/* Generated by Cython 0.16 on Thu Jul 04 15:57:37 2013 */

#define PY_SSIZE_T_CLEAN
#include "Python.h"
#ifndef Py_PYTHON_H
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  #define PyString_CheckExact          PyUnicode_CheckExact
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  #define PyBytes_Check                PyString_Check
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  #define PyBytes_FromString           PyString_FromString
  #define PyBytes_FromStringAndSize    PyString_FromStringAndSize
  #define PyBytes_FromFormat           PyString_FromFormat
  #define PyBytes_DecodeEscape         PyString_DecodeEscape
  #define PyBytes_AsString             PyString_AsString
  #define PyBytes_AsStringAndSize      PyString_AsStringAndSize
  #define PyBytes_Size                 PyString_Size
  #define PyBytes_AS_STRING            PyString_AS_STRING
  #define PyBytes_GET_SIZE             PyString_GET_SIZE
  #define PyBytes_Repr                 PyString_Repr
  #define PyBytes_Concat               PyString_Concat
  #define PyBytes_ConcatAndDel         PyString_ConcatAndDel
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  #define PyFrozenSet_Check(obj)       PyObject_TypeCheck(obj, &PyFrozenSet_Type)
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#ifndef PySet_CheckExact
  #define PySet_CheckExact(obj)        (Py_TYPE(obj) == &PySet_Type)
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#define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type)

#if PY_MAJOR_VERSION >= 3
  #define PyIntObject                  PyLongObject
  #define PyInt_Type                   PyLong_Type
  #define PyInt_Check(op)              PyLong_Check(op)
  #define PyInt_CheckExact(op)         PyLong_CheckExact(op)
  #define PyInt_FromString             PyLong_FromString
  #define PyInt_FromUnicode            PyLong_FromUnicode
  #define PyInt_FromLong               PyLong_FromLong
  #define PyInt_FromSize_t             PyLong_FromSize_t
  #define PyInt_FromSsize_t            PyLong_FromSsize_t
  #define PyInt_AsLong                 PyLong_AsLong
  #define PyInt_AS_LONG                PyLong_AS_LONG
  #define PyInt_AsSsize_t              PyLong_AsSsize_t
  #define PyInt_AsUnsignedLongMask     PyLong_AsUnsignedLongMask
  #define PyInt_AsUnsignedLongLongMask PyLong_AsUnsignedLongLongMask
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#if PY_MAJOR_VERSION >= 3
  #define PyBoolObject                 PyLongObject
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#if PY_VERSION_HEX < 0x03020000
  typedef long Py_hash_t;
  #define __Pyx_PyInt_FromHash_t PyInt_FromLong
  #define __Pyx_PyInt_AsHash_t   PyInt_AsLong
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  #define __Pyx_PyInt_FromHash_t PyInt_FromSsize_t
  #define __Pyx_PyInt_AsHash_t   PyInt_AsSsize_t
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#if (PY_MAJOR_VERSION < 3) || (PY_VERSION_HEX >= 0x03010300)
  #define __Pyx_PySequence_GetSlice(obj, a, b) PySequence_GetSlice(obj, a, b)
  #define __Pyx_PySequence_SetSlice(obj, a, b, value) PySequence_SetSlice(obj, a, b, value)
  #define __Pyx_PySequence_DelSlice(obj, a, b) PySequence_DelSlice(obj, a, b)
#else
  #define __Pyx_PySequence_GetSlice(obj, a, b) (unlikely(!(obj)) ? \
        (PyErr_SetString(PyExc_SystemError, "null argument to internal routine"), (PyObject*)0) : \
        (likely((obj)->ob_type->tp_as_mapping) ? (PySequence_GetSlice(obj, a, b)) : \
            (PyErr_Format(PyExc_TypeError, "'%.200s' object is unsliceable", (obj)->ob_type->tp_name), (PyObject*)0)))
  #define __Pyx_PySequence_SetSlice(obj, a, b, value) (unlikely(!(obj)) ? \
        (PyErr_SetString(PyExc_SystemError, "null argument to internal routine"), -1) : \
        (likely((obj)->ob_type->tp_as_mapping) ? (PySequence_SetSlice(obj, a, b, value)) : \
            (PyErr_Format(PyExc_TypeError, "'%.200s' object doesn't support slice assignment", (obj)->ob_type->tp_name), -1)))
  #define __Pyx_PySequence_DelSlice(obj, a, b) (unlikely(!(obj)) ? \
        (PyErr_SetString(PyExc_SystemError, "null argument to internal routine"), -1) : \
        (likely((obj)->ob_type->tp_as_mapping) ? (PySequence_DelSlice(obj, a, b)) : \
            (PyErr_Format(PyExc_TypeError, "'%.200s' object doesn't support slice deletion", (obj)->ob_type->tp_name), -1)))
#endif

#if PY_MAJOR_VERSION >= 3
  #define PyMethod_New(func, self, klass) ((self) ? PyMethod_New(func, self) : PyInstanceMethod_New(func))
#endif

#if PY_VERSION_HEX < 0x02050000
  #define __Pyx_GetAttrString(o,n)   PyObject_GetAttrString((o),((char *)(n)))
  #define __Pyx_SetAttrString(o,n,a) PyObject_SetAttrString((o),((char *)(n)),(a))
  #define __Pyx_DelAttrString(o,n)   PyObject_DelAttrString((o),((char *)(n)))
#else
  #define __Pyx_GetAttrString(o,n)   PyObject_GetAttrString((o),(n))
  #define __Pyx_SetAttrString(o,n,a) PyObject_SetAttrString((o),(n),(a))
  #define __Pyx_DelAttrString(o,n)   PyObject_DelAttrString((o),(n))
#endif

#if PY_VERSION_HEX < 0x02050000
  #define __Pyx_NAMESTR(n) ((char *)(n))
  #define __Pyx_DOCSTR(n)  ((char *)(n))
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  #define __Pyx_NAMESTR(n) (n)
  #define __Pyx_DOCSTR(n)  (n)
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#if PY_MAJOR_VERSION >= 3
  #define __Pyx_PyNumber_Divide(x,y)         PyNumber_TrueDivide(x,y)
  #define __Pyx_PyNumber_InPlaceDivide(x,y)  PyNumber_InPlaceTrueDivide(x,y)
#else
  #define __Pyx_PyNumber_Divide(x,y)         PyNumber_Divide(x,y)
  #define __Pyx_PyNumber_InPlaceDivide(x,y)  PyNumber_InPlaceDivide(x,y)
#endif

#ifndef __PYX_EXTERN_C
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    #define __PYX_EXTERN_C extern "C"
  #else
    #define __PYX_EXTERN_C extern
  #endif
#endif

#if defined(WIN32) || defined(MS_WINDOWS)
#define _USE_MATH_DEFINES
#endif
#include <math.h>
#define __PYX_HAVE__assimulo__solvers__euler
#define __PYX_HAVE_API__assimulo__solvers__euler
#include "stdio.h"
#include "stdlib.h"
#include "numpy/arrayobject.h"
#include "numpy/ufuncobject.h"
#ifdef _OPENMP
#include <omp.h>
#endif /* _OPENMP */

#ifdef PYREX_WITHOUT_ASSERTIONS
#define CYTHON_WITHOUT_ASSERTIONS
#endif


/* inline attribute */
#ifndef CYTHON_INLINE
  #if defined(__GNUC__)
    #define CYTHON_INLINE __inline__
  #elif defined(_MSC_VER)
    #define CYTHON_INLINE __inline
  #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
    #define CYTHON_INLINE inline
  #else
    #define CYTHON_INLINE
  #endif
#endif

/* unused attribute */
#ifndef CYTHON_UNUSED
# if defined(__GNUC__)
#   if !(defined(__cplusplus)) || (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 4))
#     define CYTHON_UNUSED __attribute__ ((__unused__))
#   else
#     define CYTHON_UNUSED
#   endif
# elif defined(__ICC) || (defined(__INTEL_COMPILER) && !defined(_MSC_VER))
#   define CYTHON_UNUSED __attribute__ ((__unused__))
# else
#   define CYTHON_UNUSED
# endif
#endif

typedef struct {PyObject **p; char *s; const long n; const char* encoding; const char is_unicode; const char is_str; const char intern; } __Pyx_StringTabEntry; /*proto*/


/* Type Conversion Predeclarations */

#define __Pyx_PyBytes_FromUString(s) PyBytes_FromString((char*)s)
#define __Pyx_PyBytes_AsUString(s)   ((unsigned char*) PyBytes_AsString(s))

#define __Pyx_Owned_Py_None(b) (Py_INCREF(Py_None), Py_None)
#define __Pyx_PyBool_FromLong(b) ((b) ? (Py_INCREF(Py_True), Py_True) : (Py_INCREF(Py_False), Py_False))
static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*);
static CYTHON_INLINE PyObject* __Pyx_PyNumber_Int(PyObject* x);

static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject*);
static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t);
static CYTHON_INLINE size_t __Pyx_PyInt_AsSize_t(PyObject*);

#define __pyx_PyFloat_AsDouble(x) (PyFloat_CheckExact(x) ? PyFloat_AS_DOUBLE(x) : PyFloat_AsDouble(x))
#define __pyx_PyFloat_AsFloat(x) ((float) __pyx_PyFloat_AsDouble(x))

#ifdef __GNUC__
  /* Test for GCC > 2.95 */
  #if __GNUC__ > 2 || (__GNUC__ == 2 && (__GNUC_MINOR__ > 95))
    #define likely(x)   __builtin_expect(!!(x), 1)
    #define unlikely(x) __builtin_expect(!!(x), 0)
  #else /* __GNUC__ > 2 ... */
    #define likely(x)   (x)
    #define unlikely(x) (x)
  #endif /* __GNUC__ > 2 ... */
#else /* __GNUC__ */
  #define likely(x)   (x)
  #define unlikely(x) (x)
#endif /* __GNUC__ */
    
static PyObject *__pyx_m;
static PyObject *__pyx_b;
static PyObject *__pyx_empty_tuple;
static PyObject *__pyx_empty_bytes;
static int __pyx_lineno;
static int __pyx_clineno = 0;
static const char * __pyx_cfilenm= __FILE__;
static const char *__pyx_filename;

#if !defined(CYTHON_CCOMPLEX)
  #if defined(__cplusplus)
    #define CYTHON_CCOMPLEX 1
  #elif defined(_Complex_I)
    #define CYTHON_CCOMPLEX 1
  #else
    #define CYTHON_CCOMPLEX 0
  #endif
#endif
#if CYTHON_CCOMPLEX
  #ifdef __cplusplus
    #include <complex>
  #else
    #include <complex.h>
  #endif
#endif
#if CYTHON_CCOMPLEX && !defined(__cplusplus) && defined(__sun__) && defined(__GNUC__)
  #undef _Complex_I
  #define _Complex_I 1.0fj
#endif


static const char *__pyx_f[] = {
  "euler.pyx",
  "numpy.pxd",
  "ode.pxd",
  "constants.pxi",
};

/* "numpy.pxd":722
 * # 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;

/* "numpy.pxd":723
 * 
 * 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;

/* "numpy.pxd":724
 * ctypedef npy_int8       int8_t
 * ctypedef npy_int16      int16_t
 * ctypedef npy_int32      int32_t             # <<<<<<<<<<<<<<
 * ctypedef npy_int64      int64_t
 * #ctypedef npy_int96      int96_t
 */
typedef npy_int32 __pyx_t_5numpy_int32_t;

/* "numpy.pxd":725
 * ctypedef npy_int16      int16_t
 * ctypedef npy_int32      int32_t
 * ctypedef npy_int64      int64_t             # <<<<<<<<<<<<<<
 * #ctypedef npy_int96      int96_t
 * #ctypedef npy_int128     int128_t
 */
typedef npy_int64 __pyx_t_5numpy_int64_t;

/* "numpy.pxd":729
 * #ctypedef npy_int128     int128_t
 * 
 * ctypedef npy_uint8      uint8_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uint16     uint16_t
 * ctypedef npy_uint32     uint32_t
 */
typedef npy_uint8 __pyx_t_5numpy_uint8_t;

/* "numpy.pxd":730
 * 
 * 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;

/* "numpy.pxd":731
 * ctypedef npy_uint8      uint8_t
 * ctypedef npy_uint16     uint16_t
 * ctypedef npy_uint32     uint32_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uint64     uint64_t
 * #ctypedef npy_uint96     uint96_t
 */
typedef npy_uint32 __pyx_t_5numpy_uint32_t;

/* "numpy.pxd":732
 * ctypedef npy_uint16     uint16_t
 * ctypedef npy_uint32     uint32_t
 * ctypedef npy_uint64     uint64_t             # <<<<<<<<<<<<<<
 * #ctypedef npy_uint96     uint96_t
 * #ctypedef npy_uint128    uint128_t
 */
typedef npy_uint64 __pyx_t_5numpy_uint64_t;

/* "numpy.pxd":736
 * #ctypedef npy_uint128    uint128_t
 * 
 * ctypedef npy_float32    float32_t             # <<<<<<<<<<<<<<
 * ctypedef npy_float64    float64_t
 * #ctypedef npy_float80    float80_t
 */
typedef npy_float32 __pyx_t_5numpy_float32_t;

/* "numpy.pxd":737
 * 
 * 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;

/* "numpy.pxd":746
 * # The int types are mapped a bit surprising --
 * # numpy.int corresponds to 'l' and numpy.long to 'q'
 * ctypedef npy_long       int_t             # <<<<<<<<<<<<<<
 * ctypedef npy_longlong   long_t
 * ctypedef npy_longlong   longlong_t
 */
typedef npy_long __pyx_t_5numpy_int_t;

/* "numpy.pxd":747
 * # numpy.int corresponds to 'l' and numpy.long to 'q'
 * ctypedef npy_long       int_t
 * ctypedef npy_longlong   long_t             # <<<<<<<<<<<<<<
 * ctypedef npy_longlong   longlong_t
 * 
 */
typedef npy_longlong __pyx_t_5numpy_long_t;

/* "numpy.pxd":748
 * ctypedef npy_long       int_t
 * ctypedef npy_longlong   long_t
 * ctypedef npy_longlong   longlong_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_ulong      uint_t
 */
typedef npy_longlong __pyx_t_5numpy_longlong_t;

/* "numpy.pxd":750
 * ctypedef npy_longlong   longlong_t
 * 
 * ctypedef npy_ulong      uint_t             # <<<<<<<<<<<<<<
 * ctypedef npy_ulonglong  ulong_t
 * ctypedef npy_ulonglong  ulonglong_t
 */
typedef npy_ulong __pyx_t_5numpy_uint_t;

/* "numpy.pxd":751
 * 
 * ctypedef npy_ulong      uint_t
 * ctypedef npy_ulonglong  ulong_t             # <<<<<<<<<<<<<<
 * ctypedef npy_ulonglong  ulonglong_t
 * 
 */
typedef npy_ulonglong __pyx_t_5numpy_ulong_t;

/* "numpy.pxd":752
 * ctypedef npy_ulong      uint_t
 * ctypedef npy_ulonglong  ulong_t
 * ctypedef npy_ulonglong  ulonglong_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_intp       intp_t
 */
typedef npy_ulonglong __pyx_t_5numpy_ulonglong_t;

/* "numpy.pxd":754
 * ctypedef npy_ulonglong  ulonglong_t
 * 
 * ctypedef npy_intp       intp_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uintp      uintp_t
 * 
 */
typedef npy_intp __pyx_t_5numpy_intp_t;

/* "numpy.pxd":755
 * 
 * ctypedef npy_intp       intp_t
 * ctypedef npy_uintp      uintp_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_double     float_t
 */
typedef npy_uintp __pyx_t_5numpy_uintp_t;

/* "numpy.pxd":757
 * 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;

/* "numpy.pxd":758
 * 
 * ctypedef npy_double     float_t
 * ctypedef npy_double     double_t             # <<<<<<<<<<<<<<
 * ctypedef npy_longdouble longdouble_t
 * 
 */
typedef npy_double __pyx_t_5numpy_double_t;

/* "numpy.pxd":759
 * ctypedef npy_double     float_t
 * ctypedef npy_double     double_t
 * ctypedef npy_longdouble longdouble_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_cfloat      cfloat_t
 */
typedef npy_longdouble __pyx_t_5numpy_longdouble_t;
#if CYTHON_CCOMPLEX
  #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

#if CYTHON_CCOMPLEX
  #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


/*--- Type declarations ---*/
struct __pyx_obj_8assimulo_3ode_ODE;
struct __pyx_obj_8assimulo_7solvers_5euler___pyx_scope_struct__set_problem_data;
struct __pyx_obj_8assimulo_12explicit_ode_Explicit_ODE;
struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler;
struct __pyx_obj_8assimulo_7solvers_5euler_ExplicitEuler;
struct __pyx_obj_8assimulo_7solvers_5euler___pyx_scope_struct_1_set_problem_data;

/* "numpy.pxd":761
 * ctypedef npy_longdouble longdouble_t
 * 
 * ctypedef npy_cfloat      cfloat_t             # <<<<<<<<<<<<<<
 * ctypedef npy_cdouble     cdouble_t
 * ctypedef npy_clongdouble clongdouble_t
 */
typedef npy_cfloat __pyx_t_5numpy_cfloat_t;

/* "numpy.pxd":762
 * 
 * ctypedef npy_cfloat      cfloat_t
 * ctypedef npy_cdouble     cdouble_t             # <<<<<<<<<<<<<<
 * ctypedef npy_clongdouble clongdouble_t
 * 
 */
typedef npy_cdouble __pyx_t_5numpy_cdouble_t;

/* "numpy.pxd":763
 * ctypedef npy_cfloat      cfloat_t
 * ctypedef npy_cdouble     cdouble_t
 * ctypedef npy_clongdouble clongdouble_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_cdouble     complex_t
 */
typedef npy_clongdouble __pyx_t_5numpy_clongdouble_t;

/* "numpy.pxd":765
 * ctypedef npy_clongdouble clongdouble_t
 * 
 * ctypedef npy_cdouble     complex_t             # <<<<<<<<<<<<<<
 * 
 * cdef inline object PyArray_MultiIterNew1(a):
 */
typedef npy_cdouble __pyx_t_5numpy_complex_t;
struct __pyx_opt_args_8assimulo_3ode_3ODE_simulate;

/* "ode.pxd":41
 *     cpdef log_message(self, message, int level)
 *     cpdef log_event(self, double time, object event_info, int level)
 *     cpdef simulate(self, double tfinal, int ncp=*, object ncp_list=*)             # <<<<<<<<<<<<<<
 *     cpdef get_options(self)
 *     cpdef get_supports(self)
 */
struct __pyx_opt_args_8assimulo_3ode_3ODE_simulate {
  int __pyx_n;
  int ncp;
  PyObject *ncp_list;
};

/* "ode.pxd":21
 * cimport numpy as N
 * 
 * cdef class ODE:             # <<<<<<<<<<<<<<
 *     cdef public dict options, solver_options, problem_info
 *     cdef public dict supports, statistics
 */
struct __pyx_obj_8assimulo_3ode_ODE {
  PyObject_HEAD
  struct __pyx_vtabstruct_8assimulo_3ode_ODE *__pyx_vtab;
  PyObject *options;
  PyObject *solver_options;
  PyObject *problem_info;
  PyObject *supports;
  PyObject *statistics;
  PyObject *event_data;
  PyObject *problem;
  double t;
  double t0;
  PyArrayObject *y;
  PyArrayObject *yd;
  PyArrayObject *p;
  PyArrayObject *y0;
  PyArrayObject *yd0;
  PyArrayObject *p0;
  PyArrayObject *sw0;
  double elapsed_step_time;
  double clock_start;
  PyObject *_event_info;
  PyObject *t_sol;
  PyObject *y_sol;
  PyObject *yd_sol;
  PyObject *p_sol;
  PyObject *sw;
};


/* "assimulo\solvers\euler.pyx":106
 *         self._inith = 0 #Used for taking an initial step of correct length after an event.
 * 
 *     def set_problem_data(self):             # <<<<<<<<<<<<<<
 *         if self.problem_info["state_events"]:
 *             def event_func(t, y):
 */
struct __pyx_obj_8assimulo_7solvers_5euler___pyx_scope_struct__set_problem_data {
  PyObject_HEAD
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};


/* "assimulo\explicit_ode.pxd":24
 * 
 * 
 * cdef class Explicit_ODE(ODE):             # <<<<<<<<<<<<<<
 * 
 *     cpdef _simulate(self, double t0, double tfinal,N.ndarray output_list,int COMPLETE_STEP, int INTERPOLATE_OUTPUT,int TIME_EVENT)
 */
struct __pyx_obj_8assimulo_12explicit_ode_Explicit_ODE {
  struct __pyx_obj_8assimulo_3ode_ODE __pyx_base;
};


/* "assimulo\solvers\euler.pyx":28
 * include "constants.pxi" #Includes the constants (textual include)
 * 
 * cdef class ImplicitEuler(Explicit_ODE):             # <<<<<<<<<<<<<<
 *     """
 *     This solver solves an explicit ordinary differential equation using
 */
struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler {
  struct __pyx_obj_8assimulo_12explicit_ode_Explicit_ODE __pyx_base;
  PyArrayObject *yd1;
  PyArrayObject *_old_jac;
  PyObject *f;
  PyObject *event_func;
  int _leny;
  double _eps;
  int _needjac;
  int _curjac;
  int _steps_since_last_jac;
  PyArrayObject *_yold;
  PyArrayObject *_ynew;
  PyArrayObject *g_old;
  double _told;
  double _h;
  double _inith;
};


/* "assimulo\solvers\euler.pyx":490
 *         self.log_message(' Solver type       : Fixed step\n',                      verbose)
 * 
 * cdef class ExplicitEuler(Explicit_ODE):             # <<<<<<<<<<<<<<
 *     """
 *     This solver solves an explicit ordinary differential equation using
 */
struct __pyx_obj_8assimulo_7solvers_5euler_ExplicitEuler {
  struct __pyx_obj_8assimulo_12explicit_ode_Explicit_ODE __pyx_base;
  PyArrayObject *yd1;
  PyObject *f;
  PyObject *event_func;
  PyArrayObject *_yold;
  PyArrayObject *_ynew;
  PyArrayObject *g_old;
  double _told;
  double _h;
  double _inith;
};


/* "assimulo\solvers\euler.pyx":544
 *         self.statistics["ngevals"]      = 0 #Root evaluations
 * 
 *     def set_problem_data(self):             # <<<<<<<<<<<<<<
 *         if self.problem_info["state_events"]:
 *             def event_func(t, y):
 */
struct __pyx_obj_8assimulo_7solvers_5euler___pyx_scope_struct_1_set_problem_data {
  PyObject_HEAD
  struct __pyx_obj_8assimulo_7solvers_5euler_ExplicitEuler *__pyx_v_self;
};



/* "ode.pxd":21
 * cimport numpy as N
 * 
 * cdef class ODE:             # <<<<<<<<<<<<<<
 *     cdef public dict options, solver_options, problem_info
 *     cdef public dict supports, statistics
 */

struct __pyx_vtabstruct_8assimulo_3ode_ODE {
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  PyObject *(*get_statistics)(struct __pyx_obj_8assimulo_3ode_ODE *, int __pyx_skip_dispatch);
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/* "assimulo\explicit_ode.pxd":24
 * 
 * 
 * cdef class Explicit_ODE(ODE):             # <<<<<<<<<<<<<<
 * 
 *     cpdef _simulate(self, double t0, double tfinal,N.ndarray output_list,int COMPLETE_STEP, int INTERPOLATE_OUTPUT,int TIME_EVENT)
 */

struct __pyx_vtabstruct_8assimulo_12explicit_ode_Explicit_ODE {
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/* "assimulo\solvers\euler.pyx":28
 * include "constants.pxi" #Includes the constants (textual include)
 * 
 * cdef class ImplicitEuler(Explicit_ODE):             # <<<<<<<<<<<<<<
 *     """
 *     This solver solves an explicit ordinary differential equation using
 */

struct __pyx_vtabstruct_8assimulo_7solvers_5euler_ImplicitEuler {
  struct __pyx_vtabstruct_8assimulo_12explicit_ode_Explicit_ODE __pyx_base;
  PyObject *(*step)(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *, double, PyArrayObject *, double, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*integrate)(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *, double, PyArrayObject *, double, PyObject *, int __pyx_skip_dispatch);
  double (*WRMS)(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *, PyArrayObject *, PyArrayObject *);
  PyObject *(*_step)(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *, double, PyArrayObject *, double);
};
static struct __pyx_vtabstruct_8assimulo_7solvers_5euler_ImplicitEuler *__pyx_vtabptr_8assimulo_7solvers_5euler_ImplicitEuler;


/* "assimulo\solvers\euler.pyx":490
 *         self.log_message(' Solver type       : Fixed step\n',                      verbose)
 * 
 * cdef class ExplicitEuler(Explicit_ODE):             # <<<<<<<<<<<<<<
 *     """
 *     This solver solves an explicit ordinary differential equation using
 */

struct __pyx_vtabstruct_8assimulo_7solvers_5euler_ExplicitEuler {
  struct __pyx_vtabstruct_8assimulo_12explicit_ode_Explicit_ODE __pyx_base;
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  PyObject *(*_step)(struct __pyx_obj_8assimulo_7solvers_5euler_ExplicitEuler *, double, PyArrayObject *, double);
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/* Module declarations from 'cpython.ref' */

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

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

/* Module declarations from 'libc.stdlib' */

/* Module declarations from 'numpy' */

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/* Module declarations from 'assimulo.solvers.euler' */
static PyTypeObject *__pyx_ptype_8assimulo_7solvers_5euler_ImplicitEuler = 0;
static PyTypeObject *__pyx_ptype_8assimulo_7solvers_5euler_ExplicitEuler = 0;
static PyTypeObject *__pyx_ptype_8assimulo_7solvers_5euler___pyx_scope_struct__set_problem_data = 0;
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#define __Pyx_MODULE_NAME "assimulo.solvers.euler"
int __pyx_module_is_main_assimulo__solvers__euler = 0;

/* Implementation of 'assimulo.solvers.euler' */
static PyObject *__pyx_builtin_property;
static PyObject *__pyx_builtin_ValueError;
static PyObject *__pyx_builtin_TypeError;
static PyObject *__pyx_builtin_range;
static PyObject *__pyx_builtin_RuntimeError;
static int __pyx_pf_8assimulo_7solvers_5euler_13ImplicitEuler___init__(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *__pyx_v_self, PyObject *__pyx_v_problem); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ImplicitEuler_16set_problem_data_event_func(PyObject *__pyx_self, PyObject *__pyx_v_t, PyObject *__pyx_v_y); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ImplicitEuler_16set_problem_data_2f(PyObject *__pyx_self, PyObject *__pyx_v_t, PyObject *__pyx_v_y); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ImplicitEuler_2set_problem_data(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ImplicitEuler_4_set_usejac(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *__pyx_v_self, PyObject *__pyx_v_jac); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ImplicitEuler_6_get_usejac(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ImplicitEuler_8step(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *__pyx_v_self, double __pyx_v_t, PyArrayObject *__pyx_v_y, double __pyx_v_tf, PyObject *__pyx_v_opts); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ImplicitEuler_10integrate(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *__pyx_v_self, double __pyx_v_t, PyArrayObject *__pyx_v_y, double __pyx_v_tf, PyObject *__pyx_v_opts); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ImplicitEuler_12_set_newt(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *__pyx_v_self, PyObject *__pyx_v_newt); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ImplicitEuler_14_get_newt(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ImplicitEuler_16_set_atol(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *__pyx_v_self, PyObject *__pyx_v_atol); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ImplicitEuler_18_get_atol(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ImplicitEuler_20_set_rtol(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *__pyx_v_self, PyObject *__pyx_v_rtol); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ImplicitEuler_22_get_rtol(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ImplicitEuler_24initialize(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ImplicitEuler_26_jacobian(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *__pyx_v_self, PyObject *__pyx_v_t, PyObject *__pyx_v_y); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ImplicitEuler_28interpolate(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *__pyx_v_self, PyObject *__pyx_v_time); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ImplicitEuler_30_set_h(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *__pyx_v_self, PyObject *__pyx_v_h); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ImplicitEuler_32_get_h(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ImplicitEuler_34state_event_info(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ImplicitEuler_36set_event_info(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *__pyx_v_self, PyObject *__pyx_v_event_info); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ImplicitEuler_38print_statistics(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *__pyx_v_self, PyObject *__pyx_v_verbose); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ImplicitEuler_10event_func___get__(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *__pyx_v_self); /* proto */
static int __pyx_pf_8assimulo_7solvers_5euler_13ImplicitEuler_10event_func_2__set__(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_8assimulo_7solvers_5euler_13ImplicitEuler_10event_func_4__del__(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ImplicitEuler_5g_old___get__(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *__pyx_v_self); /* proto */
static int __pyx_pf_8assimulo_7solvers_5euler_13ImplicitEuler_5g_old_2__set__(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_8assimulo_7solvers_5euler_13ImplicitEuler_5g_old_4__del__(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *__pyx_v_self); /* proto */
static int __pyx_pf_8assimulo_7solvers_5euler_13ExplicitEuler___init__(struct __pyx_obj_8assimulo_7solvers_5euler_ExplicitEuler *__pyx_v_self, PyObject *__pyx_v_problem); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ExplicitEuler_16set_problem_data_event_func(PyObject *__pyx_self, PyObject *__pyx_v_t, PyObject *__pyx_v_y); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ExplicitEuler_16set_problem_data_2f(PyObject *__pyx_self, PyObject *__pyx_v_t, PyObject *__pyx_v_y); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ExplicitEuler_2set_problem_data(struct __pyx_obj_8assimulo_7solvers_5euler_ExplicitEuler *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ExplicitEuler_4step(struct __pyx_obj_8assimulo_7solvers_5euler_ExplicitEuler *__pyx_v_self, double __pyx_v_t, PyArrayObject *__pyx_v_y, double __pyx_v_tf, PyObject *__pyx_v_opts); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ExplicitEuler_6integrate(struct __pyx_obj_8assimulo_7solvers_5euler_ExplicitEuler *__pyx_v_self, double __pyx_v_t, PyArrayObject *__pyx_v_y, double __pyx_v_tf, PyObject *__pyx_v_opts); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ExplicitEuler_8interpolate(struct __pyx_obj_8assimulo_7solvers_5euler_ExplicitEuler *__pyx_v_self, PyObject *__pyx_v_time); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ExplicitEuler_10_set_h(struct __pyx_obj_8assimulo_7solvers_5euler_ExplicitEuler *__pyx_v_self, PyObject *__pyx_v_h); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ExplicitEuler_12_get_h(struct __pyx_obj_8assimulo_7solvers_5euler_ExplicitEuler *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ExplicitEuler_14state_event_info(struct __pyx_obj_8assimulo_7solvers_5euler_ExplicitEuler *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ExplicitEuler_16set_event_info(struct __pyx_obj_8assimulo_7solvers_5euler_ExplicitEuler *__pyx_v_self, PyObject *__pyx_v_event_info); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ExplicitEuler_18print_statistics(struct __pyx_obj_8assimulo_7solvers_5euler_ExplicitEuler *__pyx_v_self, PyObject *__pyx_v_verbose); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ExplicitEuler_10event_func___get__(struct __pyx_obj_8assimulo_7solvers_5euler_ExplicitEuler *__pyx_v_self); /* proto */
static int __pyx_pf_8assimulo_7solvers_5euler_13ExplicitEuler_10event_func_2__set__(struct __pyx_obj_8assimulo_7solvers_5euler_ExplicitEuler *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_8assimulo_7solvers_5euler_13ExplicitEuler_10event_func_4__del__(struct __pyx_obj_8assimulo_7solvers_5euler_ExplicitEuler *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8assimulo_7solvers_5euler_13ExplicitEuler_5g_old___get__(struct __pyx_obj_8assimulo_7solvers_5euler_ExplicitEuler *__pyx_v_self); /* proto */
static int __pyx_pf_8assimulo_7solvers_5euler_13ExplicitEuler_5g_old_2__set__(struct __pyx_obj_8assimulo_7solvers_5euler_ExplicitEuler *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_8assimulo_7solvers_5euler_13ExplicitEuler_5g_old_4__del__(struct __pyx_obj_8assimulo_7solvers_5euler_ExplicitEuler *__pyx_v_self); /* proto */
static int __pyx_pf_5numpy_7ndarray___getbuffer__(PyArrayObject *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /* proto */
static void __pyx_pf_5numpy_7ndarray_2__releasebuffer__(PyArrayObject *__pyx_v_self, Py_buffer *__pyx_v_info); /* proto */
static char __pyx_k_4[] = "C:\\Development\\Assimulo\\branches\\Assimulo-2.4.x\\build\\assimulo\\solvers\\euler.pyx";
static char __pyx_k_5[] = "assimulo.solvers.euler";
static char __pyx_k_8[] = "The newt must be an integer or float.";
static char __pyx_k_10[] = "atol must be of length one or same as the dimension of the problem.";
static char __pyx_k_12[] = "Relative tolerance must be a (scalar) float.";
static char __pyx_k_14[] = "Relative tolerance must be a positive (scalar) float.";
static char __pyx_k_16[] = "Newton iteration failed at %f";
static char __pyx_k_17[] = "Step-size must be a (scalar) float.";
static char __pyx_k_20[] = "Final Run Statistics: %s \n";
static char __pyx_k_21[] = " Number of Steps (Step-length: %s) : %s";
static char __pyx_k_22[] = " Number of Function Evaluations           : ";
static char __pyx_k_23[] = " Number of Jacobian Evaluations           : ";
static char __pyx_k_24[] = " Number of F-Eval During Jac-Eval         : ";
static char __pyx_k_25[] = " Number of Newton Iterations              : %s";
static char __pyx_k_26[] = " Number of Newton Convergence Failures    : ";
static char __pyx_k_27[] = " Number of Root Evaluations               : ";
static char __pyx_k_28[] = " Number of State-Events                   : ";
static char __pyx_k_29[] = "\nSolver options:\n";
static char __pyx_k_30[] = " Solver            : ImplicitEuler";
static char __pyx_k_31[] = " Solver type       : Fixed step\n";
static char __pyx_k_38[] = "Final Run Statistics          : %s \n";
static char __pyx_k_39[] = " Step-length                  : %s ";
static char __pyx_k_40[] = " Number of Root Evaluations   : ";
static char __pyx_k_41[] = " Number of State-Events       : ";
static char __pyx_k_42[] = " Solver            : ExplicitEuler";
static char __pyx_k_43[] = "ndarray is not C contiguous";
static char __pyx_k_45[] = "ndarray is not Fortran contiguous";
static char __pyx_k_47[] = "Non-native byte order not supported";
static char __pyx_k_49[] = "unknown dtype code in numpy.pxd (%d)";
static char __pyx_k_50[] = "Format string allocated too short, see comment in numpy.pxd";
static char __pyx_k_53[] = "Format string allocated too short.";
static char __pyx_k_55[] = "numpy.linalg";
static char __pyx_k_56[] = "*";
static char __pyx_k_57[] = "assimulo.exception";
static char __pyx_k__B[] = "B";
static char __pyx_k__H[] = "H";
static char __pyx_k__I[] = "I";
static char __pyx_k__L[] = "L";
static char __pyx_k__N[] = "N";
static char __pyx_k__O[] = "O";
static char __pyx_k__Q[] = "Q";
static char __pyx_k__T[] = "T";
static char __pyx_k__b[] = "b";
static char __pyx_k__d[] = "d";
static char __pyx_k__f[] = "f";
static char __pyx_k__g[] = "g";
static char __pyx_k__h[] = "h";
static char __pyx_k__i[] = "i";
static char __pyx_k__l[] = "l";
static char __pyx_k__q[] = "q";
static char __pyx_k__t[] = "t";
static char __pyx_k__y[] = "y";
static char __pyx_k__Zd[] = "Zd";
static char __pyx_k__Zf[] = "Zf";
static char __pyx_k__Zg[] = "Zg";
static char __pyx_k__tf[] = "tf";
static char __pyx_k__LIN[] = "LIN";
static char __pyx_k__abs[] = "abs";
static char __pyx_k__dim[] = "dim";
static char __pyx_k__eps[] = "eps";
static char __pyx_k__eye[] = "eye";
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    e = (*v)(((PyObject*)p->_old_jac), a); if (e) return e;
  }
  if (p->f) {
    e = (*v)(p->f, a); if (e) return e;
  }
  if (p->event_func) {
    e = (*v)(p->event_func, a); if (e) return e;
  }
  if (p->_yold) {
    e = (*v)(((PyObject*)p->_yold), a); if (e) return e;
  }
  if (p->_ynew) {
    e = (*v)(((PyObject*)p->_ynew), a); if (e) return e;
  }
  if (p->g_old) {
    e = (*v)(((PyObject*)p->g_old), a); if (e) return e;
  }
  return 0;
}

static int __pyx_tp_clear_8assimulo_7solvers_5euler_ImplicitEuler(PyObject *o) {
  struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *p = (struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler *)o;
  PyObject* tmp;
  if (__pyx_ptype_8assimulo_12explicit_ode_Explicit_ODE->tp_clear) {
    __pyx_ptype_8assimulo_12explicit_ode_Explicit_ODE->tp_clear(o);
  }
  tmp = ((PyObject*)p->yd1);
  p->yd1 = ((PyArrayObject *)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->_old_jac);
  p->_old_jac = ((PyArrayObject *)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->f);
  p->f = Py_None; Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->event_func);
  p->event_func = Py_None; Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->_yold);
  p->_yold = ((PyArrayObject *)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->_ynew);
  p->_ynew = ((PyArrayObject *)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->g_old);
  p->g_old = ((PyArrayObject *)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  return 0;
}

static PyObject *__pyx_getprop_8assimulo_7solvers_5euler_13ImplicitEuler_event_func(PyObject *o, void *x) {
  return __pyx_pw_8assimulo_7solvers_5euler_13ImplicitEuler_10event_func_1__get__(o);
}

static int __pyx_setprop_8assimulo_7solvers_5euler_13ImplicitEuler_event_func(PyObject *o, PyObject *v, void *x) {
  if (v) {
    return __pyx_pw_8assimulo_7solvers_5euler_13ImplicitEuler_10event_func_3__set__(o, v);
  }
  else {
    return __pyx_pw_8assimulo_7solvers_5euler_13ImplicitEuler_10event_func_5__del__(o);
  }
}

static PyObject *__pyx_getprop_8assimulo_7solvers_5euler_13ImplicitEuler_g_old(PyObject *o, void *x) {
  return __pyx_pw_8assimulo_7solvers_5euler_13ImplicitEuler_5g_old_1__get__(o);
}

static int __pyx_setprop_8assimulo_7solvers_5euler_13ImplicitEuler_g_old(PyObject *o, PyObject *v, void *x) {
  if (v) {
    return __pyx_pw_8assimulo_7solvers_5euler_13ImplicitEuler_5g_old_3__set__(o, v);
  }
  else {
    return __pyx_pw_8assimulo_7solvers_5euler_13ImplicitEuler_5g_old_5__del__(o);
  }
}

static PyMethodDef __pyx_methods_8assimulo_7solvers_5euler_ImplicitEuler[] = {
  {__Pyx_NAMESTR("set_problem_data"), (PyCFunction)__pyx_pw_8assimulo_7solvers_5euler_13ImplicitEuler_3set_problem_data, METH_NOARGS, __Pyx_DOCSTR(0)},
  {__Pyx_NAMESTR("_set_usejac"), (PyCFunction)__pyx_pw_8assimulo_7solvers_5euler_13ImplicitEuler_5_set_usejac, METH_O, __Pyx_DOCSTR(0)},
  {__Pyx_NAMESTR("_get_usejac"), (PyCFunction)__pyx_pw_8assimulo_7solvers_5euler_13ImplicitEuler_7_get_usejac, METH_NOARGS, __Pyx_DOCSTR(__pyx_doc_8assimulo_7solvers_5euler_13ImplicitEuler_6_get_usejac)},
  {__Pyx_NAMESTR("step"), (PyCFunction)__pyx_pw_8assimulo_7solvers_5euler_13ImplicitEuler_9step, METH_VARARGS|METH_KEYWORDS, __Pyx_DOCSTR(0)},
  {__Pyx_NAMESTR("integrate"), (PyCFunction)__pyx_pw_8assimulo_7solvers_5euler_13ImplicitEuler_11integrate, METH_VARARGS|METH_KEYWORDS, __Pyx_DOCSTR(0)},
  {__Pyx_NAMESTR("_set_newt"), (PyCFunction)__pyx_pw_8assimulo_7solvers_5euler_13ImplicitEuler_13_set_newt, METH_O, __Pyx_DOCSTR(__pyx_doc_8assimulo_7solvers_5euler_13ImplicitEuler_12_set_newt)},
  {__Pyx_NAMESTR("_get_newt"), (PyCFunction)__pyx_pw_8assimulo_7solvers_5euler_13ImplicitEuler_15_get_newt, METH_NOARGS, __Pyx_DOCSTR(__pyx_doc_8assimulo_7solvers_5euler_13ImplicitEuler_14_get_newt)},
  {__Pyx_NAMESTR("_set_atol"), (PyCFunction)__pyx_pw_8assimulo_7solvers_5euler_13ImplicitEuler_17_set_atol, METH_O, __Pyx_DOCSTR(0)},
  {__Pyx_NAMESTR("_get_atol"), (PyCFunction)__pyx_pw_8assimulo_7solvers_5euler_13ImplicitEuler_19_get_atol, METH_NOARGS, __Pyx_DOCSTR(__pyx_doc_8assimulo_7solvers_5euler_13ImplicitEuler_18_get_atol)},
  {__Pyx_NAMESTR("_set_rtol"), (PyCFunction)__pyx_pw_8assimulo_7solvers_5euler_13ImplicitEuler_21_set_rtol, METH_O, __Pyx_DOCSTR(0)},
  {__Pyx_NAMESTR("_get_rtol"), (PyCFunction)__pyx_pw_8assimulo_7solvers_5euler_13ImplicitEuler_23_get_rtol, METH_NOARGS, __Pyx_DOCSTR(__pyx_doc_8assimulo_7solvers_5euler_13ImplicitEuler_22_get_rtol)},
  {__Pyx_NAMESTR("initialize"), (PyCFunction)__pyx_pw_8assimulo_7solvers_5euler_13ImplicitEuler_25initialize, METH_NOARGS, __Pyx_DOCSTR(0)},
  {__Pyx_NAMESTR("_jacobian"), (PyCFunction)__pyx_pw_8assimulo_7solvers_5euler_13ImplicitEuler_27_jacobian, METH_VARARGS|METH_KEYWORDS, __Pyx_DOCSTR(__pyx_doc_8assimulo_7solvers_5euler_13ImplicitEuler_26_jacobian)},
  {__Pyx_NAMESTR("interpolate"), (PyCFunction)__pyx_pw_8assimulo_7solvers_5euler_13ImplicitEuler_29interpolate, METH_O, __Pyx_DOCSTR(0)},
  {__Pyx_NAMESTR("_set_h"), (PyCFunction)__pyx_pw_8assimulo_7solvers_5euler_13ImplicitEuler_31_set_h, METH_O, __Pyx_DOCSTR(0)},
  {__Pyx_NAMESTR("_get_h"), (PyCFunction)__pyx_pw_8assimulo_7solvers_5euler_13ImplicitEuler_33_get_h, METH_NOARGS, __Pyx_DOCSTR(__pyx_doc_8assimulo_7solvers_5euler_13ImplicitEuler_32_get_h)},
  {__Pyx_NAMESTR("state_event_info"), (PyCFunction)__pyx_pw_8assimulo_7solvers_5euler_13ImplicitEuler_35state_event_info, METH_NOARGS, __Pyx_DOCSTR(0)},
  {__Pyx_NAMESTR("set_event_info"), (PyCFunction)__pyx_pw_8assimulo_7solvers_5euler_13ImplicitEuler_37set_event_info, METH_O, __Pyx_DOCSTR(0)},
  {__Pyx_NAMESTR("print_statistics"), (PyCFunction)__pyx_pw_8assimulo_7solvers_5euler_13ImplicitEuler_39print_statistics, METH_VARARGS|METH_KEYWORDS, __Pyx_DOCSTR(__pyx_doc_8assimulo_7solvers_5euler_13ImplicitEuler_38print_statistics)},
  {0, 0, 0, 0}
};

static struct PyGetSetDef __pyx_getsets_8assimulo_7solvers_5euler_ImplicitEuler[] = {
  {(char *)"event_func", __pyx_getprop_8assimulo_7solvers_5euler_13ImplicitEuler_event_func, __pyx_setprop_8assimulo_7solvers_5euler_13ImplicitEuler_event_func, 0, 0},
  {(char *)"g_old", __pyx_getprop_8assimulo_7solvers_5euler_13ImplicitEuler_g_old, __pyx_setprop_8assimulo_7solvers_5euler_13ImplicitEuler_g_old, 0, 0},
  {0, 0, 0, 0, 0}
};

static PyNumberMethods __pyx_tp_as_number_ImplicitEuler = {
  0, /*nb_add*/
  0, /*nb_subtract*/
  0, /*nb_multiply*/
  #if PY_MAJOR_VERSION < 3
  0, /*nb_divide*/
  #endif
  0, /*nb_remainder*/
  0, /*nb_divmod*/
  0, /*nb_power*/
  0, /*nb_negative*/
  0, /*nb_positive*/
  0, /*nb_absolute*/
  0, /*nb_nonzero*/
  0, /*nb_invert*/
  0, /*nb_lshift*/
  0, /*nb_rshift*/
  0, /*nb_and*/
  0, /*nb_xor*/
  0, /*nb_or*/
  #if PY_MAJOR_VERSION < 3
  0, /*nb_coerce*/
  #endif
  0, /*nb_int*/
  #if PY_MAJOR_VERSION < 3
  0, /*nb_long*/
  #else
  0, /*reserved*/
  #endif
  0, /*nb_float*/
  #if PY_MAJOR_VERSION < 3
  0, /*nb_oct*/
  #endif
  #if PY_MAJOR_VERSION < 3
  0, /*nb_hex*/
  #endif
  0, /*nb_inplace_add*/
  0, /*nb_inplace_subtract*/
  0, /*nb_inplace_multiply*/
  #if PY_MAJOR_VERSION < 3
  0, /*nb_inplace_divide*/
  #endif
  0, /*nb_inplace_remainder*/
  0, /*nb_inplace_power*/
  0, /*nb_inplace_lshift*/
  0, /*nb_inplace_rshift*/
  0, /*nb_inplace_and*/
  0, /*nb_inplace_xor*/
  0, /*nb_inplace_or*/
  0, /*nb_floor_divide*/
  0, /*nb_true_divide*/
  0, /*nb_inplace_floor_divide*/
  0, /*nb_inplace_true_divide*/
  #if PY_VERSION_HEX >= 0x02050000
  0, /*nb_index*/
  #endif
};

static PySequenceMethods __pyx_tp_as_sequence_ImplicitEuler = {
  0, /*sq_length*/
  0, /*sq_concat*/
  0, /*sq_repeat*/
  0, /*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_ImplicitEuler = {
  0, /*mp_length*/
  0, /*mp_subscript*/
  0, /*mp_ass_subscript*/
};

static PyBufferProcs __pyx_tp_as_buffer_ImplicitEuler = {
  #if PY_MAJOR_VERSION < 3
  0, /*bf_getreadbuffer*/
  #endif
  #if PY_MAJOR_VERSION < 3
  0, /*bf_getwritebuffer*/
  #endif
  #if PY_MAJOR_VERSION < 3
  0, /*bf_getsegcount*/
  #endif
  #if PY_MAJOR_VERSION < 3
  0, /*bf_getcharbuffer*/
  #endif
  #if PY_VERSION_HEX >= 0x02060000
  0, /*bf_getbuffer*/
  #endif
  #if PY_VERSION_HEX >= 0x02060000
  0, /*bf_releasebuffer*/
  #endif
};

static PyTypeObject __pyx_type_8assimulo_7solvers_5euler_ImplicitEuler = {
  PyVarObject_HEAD_INIT(0, 0)
  __Pyx_NAMESTR("assimulo.solvers.euler.ImplicitEuler"), /*tp_name*/
  sizeof(struct __pyx_obj_8assimulo_7solvers_5euler_ImplicitEuler), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc_8assimulo_7solvers_5euler_ImplicitEuler, /*tp_dealloc*/
  0, /*tp_print*/
  0, /*tp_getattr*/
  0, /*tp_setattr*/
  #if PY_MAJOR_VERSION < 3
  0, /*tp_compare*/
  #else
  0, /*reserved*/
  #endif
  0, /*tp_repr*/
  &__pyx_tp_as_number_ImplicitEuler, /*tp_as_number*/
  &__pyx_tp_as_sequence_ImplicitEuler, /*tp_as_sequence*/
  &__pyx_tp_as_mapping_ImplicitEuler, /*tp_as_mapping*/
  0, /*tp_hash*/
  0, /*tp_call*/
  0, /*tp_str*/
  0, /*tp_getattro*/
  0, /*tp_setattro*/
  &__pyx_tp_as_buffer_ImplicitEuler, /*tp_as_buffer*/
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC, /*tp_flags*/
  __Pyx_DOCSTR("\n    This solver solves an explicit ordinary differential equation using \n    the implicit Euler method.\n    \n    We want to approximate the solution to the ordinary differential \n    equation of the form,\n    \n    .. math::\n\n        \\dot{y} = f(t,y), \\quad y(t_0) = y_0 .\n        \n    Using the implicit Euler method, the approximation is defined as \n    follow,\n    \n    .. math::\n    \n        y_{n+1} = y_n + hf(t_{n+1},y_{n+1})\n        \n    with :math:`h` being the step-size and :math:`y_n` the previous \n    solution to the equation.\n    "), /*tp_doc*/
  __pyx_tp_traverse_8assimulo_7solvers_5euler_ImplicitEuler, /*tp_traverse*/
  __pyx_tp_clear_8assimulo_7solvers_5euler_ImplicitEuler, /*tp_clear*/
  0, /*tp_richcompare*/
  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
  0, /*tp_iternext*/
  __pyx_methods_8assimulo_7solvers_5euler_ImplicitEuler, /*tp_methods*/
  0, /*tp_members*/
  __pyx_getsets_8assimulo_7solvers_5euler_ImplicitEuler, /*tp_getset*/
  0, /*tp_base*/
  0, /*tp_dict*/
  0, /*tp_descr_get*/
  0, /*tp_descr_set*/
  0, /*tp_dictoffset*/
  __pyx_pw_8assimulo_7solvers_5euler_13ImplicitEuler_1__init__, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_8assimulo_7solvers_5euler_ImplicitEuler, /*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*/
  #if PY_VERSION_HEX >= 0x02060000
  0, /*tp_version_tag*/
  #endif
};
static struct __pyx_vtabstruct_8assimulo_7solvers_5euler_ExplicitEuler __pyx_vtable_8assimulo_7solvers_5euler_ExplicitEuler;

static PyObject *__pyx_tp_new_8assimulo_7solvers_5euler_ExplicitEuler(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_8assimulo_7solvers_5euler_ExplicitEuler *p;
  PyObject *o = __pyx_ptype_8assimulo_12explicit_ode_Explicit_ODE->tp_new(t, a, k);
  if (!o) return 0;
  p = ((struct __pyx_obj_8assimulo_7solvers_5euler_ExplicitEuler *)o);
  p->__pyx_base.__pyx_base.__pyx_vtab = (struct __pyx_vtabstruct_8assimulo_3ode_ODE*)__pyx_vtabptr_8assimulo_7solvers_5euler_ExplicitEuler;
  p->yd1 = ((PyArrayObject *)Py_None); Py_INCREF(Py_None);
  p->f = Py_None; Py_INCREF(Py_None);
  p->event_func = Py_None; Py_INCREF(Py_None);
  p->_yold = ((PyArrayObject *)Py_None); Py_INCREF(Py_None);
  p->_ynew = ((PyArrayObject *)Py_None); Py_INCREF(Py_None);
  p->g_old = ((PyArrayObject *)Py_None); Py_INCREF(Py_None);
  return o;
}

static void __pyx_tp_dealloc_8assimulo_7solvers_5euler_ExplicitEuler(PyObject *o) {
  struct __pyx_obj_8assimulo_7solvers_5euler_ExplicitEuler *p = (struct __pyx_obj_8assimulo_7solvers_5euler_ExplicitEuler *)o;
  Py_XDECREF(((PyObject *)p->yd1));
  Py_XDECREF(p->f);
  Py_XDECREF(p->event_func);
  Py_XDECREF(((PyObject *)p->_yold));
  Py_XDECREF(((PyObject *)p->_ynew));
  Py_XDECREF(((PyObject *)p->g_old));
  __pyx_ptype_8assimulo_12explicit_ode_Explicit_ODE->tp_dealloc(o);
}

static int __pyx_tp_traverse_8assimulo_7solvers_5euler_ExplicitEuler(PyObject *o, visitproc v, void *a) {
  int e;
  struct __pyx_obj_8assimulo_7solvers_5euler_ExplicitEuler *p = (struct __pyx_obj_8assimulo_7solvers_5euler_ExplicitEuler *)o;
  if (__pyx_ptype_8assimulo_12explicit_ode_Explicit_ODE->tp_traverse) {
    e = __pyx_ptype_8assimulo_12explicit_ode_Explicit_ODE->tp_traverse(o, v, a); if (e) return e;
  }
  if (p->yd1) {
    e = (*v)(((PyObject*)p->yd1), a); if (e) return e;
  }
  if (p->f) {
    e = (*v)(p->f, a); if (e) return e;
  }
  if (p->event_func) {
    e = (*v)(p->event_func, a); if (e) return e;
  }
  if (p->_yold) {
    e = (*v)(((PyObject*)p->_yold), a); if (e) return e;
  }
  if (p->_ynew) {
    e = (*v)(((PyObject*)p->_ynew), a); if (e) return e;
  }
  if (p->g_old) {
    e = (*v)(((PyObject*)p->g_old), a); if (e) return e;
  }
  return 0;
}

static int __pyx_tp_clear_8assimulo_7solvers_5euler_ExplicitEuler(PyObject *o) {
  struct __pyx_obj_8assimulo_7solvers_5euler_ExplicitEuler *p = (struct __pyx_obj_8assimulo_7solvers_5euler_ExplicitEuler *)o;
  PyObject* tmp;
  if (__pyx_ptype_8assimulo_12explicit_ode_Explicit_ODE->tp_clear) {
    __pyx_ptype_8assimulo_12explicit_ode_Explicit_ODE->tp_clear(o);
  }
  tmp = ((PyObject*)p->yd1);
  p->yd1 = ((PyArrayObject *)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->f);
  p->f = Py_None; Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->event_func);
  p->event_func = Py_None; Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->_yold);
  p->_yold = ((PyArrayObject *)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->_ynew);
  p->_ynew = ((PyArrayObject *)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->g_old);
  p->g_old = ((PyArrayObject *)Py_None); Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  return 0;
}

static PyObject *__pyx_getprop_8assimulo_7solvers_5euler_13ExplicitEuler_event_func(PyObject *o, void *x) {
  return __pyx_pw_8assimulo_7solvers_5euler_13ExplicitEuler_10event_func_1__get__(o);
}

static int __pyx_setprop_8assimulo_7solvers_5euler_13ExplicitEuler_event_func(PyObject *o, PyObject *v, void *x) {
  if (v) {
    return __pyx_pw_8assimulo_7solvers_5euler_13ExplicitEuler_10event_func_3__set__(o, v);
  }
  else {
    return __pyx_pw_8assimulo_7solvers_5euler_13ExplicitEuler_10event_func_5__del__(o);
  }
}

static PyObject *__pyx_getprop_8assimulo_7solvers_5euler_13ExplicitEuler_g_old(PyObject *o, void *x) {
  return __pyx_pw_8assimulo_7solvers_5euler_13ExplicitEuler_5g_old_1__get__(o);
}

static int __pyx_setprop_8assimulo_7solvers_5euler_13ExplicitEuler_g_old(PyObject *o, PyObject *v, void *x) {
  if (v) {
    return __pyx_pw_8assimulo_7solvers_5euler_13ExplicitEuler_5g_old_3__set__(o, v);
  }
  else {
    return __pyx_pw_8assimulo_7solvers_5euler_13ExplicitEuler_5g_old_5__del__(o);
  }
}

static PyMethodDef __pyx_methods_8assimulo_7solvers_5euler_ExplicitEuler[] = {
  {__Pyx_NAMESTR("set_problem_data"), (PyCFunction)__pyx_pw_8assimulo_7solvers_5euler_13ExplicitEuler_3set_problem_data, METH_NOARGS, __Pyx_DOCSTR(0)},
  {__Pyx_NAMESTR("step"), (PyCFunction)__pyx_pw_8assimulo_7solvers_5euler_13ExplicitEuler_5step, METH_VARARGS|METH_KEYWORDS, __Pyx_DOCSTR(0)},
  {__Pyx_NAMESTR("integrate"), (PyCFunction)__pyx_pw_8assimulo_7solvers_5euler_13ExplicitEuler_7integrate, METH_VARARGS|METH_KEYWORDS, __Pyx_DOCSTR(0)},
  {__Pyx_NAMESTR("interpolate"), (PyCFunction)__pyx_pw_8assimulo_7solvers_5euler_13ExplicitEuler_9interpolate, METH_O, __Pyx_DOCSTR(0)},
  {__Pyx_NAMESTR("_set_h"), (PyCFunction)__pyx_pw_8assimulo_7solvers_5euler_13ExplicitEuler_11_set_h, METH_O, __Pyx_DOCSTR(0)},
  {__Pyx_NAMESTR("_get_h"), (PyCFunction)__pyx_pw_8assimulo_7solvers_5euler_13ExplicitEuler_13_get_h, METH_NOARGS, __Pyx_DOCSTR(__pyx_doc_8assimulo_7solvers_5euler_13ExplicitEuler_12_get_h)},
  {__Pyx_NAMESTR("state_event_info"), (PyCFunction)__pyx_pw_8assimulo_7solvers_5euler_13ExplicitEuler_15state_event_info, METH_NOARGS, __Pyx_DOCSTR(0)},
  {__Pyx_NAMESTR("set_event_info"), (PyCFunction)__pyx_pw_8assimulo_7solvers_5euler_13ExplicitEuler_17set_event_info, METH_O, __Pyx_DOCSTR(0)},
  {__Pyx_NAMESTR("print_statistics"), (PyCFunction)__pyx_pw_8assimulo_7solvers_5euler_13ExplicitEuler_19print_statistics, METH_VARARGS|METH_KEYWORDS, __Pyx_DOCSTR(__pyx_doc_8assimulo_7solvers_5euler_13ExplicitEuler_18print_statistics)},
  {0, 0, 0, 0}
};

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    return 0;
bad:
    *type = 0;
    *value = 0;
    *tb = 0;
    Py_XDECREF(local_type);
    Py_XDECREF(local_value);
    Py_XDECREF(local_tb);
    return -1;
}

static CYTHON_INLINE void __Pyx_ErrRestore(PyObject *type, PyObject *value, PyObject *tb) {
#if CYTHON_COMPILING_IN_CPYTHON
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    PyThreadState *tstate = PyThreadState_GET();
    tmp_type = tstate->curexc_type;
    tmp_value = tstate->curexc_value;
    tmp_tb = tstate->curexc_traceback;
    tstate->curexc_type = type;
    tstate->curexc_value = value;
    tstate->curexc_traceback = tb;
    Py_XDECREF(tmp_type);
    Py_XDECREF(tmp_value);
    Py_XDECREF(tmp_tb);
#else
    PyErr_Restore(type, value, tb);
#endif
}
static CYTHON_INLINE void __Pyx_ErrFetch(PyObject **type, PyObject **value, PyObject **tb) {
#if CYTHON_COMPILING_IN_CPYTHON
    PyThreadState *tstate = PyThreadState_GET();
    *type = tstate->curexc_type;
    *value = tstate->curexc_value;
    *tb = tstate->curexc_traceback;
    tstate->curexc_type = 0;
    tstate->curexc_value = 0;
    tstate->curexc_traceback = 0;
#else
    PyErr_Fetch(type, value, tb);
#endif
}

#if PY_MAJOR_VERSION < 3
static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb,
                        CYTHON_UNUSED PyObject *cause) {
    Py_XINCREF(type);
    Py_XINCREF(value);
    Py_XINCREF(tb);
    if (tb == Py_None) {
        Py_DECREF(tb);
        tb = 0;
    }
    else if (tb != NULL && !PyTraceBack_Check(tb)) {
        PyErr_SetString(PyExc_TypeError,
            "raise: arg 3 must be a traceback or None");
        goto raise_error;
    }
    if (value == NULL) {
        value = Py_None;
        Py_INCREF(value);
    }
    #if PY_VERSION_HEX < 0x02050000
    if (!PyClass_Check(type))
    #else
    if (!PyType_Check(type))
    #endif
    {
        if (value != Py_None) {
            PyErr_SetString(PyExc_TypeError,
                "instance exception may not have a separate value");
            goto raise_error;
        }
        Py_DECREF(value);
        value = type;
        #if PY_VERSION_HEX < 0x02050000
            if (PyInstance_Check(type)) {
                type = (PyObject*) ((PyInstanceObject*)type)->in_class;
                Py_INCREF(type);
            }
            else {
                type = 0;
                PyErr_SetString(PyExc_TypeError,
                    "raise: exception must be an old-style class or instance");
                goto raise_error;
            }
        #else
            type = (PyObject*) Py_TYPE(type);
            Py_INCREF(type);
            if (!PyType_IsSubtype((PyTypeObject *)type, (PyTypeObject *)PyExc_BaseException)) {
                PyErr_SetString(PyExc_TypeError,
                    "raise: exception class must be a subclass of BaseException");
                goto raise_error;
            }
        #endif
    }
    __Pyx_ErrRestore(type, value, tb);
    return;
raise_error:
    Py_XDECREF(value);
    Py_XDECREF(type);
    Py_XDECREF(tb);
    return;
}
#else /* Python 3+ */
static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause) {
    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)) {
        PyErr_SetString(PyExc_TypeError,
            "raise: exception class must be a subclass of BaseException");
        goto bad;
    }
    if (cause) {
        PyObject *fixed_cause;
        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;
        }
        if (!value) {
            value = PyObject_CallObject(type, NULL);
        }
        PyException_SetCause(value, fixed_cause);
    }
    PyErr_SetObject(type, value);
    if (tb) {
        PyThreadState *tstate = PyThreadState_GET();
        PyObject* tmp_tb = tstate->curexc_traceback;
        if (tb != tmp_tb) {
            Py_INCREF(tb);
            tstate->curexc_traceback = tb;
            Py_XDECREF(tmp_tb);
        }
    }
bad:
    return;
}
#endif

static double __Pyx__PyObject_AsDouble(PyObject* obj) {
    PyObject* float_value;
    if (Py_TYPE(obj)->tp_as_number && Py_TYPE(obj)->tp_as_number->nb_float) {
        return PyFloat_AsDouble(obj);
    } else if (PyUnicode_CheckExact(obj) || PyBytes_CheckExact(obj)) {
#if PY_MAJOR_VERSION >= 3
        float_value = PyFloat_FromString(obj);
#else
        float_value = PyFloat_FromString(obj, 0);
#endif
    } else {
        PyObject* args = PyTuple_New(1);
        if (unlikely(!args)) goto bad;
        PyTuple_SET_ITEM(args, 0, obj);
        float_value = PyObject_Call((PyObject*)&PyFloat_Type, args, 0);
        PyTuple_SET_ITEM(args, 0, 0);
        Py_DECREF(args);
    }
    if (likely(float_value)) {
        double value = PyFloat_AS_DOUBLE(float_value);
        Py_DECREF(float_value);
        return value;
    }
bad:
    return (double)-1;
}



static CYTHON_INLINE void __Pyx_ExceptionSave(PyObject **type, PyObject **value, PyObject **tb) {
    PyThreadState *tstate = PyThreadState_GET();
    *type = tstate->exc_type;
    *value = tstate->exc_value;
    *tb = tstate->exc_traceback;
    Py_XINCREF(*type);
    Py_XINCREF(*value);
    Py_XINCREF(*tb);
}
static void __Pyx_ExceptionReset(PyObject *type, PyObject *value, PyObject *tb) {
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    PyThreadState *tstate = PyThreadState_GET();
    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;
    Py_XDECREF(tmp_type);
    Py_XDECREF(tmp_value);
    Py_XDECREF(tmp_tb);
}

static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, long level) {
    PyObject *py_import = 0;
    PyObject *empty_list = 0;
    PyObject *module = 0;
    PyObject *global_dict = 0;
    PyObject *empty_dict = 0;
    PyObject *list;
    py_import = __Pyx_GetAttrString(__pyx_b, "__import__");
    if (!py_import)
        goto bad;
    if (from_list)
        list = from_list;
    else {
        empty_list = PyList_New(0);
        if (!empty_list)
            goto bad;
        list = empty_list;
    }
    global_dict = PyModule_GetDict(__pyx_m);
    if (!global_dict)
        goto bad;
    empty_dict = PyDict_New();
    if (!empty_dict)
        goto bad;
    #if PY_VERSION_HEX >= 0x02050000
    {
        #if PY_MAJOR_VERSION >= 3
        if (level == -1) {
            if (strchr(__Pyx_MODULE_NAME, '.')) {
                /* try package relative import first */
                PyObject *py_level = PyInt_FromLong(1);
                if (!py_level)
                    goto bad;
                module = PyObject_CallFunctionObjArgs(py_import,
                    name, global_dict, empty_dict, list, py_level, NULL);
                Py_DECREF(py_level);
                if (!module) {
                    if (!PyErr_ExceptionMatches(PyExc_ImportError))
                        goto bad;
                    PyErr_Clear();
                }
            }
            level = 0; /* try absolute import on failure */
        }
        #endif
        if (!module) {
            PyObject *py_level = PyInt_FromLong(level);
            if (!py_level)
                goto bad;
            module = PyObject_CallFunctionObjArgs(py_import,
                name, global_dict, empty_dict, list, py_level, NULL);
            Py_DECREF(py_level);
        }
    }
    #else
    if (level>0) {
        PyErr_SetString(PyExc_RuntimeError, "Relative import is not supported for Python <=2.4.");
        goto bad;
    }
    module = PyObject_CallFunctionObjArgs(py_import,
        name, global_dict, empty_dict, list, NULL);
    #endif
bad:
    Py_XDECREF(empty_list);
    Py_XDECREF(py_import);
    Py_XDECREF(empty_dict);
    return module;
}

static PyObject *
__Pyx_CyFunction_get_doc(__pyx_CyFunctionObject *op, CYTHON_UNUSED void *closure)
{
    if (op->func_doc == NULL && op->func.m_ml->ml_doc) {
#if PY_MAJOR_VERSION >= 3
        op->func_doc = PyUnicode_FromString(op->func.m_ml->ml_doc);
#else
        op->func_doc = PyString_FromString(op->func.m_ml->ml_doc);
#endif
    }
    if (op->func_doc == 0) {
        Py_INCREF(Py_None);
        return Py_None;
    }
    Py_INCREF(op->func_doc);
    return op->func_doc;
}
static int
__Pyx_CyFunction_set_doc(__pyx_CyFunctionObject *op, PyObject *value)
{
    PyObject *tmp = op->func_doc;
    if (value == NULL)
        op->func_doc = Py_None; /* Mark as deleted */
    else
        op->func_doc = value;
    Py_INCREF(op->func_doc);
    Py_XDECREF(tmp);
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_name(__pyx_CyFunctionObject *op)
{
    if (op->func_name == NULL) {
#if PY_MAJOR_VERSION >= 3
        op->func_name = PyUnicode_InternFromString(op->func.m_ml->ml_name);
#else
        op->func_name = PyString_InternFromString(op->func.m_ml->ml_name);
#endif
    }
    Py_INCREF(op->func_name);
    return op->func_name;
}
static int
__Pyx_CyFunction_set_name(__pyx_CyFunctionObject *op, PyObject *value)
{
    PyObject *tmp;
#if PY_MAJOR_VERSION >= 3
    if (value == NULL || !PyUnicode_Check(value)) {
#else
    if (value == NULL || !PyString_Check(value)) {
#endif
        PyErr_SetString(PyExc_TypeError,
                        "__name__ must be set to a string object");
        return -1;
    }
    tmp = op->func_name;
    Py_INCREF(value);
    op->func_name = value;
    Py_XDECREF(tmp);
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_self(__pyx_CyFunctionObject *m, CYTHON_UNUSED void *closure)
{
    PyObject *self;
    self = m->func_closure;
    if (self == NULL)
        self = Py_None;
    Py_INCREF(self);
    return self;
}
static PyObject *
__Pyx_CyFunction_get_dict(__pyx_CyFunctionObject *op)
{
    if (op->func_dict == NULL) {
        op->func_dict = PyDict_New();
        if (op->func_dict == NULL)
            return NULL;
    }
    Py_INCREF(op->func_dict);
    return op->func_dict;
}
static int
__Pyx_CyFunction_set_dict(__pyx_CyFunctionObject *op, PyObject *value)
{
    PyObject *tmp;
    if (value == NULL) {
        PyErr_SetString(PyExc_TypeError,
               "function's dictionary may not be deleted");
        return -1;
    }
    if (!PyDict_Check(value)) {
        PyErr_SetString(PyExc_TypeError,
               "setting function's dictionary to a non-dict");
        return -1;
    }
    tmp = op->func_dict;
    Py_INCREF(value);
    op->func_dict = value;
    Py_XDECREF(tmp);
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_globals(CYTHON_UNUSED __pyx_CyFunctionObject *op)
{
    PyObject* dict = PyModule_GetDict(__pyx_m);
    Py_XINCREF(dict);
    return dict;
}
static PyObject *
__Pyx_CyFunction_get_closure(CYTHON_UNUSED __pyx_CyFunctionObject *op)
{
    Py_INCREF(Py_None);
    return Py_None;
}
static PyObject *
__Pyx_CyFunction_get_code(__pyx_CyFunctionObject *op)
{
    PyObject* result = (op->func_code) ? op->func_code : Py_None;
    Py_INCREF(result);
    return result;
}
static PyObject *
__Pyx_CyFunction_get_defaults(__pyx_CyFunctionObject *op)
{
    if (op->defaults_tuple) {
        Py_INCREF(op->defaults_tuple);
        return op->defaults_tuple;
    }
    if (op->defaults_getter) {
        PyObject *res = op->defaults_getter((PyObject *) op);
        if (res) {
            Py_INCREF(res);
            op->defaults_tuple = res;
        }
        return res;
    }
    Py_INCREF(Py_None);
    return Py_None;
}
static PyGetSetDef __pyx_CyFunction_getsets[] = {
    {(char *) "func_doc", (getter)__Pyx_CyFunction_get_doc, (setter)__Pyx_CyFunction_set_doc, 0, 0},
    {(char *) "__doc__",  (getter)__Pyx_CyFunction_get_doc, (setter)__Pyx_CyFunction_set_doc, 0, 0},
    {(char *) "func_name", (getter)__Pyx_CyFunction_get_name, (setter)__Pyx_CyFunction_set_name, 0, 0},
    {(char *) "__name__", (getter)__Pyx_CyFunction_get_name, (setter)__Pyx_CyFunction_set_name, 0, 0},
    {(char *) "__self__", (getter)__Pyx_CyFunction_get_self, 0, 0, 0},
    {(char *) "func_dict", (getter)__Pyx_CyFunction_get_dict, (setter)__Pyx_CyFunction_set_dict, 0, 0},
    {(char *) "__dict__", (getter)__Pyx_CyFunction_get_dict, (setter)__Pyx_CyFunction_set_dict, 0, 0},
    {(char *) "func_globals", (getter)__Pyx_CyFunction_get_globals, 0, 0, 0},
    {(char *) "__globals__", (getter)__Pyx_CyFunction_get_globals, 0, 0, 0},
    {(char *) "func_closure", (getter)__Pyx_CyFunction_get_closure, 0, 0, 0},
    {(char *) "__closure__", (getter)__Pyx_CyFunction_get_closure, 0, 0, 0},
    {(char *) "func_code", (getter)__Pyx_CyFunction_get_code, 0, 0, 0},
    {(char *) "__code__", (getter)__Pyx_CyFunction_get_code, 0, 0, 0},
    {(char *) "func_defaults", (getter)__Pyx_CyFunction_get_defaults, 0, 0, 0},
    {(char *) "__defaults__", (getter)__Pyx_CyFunction_get_defaults, 0, 0, 0},
    {0, 0, 0, 0, 0}
};
#ifndef PY_WRITE_RESTRICTED /* < Py2.5 */
#define PY_WRITE_RESTRICTED WRITE_RESTRICTED
#endif
static PyMemberDef __pyx_CyFunction_members[] = {
    {(char *) "__module__", T_OBJECT, offsetof(__pyx_CyFunctionObject, func.m_module), PY_WRITE_RESTRICTED, 0},
    {0, 0, 0,  0, 0}
};
static PyObject *
__Pyx_CyFunction_reduce(__pyx_CyFunctionObject *m, CYTHON_UNUSED PyObject *args)
{
#if PY_MAJOR_VERSION >= 3
    return PyUnicode_FromString(m->func.m_ml->ml_name);
#else
    return PyString_FromString(m->func.m_ml->ml_name);
#endif
}
static PyMethodDef __pyx_CyFunction_methods[] = {
    {__Pyx_NAMESTR("__reduce__"), (PyCFunction)__Pyx_CyFunction_reduce, METH_VARARGS, 0},
    {0, 0, 0, 0}
};
static PyObject *__Pyx_CyFunction_New(PyTypeObject *type, PyMethodDef *ml, int flags,
                                      PyObject *closure, PyObject *module, PyObject* code) {
    __pyx_CyFunctionObject *op = PyObject_GC_New(__pyx_CyFunctionObject, type);
    if (op == NULL)
        return NULL;
    op->flags = flags;
    op->func_weakreflist = NULL;
    op->func.m_ml = ml;
    op->func.m_self = (PyObject *) op;
    Py_XINCREF(closure);
    op->func_closure = closure;
    Py_XINCREF(module);
    op->func.m_module = module;
    op->func_dict = NULL;
    op->func_name = NULL;
    op->func_doc = NULL;
    op->func_classobj = NULL;
    Py_XINCREF(code);
    op->func_code = code;
    op->defaults_pyobjects = 0;
    op->defaults = NULL;
    op->defaults_tuple = NULL;
    op->defaults_getter = NULL;
    PyObject_GC_Track(op);
    return (PyObject *) op;
}
static int
__Pyx_CyFunction_clear(__pyx_CyFunctionObject *m)
{
    Py_CLEAR(m->func_closure);
    Py_CLEAR(m->func.m_module);
    Py_CLEAR(m->func_dict);
    Py_CLEAR(m->func_name);
    Py_CLEAR(m->func_doc);
    Py_CLEAR(m->func_code);
    Py_CLEAR(m->func_classobj);
    Py_CLEAR(m->defaults_tuple);
    if (m->defaults) {
        PyObject **pydefaults = __Pyx_CyFunction_Defaults(PyObject *, m);
        int i;
        for (i = 0; i < m->defaults_pyobjects; i++)
            Py_XDECREF(pydefaults[i]);
        PyMem_Free(m->defaults);
        m->defaults = NULL;
    }
    return 0;
}
static void __Pyx_CyFunction_dealloc(__pyx_CyFunctionObject *m)
{
    PyObject_GC_UnTrack(m);
    if (m->func_weakreflist != NULL)
        PyObject_ClearWeakRefs((PyObject *) m);
    __Pyx_CyFunction_clear(m);
    PyObject_GC_Del(m);
}
static int __Pyx_CyFunction_traverse(__pyx_CyFunctionObject *m, visitproc visit, void *arg)
{
    Py_VISIT(m->func_closure);
    Py_VISIT(m->func.m_module);
    Py_VISIT(m->func_dict);
    Py_VISIT(m->func_name);
    Py_VISIT(m->func_doc);
    Py_VISIT(m->func_code);
    Py_VISIT(m->func_classobj);
    Py_VISIT(m->defaults_tuple);
    if (m->defaults) {
        PyObject **pydefaults = __Pyx_CyFunction_Defaults(PyObject *, m);
        int i;
        for (i = 0; i < m->defaults_pyobjects; i++)
            Py_VISIT(pydefaults[i]);
    }
    return 0;
}
static PyObject *__Pyx_CyFunction_descr_get(PyObject *func, PyObject *obj, PyObject *type)
{
    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
    if (m->flags & __Pyx_CYFUNCTION_STATICMETHOD) {
        Py_INCREF(func);
        return func;
    }
    if (m->flags & __Pyx_CYFUNCTION_CLASSMETHOD) {
        if (type == NULL)
            type = (PyObject *)(Py_TYPE(obj));
        return PyMethod_New(func,
                            type, (PyObject *)(Py_TYPE(type)));
    }
    if (obj == Py_None)
        obj = NULL;
    return PyMethod_New(func, obj, type);
}
static PyObject*
__Pyx_CyFunction_repr(__pyx_CyFunctionObject *op)
{
    PyObject *func_name = __Pyx_CyFunction_get_name(op);
#if PY_MAJOR_VERSION >= 3
    return PyUnicode_FromFormat("<cyfunction %U at %p>",
                                func_name, (void *)op);
#else
    return PyString_FromFormat("<cyfunction %s at %p>",
                               PyString_AsString(func_name), (void *)op);
#endif
}
static PyTypeObject __pyx_CyFunctionType_type = {
    PyVarObject_HEAD_INIT(0, 0)
    __Pyx_NAMESTR("cython_function_or_method"), /*tp_name*/
    sizeof(__pyx_CyFunctionObject),   /*tp_basicsize*/
    0,                                  /*tp_itemsize*/
    (destructor) __Pyx_CyFunction_dealloc, /*tp_dealloc*/
    0,                                  /*tp_print*/
    0,                                  /*tp_getattr*/
    0,                                  /*tp_setattr*/
#if PY_MAJOR_VERSION < 3
    0,                                  /*tp_compare*/
#else
    0,                                  /*reserved*/
#endif
    (reprfunc) __Pyx_CyFunction_repr,   /*tp_repr*/
    0,                                  /*tp_as_number*/
    0,                                  /*tp_as_sequence*/
    0,                                  /*tp_as_mapping*/
    0,                                  /*tp_hash*/
    __Pyx_PyCFunction_Call,             /*tp_call*/
    0,                                  /*tp_str*/
    0,                                  /*tp_getattro*/
    0,                                  /*tp_setattro*/
    0,                                  /*tp_as_buffer*/
    Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC, /* tp_flags*/
    0,                                  /*tp_doc*/
    (traverseproc) __Pyx_CyFunction_traverse,   /*tp_traverse*/
    (inquiry) __Pyx_CyFunction_clear,   /*tp_clear*/
    0,                                  /*tp_richcompare*/
    offsetof(__pyx_CyFunctionObject, func_weakreflist), /* tp_weaklistoffse */
    0,                                  /*tp_iter*/
    0,                                  /*tp_iternext*/
    __pyx_CyFunction_methods,           /*tp_methods*/
    __pyx_CyFunction_members,           /*tp_members*/
    __pyx_CyFunction_getsets,           /*tp_getset*/
    0,                                  /*tp_base*/
    0,                                  /*tp_dict*/
    __Pyx_CyFunction_descr_get,         /*tp_descr_get*/
    0,                                  /*tp_descr_set*/
    offsetof(__pyx_CyFunctionObject, func_dict),/*tp_dictoffset*/
    0,                                  /*tp_init*/
    0,                                  /*tp_alloc*/
    0,                                  /*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*/
#if PY_VERSION_HEX >= 0x02060000
    0,                                  /*tp_version_tag*/
#endif
};
static int __Pyx_CyFunction_init(void)
{
    if (PyType_Ready(&__pyx_CyFunctionType_type) < 0)
        return -1;
    __pyx_CyFunctionType = &__pyx_CyFunctionType_type;
    return 0;
}
void *__Pyx_CyFunction_InitDefaults(PyObject *func, size_t size, int pyobjects)
{
    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
    m->defaults = PyMem_Malloc(size);
    if (!m->defaults)
        return PyErr_NoMemory();
    memset(m->defaults, 0, sizeof(size));
    m->defaults_pyobjects = pyobjects;
    return m->defaults;
}
static void __Pyx_CyFunction_SetDefaultsTuple(PyObject *func, PyObject *tuple)
{
    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
    m->defaults_tuple = tuple;
    Py_INCREF(tuple);
}

#if CYTHON_CCOMPLEX
  #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

#if CYTHON_CCOMPLEX
#else
    static CYTHON_INLINE int __Pyx_c_eqf(__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_sumf(__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_difff(__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_prodf(__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;
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quotf(__pyx_t_float_complex a, __pyx_t_float_complex b) {
        __pyx_t_float_complex z;
        float denom = b.real * b.real + b.imag * b.imag;
        z.real = (a.real * b.real + a.imag * b.imag) / denom;
        z.imag = (a.imag * b.real - a.real * b.imag) / denom;
        return z;
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_negf(__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_zerof(__pyx_t_float_complex a) {
       return (a.real == 0) && (a.imag == 0);
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conjf(__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_absf(__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_powf(__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:
                        z = __Pyx_c_prodf(a, a);
                        return __Pyx_c_prodf(a, a);
                    case 3:
                        z = __Pyx_c_prodf(a, a);
                        return __Pyx_c_prodf(z, a);
                    case 4:
                        z = __Pyx_c_prodf(a, a);
                        return __Pyx_c_prodf(z, z);
                }
            }
            if (a.imag == 0) {
                if (a.real == 0) {
                    return a;
                }
                r = a.real;
                theta = 0;
            } else {
                r = __Pyx_c_absf(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

#if CYTHON_CCOMPLEX
  #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

#if CYTHON_CCOMPLEX
#else
    static CYTHON_INLINE int __Pyx_c_eq(__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(__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(__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(__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;
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        __pyx_t_double_complex z;
        double denom = b.real * b.real + b.imag * b.imag;
        z.real = (a.real * b.real + a.imag * b.imag) / denom;
        z.imag = (a.imag * b.real - a.real * b.imag) / denom;
        return z;
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg(__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(__pyx_t_double_complex a) {
       return (a.real == 0) && (a.imag == 0);
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj(__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(__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(__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:
                        z = __Pyx_c_prod(a, a);
                        return __Pyx_c_prod(a, a);
                    case 3:
                        z = __Pyx_c_prod(a, a);
                        return __Pyx_c_prod(z, a);
                    case 4:
                        z = __Pyx_c_prod(a, a);
                        return __Pyx_c_prod(z, z);
                }
            }
            if (a.imag == 0) {
                if (a.real == 0) {
                    return a;
                }
                r = a.real;
                theta = 0;
            } else {
                r = __Pyx_c_abs(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

static CYTHON_INLINE unsigned char __Pyx_PyInt_AsUnsignedChar(PyObject* x) {
    const unsigned char neg_one = (unsigned char)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
    if (sizeof(unsigned char) < sizeof(long)) {
        long val = __Pyx_PyInt_AsLong(x);
        if (unlikely(val != (long)(unsigned char)val)) {
            if (!unlikely(val == -1 && PyErr_Occurred())) {
                PyErr_SetString(PyExc_OverflowError,
                    (is_unsigned && unlikely(val < 0)) ?
                    "can't convert negative value to unsigned char" :
                    "value too large to convert to unsigned char");
            }
            return (unsigned char)-1;
        }
        return (unsigned char)val;
    }
    return (unsigned char)__Pyx_PyInt_AsUnsignedLong(x);
}

static CYTHON_INLINE unsigned short __Pyx_PyInt_AsUnsignedShort(PyObject* x) {
    const unsigned short neg_one = (unsigned short)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
    if (sizeof(unsigned short) < sizeof(long)) {
        long val = __Pyx_PyInt_AsLong(x);
        if (unlikely(val != (long)(unsigned short)val)) {
            if (!unlikely(val == -1 && PyErr_Occurred())) {
                PyErr_SetString(PyExc_OverflowError,
                    (is_unsigned && unlikely(val < 0)) ?
                    "can't convert negative value to unsigned short" :
                    "value too large to convert to unsigned short");
            }
            return (unsigned short)-1;
        }
        return (unsigned short)val;
    }
    return (unsigned short)__Pyx_PyInt_AsUnsignedLong(x);
}

static CYTHON_INLINE unsigned int __Pyx_PyInt_AsUnsignedInt(PyObject* x) {
    const unsigned int neg_one = (unsigned int)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
    if (sizeof(unsigned int) < sizeof(long)) {
        long val = __Pyx_PyInt_AsLong(x);
        if (unlikely(val != (long)(unsigned int)val)) {
            if (!unlikely(val == -1 && PyErr_Occurred())) {
                PyErr_SetString(PyExc_OverflowError,
                    (is_unsigned && unlikely(val < 0)) ?
                    "can't convert negative value to unsigned int" :
                    "value too large to convert to unsigned int");
            }
            return (unsigned int)-1;
        }
        return (unsigned int)val;
    }
    return (unsigned int)__Pyx_PyInt_AsUnsignedLong(x);
}

static CYTHON_INLINE char __Pyx_PyInt_AsChar(PyObject* x) {
    const char neg_one = (char)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
    if (sizeof(char) < sizeof(long)) {
        long val = __Pyx_PyInt_AsLong(x);
        if (unlikely(val != (long)(char)val)) {
            if (!unlikely(val == -1 && PyErr_Occurred())) {
                PyErr_SetString(PyExc_OverflowError,
                    (is_unsigned && unlikely(val < 0)) ?
                    "can't convert negative value to char" :
                    "value too large to convert to char");
            }
            return (char)-1;
        }
        return (char)val;
    }
    return (char)__Pyx_PyInt_AsLong(x);
}

static CYTHON_INLINE short __Pyx_PyInt_AsShort(PyObject* x) {
    const short neg_one = (short)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
    if (sizeof(short) < sizeof(long)) {
        long val = __Pyx_PyInt_AsLong(x);
        if (unlikely(val != (long)(short)val)) {
            if (!unlikely(val == -1 && PyErr_Occurred())) {
                PyErr_SetString(PyExc_OverflowError,
                    (is_unsigned && unlikely(val < 0)) ?
                    "can't convert negative value to short" :
                    "value too large to convert to short");
            }
            return (short)-1;
        }
        return (short)val;
    }
    return (short)__Pyx_PyInt_AsLong(x);
}

static CYTHON_INLINE int __Pyx_PyInt_AsInt(PyObject* x) {
    const int neg_one = (int)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
    if (sizeof(int) < sizeof(long)) {
        long val = __Pyx_PyInt_AsLong(x);
        if (unlikely(val != (long)(int)val)) {
            if (!unlikely(val == -1 && PyErr_Occurred())) {
                PyErr_SetString(PyExc_OverflowError,
                    (is_unsigned && unlikely(val < 0)) ?
                    "can't convert negative value to int" :
                    "value too large to convert to int");
            }
            return (int)-1;
        }
        return (int)val;
    }
    return (int)__Pyx_PyInt_AsLong(x);
}

static CYTHON_INLINE signed char __Pyx_PyInt_AsSignedChar(PyObject* x) {
    const signed char neg_one = (signed char)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
    if (sizeof(signed char) < sizeof(long)) {
        long val = __Pyx_PyInt_AsLong(x);
        if (unlikely(val != (long)(signed char)val)) {
            if (!unlikely(val == -1 && PyErr_Occurred())) {
                PyErr_SetString(PyExc_OverflowError,
                    (is_unsigned && unlikely(val < 0)) ?
                    "can't convert negative value to signed char" :
                    "value too large to convert to signed char");
            }
            return (signed char)-1;
        }
        return (signed char)val;
    }
    return (signed char)__Pyx_PyInt_AsSignedLong(x);
}

static CYTHON_INLINE signed short __Pyx_PyInt_AsSignedShort(PyObject* x) {
    const signed short neg_one = (signed short)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
    if (sizeof(signed short) < sizeof(long)) {
        long val = __Pyx_PyInt_AsLong(x);
        if (unlikely(val != (long)(signed short)val)) {
            if (!unlikely(val == -1 && PyErr_Occurred())) {
                PyErr_SetString(PyExc_OverflowError,
                    (is_unsigned && unlikely(val < 0)) ?
                    "can't convert negative value to signed short" :
                    "value too large to convert to signed short");
            }
            return (signed short)-1;
        }
        return (signed short)val;
    }
    return (signed short)__Pyx_PyInt_AsSignedLong(x);
}

static CYTHON_INLINE signed int __Pyx_PyInt_AsSignedInt(PyObject* x) {
    const signed int neg_one = (signed int)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
    if (sizeof(signed int) < sizeof(long)) {
        long val = __Pyx_PyInt_AsLong(x);
        if (unlikely(val != (long)(signed int)val)) {
            if (!unlikely(val == -1 && PyErr_Occurred())) {
                PyErr_SetString(PyExc_OverflowError,
                    (is_unsigned && unlikely(val < 0)) ?
                    "can't convert negative value to signed int" :
                    "value too large to convert to signed int");
            }
            return (signed int)-1;
        }
        return (signed int)val;
    }
    return (signed int)__Pyx_PyInt_AsSignedLong(x);
}

static CYTHON_INLINE int __Pyx_PyInt_AsLongDouble(PyObject* x) {
    const int neg_one = (int)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
    if (sizeof(int) < sizeof(long)) {
        long val = __Pyx_PyInt_AsLong(x);
        if (unlikely(val != (long)(int)val)) {
            if (!unlikely(val == -1 && PyErr_Occurred())) {
                PyErr_SetString(PyExc_OverflowError,
                    (is_unsigned && unlikely(val < 0)) ?
                    "can't convert negative value to int" :
                    "value too large to convert to int");
            }
            return (int)-1;
        }
        return (int)val;
    }
    return (int)__Pyx_PyInt_AsLong(x);
}

static CYTHON_INLINE unsigned long __Pyx_PyInt_AsUnsignedLong(PyObject* x) {
    const unsigned long neg_one = (unsigned long)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_VERSION_HEX < 0x03000000
    if (likely(PyInt_Check(x))) {
        long val = PyInt_AS_LONG(x);
        if (is_unsigned && unlikely(val < 0)) {
            PyErr_SetString(PyExc_OverflowError,
                            "can't convert negative value to unsigned long");
            return (unsigned long)-1;
        }
        return (unsigned long)val;
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
            if (unlikely(Py_SIZE(x) < 0)) {
                PyErr_SetString(PyExc_OverflowError,
                                "can't convert negative value to unsigned long");
                return (unsigned long)-1;
            }
            return (unsigned long)PyLong_AsUnsignedLong(x);
        } else {
            return (unsigned long)PyLong_AsLong(x);
        }
    } else {
        unsigned long val;
        PyObject *tmp = __Pyx_PyNumber_Int(x);
        if (!tmp) return (unsigned long)-1;
        val = __Pyx_PyInt_AsUnsignedLong(tmp);
        Py_DECREF(tmp);
        return val;
    }
}

static CYTHON_INLINE unsigned PY_LONG_LONG __Pyx_PyInt_AsUnsignedLongLong(PyObject* x) {
    const unsigned PY_LONG_LONG neg_one = (unsigned PY_LONG_LONG)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_VERSION_HEX < 0x03000000
    if (likely(PyInt_Check(x))) {
        long val = PyInt_AS_LONG(x);
        if (is_unsigned && unlikely(val < 0)) {
            PyErr_SetString(PyExc_OverflowError,
                            "can't convert negative value to unsigned PY_LONG_LONG");
            return (unsigned PY_LONG_LONG)-1;
        }
        return (unsigned PY_LONG_LONG)val;
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
            if (unlikely(Py_SIZE(x) < 0)) {
                PyErr_SetString(PyExc_OverflowError,
                                "can't convert negative value to unsigned PY_LONG_LONG");
                return (unsigned PY_LONG_LONG)-1;
            }
            return (unsigned PY_LONG_LONG)PyLong_AsUnsignedLongLong(x);
        } else {
            return (unsigned PY_LONG_LONG)PyLong_AsLongLong(x);
        }
    } else {
        unsigned PY_LONG_LONG val;
        PyObject *tmp = __Pyx_PyNumber_Int(x);
        if (!tmp) return (unsigned PY_LONG_LONG)-1;
        val = __Pyx_PyInt_AsUnsignedLongLong(tmp);
        Py_DECREF(tmp);
        return val;
    }
}

static CYTHON_INLINE long __Pyx_PyInt_AsLong(PyObject* x) {
    const long neg_one = (long)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_VERSION_HEX < 0x03000000
    if (likely(PyInt_Check(x))) {
        long val = PyInt_AS_LONG(x);
        if (is_unsigned && unlikely(val < 0)) {
            PyErr_SetString(PyExc_OverflowError,
                            "can't convert negative value to long");
            return (long)-1;
        }
        return (long)val;
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
            if (unlikely(Py_SIZE(x) < 0)) {
                PyErr_SetString(PyExc_OverflowError,
                                "can't convert negative value to long");
                return (long)-1;
            }
            return (long)PyLong_AsUnsignedLong(x);
        } else {
            return (long)PyLong_AsLong(x);
        }
    } else {
        long val;
        PyObject *tmp = __Pyx_PyNumber_Int(x);
        if (!tmp) return (long)-1;
        val = __Pyx_PyInt_AsLong(tmp);
        Py_DECREF(tmp);
        return val;
    }
}

static CYTHON_INLINE PY_LONG_LONG __Pyx_PyInt_AsLongLong(PyObject* x) {
    const PY_LONG_LONG neg_one = (PY_LONG_LONG)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_VERSION_HEX < 0x03000000
    if (likely(PyInt_Check(x))) {
        long val = PyInt_AS_LONG(x);
        if (is_unsigned && unlikely(val < 0)) {
            PyErr_SetString(PyExc_OverflowError,
                            "can't convert negative value to PY_LONG_LONG");
            return (PY_LONG_LONG)-1;
        }
        return (PY_LONG_LONG)val;
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
            if (unlikely(Py_SIZE(x) < 0)) {
                PyErr_SetString(PyExc_OverflowError,
                                "can't convert negative value to PY_LONG_LONG");
                return (PY_LONG_LONG)-1;
            }
            return (PY_LONG_LONG)PyLong_AsUnsignedLongLong(x);
        } else {
            return (PY_LONG_LONG)PyLong_AsLongLong(x);
        }
    } else {
        PY_LONG_LONG val;
        PyObject *tmp = __Pyx_PyNumber_Int(x);
        if (!tmp) return (PY_LONG_LONG)-1;
        val = __Pyx_PyInt_AsLongLong(tmp);
        Py_DECREF(tmp);
        return val;
    }
}

static CYTHON_INLINE signed long __Pyx_PyInt_AsSignedLong(PyObject* x) {
    const signed long neg_one = (signed long)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_VERSION_HEX < 0x03000000
    if (likely(PyInt_Check(x))) {
        long val = PyInt_AS_LONG(x);
        if (is_unsigned && unlikely(val < 0)) {
            PyErr_SetString(PyExc_OverflowError,
                            "can't convert negative value to signed long");
            return (signed long)-1;
        }
        return (signed long)val;
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
            if (unlikely(Py_SIZE(x) < 0)) {
                PyErr_SetString(PyExc_OverflowError,
                                "can't convert negative value to signed long");
                return (signed long)-1;
            }
            return (signed long)PyLong_AsUnsignedLong(x);
        } else {
            return (signed long)PyLong_AsLong(x);
        }
    } else {
        signed long val;
        PyObject *tmp = __Pyx_PyNumber_Int(x);
        if (!tmp) return (signed long)-1;
        val = __Pyx_PyInt_AsSignedLong(tmp);
        Py_DECREF(tmp);
        return val;
    }
}

static CYTHON_INLINE signed PY_LONG_LONG __Pyx_PyInt_AsSignedLongLong(PyObject* x) {
    const signed PY_LONG_LONG neg_one = (signed PY_LONG_LONG)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_VERSION_HEX < 0x03000000
    if (likely(PyInt_Check(x))) {
        long val = PyInt_AS_LONG(x);
        if (is_unsigned && unlikely(val < 0)) {
            PyErr_SetString(PyExc_OverflowError,
                            "can't convert negative value to signed PY_LONG_LONG");
            return (signed PY_LONG_LONG)-1;
        }
        return (signed PY_LONG_LONG)val;
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
            if (unlikely(Py_SIZE(x) < 0)) {
                PyErr_SetString(PyExc_OverflowError,
                                "can't convert negative value to signed PY_LONG_LONG");
                return (signed PY_LONG_LONG)-1;
            }
            return (signed PY_LONG_LONG)PyLong_AsUnsignedLongLong(x);
        } else {
            return (signed PY_LONG_LONG)PyLong_AsLongLong(x);
        }
    } else {
        signed PY_LONG_LONG val;
        PyObject *tmp = __Pyx_PyNumber_Int(x);
        if (!tmp) return (signed PY_LONG_LONG)-1;
        val = __Pyx_PyInt_AsSignedLongLong(tmp);
        Py_DECREF(tmp);
        return val;
    }
}

static void __Pyx_WriteUnraisable(const char *name, int clineno,
                                  int lineno, const char *filename) {
    PyObject *old_exc, *old_val, *old_tb;
    PyObject *ctx;
    __Pyx_ErrFetch(&old_exc, &old_val, &old_tb);
    #if PY_MAJOR_VERSION < 3
    ctx = PyString_FromString(name);
    #else
    ctx = PyUnicode_FromString(name);
    #endif
    __Pyx_ErrRestore(old_exc, old_val, old_tb);
    if (!ctx) {
        PyErr_WriteUnraisable(Py_None);
    } else {
        PyErr_WriteUnraisable(ctx);
        Py_DECREF(ctx);
    }
}

static CYTHON_INLINE int __Pyx_StrEq(const char *s1, const char *s2) {
     while (*s1 != '\0' && *s1 == *s2) { s1++; s2++; }
     return *s1 == *s2;
}

static int __Pyx_check_binary_version(void) {
    char ctversion[4], rtversion[4];
    PyOS_snprintf(ctversion, 4, "%d.%d", PY_MAJOR_VERSION, PY_MINOR_VERSION);
    PyOS_snprintf(rtversion, 4, "%s", Py_GetVersion());
    if (ctversion[0] != rtversion[0] || ctversion[2] != rtversion[2]) {
        char message[200];
        PyOS_snprintf(message, sizeof(message),
                      "compiletime version %s of module '%.100s' "
                      "does not match runtime version %s",
                      ctversion, __Pyx_MODULE_NAME, rtversion);
        #if PY_VERSION_HEX < 0x02050000
        return PyErr_Warn(NULL, message);
        #else
        return PyErr_WarnEx(NULL, message, 1);
        #endif
    }
    return 0;
}

#ifndef __PYX_HAVE_RT_ImportType
#define __PYX_HAVE_RT_ImportType
static PyTypeObject *__Pyx_ImportType(const char *module_name, const char *class_name,
    size_t size, int strict)
{
    PyObject *py_module = 0;
    PyObject *result = 0;
    PyObject *py_name = 0;
    char warning[200];
    py_module = __Pyx_ImportModule(module_name);
    if (!py_module)
        goto bad;
    py_name = __Pyx_PyIdentifier_FromString(class_name);
    if (!py_name)
        goto bad;
    result = PyObject_GetAttr(py_module, py_name);
    Py_DECREF(py_name);
    py_name = 0;
    Py_DECREF(py_module);
    py_module = 0;
    if (!result)
        goto bad;
    if (!PyType_Check(result)) {
        PyErr_Format(PyExc_TypeError,
            "%s.%s is not a type object",
            module_name, class_name);
        goto bad;
    }
    if (!strict && (size_t)((PyTypeObject *)result)->tp_basicsize > size) {
        PyOS_snprintf(warning, sizeof(warning),
            "%s.%s size changed, may indicate binary incompatibility",
            module_name, class_name);
        #if PY_VERSION_HEX < 0x02050000
        if (PyErr_Warn(NULL, warning) < 0) goto bad;
        #else
        if (PyErr_WarnEx(NULL, warning, 0) < 0) goto bad;
        #endif
    }
    else if ((size_t)((PyTypeObject *)result)->tp_basicsize != size) {
        PyErr_Format(PyExc_ValueError,
            "%s.%s has the wrong size, try recompiling",
            module_name, class_name);
        goto bad;
    }
    return (PyTypeObject *)result;
bad:
    Py_XDECREF(py_module);
    Py_XDECREF(result);
    return NULL;
}
#endif

#ifndef __PYX_HAVE_RT_ImportModule
#define __PYX_HAVE_RT_ImportModule
static PyObject *__Pyx_ImportModule(const char *name) {
    PyObject *py_name = 0;
    PyObject *py_module = 0;
    py_name = __Pyx_PyIdentifier_FromString(name);
    if (!py_name)
        goto bad;
    py_module = PyImport_Import(py_name);
    Py_DECREF(py_name);
    return py_module;
bad:
    Py_XDECREF(py_name);
    return 0;
}
#endif

static void* __Pyx_GetVtable(PyObject *dict) {
    void* ptr;
    PyObject *ob = PyMapping_GetItemString(dict, (char *)"__pyx_vtable__");
    if (!ob)
        goto bad;
#if PY_VERSION_HEX >= 0x02070000 && !(PY_MAJOR_VERSION==3&&PY_MINOR_VERSION==0)
    ptr = PyCapsule_GetPointer(ob, 0);
#else
    ptr = PyCObject_AsVoidPtr(ob);
#endif
    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;
}

static int __Pyx_SetVtable(PyObject *dict, void *vtable) {
#if PY_VERSION_HEX >= 0x02070000 && !(PY_MAJOR_VERSION==3&&PY_MINOR_VERSION==0)
    PyObject *ob = PyCapsule_New(vtable, 0, 0);
#else
    PyObject *ob = PyCObject_FromVoidPtr(vtable, 0);
#endif
    if (!ob)
        goto bad;
    if (PyDict_SetItemString(dict, "__pyx_vtable__", ob) < 0)
        goto bad;
    Py_DECREF(ob);
    return 0;
bad:
    Py_XDECREF(ob);
    return -1;
}

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) / 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 PyCodeObject *__pyx_find_code_object(int code_line) {
    PyCodeObject* code_object;
    int pos;
    if (unlikely(!code_line) || unlikely(!__pyx_code_cache.entries)) {
        return NULL;
    }
    pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
    if (unlikely(pos >= __pyx_code_cache.count) || unlikely(__pyx_code_cache.entries[pos].code_line != code_line)) {
        return NULL;
    }
    code_object = __pyx_code_cache.entries[pos].code_object;
    Py_INCREF(code_object);
    return code_object;
}
static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object) {
    int pos, i;
    __Pyx_CodeObjectCacheEntry* entries = __pyx_code_cache.entries;
    if (unlikely(!code_line)) {
        return;
    }
    if (unlikely(!entries)) {
        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Malloc(64*sizeof(__Pyx_CodeObjectCacheEntry));
        if (likely(entries)) {
            __pyx_code_cache.entries = entries;
            __pyx_code_cache.max_count = 64;
            __pyx_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(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
    if ((pos < __pyx_code_cache.count) && unlikely(__pyx_code_cache.entries[pos].code_line == code_line)) {
        PyCodeObject* tmp = entries[pos].code_object;
        entries[pos].code_object = code_object;
        Py_DECREF(tmp);
        return;
    }
    if (__pyx_code_cache.count == __pyx_code_cache.max_count) {
        int new_max = __pyx_code_cache.max_count + 64;
        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Realloc(
            __pyx_code_cache.entries, new_max*sizeof(__Pyx_CodeObjectCacheEntry));
        if (unlikely(!entries)) {
            return;
        }
        __pyx_code_cache.entries = entries;
        __pyx_code_cache.max_count = new_max;
    }
    for (i=__pyx_code_cache.count; i>pos; i--) {
        entries[i] = entries[i-1];
    }
    entries[pos].code_line = code_line;
    entries[pos].code_object = code_object;
    __pyx_code_cache.count++;
    Py_INCREF(code_object);
}

#include "compile.h"
#include "frameobject.h"
#include "traceback.h"
static PyCodeObject* __Pyx_CreateCodeObjectForTraceback(
            const char *funcname, int c_line,
            int py_line, const char *filename) {
    PyCodeObject *py_code = 0;
    PyObject *py_srcfile = 0;
    PyObject *py_funcname = 0;
    #if PY_MAJOR_VERSION < 3
    py_srcfile = PyString_FromString(filename);
    #else
    py_srcfile = PyUnicode_FromString(filename);
    #endif
    if (!py_srcfile) goto bad;
    if (c_line) {
        #if PY_MAJOR_VERSION < 3
        py_funcname = PyString_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
        #else
        py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
        #endif
    }
    else {
        #if PY_MAJOR_VERSION < 3
        py_funcname = PyString_FromString(funcname);
        #else
        py_funcname = PyUnicode_FromString(funcname);
        #endif
    }
    if (!py_funcname) goto bad;
    py_code = __Pyx_PyCode_New(
        0,            /*int argcount,*/
        0,            /*int kwonlyargcount,*/
        0,            /*int nlocals,*/
        0,            /*int stacksize,*/
        0,            /*int flags,*/
        __pyx_empty_bytes, /*PyObject *code,*/
        __pyx_empty_tuple, /*PyObject *consts,*/
        __pyx_empty_tuple, /*PyObject *names,*/
        __pyx_empty_tuple, /*PyObject *varnames,*/
        __pyx_empty_tuple, /*PyObject *freevars,*/
        __pyx_empty_tuple, /*PyObject *cellvars,*/
        py_srcfile,   /*PyObject *filename,*/
        py_funcname,  /*PyObject *name,*/
        py_line,      /*int firstlineno,*/
        __pyx_empty_bytes  /*PyObject *lnotab*/
    );
    Py_DECREF(py_srcfile);
    Py_DECREF(py_funcname);
    return py_code;
bad:
    Py_XDECREF(py_srcfile);
    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;
    PyObject *py_globals = 0;
    PyFrameObject *py_frame = 0;
    py_code = __pyx_find_code_object(c_line ? c_line : py_line);
    if (!py_code) {
        py_code = __Pyx_CreateCodeObjectForTraceback(
            funcname, c_line, py_line, filename);
        if (!py_code) goto bad;
        __pyx_insert_code_object(c_line ? c_line : py_line, py_code);
    }
    py_globals = PyModule_GetDict(__pyx_m);
    if (!py_globals) goto bad;
    py_frame = PyFrame_New(
        PyThreadState_GET(), /*PyThreadState *tstate,*/
        py_code,             /*PyCodeObject *code,*/
        py_globals,          /*PyObject *globals,*/
        0                    /*PyObject *locals*/
    );
    if (!py_frame) goto bad;
    py_frame->f_lineno = py_line;
    PyTraceBack_Here(py_frame);
bad:
    Py_XDECREF(py_code);
    Py_XDECREF(py_frame);
}

static int __Pyx_InitStrings(__Pyx_StringTabEntry *t) {
    while (t->p) {
        #if PY_MAJOR_VERSION < 3
        if (t->is_unicode) {
            *t->p = PyUnicode_DecodeUTF8(t->s, t->n - 1, NULL);
        } else if (t->intern) {
            *t->p = PyString_InternFromString(t->s);
        } else {
            *t->p = PyString_FromStringAndSize(t->s, t->n - 1);
        }
        #else  /* Python 3+ has unicode identifiers */
        if (t->is_unicode | t->is_str) {
            if (t->intern) {
                *t->p = PyUnicode_InternFromString(t->s);
            } else if (t->encoding) {
                *t->p = PyUnicode_Decode(t->s, t->n - 1, t->encoding, NULL);
            } else {
                *t->p = PyUnicode_FromStringAndSize(t->s, t->n - 1);
            }
        } else {
            *t->p = PyBytes_FromStringAndSize(t->s, t->n - 1);
        }
        #endif
        if (!*t->p)
            return -1;
        ++t;
    }
    return 0;
}


/* Type Conversion Functions */

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 PyObject* __Pyx_PyNumber_Int(PyObject* x) {
  PyNumberMethods *m;
  const char *name = NULL;
  PyObject *res = NULL;
#if PY_VERSION_HEX < 0x03000000
  if (PyInt_Check(x) || PyLong_Check(x))
#else
  if (PyLong_Check(x))
#endif
    return Py_INCREF(x), x;
  m = Py_TYPE(x)->tp_as_number;
#if PY_VERSION_HEX < 0x03000000
  if (m && m->nb_int) {
    name = "int";
    res = PyNumber_Int(x);
  }
  else if (m && m->nb_long) {
    name = "long";
    res = PyNumber_Long(x);
  }
#else
  if (m && m->nb_int) {
    name = "int";
    res = PyNumber_Long(x);
  }
#endif
  if (res) {
#if PY_VERSION_HEX < 0x03000000
    if (!PyInt_Check(res) && !PyLong_Check(res)) {
#else
    if (!PyLong_Check(res)) {
#endif
      PyErr_Format(PyExc_TypeError,
                   "__%s__ returned non-%s (type %.200s)",
                   name, name, Py_TYPE(res)->tp_name);
      Py_DECREF(res);
      return NULL;
    }
  }
  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 = PyNumber_Index(b);
  if (!x) return -1;
  ival = PyInt_AsSsize_t(x);
  Py_DECREF(x);
  return ival;
}

static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) {
#if PY_VERSION_HEX < 0x02050000
   if (ival <= LONG_MAX)
       return PyInt_FromLong((long)ival);
   else {
       unsigned char *bytes = (unsigned char *) &ival;
       int one = 1; int little = (int)*(unsigned char*)&one;
       return _PyLong_FromByteArray(bytes, sizeof(size_t), little, 0);
   }
#else
   return PyInt_FromSize_t(ival);
#endif
}

static CYTHON_INLINE size_t __Pyx_PyInt_AsSize_t(PyObject* x) {
   unsigned PY_LONG_LONG val = __Pyx_PyInt_AsUnsignedLongLong(x);
   if (unlikely(val == (unsigned PY_LONG_LONG)-1 && PyErr_Occurred())) {
       return (size_t)-1;
   } else if (unlikely(val != (unsigned PY_LONG_LONG)(size_t)val)) {
       PyErr_SetString(PyExc_OverflowError,
                       "value too large to convert to size_t");
       return (size_t)-1;
   }
   return (size_t)val;
}


#endif /* Py_PYTHON_H */
