/* Generated by Cython 0.13 on Sun Feb 27 00:36:13 2011 */

#define PY_SSIZE_T_CLEAN
#include "Python.h"
#ifndef Py_PYTHON_H
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#else

#include <stddef.h> /* For offsetof */
#ifndef offsetof
#define offsetof(type, member) ( (size_t) & ((type*)0) -> member )
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#ifndef DL_IMPORT
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#ifndef DL_EXPORT
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#ifndef PY_LONG_LONG
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  #define PyInt_AsSsize_t(o)   PyInt_AsLong(o)
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  #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
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  #define PyBytes_GET_SIZE             PyString_GET_SIZE
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#define __PYX_HAVE_API__dipy__reconst__recspeed
#include "stdio.h"
#include "stdlib.h"
#include "numpy/arrayobject.h"
#include "numpy/ufuncobject.h"
#include "math.h"

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/* unused attribute */
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#   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)
#   define CYTHON_UNUSED __attribute__ ((__unused__)) 
# else
#   define CYTHON_UNUSED 
# endif
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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_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))


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#define likely(x)   __builtin_expect(!!(x), 1)
#define unlikely(x) __builtin_expect(!!(x), 0)
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#define likely(x)   (x)
#define unlikely(x) (x)
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#define likely(x)   (x)
#define unlikely(x) (x)
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static PyObject *__pyx_m;
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static PyObject *__pyx_empty_tuple;
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#if !defined(CYTHON_CCOMPLEX)
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#if CYTHON_CCOMPLEX
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#if CYTHON_CCOMPLEX && !defined(__cplusplus) && defined(__sun__) && defined(__GNUC__)
  #undef _Complex_I
  #define _Complex_I 1.0fj
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static const char *__pyx_f[] = {
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typedef npy_int8 __pyx_t_5numpy_int8_t;

typedef npy_int16 __pyx_t_5numpy_int16_t;

typedef npy_int32 __pyx_t_5numpy_int32_t;

typedef npy_int64 __pyx_t_5numpy_int64_t;

typedef npy_uint8 __pyx_t_5numpy_uint8_t;

typedef npy_uint16 __pyx_t_5numpy_uint16_t;

typedef npy_uint32 __pyx_t_5numpy_uint32_t;

typedef npy_uint64 __pyx_t_5numpy_uint64_t;

typedef npy_float32 __pyx_t_5numpy_float32_t;

typedef npy_float64 __pyx_t_5numpy_float64_t;

typedef npy_long __pyx_t_5numpy_int_t;

typedef npy_longlong __pyx_t_5numpy_long_t;

typedef npy_intp __pyx_t_5numpy_intp_t;

typedef npy_uintp __pyx_t_5numpy_uintp_t;

typedef npy_ulong __pyx_t_5numpy_uint_t;

typedef npy_ulonglong __pyx_t_5numpy_ulong_t;

typedef npy_double __pyx_t_5numpy_float_t;

typedef npy_double __pyx_t_5numpy_double_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;
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#else
    typedef struct { float real, imag; } __pyx_t_float_complex;
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#if CYTHON_CCOMPLEX
  #ifdef __cplusplus
    typedef ::std::complex< double > __pyx_t_double_complex;
  #else
    typedef double _Complex __pyx_t_double_complex;
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#else
    typedef struct { double real, imag; } __pyx_t_double_complex;
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/* Type declarations */

typedef npy_cfloat __pyx_t_5numpy_cfloat_t;

typedef npy_cdouble __pyx_t_5numpy_cdouble_t;

typedef npy_clongdouble __pyx_t_5numpy_clongdouble_t;

typedef npy_cdouble __pyx_t_5numpy_complex_t;

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#define __Pyx_XGIVEREF(r) do { if((r) != NULL) {__Pyx_GIVEREF(r);} } while(0)
#define __Pyx_XGOTREF(r) do { if((r) != NULL) {__Pyx_GOTREF(r);} } while(0)

static PyObject *__Pyx_GetName(PyObject *dict, PyObject *name); /*proto*/

static void __Pyx_RaiseDoubleKeywordsError(
    const char* func_name, PyObject* kw_name); /*proto*/

static void __Pyx_RaiseArgtupleInvalid(const char* func_name, int exact,
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static int __Pyx_ParseOptionalKeywords(PyObject *kwds, PyObject **argnames[],     PyObject *kwds2, PyObject *values[], Py_ssize_t num_pos_args,     const char* function_name); /*proto*/

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

/* Run-time type information about structs used with buffers */
struct __Pyx_StructField_;

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static CYTHON_INLINE int  __Pyx_GetBufferAndValidate(Py_buffer* buf, PyObject* obj, __Pyx_TypeInfo* dtype, int flags, int nd, int cast, __Pyx_BufFmt_StackElem* stack);
static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info);
static void __Pyx_RaiseBufferIndexError(int axis); /*proto*/
#define __Pyx_BufPtrStrided2d(type, buf, i0, s0, i1, s1) (type)((char*)buf + i0 * s0 + i1 * s1)
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static void __Pyx_RaiseBufferFallbackError(void); /*proto*/


static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j) {
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static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i) {
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#define __Pyx_GetItemInt(o, i, size, to_py_func) (((size) <= sizeof(Py_ssize_t)) ? \
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static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i) {
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static CYTHON_INLINE void __Pyx_ErrRestore(PyObject *type, PyObject *value, PyObject *tb); /*proto*/
static CYTHON_INLINE void __Pyx_ErrFetch(PyObject **type, PyObject **value, PyObject **tb); /*proto*/

static CYTHON_INLINE Py_ssize_t __Pyx_div_Py_ssize_t(Py_ssize_t, Py_ssize_t); /* proto */

static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index);

static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected);

static PyObject *__Pyx_UnpackItem(PyObject *, Py_ssize_t index); /*proto*/
static int __Pyx_EndUnpack(PyObject *, Py_ssize_t expected); /*proto*/

static CYTHON_INLINE PyObject* __Pyx_PyObject_Append(PyObject* L, PyObject* x) {
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    else {
        PyObject *r, *m;
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        r = PyObject_CallFunctionObjArgs(m, x, NULL);
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static int __Pyx_ArgTypeTest(PyObject *obj, PyTypeObject *type, int none_allowed,
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static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void);

static void __Pyx_UnpackTupleError(PyObject *, Py_ssize_t index); /*proto*/
#if PY_MAJOR_VERSION < 3
static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags);
static void __Pyx_ReleaseBuffer(Py_buffer *view);
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#define __Pyx_GetBuffer PyObject_GetBuffer
#define __Pyx_ReleaseBuffer PyBuffer_Release
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Py_ssize_t __Pyx_zeros[] = {0, 0};
Py_ssize_t __Pyx_minusones[] = {-1, -1};

static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list); /*proto*/

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

static CYTHON_INLINE PyObject *__Pyx_PyInt_to_py_Py_intptr_t(Py_intptr_t);

static CYTHON_INLINE Py_intptr_t __Pyx_PyInt_from_py_Py_intptr_t(PyObject *);

#if CYTHON_CCOMPLEX
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    #define __Pyx_CREAL(z) (__real__(z))
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    case 'd': return sizeof(double) * (is_complex ? 2 : 1);
    case 'g': return sizeof(long double) * (is_complex ? 2 : 1);
    case 'O': case 'P': return sizeof(void*);
    default: {
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }    
  }
}

typedef struct { char c; short x; } __Pyx_st_short;
typedef struct { char c; int x; } __Pyx_st_int;
typedef struct { char c; long x; } __Pyx_st_long;
typedef struct { char c; float x; } __Pyx_st_float;
typedef struct { char c; double x; } __Pyx_st_double;
typedef struct { char c; long double x; } __Pyx_st_longdouble;
typedef struct { char c; void *x; } __Pyx_st_void_p;
#ifdef HAVE_LONG_LONG
typedef struct { char c; PY_LONG_LONG x; } __Pyx_s_long_long;
#endif

static size_t __Pyx_BufFmt_TypeCharToAlignment(char ch, int is_complex) {
  switch (ch) {
    case '?': case 'c': case 'b': case 'B': return 1;
    case 'h': case 'H': return sizeof(__Pyx_st_short) - sizeof(short);
    case 'i': case 'I': return sizeof(__Pyx_st_int) - sizeof(int);
    case 'l': case 'L': return sizeof(__Pyx_st_long) - sizeof(long);
#ifdef HAVE_LONG_LONG
    case 'q': case 'Q': return sizeof(__Pyx_s_long_long) - sizeof(PY_LONG_LONG);
#endif
    case 'f': return sizeof(__Pyx_st_float) - sizeof(float);
    case 'd': return sizeof(__Pyx_st_double) - sizeof(double);
    case 'g': return sizeof(__Pyx_st_longdouble) - sizeof(long double);
    case 'P': case 'O': return sizeof(__Pyx_st_void_p) - sizeof(void*);
    default:
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
}

static size_t __Pyx_BufFmt_TypeCharToGroup(char ch, int is_complex) {
  switch (ch) {
    case 'c': case 'b': case 'h': case 'i': case 'l': case 'q': return 'I';
    case 'B': case 'H': case 'I': case 'L': case 'Q': return 'U';
    case 'f': case 'd': case 'g': return (is_complex ? 'C' : 'R');
    case 'O': return 'O';
    case 'P': return 'P';
    default: {
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }    
  }
}

static void __Pyx_BufFmt_RaiseExpected(__Pyx_BufFmt_Context* ctx) {
  if (ctx->head == NULL || ctx->head->field == &ctx->root) {
    const char* expected;
    const char* quote;
    if (ctx->head == NULL) {
      expected = "end";
      quote = "";
    } else {
      expected = ctx->head->field->type->name;
      quote = "'";
    }
    PyErr_Format(PyExc_ValueError,
                 "Buffer dtype mismatch, expected %s%s%s but got %s",
                 quote, expected, quote,
                 __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex));
  } else {
    __Pyx_StructField* field = ctx->head->field;
    __Pyx_StructField* parent = (ctx->head - 1)->field;
    PyErr_Format(PyExc_ValueError,
                 "Buffer dtype mismatch, expected '%s' but got %s in '%s.%s'",
                 field->type->name, __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex),
                 parent->type->name, field->name);
  }
}

static int __Pyx_BufFmt_ProcessTypeChunk(__Pyx_BufFmt_Context* ctx) {
  char group;
  size_t size, offset;
  if (ctx->enc_type == 0) return 0;
  group = __Pyx_BufFmt_TypeCharToGroup(ctx->enc_type, ctx->is_complex);
  do {
    __Pyx_StructField* field = ctx->head->field;
    __Pyx_TypeInfo* type = field->type;
  
    if (ctx->packmode == '@' || ctx->packmode == '^') {
      size = __Pyx_BufFmt_TypeCharToNativeSize(ctx->enc_type, ctx->is_complex);
    } else {
      size = __Pyx_BufFmt_TypeCharToStandardSize(ctx->enc_type, ctx->is_complex);
    }
    if (ctx->packmode == '@') {
      int align_at = __Pyx_BufFmt_TypeCharToAlignment(ctx->enc_type, ctx->is_complex);
      int align_mod_offset;
      if (align_at == 0) return -1;
      align_mod_offset = ctx->fmt_offset % align_at;
      if (align_mod_offset > 0) ctx->fmt_offset += align_at - align_mod_offset;
    }

    if (type->size != size || type->typegroup != group) {
      if (type->typegroup == 'C' && type->fields != NULL) {
        /* special case -- treat as struct rather than complex number */
        size_t parent_offset = ctx->head->parent_offset + field->offset;
        ++ctx->head;
        ctx->head->field = type->fields;
        ctx->head->parent_offset = parent_offset;
        continue;
      }
    
      __Pyx_BufFmt_RaiseExpected(ctx);
      return -1;
    }

    offset = ctx->head->parent_offset + field->offset;
    if (ctx->fmt_offset != offset) {
      PyErr_Format(PyExc_ValueError,
                   "Buffer dtype mismatch; next field is at offset %"PY_FORMAT_SIZE_T"d "
                   "but %"PY_FORMAT_SIZE_T"d expected", ctx->fmt_offset, offset);
      return -1;
    }

    ctx->fmt_offset += size;
  
    --ctx->enc_count; /* Consume from buffer string */

    /* Done checking, move to next field, pushing or popping struct stack if needed */
    while (1) {
      if (field == &ctx->root) {
        ctx->head = NULL;
        if (ctx->enc_count != 0) {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return -1;
        }
        break; /* breaks both loops as ctx->enc_count == 0 */
      }
      ctx->head->field = ++field;
      if (field->type == NULL) {
        --ctx->head;
        field = ctx->head->field;
        continue;
      } else if (field->type->typegroup == 'S') {
        size_t parent_offset = ctx->head->parent_offset + field->offset;
        if (field->type->fields->type == NULL) continue; /* empty struct */
        field = field->type->fields;
        ++ctx->head;
        ctx->head->field = field;
        ctx->head->parent_offset = parent_offset;
        break;
      } else {
        break;
      }
    }
  } while (ctx->enc_count);
  ctx->enc_type = 0;
  ctx->is_complex = 0;
  return 0;    
}

static int __Pyx_BufFmt_FirstPack(__Pyx_BufFmt_Context* ctx) {
  if (ctx->enc_type != 0 || ctx->packmode != '@') {
    PyErr_SetString(PyExc_ValueError, "Buffer packing mode currently only allowed at beginning of format string (this is a defect)");
    return -1;
  }
  return 0;
}

static const char* __Pyx_BufFmt_CheckString(__Pyx_BufFmt_Context* ctx, const char* ts) {
  int got_Z = 0;
  while (1) {
    switch(*ts) {
      case 0:
        if (ctx->enc_type != 0 && ctx->head == NULL) {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return NULL;
        }
        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
        if (ctx->head != NULL) {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return NULL;
        }
        return ts;
      case ' ':
      case 10:
      case 13:
        ++ts;
        break;
      case '<':
        if (!__Pyx_IsLittleEndian()) {
          PyErr_SetString(PyExc_ValueError, "Little-endian buffer not supported on big-endian compiler");
          return NULL;
        }
        if (__Pyx_BufFmt_FirstPack(ctx) == -1) return NULL;
        ctx->packmode = '=';
        ++ts;
        break;
      case '>':
      case '!':
        if (__Pyx_IsLittleEndian()) {
          PyErr_SetString(PyExc_ValueError, "Big-endian buffer not supported on little-endian compiler");
          return NULL;
        }
        if (__Pyx_BufFmt_FirstPack(ctx) == -1) return NULL;
        ctx->packmode = '=';
        ++ts;
        break;
      case '=':
      case '@':
      case '^':
        if (__Pyx_BufFmt_FirstPack(ctx) == -1) return NULL;
        ctx->packmode = *ts++;
        break;
      case 'T': /* substruct */
        {
          int i;
          const char* ts_after_sub;
          int struct_count = ctx->new_count;
          ctx->new_count = 1;
          ++ts;
          if (*ts != '{') {
            PyErr_SetString(PyExc_ValueError, "Buffer acquisition: Expected '{' after 'T'");
            return NULL;
          }
          ++ts;
          ts_after_sub = ts;
          for (i = 0; i != struct_count; ++i) {
            ts_after_sub = __Pyx_BufFmt_CheckString(ctx, ts);
            if (!ts_after_sub) return NULL;
          }
          ts = ts_after_sub;
        }
        break;
      case '}': /* end of substruct; either repeat or move on */
        ++ts;
        return ts;
      case 'x':
        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
        ctx->fmt_offset += ctx->new_count;
        ctx->new_count = 1;
        ctx->enc_count = 0;
        ctx->enc_type = 0;
        ++ts;
        break;
      case 'Z':
        got_Z = 1;
        ++ts;
        if (*ts != 'f' && *ts != 'd' && *ts != 'g') {
          __Pyx_BufFmt_RaiseUnexpectedChar('Z');
          return NULL;
        }        /* fall through */
      case 'c': case 'b': case 'B': case 'h': case 'H': case 'i': case 'I':
      case 'l': case 'L': case 'q': case 'Q':
      case 'f': case 'd': case 'g':
      case 'O':
        if (ctx->enc_type == *ts && got_Z == ctx->is_complex) {
          /* Continue pooling same type */
          ctx->enc_count += ctx->new_count;
        } else {
          /* New type */
          if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
          ctx->enc_count = ctx->new_count;
          ctx->enc_type = *ts;
          ctx->is_complex = got_Z;
        }
        ++ts;
        ctx->new_count = 1;
        got_Z = 0;
        break;
      default:
        {
          ctx->new_count = __Pyx_BufFmt_ParseNumber(&ts);
          if (ctx->new_count == -1) { /* First char was not a digit */
            char msg[2] = { *ts, 0 };
            PyErr_Format(PyExc_ValueError,
                         "Does not understand character buffer dtype format string ('%s')", msg);
            return NULL;
          }
        }
      
    }
  }
}

static CYTHON_INLINE void __Pyx_ZeroBuffer(Py_buffer* buf) {
  buf->buf = NULL;
  buf->obj = NULL;
  buf->strides = __Pyx_zeros;
  buf->shape = __Pyx_zeros;
  buf->suboffsets = __Pyx_minusones;
}

static CYTHON_INLINE int __Pyx_GetBufferAndValidate(Py_buffer* buf, PyObject* obj, __Pyx_TypeInfo* dtype, int flags, int nd, int cast, __Pyx_BufFmt_StackElem* stack) {
  if (obj == Py_None) {
    __Pyx_ZeroBuffer(buf);
    return 0;
  }
  buf->buf = NULL;
  if (__Pyx_GetBuffer(obj, buf, flags) == -1) goto fail;
  if (buf->ndim != nd) {
    PyErr_Format(PyExc_ValueError,
                 "Buffer has wrong number of dimensions (expected %d, got %d)",
                 nd, buf->ndim);
    goto fail;
  }
  if (!cast) {
    __Pyx_BufFmt_Context ctx;
    __Pyx_BufFmt_Init(&ctx, stack, dtype);
    if (!__Pyx_BufFmt_CheckString(&ctx, buf->format)) goto fail;
  }
  if ((unsigned)buf->itemsize != dtype->size) {
    PyErr_Format(PyExc_ValueError,
      "Item size of buffer (%"PY_FORMAT_SIZE_T"d byte%s) does not match size of '%s' (%"PY_FORMAT_SIZE_T"d byte%s)",
      buf->itemsize, (buf->itemsize > 1) ? "s" : "",
      dtype->name,
      dtype->size, (dtype->size > 1) ? "s" : "");
    goto fail;
  }
  if (buf->suboffsets == NULL) buf->suboffsets = __Pyx_minusones;
  return 0;
fail:;
  __Pyx_ZeroBuffer(buf);
  return -1;
}

static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info) {
  if (info->buf == NULL) return;
  if (info->suboffsets == __Pyx_minusones) info->suboffsets = NULL;
  __Pyx_ReleaseBuffer(info);
}
static void __Pyx_RaiseBufferIndexError(int axis) {
  PyErr_Format(PyExc_IndexError,
     "Out of bounds on buffer access (axis %d)", axis);
}


static void __Pyx_RaiseBufferFallbackError(void) {
  PyErr_Format(PyExc_ValueError,
     "Buffer acquisition failed on assignment; and then reacquiring the old buffer failed too!");
}



static CYTHON_INLINE void __Pyx_ErrRestore(PyObject *type, PyObject *value, PyObject *tb) {
    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);
}

static CYTHON_INLINE void __Pyx_ErrFetch(PyObject **type, PyObject **value, PyObject **tb) {
    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;
}


static CYTHON_INLINE Py_ssize_t __Pyx_div_Py_ssize_t(Py_ssize_t a, Py_ssize_t b) {
    Py_ssize_t q = a / b;
    Py_ssize_t r = a - q*b;
    q -= ((r != 0) & ((r ^ b) < 0));
    return q;
}

static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index) {
    PyErr_Format(PyExc_ValueError,
        #if PY_VERSION_HEX < 0x02050000
                 "need more than %d value%s to unpack", (int)index,
        #else
                 "need more than %zd value%s to unpack", index,
        #endif
                 (index == 1) ? "" : "s");
}

static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected) {
    PyErr_Format(PyExc_ValueError,
        #if PY_VERSION_HEX < 0x02050000
            "too many values to unpack (expected %d)", (int)expected);
        #else
            "too many values to unpack (expected %zd)", expected);
        #endif
}

static PyObject *__Pyx_UnpackItem(PyObject *iter, Py_ssize_t index) {
    PyObject *item;
    if (!(item = PyIter_Next(iter))) {
        if (!PyErr_Occurred()) {
            __Pyx_RaiseNeedMoreValuesError(index);
        }
    }
    return item;
}

static int __Pyx_EndUnpack(PyObject *iter, Py_ssize_t expected) {
    PyObject *item;
    if ((item = PyIter_Next(iter))) {
        Py_DECREF(item);
        __Pyx_RaiseTooManyValuesError(expected);
        return -1;
    }
    else if (!PyErr_Occurred())
        return 0;
    else
        return -1;
}

static int __Pyx_ArgTypeTest(PyObject *obj, PyTypeObject *type, int none_allowed,
    const char *name, int exact)
{
    if (!type) {
        PyErr_Format(PyExc_SystemError, "Missing type object");
        return 0;
    }
    if (none_allowed && obj == Py_None) return 1;
    else if (exact) {
        if (Py_TYPE(obj) == type) return 1;
    }
    else {
        if (PyObject_TypeCheck(obj, type)) return 1;
    }
    PyErr_Format(PyExc_TypeError,
        "Argument '%s' has incorrect type (expected %s, got %s)",
        name, type->tp_name, Py_TYPE(obj)->tp_name);
    return 0;
}

static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void) {
    PyErr_SetString(PyExc_TypeError, "'NoneType' object is not iterable");
}

static void __Pyx_UnpackTupleError(PyObject *t, Py_ssize_t index) {
    if (t == Py_None) {
      __Pyx_RaiseNoneNotIterableError();
    } else if (PyTuple_GET_SIZE(t) < index) {
      __Pyx_RaiseNeedMoreValuesError(PyTuple_GET_SIZE(t));
    } else {
      __Pyx_RaiseTooManyValuesError(index);
    }
}

#if PY_MAJOR_VERSION < 3
static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags) {
  #if PY_VERSION_HEX >= 0x02060000
  if (Py_TYPE(obj)->tp_flags & Py_TPFLAGS_HAVE_NEWBUFFER)
      return PyObject_GetBuffer(obj, view, flags);
  #endif
  if (PyObject_TypeCheck(obj, __pyx_ptype_5numpy_ndarray)) return __pyx_pf_5numpy_7ndarray___getbuffer__(obj, view, flags);
  else {
  PyErr_Format(PyExc_TypeError, "'%100s' does not have the buffer interface", Py_TYPE(obj)->tp_name);
  return -1;
    }
}

static void __Pyx_ReleaseBuffer(Py_buffer *view) {
  PyObject* obj = view->obj;
  if (obj) {
if (PyObject_TypeCheck(obj, __pyx_ptype_5numpy_ndarray)) __pyx_pf_5numpy_7ndarray___releasebuffer__(obj, view);
    Py_DECREF(obj);
    view->obj = NULL;
  }
}

#endif

static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list) {
    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;
    module = PyObject_CallFunctionObjArgs(py_import,
        name, global_dict, empty_dict, list, NULL);
bad:
    Py_XDECREF(empty_list);
    Py_XDECREF(py_import);
    Py_XDECREF(empty_dict);
    return module;
}

#if PY_MAJOR_VERSION < 3
static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb) {
    Py_XINCREF(type);
    Py_XINCREF(value);
    Py_XINCREF(tb);
    /* First, check the traceback argument, replacing None with NULL. */
    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;
    }
    /* Next, replace a missing value with None */
    if (value == NULL) {
        value = Py_None;
        Py_INCREF(value);
    }
    #if PY_VERSION_HEX < 0x02050000
    if (!PyClass_Check(type))
    #else
    if (!PyType_Check(type))
    #endif
    {
        /* Raising an instance.  The value should be a dummy. */
        if (value != Py_None) {
            PyErr_SetString(PyExc_TypeError,
                "instance exception may not have a separate value");
            goto raise_error;
        }
        /* Normalize to raise <class>, <instance> */
        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) {
    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;
    }

    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 CYTHON_INLINE PyObject *__Pyx_PyInt_to_py_Py_intptr_t(Py_intptr_t val) {
    const Py_intptr_t neg_one = (Py_intptr_t)-1, const_zero = (Py_intptr_t)0;
    const int is_unsigned = const_zero < neg_one;
    if ((sizeof(Py_intptr_t) == sizeof(char))  ||
        (sizeof(Py_intptr_t) == sizeof(short))) {
        return PyInt_FromLong((long)val);
    } else if ((sizeof(Py_intptr_t) == sizeof(int)) ||
               (sizeof(Py_intptr_t) == sizeof(long))) {
        if (is_unsigned)
            return PyLong_FromUnsignedLong((unsigned long)val);
        else
            return PyInt_FromLong((long)val);
    } else if (sizeof(Py_intptr_t) == sizeof(PY_LONG_LONG)) {
        if (is_unsigned)
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG)val);
        else
            return PyLong_FromLongLong((PY_LONG_LONG)val);
    } else {
        int one = 1; int little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&val;
        return _PyLong_FromByteArray(bytes, sizeof(Py_intptr_t), 
                                     little, !is_unsigned);
    }
}

static CYTHON_INLINE Py_intptr_t __Pyx_PyInt_from_py_Py_intptr_t(PyObject* x) {
    const Py_intptr_t neg_one = (Py_intptr_t)-1, const_zero = (Py_intptr_t)0;
    const int is_unsigned = const_zero < neg_one;
    if (sizeof(Py_intptr_t) == sizeof(char)) {
        if (is_unsigned)
            return (Py_intptr_t)__Pyx_PyInt_AsUnsignedChar(x);
        else
            return (Py_intptr_t)__Pyx_PyInt_AsSignedChar(x);
    } else if (sizeof(Py_intptr_t) == sizeof(short)) {
        if (is_unsigned)
            return (Py_intptr_t)__Pyx_PyInt_AsUnsignedShort(x);
        else
            return (Py_intptr_t)__Pyx_PyInt_AsSignedShort(x);
    } else if (sizeof(Py_intptr_t) == sizeof(int)) {
        if (is_unsigned)
            return (Py_intptr_t)__Pyx_PyInt_AsUnsignedInt(x);
        else
            return (Py_intptr_t)__Pyx_PyInt_AsSignedInt(x);
    } else if (sizeof(Py_intptr_t) == sizeof(long)) {
        if (is_unsigned)
            return (Py_intptr_t)__Pyx_PyInt_AsUnsignedLong(x);
        else
            return (Py_intptr_t)__Pyx_PyInt_AsSignedLong(x);
    } else if (sizeof(Py_intptr_t) == sizeof(PY_LONG_LONG)) {
        if (is_unsigned)
            return (Py_intptr_t)__Pyx_PyInt_AsUnsignedLongLong(x);
        else
            return (Py_intptr_t)__Pyx_PyInt_AsSignedLongLong(x);
    }  else {
        Py_intptr_t val;
        PyObject *v = __Pyx_PyNumber_Int(x);
        #if PY_VERSION_HEX < 0x03000000
        if (likely(v) && !PyLong_Check(v)) {
            PyObject *tmp = v;
            v = PyNumber_Long(tmp);
            Py_DECREF(tmp);
        }
        #endif
        if (likely(v)) {
            int one = 1; int is_little = (int)*(unsigned char *)&one;
            unsigned char *bytes = (unsigned char *)&val;
            int ret = _PyLong_AsByteArray((PyLongObject *)v,
                                          bytes, sizeof(val),
                                          is_little, !is_unsigned);
            Py_DECREF(v);
            if (likely(!ret))
                return val;
        }
        return (Py_intptr_t)-1;
    }
}

#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;
    }
/*
    static CYTHON_INLINE float __Pyx_c_absf(__pyx_t_float_complex z) {
#if HAVE_HYPOT
        return hypotf(z.real, z.imag);
#else
        return sqrtf(z.real*z.real + z.imag*z.imag);
#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;
    }
/*
    static CYTHON_INLINE double __Pyx_c_abs(__pyx_t_double_complex z) {
#if HAVE_HYPOT
        return hypot(z.real, z.imag);
#else
        return sqrt(z.real*z.real + z.imag*z.imag);
#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 PyLong_AsUnsignedLong(x);
        } else {
            return 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 PyLong_AsUnsignedLongLong(x);
        } else {
            return 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 PyLong_AsUnsignedLong(x);
        } else {
            return 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 PyLong_AsUnsignedLongLong(x);
        } else {
            return 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 PyLong_AsUnsignedLong(x);
        } else {
            return 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 PyLong_AsUnsignedLongLong(x);
        } else {
            return 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;
    }
}

#ifndef __PYX_HAVE_RT_ImportType
#define __PYX_HAVE_RT_ImportType
static PyTypeObject *__Pyx_ImportType(const char *module_name, const char *class_name,
    long 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;
    #if PY_MAJOR_VERSION < 3
    py_name = PyString_FromString(class_name);
    #else
    py_name = PyUnicode_FromString(class_name);
    #endif
    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 && ((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
        PyErr_Warn(NULL, warning);
        #else
        PyErr_WarnEx(NULL, warning, 0);
        #endif
    }
    else if (((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 0;
}
#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;

    #if PY_MAJOR_VERSION < 3
    py_name = PyString_FromString(name);
    #else
    py_name = PyUnicode_FromString(name);
    #endif
    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

#include "compile.h"
#include "frameobject.h"
#include "traceback.h"

static void __Pyx_AddTraceback(const char *funcname) {
    PyObject *py_srcfile = 0;
    PyObject *py_funcname = 0;
    PyObject *py_globals = 0;
    PyCodeObject *py_code = 0;
    PyFrameObject *py_frame = 0;

    #if PY_MAJOR_VERSION < 3
    py_srcfile = PyString_FromString(__pyx_filename);
    #else
    py_srcfile = PyUnicode_FromString(__pyx_filename);
    #endif
    if (!py_srcfile) goto bad;
    if (__pyx_clineno) {
        #if PY_MAJOR_VERSION < 3
        py_funcname = PyString_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, __pyx_clineno);
        #else
        py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, __pyx_clineno);
        #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_globals = PyModule_GetDict(__pyx_m);
    if (!py_globals) goto bad;
    py_code = PyCode_New(
        0,            /*int argcount,*/
        #if PY_MAJOR_VERSION >= 3
        0,            /*int kwonlyargcount,*/
        #endif
        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,*/
        __pyx_lineno,   /*int firstlineno,*/
        __pyx_empty_bytes  /*PyObject *lnotab*/
    );
    if (!py_code) 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 = __pyx_lineno;
    PyTraceBack_Here(py_frame);
bad:
    Py_XDECREF(py_srcfile);
    Py_XDECREF(py_funcname);
    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 */
