CYTHON_COMPILING_IN_CPYTHON
static int __Pyx_InBases(PyTypeObject *a, PyTypeObject *b) {
    while (a) {
        a = __Pyx_PyType_GetSlot(a, tp_base, PyTypeObject*);
        if (a == b)
            return 1;
    }
    return b == &PyBaseObject_Type;
}
static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b) {
    PyObject *mro;
    if (a == b) return 1;
    mro = a->tp_mro;
    if (likely(mro)) {
        Py_ssize_t i, n;
        n = PyTuple_GET_SIZE(mro);
        for (i = 0; i < n; i++) {
            if (PyTuple_GET_ITEM(mro, i) == (PyObject *)b)
                return 1;
        }
        return 0;
    }
    return __Pyx_InBases(a, b);
}
static CYTHON_INLINE int __Pyx_IsAnySubtype2(PyTypeObject *cls, PyTypeObject *a, PyTypeObject *b) {
    PyObject *mro;
    if (cls == a || cls == b) return 1;
    mro = cls->tp_mro;
    if (likely(mro)) {
        Py_ssize_t i, n;
        n = PyTuple_GET_SIZE(mro);
        for (i = 0; i < n; i++) {
            PyObject *base = PyTuple_GET_ITEM(mro, i);
            if (base == (PyObject *)a || base == (PyObject *)b)
                return 1;
        }
        return 0;
    }
    return __Pyx_InBases(cls, a) || __Pyx_InBases(cls, b);
}
static CYTHON_INLINE int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject *exc_type2) {
    if (exc_type1) {
        return __Pyx_IsAnySubtype2((PyTypeObject*)err, (PyTypeObject*)exc_type1, (PyTypeObject*)exc_type2);
    } else {
        return __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type2);
    }
}
static int __Pyx_PyErr_GivenExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) {
    Py_ssize_t i, n;
    assert(PyExceptionClass_Check(exc_type));
    n = PyTuple_GET_SIZE(tuple);
    for (i=0; i<n; i++) {
        if (exc_type == PyTuple_GET_ITEM(tuple, i)) return 1;
    }
    for (i=0; i<n; i++) {
        PyObject *t = PyTuple_GET_ITEM(tuple, i);
        if (likely(PyExceptionClass_Check(t))) {
            if (__Pyx_inner_PyErr_GivenExceptionMatches2(exc_type, NULL, t)) return 1;
        } else {
        }
    }
    return 0;
}
static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject* exc_type) {
    if (likely(err == exc_type)) return 1;
    if (likely(PyExceptionClass_Check(err))) {
        if (likely(PyExceptionClass_Check(exc_type))) {
            return __Pyx_inner_PyErr_GivenExceptionMatches2(err, NULL, exc_type);
        } else if (likely(PyTuple_Check(exc_type))) {
            return __Pyx_PyErr_GivenExceptionMatchesTuple(err, exc_type);
        } else {
        }
    }
    return PyErr_GivenExceptionMatches(err, exc_type);
}
static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *exc_type1, PyObject *exc_type2) {
    assert(PyExceptionClass_Check(exc_type1));
    assert(PyExceptionClass_Check(exc_type2));
    if (likely(err == exc_type1 || err == exc_type2)) return 1;
    if (likely(PyExceptionClass_Check(err))) {
        return __Pyx_inner_PyErr_GivenExceptionMatches2(err, exc_type1, exc_type2);
    }
    return (PyErr_GivenExceptionMatches(err, exc_type1) || PyErr_GivenExceptionMatches(err, exc_type2));
}
#endif

/* PySequenceMultiply */
static PyObject* __Pyx_PySequence_Multiply_Generic(PyObject *seq, Py_ssize_t mul) {
    PyObject *result, *pymul = PyLong_FromSsize_t(mul);
    if (unlikely(!pymul))
        return NULL;
    result = PyNumber_Multiply(seq, pymul);
    Py_DECREF(pymul);
    return result;
}
static CYTHON_INLINE PyObject* __Pyx_PySequence_Multiply(PyObject *seq, Py_ssize_t mul) {
#if CYTHON_USE_TYPE_SLOTS
    PyTypeObject *type = Py_TYPE(seq);
    if (likely(type->tp_as_sequence && type->tp_as_sequence->sq_repeat)) {
        return type->tp_as_sequence->sq_repeat(seq, mul);
    } else
#endif
    {
        return __Pyx_PySequence_Multiply_Generic(seq, mul);
    }
}

/* PyObjectFormatAndDecref */
static CYTHON_INLINE PyObject* __Pyx_PyObject_FormatSimpleAndDecref(PyObject* s, PyObject* f) {
    if (unlikely(!s)) return NULL;
    if (likely(PyUnicode_CheckExact(s))) return s;
    return __Pyx_PyObject_FormatAndDecref(s, f);
}
static CYTHON_INLINE PyObject* __Pyx_PyObject_FormatAndDecref(PyObject* s, PyObject* f) {
    PyObject *result;
    if (unlikely(!s)) return NULL;
    result = PyObject_Format(s, f);
    Py_DECREF(s);
    return result;
}

/* PyObjectFormat */
#if CYTHON_USE_UNICODE_WRITER
static PyObject* __Pyx_PyObject_Format(PyObject* obj, PyObject* format_spec) {
    int ret;
    _PyUnicodeWriter writer;
    if (likely(PyFloat_CheckExact(obj))) {
        _PyUnicodeWriter_Init(&writer);
        ret = _PyFloat_FormatAdvancedWriter(
            &writer,
            obj,
            format_spec, 0, PyUnicode_GET_LENGTH(format_spec));
    } else if (likely(PyLong_CheckExact(obj))) {
        _PyUnicodeWriter_Init(&writer);
        ret = _PyLong_FormatAdvancedWriter(
            &writer,
            obj,
            format_spec, 0, PyUnicode_GET_LENGTH(format_spec));
    } else {
        return PyObject_Format(obj, format_spec);
    }
    if (unlikely(ret == -1)) {
        _PyUnicodeWriter_Dealloc(&writer);
        return NULL;
    }
    return _PyUnicodeWriter_Finish(&writer);
}
#endif

/* SetItemInt */
static int __Pyx_SetItemInt_Generic(PyObject *o, PyObject *j, PyObject *v) {
    int r;
    if (unlikely(!j)) return -1;
    r = PyObject_SetItem(o, j, v);
    Py_DECREF(j);
    return r;
}
static CYTHON_INLINE int __Pyx_SetItemInt_Fast(PyObject *o, Py_ssize_t i, PyObject *v, int is_list,
                                               CYTHON_NCP_UNUSED int wraparound, CYTHON_NCP_UNUSED int boundscheck) {
#if CYTHON_ASSUME_SAFE_MACROS && CYTHON_ASSUME_SAFE_SIZE && !CYTHON_AVOID_BORROWED_REFS && CYTHON_USE_TYPE_SLOTS
    if (is_list || PyList_CheckExact(o)) {
        Py_ssize_t n = (!wraparound) ? i : ((likely(i >= 0)) ? i : i + PyList_GET_SIZE(o));
        if ((!boundscheck) || likely(__Pyx_is_valid_index(n, PyList_GET_SIZE(o)))) {
            Py_INCREF(v);
#if CYTHON_AVOID_THREAD_UNSAFE_BORROWED_REFS
            PyList_SetItem(o, n, v);
#else
            PyObject* old = PyList_GET_ITEM(o, n);
            PyList_SET_ITEM(o, n, v);
            Py_DECREF(old);
#endif
            return 1;
        }
    } else {
        PyMappingMethods *mm = Py_TYPE(o)->tp_as_mapping;
        PySequenceMethods *sm = Py_TYPE(o)->tp_as_sequence;
        if (mm && mm->mp_ass_subscript) {
            int r;
            PyObject *key = PyLong_FromSsize_t(i);
            if (unlikely(!key)) return -1;
            r = mm->mp_ass_subscript(o, key, v);
            Py_DECREF(key);
            return r;
        }
        if (likely(sm && sm->sq_ass_item)) {
            if (wraparound && unlikely(i < 0) && likely(sm->sq_length)) {
                Py_ssize_t l = sm->sq_length(o);
                if (likely(l >= 0)) {
                    i += l;
                } else {
                    if (!PyErr_ExceptionMatches(PyExc_OverflowError))
                        return -1;
                    PyErr_Clear();
                }
            }
            return sm->sq_ass_item(o, i, v);
        }
    }
#else
    if (is_list || !PyMapping_Check(o))
    {
        return PySequence_SetItem(o, i, v);
    }
#endif
    return __Pyx_SetItemInt_Generic(o, PyLong_FromSsize_t(i), v);
}

/* RaiseUnboundLocalError */
static void __Pyx_RaiseUnboundLocalError(const char *varname) {
    PyErr_Format(PyExc_UnboundLocalError, "local variable '%s' referenced before assignment", varname);
}

/* DivInt[long] */
static CYTHON_INLINE long __Pyx_div_long(long a, long b, int b_is_constant) {
    long q = a / b;
    long r = a - q*b;
    long adapt_python = (b_is_constant ?
        ((r != 0) & ((r < 0) ^ (b < 0))) :
        ((r != 0) & ((r ^ b) < 0))
    );
    return q - adapt_python;
}

/* ImportFrom */
static PyObject* __Pyx_ImportFrom(PyObject* module, PyObject* name) {
    PyObject* value = __Pyx_PyObject_GetAttrStr(module, name);
    if (unlikely(!value) && PyErr_ExceptionMatches(PyExc_AttributeError)) {
        const char* module_name_str = 0;
        PyObject* module_name = 0;
        PyObject* module_dot = 0;
        PyObject* full_name = 0;
        PyErr_Clear();
        module_name_str = PyModule_GetName(module);
        if (unlikely(!module_name_str)) { goto modbad; }
        module_name = PyUnicode_FromString(module_name_str);
        if (unlikely(!module_name)) { goto modbad; }
        module_dot = PyUnicode_Concat(module_name, __pyx_mstate_global->__pyx_kp_u__2);
        if (unlikely(!module_dot)) { goto modbad; }
        full_name = PyUnicode_Concat(module_dot, name);
        if (unlikely(!full_name)) { goto modbad; }
        #if (CYTHON_COMPILING_IN_PYPY && PYPY_VERSION_NUM  < 0x07030400) ||\
                CYTHON_COMPILING_IN_GRAAL
        {
            PyObject *modules = PyImport_GetModuleDict();
            if (unlikely(!modules))
                goto modbad;
            value = PyObject_GetItem(modules, full_name);
        }
        #else
        value = PyImport_GetModule(full_name);
        #endif
      modbad:
        Py_XDECREF(full_name);
        Py_XDECREF(module_dot);
        Py_XDECREF(module_name);
    }
    if (unlikely(!value)) {
        PyErr_Format(PyExc_ImportError, "cannot import name %S", name);
    }
    return value;
}

/* HasAttr */
#if __PYX_LIMITED_VERSION_HEX < 0x030d0000
static CYTHON_INLINE int __Pyx_HasAttr(PyObject *o, PyObject *n) {
    PyObject *r;
    if (unlikely(!PyUnicode_Check(n))) {
        PyErr_SetString(PyExc_TypeError,
                        "hasattr(): attribute name must be string");
        return -1;
    }
    r = __Pyx_PyObject_GetAttrStrNoError(o, n);
    if (!r) {
        return (unlikely(PyErr_Occurred())) ? -1 : 0;
    } else {
        Py_DECREF(r);
        return 1;
    }
}
#endif

/* DictGetItem */
#if !CYTHON_COMPILING_IN_PYPY
static PyObject *__Pyx_PyDict_GetItem(PyObject *d, PyObject* key) {
    PyObject *value;
    if (unlikely(__Pyx_PyDict_GetItemRef(d, key, &value) == 0)) { // no value, no error
        if (unlikely(PyTuple_Check(key))) {
            PyObject* args = PyTuple_Pack(1, key);
            if (likely(args)) {
                PyErr_SetObject(PyExc_KeyError, args);
                Py_DECREF(args);
            }
        } else {
            PyErr_SetObject(PyExc_KeyError, key);
        }
    }
    return value;
}
#endif

/* PyFloatBinop */
#if !CYTHON_COMPILING_IN_PYPY
static PyObject* __Pyx_PyFloat_TrueDivideCObj(PyObject *op1, PyObject *op2, double floatval, int inplace, int zerodivision_check) {
    const double a = floatval;
    double b, result;
    CYTHON_UNUSED_VAR(inplace);
    CYTHON_UNUSED_VAR(zerodivision_check);
    if (likely(PyFloat_CheckExact(op2))) {
        b = __Pyx_PyFloat_AS_DOUBLE(op2);
        if (unlikely(zerodivision_check && ((b) == 0.0))) { PyErr_SetString(PyExc_ZeroDivisionError, "float division by zero"); return NULL;}
    } else
    if (likely(PyLong_CheckExact(op2))) {
        #if CYTHON_USE_PYLONG_INTERNALS
        if (__Pyx_PyLong_IsZero(op2)) {
            b = 0.0;
            if (unlikely(zerodivision_check && ((b) == 0.0))) { PyErr_SetString(PyExc_ZeroDivisionError, "float division by zero"); return NULL;}
        } else if (__Pyx_PyLong_IsCompact(op2)) {
            b = (double) __Pyx_PyLong_CompactValue(op2);
        } else {
            const digit* digits = __Pyx_PyLong_Digits(op2);
            const Py_ssize_t size = __Pyx_PyLong_SignedDigitCount(op2);
            switch (size) {
                case -2:
                case 2:
                    if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (1 * PyLong_SHIFT < 53))) {
                        b = (double) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        if ((8 * sizeof(unsigned long) < 53) || (2 * PyLong_SHIFT < 53) || (b < (double) ((PY_LONG_LONG)1 << 53))) {
                            if (size == -2)
                                b = -b;
                            break;
                        }
                    }
                    CYTHON_FALLTHROUGH;
                case -3:
                case 3:
                    if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (2 * PyLong_SHIFT < 53))) {
                        b = (double) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        if ((8 * sizeof(unsigned long) < 53) || (3 * PyLong_SHIFT < 53) || (b < (double) ((PY_LONG_LONG)1 << 53))) {
                            if (size == -3)
                                b = -b;
                            break;
                        }
                    }
                    CYTHON_FALLTHROUGH;
                case -4:
                case 4:
                    if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (3 * PyLong_SHIFT < 53))) {
                        b = (double) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        if ((8 * sizeof(unsigned long) < 53) || (4 * PyLong_SHIFT < 53) || (b < (double) ((PY_LONG_LONG)1 << 53))) {
                            if (size == -4)
                                b = -b;
                            break;
                        }
                    }
                    CYTHON_FALLTHROUGH;
                default:
        #endif
                    b = PyLong_AsDouble(op2);
                    if (unlikely(b == -1.0 && PyErr_Occurred())) return NULL;
                    #if !CYTHON_USE_PYLONG_INTERNALS
                    if (unlikely(zerodivision_check && ((b) == 0.0))) { PyErr_SetString(PyExc_ZeroDivisionError, "float division by zero"); return NULL;}
                    #endif
        #if CYTHON_USE_PYLONG_INTERNALS
            }
        }
        #endif
    } else {
        return (inplace ? PyNumber_InPlaceTrueDivide : PyNumber_TrueDivide)(op1, op2);
    }
        result = a / b;
        return PyFloat_FromDouble(result);
}
#endif

/* PyLongCompare */
static CYTHON_INLINE int __Pyx_PyLong_BoolEqObjC(PyObject *op1, PyObject *op2, long intval, long inplace) {
    CYTHON_MAYBE_UNUSED_VAR(intval);
    CYTHON_UNUSED_VAR(inplace);
    if (op1 == op2) {
        return 1;
    }
    #if CYTHON_USE_PYLONG_INTERNALS
    if (likely(PyLong_CheckExact(op1))) {
        int unequal;
        unsigned long uintval;
        Py_ssize_t size = __Pyx_PyLong_DigitCount(op1);
        const digit* digits = __Pyx_PyLong_Digits(op1);
        if (intval == 0) {
            return (__Pyx_PyLong_IsZero(op1) == 1);
        } else if (intval < 0) {
            if (__Pyx_PyLong_IsNonNeg(op1))
                return 0;
            intval = -intval;
        } else {
            if (__Pyx_PyLong_IsNeg(op1))
                return 0;
        }
        uintval = (unsigned long) intval;
#if PyLong_SHIFT * 4 < SIZEOF_LONG*8
        if (uintval >> (PyLong_SHIFT * 4)) {
            unequal = (size != 5) || (digits[0] != (uintval & (unsigned long) PyLong_MASK))
                 | (digits[1] != ((uintval >> (1 * PyLong_SHIFT)) & (unsigned long) PyLong_MASK)) | (digits[2] != ((uintval >> (2 * PyLong_SHIFT)) & (unsigned long) PyLong_MASK)) | (digits[3] != ((uintval >> (3 * PyLong_SHIFT)) & (unsigned long) PyLong_MASK)) | (digits[4] != ((uintval >> (4 * PyLong_SHIFT)) & (unsigned long) PyLong_MASK));
        } else
#endif
#if PyLong_SHIFT * 3 < SIZEOF_LONG*8
        if (uintval >> (PyLong_SHIFT * 3)) {
            unequal = (size != 4) || (digits[0] != (uintval & (unsigned long) PyLong_MASK))
                 | (digits[1] != ((uintval >> (1 * PyLong_SHIFT)) & (unsigned long) PyLong_MASK)) | (digits[2] != ((uintval >> (2 * PyLong_SHIFT)) & (unsigned long) PyLong_MASK)) | (digits[3] != ((uintval >> (3 * PyLong_SHIFT)) & (unsigned long) PyLong_MASK));
        } else
#endif
#if PyLong_SHIFT * 2 < SIZEOF_LONG*8
        if (uintval >> (PyLong_SHIFT * 2)) {
            unequal = (size != 3) || (digits[0] != (uintval & (unsigned long) PyLong_MASK))
                 | (digits[1] != ((uintval >> (1 * PyLong_SHIFT)) & (unsigned long) PyLong_MASK)) | (digits[2] != ((uintval >> (2 * PyLong_SHIFT)) & (unsigned long) PyLong_MASK));
        } else
#endif
#if PyLong_SHIFT * 1 < SIZEOF_LONG*8
        if (uintval >> (PyLong_SHIFT * 1)) {
            unequal = (size != 2) || (digits[0] != (uintval & (unsigned long) PyLong_MASK))
                 | (digits[1] != ((uintval >> (1 * PyLong_SHIFT)) & (unsigned long) PyLong_MASK));
        } else
#endif
            unequal = (size != 1) || (((unsigned long) digits[0]) != (uintval & (unsigned long) PyLong_MASK));
        return (unequal == 0);
    }
    #endif
    if (PyFloat_CheckExact(op1)) {
        const long b = intval;
        double a = __Pyx_PyFloat_AS_DOUBLE(op1);
        return ((double)a == (double)b);
    }
    return __Pyx_PyObject_IsTrueAndDecref(
        PyObject_RichCompare(op1, op2, Py_EQ));
}

/* IsLittleEndian */
static CYTHON_INLINE int __Pyx_Is_Little_Endian(void)
{
  union {
    uint32_t u32;
    uint8_t u8[4];
  } S;
  S.u32 = 0x01020304;
  return S.u8[0] == 4;
}

/* BufferFormatCheck */
static void __Pyx_BufFmt_Init(__Pyx_BufFmt_Context* ctx,
                              __Pyx_BufFmt_StackElem* stack,
                              const __Pyx_TypeInfo* type) {
  stack[0].field = &ctx->root;
  stack[0].parent_offset = 0;
  ctx->root.type = type;
  ctx->root.name = "buffer dtype";
  ctx->root.offset = 0;
  ctx->head = stack;
  ctx->head->field = &ctx->root;
  ctx->fmt_offset = 0;
  ctx->head->parent_offset = 0;
  ctx->new_packmode = '@';
  ctx->enc_packmode = '@';
  ctx->new_count = 1;
  ctx->enc_count = 0;
  ctx->enc_type = 0;
  ctx->is_complex = 0;
  ctx->is_valid_array = 0;
  ctx->struct_alignment = 0;
  while (type->typegroup == 'S') {
    ++ctx->head;
    ctx->head->field = type->fields;
    ctx->head->parent_offset = 0;
    type = type->fields->type;
  }
}
static int __Pyx_BufFmt_ParseNumber(const char** ts) {
    int count;
    const char* t = *ts;
    if (*t < '0' || *t > '9') {
      return -1;
    } else {
        count = *t++ - '0';
        while (*t >= '0' && *t <= '9') {
            count *= 10;
            count += *t++ - '0';
        }
    }
    *ts = t;
    return count;
}
static int __Pyx_BufFmt_ExpectNumber(const char **ts) {
    int number = __Pyx_BufFmt_ParseNumber(ts);
    if (number == -1)
        PyErr_Format(PyExc_ValueError,\
                     "Does not understand character buffer dtype format string ('%c')", **ts);
    return number;
}
static void __Pyx_BufFmt_RaiseUnexpectedChar(char ch) {
  PyErr_Format(PyExc_ValueError,
               "Unexpected format string character: '%c'", ch);
}
static const char* __Pyx_BufFmt_DescribeTypeChar(char ch, int is_complex) {
  switch (ch) {
    case '?': return "'bool'";
    case 'c': return "'char'";
    case 'b': return "'signed char'";
    case 'B': return "'unsigned char'";
    case 'h': return "'short'";
    case 'H': return "'unsigned short'";
    case 'i': return "'int'";
    case 'I': return "'unsigned int'";
    case 'l': return "'long'";
    case 'L': return "'unsigned long'";
    case 'q': return "'long long'";
    case 'Q': return "'unsigned long long'";
    case 'f': return (is_complex ? "'complex float'" : "'float'");
    case 'd': return (is_complex ? "'complex double'" : "'double'");
    case 'g': return (is_complex ? "'complex long double'" : "'long double'");
    case 'T': return "a struct";
    case 'O': return "Python object";
    case 'P': return "a pointer";
    case 's': case 'p': return "a string";
    case 0: return "end";
    default: return "unparsable format string";
  }
}
static size_t __Pyx_BufFmt_TypeCharToStandardSize(char ch, int is_complex) {
  switch (ch) {
    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return 2;
    case 'i': case 'I': case 'l': case 'L': return 4;
    case 'q': case 'Q': return 8;
    case 'f': return (is_complex ? 8 : 4);
    case 'd': return (is_complex ? 16 : 8);
    case 'g': {
      PyErr_SetString(PyExc_ValueError, "Python does not define a standard format string size for long double ('g')..");
      return 0;
    }
    case 'O': case 'P': return sizeof(void*);
    default:
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
}
static size_t __Pyx_BufFmt_TypeCharToNativeSize(char ch, int is_complex) {
  switch (ch) {
    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return sizeof(short);
    case 'i': case 'I': return sizeof(int);
    case 'l': case 'L': return sizeof(long);
    #ifdef HAVE_LONG_LONG
    case 'q': case 'Q': return sizeof(PY_LONG_LONG);
    #endif
    case 'f': return sizeof(float) * (is_complex ? 2 : 1);
    case 'd': return sizeof(double) * (is_complex ? 2 : 1);
    case 'g': return sizeof(long double) * (is_complex ? 2 : 1);
    case 'O': case 'P': return sizeof(void*);
    default: {
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
  }
}
typedef struct { char c; short x; } __Pyx_st_short;
typedef struct { char c; int x; } __Pyx_st_int;
typedef struct { char c; long x; } __Pyx_st_long;
typedef struct { char c; float x; } __Pyx_st_float;
typedef struct { char c; double x; } __Pyx_st_double;
typedef struct { char c; long double x; } __Pyx_st_longdouble;
typedef struct { char c; void *x; } __Pyx_st_void_p;
#ifdef HAVE_LONG_LONG
typedef struct { char c; PY_LONG_LONG x; } __Pyx_st_longlong;
#endif
static size_t __Pyx_BufFmt_TypeCharToAlignment(char ch, int is_complex) {
  CYTHON_UNUSED_VAR(is_complex);
  switch (ch) {
    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return sizeof(__Pyx_st_short) - sizeof(short);
    case 'i': case 'I': return sizeof(__Pyx_st_int) - sizeof(int);
    case 'l': case 'L': return sizeof(__Pyx_st_long) - sizeof(long);
#ifdef HAVE_LONG_LONG
    case 'q': case 'Q': return sizeof(__Pyx_st_longlong) - sizeof(PY_LONG_LONG);
#endif
    case 'f': return sizeof(__Pyx_st_float) - sizeof(float);
    case 'd': return sizeof(__Pyx_st_double) - sizeof(double);
    case 'g': return sizeof(__Pyx_st_longdouble) - sizeof(long double);
    case 'P': case 'O': return sizeof(__Pyx_st_void_p) - sizeof(void*);
    default:
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
}
/* These are for computing the padding at the end of the struct to align
   on the first member of the struct. This will probably the same as above,
   but we don't have any guarantees.
 */
typedef struct { short x; char c; } __Pyx_pad_short;
typedef struct { int x; char c; } __Pyx_pad_int;
typedef struct { long x; char c; } __Pyx_pad_long;
typedef struct { float x; char c; } __Pyx_pad_float;
typedef struct { double x; char c; } __Pyx_pad_double;
typedef struct { long double x; char c; } __Pyx_pad_longdouble;
typedef struct { void *x; char c; } __Pyx_pad_void_p;
#ifdef HAVE_LONG_LONG
typedef struct { PY_LONG_LONG x; char c; } __Pyx_pad_longlong;
#endif
static size_t __Pyx_BufFmt_TypeCharToPadding(char ch, int is_complex) {
  CYTHON_UNUSED_VAR(is_complex);
  switch (ch) {
    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return sizeof(__Pyx_pad_short) - sizeof(short);
    case 'i': case 'I': return sizeof(__Pyx_pad_int) - sizeof(int);
    case 'l': case 'L': return sizeof(__Pyx_pad_long) - sizeof(long);
#ifdef HAVE_LONG_LONG
    case 'q': case 'Q': return sizeof(__Pyx_pad_longlong) - sizeof(PY_LONG_LONG);
#endif
    case 'f': return sizeof(__Pyx_pad_float) - sizeof(float);
    case 'd': return sizeof(__Pyx_pad_double) - sizeof(double);
    case 'g': return sizeof(__Pyx_pad_longdouble) - sizeof(long double);
    case 'P': case 'O': return sizeof(__Pyx_pad_void_p) - sizeof(void*);
    default:
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
}
static char __Pyx_BufFmt_TypeCharToGroup(char ch, int is_complex) {
  switch (ch) {
    case 'c':
        return 'H';
    case 'b': case 'h': case 'i':
    case 'l': case 'q': case 's': case 'p':
        return 'I';
    case '?': case 'B': case 'H': case 'I': case 'L': case 'Q':
        return 'U';
    case 'f': case 'd': case 'g':
        return (is_complex ? 'C' : 'R');
    case 'O':
        return 'O';
    case 'P':
        return 'P';
    default: {
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
  }
}
static void __Pyx_BufFmt_RaiseExpected(__Pyx_BufFmt_Context* ctx) {
  if (ctx->head == NULL || ctx->head->field == &ctx->root) {
    const char* expected;
    const char* quote;
    if (ctx->head == NULL) {
      expected = "end";
      quote = "";
    } else {
      expected = ctx->head->field->type->name;
      quote = "'";
    }
    PyErr_Format(PyExc_ValueError,
                 "Buffer dtype mismatch, expected %s%s%s but got %s",
                 quote, expected, quote,
                 __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex));
  } else {
    const __Pyx_StructField* field = ctx->head->field;
    const __Pyx_StructField* parent = (ctx->head - 1)->field;
    PyErr_Format(PyExc_ValueError,
                 "Buffer dtype mismatch, expected '%s' but got %s in '%s.%s'",
                 field->type->name, __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex),
                 parent->type->name, field->name);
  }
}
static int __Pyx_BufFmt_ProcessTypeChunk(__Pyx_BufFmt_Context* ctx) {
  char group;
  size_t size, offset, arraysize = 1;
  if (ctx->enc_type == 0) return 0;
  if (ctx->head->field->type->arraysize[0]) {
    int i, ndim = 0;
    if (ctx->enc_type == 's' || ctx->enc_type == 'p') {
        ctx->is_valid_array = ctx->head->field->type->ndim == 1;
        ndim = 1;
        if (ctx->enc_count != ctx->head->field->type->arraysize[0]) {
            PyErr_Format(PyExc_ValueError,
                         "Expected a dimension of size %zu, got %zu",
                         ctx->head->field->type->arraysize[0], ctx->enc_count);
            return -1;
        }
    }
    if (!ctx->is_valid_array) {
      PyErr_Format(PyExc_ValueError, "Expected %d dimensions, got %d",
                   ctx->head->field->type->ndim, ndim);
      return -1;
    }
    for (i = 0; i < ctx->head->field->type->ndim; i++) {
      arraysize *= ctx->head->field->type->arraysize[i];
    }
    ctx->is_valid_array = 0;
    ctx->enc_count = 1;
  }
  group = __Pyx_BufFmt_TypeCharToGroup(ctx->enc_type, ctx->is_complex);
  do {
    const __Pyx_StructField* field = ctx->head->field;
    const __Pyx_TypeInfo* type = field->type;
    if (ctx->enc_packmode == '@' || ctx->enc_packmode == '^') {
      size = __Pyx_BufFmt_TypeCharToNativeSize(ctx->enc_type, ctx->is_complex);
    } else {
      size = __Pyx_BufFmt_TypeCharToStandardSize(ctx->enc_type, ctx->is_complex);
    }
    if (ctx->enc_packmode == '@') {
      size_t align_at = __Pyx_BufFmt_TypeCharToAlignment(ctx->enc_type, ctx->is_complex);
      size_t align_mod_offset;
      if (align_at == 0) return -1;
      align_mod_offset = ctx->fmt_offset % align_at;
      if (align_mod_offset > 0) ctx->fmt_offset += align_at - align_mod_offset;
      if (ctx->struct_alignment == 0)
          ctx->struct_alignment = __Pyx_BufFmt_TypeCharToPadding(ctx->enc_type,
                                                                 ctx->is_complex);
    }
    if (type->size != size || type->typegroup != group) {
      if (type->typegroup == 'C' && type->fields != NULL) {
        size_t parent_offset = ctx->head->parent_offset + field->offset;
        ++ctx->head;
        ctx->head->field = type->fields;
        ctx->head->parent_offset = parent_offset;
        continue;
      }
      if ((type->typegroup == 'H' || group == 'H') && type->size == size) {
      } else {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return -1;
      }
    }
    offset = ctx->head->parent_offset + field->offset;
    if (ctx->fmt_offset != offset) {
      PyErr_Format(PyExc_ValueError,
                   "Buffer dtype mismatch; next field is at offset %" CYTHON_FORMAT_SSIZE_T "d but %" CYTHON_FORMAT_SSIZE_T "d expected",
                   (Py_ssize_t)ctx->fmt_offset, (Py_ssize_t)offset);
      return -1;
    }
    ctx->fmt_offset += size;
    if (arraysize)
      ctx->fmt_offset += (arraysize - 1) * size;
    --ctx->enc_count;
    while (1) {
      if (field == &ctx->root) {
        ctx->head = NULL;
        if (ctx->enc_count != 0) {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return -1;
        }
        break;
      }
      ctx->head->field = ++field;
      if (field->type == NULL) {
        --ctx->head;
        field = ctx->head->field;
        continue;
      } else if (field->type->typegroup == 'S') {
        size_t parent_offset = ctx->head->parent_offset + field->offset;
        if (field->type->fields->type == NULL) continue;
        field = field->type->fields;
        ++ctx->head;
        ctx->head->field = field;
        ctx->head->parent_offset = parent_offset;
        break;
      } else {
        break;
      }
    }
  } while (ctx->enc_count);
  ctx->enc_type = 0;
  ctx->is_complex = 0;
  return 0;
}
static int
__pyx_buffmt_parse_array(__Pyx_BufFmt_Context* ctx, const char** tsp)
{
    const char *ts = *tsp;
    int i = 0, number, ndim;
    ++ts;
    if (ctx->new_count != 1) {
        PyErr_SetString(PyExc_ValueError,
                        "Cannot handle repeated arrays in format string");
        return -1;
    }
    if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return -1;
    ndim = ctx->head->field->type->ndim;
    while (*ts && *ts != ')') {
        switch (*ts) {
            case ' ': case '\f': case '\r': case '\n': case '\t': case '\v':  continue;
            default:  break;
        }
        number = __Pyx_BufFmt_ExpectNumber(&ts);
        if (number == -1) return -1;
        if (i < ndim && (size_t) number != ctx->head->field->type->arraysize[i]) {
            PyErr_Format(PyExc_ValueError,
                        "Expected a dimension of size %zu, got %d",
                        ctx->head->field->type->arraysize[i], number);
            return -1;
        }
        if (*ts != ',' && *ts != ')') {
            PyErr_Format(PyExc_ValueError,
                                "Expected a comma in format string, got '%c'", *ts);
            return -1;
        }
        if (*ts == ',') ts++;
        i++;
    }
    if (i != ndim) {
        PyErr_Format(PyExc_ValueError, "Expected %d dimension(s), got %d",
                            ctx->head->field->type->ndim, i);
        return -1;
    }
    if (!*ts) {
        PyErr_SetString(PyExc_ValueError,
                        "Unexpected end of format string, expected ')'");
        return -1;
    }
    ctx->is_valid_array = 1;
    ctx->new_count = 1;
    *tsp = ++ts;
    return 0;
}
static const char* __Pyx_BufFmt_CheckString(__Pyx_BufFmt_Context* ctx, const char* ts) {
  int got_Z = 0;
  while (1) {
    switch(*ts) {
      case 0:
        if (ctx->enc_type != 0 && ctx->head == NULL) {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return NULL;
        }
        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
        if (ctx->head != NULL) {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return NULL;
        }
        return ts;
      case ' ':
      case '\r':
      case '\n':
        ++ts;
        break;
      case '<':
        if (!__Pyx_Is_Little_Endian()) {
          PyErr_SetString(PyExc_ValueError, "Little-endian buffer not supported on big-endian compiler");
          return NULL;
        }
        ctx->new_packmode = '=';
        ++ts;
        break;
      case '>':
      case '!':
        if (__Pyx_Is_Little_Endian()) {
          PyErr_SetString(PyExc_ValueError, "Big-endian buffer not supported on little-endian compiler");
          return NULL;
        }
        ctx->new_packmode = '=';
        ++ts;
        break;
      case '=':
      case '@':
      case '^':
        ctx->new_packmode = *ts++;
        break;
      case 'T':
        {
          const char* ts_after_sub;
          size_t i, struct_count = ctx->new_count;
          size_t struct_alignment = ctx->struct_alignment;
          ctx->new_count = 1;
          ++ts;
          if (*ts != '{') {
            PyErr_SetString(PyExc_ValueError, "Buffer acquisition: Expected '{' after 'T'");
            return NULL;
          }
          if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
          ctx->enc_type = 0;
          ctx->enc_count = 0;
          ctx->struct_alignment = 0;
          ++ts;
          ts_after_sub = ts;
          for (i = 0; i != struct_count; ++i) {
            ts_after_sub = __Pyx_BufFmt_CheckString(ctx, ts);
            if (!ts_after_sub) return NULL;
          }
          ts = ts_after_sub;
          if (struct_alignment) ctx->struct_alignment = struct_alignment;
        }
        break;
      case '}':
        {
          size_t alignment = ctx->struct_alignment;
          ++ts;
          if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
          ctx->enc_type = 0;
          if (alignment && ctx->fmt_offset % alignment) {
            ctx->fmt_offset += alignment - (ctx->fmt_offset % alignment);
          }
        }
        return ts;
      case 'x':
        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
        ctx->fmt_offset += ctx->new_count;
        ctx->new_count = 1;
        ctx->enc_count = 0;
        ctx->enc_type = 0;
        ctx->enc_packmode = ctx->new_packmode;
        ++ts;
        break;
      case 'Z':
        got_Z = 1;
        ++ts;
        if (*ts != 'f' && *ts != 'd' && *ts != 'g') {
          __Pyx_BufFmt_RaiseUnexpectedChar('Z');
          return NULL;
        }
        CYTHON_FALLTHROUGH;
      case '?': case 'c': case 'b': case 'B': case 'h': case 'H': case 'i': case 'I':
      case 'l': case 'L': case 'q': case 'Q':
      case 'f': case 'd': case 'g':
      case 'O': case 'p':
        if ((ctx->enc_type == *ts) && (got_Z == ctx->is_complex) &&
            (ctx->enc_packmode == ctx->new_packmode) && (!ctx->is_valid_array)) {
          ctx->enc_count += ctx->new_count;
          ctx->new_count = 1;
          got_Z = 0;
          ++ts;
          break;
        }
        CYTHON_FALLTHROUGH;
      case 's':
        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
        ctx->enc_count = ctx->new_count;
        ctx->enc_packmode = ctx->new_packmode;
        ctx->enc_type = *ts;
        ctx->is_complex = got_Z;
        ++ts;
        ctx->new_count = 1;
        got_Z = 0;
        break;
      case ':':
        ++ts;
        while(*ts != ':') ++ts;
        ++ts;
        break;
      case '(':
        if (__pyx_buffmt_parse_array(ctx, &ts) < 0) return NULL;
        break;
      default:
        {
          int number = __Pyx_BufFmt_ExpectNumber(&ts);
          if (number == -1) return NULL;
          ctx->new_count = (size_t)number;
        }
    }
  }
}

/* BufferGetAndValidate */
  static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info) {
  if (unlikely(info->buf == NULL)) return;
  if (info->suboffsets == __Pyx_minusones) info->suboffsets = NULL;
  PyBuffer_Release(info);
}
static void __Pyx_ZeroBuffer(Py_buffer* buf) {
  buf->buf = NULL;
  buf->obj = NULL;
  buf->strides = __Pyx_zeros;
  buf->shape = __Pyx_zeros;
  buf->suboffsets = __Pyx_minusones;
}
static int __Pyx__GetBufferAndValidate(
        Py_buffer* buf, PyObject* obj,  const __Pyx_TypeInfo* dtype, int flags,
        int nd, int cast, __Pyx_BufFmt_StackElem* stack)
{
  buf->buf = NULL;
  if (unlikely(PyObject_GetBuffer(obj, buf, flags) == -1)) {
    __Pyx_ZeroBuffer(buf);
    return -1;
  }
  if (unlikely(buf->ndim != nd)) {
    PyErr_Format(PyExc_ValueError,
                 "Buffer has wrong number of dimensions (expected %d, got %d)",
                 nd, buf->ndim);
    goto fail;
  }
  if (!cast) {
    __Pyx_BufFmt_Context ctx;
    __Pyx_BufFmt_Init(&ctx, stack, dtype);
    if (!__Pyx_BufFmt_CheckString(&ctx, buf->format)) goto fail;
  }
  if (unlikely((size_t)buf->itemsize != dtype->size)) {
    PyErr_Format(PyExc_ValueError,
      "Item size of buffer (%" CYTHON_FORMAT_SSIZE_T "d byte%s) does not match size of '%s' (%" CYTHON_FORMAT_SSIZE_T "d byte%s)",
      buf->itemsize, (buf->itemsize > 1) ? "s" : "",
      dtype->name, (Py_ssize_t)dtype->size, (dtype->size > 1) ? "s" : "");
    goto fail;
  }
  if (buf->suboffsets == NULL) buf->suboffsets = __Pyx_minusones;
  return 0;
fail:;
  __Pyx_SafeReleaseBuffer(buf);
  return -1;
}

/* PyLongBinop */
  #if !CYTHON_COMPILING_IN_PYPY
static PyObject* __Pyx_Fallback___Pyx_PyLong_AddCObj(PyObject *op1, PyObject *op2, int inplace) {
    return (inplace ? PyNumber_InPlaceAdd : PyNumber_Add)(op1, op2);
}
#if CYTHON_USE_PYLONG_INTERNALS
static PyObject* __Pyx_Unpacked___Pyx_PyLong_AddCObj(PyObject *op1, PyObject *op2, long intval, int inplace, int zerodivision_check) {
    CYTHON_MAYBE_UNUSED_VAR(inplace);
    CYTHON_UNUSED_VAR(zerodivision_check);
    const long a = intval;
    long b, x;
#ifdef HAVE_LONG_LONG
    const PY_LONG_LONG lla = intval;
    PY_LONG_LONG llb, llx;
#endif
    if (unlikely(__Pyx_PyLong_IsZero(op2))) {
        return __Pyx_NewRef(op1);
    }
    if (unlikely(!__Pyx_PyLong_CompactAsLong(op2, &b))) {
        const digit* digits = __Pyx_PyLong_Digits(op2);
        const Py_ssize_t size = __Pyx_PyLong_SignedDigitCount(op2);
        switch (size) {
            case -2:
                if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                    b = -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
                    llb = -(PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            case 2:
                if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                    b = (long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
                    llb = (PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            case -3:
                if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                    b = -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
                    llb = -(PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            case 3:
                if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                    b = (long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
                    llb = (PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            case -4:
                if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                    b = -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
                    llb = -(PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            case 4:
                if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                    b = (long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
                    llb = (PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            default: return PyLong_Type.tp_as_number->nb_add(op1, op2);
        }
    }
            x = a + b;
        return PyLong_FromLong(x);
#ifdef HAVE_LONG_LONG
    long_long:
            llx = lla + llb;
        return PyLong_FromLongLong(llx);
#endif
    return __Pyx_Fallback___Pyx_PyLong_AddCObj(op1, op2, inplace);
    
    
}
#endif
static PyObject* __Pyx_Float___Pyx_PyLong_AddCObj(PyObject *float_val, long intval, int zerodivision_check) {
    CYTHON_UNUSED_VAR(zerodivision_check);
    const long a = intval;
    double b = __Pyx_PyFloat_AS_DOUBLE(float_val);
        double result;
        
        result = ((double)a) + (double)b;
        return PyFloat_FromDouble(result);
}
static CYTHON_INLINE PyObject* __Pyx_PyLong_AddCObj(PyObject *op1, PyObject *op2, long intval, int inplace, int zerodivision_check) {
    CYTHON_MAYBE_UNUSED_VAR(intval);
    CYTHON_UNUSED_VAR(zerodivision_check);
    #if CYTHON_USE_PYLONG_INTERNALS
    if (likely(PyLong_CheckExact(op2))) {
        return __Pyx_Unpacked___Pyx_PyLong_AddCObj(op1, op2, intval, inplace, zerodivision_check);
    }
    #endif
    if (PyFloat_CheckExact(op2)) {
        return __Pyx_Float___Pyx_PyLong_AddCObj(op2, intval, zerodivision_check);
    }
    return __Pyx_Fallback___Pyx_PyLong_AddCObj(op1, op2, inplace);
}
#endif

/* PyLongBinop */
  #if !CYTHON_COMPILING_IN_PYPY
static PyObject* __Pyx_Fallback___Pyx_PyLong_MultiplyCObj(PyObject *op1, PyObject *op2, int inplace) {
    return (inplace ? PyNumber_InPlaceMultiply : PyNumber_Multiply)(op1, op2);
}
#if CYTHON_USE_PYLONG_INTERNALS
static PyObject* __Pyx_Unpacked___Pyx_PyLong_MultiplyCObj(PyObject *op1, PyObject *op2, long intval, int inplace, int zerodivision_check) {
    CYTHON_MAYBE_UNUSED_VAR(inplace);
    CYTHON_UNUSED_VAR(zerodivision_check);
    const long a = intval;
    long b, x;
#ifdef HAVE_LONG_LONG
    const PY_LONG_LONG lla = intval;
    PY_LONG_LONG llb, llx;
#endif
    if (unlikely(__Pyx_PyLong_IsZero(op2))) {
        return __Pyx_NewRef(op2);
    }
    if (unlikely(!__Pyx_PyLong_CompactAsLong(op2, &b))) {
        const digit* digits = __Pyx_PyLong_Digits(op2);
        const Py_ssize_t size = __Pyx_PyLong_SignedDigitCount(op2);
        switch (size) {
            case -2:
                if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT+30) {
                    b = -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT+30) {
                    llb = -(PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            case 2:
                if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT+30) {
                    b = (long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT+30) {
                    llb = (PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            case -3:
                if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT+30) {
                    b = -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT+30) {
                    llb = -(PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            case 3:
                if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT+30) {
                    b = (long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT+30) {
                    llb = (PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            case -4:
                if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT+30) {
                    b = -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT+30) {
                    llb = -(PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            case 4:
                if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT+30) {
                    b = (long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT+30) {
                    llb = (PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            default: return PyLong_Type.tp_as_number->nb_multiply(op1, op2);
        }
    }
            CYTHON_UNUSED_VAR(a);
            CYTHON_UNUSED_VAR(b);
            #ifdef HAVE_LONG_LONG
            llb = b;
            goto long_long;
            #else
            return PyLong_Type.tp_as_number->nb_multiply(op1, op2);
            #endif
        return PyLong_FromLong(x);
#ifdef HAVE_LONG_LONG
    long_long:
            llx = lla * llb;
        return PyLong_FromLongLong(llx);
#endif
    return __Pyx_Fallback___Pyx_PyLong_MultiplyCObj(op1, op2, inplace);
    
    
}
#endif
static PyObject* __Pyx_Float___Pyx_PyLong_MultiplyCObj(PyObject *float_val, long intval, int zerodivision_check) {
    CYTHON_UNUSED_VAR(zerodivision_check);
    const long a = intval;
    double b = __Pyx_PyFloat_AS_DOUBLE(float_val);
        double result;
        
        result = ((double)a) * (double)b;
        return PyFloat_FromDouble(result);
}
static CYTHON_INLINE PyObject* __Pyx_PyLong_MultiplyCObj(PyObject *op1, PyObject *op2, long intval, int inplace, int zerodivision_check) {
    CYTHON_MAYBE_UNUSED_VAR(intval);
    CYTHON_UNUSED_VAR(zerodivision_check);
    #if CYTHON_USE_PYLONG_INTERNALS
    if (likely(PyLong_CheckExact(op2))) {
        return __Pyx_Unpacked___Pyx_PyLong_MultiplyCObj(op1, op2, intval, inplace, zerodivision_check);
    }
    #endif
    if (PyFloat_CheckExact(op2)) {
        return __Pyx_Float___Pyx_PyLong_MultiplyCObj(op2, intval, zerodivision_check);
    }
    return __Pyx_Fallback___Pyx_PyLong_MultiplyCObj(op1, op2, inplace);
}
#endif

/* PyObjectVectorCallKwBuilder */
  #if CYTHON_VECTORCALL
static int __Pyx_VectorcallBuilder_AddArg(PyObject *key, PyObject *value, PyObject *builder, PyObject **args, int n) {
    (void)__Pyx_PyObject_FastCallDict;
    if (__Pyx_PyTuple_SET_ITEM(builder, n, key) != (0)) return -1;
    Py_INCREF(key);
    args[n] = value;
    return 0;
}
CYTHON_UNUSED static int __Pyx_VectorcallBuilder_AddArg_Check(PyObject *key, PyObject *value, PyObject *builder, PyObject **args, int n) {
    (void)__Pyx_VectorcallBuilder_AddArgStr;
    if (unlikely(!PyUnicode_Check(key))) {
        PyErr_SetString(PyExc_TypeError, "keywords must be strings");
        return -1;
    }
    return __Pyx_VectorcallBuilder_AddArg(key, value, builder, args, n);
}
static int __Pyx_VectorcallBuilder_AddArgStr(const char *key, PyObject *value, PyObject *builder, PyObject **args, int n) {
    PyObject *pyKey = PyUnicode_FromString(key);
    if (!pyKey) return -1;
    return __Pyx_VectorcallBuilder_AddArg(pyKey, value, builder, args, n);
}
#else // CYTHON_VECTORCALL
CYTHON_UNUSED static int __Pyx_VectorcallBuilder_AddArg_Check(PyObject *key, PyObject *value, PyObject *builder, CYTHON_UNUSED PyObject **args, CYTHON_UNUSED int n) {
    if (unlikely(!PyUnicode_Check(key))) {
        PyErr_SetString(PyExc_TypeError, "keywords must be strings");
        return -1;
    }
    return PyDict_SetItem(builder, key, value);
}
#endif

/* PyLongBinop */
  #if !CYTHON_COMPILING_IN_PYPY
static PyObject* __Pyx_Fallback___Pyx_PyLong_SubtractObjC(PyObject *op1, PyObject *op2, int inplace) {
    return (inplace ? PyNumber_InPlaceSubtract : PyNumber_Subtract)(op1, op2);
}
#if CYTHON_USE_PYLONG_INTERNALS
static PyObject* __Pyx_Unpacked___Pyx_PyLong_SubtractObjC(PyObject *op1, PyObject *op2, long intval, int inplace, int zerodivision_check) {
    CYTHON_MAYBE_UNUSED_VAR(inplace);
    CYTHON_UNUSED_VAR(zerodivision_check);
    const long b = intval;
    long a, x;
#ifdef HAVE_LONG_LONG
    const PY_LONG_LONG llb = intval;
    PY_LONG_LONG lla, llx;
#endif
    if (unlikely(__Pyx_PyLong_IsZero(op1))) {
        return PyLong_FromLong(-intval);
    }
    if (unlikely(!__Pyx_PyLong_CompactAsLong(op1, &a))) {
        const digit* digits = __Pyx_PyLong_Digits(op1);
        const Py_ssize_t size = __Pyx_PyLong_SignedDigitCount(op1);
        switch (size) {
            case -2:
                if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                    a = -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
                    lla = -(PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            case 2:
                if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                    a = (long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
                    lla = (PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            case -3:
                if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                    a = -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
                    lla = -(PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            case 3:
                if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                    a = (long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
                    lla = (PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            case -4:
                if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                    a = -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
                    lla = -(PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            case 4:
                if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                    a = (long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
                    lla = (PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            default: return PyLong_Type.tp_as_number->nb_subtract(op1, op2);
        }
    }
            x = a - b;
        return PyLong_FromLong(x);
#ifdef HAVE_LONG_LONG
    long_long:
            llx = lla - llb;
        return PyLong_FromLongLong(llx);
#endif
    return __Pyx_Fallback___Pyx_PyLong_SubtractObjC(op1, op2, inplace);
    
    
}
#endif
static PyObject* __Pyx_Float___Pyx_PyLong_SubtractObjC(PyObject *float_val, long intval, int zerodivision_check) {
    CYTHON_UNUSED_VAR(zerodivision_check);
    const long b = intval;
    double a = __Pyx_PyFloat_AS_DOUBLE(float_val);
        double result;
        
        result = ((double)a) - (double)b;
        return PyFloat_FromDouble(result);
}
static CYTHON_INLINE PyObject* __Pyx_PyLong_SubtractObjC(PyObject *op1, PyObject *op2, long intval, int inplace, int zerodivision_check) {
    CYTHON_MAYBE_UNUSED_VAR(intval);
    CYTHON_UNUSED_VAR(zerodivision_check);
    #if CYTHON_USE_PYLONG_INTERNALS
    if (likely(PyLong_CheckExact(op1))) {
        return __Pyx_Unpacked___Pyx_PyLong_SubtractObjC(op1, op2, intval, inplace, zerodivision_check);
    }
    #endif
    if (PyFloat_CheckExact(op1)) {
        return __Pyx_Float___Pyx_PyLong_SubtractObjC(op1, intval, zerodivision_check);
    }
    return __Pyx_Fallback___Pyx_PyLong_SubtractObjC(op1, op2, inplace);
}
#endif

/* IterFinish */
  static CYTHON_INLINE int __Pyx_IterFinish(void) {
    PyObject* exc_type;
    __Pyx_PyThreadState_declare
    __Pyx_PyThreadState_assign
    exc_type = __Pyx_PyErr_CurrentExceptionType();
    if (unlikely(exc_type)) {
        if (unlikely(!__Pyx_PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration)))
            return -1;
        __Pyx_PyErr_Clear();
        return 0;
    }
    return 0;
}

/* PyObjectCallNoArg */
  static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func) {
    PyObject *arg[2] = {NULL, NULL};
    return __Pyx_PyObject_FastCall(func, arg + 1, 0 | __Pyx_PY_VECTORCALL_ARGUMENTS_OFFSET);
}

/* PyObjectGetMethod */
  static int __Pyx_PyObject_GetMethod(PyObject *obj, PyObject *name, PyObject **method) {
    PyObject *attr;
#if CYTHON_UNPACK_METHODS && CYTHON_COMPILING_IN_CPYTHON && CYTHON_USE_PYTYPE_LOOKUP
    __Pyx_TypeName type_name;
    PyTypeObject *tp = Py_TYPE(obj);
    PyObject *descr;
    descrgetfunc f = NULL;
    PyObject **dictptr, *dict;
    int meth_found = 0;
    assert (*method == NULL);
    if (unlikely(tp->tp_getattro != PyObject_GenericGetAttr)) {
        attr = __Pyx_PyObject_GetAttrStr(obj, name);
        goto try_unpack;
    }
    if (unlikely(tp->tp_dict == NULL) && unlikely(PyType_Ready(tp) < 0)) {
        return 0;
    }
    descr = _PyType_Lookup(tp, name);
    if (likely(descr != NULL)) {
        Py_INCREF(descr);
#if defined(Py_TPFLAGS_METHOD_DESCRIPTOR) && Py_TPFLAGS_METHOD_DESCRIPTOR
        if (__Pyx_PyType_HasFeature(Py_TYPE(descr), Py_TPFLAGS_METHOD_DESCRIPTOR))
#else
        #ifdef __Pyx_CyFunction_USED
        if (likely(PyFunction_Check(descr) || __Pyx_IS_TYPE(descr, &PyMethodDescr_Type) || __Pyx_CyFunction_Check(descr)))
        #else
        if (likely(PyFunction_Check(descr) || __Pyx_IS_TYPE(descr, &PyMethodDescr_Type)))
        #endif
#endif
        {
            meth_found = 1;
        } else {
            f = Py_TYPE(descr)->tp_descr_get;
            if (f != NULL && PyDescr_IsData(descr)) {
                attr = f(descr, obj, (PyObject *)Py_TYPE(obj));
                Py_DECREF(descr);
                goto try_unpack;
            }
        }
    }
    dictptr = _PyObject_GetDictPtr(obj);
    if (dictptr != NULL && (dict = *dictptr) != NULL) {
        Py_INCREF(dict);
        attr = __Pyx_PyDict_GetItemStr(dict, name);
        if (attr != NULL) {
            Py_INCREF(attr);
            Py_DECREF(dict);
            Py_XDECREF(descr);
            goto try_unpack;
        }
        Py_DECREF(dict);
    }
    if (meth_found) {
        *method = descr;
        return 1;
    }
    if (f != NULL) {
        attr = f(descr, obj, (PyObject *)Py_TYPE(obj));
        Py_DECREF(descr);
        goto try_unpack;
    }
    if (likely(descr != NULL)) {
        *method = descr;
        return 0;
    }
    type_name = __Pyx_PyType_GetFullyQualifiedName(tp);
    PyErr_Format(PyExc_AttributeError,
                 "'" __Pyx_FMT_TYPENAME "' object has no attribute '%U'",
                 type_name, name);
    __Pyx_DECREF_TypeName(type_name);
    return 0;
#else
    attr = __Pyx_PyObject_GetAttrStr(obj, name);
    goto try_unpack;
#endif
try_unpack:
#if CYTHON_UNPACK_METHODS
    if (likely(attr) && PyMethod_Check(attr) && likely(PyMethod_GET_SELF(attr) == obj)) {
        PyObject *function = PyMethod_GET_FUNCTION(attr);
        Py_INCREF(function);
        Py_DECREF(attr);
        *method = function;
        return 1;
    }
#endif
    *method = attr;
    return 0;
}

/* PyObjectCallMethod0 */
  static PyObject* __Pyx_PyObject_CallMethod0(PyObject* obj, PyObject* method_name) {
#if CYTHON_VECTORCALL && (__PYX_LIMITED_VERSION_HEX >= 0x030C0000 || (!CYTHON_COMPILING_IN_LIMITED_API && PY_VERSION_HEX >= 0x03090000))
    PyObject *args[1] = {obj};
    (void) __Pyx_PyObject_GetMethod;
    (void) __Pyx_PyObject_CallOneArg;
    (void) __Pyx_PyObject_CallNoArg;
    return PyObject_VectorcallMethod(method_name, args, 1 | PY_VECTORCALL_ARGUMENTS_OFFSET, NULL);
#else
    PyObject *method = NULL, *result = NULL;
    int is_method = __Pyx_PyObject_GetMethod(obj, method_name, &method);
    if (likely(is_method)) {
        result = __Pyx_PyObject_CallOneArg(method, obj);
        Py_DECREF(method);
        return result;
    }
    if (unlikely(!method)) goto bad;
    result = __Pyx_PyObject_CallNoArg(method);
    Py_DECREF(method);
bad:
    return result;
#endif
}

/* UnpackItemEndCheck */
  static int __Pyx_IternextUnpackEndCheck(PyObject *retval, Py_ssize_t expected) {
    if (unlikely(retval)) {
        Py_DECREF(retval);
        __Pyx_RaiseTooManyValuesError(expected);
        return -1;
    }
    return __Pyx_IterFinish();
}

/* UnpackTupleError */
  static void __Pyx_UnpackTupleError(PyObject *t, Py_ssize_t index) {
    if (t == Py_None) {
      __Pyx_RaiseNoneNotIterableError();
    } else {
      Py_ssize_t size = __Pyx_PyTuple_GET_SIZE(t);
 #if !CYTHON_ASSUME_SAFE_SIZE
      if (unlikely(size < 0)) return;
 #endif
      if (size < index) {
        __Pyx_RaiseNeedMoreValuesError(size);
      } else {
        __Pyx_RaiseTooManyValuesError(index);
      }
    }
}

/* UnpackTuple2 */
  static CYTHON_INLINE int __Pyx_unpack_tuple2(
        PyObject* tuple, PyObject** value1, PyObject** value2, int is_tuple, int has_known_size, int decref_tuple) {
    if (likely(is_tuple || PyTuple_Check(tuple))) {
        Py_ssize_t size;
        if (has_known_size) {
            return __Pyx_unpack_tuple2_exact(tuple, value1, value2, decref_tuple);
        }
        size = __Pyx_PyTuple_GET_SIZE(tuple);
        if (likely(size == 2)) {
            return __Pyx_unpack_tuple2_exact(tuple, value1, value2, decref_tuple);
        }
        if (size >= 0) {
            __Pyx_UnpackTupleError(tuple, 2);
        }
        return -1;
    } else {
        return __Pyx_unpack_tuple2_generic(tuple, value1, value2, has_known_size, decref_tuple);
    }
}
static CYTHON_INLINE int __Pyx_unpack_tuple2_exact(
        PyObject* tuple, PyObject** pvalue1, PyObject** pvalue2, int decref_tuple) {
    PyObject *value1 = NULL, *value2 = NULL;
#if CYTHON_AVOID_BORROWED_REFS || !CYTHON_ASSUME_SAFE_MACROS
    value1 = __Pyx_PySequence_ITEM(tuple, 0);  if (unlikely(!value1)) goto bad;
    value2 = __Pyx_PySequence_ITEM(tuple, 1);  if (unlikely(!value2)) goto bad;
#else
    value1 = PyTuple_GET_ITEM(tuple, 0);  Py_INCREF(value1);
    value2 = PyTuple_GET_ITEM(tuple, 1);  Py_INCREF(value2);
#endif
    if (decref_tuple) {
        Py_DECREF(tuple);
    }
    *pvalue1 = value1;
    *pvalue2 = value2;
    return 0;
#if CYTHON_AVOID_BORROWED_REFS || !CYTHON_ASSUME_SAFE_MACROS
bad:
    Py_XDECREF(value1);
    Py_XDECREF(value2);
    if (decref_tuple) { Py_XDECREF(tuple); }
    return -1;
#endif
}
static int __Pyx_unpack_tuple2_generic(PyObject* tuple, PyObject** pvalue1, PyObject** pvalue2,
                                       int has_known_size, int decref_tuple) {
    Py_ssize_t index;
    PyObject *value1 = NULL, *value2 = NULL, *iter = NULL;
    iternextfunc iternext;
    iter = PyObject_GetIter(tuple);
    if (unlikely(!iter)) goto bad;
    if (decref_tuple) { Py_DECREF(tuple); tuple = NULL; }
    iternext = __Pyx_PyObject_GetIterNextFunc(iter);
    value1 = iternext(iter); if (unlikely(!value1)) { index = 0; goto unpacking_failed; }
    value2 = iternext(iter); if (unlikely(!value2)) { index = 1; goto unpacking_failed; }
    if (!has_known_size && unlikely(__Pyx_IternextUnpackEndCheck(iternext(iter), 2))) goto bad;
    Py_DECREF(iter);
    *pvalue1 = value1;
    *pvalue2 = value2;
    return 0;
unpacking_failed:
    if (!has_known_size && __Pyx_IterFinish() == 0)
        __Pyx_RaiseNeedMoreValuesError(index);
bad:
    Py_XDECREF(iter);
    Py_XDECREF(value1);
    Py_XDECREF(value2);
    if (decref_tuple) { Py_XDECREF(tuple); }
    return -1;
}

/* dict_iter */
  #if CYTHON_COMPILING_IN_PYPY
#include <string.h>
#endif
static CYTHON_INLINE PyObject* __Pyx_dict_iterator(PyObject* iterable, int is_dict, PyObject* method_name,
                                                   Py_ssize_t* p_orig_length, int* p_source_is_dict) {
    is_dict = is_dict || likely(PyDict_CheckExact(iterable));
    *p_source_is_dict = is_dict;
    if (is_dict) {
#if !CYTHON_COMPILING_IN_PYPY
        *p_orig_length = PyDict_Size(iterable);
        Py_INCREF(iterable);
        return iterable;
#else
        static PyObject *py_items = NULL, *py_keys = NULL, *py_values = NULL;
        PyObject **pp = NULL;
        if (method_name) {
            const char *name = PyUnicode_AsUTF8(method_name);
            if (strcmp(name, "iteritems") == 0) pp = &py_items;
            else if (strcmp(name, "iterkeys") == 0) pp = &py_keys;
            else if (strcmp(name, "itervalues") == 0) pp = &py_values;
            if (pp) {
                if (!*pp) {
                    *pp = PyUnicode_FromString(name + 4);
                    if (!*pp)
                        return NULL;
                }
                method_name = *pp;
            }
        }
#endif
    }
    *p_orig_length = 0;
    if (method_name) {
        PyObject* iter;
        iterable = __Pyx_PyObject_CallMethod0(iterable, method_name);
        if (!iterable)
            return NULL;
#if !CYTHON_COMPILING_IN_PYPY
        if (PyTuple_CheckExact(iterable) || PyList_CheckExact(iterable))
            return iterable;
#endif
        iter = PyObject_GetIter(iterable);
        Py_DECREF(iterable);
        return iter;
    }
    return PyObject_GetIter(iterable);
}
#if !CYTHON_COMPILING_IN_PYPY
static CYTHON_INLINE int __Pyx_dict_iter_next_source_is_dict(
        PyObject* iter_obj, CYTHON_NCP_UNUSED Py_ssize_t orig_length, CYTHON_NCP_UNUSED Py_ssize_t* ppos,
        PyObject** pkey, PyObject** pvalue, PyObject** pitem) {
    PyObject *key, *value;
    if (unlikely(orig_length != PyDict_Size(iter_obj))) {
        PyErr_SetString(PyExc_RuntimeError, "dictionary changed size during iteration");
        return -1;
    }
    if (unlikely(!PyDict_Next(iter_obj, ppos, &key, &value))) {
        return 0;
    }
    if (pitem) {
        PyObject* tuple = PyTuple_New(2);
        if (unlikely(!tuple)) {
            return -1;
        }
        Py_INCREF(key);
        Py_INCREF(value);
        #if CYTHON_ASSUME_SAFE_MACROS
        PyTuple_SET_ITEM(tuple, 0, key);
        PyTuple_SET_ITEM(tuple, 1, value);
        #else
        if (unlikely(PyTuple_SetItem(tuple, 0, key) < 0)) {
            Py_DECREF(value);
            Py_DECREF(tuple);
            return -1;
        }
        if (unlikely(PyTuple_SetItem(tuple, 1, value) < 0)) {
            Py_DECREF(tuple);
            return -1;
        }
        #endif
        *pitem = tuple;
    } else {
        if (pkey) {
            Py_INCREF(key);
            *pkey = key;
        }
        if (pvalue) {
            Py_INCREF(value);
            *pvalue = value;
        }
    }
    return 1;
}
#endif
static CYTHON_INLINE int __Pyx_dict_iter_next(
        PyObject* iter_obj, CYTHON_NCP_UNUSED Py_ssize_t orig_length, CYTHON_NCP_UNUSED Py_ssize_t* ppos,
        PyObject** pkey, PyObject** pvalue, PyObject** pitem, int source_is_dict) {
    PyObject* next_item;
#if !CYTHON_COMPILING_IN_PYPY
    if (source_is_dict) {
        int result;
#if PY_VERSION_HEX >= 0x030d0000 && !CYTHON_COMPILING_IN_LIMITED_API
        Py_BEGIN_CRITICAL_SECTION(iter_obj);
#endif
        result = __Pyx_dict_iter_next_source_is_dict(iter_obj, orig_length, ppos, pkey, pvalue, pitem);
#if PY_VERSION_HEX >= 0x030d0000 && !CYTHON_COMPILING_IN_LIMITED_API
        Py_END_CRITICAL_SECTION();
#endif
        return result;
    } else if (PyTuple_CheckExact(iter_obj)) {
        Py_ssize_t pos = *ppos;
        Py_ssize_t tuple_size = __Pyx_PyTuple_GET_SIZE(iter_obj);
        #if !CYTHON_ASSUME_SAFE_SIZE
        if (unlikely(tuple_size < 0)) return -1;
        #endif
        if (unlikely(pos >= tuple_size)) return 0;
        *ppos = pos + 1;
        #if CYTHON_ASSUME_SAFE_MACROS
        next_item = PyTuple_GET_ITEM(iter_obj, pos);
        #else
        next_item = PyTuple_GetItem(iter_obj, pos);
        if (unlikely(!next_item)) return -1;
        #endif
        Py_INCREF(next_item);
    } else if (PyList_CheckExact(iter_obj)) {
        Py_ssize_t pos = *ppos;
        Py_ssize_t list_size = __Pyx_PyList_GET_SIZE(iter_obj);
        #if !CYTHON_ASSUME_SAFE_SIZE
        if (unlikely(list_size < 0)) return -1;
        #endif
        if (unlikely(pos >= list_size)) return 0;
        *ppos = pos + 1;
        #if CYTHON_AVOID_THREAD_UNSAFE_BORROWED_REFS
        next_item = PyList_GetItemRef(iter_obj, pos);
        if (unlikely(!next_item)) return -1;
        #elif CYTHON_ASSUME_SAFE_MACROS
        next_item = PyList_GET_ITEM(iter_obj, pos);
        Py_INCREF(next_item);
        #else
        next_item = PyList_GetItem(iter_obj, pos);
        if (unlikely(!next_item)) return -1;
        Py_INCREF(next_item);
        #endif
    } else
#endif
    {
        next_item = PyIter_Next(iter_obj);
        if (unlikely(!next_item)) {
            return __Pyx_IterFinish();
        }
    }
    if (pitem) {
        *pitem = next_item;
    } else if (pkey && pvalue) {
        if (__Pyx_unpack_tuple2(next_item, pkey, pvalue, source_is_dict, source_is_dict, 1))
            return -1;
    } else if (pkey) {
        *pkey = next_item;
    } else {
        *pvalue = next_item;
    }
    return 1;
}

/* BufferFallbackError */
  static void __Pyx_RaiseBufferFallbackError(void) {
  PyErr_SetString(PyExc_ValueError,
     "Buffer acquisition failed on assignment; and then reacquiring the old buffer failed too!");
}

/* PyLongBinop */
  #if !CYTHON_COMPILING_IN_PYPY
static PyObject* __Pyx_Fallback___Pyx_PyLong_AddObjC(PyObject *op1, PyObject *op2, int inplace) {
    return (inplace ? PyNumber_InPlaceAdd : PyNumber_Add)(op1, op2);
}
#if CYTHON_USE_PYLONG_INTERNALS
static PyObject* __Pyx_Unpacked___Pyx_PyLong_AddObjC(PyObject *op1, PyObject *op2, long intval, int inplace, int zerodivision_check) {
    CYTHON_MAYBE_UNUSED_VAR(inplace);
    CYTHON_UNUSED_VAR(zerodivision_check);
    const long b = intval;
    long a, x;
#ifdef HAVE_LONG_LONG
    const PY_LONG_LONG llb = intval;
    PY_LONG_LONG lla, llx;
#endif
    if (unlikely(__Pyx_PyLong_IsZero(op1))) {
        return __Pyx_NewRef(op2);
    }
    if (unlikely(!__Pyx_PyLong_CompactAsLong(op1, &a))) {
        const digit* digits = __Pyx_PyLong_Digits(op1);
        const Py_ssize_t size = __Pyx_PyLong_SignedDigitCount(op1);
        switch (size) {
            case -2:
                if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                    a = -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
                    lla = -(PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            case 2:
                if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                    a = (long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
                    lla = (PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            case -3:
                if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                    a = -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
                    lla = -(PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            case 3:
                if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                    a = (long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
                    lla = (PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            case -4:
                if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                    a = -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
                    lla = -(PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            case 4:
                if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                    a = (long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
                    lla = (PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            default: return PyLong_Type.tp_as_number->nb_add(op1, op2);
        }
    }
            x = a + b;
        return PyLong_FromLong(x);
#ifdef HAVE_LONG_LONG
    long_long:
            llx = lla + llb;
        return PyLong_FromLongLong(llx);
#endif
    return __Pyx_Fallback___Pyx_PyLong_AddObjC(op1, op2, inplace);
    
    
}
#endif
static PyObject* __Pyx_Float___Pyx_PyLong_AddObjC(PyObject *float_val, long intval, int zerodivision_check) {
    CYTHON_UNUSED_VAR(zerodivision_check);
    const long b = intval;
    double a = __Pyx_PyFloat_AS_DOUBLE(float_val);
        double result;
        
        result = ((double)a) + (double)b;
        return PyFloat_FromDouble(result);
}
static CYTHON_INLINE PyObject* __Pyx_PyLong_AddObjC(PyObject *op1, PyObject *op2, long intval, int inplace, int zerodivision_check) {
    CYTHON_MAYBE_UNUSED_VAR(intval);
    CYTHON_UNUSED_VAR(zerodivision_check);
    #if CYTHON_USE_PYLONG_INTERNALS
    if (likely(PyLong_CheckExact(op1))) {
        return __Pyx_Unpacked___Pyx_PyLong_AddObjC(op1, op2, intval, inplace, zerodivision_check);
    }
    #endif
    if (PyFloat_CheckExact(op1)) {
        return __Pyx_Float___Pyx_PyLong_AddObjC(op1, intval, zerodivision_check);
    }
    return __Pyx_Fallback___Pyx_PyLong_AddObjC(op1, op2, inplace);
}
#endif

/* PyLongBinop */
  #if !CYTHON_COMPILING_IN_PYPY
static PyObject* __Pyx_Fallback___Pyx_PyLong_MultiplyObjC(PyObject *op1, PyObject *op2, int inplace) {
    return (inplace ? PyNumber_InPlaceMultiply : PyNumber_Multiply)(op1, op2);
}
#if CYTHON_USE_PYLONG_INTERNALS
static PyObject* __Pyx_Unpacked___Pyx_PyLong_MultiplyObjC(PyObject *op1, PyObject *op2, long intval, int inplace, int zerodivision_check) {
    CYTHON_MAYBE_UNUSED_VAR(inplace);
    CYTHON_UNUSED_VAR(zerodivision_check);
    const long b = intval;
    long a, x;
#ifdef HAVE_LONG_LONG
    const PY_LONG_LONG llb = intval;
    PY_LONG_LONG lla, llx;
#endif
    if (unlikely(__Pyx_PyLong_IsZero(op1))) {
        return __Pyx_NewRef(op1);
    }
    if (unlikely(!__Pyx_PyLong_CompactAsLong(op1, &a))) {
        const digit* digits = __Pyx_PyLong_Digits(op1);
        const Py_ssize_t size = __Pyx_PyLong_SignedDigitCount(op1);
        switch (size) {
            case -2:
                if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT+30) {
                    a = -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT+30) {
                    lla = -(PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            case 2:
                if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT+30) {
                    a = (long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT+30) {
                    lla = (PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            case -3:
                if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT+30) {
                    a = -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT+30) {
                    lla = -(PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            case 3:
                if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT+30) {
                    a = (long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT+30) {
                    lla = (PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            case -4:
                if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT+30) {
                    a = -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT+30) {
                    lla = -(PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            case 4:
                if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT+30) {
                    a = (long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    break;
                #ifdef HAVE_LONG_LONG
                } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT+30) {
                    lla = (PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                    goto long_long;
                #endif
                }
                CYTHON_FALLTHROUGH;
            default: return PyLong_Type.tp_as_number->nb_multiply(op1, op2);
        }
    }
            CYTHON_UNUSED_VAR(a);
            CYTHON_UNUSED_VAR(b);
            #ifdef HAVE_LONG_LONG
            lla = a;
            goto long_long;
            #else
            return PyLong_Type.tp_as_number->nb_multiply(op1, op2);
            #endif
        return PyLong_FromLong(x);
#ifdef HAVE_LONG_LONG
    long_long:
            llx = lla * llb;
        return PyLong_FromLongLong(llx);
#endif
    return __Pyx_Fallback___Pyx_PyLong_MultiplyObjC(op1, op2, inplace);
    
    
}
#endif
static PyObject* __Pyx_Float___Pyx_PyLong_MultiplyObjC(PyObject *float_val, long intval, int zerodivision_check) {
    CYTHON_UNUSED_VAR(zerodivision_check);
    const long b = intval;
    double a = __Pyx_PyFloat_AS_DOUBLE(float_val);
        double result;
        
        result = ((double)a) * (double)b;
        return PyFloat_FromDouble(result);
}
static CYTHON_INLINE PyObject* __Pyx_PyLong_MultiplyObjC(PyObject *op1, PyObject *op2, long intval, int inplace, int zerodivision_check) {
    CYTHON_MAYBE_UNUSED_VAR(intval);
    CYTHON_UNUSED_VAR(zerodivision_check);
    #if CYTHON_USE_PYLONG_INTERNALS
    if (likely(PyLong_CheckExact(op1))) {
        return __Pyx_Unpacked___Pyx_PyLong_MultiplyObjC(op1, op2, intval, inplace, zerodivision_check);
    }
    #endif
    if (PyFloat_CheckExact(op1)) {
        return __Pyx_Float___Pyx_PyLong_MultiplyObjC(op1, intval, zerodivision_check);
    }
    return __Pyx_Fallback___Pyx_PyLong_MultiplyObjC(op1, op2, inplace);
}
#endif

/* CallUnboundCMethod0 */
  #if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_CallUnboundCMethod0(__Pyx_CachedCFunction* cfunc, PyObject* self) {
    int was_initialized = __Pyx_CachedCFunction_GetAndSetInitializing(cfunc);
    if (likely(was_initialized == 2 && cfunc->func)) {
        if (likely(cfunc->flag == METH_NOARGS))
            return __Pyx_CallCFunction(cfunc, self, NULL);
        if (likely(cfunc->flag == METH_FASTCALL))
            return __Pyx_CallCFunctionFast(cfunc, self, NULL, 0);
        if (cfunc->flag == (METH_FASTCALL | METH_KEYWORDS))
            return __Pyx_CallCFunctionFastWithKeywords(cfunc, self, NULL, 0, NULL);
        if (likely(cfunc->flag == (METH_VARARGS | METH_KEYWORDS)))
            return __Pyx_CallCFunctionWithKeywords(cfunc, self, __pyx_mstate_global->__pyx_empty_tuple, NULL);
        if (cfunc->flag == METH_VARARGS)
            return __Pyx_CallCFunction(cfunc, self, __pyx_mstate_global->__pyx_empty_tuple);
        return __Pyx__CallUnboundCMethod0(cfunc, self);
    }
#if CYTHON_COMPILING_IN_CPYTHON_FREETHREADING
    else if (unlikely(was_initialized == 1)) {
        __Pyx_CachedCFunction tmp_cfunc = {
#ifndef __cplusplus
            0
#endif
        };
        tmp_cfunc.type = cfunc->type;
        tmp_cfunc.method_name = cfunc->method_name;
        return __Pyx__CallUnboundCMethod0(&tmp_cfunc, self);
    }
#endif
    PyObject *result = __Pyx__CallUnboundCMethod0(cfunc, self);
    __Pyx_CachedCFunction_SetFinishedInitializing(cfunc);
    return result;
}
#endif
static PyObject* __Pyx__CallUnboundCMethod0(__Pyx_CachedCFunction* cfunc, PyObject* self) {
    PyObject *result;
    if (unlikely(!cfunc->method) && unlikely(__Pyx_TryUnpackUnboundCMethod(cfunc) < 0)) return NULL;
    result = __Pyx_PyObject_CallOneArg(cfunc->method, self);
    return result;
}

/* py_dict_keys */
  static CYTHON_INLINE PyObject* __Pyx_PyDict_Keys(PyObject* d) {
    return __Pyx_CallUnboundCMethod0(&__pyx_mstate_global->__pyx_umethod_PyDict_Type_keys, d);
}

/* PyFloatBinop */
  #if !CYTHON_COMPILING_IN_PYPY
static PyObject* __Pyx_PyFloat_AddCObj(PyObject *op1, PyObject *op2, double floatval, int inplace, int zerodivision_check) {
    const double a = floatval;
    double b, result;
    CYTHON_UNUSED_VAR(inplace);
    CYTHON_UNUSED_VAR(zerodivision_check);
    if (likely(PyFloat_CheckExact(op2))) {
        b = __Pyx_PyFloat_AS_DOUBLE(op2);
        
    } else
    if (likely(PyLong_CheckExact(op2))) {
        #if CYTHON_USE_PYLONG_INTERNALS
        if (__Pyx_PyLong_IsZero(op2)) {
            b = 0.0;
            
        } else if (__Pyx_PyLong_IsCompact(op2)) {
            b = (double) __Pyx_PyLong_CompactValue(op2);
        } else {
            const digit* digits = __Pyx_PyLong_Digits(op2);
            const Py_ssize_t size = __Pyx_PyLong_SignedDigitCount(op2);
            switch (size) {
                case -2:
                case 2:
                    if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (1 * PyLong_SHIFT < 53))) {
                        b = (double) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        if ((8 * sizeof(unsigned long) < 53) || (2 * PyLong_SHIFT < 53) || (b < (double) ((PY_LONG_LONG)1 << 53))) {
                            if (size == -2)
                                b = -b;
                            break;
                        }
                    }
                    CYTHON_FALLTHROUGH;
                case -3:
                case 3:
                    if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (2 * PyLong_SHIFT < 53))) {
                        b = (double) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        if ((8 * sizeof(unsigned long) < 53) || (3 * PyLong_SHIFT < 53) || (b < (double) ((PY_LONG_LONG)1 << 53))) {
                            if (size == -3)
                                b = -b;
                            break;
                        }
                    }
                    CYTHON_FALLTHROUGH;
                case -4:
                case 4:
                    if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (3 * PyLong_SHIFT < 53))) {
                        b = (double) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        if ((8 * sizeof(unsigned long) < 53) || (4 * PyLong_SHIFT < 53) || (b < (double) ((PY_LONG_LONG)1 << 53))) {
                            if (size == -4)
                                b = -b;
                            break;
                        }
                    }
                    CYTHON_FALLTHROUGH;
                default:
        #endif
                    b = PyLong_AsDouble(op2);
                    if (unlikely(b == -1.0 && PyErr_Occurred())) return NULL;
        #if CYTHON_USE_PYLONG_INTERNALS
            }
        }
        #endif
    } else {
        return (inplace ? PyNumber_InPlaceAdd : PyNumber_Add)(op1, op2);
    }
        result = a + b;
        return PyFloat_FromDouble(result);
}
#endif

/* CallTypeTraverse */
  #if !CYTHON_USE_TYPE_SPECS || (!CYTHON_COMPILING_IN_LIMITED_API && PY_VERSION_HEX < 0x03090000)
#else
static int __Pyx_call_type_traverse(PyObject *o, int always_call, visitproc visit, void *arg) {
    #if CYTHON_COMPILING_IN_LIMITED_API && __PYX_LIMITED_VERSION_HEX < 0x03090000
    if (__Pyx_get_runtime_version() < 0x03090000) return 0;
    #endif
    if (!always_call) {
        PyTypeObject *base = __Pyx_PyObject_GetSlot(o, tp_base, PyTypeObject*);
        unsigned long flags = PyType_GetFlags(base);
        if (flags & Py_TPFLAGS_HEAPTYPE) {
            return 0;
        }
    }
    Py_VISIT((PyObject*)Py_TYPE(o));
    return 0;
}
#endif

/* LimitedApiGetTypeDict */
  #if CYTHON_COMPILING_IN_LIMITED_API
static Py_ssize_t __Pyx_GetTypeDictOffset(void) {
    PyObject *tp_dictoffset_o;
    Py_ssize_t tp_dictoffset;
    tp_dictoffset_o = PyObject_GetAttrString((PyObject*)(&PyType_Type), "__dictoffset__");
    if (unlikely(!tp_dictoffset_o)) return -1;
    tp_dictoffset = PyLong_AsSsize_t(tp_dictoffset_o);
    Py_DECREF(tp_dictoffset_o);
    if (unlikely(tp_dictoffset == 0)) {
        PyErr_SetString(
            PyExc_TypeError,
            "'type' doesn't have a dictoffset");
        return -1;
    } else if (unlikely(tp_dictoffset < 0)) {
        PyErr_SetString(
            PyExc_TypeError,
            "'type' has an unexpected negative dictoffset. "
            "Please report this as Cython bug");
        return -1;
    }
    return tp_dictoffset;
}
static PyObject *__Pyx_GetTypeDict(PyTypeObject *tp) {
    static Py_ssize_t tp_dictoffset = 0;
    if (unlikely(tp_dictoffset == 0)) {
        tp_dictoffset = __Pyx_GetTypeDictOffset();
        if (unlikely(tp_dictoffset == -1 && PyErr_Occurred())) {
            tp_dictoffset = 0; // try again next time?
            return NULL;
        }
    }
    return *(PyObject**)((char*)tp + tp_dictoffset);
}
#endif

/* SetItemOnTypeDict */
  static int __Pyx__SetItemOnTypeDict(PyTypeObject *tp, PyObject *k, PyObject *v) {
    int result;
    PyObject *tp_dict;
#if CYTHON_COMPILING_IN_LIMITED_API
    tp_dict = __Pyx_GetTypeDict(tp);
    if (unlikely(!tp_dict)) return -1;
#else
    tp_dict = tp->tp_dict;
#endif
    result = PyDict_SetItem(tp_dict, k, v);
    if (likely(!result)) {
        PyType_Modified(tp);
        if (unlikely(PyObject_HasAttr(v, __pyx_mstate_global->__pyx_n_u_set_name))) {
            PyObject *setNameResult = PyObject_CallMethodObjArgs(v, __pyx_mstate_global->__pyx_n_u_set_name,  (PyObject *) tp, k, NULL);
            if (!setNameResult) return -1;
            Py_DECREF(setNameResult);
        }
    }
    return result;
}

/* FixUpExtensionType */
  static int __Pyx_fix_up_extension_type_from_spec(PyType_Spec *spec, PyTypeObject *type) {
#if __PYX_LIMITED_VERSION_HEX > 0x030900B1
    CYTHON_UNUSED_VAR(spec);
    CYTHON_UNUSED_VAR(type);
    CYTHON_UNUSED_VAR(__Pyx__SetItemOnTypeDict);
#else
    const PyType_Slot *slot = spec->slots;
    int changed = 0;
#if !CYTHON_COMPILING_IN_LIMITED_API
    while (slot && slot->slot && slot->slot != Py_tp_members)
        slot++;
    if (slot && slot->slot == Py_tp_members) {
#if !CYTHON_COMPILING_IN_CPYTHON
        const
#endif  // !CYTHON_COMPILING_IN_CPYTHON)
            PyMemberDef *memb = (PyMemberDef*) slot->pfunc;
        while (memb && memb->name) {
            if (memb->name[0] == '_' && memb->name[1] == '_') {
                if (strcmp(memb->name, "__weaklistoffset__") == 0) {
                    assert(memb->type == T_PYSSIZET);
                    assert(memb->flags == READONLY);
                    type->tp_weaklistoffset = memb->offset;
                    changed = 1;
                }
                else if (strcmp(memb->name, "__dictoffset__") == 0) {
                    assert(memb->type == T_PYSSIZET);
                    assert(memb->flags == READONLY);
                    type->tp_dictoffset = memb->offset;
                    changed = 1;
                }
#if CYTHON_METH_FASTCALL
                else if (strcmp(memb->name, "__vectorcalloffset__") == 0) {
                    assert(memb->type == T_PYSSIZET);
                    assert(memb->flags == READONLY);
#if PY_VERSION_HEX >= 0x030800b4
                    type->tp_vectorcall_offset = memb->offset;
#else
                    type->tp_print = (printfunc) memb->offset;
#endif
                    changed = 1;
                }
#endif  // CYTHON_METH_FASTCALL
#if !CYTHON_COMPILING_IN_PYPY
                else if (strcmp(memb->name, "__module__") == 0) {
                    PyObject *descr;
                    assert(memb->type == T_OBJECT);
                    assert(memb->flags == 0 || memb->flags == READONLY);
                    descr = PyDescr_NewMember(type, memb);
                    if (unlikely(!descr))
                        return -1;
                    int set_item_result = PyDict_SetItem(type->tp_dict, PyDescr_NAME(descr), descr);
                    Py_DECREF(descr);
                    if (unlikely(set_item_result < 0)) {
                        return -1;
                    }
                    changed = 1;
                }
#endif  // !CYTHON_COMPILING_IN_PYPY
            }
            memb++;
        }
    }
#endif  // !CYTHON_COMPILING_IN_LIMITED_API
#if !CYTHON_COMPILING_IN_PYPY
    slot = spec->slots;
    while (slot && slot->slot && slot->slot != Py_tp_getset)
        slot++;
    if (slot && slot->slot == Py_tp_getset) {
        PyGetSetDef *getset = (PyGetSetDef*) slot->pfunc;
        while (getset && getset->name) {
            if (getset->name[0] == '_' && getset->name[1] == '_' && strcmp(getset->name, "__module__") == 0) {
                PyObject *descr = PyDescr_NewGetSet(type, getset);
                if (unlikely(!descr))
                    return -1;
                #if CYTHON_COMPILING_IN_LIMITED_API
                PyObject *pyname = PyUnicode_FromString(getset->name);
                if (unlikely(!pyname)) {
                    Py_DECREF(descr);
                    return -1;
                }
                int set_item_result = __Pyx_SetItemOnTypeDict(type, pyname, descr);
                Py_DECREF(pyname);
                #else
                CYTHON_UNUSED_VAR(__Pyx__SetItemOnTypeDict);
                int set_item_result = PyDict_SetItem(type->tp_dict, PyDescr_NAME(descr), descr);
                #endif
                Py_DECREF(descr);
                if (unlikely(set_item_result < 0)) {
                    return -1;
                }
                changed = 1;
            }
            ++getset;
        }
    }
#endif  // !CYTHON_COMPILING_IN_PYPY
    if (changed)
        PyType_Modified(type);
#endif  // PY_VERSION_HEX > 0x030900B1
    return 0;
}

/* ValidateBasesTuple */
  #if CYTHON_COMPILING_IN_CPYTHON || CYTHON_COMPILING_IN_LIMITED_API || CYTHON_USE_TYPE_SPECS
static int __Pyx_validate_bases_tuple(const char *type_name, Py_ssize_t dictoffset, PyObject *bases) {
    Py_ssize_t i, n;
#if CYTHON_ASSUME_SAFE_SIZE
    n = PyTuple_GET_SIZE(bases);
#else
    n = PyTuple_Size(bases);
    if (unlikely(n < 0)) return -1;
#endif
    for (i = 1; i < n; i++)
    {
        PyTypeObject *b;
#if CYTHON_AVOID_BORROWED_REFS
        PyObject *b0 = PySequence_GetItem(bases, i);
        if (!b0) return -1;
#elif CYTHON_ASSUME_SAFE_MACROS
        PyObject *b0 = PyTuple_GET_ITEM(bases, i);
#else
        PyObject *b0 = PyTuple_GetItem(bases, i);
        if (!b0) return -1;
#endif
        b = (PyTypeObject*) b0;
        if (!__Pyx_PyType_HasFeature(b, Py_TPFLAGS_HEAPTYPE))
        {
            __Pyx_TypeName b_name = __Pyx_PyType_GetFullyQualifiedName(b);
            PyErr_Format(PyExc_TypeError,
                "base class '" __Pyx_FMT_TYPENAME "' is not a heap type", b_name);
            __Pyx_DECREF_TypeName(b_name);
#if CYTHON_AVOID_BORROWED_REFS
            Py_DECREF(b0);
#endif
            return -1;
        }
        if (dictoffset == 0)
        {
            Py_ssize_t b_dictoffset = 0;
#if CYTHON_USE_TYPE_SLOTS
            b_dictoffset = b->tp_dictoffset;
#else
            PyObject *py_b_dictoffset = PyObject_GetAttrString((PyObject*)b, "__dictoffset__");
            if (!py_b_dictoffset) goto dictoffset_return;
            b_dictoffset = PyLong_AsSsize_t(py_b_dictoffset);
            Py_DECREF(py_b_dictoffset);
            if (b_dictoffset == -1 && PyErr_Occurred()) goto dictoffset_return;
#endif
            if (b_dictoffset) {
                {
                    __Pyx_TypeName b_name = __Pyx_PyType_GetFullyQualifiedName(b);
                    PyErr_Format(PyExc_TypeError,
                        "extension type '%.200s' has no __dict__ slot, "
                        "but base type '" __Pyx_FMT_TYPENAME "' has: "
                        "either add 'cdef dict __dict__' to the extension type "
                        "or add '__slots__ = [...]' to the base type",
                        type_name, b_name);
                    __Pyx_DECREF_TypeName(b_name);
                }
#if !CYTHON_USE_TYPE_SLOTS
              dictoffset_return:
#endif
#if CYTHON_AVOID_BORROWED_REFS
                Py_DECREF(b0);
#endif
                return -1;
            }
        }
#if CYTHON_AVOID_BORROWED_REFS
        Py_DECREF(b0);
#endif
    }
    return 0;
}
#endif

/* PyType_Ready */
  CYTHON_UNUSED static int __Pyx_PyType_HasMultipleInheritance(PyTypeObject *t) {
    while (t) {
        PyObject *bases = __Pyx_PyType_GetSlot(t, tp_bases, PyObject*);
        if (bases) {
            return 1;
        }
        t = __Pyx_PyType_GetSlot(t, tp_base, PyTypeObject*);
    }
    return 0;
}
static int __Pyx_PyType_Ready(PyTypeObject *t) {
#if CYTHON_USE_TYPE_SPECS || !CYTHON_COMPILING_IN_CPYTHON || defined(PYSTON_MAJOR_VERSION)
    (void)__Pyx_PyObject_CallMethod0;
#if CYTHON_USE_TYPE_SPECS
    (void)__Pyx_validate_bases_tuple;
#endif
    return PyType_Ready(t);
#else
    int r;
    if (!__Pyx_PyType_HasMultipleInheritance(t)) {
        return PyType_Ready(t);
    }
    PyObject *bases = __Pyx_PyType_GetSlot(t, tp_bases, PyObject*);
    if (bases && unlikely(__Pyx_validate_bases_tuple(t->tp_name, t->tp_dictoffset, bases) == -1))
        return -1;
#if !defined(PYSTON_MAJOR_VERSION)
    {
        int gc_was_enabled;
    #if PY_VERSION_HEX >= 0x030A00b1
        gc_was_enabled = PyGC_Disable();
        (void)__Pyx_PyObject_CallMethod0;
    #else
        PyObject *ret, *py_status;
        PyObject *gc = NULL;
        #if (!CYTHON_COMPILING_IN_PYPY || PYPY_VERSION_NUM+0 >= 0x07030400) &&\
                !CYTHON_COMPILING_IN_GRAAL
        gc = PyImport_GetModule(__pyx_mstate_global->__pyx_kp_u_gc);
        #endif
        if (unlikely(!gc)) gc = PyImport_Import(__pyx_mstate_global->__pyx_kp_u_gc);
        if (unlikely(!gc)) return -1;
        py_status = __Pyx_PyObject_CallMethod0(gc, __pyx_mstate_global->__pyx_kp_u_isenabled);
        if (unlikely(!py_status)) {
            Py_DECREF(gc);
            return -1;
        }
        gc_was_enabled = __Pyx_PyObject_IsTrue(py_status);
        Py_DECREF(py_status);
        if (gc_was_enabled > 0) {
            ret = __Pyx_PyObject_CallMethod0(gc, __pyx_mstate_global->__pyx_kp_u_disable);
            if (unlikely(!ret)) {
                Py_DECREF(gc);
                return -1;
            }
            Py_DECREF(ret);
        } else if (unlikely(gc_was_enabled == -1)) {
            Py_DECREF(gc);
            return -1;
        }
    #endif
        t->tp_flags |= Py_TPFLAGS_HEAPTYPE;
#if PY_VERSION_HEX >= 0x030A0000
        t->tp_flags |= Py_TPFLAGS_IMMUTABLETYPE;
#endif
#else
        (void)__Pyx_PyObject_CallMethod0;
#endif
    r = PyType_Ready(t);
#if !defined(PYSTON_MAJOR_VERSION)
        t->tp_flags &= ~Py_TPFLAGS_HEAPTYPE;
    #if PY_VERSION_HEX >= 0x030A00b1
        if (gc_was_enabled)
            PyGC_Enable();
    #else
        if (gc_was_enabled) {
            PyObject *tp, *v, *tb;
            PyErr_Fetch(&tp, &v, &tb);
            ret = __Pyx_PyObject_CallMethod0(gc, __pyx_mstate_global->__pyx_kp_u_enable);
            if (likely(ret || r == -1)) {
                Py_XDECREF(ret);
                PyErr_Restore(tp, v, tb);
            } else {
                Py_XDECREF(tp);
                Py_XDECREF(v);
                Py_XDECREF(tb);
                r = -1;
            }
        }
        Py_DECREF(gc);
    #endif
    }
#endif
    return r;
#endif
}

/* SetVTable */
  static int __Pyx_SetVtable(PyTypeObject *type, void *vtable) {
    PyObject *ob = PyCapsule_New(vtable, 0, 0);
    if (unlikely(!ob))
        goto bad;
#if CYTHON_COMPILING_IN_LIMITED_API
    if (unlikely(PyObject_SetAttr((PyObject *) type, __pyx_mstate_global->__pyx_n_u_pyx_vtable, ob) < 0))
#else
    if (unlikely(PyDict_SetItem(type->tp_dict, __pyx_mstate_global->__pyx_n_u_pyx_vtable, ob) < 0))
#endif
        goto bad;
    Py_DECREF(ob);
    return 0;
bad:
    Py_XDECREF(ob);
    return -1;
}

/* GetVTable */
  static void* __Pyx_GetVtable(PyTypeObject *type) {
    void* ptr;
#if CYTHON_COMPILING_IN_LIMITED_API
    PyObject *ob = PyObject_GetAttr((PyObject *)type, __pyx_mstate_global->__pyx_n_u_pyx_vtable);
#else
    PyObject *ob = PyObject_GetItem(type->tp_dict, __pyx_mstate_global->__pyx_n_u_pyx_vtable);
#endif
    if (!ob)
        goto bad;
    ptr = PyCapsule_GetPointer(ob, 0);
    if (!ptr && !PyErr_Occurred())
        PyErr_SetString(PyExc_RuntimeError, "invalid vtable found for imported type");
    Py_DECREF(ob);
    return ptr;
bad:
    Py_XDECREF(ob);
    return NULL;
}

/* MergeVTables */
  static int __Pyx_MergeVtables(PyTypeObject *type) {
    int i=0;
    Py_ssize_t size;
    void** base_vtables;
    __Pyx_TypeName tp_base_name = NULL;
    __Pyx_TypeName base_name = NULL;
    void* unknown = (void*)-1;
    PyObject* bases = __Pyx_PyType_GetSlot(type, tp_bases, PyObject*);
    int base_depth = 0;
    {
        PyTypeObject* base = __Pyx_PyType_GetSlot(type, tp_base, PyTypeObject*);
        while (base) {
            base_depth += 1;
            base = __Pyx_PyType_GetSlot(base, tp_base, PyTypeObject*);
        }
    }
    base_vtables = (void**) PyMem_Malloc(sizeof(void*) * (size_t)(base_depth + 1));
    base_vtables[0] = unknown;
#if CYTHON_COMPILING_IN_LIMITED_API
    size = PyTuple_Size(bases);
    if (size < 0) goto other_failure;
#else
    size = PyTuple_GET_SIZE(bases);
#endif
    for (i = 1; i < size; i++) {
        PyObject *basei;
        void* base_vtable;
#if CYTHON_AVOID_BORROWED_REFS
        basei = PySequence_GetItem(bases, i);
        if (unlikely(!basei)) goto other_failure;
#elif !CYTHON_ASSUME_SAFE_MACROS
        basei = PyTuple_GetItem(bases, i);
        if (unlikely(!basei)) goto other_failure;
#else
        basei = PyTuple_GET_ITEM(bases, i);
#endif
        base_vtable = __Pyx_GetVtable((PyTypeObject*)basei);
#if CYTHON_AVOID_BORROWED_REFS
        Py_DECREF(basei);
#endif
        if (base_vtable != NULL) {
            int j;
            PyTypeObject* base = __Pyx_PyType_GetSlot(type, tp_base, PyTypeObject*);
            for (j = 0; j < base_depth; j++) {
                if (base_vtables[j] == unknown) {
                    base_vtables[j] = __Pyx_GetVtable(base);
                    base_vtables[j + 1] = unknown;
                }
                if (base_vtables[j] == base_vtable) {
                    break;
                } else if (base_vtables[j] == NULL) {
                    goto bad;
                }
                base = __Pyx_PyType_GetSlot(base, tp_base, PyTypeObject*);
            }
        }
    }
    PyErr_Clear();
    PyMem_Free(base_vtables);
    return 0;
bad:
    {
        PyTypeObject* basei = NULL;
        PyTypeObject* tp_base = __Pyx_PyType_GetSlot(type, tp_base, PyTypeObject*);
        tp_base_name = __Pyx_PyType_GetFullyQualifiedName(tp_base);
#if CYTHON_AVOID_BORROWED_REFS
        basei = (PyTypeObject*)PySequence_GetItem(bases, i);
        if (unlikely(!basei)) goto really_bad;
#elif !CYTHON_ASSUME_SAFE_MACROS
        basei = (PyTypeObject*)PyTuple_GetItem(bases, i);
        if (unlikely(!basei)) goto really_bad;
#else
        basei = (PyTypeObject*)PyTuple_GET_ITEM(bases, i);
#endif
        base_name = __Pyx_PyType_GetFullyQualifiedName(basei);
#if CYTHON_AVOID_BORROWED_REFS
        Py_DECREF(basei);
#endif
    }
    PyErr_Format(PyExc_TypeError,
        "multiple bases have vtable conflict: '" __Pyx_FMT_TYPENAME "' and '" __Pyx_FMT_TYPENAME "'", tp_base_name, base_name);
#if CYTHON_AVOID_BORROWED_REFS || !CYTHON_ASSUME_SAFE_MACROS
really_bad: // bad has failed!
#endif
    __Pyx_DECREF_TypeName(tp_base_name);
    __Pyx_DECREF_TypeName(base_name);
#if CYTHON_COMPILING_IN_LIMITED_API || CYTHON_AVOID_BORROWED_REFS || !CYTHON_ASSUME_SAFE_MACROS
other_failure:
#endif
    PyMem_Free(base_vtables);
    return -1;
}

/* DelItemOnTypeDict */
  static int __Pyx__DelItemOnTypeDict(PyTypeObject *tp, PyObject *k) {
    int result;
    PyObject *tp_dict;
#if CYTHON_COMPILING_IN_LIMITED_API
    tp_dict = __Pyx_GetTypeDict(tp);
    if (unlikely(!tp_dict)) return -1;
#else
    tp_dict = tp->tp_dict;
#endif
    result = PyDict_DelItem(tp_dict, k);
    if (likely(!result)) PyType_Modified(tp);
    return result;
}

/* SetupReduce */
  static int __Pyx_setup_reduce_is_named(PyObject* meth, PyObject* name) {
  int ret;
  PyObject *name_attr;
  name_attr = __Pyx_PyObject_GetAttrStrNoError(meth, __pyx_mstate_global->__pyx_n_u_name_2);
  if (likely(name_attr)) {
      ret = PyObject_RichCompareBool(name_attr, name, Py_EQ);
  } else {
      ret = -1;
  }
  if (unlikely(ret < 0)) {
      PyErr_Clear();
      ret = 0;
  }
  Py_XDECREF(name_attr);
  return ret;
}
static int __Pyx_setup_reduce(PyObject* type_obj) {
    int ret = 0;
    PyObject *object_reduce = NULL;
    PyObject *object_getstate = NULL;
    PyObject *object_reduce_ex = NULL;
    PyObject *reduce = NULL;
    PyObject *reduce_ex = NULL;
    PyObject *reduce_cython = NULL;
    PyObject *setstate = NULL;
    PyObject *setstate_cython = NULL;
    PyObject *getstate = NULL;
#if CYTHON_USE_PYTYPE_LOOKUP
    getstate = _PyType_Lookup((PyTypeObject*)type_obj, __pyx_mstate_global->__pyx_n_u_getstate);
#else
    getstate = __Pyx_PyObject_GetAttrStrNoError(type_obj, __pyx_mstate_global->__pyx_n_u_getstate);
    if (!getstate && PyErr_Occurred()) {
        goto __PYX_BAD;
    }
#endif
    if (getstate) {
#if CYTHON_USE_PYTYPE_LOOKUP
        object_getstate = _PyType_Lookup(&PyBaseObject_Type, __pyx_mstate_global->__pyx_n_u_getstate);
#else
        object_getstate = __Pyx_PyObject_GetAttrStrNoError((PyObject*)&PyBaseObject_Type, __pyx_mstate_global->__pyx_n_u_getstate);
        if (!object_getstate && PyErr_Occurred()) {
            goto __PYX_BAD;
        }
#endif
        if (object_getstate != getstate) {
            goto __PYX_GOOD;
        }
    }
#if CYTHON_USE_PYTYPE_LOOKUP
    object_reduce_ex = _PyType_Lookup(&PyBaseObject_Type, __pyx_mstate_global->__pyx_n_u_reduce_ex); if (!object_reduce_ex) goto __PYX_BAD;
#else
    object_reduce_ex = __Pyx_PyObject_GetAttrStr((PyObject*)&PyBaseObject_Type, __pyx_mstate_global->__pyx_n_u_reduce_ex); if (!object_reduce_ex) goto __PYX_BAD;
#endif
    reduce_ex = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_mstate_global->__pyx_n_u_reduce_ex); if (unlikely(!reduce_ex)) goto __PYX_BAD;
    if (reduce_ex == object_reduce_ex) {
#if CYTHON_USE_PYTYPE_LOOKUP
        object_reduce = _PyType_Lookup(&PyBaseObject_Type, __pyx_mstate_global->__pyx_n_u_reduce); if (!object_reduce) goto __PYX_BAD;
#else
        object_reduce = __Pyx_PyObject_GetAttrStr((PyObject*)&PyBaseObject_Type, __pyx_mstate_global->__pyx_n_u_reduce); if (!object_reduce) goto __PYX_BAD;
#endif
        reduce = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_mstate_global->__pyx_n_u_reduce); if (unlikely(!reduce)) goto __PYX_BAD;
        if (reduce == object_reduce || __Pyx_setup_reduce_is_named(reduce, __pyx_mstate_global->__pyx_n_u_reduce_cython)) {
            reduce_cython = __Pyx_PyObject_GetAttrStrNoError(type_obj, __pyx_mstate_global->__pyx_n_u_reduce_cython);
            if (likely(reduce_cython)) {
                ret = __Pyx_SetItemOnTypeDict((PyTypeObject*)type_obj, __pyx_mstate_global->__pyx_n_u_reduce, reduce_cython); if (unlikely(ret < 0)) goto __PYX_BAD;
                ret = __Pyx_DelItemOnTypeDict((PyTypeObject*)type_obj, __pyx_mstate_global->__pyx_n_u_reduce_cython); if (unlikely(ret < 0)) goto __PYX_BAD;
            } else if (reduce == object_reduce || PyErr_Occurred()) {
                goto __PYX_BAD;
            }
            setstate = __Pyx_PyObject_GetAttrStrNoError(type_obj, __pyx_mstate_global->__pyx_n_u_setstate);
            if (!setstate) PyErr_Clear();
            if (!setstate || __Pyx_setup_reduce_is_named(setstate, __pyx_mstate_global->__pyx_n_u_setstate_cython)) {
                setstate_cython = __Pyx_PyObject_GetAttrStrNoError(type_obj, __pyx_mstate_global->__pyx_n_u_setstate_cython);
                if (likely(setstate_cython)) {
                    ret = __Pyx_SetItemOnTypeDict((PyTypeObject*)type_obj, __pyx_mstate_global->__pyx_n_u_setstate, setstate_cython); if (unlikely(ret < 0)) goto __PYX_BAD;
                    ret = __Pyx_DelItemOnTypeDict((PyTypeObject*)type_obj, __pyx_mstate_global->__pyx_n_u_setstate_cython); if (unlikely(ret < 0)) goto __PYX_BAD;
                } else if (!setstate || PyErr_Occurred()) {
                    goto __PYX_BAD;
                }
            }
            PyType_Modified((PyTypeObject*)type_obj);
        }
    }
    goto __PYX_GOOD;
__PYX_BAD:
    if (!PyErr_Occurred()) {
        __Pyx_TypeName type_obj_name =
            __Pyx_PyType_GetFullyQualifiedName((PyTypeObject*)type_obj);
        PyErr_Format(PyExc_RuntimeError,
            "Unable to initialize pickling for " __Pyx_FMT_TYPENAME, type_obj_name);
        __Pyx_DECREF_TypeName(type_obj_name);
    }
    ret = -1;
__PYX_GOOD:
#if !CYTHON_USE_PYTYPE_LOOKUP
    Py_XDECREF(object_reduce);
    Py_XDECREF(object_reduce_ex);
    Py_XDECREF(object_getstate);
    Py_XDECREF(getstate);
#endif
    Py_XDECREF(reduce);
    Py_XDECREF(reduce_ex);
    Py_XDECREF(reduce_cython);
    Py_XDECREF(setstate);
    Py_XDECREF(setstate_cython);
    return ret;
}

/* TypeImport */
  #ifndef __PYX_HAVE_RT_ImportType_3_1_6
#define __PYX_HAVE_RT_ImportType_3_1_6
static PyTypeObject *__Pyx_ImportType_3_1_6(PyObject *module, const char *module_name, const char *class_name,
    size_t size, size_t alignment, enum __Pyx_ImportType_CheckSize_3_1_6 check_size)
{
    PyObject *result = 0;
    Py_ssize_t basicsize;
    Py_ssize_t itemsize;
#if defined(Py_LIMITED_API) || (defined(CYTHON_COMPILING_IN_LIMITED_API) && CYTHON_COMPILING_IN_LIMITED_API)
    PyObject *py_basicsize;
    PyObject *py_itemsize;
#endif
    result = PyObject_GetAttrString(module, class_name);
    if (!result)
        goto bad;
    if (!PyType_Check(result)) {
        PyErr_Format(PyExc_TypeError,
            "%.200s.%.200s is not a type object",
            module_name, class_name);
        goto bad;
    }
#if !( defined(Py_LIMITED_API) || (defined(CYTHON_COMPILING_IN_LIMITED_API) && CYTHON_COMPILING_IN_LIMITED_API) )
    basicsize = ((PyTypeObject *)result)->tp_basicsize;
    itemsize = ((PyTypeObject *)result)->tp_itemsize;
#else
    if (size == 0) {
        return (PyTypeObject *)result;
    }
    py_basicsize = PyObject_GetAttrString(result, "__basicsize__");
    if (!py_basicsize)
        goto bad;
    basicsize = PyLong_AsSsize_t(py_basicsize);
    Py_DECREF(py_basicsize);
    py_basicsize = 0;
    if (basicsize == (Py_ssize_t)-1 && PyErr_Occurred())
        goto bad;
    py_itemsize = PyObject_GetAttrString(result, "__itemsize__");
    if (!py_itemsize)
        goto bad;
    itemsize = PyLong_AsSsize_t(py_itemsize);
    Py_DECREF(py_itemsize);
    py_itemsize = 0;
    if (itemsize == (Py_ssize_t)-1 && PyErr_Occurred())
        goto bad;
#endif
    if (itemsize) {
        if (size % alignment) {
            alignment = size % alignment;
        }
        if (itemsize < (Py_ssize_t)alignment)
            itemsize = (Py_ssize_t)alignment;
    }
    if ((size_t)(basicsize + itemsize) < size) {
        PyErr_Format(PyExc_ValueError,
            "%.200s.%.200s size changed, may indicate binary incompatibility. "
            "Expected %zd from C header, got %zd from PyObject",
            module_name, class_name, size, basicsize+itemsize);
        goto bad;
    }
    if (check_size == __Pyx_ImportType_CheckSize_Error_3_1_6 &&
            ((size_t)basicsize > size || (size_t)(basicsize + itemsize) < size)) {
        PyErr_Format(PyExc_ValueError,
            "%.200s.%.200s size changed, may indicate binary incompatibility. "
            "Expected %zd from C header, got %zd-%zd from PyObject",
            module_name, class_name, size, basicsize, basicsize+itemsize);
        goto bad;
    }
    else if (check_size == __Pyx_ImportType_CheckSize_Warn_3_1_6 && (size_t)basicsize > size) {
        if (PyErr_WarnFormat(NULL, 0,
                "%.200s.%.200s size changed, may indicate binary incompatibility. "
                "Expected %zd from C header, got %zd from PyObject",
                module_name, class_name, size, basicsize) < 0) {
            goto bad;
        }
    }
    return (PyTypeObject *)result;
bad:
    Py_XDECREF(result);
    return NULL;
}
#endif

/* ListPack */
  static PyObject *__Pyx_PyList_Pack(Py_ssize_t n, ...) {
    va_list va;
    PyObject *l = PyList_New(n);
    va_start(va, n);
    if (unlikely(!l)) goto end;
    for (Py_ssize_t i=0; i<n; ++i) {
        PyObject *arg = va_arg(va, PyObject*);
        Py_INCREF(arg);
        if (__Pyx_PyList_SET_ITEM(l, i, arg) != (0)) {
            Py_CLEAR(l);
            goto end;
        }
    }
    end:
    va_end(va);
    return l;
}

/* FetchSharedCythonModule */
  static PyObject *__Pyx_FetchSharedCythonABIModule(void) {
    return __Pyx_PyImport_AddModuleRef(__PYX_ABI_MODULE_NAME);
}

/* dict_setdefault */
  static CYTHON_INLINE PyObject *__Pyx_PyDict_SetDefault(PyObject *d, PyObject *key, PyObject *default_value,
                                                       int is_safe_type) {
    PyObject* value;
    CYTHON_MAYBE_UNUSED_VAR(is_safe_type);
#if CYTHON_COMPILING_IN_LIMITED_API
    value = PyObject_CallMethod(d, "setdefault", "OO", key, default_value);
#elif PY_VERSION_HEX >= 0x030d0000
    PyDict_SetDefaultRef(d, key, default_value, &value);
#else
    value = PyDict_SetDefault(d, key, default_value);
    if (unlikely(!value)) return NULL;
    Py_INCREF(value);
#endif
    return value;
}

/* FetchCommonType */
  #if __PYX_LIMITED_VERSION_HEX < 0x030C0000
static PyObject* __Pyx_PyType_FromMetaclass(PyTypeObject *metaclass, PyObject *module, PyType_Spec *spec, PyObject *bases) {
    PyObject *result = __Pyx_PyType_FromModuleAndSpec(module, spec, bases);
    if (result && metaclass) {
        PyObject *old_tp = (PyObject*)Py_TYPE(result);
    Py_INCREF((PyObject*)metaclass);
#if __PYX_LIMITED_VERSION_HEX >= 0x03090000
        Py_SET_TYPE(result, metaclass);
#else
        result->ob_type = metaclass;
#endif
        Py_DECREF(old_tp);
    }
    return result;
}
#else
#define __Pyx_PyType_FromMetaclass(me, mo, s, b) PyType_FromMetaclass(me, mo, s, b)
#endif
static int __Pyx_VerifyCachedType(PyObject *cached_type,
                               const char *name,
                               Py_ssize_t expected_basicsize) {
    Py_ssize_t basicsize;
    if (!PyType_Check(cached_type)) {
        PyErr_Format(PyExc_TypeError,
            "Shared Cython type %.200s is not a type object", name);
        return -1;
    }
    if (expected_basicsize == 0) {
        return 0; // size is inherited, nothing useful to check
    }
#if CYTHON_COMPILING_IN_LIMITED_API
    PyObject *py_basicsize;
    py_basicsize = PyObject_GetAttrString(cached_type, "__basicsize__");
    if (unlikely(!py_basicsize)) return -1;
    basicsize = PyLong_AsSsize_t(py_basicsize);
    Py_DECREF(py_basicsize);
    py_basicsize = NULL;
    if (unlikely(basicsize == (Py_ssize_t)-1) && PyErr_Occurred()) return -1;
#else
    basicsize = ((PyTypeObject*) cached_type)->tp_basicsize;
#endif
    if (basicsize != expected_basicsize) {
        PyErr_Format(PyExc_TypeError,
            "Shared Cython type %.200s has the wrong size, try recompiling",
            name);
        return -1;
    }
    return 0;
}
static PyTypeObject *__Pyx_FetchCommonTypeFromSpec(PyTypeObject *metaclass, PyObject *module, PyType_Spec *spec, PyObject *bases) {
    PyObject *abi_module = NULL, *cached_type = NULL, *abi_module_dict, *new_cached_type, *py_object_name;
    int get_item_ref_result;
    const char* object_name = strrchr(spec->name, '.');
    object_name = object_name ? object_name+1 : spec->name;
    py_object_name = PyUnicode_FromString(object_name);
    if (!py_object_name) return NULL;
    abi_module = __Pyx_FetchSharedCythonABIModule();
    if (!abi_module) goto done;
    abi_module_dict = PyModule_GetDict(abi_module);
    if (!abi_module_dict) goto done;
    get_item_ref_result = __Pyx_PyDict_GetItemRef(abi_module_dict, py_object_name, &cached_type);
    if (get_item_ref_result == 1) {
        if (__Pyx_VerifyCachedType(
              cached_type,
              object_name,
              spec->basicsize) < 0) {
            goto bad;
        }
        goto done;
    } else if (unlikely(get_item_ref_result == -1)) {
        goto bad;
    }
    CYTHON_UNUSED_VAR(module);
    cached_type = __Pyx_PyType_FromMetaclass(metaclass, abi_module, spec, bases);
    if (unlikely(!cached_type)) goto bad;
    if (unlikely(__Pyx_fix_up_extension_type_from_spec(spec, (PyTypeObject *) cached_type) < 0)) goto bad;
    new_cached_type = __Pyx_PyDict_SetDefault(abi_module_dict, py_object_name, cached_type, 1);
    if (unlikely(new_cached_type != cached_type)) {
        if (unlikely(!new_cached_type)) goto bad;
        Py_DECREF(cached_type);
        cached_type = new_cached_type;
        if (__Pyx_VerifyCachedType(
                cached_type,
                object_name,
                spec->basicsize) < 0) {
            goto bad;
        }
        goto done;
    } else {
        Py_DECREF(new_cached_type);
    }
done:
    Py_XDECREF(abi_module);
    Py_DECREF(py_object_name);
    assert(cached_type == NULL || PyType_Check(cached_type));
    return (PyTypeObject *) cached_type;
bad:
    Py_XDECREF(cached_type);
    cached_type = NULL;
    goto done;
}

/* CommonTypesMetaclass */
  static PyObject* __pyx_CommonTypesMetaclass_get_module(CYTHON_UNUSED PyObject *self, CYTHON_UNUSED void* context) {
    return PyUnicode_FromString(__PYX_ABI_MODULE_NAME);
}
static PyGetSetDef __pyx_CommonTypesMetaclass_getset[] = {
    {"__module__", __pyx_CommonTypesMetaclass_get_module, NULL, NULL, NULL},
    {0, 0, 0, 0, 0}
};
static PyType_Slot __pyx_CommonTypesMetaclass_slots[] = {
    {Py_tp_getset, (void *)__pyx_CommonTypesMetaclass_getset},
    {0, 0}
};
static PyType_Spec __pyx_CommonTypesMetaclass_spec = {
    __PYX_TYPE_MODULE_PREFIX "_common_types_metatype",
    0,
    0,
#if PY_VERSION_HEX >= 0x030A0000
    Py_TPFLAGS_IMMUTABLETYPE |
    Py_TPFLAGS_DISALLOW_INSTANTIATION |
#endif
    Py_TPFLAGS_DEFAULT,
    __pyx_CommonTypesMetaclass_slots
};
static int __pyx_CommonTypesMetaclass_init(PyObject *module) {
    __pyx_mstatetype *mstate = __Pyx_PyModule_GetState(module);
    PyObject *bases = PyTuple_Pack(1, &PyType_Type);
    if (unlikely(!bases)) {
        return -1;
    }
    mstate->__pyx_CommonTypesMetaclassType = __Pyx_FetchCommonTypeFromSpec(NULL, module, &__pyx_CommonTypesMetaclass_spec, bases);
    Py_DECREF(bases);
    if (unlikely(mstate->__pyx_CommonTypesMetaclassType == NULL)) {
        return -1;
    }
    return 0;
}

/* PyMethodNew */
  #if CYTHON_COMPILING_IN_LIMITED_API
static PyObject *__Pyx_PyMethod_New(PyObject *func, PyObject *self, PyObject *typ) {
    PyObject *result;
    CYTHON_UNUSED_VAR(typ);
    if (!self)
        return __Pyx_NewRef(func);
    #if __PYX_LIMITED_VERSION_HEX >= 0x030C0000
    {
        PyObject *args[] = {func, self};
        result = PyObject_Vectorcall(__pyx_mstate_global->__Pyx_CachedMethodType, args, 2, NULL);
    }
    #else
    result = PyObject_CallFunctionObjArgs(__pyx_mstate_global->__Pyx_CachedMethodType, func, self, NULL);
    #endif
    return result;
}
#else
static PyObject *__Pyx_PyMethod_New(PyObject *func, PyObject *self, PyObject *typ) {
    CYTHON_UNUSED_VAR(typ);
    if (!self)
        return __Pyx_NewRef(func);
    return PyMethod_New(func, self);
}
#endif

/* PyVectorcallFastCallDict */
  #if CYTHON_METH_FASTCALL && (CYTHON_VECTORCALL || CYTHON_BACKPORT_VECTORCALL)
static PyObject *__Pyx_PyVectorcall_FastCallDict_kw(PyObject *func, __pyx_vectorcallfunc vc, PyObject *const *args, size_t nargs, PyObject *kw)
{
    PyObject *res = NULL;
    PyObject *kwnames;
    PyObject **newargs;
    PyObject **kwvalues;
    Py_ssize_t i, pos;
    size_t j;
    PyObject *key, *value;
    unsigned long keys_are_strings;
    #if !CYTHON_ASSUME_SAFE_SIZE
    Py_ssize_t nkw = PyDict_Size(kw);
    if (unlikely(nkw == -1)) return NULL;
    #else
    Py_ssize_t nkw = PyDict_GET_SIZE(kw);
    #endif
    newargs = (PyObject **)PyMem_Malloc((nargs + (size_t)nkw) * sizeof(args[0]));
    if (unlikely(newargs == NULL)) {
        PyErr_NoMemory();
        return NULL;
    }
    for (j = 0; j < nargs; j++) newargs[j] = args[j];
    kwnames = PyTuple_New(nkw);
    if (unlikely(kwnames == NULL)) {
        PyMem_Free(newargs);
        return NULL;
    }
    kwvalues = newargs + nargs;
    pos = i = 0;
    keys_are_strings = Py_TPFLAGS_UNICODE_SUBCLASS;
    while (PyDict_Next(kw, &pos, &key, &value)) {
        keys_are_strings &=
        #if CYTHON_COMPILING_IN_LIMITED_API
            PyType_GetFlags(Py_TYPE(key));
        #else
            Py_TYPE(key)->tp_flags;
        #endif
        Py_INCREF(key);
        Py_INCREF(value);
        #if !CYTHON_ASSUME_SAFE_MACROS
        if (unlikely(PyTuple_SetItem(kwnames, i, key) < 0)) goto cleanup;
        #else
        PyTuple_SET_ITEM(kwnames, i, key);
        #endif
        kwvalues[i] = value;
        i++;
    }
    if (unlikely(!keys_are_strings)) {
        PyErr_SetString(PyExc_TypeError, "keywords must be strings");
        goto cleanup;
    }
    res = vc(func, newargs, nargs, kwnames);
cleanup:
    Py_DECREF(kwnames);
    for (i = 0; i < nkw; i++)
        Py_DECREF(kwvalues[i]);
    PyMem_Free(newargs);
    return res;
}
static CYTHON_INLINE PyObject *__Pyx_PyVectorcall_FastCallDict(PyObject *func, __pyx_vectorcallfunc vc, PyObject *const *args, size_t nargs, PyObject *kw)
{
    Py_ssize_t kw_size =
        likely(kw == NULL) ?
        0 :
#if !CYTHON_ASSUME_SAFE_SIZE
        PyDict_Size(kw);
#else
        PyDict_GET_SIZE(kw);
#endif
    if (kw_size == 0) {
        return vc(func, args, nargs, NULL);
    }
#if !CYTHON_ASSUME_SAFE_SIZE
    else if (unlikely(kw_size == -1)) {
        return NULL;
    }
#endif
    return __Pyx_PyVectorcall_FastCallDict_kw(func, vc, args, nargs, kw);
}
#endif

/* CythonFunctionShared */
  #if CYTHON_COMPILING_IN_LIMITED_API
static CYTHON_INLINE int __Pyx__IsSameCyOrCFunctionNoMethod(PyObject *func, void (*cfunc)(void)) {
    if (__Pyx_CyFunction_Check(func)) {
        return PyCFunction_GetFunction(((__pyx_CyFunctionObject*)func)->func) == (PyCFunction) cfunc;
    } else if (PyCFunction_Check(func)) {
        return PyCFunction_GetFunction(func) == (PyCFunction) cfunc;
    }
    return 0;
}
static CYTHON_INLINE int __Pyx__IsSameCyOrCFunction(PyObject *func, void (*cfunc)(void)) {
    if ((PyObject*)Py_TYPE(func) == __pyx_mstate_global->__Pyx_CachedMethodType) {
        int result;
        PyObject *newFunc = PyObject_GetAttr(func, __pyx_mstate_global->__pyx_n_u_func);
        if (unlikely(!newFunc)) {
            PyErr_Clear(); // It's only an optimization, so don't throw an error
            return 0;
        }
        result = __Pyx__IsSameCyOrCFunctionNoMethod(newFunc, cfunc);
        Py_DECREF(newFunc);
        return result;
    }
    return __Pyx__IsSameCyOrCFunctionNoMethod(func, cfunc);
}
#else
static CYTHON_INLINE int __Pyx__IsSameCyOrCFunction(PyObject *func, void (*cfunc)(void)) {
    if (PyMethod_Check(func)) {
        func = PyMethod_GET_FUNCTION(func);
    }
    return __Pyx_CyOrPyCFunction_Check(func) && __Pyx_CyOrPyCFunction_GET_FUNCTION(func) == (PyCFunction) cfunc;
}
#endif
static CYTHON_INLINE void __Pyx__CyFunction_SetClassObj(__pyx_CyFunctionObject* f, PyObject* classobj) {
#if PY_VERSION_HEX < 0x030900B1 || CYTHON_COMPILING_IN_LIMITED_API
    __Pyx_Py_XDECREF_SET(
        __Pyx_CyFunction_GetClassObj(f),
            ((classobj) ? __Pyx_NewRef(classobj) : NULL));
#else
    __Pyx_Py_XDECREF_SET(
        ((PyCMethodObject *) (f))->mm_class,
        (PyTypeObject*)((classobj) ? __Pyx_NewRef(classobj) : NULL));
#endif
}
static PyObject *
__Pyx_CyFunction_get_doc_locked(__pyx_CyFunctionObject *op)
{
    if (unlikely(op->func_doc == NULL)) {
#if CYTHON_COMPILING_IN_LIMITED_API
        op->func_doc = PyObject_GetAttrString(op->func, "__doc__");
        if (unlikely(!op->func_doc)) return NULL;
#else
        if (((PyCFunctionObject*)op)->m_ml->ml_doc) {
            op->func_doc = PyUnicode_FromString(((PyCFunctionObject*)op)->m_ml->ml_doc);
            if (unlikely(op->func_doc == NULL))
                return NULL;
        } else {
            Py_INCREF(Py_None);
            return Py_None;
        }
#endif
    }
    Py_INCREF(op->func_doc);
    return op->func_doc;
}
static PyObject *
__Pyx_CyFunction_get_doc(__pyx_CyFunctionObject *op, void *closure) {
    PyObject *result;
    CYTHON_UNUSED_VAR(closure);
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    result = __Pyx_CyFunction_get_doc_locked(op);
    __Pyx_END_CRITICAL_SECTION();
    return result;
}
static int
__Pyx_CyFunction_set_doc(__pyx_CyFunctionObject *op, PyObject *value, void *context)
{
    CYTHON_UNUSED_VAR(context);
    if (value == NULL) {
        value = Py_None;
    }
    Py_INCREF(value);
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    __Pyx_Py_XDECREF_SET(op->func_doc, value);
    __Pyx_END_CRITICAL_SECTION();
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_name_locked(__pyx_CyFunctionObject *op)
{
    if (unlikely(op->func_name == NULL)) {
#if CYTHON_COMPILING_IN_LIMITED_API
        op->func_name = PyObject_GetAttrString(op->func, "__name__");
#else
        op->func_name = PyUnicode_InternFromString(((PyCFunctionObject*)op)->m_ml->ml_name);
#endif
        if (unlikely(op->func_name == NULL))
            return NULL;
    }
    Py_INCREF(op->func_name);
    return op->func_name;
}
static PyObject *
__Pyx_CyFunction_get_name(__pyx_CyFunctionObject *op, void *context)
{
    PyObject *result = NULL;
    CYTHON_UNUSED_VAR(context);
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    result = __Pyx_CyFunction_get_name_locked(op);
    __Pyx_END_CRITICAL_SECTION();
    return result;
}
static int
__Pyx_CyFunction_set_name(__pyx_CyFunctionObject *op, PyObject *value, void *context)
{
    CYTHON_UNUSED_VAR(context);
    if (unlikely(value == NULL || !PyUnicode_Check(value))) {
        PyErr_SetString(PyExc_TypeError,
                        "__name__ must be set to a string object");
        return -1;
    }
    Py_INCREF(value);
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    __Pyx_Py_XDECREF_SET(op->func_name, value);
    __Pyx_END_CRITICAL_SECTION();
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_qualname(__pyx_CyFunctionObject *op, void *context)
{
    CYTHON_UNUSED_VAR(context);
    PyObject *result;
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    Py_INCREF(op->func_qualname);
    result = op->func_qualname;
    __Pyx_END_CRITICAL_SECTION();
    return result;
}
static int
__Pyx_CyFunction_set_qualname(__pyx_CyFunctionObject *op, PyObject *value, void *context)
{
    CYTHON_UNUSED_VAR(context);
    if (unlikely(value == NULL || !PyUnicode_Check(value))) {
        PyErr_SetString(PyExc_TypeError,
                        "__qualname__ must be set to a string object");
        return -1;
    }
    Py_INCREF(value);
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    __Pyx_Py_XDECREF_SET(op->func_qualname, value);
    __Pyx_END_CRITICAL_SECTION();
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_dict_locked(__pyx_CyFunctionObject *op)
{
    if (unlikely(op->func_dict == NULL)) {
        op->func_dict = PyDict_New();
        if (unlikely(op->func_dict == NULL))
            return NULL;
    }
    Py_INCREF(op->func_dict);
    return op->func_dict;
}
static PyObject *
__Pyx_CyFunction_get_dict(__pyx_CyFunctionObject *op, void *context)
{
    CYTHON_UNUSED_VAR(context);
    PyObject *result;
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    result = __Pyx_CyFunction_get_dict_locked(op);
    __Pyx_END_CRITICAL_SECTION();
    return result;
}
static int
__Pyx_CyFunction_set_dict(__pyx_CyFunctionObject *op, PyObject *value, void *context)
{
    CYTHON_UNUSED_VAR(context);
    if (unlikely(value == NULL)) {
        PyErr_SetString(PyExc_TypeError,
               "function's dictionary may not be deleted");
        return -1;
    }
    if (unlikely(!PyDict_Check(value))) {
        PyErr_SetString(PyExc_TypeError,
               "setting function's dictionary to a non-dict");
        return -1;
    }
    Py_INCREF(value);
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    __Pyx_Py_XDECREF_SET(op->func_dict, value);
    __Pyx_END_CRITICAL_SECTION();
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_globals(__pyx_CyFunctionObject *op, void *context)
{
    CYTHON_UNUSED_VAR(context);
    Py_INCREF(op->func_globals);
    return op->func_globals;
}
static PyObject *
__Pyx_CyFunction_get_closure(__pyx_CyFunctionObject *op, void *context)
{
    CYTHON_UNUSED_VAR(op);
    CYTHON_UNUSED_VAR(context);
    Py_INCREF(Py_None);
    return Py_None;
}
static PyObject *
__Pyx_CyFunction_get_code(__pyx_CyFunctionObject *op, void *context)
{
    PyObject* result = (op->func_code) ? op->func_code : Py_None;
    CYTHON_UNUSED_VAR(context);
    Py_INCREF(result);
    return result;
}
static int
__Pyx_CyFunction_init_defaults(__pyx_CyFunctionObject *op) {
    int result = 0;
    PyObject *res = op->defaults_getter((PyObject *) op);
    if (unlikely(!res))
        return -1;
    #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
    op->defaults_tuple = PyTuple_GET_ITEM(res, 0);
    Py_INCREF(op->defaults_tuple);
    op->defaults_kwdict = PyTuple_GET_ITEM(res, 1);
    Py_INCREF(op->defaults_kwdict);
    #else
    op->defaults_tuple = __Pyx_PySequence_ITEM(res, 0);
    if (unlikely(!op->defaults_tuple)) result = -1;
    else {
        op->defaults_kwdict = __Pyx_PySequence_ITEM(res, 1);
        if (unlikely(!op->defaults_kwdict)) result = -1;
    }
    #endif
    Py_DECREF(res);
    return result;
}
static int
__Pyx_CyFunction_set_defaults(__pyx_CyFunctionObject *op, PyObject* value, void *context) {
    CYTHON_UNUSED_VAR(context);
    if (!value) {
        value = Py_None;
    } else if (unlikely(value != Py_None && !PyTuple_Check(value))) {
        PyErr_SetString(PyExc_TypeError,
                        "__defaults__ must be set to a tuple object");
        return -1;
    }
    PyErr_WarnEx(PyExc_RuntimeWarning, "changes to cyfunction.__defaults__ will not "
                 "currently affect the values used in function calls", 1);
    Py_INCREF(value);
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    __Pyx_Py_XDECREF_SET(op->defaults_tuple, value);
    __Pyx_END_CRITICAL_SECTION();
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_defaults_locked(__pyx_CyFunctionObject *op) {
    PyObject* result = op->defaults_tuple;
    if (unlikely(!result)) {
        if (op->defaults_getter) {
            if (unlikely(__Pyx_CyFunction_init_defaults(op) < 0)) return NULL;
            result = op->defaults_tuple;
        } else {
            result = Py_None;
        }
    }
    Py_INCREF(result);
    return result;
}
static PyObject *
__Pyx_CyFunction_get_defaults(__pyx_CyFunctionObject *op, void *context) {
    PyObject* result = NULL;
    CYTHON_UNUSED_VAR(context);
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    result = __Pyx_CyFunction_get_defaults_locked(op);
    __Pyx_END_CRITICAL_SECTION();
    return result;
}
static int
__Pyx_CyFunction_set_kwdefaults(__pyx_CyFunctionObject *op, PyObject* value, void *context) {
    CYTHON_UNUSED_VAR(context);
    if (!value) {
        value = Py_None;
    } else if (unlikely(value != Py_None && !PyDict_Check(value))) {
        PyErr_SetString(PyExc_TypeError,
                        "__kwdefaults__ must be set to a dict object");
        return -1;
    }
    PyErr_WarnEx(PyExc_RuntimeWarning, "changes to cyfunction.__kwdefaults__ will not "
                 "currently affect the values used in function calls", 1);
    Py_INCREF(value);
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    __Pyx_Py_XDECREF_SET(op->defaults_kwdict, value);
    __Pyx_END_CRITICAL_SECTION();
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_kwdefaults_locked(__pyx_CyFunctionObject *op) {
    PyObject* result = op->defaults_kwdict;
    if (unlikely(!result)) {
        if (op->defaults_getter) {
            if (unlikely(__Pyx_CyFunction_init_defaults(op) < 0)) return NULL;
            result = op->defaults_kwdict;
        } else {
            result = Py_None;
        }
    }
    Py_INCREF(result);
    return result;
}
static PyObject *
__Pyx_CyFunction_get_kwdefaults(__pyx_CyFunctionObject *op, void *context) {
    PyObject* result;
    CYTHON_UNUSED_VAR(context);
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    result = __Pyx_CyFunction_get_kwdefaults_locked(op);
    __Pyx_END_CRITICAL_SECTION();
    return result;
}
static int
__Pyx_CyFunction_set_annotations(__pyx_CyFunctionObject *op, PyObject* value, void *context) {
    CYTHON_UNUSED_VAR(context);
    if (!value || value == Py_None) {
        value = NULL;
    } else if (unlikely(!PyDict_Check(value))) {
        PyErr_SetString(PyExc_TypeError,
                        "__annotations__ must be set to a dict object");
        return -1;
    }
    Py_XINCREF(value);
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    __Pyx_Py_XDECREF_SET(op->func_annotations, value);
    __Pyx_END_CRITICAL_SECTION();
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_annotations_locked(__pyx_CyFunctionObject *op) {
    PyObject* result = op->func_annotations;
    if (unlikely(!result)) {
        result = PyDict_New();
        if (unlikely(!result)) return NULL;
        op->func_annotations = result;
    }
    Py_INCREF(result);
    return result;
}
static PyObject *
__Pyx_CyFunction_get_annotations(__pyx_CyFunctionObject *op, void *context) {
    PyObject *result;
    CYTHON_UNUSED_VAR(context);
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    result = __Pyx_CyFunction_get_annotations_locked(op);
    __Pyx_END_CRITICAL_SECTION();
    return result;
}
static PyObject *
__Pyx_CyFunction_get_is_coroutine_value(__pyx_CyFunctionObject *op) {
    int is_coroutine = op->flags & __Pyx_CYFUNCTION_COROUTINE;
    if (is_coroutine) {
        PyObject *is_coroutine_value, *module, *fromlist, *marker = __pyx_mstate_global->__pyx_n_u_is_coroutine;
        fromlist = PyList_New(1);
        if (unlikely(!fromlist)) return NULL;
        Py_INCREF(marker);
#if CYTHON_ASSUME_SAFE_MACROS
        PyList_SET_ITEM(fromlist, 0, marker);
#else
        if (unlikely(PyList_SetItem(fromlist, 0, marker) < 0)) {
            Py_DECREF(marker);
            Py_DECREF(fromlist);
            return NULL;
        }
#endif
        module = PyImport_ImportModuleLevelObject(__pyx_mstate_global->__pyx_n_u_asyncio_coroutines, NULL, NULL, fromlist, 0);
        Py_DECREF(fromlist);
        if (unlikely(!module)) goto ignore;
        is_coroutine_value = __Pyx_PyObject_GetAttrStr(module, marker);
        Py_DECREF(module);
        if (likely(is_coroutine_value)) {
            return is_coroutine_value;
        }
ignore:
        PyErr_Clear();
    }
    return __Pyx_PyBool_FromLong(is_coroutine);
}
static PyObject *
__Pyx_CyFunction_get_is_coroutine(__pyx_CyFunctionObject *op, void *context) {
    PyObject *result;
    CYTHON_UNUSED_VAR(context);
    if (op->func_is_coroutine) {
        return __Pyx_NewRef(op->func_is_coroutine);
    }
    result = __Pyx_CyFunction_get_is_coroutine_value(op);
    if (unlikely(!result))
        return NULL;
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    if (op->func_is_coroutine) {
        Py_DECREF(result);
        result = __Pyx_NewRef(op->func_is_coroutine);
    } else {
        op->func_is_coroutine = __Pyx_NewRef(result);
    }
    __Pyx_END_CRITICAL_SECTION();
    return result;
}
static void __Pyx_CyFunction_raise_argument_count_error(__pyx_CyFunctionObject *func, const char* message, Py_ssize_t size) {
#if CYTHON_COMPILING_IN_LIMITED_API
    PyObject *py_name = __Pyx_CyFunction_get_name(func, NULL);
    if (!py_name) return;
    PyErr_Format(PyExc_TypeError,
        "%.200S() %s (%" CYTHON_FORMAT_SSIZE_T "d given)",
        py_name, message, size);
    Py_DECREF(py_name);
#else
    const char* name = ((PyCFunctionObject*)func)->m_ml->ml_name;
    PyErr_Format(PyExc_TypeError,
        "%.200s() %s (%" CYTHON_FORMAT_SSIZE_T "d given)",
        name, message, size);
#endif
}
static void __Pyx_CyFunction_raise_type_error(__pyx_CyFunctionObject *func, const char* message) {
#if CYTHON_COMPILING_IN_LIMITED_API
    PyObject *py_name = __Pyx_CyFunction_get_name(func, NULL);
    if (!py_name) return;
    PyErr_Format(PyExc_TypeError,
        "%.200S() %s",
        py_name, message);
    Py_DECREF(py_name);
#else
    const char* name = ((PyCFunctionObject*)func)->m_ml->ml_name;
    PyErr_Format(PyExc_TypeError,
        "%.200s() %s",
        name, message);
#endif
}
#if CYTHON_COMPILING_IN_LIMITED_API
static PyObject *
__Pyx_CyFunction_get_module(__pyx_CyFunctionObject *op, void *context) {
    CYTHON_UNUSED_VAR(context);
    return PyObject_GetAttrString(op->func, "__module__");
}
static int
__Pyx_CyFunction_set_module(__pyx_CyFunctionObject *op, PyObject* value, void *context) {
    CYTHON_UNUSED_VAR(context);
    return PyObject_SetAttrString(op->func, "__module__", value);
}
#endif
static PyGetSetDef __pyx_CyFunction_getsets[] = {
    {"func_doc", (getter)__Pyx_CyFunction_get_doc, (setter)__Pyx_CyFunction_set_doc, 0, 0},
    {"__doc__",  (getter)__Pyx_CyFunction_get_doc, (setter)__Pyx_CyFunction_set_doc, 0, 0},
    {"func_name", (getter)__Pyx_CyFunction_get_name, (setter)__Pyx_CyFunction_set_name, 0, 0},
    {"__name__", (getter)__Pyx_CyFunction_get_name, (setter)__Pyx_CyFunction_set_name, 0, 0},
    {"__qualname__", (getter)__Pyx_CyFunction_get_qualname, (setter)__Pyx_CyFunction_set_qualname, 0, 0},
    {"func_dict", (getter)__Pyx_CyFunction_get_dict, (setter)__Pyx_CyFunction_set_dict, 0, 0},
    {"__dict__", (getter)__Pyx_CyFunction_get_dict, (setter)__Pyx_CyFunction_set_dict, 0, 0},
    {"func_globals", (getter)__Pyx_CyFunction_get_globals, 0, 0, 0},
    {"__globals__", (getter)__Pyx_CyFunction_get_globals, 0, 0, 0},
    {"func_closure", (getter)__Pyx_CyFunction_get_closure, 0, 0, 0},
    {"__closure__", (getter)__Pyx_CyFunction_get_closure, 0, 0, 0},
    {"func_code", (getter)__Pyx_CyFunction_get_code, 0, 0, 0},
    {"__code__", (getter)__Pyx_CyFunction_get_code, 0, 0, 0},
    {"func_defaults", (getter)__Pyx_CyFunction_get_defaults, (setter)__Pyx_CyFunction_set_defaults, 0, 0},
    {"__defaults__", (getter)__Pyx_CyFunction_get_defaults, (setter)__Pyx_CyFunction_set_defaults, 0, 0},
    {"__kwdefaults__", (getter)__Pyx_CyFunction_get_kwdefaults, (setter)__Pyx_CyFunction_set_kwdefaults, 0, 0},
    {"__annotations__", (getter)__Pyx_CyFunction_get_annotations, (setter)__Pyx_CyFunction_set_annotations, 0, 0},
    {"_is_coroutine", (getter)__Pyx_CyFunction_get_is_coroutine, 0, 0, 0},
#if CYTHON_COMPILING_IN_LIMITED_API
    {"__module__", (getter)__Pyx_CyFunction_get_module, (setter)__Pyx_CyFunction_set_module, 0, 0},
#endif
    {0, 0, 0, 0, 0}
};
static PyMemberDef __pyx_CyFunction_members[] = {
#if !CYTHON_COMPILING_IN_LIMITED_API
    {"__module__", T_OBJECT, offsetof(PyCFunctionObject, m_module), 0, 0},
#endif
    {"__dictoffset__", T_PYSSIZET, offsetof(__pyx_CyFunctionObject, func_dict), READONLY, 0},
#if CYTHON_METH_FASTCALL
#if CYTHON_BACKPORT_VECTORCALL || CYTHON_COMPILING_IN_LIMITED_API
    {"__vectorcalloffset__", T_PYSSIZET, offsetof(__pyx_CyFunctionObject, func_vectorcall), READONLY, 0},
#else
    {"__vectorcalloffset__", T_PYSSIZET, offsetof(PyCFunctionObject, vectorcall), READONLY, 0},
#endif
#if CYTHON_COMPILING_IN_LIMITED_API
    {"__weaklistoffset__", T_PYSSIZET, offsetof(__pyx_CyFunctionObject, func_weakreflist), READONLY, 0},
#else
    {"__weaklistoffset__", T_PYSSIZET, offsetof(PyCFunctionObject, m_weakreflist), READONLY, 0},
#endif
#endif
    {0, 0, 0,  0, 0}
};
static PyObject *
__Pyx_CyFunction_reduce(__pyx_CyFunctionObject *m, PyObject *args)
{
    PyObject *result = NULL;
    CYTHON_UNUSED_VAR(args);
    __Pyx_BEGIN_CRITICAL_SECTION(m);
    Py_INCREF(m->func_qualname);
    result = m->func_qualname;
    __Pyx_END_CRITICAL_SECTION();
    return result;
}
static PyMethodDef __pyx_CyFunction_methods[] = {
    {"__reduce__", (PyCFunction)__Pyx_CyFunction_reduce, METH_VARARGS, 0},
    {0, 0, 0, 0}
};
#if CYTHON_COMPILING_IN_LIMITED_API
#define __Pyx_CyFunction_weakreflist(cyfunc) ((cyfunc)->func_weakreflist)
#else
#define __Pyx_CyFunction_weakreflist(cyfunc) (((PyCFunctionObject*)cyfunc)->m_weakreflist)
#endif
static PyObject *__Pyx_CyFunction_Init(__pyx_CyFunctionObject *op, PyMethodDef *ml, int flags, PyObject* qualname,
                                       PyObject *closure, PyObject *module, PyObject* globals, PyObject* code) {
#if !CYTHON_COMPILING_IN_LIMITED_API
    PyCFunctionObject *cf = (PyCFunctionObject*) op;
#endif
    if (unlikely(op == NULL))
        return NULL;
#if CYTHON_COMPILING_IN_LIMITED_API
    op->func = PyCFunction_NewEx(ml, (PyObject*)op, module);
    if (unlikely(!op->func)) return NULL;
#endif
    op->flags = flags;
    __Pyx_CyFunction_weakreflist(op) = NULL;
#if !CYTHON_COMPILING_IN_LIMITED_API
    cf->m_ml = ml;
    cf->m_self = (PyObject *) op;
#endif
    Py_XINCREF(closure);
    op->func_closure = closure;
#if !CYTHON_COMPILING_IN_LIMITED_API
    Py_XINCREF(module);
    cf->m_module = module;
#endif
    op->func_dict = NULL;
    op->func_name = NULL;
    Py_INCREF(qualname);
    op->func_qualname = qualname;
    op->func_doc = NULL;
#if PY_VERSION_HEX < 0x030900B1 || CYTHON_COMPILING_IN_LIMITED_API
    op->func_classobj = NULL;
#else
    ((PyCMethodObject*)op)->mm_class = NULL;
#endif
    op->func_globals = globals;
    Py_INCREF(op->func_globals);
    Py_XINCREF(code);
    op->func_code = code;
    op->defaults = NULL;
    op->defaults_tuple = NULL;
    op->defaults_kwdict = NULL;
    op->defaults_getter = NULL;
    op->func_annotations = NULL;
    op->func_is_coroutine = NULL;
#if CYTHON_METH_FASTCALL
    switch (ml->ml_flags & (METH_VARARGS | METH_FASTCALL | METH_NOARGS | METH_O | METH_KEYWORDS | METH_METHOD)) {
    case METH_NOARGS:
        __Pyx_CyFunction_func_vectorcall(op) = __Pyx_CyFunction_Vectorcall_NOARGS;
        break;
    case METH_O:
        __Pyx_CyFunction_func_vectorcall(op) = __Pyx_CyFunction_Vectorcall_O;
        break;
    case METH_METHOD | METH_FASTCALL | METH_KEYWORDS:
        __Pyx_CyFunction_func_vectorcall(op) = __Pyx_CyFunction_Vectorcall_FASTCALL_KEYWORDS_METHOD;
        break;
    case METH_FASTCALL | METH_KEYWORDS:
        __Pyx_CyFunction_func_vectorcall(op) = __Pyx_CyFunction_Vectorcall_FASTCALL_KEYWORDS;
        break;
    case METH_VARARGS | METH_KEYWORDS:
        __Pyx_CyFunction_func_vectorcall(op) = NULL;
        break;
    default:
        PyErr_SetString(PyExc_SystemError, "Bad call flags for CyFunction");
        Py_DECREF(op);
        return NULL;
    }
#endif
    return (PyObject *) op;
}
static int
__Pyx_CyFunction_clear(__pyx_CyFunctionObject *m)
{
    Py_CLEAR(m->func_closure);
#if CYTHON_COMPILING_IN_LIMITED_API
    Py_CLEAR(m->func);
#else
    Py_CLEAR(((PyCFunctionObject*)m)->m_module);
#endif
    Py_CLEAR(m->func_dict);
    Py_CLEAR(m->func_name);
    Py_CLEAR(m->func_qualname);
    Py_CLEAR(m->func_doc);
    Py_CLEAR(m->func_globals);
    Py_CLEAR(m->func_code);
#if !CYTHON_COMPILING_IN_LIMITED_API
#if PY_VERSION_HEX < 0x030900B1
    Py_CLEAR(__Pyx_CyFunction_GetClassObj(m));
#else
    {
        PyObject *cls = (PyObject*) ((PyCMethodObject *) (m))->mm_class;
        ((PyCMethodObject *) (m))->mm_class = NULL;
        Py_XDECREF(cls);
    }
#endif
#endif
    Py_CLEAR(m->defaults_tuple);
    Py_CLEAR(m->defaults_kwdict);
    Py_CLEAR(m->func_annotations);
    Py_CLEAR(m->func_is_coroutine);
    Py_CLEAR(m->defaults);
    return 0;
}
static void __Pyx__CyFunction_dealloc(__pyx_CyFunctionObject *m)
{
    if (__Pyx_CyFunction_weakreflist(m) != NULL)
        PyObject_ClearWeakRefs((PyObject *) m);
    __Pyx_CyFunction_clear(m);
    __Pyx_PyHeapTypeObject_GC_Del(m);
}
static void __Pyx_CyFunction_dealloc(__pyx_CyFunctionObject *m)
{
    PyObject_GC_UnTrack(m);
    __Pyx__CyFunction_dealloc(m);
}
static int __Pyx_CyFunction_traverse(__pyx_CyFunctionObject *m, visitproc visit, void *arg)
{
    {
        int e = __Pyx_call_type_traverse((PyObject*)m, 1, visit, arg);
        if (e) return e;
    }
    Py_VISIT(m->func_closure);
#if CYTHON_COMPILING_IN_LIMITED_API
    Py_VISIT(m->func);
#else
    Py_VISIT(((PyCFunctionObject*)m)->m_module);
#endif
    Py_VISIT(m->func_dict);
    __Pyx_VISIT_CONST(m->func_name);
    __Pyx_VISIT_CONST(m->func_qualname);
    Py_VISIT(m->func_doc);
    Py_VISIT(m->func_globals);
    __Pyx_VISIT_CONST(m->func_code);
#if !CYTHON_COMPILING_IN_LIMITED_API
    Py_VISIT(__Pyx_CyFunction_GetClassObj(m));
#endif
    Py_VISIT(m->defaults_tuple);
    Py_VISIT(m->defaults_kwdict);
    Py_VISIT(m->func_is_coroutine);
    Py_VISIT(m->defaults);
    return 0;
}
static PyObject*
__Pyx_CyFunction_repr(__pyx_CyFunctionObject *op)
{
    PyObject *repr;
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    repr = PyUnicode_FromFormat("<cyfunction %U at %p>",
                                op->func_qualname, (void *)op);
    __Pyx_END_CRITICAL_SECTION();
    return repr;
}
static PyObject * __Pyx_CyFunction_CallMethod(PyObject *func, PyObject *self, PyObject *arg, PyObject *kw) {
#if CYTHON_COMPILING_IN_LIMITED_API
    PyObject *f = ((__pyx_CyFunctionObject*)func)->func;
    PyCFunction meth;
    int flags;
    meth = PyCFunction_GetFunction(f);
    if (unlikely(!meth)) return NULL;
    flags = PyCFunction_GetFlags(f);
    if (unlikely(flags < 0)) return NULL;
#else
    PyCFunctionObject* f = (PyCFunctionObject*)func;
    PyCFunction meth = f->m_ml->ml_meth;
    int flags = f->m_ml->ml_flags;
#endif
    Py_ssize_t size;
    switch (flags & (METH_VARARGS | METH_KEYWORDS | METH_NOARGS | METH_O)) {
    case METH_VARARGS:
        if (likely(kw == NULL || PyDict_Size(kw) == 0))
            return (*meth)(self, arg);
        break;
    case METH_VARARGS | METH_KEYWORDS:
        return (*(PyCFunctionWithKeywords)(void(*)(void))meth)(self, arg, kw);
    case METH_NOARGS:
        if (likely(kw == NULL || PyDict_Size(kw) == 0)) {
#if CYTHON_ASSUME_SAFE_SIZE
            size = PyTuple_GET_SIZE(arg);
#else
            size = PyTuple_Size(arg);
            if (unlikely(size < 0)) return NULL;
#endif
            if (likely(size == 0))
                return (*meth)(self, NULL);
            __Pyx_CyFunction_raise_argument_count_error(
                (__pyx_CyFunctionObject*)func,
                "takes no arguments", size);
            return NULL;
        }
        break;
    case METH_O:
        if (likely(kw == NULL || PyDict_Size(kw) == 0)) {
#if CYTHON_ASSUME_SAFE_SIZE
            size = PyTuple_GET_SIZE(arg);
#else
            size = PyTuple_Size(arg);
            if (unlikely(size < 0)) return NULL;
#endif
            if (likely(size == 1)) {
                PyObject *result, *arg0;
                #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
                arg0 = PyTuple_GET_ITEM(arg, 0);
                #else
                arg0 = __Pyx_PySequence_ITEM(arg, 0); if (unlikely(!arg0)) return NULL;
                #endif
                result = (*meth)(self, arg0);
                #if !(CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS)
                Py_DECREF(arg0);
                #endif
                return result;
            }
            __Pyx_CyFunction_raise_argument_count_error(
                (__pyx_CyFunctionObject*)func,
                "takes exactly one argument", size);
            return NULL;
        }
        break;
    default:
        PyErr_SetString(PyExc_SystemError, "Bad call flags for CyFunction");
        return NULL;
    }
    __Pyx_CyFunction_raise_type_error(
        (__pyx_CyFunctionObject*)func, "takes no keyword arguments");
    return NULL;
}
static CYTHON_INLINE PyObject *__Pyx_CyFunction_Call(PyObject *func, PyObject *arg, PyObject *kw) {
    PyObject *self, *result;
#if CYTHON_COMPILING_IN_LIMITED_API
    self = PyCFunction_GetSelf(((__pyx_CyFunctionObject*)func)->func);
    if (unlikely(!self) && PyErr_Occurred()) return NULL;
#else
    self = ((PyCFunctionObject*)func)->m_self;
#endif
    result = __Pyx_CyFunction_CallMethod(func, self, arg, kw);
    return result;
}
static PyObject *__Pyx_CyFunction_CallAsMethod(PyObject *func, PyObject *args, PyObject *kw) {
    PyObject *result;
    __pyx_CyFunctionObject *cyfunc = (__pyx_CyFunctionObject *) func;
#if CYTHON_METH_FASTCALL && (CYTHON_VECTORCALL || CYTHON_BACKPORT_VECTORCALL)
     __pyx_vectorcallfunc vc = __Pyx_CyFunction_func_vectorcall(cyfunc);
    if (vc) {
#if CYTHON_ASSUME_SAFE_MACROS && CYTHON_ASSUME_SAFE_SIZE
        return __Pyx_PyVectorcall_FastCallDict(func, vc, &PyTuple_GET_ITEM(args, 0), (size_t)PyTuple_GET_SIZE(args), kw);
#else
        (void) &__Pyx_PyVectorcall_FastCallDict;
        return PyVectorcall_Call(func, args, kw);
#endif
    }
#endif
    if ((cyfunc->flags & __Pyx_CYFUNCTION_CCLASS) && !(cyfunc->flags & __Pyx_CYFUNCTION_STATICMETHOD)) {
        Py_ssize_t argc;
        PyObject *new_args;
        PyObject *self;
#if CYTHON_ASSUME_SAFE_SIZE
        argc = PyTuple_GET_SIZE(args);
#else
        argc = PyTuple_Size(args);
        if (unlikely(argc < 0)) return NULL;
#endif
        new_args = PyTuple_GetSlice(args, 1, argc);
        if (unlikely(!new_args))
            return NULL;
        self = PyTuple_GetItem(args, 0);
        if (unlikely(!self)) {
            Py_DECREF(new_args);
            PyErr_Format(PyExc_TypeError,
                         "unbound method %.200S() needs an argument",
                         cyfunc->func_qualname);
            return NULL;
        }
        result = __Pyx_CyFunction_CallMethod(func, self, new_args, kw);
        Py_DECREF(new_args);
    } else {
        result = __Pyx_CyFunction_Call(func, args, kw);
    }
    return result;
}
#if CYTHON_METH_FASTCALL && (CYTHON_VECTORCALL || CYTHON_BACKPORT_VECTORCALL)
static CYTHON_INLINE int __Pyx_CyFunction_Vectorcall_CheckArgs(__pyx_CyFunctionObject *cyfunc, Py_ssize_t nargs, PyObject *kwnames)
{
    int ret = 0;
    if ((cyfunc->flags & __Pyx_CYFUNCTION_CCLASS) && !(cyfunc->flags & __Pyx_CYFUNCTION_STATICMETHOD)) {
        if (unlikely(nargs < 1)) {
            __Pyx_CyFunction_raise_type_error(
                cyfunc, "needs an argument");
            return -1;
        }
        ret = 1;
    }
    if (unlikely(kwnames) && unlikely(__Pyx_PyTuple_GET_SIZE(kwnames))) {
        __Pyx_CyFunction_raise_type_error(
            cyfunc, "takes no keyword arguments");
        return -1;
    }
    return ret;
}
static PyObject * __Pyx_CyFunction_Vectorcall_NOARGS(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames)
{
    __pyx_CyFunctionObject *cyfunc = (__pyx_CyFunctionObject *)func;
#if CYTHON_BACKPORT_VECTORCALL
    Py_ssize_t nargs = (Py_ssize_t)nargsf;
#else
    Py_ssize_t nargs = PyVectorcall_NARGS(nargsf);
#endif
    PyObject *self;
#if CYTHON_COMPILING_IN_LIMITED_API
    PyCFunction meth = PyCFunction_GetFunction(cyfunc->func);
    if (unlikely(!meth)) return NULL;
#else
    PyCFunction meth = ((PyCFunctionObject*)cyfunc)->m_ml->ml_meth;
#endif
    switch (__Pyx_CyFunction_Vectorcall_CheckArgs(cyfunc, nargs, kwnames)) {
    case 1:
        self = args[0];
        args += 1;
        nargs -= 1;
        break;
    case 0:
#if CYTHON_COMPILING_IN_LIMITED_API
        self = PyCFunction_GetSelf(((__pyx_CyFunctionObject*)cyfunc)->func);
        if (unlikely(!self) && PyErr_Occurred()) return NULL;
#else
        self = ((PyCFunctionObject*)cyfunc)->m_self;
#endif
        break;
    default:
        return NULL;
    }
    if (unlikely(nargs != 0)) {
        __Pyx_CyFunction_raise_argument_count_error(
            cyfunc, "takes no arguments", nargs);
        return NULL;
    }
    return meth(self, NULL);
}
static PyObject * __Pyx_CyFunction_Vectorcall_O(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames)
{
    __pyx_CyFunctionObject *cyfunc = (__pyx_CyFunctionObject *)func;
#if CYTHON_BACKPORT_VECTORCALL
    Py_ssize_t nargs = (Py_ssize_t)nargsf;
#else
    Py_ssize_t nargs = PyVectorcall_NARGS(nargsf);
#endif
    PyObject *self;
#if CYTHON_COMPILING_IN_LIMITED_API
    PyCFunction meth = PyCFunction_GetFunction(cyfunc->func);
    if (unlikely(!meth)) return NULL;
#else
    PyCFunction meth = ((PyCFunctionObject*)cyfunc)->m_ml->ml_meth;
#endif
    switch (__Pyx_CyFunction_Vectorcall_CheckArgs(cyfunc, nargs, kwnames)) {
    case 1:
        self = args[0];
        args += 1;
        nargs -= 1;
        break;
    case 0:
#if CYTHON_COMPILING_IN_LIMITED_API
        self = PyCFunction_GetSelf(((__pyx_CyFunctionObject*)cyfunc)->func);
        if (unlikely(!self) && PyErr_Occurred()) return NULL;
#else
        self = ((PyCFunctionObject*)cyfunc)->m_self;
#endif
        break;
    default:
        return NULL;
    }
    if (unlikely(nargs != 1)) {
        __Pyx_CyFunction_raise_argument_count_error(
            cyfunc, "takes exactly one argument", nargs);
        return NULL;
    }
    return meth(self, args[0]);
}
static PyObject * __Pyx_CyFunction_Vectorcall_FASTCALL_KEYWORDS(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames)
{
    __pyx_CyFunctionObject *cyfunc = (__pyx_CyFunctionObject *)func;
#if CYTHON_BACKPORT_VECTORCALL
    Py_ssize_t nargs = (Py_ssize_t)nargsf;
#else
    Py_ssize_t nargs = PyVectorcall_NARGS(nargsf);
#endif
    PyObject *self;
#if CYTHON_COMPILING_IN_LIMITED_API
    PyCFunction meth = PyCFunction_GetFunction(cyfunc->func);
    if (unlikely(!meth)) return NULL;
#else
    PyCFunction meth = ((PyCFunctionObject*)cyfunc)->m_ml->ml_meth;
#endif
    switch (__Pyx_CyFunction_Vectorcall_CheckArgs(cyfunc, nargs, NULL)) {
    case 1:
        self = args[0];
        args += 1;
        nargs -= 1;
        break;
    case 0:
#if CYTHON_COMPILING_IN_LIMITED_API
        self = PyCFunction_GetSelf(((__pyx_CyFunctionObject*)cyfunc)->func);
        if (unlikely(!self) && PyErr_Occurred()) return NULL;
#else
        self = ((PyCFunctionObject*)cyfunc)->m_self;
#endif
        break;
    default:
        return NULL;
    }
    return ((__Pyx_PyCFunctionFastWithKeywords)(void(*)(void))meth)(self, args, nargs, kwnames);
}
static PyObject * __Pyx_CyFunction_Vectorcall_FASTCALL_KEYWORDS_METHOD(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames)
{
    __pyx_CyFunctionObject *cyfunc = (__pyx_CyFunctionObject *)func;
    PyTypeObject *cls = (PyTypeObject *) __Pyx_CyFunction_GetClassObj(cyfunc);
#if CYTHON_BACKPORT_VECTORCALL
    Py_ssize_t nargs = (Py_ssize_t)nargsf;
#else
    Py_ssize_t nargs = PyVectorcall_NARGS(nargsf);
#endif
    PyObject *self;
#if CYTHON_COMPILING_IN_LIMITED_API
    PyCFunction meth = PyCFunction_GetFunction(cyfunc->func);
    if (unlikely(!meth)) return NULL;
#else
    PyCFunction meth = ((PyCFunctionObject*)cyfunc)->m_ml->ml_meth;
#endif
    switch (__Pyx_CyFunction_Vectorcall_CheckArgs(cyfunc, nargs, NULL)) {
    case 1:
        self = args[0];
        args += 1;
        nargs -= 1;
        break;
    case 0:
#if CYTHON_COMPILING_IN_LIMITED_API
        self = PyCFunction_GetSelf(((__pyx_CyFunctionObject*)cyfunc)->func);
        if (unlikely(!self) && PyErr_Occurred()) return NULL;
#else
        self = ((PyCFunctionObject*)cyfunc)->m_self;
#endif
        break;
    default:
        return NULL;
    }
    return ((__Pyx_PyCMethod)(void(*)(void))meth)(self, cls, args, (size_t)nargs, kwnames);
}
#endif
static PyType_Slot __pyx_CyFunctionType_slots[] = {
    {Py_tp_dealloc, (void *)__Pyx_CyFunction_dealloc},
    {Py_tp_repr, (void *)__Pyx_CyFunction_repr},
    {Py_tp_call, (void *)__Pyx_CyFunction_CallAsMethod},
    {Py_tp_traverse, (void *)__Pyx_CyFunction_traverse},
    {Py_tp_clear, (void *)__Pyx_CyFunction_clear},
    {Py_tp_methods, (void *)__pyx_CyFunction_methods},
    {Py_tp_members, (void *)__pyx_CyFunction_members},
    {Py_tp_getset, (void *)__pyx_CyFunction_getsets},
    {Py_tp_descr_get, (void *)__Pyx_PyMethod_New},
    {0, 0},
};
static PyType_Spec __pyx_CyFunctionType_spec = {
    __PYX_TYPE_MODULE_PREFIX "cython_function_or_method",
    sizeof(__pyx_CyFunctionObject),
    0,
#ifdef Py_TPFLAGS_METHOD_DESCRIPTOR
    Py_TPFLAGS_METHOD_DESCRIPTOR |
#endif
#if CYTHON_METH_FASTCALL
#if defined(Py_TPFLAGS_HAVE_VECTORCALL)
    Py_TPFLAGS_HAVE_VECTORCALL |
#elif defined(_Py_TPFLAGS_HAVE_VECTORCALL)
    _Py_TPFLAGS_HAVE_VECTORCALL |
#endif
#endif // CYTHON_METH_FASTCALL
#if PY_VERSION_HEX >= 0x030A0000
    Py_TPFLAGS_IMMUTABLETYPE |
#endif
    Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC | Py_TPFLAGS_BASETYPE,
    __pyx_CyFunctionType_slots
};
static int __pyx_CyFunction_init(PyObject *module) {
    __pyx_mstatetype *mstate = __Pyx_PyModule_GetState(module);
    mstate->__pyx_CyFunctionType = __Pyx_FetchCommonTypeFromSpec(
        mstate->__pyx_CommonTypesMetaclassType, module, &__pyx_CyFunctionType_spec, NULL);
    if (unlikely(mstate->__pyx_CyFunctionType == NULL)) {
        return -1;
    }
    return 0;
}
static CYTHON_INLINE PyObject *__Pyx_CyFunction_InitDefaults(PyObject *func, PyTypeObject *defaults_type) {
    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
    m->defaults = PyObject_CallObject((PyObject*)defaults_type, NULL); // _PyObject_New(defaults_type);
    if (unlikely(!m->defaults))
        return NULL;
    return m->defaults;
}
static CYTHON_INLINE void __Pyx_CyFunction_SetDefaultsTuple(PyObject *func, PyObject *tuple) {
    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
    m->defaults_tuple = tuple;
    Py_INCREF(tuple);
}
static CYTHON_INLINE void __Pyx_CyFunction_SetDefaultsKwDict(PyObject *func, PyObject *dict) {
    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
    m->defaults_kwdict = dict;
    Py_INCREF(dict);
}
static CYTHON_INLINE void __Pyx_CyFunction_SetAnnotationsDict(PyObject *func, PyObject *dict) {
    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
    m->func_annotations = dict;
    Py_INCREF(dict);
}

/* CythonFunction */
  static PyObject *__Pyx_CyFunction_New(PyMethodDef *ml, int flags, PyObject* qualname,
                                      PyObject *closure, PyObject *module, PyObject* globals, PyObject* code) {
    PyObject *op = __Pyx_CyFunction_Init(
        PyObject_GC_New(__pyx_CyFunctionObject, __pyx_mstate_global->__pyx_CyFunctionType),
        ml, flags, qualname, closure, module, globals, code
    );
    if (likely(op)) {
        PyObject_GC_Track(op);
    }
    return op;
}

/* CLineInTraceback */
  #if CYTHON_CLINE_IN_TRACEBACK && CYTHON_CLINE_IN_TRACEBACK_RUNTIME
static int __Pyx_CLineForTraceback(PyThreadState *tstate, int c_line) {
    PyObject *use_cline;
    PyObject *ptype, *pvalue, *ptraceback;
#if CYTHON_COMPILING_IN_CPYTHON
    PyObject **cython_runtime_dict;
#endif
    CYTHON_MAYBE_UNUSED_VAR(tstate);
    if (unlikely(!__pyx_mstate_global->__pyx_cython_runtime)) {
        return c_line;
    }
    __Pyx_ErrFetchInState(tstate, &ptype, &pvalue, &ptraceback);
#if CYTHON_COMPILING_IN_CPYTHON
    cython_runtime_dict = _PyObject_GetDictPtr(__pyx_mstate_global->__pyx_cython_runtime);
    if (likely(cython_runtime_dict)) {
        __Pyx_BEGIN_CRITICAL_SECTION(*cython_runtime_dict);
        __PYX_PY_DICT_LOOKUP_IF_MODIFIED(
            use_cline, *cython_runtime_dict,
            __Pyx_PyDict_GetItemStr(*cython_runtime_dict, __pyx_mstate_global->__pyx_n_u_cline_in_traceback))
        Py_XINCREF(use_cline);
        __Pyx_END_CRITICAL_SECTION();
    } else
#endif
    {
      PyObject *use_cline_obj = __Pyx_PyObject_GetAttrStrNoError(__pyx_mstate_global->__pyx_cython_runtime, __pyx_mstate_global->__pyx_n_u_cline_in_traceback);
      if (use_cline_obj) {
        use_cline = PyObject_Not(use_cline_obj) ? Py_False : Py_True;
        Py_INCREF(use_cline);
        Py_DECREF(use_cline_obj);
      } else {
        PyErr_Clear();
        use_cline = NULL;
      }
    }
    if (!use_cline) {
        c_line = 0;
        (void) PyObject_SetAttr(__pyx_mstate_global->__pyx_cython_runtime, __pyx_mstate_global->__pyx_n_u_cline_in_traceback, Py_False);
    }
    else if (use_cline == Py_False || (use_cline != Py_True && PyObject_Not(use_cline) != 0)) {
        c_line = 0;
    }
    Py_XDECREF(use_cline);
    __Pyx_ErrRestoreInState(tstate, ptype, pvalue, ptraceback);
    return c_line;
}
#endif

/* CodeObjectCache */
  static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line) {
    int start = 0, mid = 0, end = count - 1;
    if (end >= 0 && code_line > entries[end].code_line) {
        return count;
    }
    while (start < end) {
        mid = start + (end - start) / 2;
        if (code_line < entries[mid].code_line) {
            end = mid;
        } else if (code_line > entries[mid].code_line) {
             start = mid + 1;
        } else {
            return mid;
        }
    }
    if (code_line <= entries[mid].code_line) {
        return mid;
    } else {
        return mid + 1;
    }
}
static __Pyx_CachedCodeObjectType *__pyx__find_code_object(struct __Pyx_CodeObjectCache *code_cache, int code_line) {
    __Pyx_CachedCodeObjectType* code_object;
    int pos;
    if (unlikely(!code_line) || unlikely(!code_cache->entries)) {
        return NULL;
    }
    pos = __pyx_bisect_code_objects(code_cache->entries, code_cache->count, code_line);
    if (unlikely(pos >= code_cache->count) || unlikely(code_cache->entries[pos].code_line != code_line)) {
        return NULL;
    }
    code_object = code_cache->entries[pos].code_object;
    Py_INCREF(code_object);
    return code_object;
}
static __Pyx_CachedCodeObjectType *__pyx_find_code_object(int code_line) {
#if CYTHON_COMPILING_IN_CPYTHON_FREETHREADING && !CYTHON_ATOMICS
    (void)__pyx__find_code_object;
    return NULL; // Most implementation should have atomics. But otherwise, don't make it thread-safe, just miss.
#else
    struct __Pyx_CodeObjectCache *code_cache = &__pyx_mstate_global->__pyx_code_cache;
#if CYTHON_COMPILING_IN_CPYTHON_FREETHREADING
    __pyx_nonatomic_int_type old_count = __pyx_atomic_incr_acq_rel(&code_cache->accessor_count);
    if (old_count < 0) {
        __pyx_atomic_decr_acq_rel(&code_cache->accessor_count);
        return NULL;
    }
#endif
    __Pyx_CachedCodeObjectType *result = __pyx__find_code_object(code_cache, code_line);
#if CYTHON_COMPILING_IN_CPYTHON_FREETHREADING
    __pyx_atomic_decr_acq_rel(&code_cache->accessor_count);
#endif
    return result;
#endif
}
static void __pyx__insert_code_object(struct __Pyx_CodeObjectCache *code_cache, int code_line, __Pyx_CachedCodeObjectType* code_object)
{
    int pos, i;
    __Pyx_CodeObjectCacheEntry* entries = code_cache->entries;
    if (unlikely(!code_line)) {
        return;
    }
    if (unlikely(!entries)) {
        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Malloc(64*sizeof(__Pyx_CodeObjectCacheEntry));
        if (likely(entries)) {
            code_cache->entries = entries;
            code_cache->max_count = 64;
            code_cache->count = 1;
            entries[0].code_line = code_line;
            entries[0].code_object = code_object;
            Py_INCREF(code_object);
        }
        return;
    }
    pos = __pyx_bisect_code_objects(code_cache->entries, code_cache->count, code_line);
    if ((pos < code_cache->count) && unlikely(code_cache->entries[pos].code_line == code_line)) {
        __Pyx_CachedCodeObjectType* tmp = entries[pos].code_object;
        entries[pos].code_object = code_object;
        Py_INCREF(code_object);
        Py_DECREF(tmp);
        return;
    }
    if (code_cache->count == code_cache->max_count) {
        int new_max = code_cache->max_count + 64;
        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Realloc(
            code_cache->entries, ((size_t)new_max) * sizeof(__Pyx_CodeObjectCacheEntry));
        if (unlikely(!entries)) {
            return;
        }
        code_cache->entries = entries;
        code_cache->max_count = new_max;
    }
    for (i=code_cache->count; i>pos; i--) {
        entries[i] = entries[i-1];
    }
    entries[pos].code_line = code_line;
    entries[pos].code_object = code_object;
    code_cache->count++;
    Py_INCREF(code_object);
}
static void __pyx_insert_code_object(int code_line, __Pyx_CachedCodeObjectType* code_object) {
#if CYTHON_COMPILING_IN_CPYTHON_FREETHREADING && !CYTHON_ATOMICS
    (void)__pyx__insert_code_object;
    return; // Most implementation should have atomics. But otherwise, don't make it thread-safe, just fail.
#else
    struct __Pyx_CodeObjectCache *code_cache = &__pyx_mstate_global->__pyx_code_cache;
#if CYTHON_COMPILING_IN_CPYTHON_FREETHREADING
    __pyx_nonatomic_int_type expected = 0;
    if (!__pyx_atomic_int_cmp_exchange(&code_cache->accessor_count, &expected, INT_MIN)) {
        return;
    }
#endif
    __pyx__insert_code_object(code_cache, code_line, code_object);
#if CYTHON_COMPILING_IN_CPYTHON_FREETHREADING
    __pyx_atomic_sub(&code_cache->accessor_count, INT_MIN);
#endif
#endif
}

/* AddTraceback */
  #include "compile.h"
#include "frameobject.h"
#include "traceback.h"
#if PY_VERSION_HEX >= 0x030b00a6 && !CYTHON_COMPILING_IN_LIMITED_API && !defined(PYPY_VERSION)
  #ifndef Py_BUILD_CORE
    #define Py_BUILD_CORE 1
  #endif
  #include "internal/pycore_frame.h"
#endif
#if CYTHON_COMPILING_IN_LIMITED_API
static PyObject *__Pyx_PyCode_Replace_For_AddTraceback(PyObject *code, PyObject *scratch_dict,
                                                       PyObject *firstlineno, PyObject *name) {
    PyObject *replace = NULL;
    if (unlikely(PyDict_SetItemString(scratch_dict, "co_firstlineno", firstlineno))) return NULL;
    if (unlikely(PyDict_SetItemString(scratch_dict, "co_name", name))) return NULL;
    replace = PyObject_GetAttrString(code, "replace");
    if (likely(replace)) {
        PyObject *result = PyObject_Call(replace, __pyx_mstate_global->__pyx_empty_tuple, scratch_dict);
        Py_DECREF(replace);
        return result;
    }
    PyErr_Clear();
    return NULL;
}
static void __Pyx_AddTraceback(const char *funcname, int c_line,
                               int py_line, const char *filename) {
    PyObject *code_object = NULL, *py_py_line = NULL, *py_funcname = NULL, *dict = NULL;
    PyObject *replace = NULL, *getframe = NULL, *frame = NULL;
    PyObject *exc_type, *exc_value, *exc_traceback;
    int success = 0;
    if (c_line) {
        (void) __pyx_cfilenm;
        (void) __Pyx_CLineForTraceback(__Pyx_PyThreadState_Current, c_line);
    }
    PyErr_Fetch(&exc_type, &exc_value, &exc_traceback);
    code_object = __pyx_find_code_object(c_line ? -c_line : py_line);
    if (!code_object) {
        code_object = Py_CompileString("_getframe()", filename, Py_eval_input);
        if (unlikely(!code_object)) goto bad;
        py_py_line = PyLong_FromLong(py_line);
        if (unlikely(!py_py_line)) goto bad;
        py_funcname = PyUnicode_FromString(funcname);
        if (unlikely(!py_funcname)) goto bad;
        dict = PyDict_New();
        if (unlikely(!dict)) goto bad;
        {
            PyObject *old_code_object = code_object;
            code_object = __Pyx_PyCode_Replace_For_AddTraceback(code_object, dict, py_py_line, py_funcname);
            Py_DECREF(old_code_object);
        }
        if (unlikely(!code_object)) goto bad;
        __pyx_insert_code_object(c_line ? -c_line : py_line, code_object);
    } else {
        dict = PyDict_New();
    }
    getframe = PySys_GetObject("_getframe");
    if (unlikely(!getframe)) goto bad;
    if (unlikely(PyDict_SetItemString(dict, "_getframe", getframe))) goto bad;
    frame = PyEval_EvalCode(code_object, dict, dict);
    if (unlikely(!frame) || frame == Py_None) goto bad;
    success = 1;
  bad:
    PyErr_Restore(exc_type, exc_value, exc_traceback);
    Py_XDECREF(code_object);
    Py_XDECREF(py_py_line);
    Py_XDECREF(py_funcname);
    Py_XDECREF(dict);
    Py_XDECREF(replace);
    if (success) {
        PyTraceBack_Here(
            (struct _frame*)frame);
    }
    Py_XDECREF(frame);
}
#else
static PyCodeObject* __Pyx_CreateCodeObjectForTraceback(
            const char *funcname, int c_line,
            int py_line, const char *filename) {
    PyCodeObject *py_code = NULL;
    PyObject *py_funcname = NULL;
    if (c_line) {
        py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
        if (!py_funcname) goto bad;
        funcname = PyUnicode_AsUTF8(py_funcname);
        if (!funcname) goto bad;
    }
    py_code = PyCode_NewEmpty(filename, funcname, py_line);
    Py_XDECREF(py_funcname);
    return py_code;
bad:
    Py_XDECREF(py_funcname);
    return NULL;
}
static void __Pyx_AddTraceback(const char *funcname, int c_line,
                               int py_line, const char *filename) {
    PyCodeObject *py_code = 0;
    PyFrameObject *py_frame = 0;
    PyThreadState *tstate = __Pyx_PyThreadState_Current;
    PyObject *ptype, *pvalue, *ptraceback;
    if (c_line) {
        c_line = __Pyx_CLineForTraceback(tstate, c_line);
    }
    py_code = __pyx_find_code_object(c_line ? -c_line : py_line);
    if (!py_code) {
        __Pyx_ErrFetchInState(tstate, &ptype, &pvalue, &ptraceback);
        py_code = __Pyx_CreateCodeObjectForTraceback(
            funcname, c_line, py_line, filename);
        if (!py_code) {
            /* If the code object creation fails, then we should clear the
               fetched exception references and propagate the new exception */
            Py_XDECREF(ptype);
            Py_XDECREF(pvalue);
            Py_XDECREF(ptraceback);
            goto bad;
        }
        __Pyx_ErrRestoreInState(tstate, ptype, pvalue, ptraceback);
        __pyx_insert_code_object(c_line ? -c_line : py_line, py_code);
    }
    py_frame = PyFrame_New(
        tstate,            /*PyThreadState *tstate,*/
        py_code,           /*PyCodeObject *code,*/
        __pyx_mstate_global->__pyx_d,    /*PyObject *globals,*/
        0                  /*PyObject *locals*/
    );
    if (!py_frame) goto bad;
    __Pyx_PyFrame_SetLineNumber(py_frame, py_line);
    PyTraceBack_Here(py_frame);
bad:
    Py_XDECREF(py_code);
    Py_XDECREF(py_frame);
}
#endif

/* Declarations */
  #if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus)
  #ifdef __cplusplus
    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
      return ::std::complex< double >(x, y);
    }
  #else
    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
      return x + y*(__pyx_t_double_complex)_Complex_I;
    }
  #endif
#else
    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
      __pyx_t_double_complex z;
      z.real = x;
      z.imag = y;
      return z;
    }
#endif

/* Arithmetic */
  #if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus)
#else
    static CYTHON_INLINE int __Pyx_c_eq_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
       return (a.real == b.real) && (a.imag == b.imag);
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        __pyx_t_double_complex z;
        z.real = a.real + b.real;
        z.imag = a.imag + b.imag;
        return z;
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        __pyx_t_double_complex z;
        z.real = a.real - b.real;
        z.imag = a.imag - b.imag;
        return z;
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        __pyx_t_double_complex z;
        z.real = a.real * b.real - a.imag * b.imag;
        z.imag = a.real * b.imag + a.imag * b.real;
        return z;
    }
    #if 1
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        if (b.imag == 0) {
            return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real);
        } else if (fabs(b.real) >= fabs(b.imag)) {
            if (b.real == 0 && b.imag == 0) {
                return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.imag);
            } else {
                double r = b.imag / b.real;
                double s = (double)(1.0) / (b.real + b.imag * r);
                return __pyx_t_double_complex_from_parts(
                    (a.real + a.imag * r) * s, (a.imag - a.real * r) * s);
            }
        } else {
            double r = b.real / b.imag;
            double s = (double)(1.0) / (b.imag + b.real * r);
            return __pyx_t_double_complex_from_parts(
                (a.real * r + a.imag) * s, (a.imag * r - a.real) * s);
        }
    }
    #else
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        if (b.imag == 0) {
            return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real);
        } else {
            double denom = b.real * b.real + b.imag * b.imag;
            return __pyx_t_double_complex_from_parts(
                (a.real * b.real + a.imag * b.imag) / denom,
                (a.imag * b.real - a.real * b.imag) / denom);
        }
    }
    #endif
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__pyx_t_double_complex a) {
        __pyx_t_double_complex z;
        z.real = -a.real;
        z.imag = -a.imag;
        return z;
    }
    static CYTHON_INLINE int __Pyx_c_is_zero_double(__pyx_t_double_complex a) {
       return (a.real == 0) && (a.imag == 0);
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__pyx_t_double_complex a) {
        __pyx_t_double_complex z;
        z.real =  a.real;
        z.imag = -a.imag;
        return z;
    }
    #if 1
        static CYTHON_INLINE double __Pyx_c_abs_double(__pyx_t_double_complex z) {
          #if !defined(HAVE_HYPOT) || defined(_MSC_VER)
            return sqrt(z.real*z.real + z.imag*z.imag);
          #else
            return hypot(z.real, z.imag);
          #endif
        }
        static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
            __pyx_t_double_complex z;
            double r, lnr, theta, z_r, z_theta;
            if (b.imag == 0 && b.real == (int)b.real) {
                if (b.real < 0) {
                    double denom = a.real * a.real + a.imag * a.imag;
                    a.real = a.real / denom;
                    a.imag = -a.imag / denom;
                    b.real = -b.real;
                }
                switch ((int)b.real) {
                    case 0:
                        z.real = 1;
                        z.imag = 0;
                        return z;
                    case 1:
                        return a;
                    case 2:
                        return __Pyx_c_prod_double(a, a);
                    case 3:
                        z = __Pyx_c_prod_double(a, a);
                        return __Pyx_c_prod_double(z, a);
                    case 4:
                        z = __Pyx_c_prod_double(a, a);
                        return __Pyx_c_prod_double(z, z);
                }
            }
            if (a.imag == 0) {
                if (a.real == 0) {
                    return a;
                } else if ((b.imag == 0) && (a.real >= 0)) {
                    z.real = pow(a.real, b.real);
                    z.imag = 0;
                    return z;
                } else if (a.real > 0) {
                    r = a.real;
                    theta = 0;
                } else {
                    r = -a.real;
                    theta = atan2(0.0, -1.0);
                }
            } else {
                r = __Pyx_c_abs_double(a);
                theta = atan2(a.imag, a.real);
            }
            lnr = log(r);
            z_r = exp(lnr * b.real - theta * b.imag);
            z_theta = theta * b.real + lnr * b.imag;
            z.real = z_r * cos(z_theta);
            z.imag = z_r * sin(z_theta);
            return z;
        }
    #endif
#endif

/* MemviewSliceIsContig */
  static int
__pyx_memviewslice_is_contig(const __Pyx_memviewslice mvs, char order, int ndim)
{
    int i, index, step, start;
    Py_ssize_t itemsize = mvs.memview->view.itemsize;
    if (order == 'F') {
        step = 1;
        start = 0;
    } else {
        step = -1;
        start = ndim - 1;
    }
    for (i = 0; i < ndim; i++) {
        index = start + step * i;
        if (mvs.suboffsets[index] >= 0 || mvs.strides[index] != itemsize)
            return 0;
        itemsize *= mvs.shape[index];
    }
    return 1;
}

/* OverlappingSlices */
  static void
__pyx_get_array_memory_extents(__Pyx_memviewslice *slice,
                               void **out_start, void **out_end,
                               int ndim, size_t itemsize)
{
    char *start, *end;
    int i;
    start = end = slice->data;
    for (i = 0; i < ndim; i++) {
        Py_ssize_t stride = slice->strides[i];
        Py_ssize_t extent = slice->shape[i];
        if (extent == 0) {
            *out_start = *out_end = start;
            return;
        } else {
            if (stride > 0)
                end += stride * (extent - 1);
            else
                start += stride * (extent - 1);
        }
    }
    *out_start = start;
    *out_end = end + itemsize;
}
static int
__pyx_slices_overlap(__Pyx_memviewslice *slice1,
                     __Pyx_memviewslice *slice2,
                     int ndim, size_t itemsize)
{
    void *start1, *end1, *start2, *end2;
    __pyx_get_array_memory_extents(slice1, &start1, &end1, ndim, itemsize);
    __pyx_get_array_memory_extents(slice2, &start2, &end2, ndim, itemsize);
    return (start1 < end2) && (start2 < end1);
}

/* CIntFromPyVerify */
  #define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)\
    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 0)
#define __PYX_VERIFY_RETURN_INT_EXC(target_type, func_type, func_value)\
    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 1)
#define __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, exc)\
    {\
        func_type value = func_value;\
        if (sizeof(target_type) < sizeof(func_type)) {\
            if (unlikely(value != (func_type) (target_type) value)) {\
                func_type zero = 0;\
                if (exc && unlikely(value == (func_type)-1 && PyErr_Occurred()))\
                    return (target_type) -1;\
                if (is_unsigned && unlikely(value < zero))\
                    goto raise_neg_overflow;\
                else\
                    goto raise_overflow;\
            }\
        }\
        return (target_type) value;\
    }

/* FromPy */
  static __pyx_t_double_complex __Pyx_PyComplex_As___pyx_t_double_complex(PyObject* o) {
#if CYTHON_COMPILING_IN_LIMITED_API
    double real=-1.0, imag=-1.0;
    real = PyComplex_RealAsDouble(o);
    if (unlikely(real == -1.0 && PyErr_Occurred())) goto end;
    imag = PyComplex_ImagAsDouble(o);
  end:
    return __pyx_t_double_complex_from_parts(
        (double)real, (double)imag
    );
#else
    Py_complex cval;
#if !CYTHON_COMPILING_IN_PYPY && !CYTHON_COMPILING_IN_GRAAL
    if (PyComplex_CheckExact(o))
        cval = ((PyComplexObject *)o)->cval;
    else
#endif
        cval = PyComplex_AsCComplex(o);
    return __pyx_t_double_complex_from_parts(
               (double)cval.real,
               (double)cval.imag);
#endif
}

/* TypeInfoCompare */
  static int
__pyx_typeinfo_cmp(const __Pyx_TypeInfo *a, const __Pyx_TypeInfo *b)
{
    int i;
    if (!a || !b)
        return 0;
    if (a == b)
        return 1;
    if (a->size != b->size || a->typegroup != b->typegroup ||
            a->is_unsigned != b->is_unsigned || a->ndim != b->ndim) {
        if (a->typegroup == 'H' || b->typegroup == 'H') {
            return a->size == b->size;
        } else {
            return 0;
        }
    }
    if (a->ndim) {
        for (i = 0; i < a->ndim; i++)
            if (a->arraysize[i] != b->arraysize[i])
                return 0;
    }
    if (a->typegroup == 'S') {
        if (a->flags != b->flags)
            return 0;
        if (a->fields || b->fields) {
            if (!(a->fields && b->fields))
                return 0;
            for (i = 0; a->fields[i].type && b->fields[i].type; i++) {
                const __Pyx_StructField *field_a = a->fields + i;
                const __Pyx_StructField *field_b = b->fields + i;
                if (field_a->offset != field_b->offset ||
                    !__pyx_typeinfo_cmp(field_a->type, field_b->type))
                    return 0;
            }
            return !a->fields[i].type && !b->fields[i].type;
        }
    }
    return 1;
}

/* MemviewSliceValidateAndInit */
  static int
__pyx_check_strides(Py_buffer *buf, int dim, int ndim, int spec)
{
    if (buf->shape[dim] <= 1)
        return 1;
    if (buf->strides) {
        if (spec & __Pyx_MEMVIEW_CONTIG) {
            if (spec & (__Pyx_MEMVIEW_PTR|__Pyx_MEMVIEW_FULL)) {
                if (unlikely(buf->strides[dim] != sizeof(void *))) {
                    PyErr_Format(PyExc_ValueError,
                                 "Buffer is not indirectly contiguous "
                                 "in dimension %d.", dim);
                    goto fail;
                }
            } else if (unlikely(buf->strides[dim] != buf->itemsize)) {
                PyErr_SetString(PyExc_ValueError,
                                "Buffer and memoryview are not contiguous "
                                "in the same dimension.");
                goto fail;
            }
        }
        if (spec & __Pyx_MEMVIEW_FOLLOW) {
            Py_ssize_t stride = buf->strides[dim];
            if (stride < 0)
                stride = -stride;
            if (unlikely(stride < buf->itemsize)) {
                PyErr_SetString(PyExc_ValueError,
                                "Buffer and memoryview are not contiguous "
                                "in the same dimension.");
                goto fail;
            }
        }
    } else {
        if (unlikely(spec & __Pyx_MEMVIEW_CONTIG && dim != ndim - 1)) {
            PyErr_Format(PyExc_ValueError,
                         "C-contiguous buffer is not contiguous in "
                         "dimension %d", dim);
            goto fail;
        } else if (unlikely(spec & (__Pyx_MEMVIEW_PTR))) {
            PyErr_Format(PyExc_ValueError,
                         "C-contiguous buffer is not indirect in "
                         "dimension %d", dim);
            goto fail;
        } else if (unlikely(buf->suboffsets)) {
            PyErr_SetString(PyExc_ValueError,
                            "Buffer exposes suboffsets but no strides");
            goto fail;
        }
    }
    return 1;
fail:
    return 0;
}
static int
__pyx_check_suboffsets(Py_buffer *buf, int dim, int ndim, int spec)
{
    CYTHON_UNUSED_VAR(ndim);
    if (spec & __Pyx_MEMVIEW_DIRECT) {
        if (unlikely(buf->suboffsets && buf->suboffsets[dim] >= 0)) {
            PyErr_Format(PyExc_ValueError,
                         "Buffer not compatible with direct access "
                         "in dimension %d.", dim);
            goto fail;
        }
    }
    if (spec & __Pyx_MEMVIEW_PTR) {
        if (unlikely(!buf->suboffsets || (buf->suboffsets[dim] < 0))) {
            PyErr_Format(PyExc_ValueError,
                         "Buffer is not indirectly accessible "
                         "in dimension %d.", dim);
            goto fail;
        }
    }
    return 1;
fail:
    return 0;
}
static int
__pyx_verify_contig(Py_buffer *buf, int ndim, int c_or_f_flag)
{
    int i;
    if (c_or_f_flag & __Pyx_IS_F_CONTIG) {
        Py_ssize_t stride = 1;
        for (i = 0; i < ndim; i++) {
            if (unlikely(stride * buf->itemsize != buf->strides[i]  &&  buf->shape[i] > 1)) {
                PyErr_SetString(PyExc_ValueError,
                    "Buffer not fortran contiguous.");
                goto fail;
            }
            stride = stride * buf->shape[i];
        }
    } else if (c_or_f_flag & __Pyx_IS_C_CONTIG) {
        Py_ssize_t stride = 1;
        for (i = ndim - 1; i >- 1; i--) {
            if (unlikely(stride * buf->itemsize != buf->strides[i]  &&  buf->shape[i] > 1)) {
                PyErr_SetString(PyExc_ValueError,
                    "Buffer not C contiguous.");
                goto fail;
            }
            stride = stride * buf->shape[i];
        }
    }
    return 1;
fail:
    return 0;
}
static int __Pyx_ValidateAndInit_memviewslice(
                int *axes_specs,
                int c_or_f_flag,
                int buf_flags,
                int ndim,
                const __Pyx_TypeInfo *dtype,
                __Pyx_BufFmt_StackElem stack[],
                __Pyx_memviewslice *memviewslice,
                PyObject *original_obj)
{
    struct __pyx_memoryview_obj *memview, *new_memview;
    __Pyx_RefNannyDeclarations
    Py_buffer *buf;
    int i, spec = 0, retval = -1;
    __Pyx_BufFmt_Context ctx;
    int from_memoryview = __pyx_memoryview_check(original_obj);
    __Pyx_RefNannySetupContext("ValidateAndInit_memviewslice", 0);
    if (from_memoryview && __pyx_typeinfo_cmp(dtype, ((struct __pyx_memoryview_obj *)
                                                            original_obj)->typeinfo)) {
        memview = (struct __pyx_memoryview_obj *) original_obj;
        new_memview = NULL;
    } else {
        memview = (struct __pyx_memoryview_obj *) __pyx_memoryview_new(
                                            original_obj, buf_flags, 0, dtype);
        new_memview = memview;
        if (unlikely(!memview))
            goto fail;
    }
    buf = &memview->view;
    if (unlikely(buf->ndim != ndim)) {
        PyErr_Format(PyExc_ValueError,
                "Buffer has wrong number of dimensions (expected %d, got %d)",
                ndim, buf->ndim);
        goto fail;
    }
    if (new_memview) {
        __Pyx_BufFmt_Init(&ctx, stack, dtype);
        if (unlikely(!__Pyx_BufFmt_CheckString(&ctx, buf->format))) goto fail;
    }
    if (unlikely((unsigned) buf->itemsize != dtype->size)) {
        PyErr_Format(PyExc_ValueError,
                     "Item size of buffer (%" CYTHON_FORMAT_SSIZE_T "u byte%s) "
                     "does not match size of '%s' (%" CYTHON_FORMAT_SSIZE_T "u byte%s)",
                     buf->itemsize,
                     (buf->itemsize > 1) ? "s" : "",
                     dtype->name,
                     dtype->size,
                     (dtype->size > 1) ? "s" : "");
        goto fail;
    }
    if (buf->len > 0) {
        for (i = 0; i < ndim; i++) {
            spec = axes_specs[i];
            if (unlikely(!__pyx_check_strides(buf, i, ndim, spec)))
                goto fail;
            if (unlikely(!__pyx_check_suboffsets(buf, i, ndim, spec)))
                goto fail;
        }
        if (unlikely(buf->strides && !__pyx_verify_contig(buf, ndim, c_or_f_flag)))
            goto fail;
    }
    if (unlikely(__Pyx_init_memviewslice(memview, ndim, memviewslice,
                                         new_memview != NULL) == -1)) {
        goto fail;
    }
    retval = 0;
    goto no_fail;
fail:
    Py_XDECREF((PyObject*)new_memview);
    retval = -1;
no_fail:
    __Pyx_RefNannyFinishContext();
    return retval;
}

/* ObjectToMemviewSlice */
  static CYTHON_INLINE __Pyx_memviewslice __Pyx_PyObject_to_MemoryviewSlice_dc___pyx_t_double_complex(PyObject *obj, int writable_flag) {
    __Pyx_memviewslice result = { 0, 0, { 0 }, { 0 }, { 0 } };
    __Pyx_BufFmt_StackElem stack[1];
    int axes_specs[] = { (__Pyx_MEMVIEW_DIRECT | __Pyx_MEMVIEW_CONTIG) };
    int retcode;
    if (obj == Py_None) {
        result.memview = (struct __pyx_memoryview_obj *) Py_None;
        return result;
    }
    retcode = __Pyx_ValidateAndInit_memviewslice(axes_specs, __Pyx_IS_C_CONTIG,
                                                 (PyBUF_C_CONTIGUOUS | PyBUF_FORMAT) | writable_flag, 1,
                                                 &__Pyx_TypeInfo___pyx_t_double_complex, stack,
                                                 &result, obj);
    if (unlikely(retcode == -1))
        goto __pyx_fail;
    return result;
__pyx_fail:
    result.memview = NULL;
    result.data = NULL;
    return result;
}

/* ObjectToMemviewSlice */
  static CYTHON_INLINE __Pyx_memviewslice __Pyx_PyObject_to_MemoryviewSlice_dc_double(PyObject *obj, int writable_flag) {
    __Pyx_memviewslice result = { 0, 0, { 0 }, { 0 }, { 0 } };
    __Pyx_BufFmt_StackElem stack[1];
    int axes_specs[] = { (__Pyx_MEMVIEW_DIRECT | __Pyx_MEMVIEW_CONTIG) };
    int retcode;
    if (obj == Py_None) {
        result.memview = (struct __pyx_memoryview_obj *) Py_None;
        return result;
    }
    retcode = __Pyx_ValidateAndInit_memviewslice(axes_specs, __Pyx_IS_C_CONTIG,
                                                 (PyBUF_C_CONTIGUOUS | PyBUF_FORMAT) | writable_flag, 1,
                                                 &__Pyx_TypeInfo_double, stack,
                                                 &result, obj);
    if (unlikely(retcode == -1))
        goto __pyx_fail;
    return result;
__pyx_fail:
    result.memview = NULL;
    result.data = NULL;
    return result;
}

/* Declarations */
  #if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus)
  #ifdef __cplusplus
    static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
      return ::std::complex< float >(x, y);
    }
  #else
    static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
      return x + y*(__pyx_t_float_complex)_Complex_I;
    }
  #endif
#else
    static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
      __pyx_t_float_complex z;
      z.real = x;
      z.imag = y;
      return z;
    }
#endif

/* Arithmetic */
  #if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus)
#else
    static CYTHON_INLINE int __Pyx_c_eq_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
       return (a.real == b.real) && (a.imag == b.imag);
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sum_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
        __pyx_t_float_complex z;
        z.real = a.real + b.real;
        z.imag = a.imag + b.imag;
        return z;
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_diff_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
        __pyx_t_float_complex z;
        z.real = a.real - b.real;
        z.imag = a.imag - b.imag;
        return z;
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prod_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
        __pyx_t_float_complex z;
        z.real = a.real * b.real - a.imag * b.imag;
        z.imag = a.real * b.imag + a.imag * b.real;
        return z;
    }
    #if 1
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
        if (b.imag == 0) {
            return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.real);
        } else if (fabsf(b.real) >= fabsf(b.imag)) {
            if (b.real == 0 && b.imag == 0) {
                return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.imag);
            } else {
                float r = b.imag / b.real;
                float s = (float)(1.0) / (b.real + b.imag * r);
                return __pyx_t_float_complex_from_parts(
                    (a.real + a.imag * r) * s, (a.imag - a.real * r) * s);
            }
        } else {
            float r = b.real / b.imag;
            float s = (float)(1.0) / (b.imag + b.real * r);
            return __pyx_t_float_complex_from_parts(
                (a.real * r + a.imag) * s, (a.imag * r - a.real) * s);
        }
    }
    #else
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
        if (b.imag == 0) {
            return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.real);
        } else {
            float denom = b.real * b.real + b.imag * b.imag;
            return __pyx_t_float_complex_from_parts(
                (a.real * b.real + a.imag * b.imag) / denom,
                (a.imag * b.real - a.real * b.imag) / denom);
        }
    }
    #endif
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_neg_float(__pyx_t_float_complex a) {
        __pyx_t_float_complex z;
        z.real = -a.real;
        z.imag = -a.imag;
        return z;
    }
    static CYTHON_INLINE int __Pyx_c_is_zero_float(__pyx_t_float_complex a) {
       return (a.real == 0) && (a.imag == 0);
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conj_float(__pyx_t_float_complex a) {
        __pyx_t_float_complex z;
        z.real =  a.real;
        z.imag = -a.imag;
        return z;
    }
    #if 1
        static CYTHON_INLINE float __Pyx_c_abs_float(__pyx_t_float_complex z) {
          #if !defined(HAVE_HYPOT) || defined(_MSC_VER)
            return sqrtf(z.real*z.real + z.imag*z.imag);
          #else
            return hypotf(z.real, z.imag);
          #endif
        }
        static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_pow_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
            __pyx_t_float_complex z;
            float r, lnr, theta, z_r, z_theta;
            if (b.imag == 0 && b.real == (int)b.real) {
                if (b.real < 0) {
                    float denom = a.real * a.real + a.imag * a.imag;
                    a.real = a.real / denom;
                    a.imag = -a.imag / denom;
                    b.real = -b.real;
                }
                switch ((int)b.real) {
                    case 0:
                        z.real = 1;
                        z.imag = 0;
                        return z;
                    case 1:
                        return a;
                    case 2:
                        return __Pyx_c_prod_float(a, a);
                    case 3:
                        z = __Pyx_c_prod_float(a, a);
                        return __Pyx_c_prod_float(z, a);
                    case 4:
                        z = __Pyx_c_prod_float(a, a);
                        return __Pyx_c_prod_float(z, z);
                }
            }
            if (a.imag == 0) {
                if (a.real == 0) {
                    return a;
                } else if ((b.imag == 0) && (a.real >= 0)) {
                    z.real = powf(a.real, b.real);
                    z.imag = 0;
                    return z;
                } else if (a.real > 0) {
                    r = a.real;
                    theta = 0;
                } else {
                    r = -a.real;
                    theta = atan2f(0.0, -1.0);
                }
            } else {
                r = __Pyx_c_abs_float(a);
                theta = atan2f(a.imag, a.real);
            }
            lnr = logf(r);
            z_r = expf(lnr * b.real - theta * b.imag);
            z_theta = theta * b.real + lnr * b.imag;
            z.real = z_r * cosf(z_theta);
            z.imag = z_r * sinf(z_theta);
            return z;
        }
    #endif
#endif

/* Declarations */
  #if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus)
  #ifdef __cplusplus
    static CYTHON_INLINE __pyx_t_long_double_complex __pyx_t_long_double_complex_from_parts(long double x, long double y) {
      return ::std::complex< long double >(x, y);
    }
  #else
    static CYTHON_INLINE __pyx_t_long_double_complex __pyx_t_long_double_complex_from_parts(long double x, long double y) {
      return x + y*(__pyx_t_long_double_complex)_Complex_I;
    }
  #endif
#else
    static CYTHON_INLINE __pyx_t_long_double_complex __pyx_t_long_double_complex_from_parts(long double x, long double y) {
      __pyx_t_long_double_complex z;
      z.real = x;
      z.imag = y;
      return z;
    }
#endif

/* Arithmetic */
  #if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus)
#else
    static CYTHON_INLINE int __Pyx_c_eq_long__double(__pyx_t_long_double_complex a, __pyx_t_long_double_complex b) {
       return (a.real == b.real) && (a.imag == b.imag);
    }
    static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_sum_long__double(__pyx_t_long_double_complex a, __pyx_t_long_double_complex b) {
        __pyx_t_long_double_complex z;
        z.real = a.real + b.real;
        z.imag = a.imag + b.imag;
        return z;
    }
    static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_diff_long__double(__pyx_t_long_double_complex a, __pyx_t_long_double_complex b) {
        __pyx_t_long_double_complex z;
        z.real = a.real - b.real;
        z.imag = a.imag - b.imag;
        return z;
    }
    static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_prod_long__double(__pyx_t_long_double_complex a, __pyx_t_long_double_complex b) {
        __pyx_t_long_double_complex z;
        z.real = a.real * b.real - a.imag * b.imag;
        z.imag = a.real * b.imag + a.imag * b.real;
        return z;
    }
    #if 1
    static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_quot_long__double(__pyx_t_long_double_complex a, __pyx_t_long_double_complex b) {
        if (b.imag == 0) {
            return __pyx_t_long_double_complex_from_parts(a.real / b.real, a.imag / b.real);
        } else if (fabsl(b.real) >= fabsl(b.imag)) {
            if (b.real == 0 && b.imag == 0) {
                return __pyx_t_long_double_complex_from_parts(a.real / b.real, a.imag / b.imag);
            } else {
                long double r = b.imag / b.real;
                long double s = (long double)(1.0) / (b.real + b.imag * r);
                return __pyx_t_long_double_complex_from_parts(
                    (a.real + a.imag * r) * s, (a.imag - a.real * r) * s);
            }
        } else {
            long double r = b.real / b.imag;
            long double s = (long double)(1.0) / (b.imag + b.real * r);
            return __pyx_t_long_double_complex_from_parts(
                (a.real * r + a.imag) * s, (a.imag * r - a.real) * s);
        }
    }
    #else
    static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_quot_long__double(__pyx_t_long_double_complex a, __pyx_t_long_double_complex b) {
        if (b.imag == 0) {
            return __pyx_t_long_double_complex_from_parts(a.real / b.real, a.imag / b.real);
        } else {
            long double denom = b.real * b.real + b.imag * b.imag;
            return __pyx_t_long_double_complex_from_parts(
                (a.real * b.real + a.imag * b.imag) / denom,
                (a.imag * b.real - a.real * b.imag) / denom);
        }
    }
    #endif
    static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_neg_long__double(__pyx_t_long_double_complex a) {
        __pyx_t_long_double_complex z;
        z.real = -a.real;
        z.imag = -a.imag;
        return z;
    }
    static CYTHON_INLINE int __Pyx_c_is_zero_long__double(__pyx_t_long_double_complex a) {
       return (a.real == 0) && (a.imag == 0);
    }
    static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_conj_long__double(__pyx_t_long_double_complex a) {
        __pyx_t_long_double_complex z;
        z.real =  a.real;
        z.imag = -a.imag;
        return z;
    }
    #if 1
        static CYTHON_INLINE long double __Pyx_c_abs_long__double(__pyx_t_long_double_complex z) {
          #if !defined(HAVE_HYPOT) || defined(_MSC_VER)
            return sqrtl(z.real*z.real + z.imag*z.imag);
          #else
            return hypotl(z.real, z.imag);
          #endif
        }
        static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_pow_long__double(__pyx_t_long_double_complex a, __pyx_t_long_double_complex b) {
            __pyx_t_long_double_complex z;
            long double r, lnr, theta, z_r, z_theta;
            if (b.imag == 0 && b.real == (int)b.real) {
                if (b.real < 0) {
                    long double denom = a.real * a.real + a.imag * a.imag;
                    a.real = a.real / denom;
                    a.imag = -a.imag / denom;
                    b.real = -b.real;
                }
                switch ((int)b.real) {
                    case 0:
                        z.real = 1;
                        z.imag = 0;
                        return z;
                    case 1:
                        return a;
                    case 2:
                        return __Pyx_c_prod_long__double(a, a);
                    case 3:
                        z = __Pyx_c_prod_long__double(a, a);
                        return __Pyx_c_prod_long__double(z, a);
                    case 4:
                        z = __Pyx_c_prod_long__double(a, a);
                        return __Pyx_c_prod_long__double(z, z);
                }
            }
            if (a.imag == 0) {
                if (a.real == 0) {
                    return a;
                } else if ((b.imag == 0) && (a.real >= 0)) {
                    z.real = powl(a.real, b.real);
                    z.imag = 0;
                    return z;
                } else if (a.real > 0) {
                    r = a.real;
                    theta = 0;
                } else {
                    r = -a.real;
                    theta = atan2l(0.0, -1.0);
                }
            } else {
                r = __Pyx_c_abs_long__double(a);
                theta = atan2l(a.imag, a.real);
            }
            lnr = logl(r);
            z_r = expl(lnr * b.real - theta * b.imag);
            z_theta = theta * b.real + lnr * b.imag;
            z.real = z_r * cosl(z_theta);
            z.imag = z_r * sinl(z_theta);
            return z;
        }
    #endif
#endif

/* MemviewSliceCopyTemplate */
  static __Pyx_memviewslice
__pyx_memoryview_copy_new_contig(const __Pyx_memviewslice *from_mvs,
                                 const char *mode, int ndim,
                                 size_t sizeof_dtype, int contig_flag,
                                 int dtype_is_object)
{
    __Pyx_RefNannyDeclarations
    int i;
    __Pyx_memviewslice new_mvs = { 0, 0, { 0 }, { 0 }, { 0 } };
    struct __pyx_memoryview_obj *from_memview = from_mvs->memview;
    Py_buffer *buf = &from_memview->view;
    PyObject *shape_tuple = NULL;
    PyObject *temp_int = NULL;
    struct __pyx_array_obj *array_obj = NULL;
    struct __pyx_memoryview_obj *memview_obj = NULL;
    __Pyx_RefNannySetupContext("__pyx_memoryview_copy_new_contig", 0);
    for (i = 0; i < ndim; i++) {
        if (unlikely(from_mvs->suboffsets[i] >= 0)) {
            PyErr_Format(PyExc_ValueError, "Cannot copy memoryview slice with "
                                           "indirect dimensions (axis %d)", i);
            goto fail;
        }
    }
    shape_tuple = PyTuple_New(ndim);
    if (unlikely(!shape_tuple)) {
        goto fail;
    }
    __Pyx_GOTREF(shape_tuple);
    for(i = 0; i < ndim; i++) {
        temp_int = PyLong_FromSsize_t(from_mvs->shape[i]);
        if(unlikely(!temp_int)) {
            goto fail;
        } else {
#if CYTHON_ASSUME_SAFE_MACROS
            PyTuple_SET_ITEM(shape_tuple, i, temp_int);
#else
            if (PyTuple_SetItem(shape_tuple, i, temp_int) < 0) {
                goto fail;
            }
#endif
            temp_int = NULL;
        }
    }
    array_obj = __pyx_array_new(shape_tuple, sizeof_dtype, buf->format, mode, NULL);
    if (unlikely(!array_obj)) {
        goto fail;
    }
    __Pyx_GOTREF(array_obj);
    memview_obj = (struct __pyx_memoryview_obj *) __pyx_memoryview_new(
                                    (PyObject *) array_obj, contig_flag,
                                    dtype_is_object,
                                    from_mvs->memview->typeinfo);
    if (unlikely(!memview_obj))
        goto fail;
    if (unlikely(__Pyx_init_memviewslice(memview_obj, ndim, &new_mvs, 1) < 0))
        goto fail;
    if (unlikely(__pyx_memoryview_copy_contents(*from_mvs, new_mvs, ndim, ndim,
                                                dtype_is_object) < 0))
        goto fail;
    goto no_fail;
fail:
    __Pyx_XDECREF((PyObject *) new_mvs.memview);
    new_mvs.memview = NULL;
    new_mvs.data = NULL;
no_fail:
    __Pyx_XDECREF(shape_tuple);
    __Pyx_XDECREF(temp_int);
    __Pyx_XDECREF((PyObject *) array_obj);
    __Pyx_RefNannyFinishContext();
    return new_mvs;
}

/* MemviewSliceInit */
  static int
__Pyx_init_memviewslice(struct __pyx_memoryview_obj *memview,
                        int ndim,
                        __Pyx_memviewslice *memviewslice,
                        int memview_is_new_reference)
{
    __Pyx_RefNannyDeclarations
    int i, retval=-1;
    Py_buffer *buf = &memview->view;
    __Pyx_RefNannySetupContext("init_memviewslice", 0);
    if (unlikely(memviewslice->memview || memviewslice->data)) {
        PyErr_SetString(PyExc_ValueError,
            "memviewslice is already initialized!");
        goto fail;
    }
    if (buf->strides) {
        for (i = 0; i < ndim; i++) {
            memviewslice->strides[i] = buf->strides[i];
        }
    } else {
        Py_ssize_t stride = buf->itemsize;
        for (i = ndim - 1; i >= 0; i--) {
            memviewslice->strides[i] = stride;
            stride *= buf->shape[i];
        }
    }
    for (i = 0; i < ndim; i++) {
        memviewslice->shape[i]   = buf->shape[i];
        if (buf->suboffsets) {
            memviewslice->suboffsets[i] = buf->suboffsets[i];
        } else {
            memviewslice->suboffsets[i] = -1;
        }
    }
    memviewslice->memview = memview;
    memviewslice->data = (char *)buf->buf;
    if (__pyx_add_acquisition_count(memview) == 0 && !memview_is_new_reference) {
        Py_INCREF((PyObject*)memview);
    }
    retval = 0;
    goto no_fail;
fail:
    memviewslice->memview = 0;
    memviewslice->data = 0;
    retval = -1;
no_fail:
    __Pyx_RefNannyFinishContext();
    return retval;
}
#ifndef Py_NO_RETURN
#define Py_NO_RETURN
#endif
static void __pyx_fatalerror(const char *fmt, ...) Py_NO_RETURN {
    va_list vargs;
    char msg[200];
#if PY_VERSION_HEX >= 0x030A0000 || defined(HAVE_STDARG_PROTOTYPES)
    va_start(vargs, fmt);
#else
    va_start(vargs);
#endif
    vsnprintf(msg, 200, fmt, vargs);
    va_end(vargs);
    Py_FatalError(msg);
}
static CYTHON_INLINE int
__pyx_add_acquisition_count_locked(__pyx_atomic_int_type *acquisition_count,
                                   PyThread_type_lock lock)
{
    int result;
    PyThread_acquire_lock(lock, 1);
    result = (*acquisition_count)++;
    PyThread_release_lock(lock);
    return result;
}
static CYTHON_INLINE int
__pyx_sub_acquisition_count_locked(__pyx_atomic_int_type *acquisition_count,
                                   PyThread_type_lock lock)
{
    int result;
    PyThread_acquire_lock(lock, 1);
    result = (*acquisition_count)--;
    PyThread_release_lock(lock);
    return result;
}
static CYTHON_INLINE void
__Pyx_INC_MEMVIEW(__Pyx_memviewslice *memslice, int have_gil, int lineno)
{
    __pyx_nonatomic_int_type old_acquisition_count;
    struct __pyx_memoryview_obj *memview = memslice->memview;
    if (unlikely(!memview || (PyObject *) memview == Py_None)) {
        return;
    }
    old_acquisition_count = __pyx_add_acquisition_count(memview);
    if (unlikely(old_acquisition_count <= 0)) {
        if (likely(old_acquisition_count == 0)) {
            if (have_gil) {
                Py_INCREF((PyObject *) memview);
            } else {
                PyGILState_STATE _gilstate = PyGILState_Ensure();
                Py_INCREF((PyObject *) memview);
                PyGILState_Release(_gilstate);
            }
        } else {
            __pyx_fatalerror("Acquisition count is %d (line %d)",
                             old_acquisition_count+1, lineno);
        }
    }
}
static CYTHON_INLINE void __Pyx_XCLEAR_MEMVIEW(__Pyx_memviewslice *memslice,
                                             int have_gil, int lineno) {
    __pyx_nonatomic_int_type old_acquisition_count;
    struct __pyx_memoryview_obj *memview = memslice->memview;
    if (unlikely(!memview || (PyObject *) memview == Py_None)) {
        memslice->memview = NULL;
        return;
    }
    old_acquisition_count = __pyx_sub_acquisition_count(memview);
    memslice->data = NULL;
    if (likely(old_acquisition_count > 1)) {
        memslice->memview = NULL;
    } else if (likely(old_acquisition_count == 1)) {
        if (have_gil) {
            Py_CLEAR(memslice->memview);
        } else {
            PyGILState_STATE _gilstate = PyGILState_Ensure();
            Py_CLEAR(memslice->memview);
            PyGILState_Release(_gilstate);
        }
    } else {
        __pyx_fatalerror("Acquisition count is %d (line %d)",
                         old_acquisition_count-1, lineno);
    }
}

/* CIntToPy */
  static CYTHON_INLINE PyObject* __Pyx_PyLong_From_int(int value) {
#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wconversion"
#endif
    const int neg_one = (int) -1, const_zero = (int) 0;
#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
#pragma GCC diagnostic pop
#endif
    const int is_unsigned = neg_one > const_zero;
    if (is_unsigned) {
        if (sizeof(int) < sizeof(long)) {
            return PyLong_FromLong((long) value);
        } else if (sizeof(int) <= sizeof(unsigned long)) {
            return PyLong_FromUnsignedLong((unsigned long) value);
#if defined(HAVE_LONG_LONG) && !CYTHON_COMPILING_IN_PYPY
        } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
#endif
        }
    } else {
        if (sizeof(int) <= sizeof(long)) {
            return PyLong_FromLong((long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
            return PyLong_FromLongLong((PY_LONG_LONG) value);
#endif
        }
    }
    {
        unsigned char *bytes = (unsigned char *)&value;
#if !CYTHON_COMPILING_IN_LIMITED_API && PY_VERSION_HEX >= 0x030d00A4
        if (is_unsigned) {
            return PyLong_FromUnsignedNativeBytes(bytes, sizeof(value), -1);
        } else {
            return PyLong_FromNativeBytes(bytes, sizeof(value), -1);
        }
#elif !CYTHON_COMPILING_IN_LIMITED_API && PY_VERSION_HEX < 0x030d0000
        int one = 1; int little = (int)*(unsigned char *)&one;
        return _PyLong_FromByteArray(bytes, sizeof(int),
                                     little, !is_unsigned);
#else
        int one = 1; int little = (int)*(unsigned char *)&one;
        PyObject *from_bytes, *result = NULL, *kwds = NULL;
        PyObject *py_bytes = NULL, *order_str = NULL;
        from_bytes = PyObject_GetAttrString((PyObject*)&PyLong_Type, "from_bytes");
        if (!from_bytes) return NULL;
        py_bytes = PyBytes_FromStringAndSize((char*)bytes, sizeof(int));
        if (!py_bytes) goto limited_bad;
        order_str = PyUnicode_FromString(little ? "little" : "big");
        if (!order_str) goto limited_bad;
        {
            PyObject *args[3+(CYTHON_VECTORCALL ? 1 : 0)] = { NULL, py_bytes, order_str };
            if (!is_unsigned) {
                kwds = __Pyx_MakeVectorcallBuilderKwds(1);
                if (!kwds) goto limited_bad;
                if (__Pyx_VectorcallBuilder_AddArgStr("signed", __Pyx_NewRef(Py_True), kwds, args+3, 0) < 0) goto limited_bad;
            }
            result = __Pyx_Object_Vectorcall_CallFromBuilder(from_bytes, args+1, 2 | __Pyx_PY_VECTORCALL_ARGUMENTS_OFFSET, kwds);
        }
        limited_bad:
        Py_XDECREF(kwds);
        Py_XDECREF(order_str);
        Py_XDECREF(py_bytes);
        Py_XDECREF(from_bytes);
        return result;
#endif
    }
}

/* CIntFromPy */
  static CYTHON_INLINE int __Pyx_PyLong_As_int(PyObject *x) {
#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wconversion"
#endif
    const int neg_one = (int) -1, const_zero = (int) 0;
#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
#pragma GCC diagnostic pop
#endif
    const int is_unsigned = neg_one > const_zero;
    if (unlikely(!PyLong_Check(x))) {
        int val;
        PyObject *tmp = __Pyx_PyNumber_Long(x);
        if (!tmp) return (int) -1;
        val = __Pyx_PyLong_As_int(tmp);
        Py_DECREF(tmp);
        return val;
    }
    if (is_unsigned) {
#if CYTHON_USE_PYLONG_INTERNALS
        if (unlikely(__Pyx_PyLong_IsNeg(x))) {
            goto raise_neg_overflow;
        } else if (__Pyx_PyLong_IsCompact(x)) {
            __PYX_VERIFY_RETURN_INT(int, __Pyx_compact_upylong, __Pyx_PyLong_CompactValueUnsigned(x))
        } else {
            const digit* digits = __Pyx_PyLong_Digits(x);
            assert(__Pyx_PyLong_DigitCount(x) > 1);
            switch (__Pyx_PyLong_DigitCount(x)) {
                case 2:
                    if ((8 * sizeof(int) > 1 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(int) >= 2 * PyLong_SHIFT)) {
                            return (int) (((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
                        }
                    }
                    break;
                case 3:
                    if ((8 * sizeof(int) > 2 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(int) >= 3 * PyLong_SHIFT)) {
                            return (int) (((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
                        }
                    }
                    break;
                case 4:
                    if ((8 * sizeof(int) > 3 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(int) >= 4 * PyLong_SHIFT)) {
                            return (int) (((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
                        }
                    }
                    break;
            }
        }
#endif
#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX < 0x030C00A7
        if (unlikely(Py_SIZE(x) < 0)) {
            goto raise_neg_overflow;
        }
#else
        {
            int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
            if (unlikely(result < 0))
                return (int) -1;
            if (unlikely(result == 1))
                goto raise_neg_overflow;
        }
#endif
        if ((sizeof(int) <= sizeof(unsigned long))) {
            __PYX_VERIFY_RETURN_INT_EXC(int, unsigned long, PyLong_AsUnsignedLong(x))
#ifdef HAVE_LONG_LONG
        } else if ((sizeof(int) <= sizeof(unsigned PY_LONG_LONG))) {
            __PYX_VERIFY_RETURN_INT_EXC(int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
#endif
        }
    } else {
#if CYTHON_USE_PYLONG_INTERNALS
        if (__Pyx_PyLong_IsCompact(x)) {
            __PYX_VERIFY_RETURN_INT(int, __Pyx_compact_pylong, __Pyx_PyLong_CompactValue(x))
        } else {
            const digit* digits = __Pyx_PyLong_Digits(x);
            assert(__Pyx_PyLong_DigitCount(x) > 1);
            switch (__Pyx_PyLong_SignedDigitCount(x)) {
                case -2:
                    if ((8 * sizeof(int) - 1 > 1 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(int) - 1 > 2 * PyLong_SHIFT)) {
                            return (int) (((int)-1)*(((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case 2:
                    if ((8 * sizeof(int) > 1 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(int) - 1 > 2 * PyLong_SHIFT)) {
                            return (int) ((((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case -3:
                    if ((8 * sizeof(int) - 1 > 2 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(int) - 1 > 3 * PyLong_SHIFT)) {
                            return (int) (((int)-1)*(((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case 3:
                    if ((8 * sizeof(int) > 2 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(int) - 1 > 3 * PyLong_SHIFT)) {
                            return (int) ((((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case -4:
                    if ((8 * sizeof(int) - 1 > 3 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(int) - 1 > 4 * PyLong_SHIFT)) {
                            return (int) (((int)-1)*(((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case 4:
                    if ((8 * sizeof(int) > 3 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(int) - 1 > 4 * PyLong_SHIFT)) {
                            return (int) ((((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
            }
        }
#endif
        if ((sizeof(int) <= sizeof(long))) {
            __PYX_VERIFY_RETURN_INT_EXC(int, long, PyLong_AsLong(x))
#ifdef HAVE_LONG_LONG
        } else if ((sizeof(int) <= sizeof(PY_LONG_LONG))) {
            __PYX_VERIFY_RETURN_INT_EXC(int, PY_LONG_LONG, PyLong_AsLongLong(x))
#endif
        }
    }
    {
        int val;
        int ret = -1;
#if PY_VERSION_HEX >= 0x030d00A6 && !CYTHON_COMPILING_IN_LIMITED_API
        Py_ssize_t bytes_copied = PyLong_AsNativeBytes(
            x, &val, sizeof(val), Py_ASNATIVEBYTES_NATIVE_ENDIAN | (is_unsigned ? Py_ASNATIVEBYTES_UNSIGNED_BUFFER | Py_ASNATIVEBYTES_REJECT_NEGATIVE : 0));
        if (unlikely(bytes_copied == -1)) {
        } else if (unlikely(bytes_copied > (Py_ssize_t) sizeof(val))) {
            goto raise_overflow;
        } else {
            ret = 0;
        }
#elif PY_VERSION_HEX < 0x030d0000 && !(CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_LIMITED_API) || defined(_PyLong_AsByteArray)
        int one = 1; int is_little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&val;
        ret = _PyLong_AsByteArray((PyLongObject *)x,
                                    bytes, sizeof(val),
                                    is_little, !is_unsigned);
#else
        PyObject *v;
        PyObject *stepval = NULL, *mask = NULL, *shift = NULL;
        int bits, remaining_bits, is_negative = 0;
        int chunk_size = (sizeof(long) < 8) ? 30 : 62;
        if (likely(PyLong_CheckExact(x))) {
            v = __Pyx_NewRef(x);
        } else {
            v = PyNumber_Long(x);
            if (unlikely(!v)) return (int) -1;
            assert(PyLong_CheckExact(v));
        }
        {
            int result = PyObject_RichCompareBool(v, Py_False, Py_LT);
            if (unlikely(result < 0)) {
                Py_DECREF(v);
                return (int) -1;
            }
            is_negative = result == 1;
        }
        if (is_unsigned && unlikely(is_negative)) {
            Py_DECREF(v);
            goto raise_neg_overflow;
        } else if (is_negative) {
            stepval = PyNumber_Invert(v);
            Py_DECREF(v);
            if (unlikely(!stepval))
                return (int) -1;
        } else {
            stepval = v;
        }
        v = NULL;
        val = (int) 0;
        mask = PyLong_FromLong((1L << chunk_size) - 1); if (unlikely(!mask)) goto done;
        shift = PyLong_FromLong(chunk_size); if (unlikely(!shift)) goto done;
        for (bits = 0; bits < (int) sizeof(int) * 8 - chunk_size; bits += chunk_size) {
            PyObject *tmp, *digit;
            long idigit;
            digit = PyNumber_And(stepval, mask);
            if (unlikely(!digit)) goto done;
            idigit = PyLong_AsLong(digit);
            Py_DECREF(digit);
            if (unlikely(idigit < 0)) goto done;
            val |= ((int) idigit) << bits;
            tmp = PyNumber_Rshift(stepval, shift);
            if (unlikely(!tmp)) goto done;
            Py_DECREF(stepval); stepval = tmp;
        }
        Py_DECREF(shift); shift = NULL;
        Py_DECREF(mask); mask = NULL;
        {
            long idigit = PyLong_AsLong(stepval);
            if (unlikely(idigit < 0)) goto done;
            remaining_bits = ((int) sizeof(int) * 8) - bits - (is_unsigned ? 0 : 1);
            if (unlikely(idigit >= (1L << remaining_bits)))
                goto raise_overflow;
            val |= ((int) idigit) << bits;
        }
        if (!is_unsigned) {
            if (unlikely(val & (((int) 1) << (sizeof(int) * 8 - 1))))
                goto raise_overflow;
            if (is_negative)
                val = ~val;
        }
        ret = 0;
    done:
        Py_XDECREF(shift);
        Py_XDECREF(mask);
        Py_XDECREF(stepval);
#endif
        if (unlikely(ret))
            return (int) -1;
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to int");
    return (int) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to int");
    return (int) -1;
}

/* CIntToPy */
  static CYTHON_INLINE PyObject* __Pyx_PyLong_From_long(long value) {
#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wconversion"
#endif
    const long neg_one = (long) -1, const_zero = (long) 0;
#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
#pragma GCC diagnostic pop
#endif
    const int is_unsigned = neg_one > const_zero;
    if (is_unsigned) {
        if (sizeof(long) < sizeof(long)) {
            return PyLong_FromLong((long) value);
        } else if (sizeof(long) <= sizeof(unsigned long)) {
            return PyLong_FromUnsignedLong((unsigned long) value);
#if defined(HAVE_LONG_LONG) && !CYTHON_COMPILING_IN_PYPY
        } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
#endif
        }
    } else {
        if (sizeof(long) <= sizeof(long)) {
            return PyLong_FromLong((long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
            return PyLong_FromLongLong((PY_LONG_LONG) value);
#endif
        }
    }
    {
        unsigned char *bytes = (unsigned char *)&value;
#if !CYTHON_COMPILING_IN_LIMITED_API && PY_VERSION_HEX >= 0x030d00A4
        if (is_unsigned) {
            return PyLong_FromUnsignedNativeBytes(bytes, sizeof(value), -1);
        } else {
            return PyLong_FromNativeBytes(bytes, sizeof(value), -1);
        }
#elif !CYTHON_COMPILING_IN_LIMITED_API && PY_VERSION_HEX < 0x030d0000
        int one = 1; int little = (int)*(unsigned char *)&one;
        return _PyLong_FromByteArray(bytes, sizeof(long),
                                     little, !is_unsigned);
#else
        int one = 1; int little = (int)*(unsigned char *)&one;
        PyObject *from_bytes, *result = NULL, *kwds = NULL;
        PyObject *py_bytes = NULL, *order_str = NULL;
        from_bytes = PyObject_GetAttrString((PyObject*)&PyLong_Type, "from_bytes");
        if (!from_bytes) return NULL;
        py_bytes = PyBytes_FromStringAndSize((char*)bytes, sizeof(long));
        if (!py_bytes) goto limited_bad;
        order_str = PyUnicode_FromString(little ? "little" : "big");
        if (!order_str) goto limited_bad;
        {
            PyObject *args[3+(CYTHON_VECTORCALL ? 1 : 0)] = { NULL, py_bytes, order_str };
            if (!is_unsigned) {
                kwds = __Pyx_MakeVectorcallBuilderKwds(1);
                if (!kwds) goto limited_bad;
                if (__Pyx_VectorcallBuilder_AddArgStr("signed", __Pyx_NewRef(Py_True), kwds, args+3, 0) < 0) goto limited_bad;
            }
            result = __Pyx_Object_Vectorcall_CallFromBuilder(from_bytes, args+1, 2 | __Pyx_PY_VECTORCALL_ARGUMENTS_OFFSET, kwds);
        }
        limited_bad:
        Py_XDECREF(kwds);
        Py_XDECREF(order_str);
        Py_XDECREF(py_bytes);
        Py_XDECREF(from_bytes);
        return result;
#endif
    }
}

/* CIntFromPy */
  static CYTHON_INLINE unsigned int __Pyx_PyLong_As_unsigned_int(PyObject *x) {
#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wconversion"
#endif
    const unsigned int neg_one = (unsigned int) -1, const_zero = (unsigned int) 0;
#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
#pragma GCC diagnostic pop
#endif
    const int is_unsigned = neg_one > const_zero;
    if (unlikely(!PyLong_Check(x))) {
        unsigned int val;
        PyObject *tmp = __Pyx_PyNumber_Long(x);
        if (!tmp) return (unsigned int) -1;
        val = __Pyx_PyLong_As_unsigned_int(tmp);
        Py_DECREF(tmp);
        return val;
    }
    if (is_unsigned) {
#if CYTHON_USE_PYLONG_INTERNALS
        if (unlikely(__Pyx_PyLong_IsNeg(x))) {
            goto raise_neg_overflow;
        } else if (__Pyx_PyLong_IsCompact(x)) {
            __PYX_VERIFY_RETURN_INT(unsigned int, __Pyx_compact_upylong, __Pyx_PyLong_CompactValueUnsigned(x))
        } else {
            const digit* digits = __Pyx_PyLong_Digits(x);
            assert(__Pyx_PyLong_DigitCount(x) > 1);
            switch (__Pyx_PyLong_DigitCount(x)) {
                case 2:
                    if ((8 * sizeof(unsigned int) > 1 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(unsigned int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(unsigned int) >= 2 * PyLong_SHIFT)) {
                            return (unsigned int) (((((unsigned int)digits[1]) << PyLong_SHIFT) | (unsigned int)digits[0]));
                        }
                    }
                    break;
                case 3:
                    if ((8 * sizeof(unsigned int) > 2 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(unsigned int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(unsigned int) >= 3 * PyLong_SHIFT)) {
                            return (unsigned int) (((((((unsigned int)digits[2]) << PyLong_SHIFT) | (unsigned int)digits[1]) << PyLong_SHIFT) | (unsigned int)digits[0]));
                        }
                    }
                    break;
                case 4:
                    if ((8 * sizeof(unsigned int) > 3 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(unsigned int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(unsigned int) >= 4 * PyLong_SHIFT)) {
                            return (unsigned int) (((((((((unsigned int)digits[3]) << PyLong_SHIFT) | (unsigned int)digits[2]) << PyLong_SHIFT) | (unsigned int)digits[1]) << PyLong_SHIFT) | (unsigned int)digits[0]));
                        }
                    }
                    break;
            }
        }
#endif
#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX < 0x030C00A7
        if (unlikely(Py_SIZE(x) < 0)) {
            goto raise_neg_overflow;
        }
#else
        {
            int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
            if (unlikely(result < 0))
                return (unsigned int) -1;
            if (unlikely(result == 1))
                goto raise_neg_overflow;
        }
#endif
        if ((sizeof(unsigned int) <= sizeof(unsigned long))) {
            __PYX_VERIFY_RETURN_INT_EXC(unsigned int, unsigned long, PyLong_AsUnsignedLong(x))
#ifdef HAVE_LONG_LONG
        } else if ((sizeof(unsigned int) <= sizeof(unsigned PY_LONG_LONG))) {
            __PYX_VERIFY_RETURN_INT_EXC(unsigned int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
#endif
        }
    } else {
#if CYTHON_USE_PYLONG_INTERNALS
        if (__Pyx_PyLong_IsCompact(x)) {
            __PYX_VERIFY_RETURN_INT(unsigned int, __Pyx_compact_pylong, __Pyx_PyLong_CompactValue(x))
        } else {
            const digit* digits = __Pyx_PyLong_Digits(x);
            assert(__Pyx_PyLong_DigitCount(x) > 1);
            switch (__Pyx_PyLong_SignedDigitCount(x)) {
                case -2:
                    if ((8 * sizeof(unsigned int) - 1 > 1 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(unsigned int, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(unsigned int) - 1 > 2 * PyLong_SHIFT)) {
                            return (unsigned int) (((unsigned int)-1)*(((((unsigned int)digits[1]) << PyLong_SHIFT) | (unsigned int)digits[0])));
                        }
                    }
                    break;
                case 2:
                    if ((8 * sizeof(unsigned int) > 1 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(unsigned int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(unsigned int) - 1 > 2 * PyLong_SHIFT)) {
                            return (unsigned int) ((((((unsigned int)digits[1]) << PyLong_SHIFT) | (unsigned int)digits[0])));
                        }
                    }
                    break;
                case -3:
                    if ((8 * sizeof(unsigned int) - 1 > 2 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(unsigned int, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(unsigned int) - 1 > 3 * PyLong_SHIFT)) {
                            return (unsigned int) (((unsigned int)-1)*(((((((unsigned int)digits[2]) << PyLong_SHIFT) | (unsigned int)digits[1]) << PyLong_SHIFT) | (unsigned int)digits[0])));
                        }
                    }
                    break;
                case 3:
                    if ((8 * sizeof(unsigned int) > 2 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(unsigned int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(unsigned int) - 1 > 3 * PyLong_SHIFT)) {
                            return (unsigned int) ((((((((unsigned int)digits[2]) << PyLong_SHIFT) | (unsigned int)digits[1]) << PyLong_SHIFT) | (unsigned int)digits[0])));
                        }
                    }
                    break;
                case -4:
                    if ((8 * sizeof(unsigned int) - 1 > 3 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(unsigned int, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(unsigned int) - 1 > 4 * PyLong_SHIFT)) {
                            return (unsigned int) (((unsigned int)-1)*(((((((((unsigned int)digits[3]) << PyLong_SHIFT) | (unsigned int)digits[2]) << PyLong_SHIFT) | (unsigned int)digits[1]) << PyLong_SHIFT) | (unsigned int)digits[0])));
                        }
                    }
                    break;
                case 4:
                    if ((8 * sizeof(unsigned int) > 3 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(unsigned int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(unsigned int) - 1 > 4 * PyLong_SHIFT)) {
                            return (unsigned int) ((((((((((unsigned int)digits[3]) << PyLong_SHIFT) | (unsigned int)digits[2]) << PyLong_SHIFT) | (unsigned int)digits[1]) << PyLong_SHIFT) | (unsigned int)digits[0])));
                        }
                    }
                    break;
            }
        }
#endif
        if ((sizeof(unsigned int) <= sizeof(long))) {
            __PYX_VERIFY_RETURN_INT_EXC(unsigned int, long, PyLong_AsLong(x))
#ifdef HAVE_LONG_LONG
        } else if ((sizeof(unsigned int) <= sizeof(PY_LONG_LONG))) {
            __PYX_VERIFY_RETURN_INT_EXC(unsigned int, PY_LONG_LONG, PyLong_AsLongLong(x))
#endif
        }
    }
    {
        unsigned int val;
        int ret = -1;
#if PY_VERSION_HEX >= 0x030d00A6 && !CYTHON_COMPILING_IN_LIMITED_API
        Py_ssize_t bytes_copied = PyLong_AsNativeBytes(
            x, &val, sizeof(val), Py_ASNATIVEBYTES_NATIVE_ENDIAN | (is_unsigned ? Py_ASNATIVEBYTES_UNSIGNED_BUFFER | Py_ASNATIVEBYTES_REJECT_NEGATIVE : 0));
        if (unlikely(bytes_copied == -1)) {
        } else if (unlikely(bytes_copied > (Py_ssize_t) sizeof(val))) {
            goto raise_overflow;
        } else {
            ret = 0;
        }
#elif PY_VERSION_HEX < 0x030d0000 && !(CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_LIMITED_API) || defined(_PyLong_AsByteArray)
        int one = 1; int is_little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&val;
        ret = _PyLong_AsByteArray((PyLongObject *)x,
                                    bytes, sizeof(val),
                                    is_little, !is_unsigned);
#else
        PyObject *v;
        PyObject *stepval = NULL, *mask = NULL, *shift = NULL;
        int bits, remaining_bits, is_negative = 0;
        int chunk_size = (sizeof(long) < 8) ? 30 : 62;
        if (likely(PyLong_CheckExact(x))) {
            v = __Pyx_NewRef(x);
        } else {
            v = PyNumber_Long(x);
            if (unlikely(!v)) return (unsigned int) -1;
            assert(PyLong_CheckExact(v));
        }
        {
            int result = PyObject_RichCompareBool(v, Py_False, Py_LT);
            if (unlikely(result < 0)) {
                Py_DECREF(v);
                return (unsigned int) -1;
            }
            is_negative = result == 1;
        }
        if (is_unsigned && unlikely(is_negative)) {
            Py_DECREF(v);
            goto raise_neg_overflow;
        } else if (is_negative) {
            stepval = PyNumber_Invert(v);
            Py_DECREF(v);
            if (unlikely(!stepval))
                return (unsigned int) -1;
        } else {
            stepval = v;
        }
        v = NULL;
        val = (unsigned int) 0;
        mask = PyLong_FromLong((1L << chunk_size) - 1); if (unlikely(!mask)) goto done;
        shift = PyLong_FromLong(chunk_size); if (unlikely(!shift)) goto done;
        for (bits = 0; bits < (int) sizeof(unsigned int) * 8 - chunk_size; bits += chunk_size) {
            PyObject *tmp, *digit;
            long idigit;
            digit = PyNumber_And(stepval, mask);
            if (unlikely(!digit)) goto done;
            idigit = PyLong_AsLong(digit);
            Py_DECREF(digit);
            if (unlikely(idigit < 0)) goto done;
            val |= ((unsigned int) idigit) << bits;
            tmp = PyNumber_Rshift(stepval, shift);
            if (unlikely(!tmp)) goto done;
            Py_DECREF(stepval); stepval = tmp;
        }
        Py_DECREF(shift); shift = NULL;
        Py_DECREF(mask); mask = NULL;
        {
            long idigit = PyLong_AsLong(stepval);
            if (unlikely(idigit < 0)) goto done;
            remaining_bits = ((int) sizeof(unsigned int) * 8) - bits - (is_unsigned ? 0 : 1);
            if (unlikely(idigit >= (1L << remaining_bits)))
                goto raise_overflow;
            val |= ((unsigned int) idigit) << bits;
        }
        if (!is_unsigned) {
            if (unlikely(val & (((unsigned int) 1) << (sizeof(unsigned int) * 8 - 1))))
                goto raise_overflow;
            if (is_negative)
                val = ~val;
        }
        ret = 0;
    done:
        Py_XDECREF(shift);
        Py_XDECREF(mask);
        Py_XDECREF(stepval);
#endif
        if (unlikely(ret))
            return (unsigned int) -1;
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to unsigned int");
    return (unsigned int) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to unsigned int");
    return (unsigned int) -1;
}

/* CIntFromPy */
  static CYTHON_INLINE long __Pyx_PyLong_As_long(PyObject *x) {
#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wconversion"
#endif
    const long neg_one = (long) -1, const_zero = (long) 0;
#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
#pragma GCC diagnostic pop
#endif
    const int is_unsigned = neg_one > const_zero;
    if (unlikely(!PyLong_Check(x))) {
        long val;
        PyObject *tmp = __Pyx_PyNumber_Long(x);
        if (!tmp) return (long) -1;
        val = __Pyx_PyLong_As_long(tmp);
        Py_DECREF(tmp);
        return val;
    }
    if (is_unsigned) {
#if CYTHON_USE_PYLONG_INTERNALS
        if (unlikely(__Pyx_PyLong_IsNeg(x))) {
            goto raise_neg_overflow;
        } else if (__Pyx_PyLong_IsCompact(x)) {
            __PYX_VERIFY_RETURN_INT(long, __Pyx_compact_upylong, __Pyx_PyLong_CompactValueUnsigned(x))
        } else {
            const digit* digits = __Pyx_PyLong_Digits(x);
            assert(__Pyx_PyLong_DigitCount(x) > 1);
            switch (__Pyx_PyLong_DigitCount(x)) {
                case 2:
                    if ((8 * sizeof(long) > 1 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(long) >= 2 * PyLong_SHIFT)) {
                            return (long) (((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
                        }
                    }
                    break;
                case 3:
                    if ((8 * sizeof(long) > 2 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(long) >= 3 * PyLong_SHIFT)) {
                            return (long) (((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
                        }
                    }
                    break;
                case 4:
                    if ((8 * sizeof(long) > 3 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(long) >= 4 * PyLong_SHIFT)) {
                            return (long) (((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
                        }
                    }
                    break;
            }
        }
#endif
#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX < 0x030C00A7
        if (unlikely(Py_SIZE(x) < 0)) {
            goto raise_neg_overflow;
        }
#else
        {
            int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
            if (unlikely(result < 0))
                return (long) -1;
            if (unlikely(result == 1))
                goto raise_neg_overflow;
        }
#endif
        if ((sizeof(long) <= sizeof(unsigned long))) {
            __PYX_VERIFY_RETURN_INT_EXC(long, unsigned long, PyLong_AsUnsignedLong(x))
#ifdef HAVE_LONG_LONG
        } else if ((sizeof(long) <= sizeof(unsigned PY_LONG_LONG))) {
            __PYX_VERIFY_RETURN_INT_EXC(long, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
#endif
        }
    } else {
#if CYTHON_USE_PYLONG_INTERNALS
        if (__Pyx_PyLong_IsCompact(x)) {
            __PYX_VERIFY_RETURN_INT(long, __Pyx_compact_pylong, __Pyx_PyLong_CompactValue(x))
        } else {
            const digit* digits = __Pyx_PyLong_Digits(x);
            assert(__Pyx_PyLong_DigitCount(x) > 1);
            switch (__Pyx_PyLong_SignedDigitCount(x)) {
                case -2:
                    if ((8 * sizeof(long) - 1 > 1 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(long) - 1 > 2 * PyLong_SHIFT)) {
                            return (long) (((long)-1)*(((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case 2:
                    if ((8 * sizeof(long) > 1 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(long) - 1 > 2 * PyLong_SHIFT)) {
                            return (long) ((((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case -3:
                    if ((8 * sizeof(long) - 1 > 2 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(long) - 1 > 3 * PyLong_SHIFT)) {
                            return (long) (((long)-1)*(((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case 3:
                    if ((8 * sizeof(long) > 2 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(long) - 1 > 3 * PyLong_SHIFT)) {
                            return (long) ((((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case -4:
                    if ((8 * sizeof(long) - 1 > 3 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(long) - 1 > 4 * PyLong_SHIFT)) {
                            return (long) (((long)-1)*(((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case 4:
                    if ((8 * sizeof(long) > 3 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(long) - 1 > 4 * PyLong_SHIFT)) {
                            return (long) ((((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
            }
        }
#endif
        if ((sizeof(long) <= sizeof(long))) {
            __PYX_VERIFY_RETURN_INT_EXC(long, long, PyLong_AsLong(x))
#ifdef HAVE_LONG_LONG
        } else if ((sizeof(long) <= sizeof(PY_LONG_LONG))) {
            __PYX_VERIFY_RETURN_INT_EXC(long, PY_LONG_LONG, PyLong_AsLongLong(x))
#endif
        }
    }
    {
        long val;
        int ret = -1;
#if PY_VERSION_HEX >= 0x030d00A6 && !CYTHON_COMPILING_IN_LIMITED_API
        Py_ssize_t bytes_copied = PyLong_AsNativeBytes(
            x, &val, sizeof(val), Py_ASNATIVEBYTES_NATIVE_ENDIAN | (is_unsigned ? Py_ASNATIVEBYTES_UNSIGNED_BUFFER | Py_ASNATIVEBYTES_REJECT_NEGATIVE : 0));
        if (unlikely(bytes_copied == -1)) {
        } else if (unlikely(bytes_copied > (Py_ssize_t) sizeof(val))) {
            goto raise_overflow;
        } else {
            ret = 0;
        }
#elif PY_VERSION_HEX < 0x030d0000 && !(CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_LIMITED_API) || defined(_PyLong_AsByteArray)
        int one = 1; int is_little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&val;
        ret = _PyLong_AsByteArray((PyLongObject *)x,
                                    bytes, sizeof(val),
                                    is_little, !is_unsigned);
#else
        PyObject *v;
        PyObject *stepval = NULL, *mask = NULL, *shift = NULL;
        int bits, remaining_bits, is_negative = 0;
        int chunk_size = (sizeof(long) < 8) ? 30 : 62;
        if (likely(PyLong_CheckExact(x))) {
            v = __Pyx_NewRef(x);
        } else {
            v = PyNumber_Long(x);
            if (unlikely(!v)) return (long) -1;
            assert(PyLong_CheckExact(v));
        }
        {
            int result = PyObject_RichCompareBool(v, Py_False, Py_LT);
            if (unlikely(result < 0)) {
                Py_DECREF(v);
                return (long) -1;
            }
            is_negative = result == 1;
        }
        if (is_unsigned && unlikely(is_negative)) {
            Py_DECREF(v);
            goto raise_neg_overflow;
        } else if (is_negative) {
            stepval = PyNumber_Invert(v);
            Py_DECREF(v);
            if (unlikely(!stepval))
                return (long) -1;
        } else {
            stepval = v;
        }
        v = NULL;
        val = (long) 0;
        mask = PyLong_FromLong((1L << chunk_size) - 1); if (unlikely(!mask)) goto done;
        shift = PyLong_FromLong(chunk_size); if (unlikely(!shift)) goto done;
        for (bits = 0; bits < (int) sizeof(long) * 8 - chunk_size; bits += chunk_size) {
            PyObject *tmp, *digit;
            long idigit;
            digit = PyNumber_And(stepval, mask);
            if (unlikely(!digit)) goto done;
            idigit = PyLong_AsLong(digit);
            Py_DECREF(digit);
            if (unlikely(idigit < 0)) goto done;
            val |= ((long) idigit) << bits;
            tmp = PyNumber_Rshift(stepval, shift);
            if (unlikely(!tmp)) goto done;
            Py_DECREF(stepval); stepval = tmp;
        }
        Py_DECREF(shift); shift = NULL;
        Py_DECREF(mask); mask = NULL;
        {
            long idigit = PyLong_AsLong(stepval);
            if (unlikely(idigit < 0)) goto done;
            remaining_bits = ((int) sizeof(long) * 8) - bits - (is_unsigned ? 0 : 1);
            if (unlikely(idigit >= (1L << remaining_bits)))
                goto raise_overflow;
            val |= ((long) idigit) << bits;
        }
        if (!is_unsigned) {
            if (unlikely(val & (((long) 1) << (sizeof(long) * 8 - 1))))
                goto raise_overflow;
            if (is_negative)
                val = ~val;
        }
        ret = 0;
    done:
        Py_XDECREF(shift);
        Py_XDECREF(mask);
        Py_XDECREF(stepval);
#endif
        if (unlikely(ret))
            return (long) -1;
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to long");
    return (long) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to long");
    return (long) -1;
}

/* CIntToPy */
  static CYTHON_INLINE PyObject* __Pyx_PyLong_From_unsigned_int(unsigned int value) {
#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wconversion"
#endif
    const unsigned int neg_one = (unsigned int) -1, const_zero = (unsigned int) 0;
#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
#pragma GCC diagnostic pop
#endif
    const int is_unsigned = neg_one > const_zero;
    if (is_unsigned) {
        if (sizeof(unsigned int) < sizeof(long)) {
            return PyLong_FromLong((long) value);
        } else if (sizeof(unsigned int) <= sizeof(unsigned long)) {
            return PyLong_FromUnsignedLong((unsigned long) value);
#if defined(HAVE_LONG_LONG) && !CYTHON_COMPILING_IN_PYPY
        } else if (sizeof(unsigned int) <= sizeof(unsigned PY_LONG_LONG)) {
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
#endif
        }
    } else {
        if (sizeof(unsigned int) <= sizeof(long)) {
            return PyLong_FromLong((long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(unsigned int) <= sizeof(PY_LONG_LONG)) {
            return PyLong_FromLongLong((PY_LONG_LONG) value);
#endif
        }
    }
    {
        unsigned char *bytes = (unsigned char *)&value;
#if !CYTHON_COMPILING_IN_LIMITED_API && PY_VERSION_HEX >= 0x030d00A4
        if (is_unsigned) {
            return PyLong_FromUnsignedNativeBytes(bytes, sizeof(value), -1);
        } else {
            return PyLong_FromNativeBytes(bytes, sizeof(value), -1);
        }
#elif !CYTHON_COMPILING_IN_LIMITED_API && PY_VERSION_HEX < 0x030d0000
        int one = 1; int little = (int)*(unsigned char *)&one;
        return _PyLong_FromByteArray(bytes, sizeof(unsigned int),
                                     little, !is_unsigned);
#else
        int one = 1; int little = (int)*(unsigned char *)&one;
        PyObject *from_bytes, *result = NULL, *kwds = NULL;
        PyObject *py_bytes = NULL, *order_str = NULL;
        from_bytes = PyObject_GetAttrString((PyObject*)&PyLong_Type, "from_bytes");
        if (!from_bytes) return NULL;
        py_bytes = PyBytes_FromStringAndSize((char*)bytes, sizeof(unsigned int));
        if (!py_bytes) goto limited_bad;
        order_str = PyUnicode_FromString(little ? "little" : "big");
        if (!order_str) goto limited_bad;
        {
            PyObject *args[3+(CYTHON_VECTORCALL ? 1 : 0)] = { NULL, py_bytes, order_str };
            if (!is_unsigned) {
                kwds = __Pyx_MakeVectorcallBuilderKwds(1);
                if (!kwds) goto limited_bad;
                if (__Pyx_VectorcallBuilder_AddArgStr("signed", __Pyx_NewRef(Py_True), kwds, args+3, 0) < 0) goto limited_bad;
            }
            result = __Pyx_Object_Vectorcall_CallFromBuilder(from_bytes, args+1, 2 | __Pyx_PY_VECTORCALL_ARGUMENTS_OFFSET, kwds);
        }
        limited_bad:
        Py_XDECREF(kwds);
        Py_XDECREF(order_str);
        Py_XDECREF(py_bytes);
        Py_XDECREF(from_bytes);
        return result;
#endif
    }
}

/* CIntToPy */
  static CYTHON_INLINE PyObject* __Pyx_PyLong_From_npy_intp(npy_intp value) {
#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wconversion"
#endif
    const npy_intp neg_one = (npy_intp) -1, const_zero = (npy_intp) 0;
#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
#pragma GCC diagnostic pop
#endif
    const int is_unsigned = neg_one > const_zero;
    if (is_unsigned) {
        if (sizeof(npy_intp) < sizeof(long)) {
            return PyLong_FromLong((long) value);
        } else if (sizeof(npy_intp) <= sizeof(unsigned long)) {
            return PyLong_FromUnsignedLong((unsigned long) value);
#if defined(HAVE_LONG_LONG) && !CYTHON_COMPILING_IN_PYPY
        } else if (sizeof(npy_intp) <= sizeof(unsigned PY_LONG_LONG)) {
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
#endif
        }
    } else {
        if (sizeof(npy_intp) <= sizeof(long)) {
            return PyLong_FromLong((long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(npy_intp) <= sizeof(PY_LONG_LONG)) {
            return PyLong_FromLongLong((PY_LONG_LONG) value);
#endif
        }
    }
    {
        unsigned char *bytes = (unsigned char *)&value;
#if !CYTHON_COMPILING_IN_LIMITED_API && PY_VERSION_HEX >= 0x030d00A4
        if (is_unsigned) {
            return PyLong_FromUnsignedNativeBytes(bytes, sizeof(value), -1);
        } else {
            return PyLong_FromNativeBytes(bytes, sizeof(value), -1);
        }
#elif !CYTHON_COMPILING_IN_LIMITED_API && PY_VERSION_HEX < 0x030d0000
        int one = 1; int little = (int)*(unsigned char *)&one;
        return _PyLong_FromByteArray(bytes, sizeof(npy_intp),
                                     little, !is_unsigned);
#else
        int one = 1; int little = (int)*(unsigned char *)&one;
        PyObject *from_bytes, *result = NULL, *kwds = NULL;
        PyObject *py_bytes = NULL, *order_str = NULL;
        from_bytes = PyObject_GetAttrString((PyObject*)&PyLong_Type, "from_bytes");
        if (!from_bytes) return NULL;
        py_bytes = PyBytes_FromStringAndSize((char*)bytes, sizeof(npy_intp));
        if (!py_bytes) goto limited_bad;
        order_str = PyUnicode_FromString(little ? "little" : "big");
        if (!order_str) goto limited_bad;
        {
            PyObject *args[3+(CYTHON_VECTORCALL ? 1 : 0)] = { NULL, py_bytes, order_str };
            if (!is_unsigned) {
                kwds = __Pyx_MakeVectorcallBuilderKwds(1);
                if (!kwds) goto limited_bad;
                if (__Pyx_VectorcallBuilder_AddArgStr("signed", __Pyx_NewRef(Py_True), kwds, args+3, 0) < 0) goto limited_bad;
            }
            result = __Pyx_Object_Vectorcall_CallFromBuilder(from_bytes, args+1, 2 | __Pyx_PY_VECTORCALL_ARGUMENTS_OFFSET, kwds);
        }
        limited_bad:
        Py_XDECREF(kwds);
        Py_XDECREF(order_str);
        Py_XDECREF(py_bytes);
        Py_XDECREF(from_bytes);
        return result;
#endif
    }
}

/* CIntFromPy */
  static CYTHON_INLINE char __Pyx_PyLong_As_char(PyObject *x) {
#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wconversion"
#endif
    const char neg_one = (char) -1, const_zero = (char) 0;
#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
#pragma GCC diagnostic pop
#endif
    const int is_unsigned = neg_one > const_zero;
    if (unlikely(!PyLong_Check(x))) {
        char val;
        PyObject *tmp = __Pyx_PyNumber_Long(x);
        if (!tmp) return (char) -1;
        val = __Pyx_PyLong_As_char(tmp);
        Py_DECREF(tmp);
        return val;
    }
    if (is_unsigned) {
#if CYTHON_USE_PYLONG_INTERNALS
        if (unlikely(__Pyx_PyLong_IsNeg(x))) {
            goto raise_neg_overflow;
        } else if (__Pyx_PyLong_IsCompact(x)) {
            __PYX_VERIFY_RETURN_INT(char, __Pyx_compact_upylong, __Pyx_PyLong_CompactValueUnsigned(x))
        } else {
            const digit* digits = __Pyx_PyLong_Digits(x);
            assert(__Pyx_PyLong_DigitCount(x) > 1);
            switch (__Pyx_PyLong_DigitCount(x)) {
                case 2:
                    if ((8 * sizeof(char) > 1 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(char, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(char) >= 2 * PyLong_SHIFT)) {
                            return (char) (((((char)digits[1]) << PyLong_SHIFT) | (char)digits[0]));
                        }
                    }
                    break;
                case 3:
                    if ((8 * sizeof(char) > 2 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(char, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(char) >= 3 * PyLong_SHIFT)) {
                            return (char) (((((((char)digits[2]) << PyLong_SHIFT) | (char)digits[1]) << PyLong_SHIFT) | (char)digits[0]));
                        }
                    }
                    break;
                case 4:
                    if ((8 * sizeof(char) > 3 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(char, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(char) >= 4 * PyLong_SHIFT)) {
                            return (char) (((((((((char)digits[3]) << PyLong_SHIFT) | (char)digits[2]) << PyLong_SHIFT) | (char)digits[1]) << PyLong_SHIFT) | (char)digits[0]));
                        }
                    }
                    break;
            }
        }
#endif
#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX < 0x030C00A7
        if (unlikely(Py_SIZE(x) < 0)) {
            goto raise_neg_overflow;
        }
#else
        {
            int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
            if (unlikely(result < 0))
                return (char) -1;
            if (unlikely(result == 1))
                goto raise_neg_overflow;
        }
#endif
        if ((sizeof(char) <= sizeof(unsigned long))) {
            __PYX_VERIFY_RETURN_INT_EXC(char, unsigned long, PyLong_AsUnsignedLong(x))
#ifdef HAVE_LONG_LONG
        } else if ((sizeof(char) <= sizeof(unsigned PY_LONG_LONG))) {
            __PYX_VERIFY_RETURN_INT_EXC(char, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
#endif
        }
    } else {
#if CYTHON_USE_PYLONG_INTERNALS
        if (__Pyx_PyLong_IsCompact(x)) {
            __PYX_VERIFY_RETURN_INT(char, __Pyx_compact_pylong, __Pyx_PyLong_CompactValue(x))
        } else {
            const digit* digits = __Pyx_PyLong_Digits(x);
            assert(__Pyx_PyLong_DigitCount(x) > 1);
            switch (__Pyx_PyLong_SignedDigitCount(x)) {
                case -2:
                    if ((8 * sizeof(char) - 1 > 1 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(char, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(char) - 1 > 2 * PyLong_SHIFT)) {
                            return (char) (((char)-1)*(((((char)digits[1]) << PyLong_SHIFT) | (char)digits[0])));
                        }
                    }
                    break;
                case 2:
                    if ((8 * sizeof(char) > 1 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(char, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(char) - 1 > 2 * PyLong_SHIFT)) {
                            return (char) ((((((char)digits[1]) << PyLong_SHIFT) | (char)digits[0])));
                        }
                    }
                    break;
                case -3:
                    if ((8 * sizeof(char) - 1 > 2 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(char, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(char) - 1 > 3 * PyLong_SHIFT)) {
                            return (char) (((char)-1)*(((((((char)digits[2]) << PyLong_SHIFT) | (char)digits[1]) << PyLong_SHIFT) | (char)digits[0])));
                        }
                    }
                    break;
                case 3:
                    if ((8 * sizeof(char) > 2 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(char, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(char) - 1 > 3 * PyLong_SHIFT)) {
                            return (char) ((((((((char)digits[2]) << PyLong_SHIFT) | (char)digits[1]) << PyLong_SHIFT) | (char)digits[0])));
                        }
                    }
                    break;
                case -4:
                    if ((8 * sizeof(char) - 1 > 3 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(char, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(char) - 1 > 4 * PyLong_SHIFT)) {
                            return (char) (((char)-1)*(((((((((char)digits[3]) << PyLong_SHIFT) | (char)digits[2]) << PyLong_SHIFT) | (char)digits[1]) << PyLong_SHIFT) | (char)digits[0])));
                        }
                    }
                    break;
                case 4:
                    if ((8 * sizeof(char) > 3 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(char, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(char) - 1 > 4 * PyLong_SHIFT)) {
                            return (char) ((((((((((char)digits[3]) << PyLong_SHIFT) | (char)digits[2]) << PyLong_SHIFT) | (char)digits[1]) << PyLong_SHIFT) | (char)digits[0])));
                        }
                    }
                    break;
            }
        }
#endif
        if ((sizeof(char) <= sizeof(long))) {
            __PYX_VERIFY_RETURN_INT_EXC(char, long, PyLong_AsLong(x))
#ifdef HAVE_LONG_LONG
        } else if ((sizeof(char) <= sizeof(PY_LONG_LONG))) {
            __PYX_VERIFY_RETURN_INT_EXC(char, PY_LONG_LONG, PyLong_AsLongLong(x))
#endif
        }
    }
    {
        char val;
        int ret = -1;
#if PY_VERSION_HEX >= 0x030d00A6 && !CYTHON_COMPILING_IN_LIMITED_API
        Py_ssize_t bytes_copied = PyLong_AsNativeBytes(
            x, &val, sizeof(val), Py_ASNATIVEBYTES_NATIVE_ENDIAN | (is_unsigned ? Py_ASNATIVEBYTES_UNSIGNED_BUFFER | Py_ASNATIVEBYTES_REJECT_NEGATIVE : 0));
        if (unlikely(bytes_copied == -1)) {
        } else if (unlikely(bytes_copied > (Py_ssize_t) sizeof(val))) {
            goto raise_overflow;
        } else {
            ret = 0;
        }
#elif PY_VERSION_HEX < 0x030d0000 && !(CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_LIMITED_API) || defined(_PyLong_AsByteArray)
        int one = 1; int is_little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&val;
        ret = _PyLong_AsByteArray((PyLongObject *)x,
                                    bytes, sizeof(val),
                                    is_little, !is_unsigned);
#else
        PyObject *v;
        PyObject *stepval = NULL, *mask = NULL, *shift = NULL;
        int bits, remaining_bits, is_negative = 0;
        int chunk_size = (sizeof(long) < 8) ? 30 : 62;
        if (likely(PyLong_CheckExact(x))) {
            v = __Pyx_NewRef(x);
        } else {
            v = PyNumber_Long(x);
            if (unlikely(!v)) return (char) -1;
            assert(PyLong_CheckExact(v));
        }
        {
            int result = PyObject_RichCompareBool(v, Py_False, Py_LT);
            if (unlikely(result < 0)) {
                Py_DECREF(v);
                return (char) -1;
            }
            is_negative = result == 1;
        }
        if (is_unsigned && unlikely(is_negative)) {
            Py_DECREF(v);
            goto raise_neg_overflow;
        } else if (is_negative) {
            stepval = PyNumber_Invert(v);
            Py_DECREF(v);
            if (unlikely(!stepval))
                return (char) -1;
        } else {
            stepval = v;
        }
        v = NULL;
        val = (char) 0;
        mask = PyLong_FromLong((1L << chunk_size) - 1); if (unlikely(!mask)) goto done;
        shift = PyLong_FromLong(chunk_size); if (unlikely(!shift)) goto done;
        for (bits = 0; bits < (int) sizeof(char) * 8 - chunk_size; bits += chunk_size) {
            PyObject *tmp, *digit;
            long idigit;
            digit = PyNumber_And(stepval, mask);
            if (unlikely(!digit)) goto done;
            idigit = PyLong_AsLong(digit);
            Py_DECREF(digit);
            if (unlikely(idigit < 0)) goto done;
            val |= ((char) idigit) << bits;
            tmp = PyNumber_Rshift(stepval, shift);
            if (unlikely(!tmp)) goto done;
            Py_DECREF(stepval); stepval = tmp;
        }
        Py_DECREF(shift); shift = NULL;
        Py_DECREF(mask); mask = NULL;
        {
            long idigit = PyLong_AsLong(stepval);
            if (unlikely(idigit < 0)) goto done;
            remaining_bits = ((int) sizeof(char) * 8) - bits - (is_unsigned ? 0 : 1);
            if (unlikely(idigit >= (1L << remaining_bits)))
                goto raise_overflow;
            val |= ((char) idigit) << bits;
        }
        if (!is_unsigned) {
            if (unlikely(val & (((char) 1) << (sizeof(char) * 8 - 1))))
                goto raise_overflow;
            if (is_negative)
                val = ~val;
        }
        ret = 0;
    done:
        Py_XDECREF(shift);
        Py_XDECREF(mask);
        Py_XDECREF(stepval);
#endif
        if (unlikely(ret))
            return (char) -1;
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to char");
    return (char) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to char");
    return (char) -1;
}

/* FormatTypeName */
  #if CYTHON_COMPILING_IN_LIMITED_API && __PYX_LIMITED_VERSION_HEX < 0x030d0000
static __Pyx_TypeName
__Pyx_PyType_GetFullyQualifiedName(PyTypeObject* tp)
{
    PyObject *module = NULL, *name = NULL, *result = NULL;
    #if __PYX_LIMITED_VERSION_HEX < 0x030b0000
    name = __Pyx_PyObject_GetAttrStr((PyObject *)tp,
                                               __pyx_mstate_global->__pyx_n_u_qualname);
    #else
    name = PyType_GetQualName(tp);
    #endif
    if (unlikely(name == NULL) || unlikely(!PyUnicode_Check(name))) goto bad;
    module = __Pyx_PyObject_GetAttrStr((PyObject *)tp,
                                               __pyx_mstate_global->__pyx_n_u_module);
    if (unlikely(module == NULL) || unlikely(!PyUnicode_Check(module))) goto bad;
    if (PyUnicode_CompareWithASCIIString(module, "builtins") == 0) {
        result = name;
        name = NULL;
        goto done;
    }
    result = PyUnicode_FromFormat("%U.%U", module, name);
    if (unlikely(result == NULL)) goto bad;
  done:
    Py_XDECREF(name);
    Py_XDECREF(module);
    return result;
  bad:
    PyErr_Clear();
    if (name) {
        result = name;
        name = NULL;
    } else {
        result = __Pyx_NewRef(__pyx_mstate_global->__pyx_kp_u__7);
    }
    goto done;
}
#endif

/* GetRuntimeVersion */
  static unsigned long __Pyx_get_runtime_version(void) {
#if __PYX_LIMITED_VERSION_HEX >= 0x030b0000
    return Py_Version & ~0xFFUL;
#else
    static unsigned long __Pyx_cached_runtime_version = 0;
    if (__Pyx_cached_runtime_version == 0) {
        const char* rt_version = Py_GetVersion();
        unsigned long version = 0;
        unsigned long factor = 0x01000000UL;
        unsigned int digit = 0;
        int i = 0;
        while (factor) {
            while ('0' <= rt_version[i] && rt_version[i] <= '9') {
                digit = digit * 10 + (unsigned int) (rt_version[i] - '0');
                ++i;
            }
            version += factor * digit;
            if (rt_version[i] != '.')
                break;
            digit = 0;
            factor >>= 8;
            ++i;
        }
        __Pyx_cached_runtime_version = version;
    }
    return __Pyx_cached_runtime_version;
#endif
}

/* CheckBinaryVersion */
  static int __Pyx_check_binary_version(unsigned long ct_version, unsigned long rt_version, int allow_newer) {
    const unsigned long MAJOR_MINOR = 0xFFFF0000UL;
    if ((rt_version & MAJOR_MINOR) == (ct_version & MAJOR_MINOR))
        return 0;
    if (likely(allow_newer && (rt_version & MAJOR_MINOR) > (ct_version & MAJOR_MINOR)))
        return 1;
    {
        char message[200];
        PyOS_snprintf(message, sizeof(message),
                      "compile time Python version %d.%d "
                      "of module '%.100s' "
                      "%s "
                      "runtime version %d.%d",
                       (int) (ct_version >> 24), (int) ((ct_version >> 16) & 0xFF),
                       __Pyx_MODULE_NAME,
                       (allow_newer) ? "was newer than" : "does not match",
                       (int) (rt_version >> 24), (int) ((rt_version >> 16) & 0xFF)
       );
        return PyErr_WarnEx(NULL, message, 1);
    }
}

/* PyObjectSetAttrStr */
  #if CYTHON_USE_TYPE_SLOTS
static CYTHON_INLINE int __Pyx_PyObject_SetAttrStr(PyObject* obj, PyObject* attr_name, PyObject* value) {
    PyTypeObject* tp = Py_TYPE(obj);
    if (likely(tp->tp_setattro))
        return tp->tp_setattro(obj, attr_name, value);
    return PyObject_SetAttr(obj, attr_name, value);
}
#endif

/* VoidPtrExport */
  static int __Pyx_ExportVoidPtr(PyObject *name, void *p, const char *sig) {
    PyObject *d;
    PyObject *cobj = 0;
    if (__Pyx_PyDict_GetItemRef(__pyx_mstate_global->__pyx_d, __pyx_mstate_global->__pyx_n_u_pyx_capi, &d) == -1)
        goto bad;
    if (!d) {
        d = PyDict_New();
        if (!d)
            goto bad;
        if (__Pyx_PyObject_SetAttrStr(__pyx_m, __pyx_mstate_global->__pyx_n_u_pyx_capi, d) < 0)
            goto bad;
    }
    cobj = PyCapsule_New(p, sig, 0);
    if (!cobj)
        goto bad;
    if (PyDict_SetItem(d, name, cobj) < 0)
        goto bad;
    Py_DECREF(cobj);
    Py_DECREF(d);
    return 0;
bad:
    Py_XDECREF(cobj);
    Py_XDECREF(d);
    return -1;
}

/* FunctionImport */
  #ifndef __PYX_HAVE_RT_ImportFunction_3_1_6
#define __PYX_HAVE_RT_ImportFunction_3_1_6
static int __Pyx_ImportFunction_3_1_6(PyObject *module, const char *funcname, void (**f)(void), const char *sig) {
    PyObject *d = 0;
    PyObject *cobj = 0;
    union {
        void (*fp)(void);
        void *p;
    } tmp;
    d = PyObject_GetAttrString(module, "__pyx_capi__");
    if (!d)
        goto bad;
#if (defined(Py_LIMITED_API) && Py_LIMITED_API >= 0x030d0000) || (!defined(Py_LIMITED_API) && PY_VERSION_HEX >= 0x030d0000)
    PyDict_GetItemStringRef(d, funcname, &cobj);
#else
    cobj = PyDict_GetItemString(d, funcname);
    Py_XINCREF(cobj);
#endif
    if (!cobj) {
        PyErr_Format(PyExc_ImportError,
            "%.200s does not export expected C function %.200s",
                PyModule_GetName(module), funcname);
        goto bad;
    }
    if (!PyCapsule_IsValid(cobj, sig)) {
        PyErr_Format(PyExc_TypeError,
            "C function %.200s.%.200s has wrong signature (expected %.500s, got %.500s)",
             PyModule_GetName(module), funcname, sig, PyCapsule_GetName(cobj));
        goto bad;
    }
    tmp.p = PyCapsule_GetPointer(cobj, sig);
    *f = tmp.fp;
    if (!(*f))
        goto bad;
    Py_DECREF(d);
    Py_DECREF(cobj);
    return 0;
bad:
    Py_XDECREF(d);
    Py_XDECREF(cobj);
    return -1;
}
#endif

/* NewCodeObj */
  #if CYTHON_COMPILING_IN_LIMITED_API
    static PyObject* __Pyx__PyCode_New(int a, int p, int k, int l, int s, int f,
                                       PyObject *code, PyObject *c, PyObject* n, PyObject *v,
                                       PyObject *fv, PyObject *cell, PyObject* fn,
                                       PyObject *name, int fline, PyObject *lnos) {
        PyObject *exception_table = NULL;
        PyObject *types_module=NULL, *code_type=NULL, *result=NULL;
        #if __PYX_LIMITED_VERSION_HEX < 0x030b0000
        PyObject *version_info;
        PyObject *py_minor_version = NULL;
        #endif
        long minor_version = 0;
        PyObject *type, *value, *traceback;
        PyErr_Fetch(&type, &value, &traceback);
        #if __PYX_LIMITED_VERSION_HEX >= 0x030b0000
        minor_version = 11;
        #else
        if (!(version_info = PySys_GetObject("version_info"))) goto end;
        if (!(py_minor_version = PySequence_GetItem(version_info, 1))) goto end;
        minor_version = PyLong_AsLong(py_minor_version);
        Py_DECREF(py_minor_version);
        if (minor_version == -1 && PyErr_Occurred()) goto end;
        #endif
        if (!(types_module = PyImport_ImportModule("types"))) goto end;
        if (!(code_type = PyObject_GetAttrString(types_module, "CodeType"))) goto end;
        if (minor_version <= 7) {
            (void)p;
            result = PyObject_CallFunction(code_type, "iiiiiOOOOOOiOOO", a, k, l, s, f, code,
                          c, n, v, fn, name, fline, lnos, fv, cell);
        } else if (minor_version <= 10) {
            result = PyObject_CallFunction(code_type, "iiiiiiOOOOOOiOOO", a,p, k, l, s, f, code,
                          c, n, v, fn, name, fline, lnos, fv, cell);
        } else {
            if (!(exception_table = PyBytes_FromStringAndSize(NULL, 0))) goto end;
            result = PyObject_CallFunction(code_type, "iiiiiiOOOOOOOiOOOO", a,p, k, l, s, f, code,
                          c, n, v, fn, name, name, fline, lnos, exception_table, fv, cell);
        }
    end:
        Py_XDECREF(code_type);
        Py_XDECREF(exception_table);
        Py_XDECREF(types_module);
        if (type) {
            PyErr_Restore(type, value, traceback);
        }
        return result;
    }
#elif PY_VERSION_HEX >= 0x030B0000
  static PyCodeObject* __Pyx__PyCode_New(int a, int p, int k, int l, int s, int f,
                                         PyObject *code, PyObject *c, PyObject* n, PyObject *v,
                                         PyObject *fv, PyObject *cell, PyObject* fn,
                                         PyObject *name, int fline, PyObject *lnos) {
    PyCodeObject *result;
    result =
      #if PY_VERSION_HEX >= 0x030C0000
        PyUnstable_Code_NewWithPosOnlyArgs
      #else
        PyCode_NewWithPosOnlyArgs
      #endif
        (a, p, k, l, s, f, code, c, n, v, fv, cell, fn, name, name, fline, lnos, __pyx_mstate_global->__pyx_empty_bytes);
    #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030c00A1
    if (likely(result))
        result->_co_firsttraceable = 0;
    #endif
    return result;
  }
#elif PY_VERSION_HEX >= 0x030800B2 && !CYTHON_COMPILING_IN_PYPY
  #define __Pyx__PyCode_New(a, p, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
          PyCode_NewWithPosOnlyArgs(a, p, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)
#else
  #define __Pyx__PyCode_New(a, p, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
          PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)
#endif
static PyObject* __Pyx_PyCode_New(
        const __Pyx_PyCode_New_function_description descr,
        PyObject * const *varnames,
        PyObject *filename,
        PyObject *funcname,
        const char *line_table,
        PyObject *tuple_dedup_map
) {
    PyObject *code_obj = NULL, *varnames_tuple_dedup = NULL, *code_bytes = NULL, *line_table_bytes = NULL;
    Py_ssize_t var_count = (Py_ssize_t) descr.nlocals;
    PyObject *varnames_tuple = PyTuple_New(var_count);
    if (unlikely(!varnames_tuple)) return NULL;
    for (Py_ssize_t i=0; i < var_count; i++) {
        Py_INCREF(varnames[i]);
        if (__Pyx_PyTuple_SET_ITEM(varnames_tuple, i, varnames[i]) != (0)) goto done;
    }
    #if CYTHON_COMPILING_IN_LIMITED_API
    varnames_tuple_dedup = PyDict_GetItem(tuple_dedup_map, varnames_tuple);
    if (!varnames_tuple_dedup) {
        if (unlikely(PyDict_SetItem(tuple_dedup_map, varnames_tuple, varnames_tuple) < 0)) goto done;
        varnames_tuple_dedup = varnames_tuple;
    }
    #else
    varnames_tuple_dedup = PyDict_SetDefault(tuple_dedup_map, varnames_tuple, varnames_tuple);
    if (unlikely(!varnames_tuple_dedup)) goto done;
    #endif
    #if CYTHON_AVOID_BORROWED_REFS
    Py_INCREF(varnames_tuple_dedup);
    #endif
    if (__PYX_LIMITED_VERSION_HEX >= (0x030b0000) && line_table != NULL
        && !CYTHON_COMPILING_IN_GRAAL) {
        line_table_bytes = PyBytes_FromStringAndSize(line_table, descr.line_table_length);
        if (unlikely(!line_table_bytes)) goto done;
        Py_ssize_t code_len = (descr.line_table_length * 2 + 4) & ~3;
        code_bytes = PyBytes_FromStringAndSize(NULL, code_len);
        if (unlikely(!code_bytes)) goto done;
        char* c_code_bytes = PyBytes_AsString(code_bytes);
        if (unlikely(!c_code_bytes)) goto done;
        memset(c_code_bytes, 0, (size_t) code_len);
    }
    code_obj = (PyObject*) __Pyx__PyCode_New(
        (int) descr.argcount,
        (int) descr.num_posonly_args,
        (int) descr.num_kwonly_args,
        (int) descr.nlocals,
        0,
        (int) descr.flags,
        code_bytes ? code_bytes : __pyx_mstate_global->__pyx_empty_bytes,
        __pyx_mstate_global->__pyx_empty_tuple,
        __pyx_mstate_global->__pyx_empty_tuple,
        varnames_tuple_dedup,
        __pyx_mstate_global->__pyx_empty_tuple,
        __pyx_mstate_global->__pyx_empty_tuple,
        filename,
        funcname,
        (int) descr.first_line,
        (__PYX_LIMITED_VERSION_HEX >= (0x030b0000) && line_table_bytes) ? line_table_bytes : __pyx_mstate_global->__pyx_empty_bytes
    );
done:
    Py_XDECREF(code_bytes);
    Py_XDECREF(line_table_bytes);
    #if CYTHON_AVOID_BORROWED_REFS
    Py_XDECREF(varnames_tuple_dedup);
    #endif
    Py_DECREF(varnames_tuple);
    return code_obj;
}

/* InitStrings */
  static int __Pyx_InitStrings(__Pyx_StringTabEntry const *t, PyObject **target, const char* const* encoding_names) {
    while (t->s) {
        PyObject *str;
        if (t->is_unicode) {
            if (t->intern) {
                str = PyUnicode_InternFromString(t->s);
            } else if (t->encoding) {
                str = PyUnicode_Decode(t->s, t->n - 1, encoding_names[t->encoding], NULL);
            } else {
                str = PyUnicode_FromStringAndSize(t->s, t->n - 1);
            }
        } else {
            str = PyBytes_FromStringAndSize(t->s, t->n - 1);
        }
        if (!str)
            return -1;
        *target = str;
        if (PyObject_Hash(str) == -1)
            return -1;
        ++t;
        ++target;
    }
    return 0;
}

#include <string.h>
static CYTHON_INLINE Py_ssize_t __Pyx_ssize_strlen(const char *s) {
    size_t len = strlen(s);
    if (unlikely(len > (size_t) PY_SSIZE_T_MAX)) {
        PyErr_SetString(PyExc_OverflowError, "byte string is too long");
        return -1;
    }
    return (Py_ssize_t) len;
}
static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char* c_str) {
    Py_ssize_t len = __Pyx_ssize_strlen(c_str);
    if (unlikely(len < 0)) return NULL;
    return __Pyx_PyUnicode_FromStringAndSize(c_str, len);
}
static CYTHON_INLINE PyObject* __Pyx_PyByteArray_FromString(const char* c_str) {
    Py_ssize_t len = __Pyx_ssize_strlen(c_str);
    if (unlikely(len < 0)) return NULL;
    return PyByteArray_FromStringAndSize(c_str, len);
}
static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject* o) {
    Py_ssize_t ignore;
    return __Pyx_PyObject_AsStringAndSize(o, &ignore);
}
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_UTF8
static CYTHON_INLINE const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
    if (unlikely(__Pyx_PyUnicode_READY(o) == -1)) return NULL;
#if CYTHON_COMPILING_IN_LIMITED_API
    {
        const char* result;
        Py_ssize_t unicode_length;
        CYTHON_MAYBE_UNUSED_VAR(unicode_length); // only for __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
        #if __PYX_LIMITED_VERSION_HEX < 0x030A0000
        if (unlikely(PyArg_Parse(o, "s#", &result, length) < 0)) return NULL;
        #else
        result = PyUnicode_AsUTF8AndSize(o, length);
        #endif
        #if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
        unicode_length = PyUnicode_GetLength(o);
        if (unlikely(unicode_length < 0)) return NULL;
        if (unlikely(unicode_length != *length)) {
            PyUnicode_AsASCIIString(o);
            return NULL;
        }
        #endif
        return result;
    }
#else
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
    if (likely(PyUnicode_IS_ASCII(o))) {
        *length = PyUnicode_GET_LENGTH(o);
        return PyUnicode_AsUTF8(o);
    } else {
        PyUnicode_AsASCIIString(o);
        return NULL;
    }
#else
    return PyUnicode_AsUTF8AndSize(o, length);
#endif
#endif
}
#endif
static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_UTF8
    if (PyUnicode_Check(o)) {
        return __Pyx_PyUnicode_AsStringAndSize(o, length);
    } else
#endif
    if (PyByteArray_Check(o)) {
#if (CYTHON_ASSUME_SAFE_SIZE && CYTHON_ASSUME_SAFE_MACROS) || (CYTHON_COMPILING_IN_PYPY && (defined(PyByteArray_AS_STRING) && defined(PyByteArray_GET_SIZE)))
        *length = PyByteArray_GET_SIZE(o);
        return PyByteArray_AS_STRING(o);
#else
        *length = PyByteArray_Size(o);
        if (*length == -1) return NULL;
        return PyByteArray_AsString(o);
#endif
    } else
    {
        char* result;
        int r = PyBytes_AsStringAndSize(o, &result, length);
        if (unlikely(r < 0)) {
            return NULL;
        } else {
            return result;
        }
    }
}
static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) {
   int is_true = x == Py_True;
   if (is_true | (x == Py_False) | (x == Py_None)) return is_true;
   else return PyObject_IsTrue(x);
}
static CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject* x) {
    int retval;
    if (unlikely(!x)) return -1;
    retval = __Pyx_PyObject_IsTrue(x);
    Py_DECREF(x);
    return retval;
}
static PyObject* __Pyx_PyNumber_LongWrongResultType(PyObject* result) {
    __Pyx_TypeName result_type_name = __Pyx_PyType_GetFullyQualifiedName(Py_TYPE(result));
    if (PyLong_Check(result)) {
        if (PyErr_WarnFormat(PyExc_DeprecationWarning, 1,
                "__int__ returned non-int (type " __Pyx_FMT_TYPENAME ").  "
                "The ability to return an instance of a strict subclass of int is deprecated, "
                "and may be removed in a future version of Python.",
                result_type_name)) {
            __Pyx_DECREF_TypeName(result_type_name);
            Py_DECREF(result);
            return NULL;
        }
        __Pyx_DECREF_TypeName(result_type_name);
        return result;
    }
    PyErr_Format(PyExc_TypeError,
                 "__int__ returned non-int (type " __Pyx_FMT_TYPENAME ")",
                 result_type_name);
    __Pyx_DECREF_TypeName(result_type_name);
    Py_DECREF(result);
    return NULL;
}
static CYTHON_INLINE PyObject* __Pyx_PyNumber_Long(PyObject* x) {
#if CYTHON_USE_TYPE_SLOTS
  PyNumberMethods *m;
#endif
  PyObject *res = NULL;
  if (likely(PyLong_Check(x)))
      return __Pyx_NewRef(x);
#if CYTHON_USE_TYPE_SLOTS
  m = Py_TYPE(x)->tp_as_number;
  if (likely(m && m->nb_int)) {
      res = m->nb_int(x);
  }
#else
  if (!PyBytes_CheckExact(x) && !PyUnicode_CheckExact(x)) {
      res = PyNumber_Long(x);
  }
#endif
  if (likely(res)) {
      if (unlikely(!PyLong_CheckExact(res))) {
          return __Pyx_PyNumber_LongWrongResultType(res);
      }
  }
  else if (!PyErr_Occurred()) {
      PyErr_SetString(PyExc_TypeError,
                      "an integer is required");
  }
  return res;
}
static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject* b) {
  Py_ssize_t ival;
  PyObject *x;
  if (likely(PyLong_CheckExact(b))) {
    #if CYTHON_USE_PYLONG_INTERNALS
    if (likely(__Pyx_PyLong_IsCompact(b))) {
        return __Pyx_PyLong_CompactValue(b);
    } else {
      const digit* digits = __Pyx_PyLong_Digits(b);
      const Py_ssize_t size = __Pyx_PyLong_SignedDigitCount(b);
      switch (size) {
         case 2:
           if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
             return (Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case -2:
           if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
             return -(Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case 3:
           if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
             return (Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case -3:
           if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
             return -(Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case 4:
           if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
             return (Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case -4:
           if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
             return -(Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
      }
    }
    #endif
    return PyLong_AsSsize_t(b);
  }
  x = PyNumber_Index(b);
  if (!x) return -1;
  ival = PyLong_AsSsize_t(x);
  Py_DECREF(x);
  return ival;
}
static CYTHON_INLINE Py_hash_t __Pyx_PyIndex_AsHash_t(PyObject* o) {
  if (sizeof(Py_hash_t) == sizeof(Py_ssize_t)) {
    return (Py_hash_t) __Pyx_PyIndex_AsSsize_t(o);
  } else {
    Py_ssize_t ival;
    PyObject *x;
    x = PyNumber_Index(o);
    if (!x) return -1;
    ival = PyLong_AsLong(x);
    Py_DECREF(x);
    return ival;
  }
}
static CYTHON_INLINE PyObject *__Pyx_Owned_Py_None(int b) {
    CYTHON_UNUSED_VAR(b);
    return __Pyx_NewRef(Py_None);
}
static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b) {
  return b ? __Pyx_NewRef(Py_True) : __Pyx_NewRef(Py_False);
}
static CYTHON_INLINE PyObject * __Pyx_PyLong_FromSize_t(size_t ival) {
    return PyLong_FromSize_t(ival);
}
#if CYTHON_USE_PYLONG_INTERNALS
static CYTHON_INLINE int __Pyx_PyLong_CompactAsLong(PyObject *x, long *return_value) {
    if (unlikely(!__Pyx_PyLong_IsCompact(x)))
        return 0;
    Py_ssize_t value = __Pyx_PyLong_CompactValue(x);
    if ((sizeof(long) < sizeof(Py_ssize_t)) && unlikely(value != (long) value))
        return 0;
    *return_value = (long) value;
    return 1;
}
#endif


  /* MultiPhaseInitModuleState */
  #if CYTHON_PEP489_MULTI_PHASE_INIT && CYTHON_USE_MODULE_STATE
#ifndef CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE
#if (CYTHON_COMPILING_IN_LIMITED_API || PY_VERSION_HEX >= 0x030C0000)
  #define CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE 1
#else
  #define CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE 0
#endif
#endif
#if CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE && !CYTHON_ATOMICS
#error "Module state with PEP489 requires atomics. Currently that's one of\
 C11, C++11, gcc atomic intrinsics or MSVC atomic intrinsics"
#endif
#if !CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE
#define __Pyx_ModuleStateLookup_Lock()
#define __Pyx_ModuleStateLookup_Unlock()
#elif !CYTHON_COMPILING_IN_LIMITED_API && PY_VERSION_HEX >= 0x030d0000
static PyMutex __Pyx_ModuleStateLookup_mutex = {0};
#define __Pyx_ModuleStateLookup_Lock() PyMutex_Lock(&__Pyx_ModuleStateLookup_mutex)
#define __Pyx_ModuleStateLookup_Unlock() PyMutex_Unlock(&__Pyx_ModuleStateLookup_mutex)
#elif defined(__cplusplus) && __cplusplus >= 201103L
#include <mutex>
static std::mutex __Pyx_ModuleStateLookup_mutex;
#define __Pyx_ModuleStateLookup_Lock() __Pyx_ModuleStateLookup_mutex.lock()
#define __Pyx_ModuleStateLookup_Unlock() __Pyx_ModuleStateLookup_mutex.unlock()
#elif defined(__STDC_VERSION__) && (__STDC_VERSION__ > 201112L) && !defined(__STDC_NO_THREADS__)
#include <threads.h>
static mtx_t __Pyx_ModuleStateLookup_mutex;
static once_flag __Pyx_ModuleStateLookup_mutex_once_flag = ONCE_FLAG_INIT;
static void __Pyx_ModuleStateLookup_initialize_mutex(void) {
    mtx_init(&__Pyx_ModuleStateLookup_mutex, mtx_plain);
}
#define __Pyx_ModuleStateLookup_Lock()\
  call_once(&__Pyx_ModuleStateLookup_mutex_once_flag, __Pyx_ModuleStateLookup_initialize_mutex);\
  mtx_lock(&__Pyx_ModuleStateLookup_mutex)
#define __Pyx_ModuleStateLookup_Unlock() mtx_unlock(&__Pyx_ModuleStateLookup_mutex)
#elif defined(HAVE_PTHREAD_H)
#include <pthread.h>
static pthread_mutex_t __Pyx_ModuleStateLookup_mutex = PTHREAD_MUTEX_INITIALIZER;
#define __Pyx_ModuleStateLookup_Lock() pthread_mutex_lock(&__Pyx_ModuleStateLookup_mutex)
#define __Pyx_ModuleStateLookup_Unlock() pthread_mutex_unlock(&__Pyx_ModuleStateLookup_mutex)
#elif defined(_WIN32)
#include <Windows.h>  // synchapi.h on its own doesn't work
static SRWLOCK __Pyx_ModuleStateLookup_mutex = SRWLOCK_INIT;
#define __Pyx_ModuleStateLookup_Lock() AcquireSRWLockExclusive(&__Pyx_ModuleStateLookup_mutex)
#define __Pyx_ModuleStateLookup_Unlock() ReleaseSRWLockExclusive(&__Pyx_ModuleStateLookup_mutex)
#else
#error "No suitable lock available for CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE.\
 Requires C standard >= C11, or C++ standard >= C++11,\
 or pthreads, or the Windows 32 API, or Python >= 3.13."
#endif
typedef struct {
    int64_t id;
    PyObject *module;
} __Pyx_InterpreterIdAndModule;
typedef struct {
    char interpreter_id_as_index;
    Py_ssize_t count;
    Py_ssize_t allocated;
    __Pyx_InterpreterIdAndModule table[1];
} __Pyx_ModuleStateLookupData;
#define __PYX_MODULE_STATE_LOOKUP_SMALL_SIZE 32
#if CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE
static __pyx_atomic_int_type __Pyx_ModuleStateLookup_read_counter = 0;
#endif
#if CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE
static __pyx_atomic_ptr_type __Pyx_ModuleStateLookup_data = 0;
#else
static __Pyx_ModuleStateLookupData* __Pyx_ModuleStateLookup_data = NULL;
#endif
static __Pyx_InterpreterIdAndModule* __Pyx_State_FindModuleStateLookupTableLowerBound(
        __Pyx_InterpreterIdAndModule* table,
        Py_ssize_t count,
        int64_t interpreterId) {
    __Pyx_InterpreterIdAndModule* begin = table;
    __Pyx_InterpreterIdAndModule* end = begin + count;
    if (begin->id == interpreterId) {
        return begin;
    }
    while ((end - begin) > __PYX_MODULE_STATE_LOOKUP_SMALL_SIZE) {
        __Pyx_InterpreterIdAndModule* halfway = begin + (end - begin)/2;
        if (halfway->id == interpreterId) {
            return halfway;
        }
        if (halfway->id < interpreterId) {
            begin = halfway;
        } else {
            end = halfway;
        }
    }
    for (; begin < end; ++begin) {
        if (begin->id >= interpreterId) return begin;
    }
    return begin;
}
static PyObject *__Pyx_State_FindModule(CYTHON_UNUSED void* dummy) {
    int64_t interpreter_id = PyInterpreterState_GetID(__Pyx_PyInterpreterState_Get());
    if (interpreter_id == -1) return NULL;
#if CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE
    __Pyx_ModuleStateLookupData* data = (__Pyx_ModuleStateLookupData*)__pyx_atomic_pointer_load_relaxed(&__Pyx_ModuleStateLookup_data);
    {
        __pyx_atomic_incr_acq_rel(&__Pyx_ModuleStateLookup_read_counter);
        if (likely(data)) {
            __Pyx_ModuleStateLookupData* new_data = (__Pyx_ModuleStateLookupData*)__pyx_atomic_pointer_load_acquire(&__Pyx_ModuleStateLookup_data);
            if (likely(data == new_data)) {
                goto read_finished;
            }
        }
        __pyx_atomic_decr_acq_rel(&__Pyx_ModuleStateLookup_read_counter);
        __Pyx_ModuleStateLookup_Lock();
        __pyx_atomic_incr_relaxed(&__Pyx_ModuleStateLookup_read_counter);
        data = (__Pyx_ModuleStateLookupData*)__pyx_atomic_pointer_load_relaxed(&__Pyx_ModuleStateLookup_data);
        __Pyx_ModuleStateLookup_Unlock();
    }
  read_finished:;
#else
    __Pyx_ModuleStateLookupData* data = __Pyx_ModuleStateLookup_data;
#endif
    __Pyx_InterpreterIdAndModule* found = NULL;
    if (unlikely(!data)) goto end;
    if (data->interpreter_id_as_index) {
        if (interpreter_id < data->count) {
            found = data->table+interpreter_id;
        }
    } else {
        found = __Pyx_State_FindModuleStateLookupTableLowerBound(
            data->table, data->count, interpreter_id);
    }
  end:
    {
        PyObject *result=NULL;
        if (found && found->id == interpreter_id) {
            result = found->module;
        }
#if CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE
        __pyx_atomic_decr_acq_rel(&__Pyx_ModuleStateLookup_read_counter);
#endif
        return result;
    }
}
#if CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE
static void __Pyx_ModuleStateLookup_wait_until_no_readers(void) {
    while (__pyx_atomic_load(&__Pyx_ModuleStateLookup_read_counter) != 0);
}
#else
#define __Pyx_ModuleStateLookup_wait_until_no_readers()
#endif
static int __Pyx_State_AddModuleInterpIdAsIndex(__Pyx_ModuleStateLookupData **old_data, PyObject* module, int64_t interpreter_id) {
    Py_ssize_t to_allocate = (*old_data)->allocated;
    while (to_allocate <= interpreter_id) {
        if (to_allocate == 0) to_allocate = 1;
        else to_allocate *= 2;
    }
    __Pyx_ModuleStateLookupData *new_data = *old_data;
    if (to_allocate != (*old_data)->allocated) {
         new_data = (__Pyx_ModuleStateLookupData *)realloc(
            *old_data,
            sizeof(__Pyx_ModuleStateLookupData)+(to_allocate-1)*sizeof(__Pyx_InterpreterIdAndModule));
        if (!new_data) {
            PyErr_NoMemory();
            return -1;
        }
        for (Py_ssize_t i = new_data->allocated; i < to_allocate; ++i) {
            new_data->table[i].id = i;
            new_data->table[i].module = NULL;
        }
        new_data->allocated = to_allocate;
    }
    new_data->table[interpreter_id].module = module;
    if (new_data->count < interpreter_id+1) {
        new_data->count = interpreter_id+1;
    }
    *old_data = new_data;
    return 0;
}
static void __Pyx_State_ConvertFromInterpIdAsIndex(__Pyx_ModuleStateLookupData *data) {
    __Pyx_InterpreterIdAndModule *read = data->table;
    __Pyx_InterpreterIdAndModule *write = data->table;
    __Pyx_InterpreterIdAndModule *end = read + data->count;
    for (; read<end; ++read) {
        if (read->module) {
            write->id = read->id;
            write->module = read->module;
            ++write;
        }
    }
    data->count = write - data->table;
    for (; write<end; ++write) {
        write->id = 0;
        write->module = NULL;
    }
    data->interpreter_id_as_index = 0;
}
static int __Pyx_State_AddModule(PyObject* module, CYTHON_UNUSED void* dummy) {
    int64_t interpreter_id = PyInterpreterState_GetID(__Pyx_PyInterpreterState_Get());
    if (interpreter_id == -1) return -1;
    int result = 0;
    __Pyx_ModuleStateLookup_Lock();
#if CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE
    __Pyx_ModuleStateLookupData *old_data = (__Pyx_ModuleStateLookupData *)
            __pyx_atomic_pointer_exchange(&__Pyx_ModuleStateLookup_data, 0);
#else
    __Pyx_ModuleStateLookupData *old_data = __Pyx_ModuleStateLookup_data;
#endif
    __Pyx_ModuleStateLookupData *new_data = old_data;
    if (!new_data) {
        new_data = (__Pyx_ModuleStateLookupData *)calloc(1, sizeof(__Pyx_ModuleStateLookupData));
        if (!new_data) {
            result = -1;
            PyErr_NoMemory();
            goto end;
        }
        new_data->allocated = 1;
        new_data->interpreter_id_as_index = 1;
    }
    __Pyx_ModuleStateLookup_wait_until_no_readers();
    if (new_data->interpreter_id_as_index) {
        if (interpreter_id < __PYX_MODULE_STATE_LOOKUP_SMALL_SIZE) {
            result = __Pyx_State_AddModuleInterpIdAsIndex(&new_data, module, interpreter_id);
            goto end;
        }
        __Pyx_State_ConvertFromInterpIdAsIndex(new_data);
    }
    {
        Py_ssize_t insert_at = 0;
        {
            __Pyx_InterpreterIdAndModule* lower_bound = __Pyx_State_FindModuleStateLookupTableLowerBound(
                new_data->table, new_data->count, interpreter_id);
            assert(lower_bound);
            insert_at = lower_bound - new_data->table;
            if (unlikely(insert_at < new_data->count && lower_bound->id == interpreter_id)) {
                lower_bound->module = module;
                goto end;  // already in table, nothing more to do
            }
        }
        if (new_data->count+1 >= new_data->allocated) {
            Py_ssize_t to_allocate = (new_data->count+1)*2;
            new_data =
                (__Pyx_ModuleStateLookupData*)realloc(
                    new_data,
                    sizeof(__Pyx_ModuleStateLookupData) +
                    (to_allocate-1)*sizeof(__Pyx_InterpreterIdAndModule));
            if (!new_data) {
                result = -1;
                new_data = old_data;
                PyErr_NoMemory();
                goto end;
            }
            new_data->allocated = to_allocate;
        }
        ++new_data->count;
        int64_t last_id = interpreter_id;
        PyObject *last_module = module;
        for (Py_ssize_t i=insert_at; i<new_data->count; ++i) {
            int64_t current_id = new_data->table[i].id;
            new_data->table[i].id = last_id;
            last_id = current_id;
            PyObject *current_module = new_data->table[i].module;
            new_data->table[i].module = last_module;
            last_module = current_module;
        }
    }
  end:
#if CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE
    __pyx_atomic_pointer_exchange(&__Pyx_ModuleStateLookup_data, new_data);
#else
    __Pyx_ModuleStateLookup_data = new_data;
#endif
    __Pyx_ModuleStateLookup_Unlock();
    return result;
}
static int __Pyx_State_RemoveModule(CYTHON_UNUSED void* dummy) {
    int64_t interpreter_id = PyInterpreterState_GetID(__Pyx_PyInterpreterState_Get());
    if (interpreter_id == -1) return -1;
    __Pyx_ModuleStateLookup_Lock();
#if CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE
    __Pyx_ModuleStateLookupData *data = (__Pyx_ModuleStateLookupData *)
            __pyx_atomic_pointer_exchange(&__Pyx_ModuleStateLookup_data, 0);
#else
    __Pyx_ModuleStateLookupData *data = __Pyx_ModuleStateLookup_data;
#endif
    if (data->interpreter_id_as_index) {
        if (interpreter_id < data->count) {
            data->table[interpreter_id].module = NULL;
        }
        goto done;
    }
    {
        __Pyx_ModuleStateLookup_wait_until_no_readers();
        __Pyx_InterpreterIdAndModule* lower_bound = __Pyx_State_FindModuleStateLookupTableLowerBound(
            data->table, data->count, interpreter_id);
        if (!lower_bound) goto done;
        if (lower_bound->id != interpreter_id) goto done;
        __Pyx_InterpreterIdAndModule *end = data->table+data->count;
        for (;lower_bound<end-1; ++lower_bound) {
            lower_bound->id = (lower_bound+1)->id;
            lower_bound->module = (lower_bound+1)->module;
        }
    }
    --data->count;
    if (data->count == 0) {
        free(data);
        data = NULL;
    }
  done:
#if CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE
    __pyx_atomic_pointer_exchange(&__Pyx_ModuleStateLookup_data, data);
#else
    __Pyx_ModuleStateLookup_data = data;
#endif
    __Pyx_ModuleStateLookup_Unlock();
    return 0;
}
#endif

/* #### Code section: utility_code_pragmas_end ### */
#ifdef _MSC_VER
#pragma warning( pop )
#endif



/* #### Code section: end ### */
#endif /* Py_PYTHON_H */
