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#define __Pyx_PyString_FormatSafe(a, b)   ((unlikely((a) == Py_None)) ? PyNumber_Remainder(a, b) : __Pyx_PyString_Format(a, b))
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#if PY_MAJOR_VERSION >= 3
  #define __Pyx_PyBaseString_Check(obj) PyUnicode_Check(obj)
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  #define __Pyx_PyBaseString_Check(obj) (PyString_Check(obj) || PyUnicode_Check(obj))
  #define __Pyx_PyBaseString_CheckExact(obj) (PyString_CheckExact(obj) || PyUnicode_CheckExact(obj))
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#define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type)
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  #define PyIntObject                  PyLongObject
  #define PyInt_Type                   PyLong_Type
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  #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
  #define PyNumber_Int                 PyNumber_Long
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#if PY_MAJOR_VERSION >= 3
  #define PyBoolObject                 PyLongObject
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#if PY_MAJOR_VERSION >= 3 && CYTHON_COMPILING_IN_PYPY
  #ifndef PyUnicode_InternFromString
    #define PyUnicode_InternFromString(s) PyUnicode_FromString(s)
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#if PY_VERSION_HEX < 0x030200A4
  typedef long Py_hash_t;
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  #define __Pyx_PyInt_AsHash_t   PyInt_AsLong
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  #define __Pyx_PyInt_FromHash_t PyInt_FromSsize_t
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#if PY_MAJOR_VERSION >= 3
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  #define __Pyx_PyMethod_New(func, self, klass) PyMethod_New(func, self, klass)
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#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
#ifndef CYTHON_RESTRICT
  #if defined(__GNUC__)
    #define CYTHON_RESTRICT __restrict__
  #elif defined(_MSC_VER) && _MSC_VER >= 1400
    #define CYTHON_RESTRICT __restrict
  #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
    #define CYTHON_RESTRICT restrict
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    #define CYTHON_RESTRICT
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#endif
#ifdef NAN
#define __PYX_NAN() ((float) NAN)
#else
static CYTHON_INLINE float __PYX_NAN() {
  /* Initialize NaN. The sign is irrelevant, an exponent with all bits 1 and
   a nonzero mantissa means NaN. If the first bit in the mantissa is 1, it is
   a quiet NaN. */
  float value;
  memset(&value, 0xFF, sizeof(value));
  return value;
}
#endif
#ifdef __cplusplus
template<typename T>
void __Pyx_call_destructor(T* x) {
    x->~T();
}
#endif


#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
  #ifdef __cplusplus
    #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__dipy__tracking__propspeed
#define __PYX_HAVE_API__dipy__tracking__propspeed
#include "string.h"
#include "stdio.h"
#include "stdlib.h"
#include "numpy/arrayobject.h"
#include "numpy/ufuncobject.h"
#include "dpy_math.h"
#ifdef _OPENMP
#include <omp.h>
#endif /* _OPENMP */

#ifdef PYREX_WITHOUT_ASSERTIONS
#define CYTHON_WITHOUT_ASSERTIONS
#endif

#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 Py_ssize_t n; const char* encoding;
                const char is_unicode; const char is_str; const char intern; } __Pyx_StringTabEntry;

#define __PYX_DEFAULT_STRING_ENCODING_IS_ASCII 0
#define __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT 0
#define __PYX_DEFAULT_STRING_ENCODING ""
#define __Pyx_PyObject_FromString __Pyx_PyBytes_FromString
#define __Pyx_PyObject_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
#define __Pyx_fits_Py_ssize_t(v, type, is_signed)  (    \
    (sizeof(type) < sizeof(Py_ssize_t))  ||             \
    (sizeof(type) > sizeof(Py_ssize_t) &&               \
          likely(v < (type)PY_SSIZE_T_MAX ||            \
                 v == (type)PY_SSIZE_T_MAX)  &&         \
          (!is_signed || likely(v > (type)PY_SSIZE_T_MIN ||       \
                                v == (type)PY_SSIZE_T_MIN)))  ||  \
    (sizeof(type) == sizeof(Py_ssize_t) &&              \
          (is_signed || likely(v < (type)PY_SSIZE_T_MAX ||        \
                               v == (type)PY_SSIZE_T_MAX)))  )
static CYTHON_INLINE char* __Pyx_PyObject_AsString(PyObject*);
static CYTHON_INLINE char* __Pyx_PyObject_AsStringAndSize(PyObject*, Py_ssize_t* length);
#define __Pyx_PyByteArray_FromString(s) PyByteArray_FromStringAndSize((const char*)s, strlen((const char*)s))
#define __Pyx_PyByteArray_FromStringAndSize(s, l) PyByteArray_FromStringAndSize((const char*)s, l)
#define __Pyx_PyBytes_FromString        PyBytes_FromString
#define __Pyx_PyBytes_FromStringAndSize PyBytes_FromStringAndSize
static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char*);
#if PY_MAJOR_VERSION < 3
    #define __Pyx_PyStr_FromString        __Pyx_PyBytes_FromString
    #define __Pyx_PyStr_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
#else
    #define __Pyx_PyStr_FromString        __Pyx_PyUnicode_FromString
    #define __Pyx_PyStr_FromStringAndSize __Pyx_PyUnicode_FromStringAndSize
#endif
#define __Pyx_PyObject_AsSString(s)    ((signed char*) __Pyx_PyObject_AsString(s))
#define __Pyx_PyObject_AsUString(s)    ((unsigned char*) __Pyx_PyObject_AsString(s))
#define __Pyx_PyObject_FromUString(s)  __Pyx_PyObject_FromString((const char*)s)
#define __Pyx_PyBytes_FromUString(s)   __Pyx_PyBytes_FromString((const char*)s)
#define __Pyx_PyByteArray_FromUString(s)   __Pyx_PyByteArray_FromString((const char*)s)
#define __Pyx_PyStr_FromUString(s)     __Pyx_PyStr_FromString((const char*)s)
#define __Pyx_PyUnicode_FromUString(s) __Pyx_PyUnicode_FromString((const char*)s)
#if PY_MAJOR_VERSION < 3
static CYTHON_INLINE size_t __Pyx_Py_UNICODE_strlen(const Py_UNICODE *u)
{
    const Py_UNICODE *u_end = u;
    while (*u_end++) ;
    return (size_t)(u_end - u - 1);
}
#else
#define __Pyx_Py_UNICODE_strlen Py_UNICODE_strlen
#endif
#define __Pyx_PyUnicode_FromUnicode(u)       PyUnicode_FromUnicode(u, __Pyx_Py_UNICODE_strlen(u))
#define __Pyx_PyUnicode_FromUnicodeAndLength PyUnicode_FromUnicode
#define __Pyx_PyUnicode_AsUnicode            PyUnicode_AsUnicode
#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);
#if CYTHON_COMPILING_IN_CPYTHON
#define __pyx_PyFloat_AsDouble(x) (PyFloat_CheckExact(x) ? PyFloat_AS_DOUBLE(x) : PyFloat_AsDouble(x))
#else
#define __pyx_PyFloat_AsDouble(x) PyFloat_AsDouble(x)
#endif
#define __pyx_PyFloat_AsFloat(x) ((float) __pyx_PyFloat_AsDouble(x))
#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
static int __Pyx_sys_getdefaultencoding_not_ascii;
static int __Pyx_init_sys_getdefaultencoding_params(void) {
    PyObject* sys;
    PyObject* default_encoding = NULL;
    PyObject* ascii_chars_u = NULL;
    PyObject* ascii_chars_b = NULL;
    const char* default_encoding_c;
    sys = PyImport_ImportModule("sys");
    if (!sys) goto bad;
    default_encoding = PyObject_CallMethod(sys, (char*) (const char*) "getdefaultencoding", NULL);
    Py_DECREF(sys);
    if (!default_encoding) goto bad;
    default_encoding_c = PyBytes_AsString(default_encoding);
    if (!default_encoding_c) goto bad;
    if (strcmp(default_encoding_c, "ascii") == 0) {
        __Pyx_sys_getdefaultencoding_not_ascii = 0;
    } else {
        char ascii_chars[128];
        int c;
        for (c = 0; c < 128; c++) {
            ascii_chars[c] = c;
        }
        __Pyx_sys_getdefaultencoding_not_ascii = 1;
        ascii_chars_u = PyUnicode_DecodeASCII(ascii_chars, 128, NULL);
        if (!ascii_chars_u) goto bad;
        ascii_chars_b = PyUnicode_AsEncodedString(ascii_chars_u, default_encoding_c, NULL);
        if (!ascii_chars_b || !PyBytes_Check(ascii_chars_b) || memcmp(ascii_chars, PyBytes_AS_STRING(ascii_chars_b), 128) != 0) {
            PyErr_Format(
                PyExc_ValueError,
                "This module compiled with c_string_encoding=ascii, but default encoding '%.200s' is not a superset of ascii.",
                default_encoding_c);
            goto bad;
        }
        Py_DECREF(ascii_chars_u);
        Py_DECREF(ascii_chars_b);
    }
    Py_DECREF(default_encoding);
    return 0;
bad:
    Py_XDECREF(default_encoding);
    Py_XDECREF(ascii_chars_u);
    Py_XDECREF(ascii_chars_b);
    return -1;
}
#endif
#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT && PY_MAJOR_VERSION >= 3
#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_DecodeUTF8(c_str, size, NULL)
#else
#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_Decode(c_str, size, __PYX_DEFAULT_STRING_ENCODING, NULL)
#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
static char* __PYX_DEFAULT_STRING_ENCODING;
static int __Pyx_init_sys_getdefaultencoding_params(void) {
    PyObject* sys;
    PyObject* default_encoding = NULL;
    char* default_encoding_c;
    sys = PyImport_ImportModule("sys");
    if (!sys) goto bad;
    default_encoding = PyObject_CallMethod(sys, (char*) (const char*) "getdefaultencoding", NULL);
    Py_DECREF(sys);
    if (!default_encoding) goto bad;
    default_encoding_c = PyBytes_AsString(default_encoding);
    if (!default_encoding_c) goto bad;
    __PYX_DEFAULT_STRING_ENCODING = (char*) malloc(strlen(default_encoding_c));
    if (!__PYX_DEFAULT_STRING_ENCODING) goto bad;
    strcpy(__PYX_DEFAULT_STRING_ENCODING, default_encoding_c);
    Py_DECREF(default_encoding);
    return 0;
bad:
    Py_XDECREF(default_encoding);
    return -1;
}
#endif
#endif


/* Test for GCC > 2.95 */
#if defined(__GNUC__)     && (__GNUC__ > 2 || (__GNUC__ == 2 && (__GNUC_MINOR__ > 95)))
  #define likely(x)   __builtin_expect(!!(x), 1)
  #define unlikely(x) __builtin_expect(!!(x), 0)
#else /* !__GNUC__ or GCC < 2.95 */
  #define likely(x)   (x)
  #define unlikely(x) (x)
#endif /* __GNUC__ */

static PyObject *__pyx_m;
static PyObject *__pyx_d;
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[] = {
  "dipy/tracking/propspeed.pyx",
  "__init__.pxd",
  "type.pxd",
};
#define IS_UNSIGNED(type) (((type) -1) > 0)
struct __Pyx_StructField_;
#define __PYX_BUF_FLAGS_PACKED_STRUCT (1 << 0)
typedef struct {
  const char* name;
  struct __Pyx_StructField_* fields;
  size_t size;
  size_t arraysize[8];
  int ndim;
  char typegroup;
  char is_unsigned;
  int flags;
} __Pyx_TypeInfo;
typedef struct __Pyx_StructField_ {
  __Pyx_TypeInfo* type;
  const char* name;
  size_t offset;
} __Pyx_StructField;
typedef struct {
  __Pyx_StructField* field;
  size_t parent_offset;
} __Pyx_BufFmt_StackElem;
typedef struct {
  __Pyx_StructField root;
  __Pyx_BufFmt_StackElem* head;
  size_t fmt_offset;
  size_t new_count, enc_count;
  size_t struct_alignment;
  int is_complex;
  char enc_type;
  char new_packmode;
  char enc_packmode;
  char is_valid_array;
} __Pyx_BufFmt_Context;


/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":723
 * # 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;

/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":724
 * 
 * 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;

/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":725
 * 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;

/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":726
 * 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;

/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":730
 * #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;

/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":731
 * 
 * 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;

/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":732
 * ctypedef npy_uint8      uint8_t
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 * ctypedef npy_uint32     uint32_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uint64     uint64_t
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typedef npy_uint32 __pyx_t_5numpy_uint32_t;

/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":733
 * ctypedef npy_uint16     uint16_t
 * ctypedef npy_uint32     uint32_t
 * ctypedef npy_uint64     uint64_t             # <<<<<<<<<<<<<<
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typedef npy_uint64 __pyx_t_5numpy_uint64_t;

/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":737
 * #ctypedef npy_uint128    uint128_t
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typedef npy_float32 __pyx_t_5numpy_float32_t;

/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":738
 * 
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":747
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":748
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":749
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":751
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":752
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typedef npy_ulonglong __pyx_t_5numpy_ulong_t;

/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":753
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":755
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":756
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":758
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":759
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":760
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":763
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":764
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typedef npy_clongdouble __pyx_t_5numpy_clongdouble_t;

/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":766
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static void __Pyx_RaiseDoubleKeywordsError(const char* func_name, PyObject* kw_name);

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static CYTHON_INLINE int __Pyx_ArgTypeTest(PyObject *obj, PyTypeObject *type, int none_allowed,
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static CYTHON_INLINE int __Pyx_SetItemInt_Fast(PyObject *o, Py_ssize_t i, PyObject *v,
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static CYTHON_INLINE PyObject *__Pyx_GetModuleGlobalName(PyObject *name);

static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected);

static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index);

static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void);

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static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *);

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static PyTypeObject *__Pyx_ImportType(const char *module_name, const char *class_name, size_t size, int strict);

static int __Pyx_InitStrings(__Pyx_StringTabEntry *t);


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/* Module declarations from 'cpython.type' */
static PyTypeObject *__pyx_ptype_7cpython_4type_type = 0;

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

/* Module declarations from 'numpy' */

/* Module declarations from 'numpy' */
static PyTypeObject *__pyx_ptype_5numpy_dtype = 0;
static PyTypeObject *__pyx_ptype_5numpy_flatiter = 0;
static PyTypeObject *__pyx_ptype_5numpy_broadcast = 0;
static PyTypeObject *__pyx_ptype_5numpy_ndarray = 0;
static PyTypeObject *__pyx_ptype_5numpy_ufunc = 0;
static CYTHON_INLINE char *__pyx_f_5numpy__util_dtypestring(PyArray_Descr *, char *, char *, int *); /*proto*/

/* Module declarations from 'cython' */

/* Module declarations from 'dipy.tracking.propspeed' */
static npy_intp __pyx_f_4dipy_8tracking_9propspeed__propagation_direction(double *, double *, double *, double *, double *, double, double, npy_intp *, npy_intp *, double *, double); /*proto*/
static npy_intp __pyx_f_4dipy_8tracking_9propspeed_offset(npy_intp *, npy_intp *, int, int); /*proto*/
static void __pyx_f_4dipy_8tracking_9propspeed__trilinear_interpolation_iso(double *, double *, npy_intp *); /*proto*/
static npy_intp __pyx_f_4dipy_8tracking_9propspeed__nearest_direction(double *, double *, double *, npy_intp, double *, double, double, double *); /*proto*/
static npy_intp __pyx_f_4dipy_8tracking_9propspeed__initial_direction(double *, double *, double *, double *, double, npy_intp *, npy_intp, double *); /*proto*/
static __Pyx_TypeInfo __Pyx_TypeInfo_nn_npy_intp = { "npy_intp", NULL, sizeof(npy_intp), { 0 }, 0, IS_UNSIGNED(npy_intp) ? 'U' : 'I', IS_UNSIGNED(npy_intp), 0 };
static __Pyx_TypeInfo __Pyx_TypeInfo_double = { "double", NULL, sizeof(double), { 0 }, 0, 'R', 0, 0 };
#define __Pyx_MODULE_NAME "dipy.tracking.propspeed"
int __pyx_module_is_main_dipy__tracking__propspeed = 0;

/* Implementation of 'dipy.tracking.propspeed' */
static PyObject *__pyx_builtin_ValueError;
static PyObject *__pyx_builtin_range;
static PyObject *__pyx_builtin_RuntimeError;
static PyObject *__pyx_pf_4dipy_8tracking_9propspeed_ndarray_offset(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_indices, PyArrayObject *__pyx_v_strides, int __pyx_v_lenind, int __pyx_v_typesize); /* proto */
static PyObject *__pyx_pf_4dipy_8tracking_9propspeed_2map_coordinates_trilinear_iso(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_data, PyArrayObject *__pyx_v_points, PyArrayObject *__pyx_v_data_strides, npy_intp __pyx_v_len_points, PyArrayObject *__pyx_v_result); /* proto */
static PyObject *__pyx_pf_4dipy_8tracking_9propspeed_4eudx_both_directions(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_seed, npy_intp __pyx_v_ref, PyArrayObject *__pyx_v_qa, PyArrayObject *__pyx_v_ind, PyArrayObject *__pyx_v_odf_vertices, double __pyx_v_qa_thr, double __pyx_v_ang_thr, double __pyx_v_step_sz, double __pyx_v_total_weight, npy_intp __pyx_v_max_points); /* 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_B[] = "B";
static char __pyx_k_H[] = "H";
static char __pyx_k_I[] = "I";
static char __pyx_k_L[] = "L";
static char __pyx_k_O[] = "O";
static char __pyx_k_Q[] = "Q";
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_j[] = "j";
static char __pyx_k_l[] = "l";
static char __pyx_k_q[] = "q";
static char __pyx_k_w[] = "w";
static char __pyx_k_Zd[] = "Zd";
static char __pyx_k_Zf[] = "Zf";
static char __pyx_k_Zg[] = "Zg";
static char __pyx_k_ds[] = "ds";
static char __pyx_k_dx[] = "dx";
static char __pyx_k_np[] = "np";
static char __pyx_k_ps[] = "ps";
static char __pyx_k_qa[] = "qa";
static char __pyx_k_rs[] = "rs";
static char __pyx_k_cnt[] = "cnt";
static char __pyx_k_ind[] = "ind";
static char __pyx_k_off[] = "off";
static char __pyx_k_pin[] = "pin";
static char __pyx_k_pqa[] = "pqa";
static char __pyx_k_ps2[] = "ps2";
static char __pyx_k_ref[] = "ref";
static char __pyx_k_tmp[] = "tmp";
static char __pyx_k_copy[] = "copy";
static char __pyx_k_data[] = "data";
static char __pyx_k_ftmp[] = "ftmp";
static char __pyx_k_main[] = "__main__";
static char __pyx_k_pstr[] = "pstr";
static char __pyx_k_seed[] = "seed";
static char __pyx_k_test[] = "__test__";
static char __pyx_k_array[] = "array";
static char __pyx_k_dtype[] = "dtype";
static char __pyx_k_index[] = "index";
static char __pyx_k_numpy[] = "numpy";
static char __pyx_k_point[] = "point";
static char __pyx_k_pvstr[] = "pvstr";
static char __pyx_k_range[] = "range";
static char __pyx_k_track[] = "track";
static char __pyx_k_value[] = "value";
static char __pyx_k_import[] = "__import__";
static char __pyx_k_lenind[] = "lenind";
static char __pyx_k_points[] = "points";
static char __pyx_k_pverts[] = "pverts";
static char __pyx_k_qa_thr[] = "qa_thr";
static char __pyx_k_result[] = "result";
static char __pyx_k_values[] = "values";
static char __pyx_k_weight[] = "weight";
static char __pyx_k_ang_thr[] = "ang_thr";
static char __pyx_k_float32[] = "float32";
static char __pyx_k_indices[] = "indices";
static char __pyx_k_step_sz[] = "step_sz";
static char __pyx_k_strides[] = "strides";
static char __pyx_k_qa_shape[] = "qa_shape";
static char __pyx_k_typesize[] = "typesize";
static char __pyx_k_direction[] = "direction";
static char __pyx_k_tmp_track[] = "tmp_track";
static char __pyx_k_ValueError[] = "ValueError";
static char __pyx_k_idirection[] = "idirection";
static char __pyx_k_len_points[] = "len_points";
static char __pyx_k_max_points[] = "max_points";
static char __pyx_k_RuntimeError[] = "RuntimeError";
static char __pyx_k_data_strides[] = "data_strides";
static char __pyx_k_odf_vertices[] = "odf_vertices";
static char __pyx_k_total_weight[] = "total_weight";
static char __pyx_k_ndarray_offset[] = "ndarray_offset";
static char __pyx_k_eudx_both_directions[] = "eudx_both_directions";
static char __pyx_k_ndarray_offset_line_57[] = "ndarray_offset (line 57)";
static char __pyx_k_qa_is_not_C_contiguous[] = "qa is not C contiguous";
static char __pyx_k_dipy_tracking_propspeed[] = "dipy.tracking.propspeed";
static char __pyx_k_ind_is_not_C_contiguous[] = "ind is not C contiguous";
static char __pyx_k_data_is_not_C_contiguous[] = "data is not C contiguous";
static char __pyx_k_seed_is_not_C_contiguous[] = "seed is not C contiguous";
static char __pyx_k_points_is_not_C_contiguous[] = "points is not C contiguous";
static char __pyx_k_result_is_not_C_contiguous[] = "result is not C contiguous";
static char __pyx_k_indices_is_not_C_contiguous[] = "indices is not C contiguous";
static char __pyx_k_ndarray_is_not_C_contiguous[] = "ndarray is not C contiguous";
static char __pyx_k_strides_is_not_C_contiguous[] = "strides is not C contiguous";
static char __pyx_k_map_coordinates_trilinear_iso[] = "map_coordinates_trilinear_iso";
static char __pyx_k_Find_offset_in_an_N_dimensional[] = " Find offset in an N-dimensional ndarray using strides\n\n    Parameters\n    ----------\n    indices : array, npy_intp shape (N,)\n        Indices of the array which we want to find the offset.\n    strides : array, shape (N,)\n        Strides of array.\n    lenind : int\n        len of the `indices` array.\n    typesize : int\n        Number of bytes for data type e.g. if 8 for double, 4 for int32\n\n    Returns\n    -------\n    offset : integer\n        Index position in flattened array\n\n    Examples\n    --------\n    >>> import numpy as np\n    >>> from dipy.tracking.propspeed import ndarray_offset\n    >>> I=np.array([1,1])\n    >>> A=np.array([[1,0,0],[0,2,0],[0,0,3]])\n    >>> S=np.array(A.strides)\n    >>> ndarray_offset(I,S,2,A.dtype.itemsize)\n    4\n    >>> A.ravel()[4]==A[1,1]\n    True\n    ";
static char __pyx_k_Track_propagation_performance_f[] = " Track propagation performance functions\n";
static char __pyx_k_home_eleftherios_Devel_dipy_dip[] = "/home/eleftherios/Devel/dipy/dipy/tracking/propspeed.pyx";
static char __pyx_k_unknown_dtype_code_in_numpy_pxd[] = "unknown dtype code in numpy.pxd (%d)";
static char __pyx_k_Format_string_allocated_too_shor[] = "Format string allocated too short, see comment in numpy.pxd";
static char __pyx_k_Non_native_byte_order_not_suppor[] = "Non-native byte order not supported";
static char __pyx_k_data_strides_is_not_C_contiguous[] = "data_strides is not C contiguous";
static char __pyx_k_ndarray_is_not_Fortran_contiguou[] = "ndarray is not Fortran contiguous";
static char __pyx_k_odf_vertices_is_not_C_contiguous[] = "odf_vertices is not C contiguous";
static char __pyx_k_Format_string_allocated_too_shor_2[] = "Format string allocated too short.";
static PyObject *__pyx_kp_u_Find_offset_in_an_N_dimensional;
static PyObject *__pyx_kp_u_Format_string_allocated_too_shor;
static PyObject *__pyx_kp_u_Format_string_allocated_too_shor_2;
static PyObject *__pyx_kp_u_Non_native_byte_order_not_suppor;
static PyObject *__pyx_n_s_RuntimeError;
static PyObject *__pyx_n_s_ValueError;
static PyObject *__pyx_n_s_ang_thr;
static PyObject *__pyx_n_s_array;
static PyObject *__pyx_n_s_cnt;
static PyObject *__pyx_n_s_copy;
static PyObject *__pyx_n_s_d;
static PyObject *__pyx_n_s_data;
static PyObject *__pyx_kp_u_data_is_not_C_contiguous;
static PyObject *__pyx_n_s_data_strides;
static PyObject *__pyx_kp_u_data_strides_is_not_C_contiguous;
static PyObject *__pyx_n_s_dipy_tracking_propspeed;
static PyObject *__pyx_n_s_direction;
static PyObject *__pyx_n_s_ds;
static PyObject *__pyx_n_s_dtype;
static PyObject *__pyx_n_s_dx;
static PyObject *__pyx_n_s_eudx_both_directions;
static PyObject *__pyx_n_s_float32;
static PyObject *__pyx_n_s_ftmp;
static PyObject *__pyx_kp_s_home_eleftherios_Devel_dipy_dip;
static PyObject *__pyx_n_s_i;
static PyObject *__pyx_n_s_idirection;
static PyObject *__pyx_n_s_import;
static PyObject *__pyx_n_s_ind;
static PyObject *__pyx_kp_u_ind_is_not_C_contiguous;
static PyObject *__pyx_n_s_index;
static PyObject *__pyx_n_s_indices;
static PyObject *__pyx_kp_u_indices_is_not_C_contiguous;
static PyObject *__pyx_n_s_j;
static PyObject *__pyx_n_s_len_points;
static PyObject *__pyx_n_s_lenind;
static PyObject *__pyx_n_s_main;
static PyObject *__pyx_n_s_map_coordinates_trilinear_iso;
static PyObject *__pyx_n_s_max_points;
static PyObject *__pyx_kp_u_ndarray_is_not_C_contiguous;
static PyObject *__pyx_kp_u_ndarray_is_not_Fortran_contiguou;
static PyObject *__pyx_n_s_ndarray_offset;
static PyObject *__pyx_kp_u_ndarray_offset_line_57;
static PyObject *__pyx_n_s_np;
static PyObject *__pyx_n_s_numpy;
static PyObject *__pyx_n_s_odf_vertices;
static PyObject *__pyx_kp_u_odf_vertices_is_not_C_contiguous;
static PyObject *__pyx_n_s_off;
static PyObject *__pyx_n_s_pin;
static PyObject *__pyx_n_s_point;
static PyObject *__pyx_n_s_points;
static PyObject *__pyx_kp_u_points_is_not_C_contiguous;
static PyObject *__pyx_n_s_pqa;
static PyObject *__pyx_n_s_ps;
static PyObject *__pyx_n_s_ps2;
static PyObject *__pyx_n_s_pstr;
static PyObject *__pyx_n_s_pverts;
static PyObject *__pyx_n_s_pvstr;
static PyObject *__pyx_n_s_qa;
static PyObject *__pyx_kp_u_qa_is_not_C_contiguous;
static PyObject *__pyx_n_s_qa_shape;
static PyObject *__pyx_n_s_qa_thr;
static PyObject *__pyx_n_s_range;
static PyObject *__pyx_n_s_ref;
static PyObject *__pyx_n_s_result;
static PyObject *__pyx_kp_u_result_is_not_C_contiguous;
static PyObject *__pyx_n_s_rs;
static PyObject *__pyx_n_s_seed;
static PyObject *__pyx_kp_u_seed_is_not_C_contiguous;
static PyObject *__pyx_n_s_step_sz;
static PyObject *__pyx_n_s_strides;
static PyObject *__pyx_kp_u_strides_is_not_C_contiguous;
static PyObject *__pyx_n_s_test;
static PyObject *__pyx_n_s_tmp;
static PyObject *__pyx_n_s_tmp_track;
static PyObject *__pyx_n_s_total_weight;
static PyObject *__pyx_n_s_track;
static PyObject *__pyx_n_s_typesize;
static PyObject *__pyx_kp_u_unknown_dtype_code_in_numpy_pxd;
static PyObject *__pyx_n_s_value;
static PyObject *__pyx_n_s_values;
static PyObject *__pyx_n_s_w;
static PyObject *__pyx_n_s_weight;
static PyObject *__pyx_tuple_;
static PyObject *__pyx_tuple__2;
static PyObject *__pyx_tuple__3;
static PyObject *__pyx_tuple__4;
static PyObject *__pyx_tuple__5;
static PyObject *__pyx_tuple__6;
static PyObject *__pyx_tuple__7;
static PyObject *__pyx_tuple__8;
static PyObject *__pyx_tuple__9;
static PyObject *__pyx_tuple__10;
static PyObject *__pyx_tuple__11;
static PyObject *__pyx_tuple__12;
static PyObject *__pyx_tuple__13;
static PyObject *__pyx_tuple__14;
static PyObject *__pyx_tuple__15;
static PyObject *__pyx_tuple__16;
static PyObject *__pyx_tuple__17;
static PyObject *__pyx_tuple__19;
static PyObject *__pyx_tuple__21;
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static PyObject *__pyx_codeobj__20;
static PyObject *__pyx_codeobj__22;

/* "dipy/tracking/propspeed.pyx":29
 * 
 * @cython.cdivision(True)
 * cdef cnp.npy_intp offset(cnp.npy_intp *indices,             # <<<<<<<<<<<<<<
 *                          cnp.npy_intp *strides,
 *                          int lenind,
 */

static npy_intp __pyx_f_4dipy_8tracking_9propspeed_offset(npy_intp *__pyx_v_indices, npy_intp *__pyx_v_strides, int __pyx_v_lenind, int __pyx_v_typesize) {
  int __pyx_v_i;
  npy_intp __pyx_v_summ;
  npy_intp __pyx_r;
  int __pyx_t_1;

  /* "dipy/tracking/propspeed.pyx":50
 *     '''
 *     cdef int i
 *     cdef cnp.npy_intp summ = 0             # <<<<<<<<<<<<<<
 *     for i from 0 <= i < lenind:
 *         summ += strides[i] * indices[i]
 */
  __pyx_v_summ = 0;

  /* "dipy/tracking/propspeed.pyx":51
 *     cdef int i
 *     cdef cnp.npy_intp summ = 0
 *     for i from 0 <= i < lenind:             # <<<<<<<<<<<<<<
 *         summ += strides[i] * indices[i]
 *     summ /= <cnp.npy_intp>typesize
 */
  __pyx_t_1 = __pyx_v_lenind;
  for (__pyx_v_i = 0; __pyx_v_i < __pyx_t_1; __pyx_v_i++) {

    /* "dipy/tracking/propspeed.pyx":52
 *     cdef cnp.npy_intp summ = 0
 *     for i from 0 <= i < lenind:
 *         summ += strides[i] * indices[i]             # <<<<<<<<<<<<<<
 *     summ /= <cnp.npy_intp>typesize
 *     return summ
 */
    __pyx_v_summ = (__pyx_v_summ + ((__pyx_v_strides[__pyx_v_i]) * (__pyx_v_indices[__pyx_v_i])));
  }

  /* "dipy/tracking/propspeed.pyx":53
 *     for i from 0 <= i < lenind:
 *         summ += strides[i] * indices[i]
 *     summ /= <cnp.npy_intp>typesize             # <<<<<<<<<<<<<<
 *     return summ
 * 
 */
  __pyx_v_summ = (__pyx_v_summ / ((npy_intp)__pyx_v_typesize));

  /* "dipy/tracking/propspeed.pyx":54
 *         summ += strides[i] * indices[i]
 *     summ /= <cnp.npy_intp>typesize
 *     return summ             # <<<<<<<<<<<<<<
 * 
 * 
 */
  __pyx_r = __pyx_v_summ;
  goto __pyx_L0;

  /* "dipy/tracking/propspeed.pyx":29
 * 
 * @cython.cdivision(True)
 * cdef cnp.npy_intp offset(cnp.npy_intp *indices,             # <<<<<<<<<<<<<<
 *                          cnp.npy_intp *strides,
 *                          int lenind,
 */

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

/* "dipy/tracking/propspeed.pyx":57
 * 
 * 
 * def ndarray_offset(cnp.ndarray[cnp.npy_intp, ndim=1] indices,             # <<<<<<<<<<<<<<
 *                    cnp.ndarray[cnp.npy_intp, ndim=1] strides,
 *                    int lenind,
 */

/* Python wrapper */
static PyObject *__pyx_pw_4dipy_8tracking_9propspeed_1ndarray_offset(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/
static char __pyx_doc_4dipy_8tracking_9propspeed_ndarray_offset[] = " Find offset in an N-dimensional ndarray using strides\n\n    Parameters\n    ----------\n    indices : array, npy_intp shape (N,)\n        Indices of the array which we want to find the offset.\n    strides : array, shape (N,)\n        Strides of array.\n    lenind : int\n        len of the `indices` array.\n    typesize : int\n        Number of bytes for data type e.g. if 8 for double, 4 for int32\n\n    Returns\n    -------\n    offset : integer\n        Index position in flattened array\n\n    Examples\n    --------\n    >>> import numpy as np\n    >>> from dipy.tracking.propspeed import ndarray_offset\n    >>> I=np.array([1,1])\n    >>> A=np.array([[1,0,0],[0,2,0],[0,0,3]])\n    >>> S=np.array(A.strides)\n    >>> ndarray_offset(I,S,2,A.dtype.itemsize)\n    4\n    >>> A.ravel()[4]==A[1,1]\n    True\n    ";
static PyMethodDef __pyx_mdef_4dipy_8tracking_9propspeed_1ndarray_offset = {"ndarray_offset", (PyCFunction)__pyx_pw_4dipy_8tracking_9propspeed_1ndarray_offset, METH_VARARGS|METH_KEYWORDS, __pyx_doc_4dipy_8tracking_9propspeed_ndarray_offset};
static PyObject *__pyx_pw_4dipy_8tracking_9propspeed_1ndarray_offset(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {
  PyArrayObject *__pyx_v_indices = 0;
  PyArrayObject *__pyx_v_strides = 0;
  int __pyx_v_lenind;
  int __pyx_v_typesize;
  int __pyx_lineno = 0;
  const char *__pyx_filename = NULL;
  int __pyx_clineno = 0;
  PyObject *__pyx_r = 0;
  __Pyx_RefNannyDeclarations
  __Pyx_RefNannySetupContext("ndarray_offset (wrapper)", 0);
  {
    static PyObject **__pyx_pyargnames[] = {&__pyx_n_s_indices,&__pyx_n_s_strides,&__pyx_n_s_lenind,&__pyx_n_s_typesize,0};
    PyObject* values[4] = {0,0,0,0};
    if (unlikely(__pyx_kwds)) {
      Py_ssize_t kw_args;
      const Py_ssize_t pos_args = PyTuple_GET_SIZE(__pyx_args);
      switch (pos_args) {
        case  4: values[3] = PyTuple_GET_ITEM(__pyx_args, 3);
        case  3: values[2] = PyTuple_GET_ITEM(__pyx_args, 2);
        case  2: values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
        case  1: values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
        case  0: break;
        default: goto __pyx_L5_argtuple_error;
      }
      kw_args = PyDict_Size(__pyx_kwds);
      switch (pos_args) {
        case  0:
        if (likely((values[0] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_indices)) != 0)) kw_args--;
        else goto __pyx_L5_argtuple_error;
        case  1:
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 */

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 *     W[0]=nd[0] * nd[1] * nd[2]             # <<<<<<<<<<<<<<
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 *     W[2]=nd[0] *  d[1] * nd[2]             # <<<<<<<<<<<<<<
 *     W[3]=nd[0] * nd[1] *  d[2]
 *     W[4]= d[0] *  d[1] * nd[2]
 */
  (__pyx_v_W[2]) = (((__pyx_v_nd[0]) * (__pyx_v_d[1])) * (__pyx_v_nd[2]));

  /* "dipy/tracking/propspeed.pyx":189
 *     W[1]= d[0] * nd[1] * nd[2]
 *     W[2]=nd[0] *  d[1] * nd[2]
 *     W[3]=nd[0] * nd[1] *  d[2]             # <<<<<<<<<<<<<<
 *     W[4]= d[0] *  d[1] * nd[2]
 *     W[5]=nd[0] *  d[1] *  d[2]
 */
  (__pyx_v_W[3]) = (((__pyx_v_nd[0]) * (__pyx_v_nd[1])) * (__pyx_v_d[2]));

  /* "dipy/tracking/propspeed.pyx":190
 *     W[2]=nd[0] *  d[1] * nd[2]
 *     W[3]=nd[0] * nd[1] *  d[2]
 *     W[4]= d[0] *  d[1] * nd[2]             # <<<<<<<<<<<<<<
 *     W[5]=nd[0] *  d[1] *  d[2]
 *     W[6]= d[0] * nd[1] *  d[2]
 */
  (__pyx_v_W[4]) = (((__pyx_v_d[0]) * (__pyx_v_d[1])) * (__pyx_v_nd[2]));

  /* "dipy/tracking/propspeed.pyx":191
 *     W[3]=nd[0] * nd[1] *  d[2]
 *     W[4]= d[0] *  d[1] * nd[2]
 *     W[5]=nd[0] *  d[1] *  d[2]             # <<<<<<<<<<<<<<
 *     W[6]= d[0] * nd[1] *  d[2]
 *     W[7]= d[0] *  d[1] *  d[2]
 */
  (__pyx_v_W[5]) = (((__pyx_v_nd[0]) * (__pyx_v_d[1])) * (__pyx_v_d[2]));

  /* "dipy/tracking/propspeed.pyx":192
 *     W[4]= d[0] *  d[1] * nd[2]
 *     W[5]=nd[0] *  d[1] *  d[2]
 *     W[6]= d[0] * nd[1] *  d[2]             # <<<<<<<<<<<<<<
 *     W[7]= d[0] *  d[1] *  d[2]
 *     # indices
 */
  (__pyx_v_W[6]) = (((__pyx_v_d[0]) * (__pyx_v_nd[1])) * (__pyx_v_d[2]));

  /* "dipy/tracking/propspeed.pyx":193
 *     W[5]=nd[0] *  d[1] *  d[2]
 *     W[6]= d[0] * nd[1] *  d[2]
 *     W[7]= d[0] *  d[1] *  d[2]             # <<<<<<<<<<<<<<
 *     # indices
 *     # the indices give you the indices of the neighboring voxels (the corners
 */
  (__pyx_v_W[7]) = (((__pyx_v_d[0]) * (__pyx_v_d[1])) * (__pyx_v_d[2]));

  /* "dipy/tracking/propspeed.pyx":197
 *     # the indices give you the indices of the neighboring voxels (the corners
 *     # of the box) e.g. the qa coordinates
 *     IN[0] =<cnp.npy_intp>Xf[0];   IN[1] =<cnp.npy_intp>Xf[1];    IN[2] =<cnp.npy_intp>Xf[2]             # <<<<<<<<<<<<<<
 *     IN[3] =<cnp.npy_intp>Xf[0]+1; IN[4] =<cnp.npy_intp>Xf[1];    IN[5] =<cnp.npy_intp>Xf[2]
 *     IN[6] =<cnp.npy_intp>Xf[0];   IN[7] =<cnp.npy_intp>Xf[1]+1;  IN[8] =<cnp.npy_intp>Xf[2]
 */
  (__pyx_v_IN[0]) = ((npy_intp)(__pyx_v_Xf[0]));
  (__pyx_v_IN[1]) = ((npy_intp)(__pyx_v_Xf[1]));
  (__pyx_v_IN[2]) = ((npy_intp)(__pyx_v_Xf[2]));

  /* "dipy/tracking/propspeed.pyx":198
 *     # of the box) e.g. the qa coordinates
 *     IN[0] =<cnp.npy_intp>Xf[0];   IN[1] =<cnp.npy_intp>Xf[1];    IN[2] =<cnp.npy_intp>Xf[2]
 *     IN[3] =<cnp.npy_intp>Xf[0]+1; IN[4] =<cnp.npy_intp>Xf[1];    IN[5] =<cnp.npy_intp>Xf[2]             # <<<<<<<<<<<<<<
 *     IN[6] =<cnp.npy_intp>Xf[0];   IN[7] =<cnp.npy_intp>Xf[1]+1;  IN[8] =<cnp.npy_intp>Xf[2]
 *     IN[9] =<cnp.npy_intp>Xf[0];   IN[10]=<cnp.npy_intp>Xf[1];    IN[11]=<cnp.npy_intp>Xf[2]+1
 */
  (__pyx_v_IN[3]) = (((npy_intp)(__pyx_v_Xf[0])) + 1);
  (__pyx_v_IN[4]) = ((npy_intp)(__pyx_v_Xf[1]));
  (__pyx_v_IN[5]) = ((npy_intp)(__pyx_v_Xf[2]));

  /* "dipy/tracking/propspeed.pyx":199
 *     IN[0] =<cnp.npy_intp>Xf[0];   IN[1] =<cnp.npy_intp>Xf[1];    IN[2] =<cnp.npy_intp>Xf[2]
 *     IN[3] =<cnp.npy_intp>Xf[0]+1; IN[4] =<cnp.npy_intp>Xf[1];    IN[5] =<cnp.npy_intp>Xf[2]
 *     IN[6] =<cnp.npy_intp>Xf[0];   IN[7] =<cnp.npy_intp>Xf[1]+1;  IN[8] =<cnp.npy_intp>Xf[2]             # <<<<<<<<<<<<<<
 *     IN[9] =<cnp.npy_intp>Xf[0];   IN[10]=<cnp.npy_intp>Xf[1];    IN[11]=<cnp.npy_intp>Xf[2]+1
 *     IN[12]=<cnp.npy_intp>Xf[0]+1; IN[13]=<cnp.npy_intp>Xf[1]+1;  IN[14]=<cnp.npy_intp>Xf[2]
 */
  (__pyx_v_IN[6]) = ((npy_intp)(__pyx_v_Xf[0]));
  (__pyx_v_IN[7]) = (((npy_intp)(__pyx_v_Xf[1])) + 1);
  (__pyx_v_IN[8]) = ((npy_intp)(__pyx_v_Xf[2]));

  /* "dipy/tracking/propspeed.pyx":200
 *     IN[3] =<cnp.npy_intp>Xf[0]+1; IN[4] =<cnp.npy_intp>Xf[1];    IN[5] =<cnp.npy_intp>Xf[2]
 *     IN[6] =<cnp.npy_intp>Xf[0];   IN[7] =<cnp.npy_intp>Xf[1]+1;  IN[8] =<cnp.npy_intp>Xf[2]
 *     IN[9] =<cnp.npy_intp>Xf[0];   IN[10]=<cnp.npy_intp>Xf[1];    IN[11]=<cnp.npy_intp>Xf[2]+1             # <<<<<<<<<<<<<<
 *     IN[12]=<cnp.npy_intp>Xf[0]+1; IN[13]=<cnp.npy_intp>Xf[1]+1;  IN[14]=<cnp.npy_intp>Xf[2]
 *     IN[15]=<cnp.npy_intp>Xf[0];   IN[16]=<cnp.npy_intp>Xf[1]+1;  IN[17]=<cnp.npy_intp>Xf[2]+1
 */
  (__pyx_v_IN[9]) = ((npy_intp)(__pyx_v_Xf[0]));
  (__pyx_v_IN[10]) = ((npy_intp)(__pyx_v_Xf[1]));
  (__pyx_v_IN[11]) = (((npy_intp)(__pyx_v_Xf[2])) + 1);

  /* "dipy/tracking/propspeed.pyx":201
 *     IN[6] =<cnp.npy_intp>Xf[0];   IN[7] =<cnp.npy_intp>Xf[1]+1;  IN[8] =<cnp.npy_intp>Xf[2]
 *     IN[9] =<cnp.npy_intp>Xf[0];   IN[10]=<cnp.npy_intp>Xf[1];    IN[11]=<cnp.npy_intp>Xf[2]+1
 *     IN[12]=<cnp.npy_intp>Xf[0]+1; IN[13]=<cnp.npy_intp>Xf[1]+1;  IN[14]=<cnp.npy_intp>Xf[2]             # <<<<<<<<<<<<<<
 *     IN[15]=<cnp.npy_intp>Xf[0];   IN[16]=<cnp.npy_intp>Xf[1]+1;  IN[17]=<cnp.npy_intp>Xf[2]+1
 *     IN[18]=<cnp.npy_intp>Xf[0]+1; IN[19]=<cnp.npy_intp>Xf[1];    IN[20]=<cnp.npy_intp>Xf[2]+1
 */
  (__pyx_v_IN[12]) = (((npy_intp)(__pyx_v_Xf[0])) + 1);
  (__pyx_v_IN[13]) = (((npy_intp)(__pyx_v_Xf[1])) + 1);
  (__pyx_v_IN[14]) = ((npy_intp)(__pyx_v_Xf[2]));

  /* "dipy/tracking/propspeed.pyx":202
 *     IN[9] =<cnp.npy_intp>Xf[0];   IN[10]=<cnp.npy_intp>Xf[1];    IN[11]=<cnp.npy_intp>Xf[2]+1
 *     IN[12]=<cnp.npy_intp>Xf[0]+1; IN[13]=<cnp.npy_intp>Xf[1]+1;  IN[14]=<cnp.npy_intp>Xf[2]
 *     IN[15]=<cnp.npy_intp>Xf[0];   IN[16]=<cnp.npy_intp>Xf[1]+1;  IN[17]=<cnp.npy_intp>Xf[2]+1             # <<<<<<<<<<<<<<
 *     IN[18]=<cnp.npy_intp>Xf[0]+1; IN[19]=<cnp.npy_intp>Xf[1];    IN[20]=<cnp.npy_intp>Xf[2]+1
 *     IN[21]=<cnp.npy_intp>Xf[0]+1; IN[22]=<cnp.npy_intp>Xf[1]+1;  IN[23]=<cnp.npy_intp>Xf[2]+1
 */
  (__pyx_v_IN[15]) = ((npy_intp)(__pyx_v_Xf[0]));
  (__pyx_v_IN[16]) = (((npy_intp)(__pyx_v_Xf[1])) + 1);
  (__pyx_v_IN[17]) = (((npy_intp)(__pyx_v_Xf[2])) + 1);

  /* "dipy/tracking/propspeed.pyx":203
 *     IN[12]=<cnp.npy_intp>Xf[0]+1; IN[13]=<cnp.npy_intp>Xf[1]+1;  IN[14]=<cnp.npy_intp>Xf[2]
 *     IN[15]=<cnp.npy_intp>Xf[0];   IN[16]=<cnp.npy_intp>Xf[1]+1;  IN[17]=<cnp.npy_intp>Xf[2]+1
 *     IN[18]=<cnp.npy_intp>Xf[0]+1; IN[19]=<cnp.npy_intp>Xf[1];    IN[20]=<cnp.npy_intp>Xf[2]+1             # <<<<<<<<<<<<<<
 *     IN[21]=<cnp.npy_intp>Xf[0]+1; IN[22]=<cnp.npy_intp>Xf[1]+1;  IN[23]=<cnp.npy_intp>Xf[2]+1
 *     return
 */
  (__pyx_v_IN[18]) = (((npy_intp)(__pyx_v_Xf[0])) + 1);
  (__pyx_v_IN[19]) = ((npy_intp)(__pyx_v_Xf[1]));
  (__pyx_v_IN[20]) = (((npy_intp)(__pyx_v_Xf[2])) + 1);

  /* "dipy/tracking/propspeed.pyx":204
 *     IN[15]=<cnp.npy_intp>Xf[0];   IN[16]=<cnp.npy_intp>Xf[1]+1;  IN[17]=<cnp.npy_intp>Xf[2]+1
 *     IN[18]=<cnp.npy_intp>Xf[0]+1; IN[19]=<cnp.npy_intp>Xf[1];    IN[20]=<cnp.npy_intp>Xf[2]+1
 *     IN[21]=<cnp.npy_intp>Xf[0]+1; IN[22]=<cnp.npy_intp>Xf[1]+1;  IN[23]=<cnp.npy_intp>Xf[2]+1             # <<<<<<<<<<<<<<
 *     return
 * 
 */
  (__pyx_v_IN[21]) = (((npy_intp)(__pyx_v_Xf[0])) + 1);
  (__pyx_v_IN[22]) = (((npy_intp)(__pyx_v_Xf[1])) + 1);
  (__pyx_v_IN[23]) = (((npy_intp)(__pyx_v_Xf[2])) + 1);

  /* "dipy/tracking/propspeed.pyx":205
 *     IN[18]=<cnp.npy_intp>Xf[0]+1; IN[19]=<cnp.npy_intp>Xf[1];    IN[20]=<cnp.npy_intp>Xf[2]+1
 *     IN[21]=<cnp.npy_intp>Xf[0]+1; IN[22]=<cnp.npy_intp>Xf[1]+1;  IN[23]=<cnp.npy_intp>Xf[2]+1
 *     return             # <<<<<<<<<<<<<<
 * 
 * 
 */
  goto __pyx_L0;

  /* "dipy/tracking/propspeed.pyx":163
 * 
 * 
 * cdef void _trilinear_interpolation_iso(double *X,             # <<<<<<<<<<<<<<
 *                                        double *W,
 *                                        cnp.npy_intp *IN) nogil:
 */

  /* function exit code */
  __pyx_L0:;
}

/* "dipy/tracking/propspeed.pyx":208
 * 
 * 
 * cdef cnp.npy_intp _nearest_direction(double* dx,             # <<<<<<<<<<<<<<
 *                                      double* qa,
 *                                      double *ind,
 */

static npy_intp __pyx_f_4dipy_8tracking_9propspeed__nearest_direction(double *__pyx_v_dx, double *__pyx_v_qa, double *__pyx_v_ind, npy_intp __pyx_v_peaks, double *__pyx_v_odf_vertices, double __pyx_v_qa_thr, double __pyx_v_ang_thr, double *__pyx_v_direction) {
  double __pyx_v_max_dot;
  double __pyx_v_angl;
  double __pyx_v_curr_dot;
  double __pyx_v_odfv[3];
  npy_intp __pyx_v_i;
  npy_intp __pyx_v_j;
  npy_intp __pyx_v_max_doti;
  npy_intp __pyx_r;
  int __pyx_t_1;
  npy_intp __pyx_t_2;

  /* "dipy/tracking/propspeed.pyx":243
 *     '''
 *     cdef:
 *         double max_dot = 0             # <<<<<<<<<<<<<<
 *         double angl,curr_dot
 *         double odfv[3]
 */
  __pyx_v_max_dot = 0.0;

  /* "dipy/tracking/propspeed.pyx":246
 *         double angl,curr_dot
 *         double odfv[3]
 *         cnp.npy_intp i, j, max_doti = 0             # <<<<<<<<<<<<<<
 * 
 *     # calculate the cos with radians
 */
  __pyx_v_max_doti = 0;

  /* "dipy/tracking/propspeed.pyx":249
 * 
 *     # calculate the cos with radians
 *     angl = cos((DPY_PI * ang_thr) / 180.)             # <<<<<<<<<<<<<<
 *     # if the maximum peak is lower than the threshold then there is no point
 *     # continuing tracking
 */
  __pyx_v_angl = cos(((DPY_PI * __pyx_v_ang_thr) / 180.));

  /* "dipy/tracking/propspeed.pyx":252
 *     # if the maximum peak is lower than the threshold then there is no point
 *     # continuing tracking
 *     if qa[0] <= qa_thr:             # <<<<<<<<<<<<<<
 *         return 0
 *     # for all peaks find the minimum angle between odf_vertices and dx
 */
  __pyx_t_1 = (((__pyx_v_qa[0]) <= __pyx_v_qa_thr) != 0);
  if (__pyx_t_1) {

    /* "dipy/tracking/propspeed.pyx":253
 *     # continuing tracking
 *     if qa[0] <= qa_thr:
 *         return 0             # <<<<<<<<<<<<<<
 *     # for all peaks find the minimum angle between odf_vertices and dx
 *     for i from 0 <= i < peaks:
 */
    __pyx_r = 0;
    goto __pyx_L0;
  }

  /* "dipy/tracking/propspeed.pyx":255
 *         return 0
 *     # for all peaks find the minimum angle between odf_vertices and dx
 *     for i from 0 <= i < peaks:             # <<<<<<<<<<<<<<
 *         # if the current peak is smaller than the threshold then jump out
 *         if qa[i] <= qa_thr:
 */
  __pyx_t_2 = __pyx_v_peaks;
  for (__pyx_v_i = 0; __pyx_v_i < __pyx_t_2; __pyx_v_i++) {

    /* "dipy/tracking/propspeed.pyx":257
 *     for i from 0 <= i < peaks:
 *         # if the current peak is smaller than the threshold then jump out
 *         if qa[i] <= qa_thr:             # <<<<<<<<<<<<<<
 *             break
 *         # copy odf_vertices
 */
    __pyx_t_1 = (((__pyx_v_qa[__pyx_v_i]) <= __pyx_v_qa_thr) != 0);
    if (__pyx_t_1) {

      /* "dipy/tracking/propspeed.pyx":258
 *         # if the current peak is smaller than the threshold then jump out
 *         if qa[i] <= qa_thr:
 *             break             # <<<<<<<<<<<<<<
 *         # copy odf_vertices
 *         for j from 0 <= j < 3:
 */
      goto __pyx_L5_break;
    }

    /* "dipy/tracking/propspeed.pyx":260
 *             break
 *         # copy odf_vertices
 *         for j from 0 <= j < 3:             # <<<<<<<<<<<<<<
 *             odfv[j]=odf_vertices[3 * <cnp.npy_intp>ind[i] + j]
 *         # calculate the absolute dot product between dx and odf_vertices
 */
    for (__pyx_v_j = 0; __pyx_v_j < 3; __pyx_v_j++) {

      /* "dipy/tracking/propspeed.pyx":261
 *         # copy odf_vertices
 *         for j from 0 <= j < 3:
 *             odfv[j]=odf_vertices[3 * <cnp.npy_intp>ind[i] + j]             # <<<<<<<<<<<<<<
 *         # calculate the absolute dot product between dx and odf_vertices
 *         curr_dot = dx[0] * odfv[0] + dx[1] * odfv[1] + dx[2] * odfv[2]
 */
      (__pyx_v_odfv[__pyx_v_j]) = (__pyx_v_odf_vertices[((3 * ((npy_intp)(__pyx_v_ind[__pyx_v_i]))) + __pyx_v_j)]);
    }

    /* "dipy/tracking/propspeed.pyx":263
 *             odfv[j]=odf_vertices[3 * <cnp.npy_intp>ind[i] + j]
 *         # calculate the absolute dot product between dx and odf_vertices
 *         curr_dot = dx[0] * odfv[0] + dx[1] * odfv[1] + dx[2] * odfv[2]             # <<<<<<<<<<<<<<
 *         if curr_dot < 0: #abs check
 *             curr_dot = -curr_dot
 */
    __pyx_v_curr_dot = ((((__pyx_v_dx[0]) * (__pyx_v_odfv[0])) + ((__pyx_v_dx[1]) * (__pyx_v_odfv[1]))) + ((__pyx_v_dx[2]) * (__pyx_v_odfv[2])));

    /* "dipy/tracking/propspeed.pyx":264
 *         # calculate the absolute dot product between dx and odf_vertices
 *         curr_dot = dx[0] * odfv[0] + dx[1] * odfv[1] + dx[2] * odfv[2]
 *         if curr_dot < 0: #abs check             # <<<<<<<<<<<<<<
 *             curr_dot = -curr_dot
 *         # maximum dot means minimum angle
 */
    __pyx_t_1 = ((__pyx_v_curr_dot < 0.0) != 0);
    if (__pyx_t_1) {

      /* "dipy/tracking/propspeed.pyx":265
 *         curr_dot = dx[0] * odfv[0] + dx[1] * odfv[1] + dx[2] * odfv[2]
 *         if curr_dot < 0: #abs check
 *             curr_dot = -curr_dot             # <<<<<<<<<<<<<<
 *         # maximum dot means minimum angle
 *         # store tha maximum dot and the corresponding index from the
 */
      __pyx_v_curr_dot = (-__pyx_v_curr_dot);
      goto __pyx_L9;
    }
    __pyx_L9:;

    /* "dipy/tracking/propspeed.pyx":269
 *         # store tha maximum dot and the corresponding index from the
 *         # neighboring voxel in maxdoti
 *         if curr_dot > max_dot:             # <<<<<<<<<<<<<<
 *             max_dot=curr_dot
 *             max_doti = i
 */
    __pyx_t_1 = ((__pyx_v_curr_dot > __pyx_v_max_dot) != 0);
    if (__pyx_t_1) {

      /* "dipy/tracking/propspeed.pyx":270
 *         # neighboring voxel in maxdoti
 *         if curr_dot > max_dot:
 *             max_dot=curr_dot             # <<<<<<<<<<<<<<
 *             max_doti = i
 *     # if maxdot smaller than our angular *dot* threshold stop tracking
 */
      __pyx_v_max_dot = __pyx_v_curr_dot;

      /* "dipy/tracking/propspeed.pyx":271
 *         if curr_dot > max_dot:
 *             max_dot=curr_dot
 *             max_doti = i             # <<<<<<<<<<<<<<
 *     # if maxdot smaller than our angular *dot* threshold stop tracking
 *     if max_dot < angl:
 */
      __pyx_v_max_doti = __pyx_v_i;
      goto __pyx_L10;
    }
    __pyx_L10:;
  }
  __pyx_L5_break:;

  /* "dipy/tracking/propspeed.pyx":273
 *             max_doti = i
 *     # if maxdot smaller than our angular *dot* threshold stop tracking
 *     if max_dot < angl:             # <<<<<<<<<<<<<<
 *         return 0
 *     # copy the odf_vertices for the voxel qa indices which have the smaller
 */
  __pyx_t_1 = ((__pyx_v_max_dot < __pyx_v_angl) != 0);
  if (__pyx_t_1) {

    /* "dipy/tracking/propspeed.pyx":274
 *     # if maxdot smaller than our angular *dot* threshold stop tracking
 *     if max_dot < angl:
 *         return 0             # <<<<<<<<<<<<<<
 *     # copy the odf_vertices for the voxel qa indices which have the smaller
 *     # angle
 */
    __pyx_r = 0;
    goto __pyx_L0;
  }

  /* "dipy/tracking/propspeed.pyx":277
 *     # copy the odf_vertices for the voxel qa indices which have the smaller
 *     # angle
 *     for j from 0 <= j < 3:             # <<<<<<<<<<<<<<
 *         odfv[j] = odf_vertices[3 * <cnp.npy_intp>ind[max_doti] + j]
 *     # if the dot product is negative then return the opposite direction
 */
  for (__pyx_v_j = 0; __pyx_v_j < 3; __pyx_v_j++) {

    /* "dipy/tracking/propspeed.pyx":278
 *     # angle
 *     for j from 0 <= j < 3:
 *         odfv[j] = odf_vertices[3 * <cnp.npy_intp>ind[max_doti] + j]             # <<<<<<<<<<<<<<
 *     # if the dot product is negative then return the opposite direction
 *     # otherwise return the same direction
 */
    (__pyx_v_odfv[__pyx_v_j]) = (__pyx_v_odf_vertices[((3 * ((npy_intp)(__pyx_v_ind[__pyx_v_max_doti]))) + __pyx_v_j)]);
  }

  /* "dipy/tracking/propspeed.pyx":281
 *     # if the dot product is negative then return the opposite direction
 *     # otherwise return the same direction
 *     if dx[0] * odfv[0] + dx[1] * odfv[1] + dx[2] * odfv[2] < 0:             # <<<<<<<<<<<<<<
 *         for j from 0 <= j < 3:
 *             direction[j] = -odf_vertices[3 * <cnp.npy_intp>ind[max_doti] + j]
 */
  __pyx_t_1 = ((((((__pyx_v_dx[0]) * (__pyx_v_odfv[0])) + ((__pyx_v_dx[1]) * (__pyx_v_odfv[1]))) + ((__pyx_v_dx[2]) * (__pyx_v_odfv[2]))) < 0.0) != 0);
  if (__pyx_t_1) {

    /* "dipy/tracking/propspeed.pyx":282
 *     # otherwise return the same direction
 *     if dx[0] * odfv[0] + dx[1] * odfv[1] + dx[2] * odfv[2] < 0:
 *         for j from 0 <= j < 3:             # <<<<<<<<<<<<<<
 *             direction[j] = -odf_vertices[3 * <cnp.npy_intp>ind[max_doti] + j]
 *         return 1
 */
    for (__pyx_v_j = 0; __pyx_v_j < 3; __pyx_v_j++) {

      /* "dipy/tracking/propspeed.pyx":283
 *     if dx[0] * odfv[0] + dx[1] * odfv[1] + dx[2] * odfv[2] < 0:
 *         for j from 0 <= j < 3:
 *             direction[j] = -odf_vertices[3 * <cnp.npy_intp>ind[max_doti] + j]             # <<<<<<<<<<<<<<
 *         return 1
 *     for j from 0 <= j < 3:
 */
      (__pyx_v_direction[__pyx_v_j]) = (-(__pyx_v_odf_vertices[((3 * ((npy_intp)(__pyx_v_ind[__pyx_v_max_doti]))) + __pyx_v_j)]));
    }

    /* "dipy/tracking/propspeed.pyx":284
 *         for j from 0 <= j < 3:
 *             direction[j] = -odf_vertices[3 * <cnp.npy_intp>ind[max_doti] + j]
 *         return 1             # <<<<<<<<<<<<<<
 *     for j from 0 <= j < 3:
 *         direction[j]= odf_vertices[3 * <cnp.npy_intp>ind[max_doti] + j]
 */
    __pyx_r = 1;
    goto __pyx_L0;
  }

  /* "dipy/tracking/propspeed.pyx":285
 *             direction[j] = -odf_vertices[3 * <cnp.npy_intp>ind[max_doti] + j]
 *         return 1
 *     for j from 0 <= j < 3:             # <<<<<<<<<<<<<<
 *         direction[j]= odf_vertices[3 * <cnp.npy_intp>ind[max_doti] + j]
 *     return 1
 */
  for (__pyx_v_j = 0; __pyx_v_j < 3; __pyx_v_j++) {

    /* "dipy/tracking/propspeed.pyx":286
 *         return 1
 *     for j from 0 <= j < 3:
 *         direction[j]= odf_vertices[3 * <cnp.npy_intp>ind[max_doti] + j]             # <<<<<<<<<<<<<<
 *     return 1
 * 
 */
    (__pyx_v_direction[__pyx_v_j]) = (__pyx_v_odf_vertices[((3 * ((npy_intp)(__pyx_v_ind[__pyx_v_max_doti]))) + __pyx_v_j)]);
  }

  /* "dipy/tracking/propspeed.pyx":287
 *     for j from 0 <= j < 3:
 *         direction[j]= odf_vertices[3 * <cnp.npy_intp>ind[max_doti] + j]
 *     return 1             # <<<<<<<<<<<<<<
 * 
 * 
 */
  __pyx_r = 1;
  goto __pyx_L0;

  /* "dipy/tracking/propspeed.pyx":208
 * 
 * 
 * cdef cnp.npy_intp _nearest_direction(double* dx,             # <<<<<<<<<<<<<<
 *                                      double* qa,
 *                                      double *ind,
 */

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

/* "dipy/tracking/propspeed.pyx":291
 * 
 * @cython.cdivision(True)
 * cdef cnp.npy_intp _propagation_direction(double *point,             # <<<<<<<<<<<<<<
 *                                          double* dx,
 *                                          double* qa,
 */

static npy_intp __pyx_f_4dipy_8tracking_9propspeed__propagation_direction(double *__pyx_v_point, double *__pyx_v_dx, double *__pyx_v_qa, double *__pyx_v_ind, double *__pyx_v_odf_vertices, double __pyx_v_qa_thr, double __pyx_v_ang_thr, npy_intp *__pyx_v_qa_shape, npy_intp *__pyx_v_strides, double *__pyx_v_direction, double __pyx_v_total_weight) {
  double __pyx_v_total_w;
  double __pyx_v_delta;
  double __pyx_v_new_direction[3];
  double __pyx_v_w[8];
  double __pyx_v_qa_tmp[5];
  double __pyx_v_ind_tmp[5];
  npy_intp __pyx_v_index[24];
  npy_intp __pyx_v_xyz[4];
  npy_intp __pyx_v_i;
  npy_intp __pyx_v_j;
  npy_intp __pyx_v_m;
  double __pyx_v_normd;
  npy_intp __pyx_v_peaks;
  npy_intp __pyx_v_off;
  npy_intp __pyx_r;
  int __pyx_t_1;
  int __pyx_t_2;
  npy_intp __pyx_t_3;

  /* "dipy/tracking/propspeed.pyx":303
 *                                          double total_weight) nogil:
 *     cdef:
 *         double total_w = 0 # total weighting useful for interpolation             # <<<<<<<<<<<<<<
 *         double delta = 0 # store delta function (stopping function) result
 *         double new_direction[3] # new propagation direction
 */
  __pyx_v_total_w = 0.0;

  /* "dipy/tracking/propspeed.pyx":304
 *     cdef:
 *         double total_w = 0 # total weighting useful for interpolation
 *         double delta = 0 # store delta function (stopping function) result             # <<<<<<<<<<<<<<
 *         double new_direction[3] # new propagation direction
 *         double w[8], qa_tmp[PEAK_NO], ind_tmp[PEAK_NO]
 */
  __pyx_v_delta = 0.0;

  /* "dipy/tracking/propspeed.pyx":311
 *         double normd
 *         # number of allowed peaks e.g. for fa is 1 for gqi.qa is 5
 *         cnp.npy_intp peaks = qa_shape[3]             # <<<<<<<<<<<<<<
 * 
 *     # Calculate qa & ind of each of the 8 neighboring voxels.
 */
  __pyx_v_peaks = (__pyx_v_qa_shape[3]);

  /* "dipy/tracking/propspeed.pyx":316
 *     # To do that we use trilinear interpolation and return the weights and the
 *     # indices for the weights i.e. xyz in qa[x,y,z]
 *     _trilinear_interpolation_iso(point, <double *> w, <cnp.npy_intp *> index)             # <<<<<<<<<<<<<<
 *     # check if you are outside of the volume
 *     for i from 0 <= i < 3:
 */
  __pyx_f_4dipy_8tracking_9propspeed__trilinear_interpolation_iso(__pyx_v_point, ((double *)__pyx_v_w), ((npy_intp *)__pyx_v_index));

  /* "dipy/tracking/propspeed.pyx":318
 *     _trilinear_interpolation_iso(point, <double *> w, <cnp.npy_intp *> index)
 *     # check if you are outside of the volume
 *     for i from 0 <= i < 3:             # <<<<<<<<<<<<<<
 *         new_direction[i] = 0
 *         if index[7 * 3 + i] >= qa_shape[i] or index[i] < 0:
 */
  for (__pyx_v_i = 0; __pyx_v_i < 3; __pyx_v_i++) {

    /* "dipy/tracking/propspeed.pyx":319
 *     # check if you are outside of the volume
 *     for i from 0 <= i < 3:
 *         new_direction[i] = 0             # <<<<<<<<<<<<<<
 *         if index[7 * 3 + i] >= qa_shape[i] or index[i] < 0:
 *             return 0
 */
    (__pyx_v_new_direction[__pyx_v_i]) = 0.0;

    /* "dipy/tracking/propspeed.pyx":320
 *     for i from 0 <= i < 3:
 *         new_direction[i] = 0
 *         if index[7 * 3 + i] >= qa_shape[i] or index[i] < 0:             # <<<<<<<<<<<<<<
 *             return 0
 *     # for every weight sum the total weighting
 */
    __pyx_t_2 = (((__pyx_v_index[(21 + __pyx_v_i)]) >= (__pyx_v_qa_shape[__pyx_v_i])) != 0);
    if (!__pyx_t_2) {
    } else {
      __pyx_t_1 = __pyx_t_2;
      goto __pyx_L6_bool_binop_done;
    }
    __pyx_t_2 = (((__pyx_v_index[__pyx_v_i]) < 0) != 0);
    __pyx_t_1 = __pyx_t_2;
    __pyx_L6_bool_binop_done:;
    if (__pyx_t_1) {

      /* "dipy/tracking/propspeed.pyx":321
 *         new_direction[i] = 0
 *         if index[7 * 3 + i] >= qa_shape[i] or index[i] < 0:
 *             return 0             # <<<<<<<<<<<<<<
 *     # for every weight sum the total weighting
 *     for m from 0 <= m < 8:
 */
      __pyx_r = 0;
      goto __pyx_L0;
    }
  }

  /* "dipy/tracking/propspeed.pyx":323
 *             return 0
 *     # for every weight sum the total weighting
 *     for m from 0 <= m < 8:             # <<<<<<<<<<<<<<
 *         for i from 0 <= i < 3:
 *             xyz[i]=index[m * 3 + i]
 */
  for (__pyx_v_m = 0; __pyx_v_m < 8; __pyx_v_m++) {

    /* "dipy/tracking/propspeed.pyx":324
 *     # for every weight sum the total weighting
 *     for m from 0 <= m < 8:
 *         for i from 0 <= i < 3:             # <<<<<<<<<<<<<<
 *             xyz[i]=index[m * 3 + i]
 *         # fill qa_tmp and ind_tmp
 */
    for (__pyx_v_i = 0; __pyx_v_i < 3; __pyx_v_i++) {

      /* "dipy/tracking/propspeed.pyx":325
 *     for m from 0 <= m < 8:
 *         for i from 0 <= i < 3:
 *             xyz[i]=index[m * 3 + i]             # <<<<<<<<<<<<<<
 *         # fill qa_tmp and ind_tmp
 *         for j from 0 <= j < peaks:
 */
      (__pyx_v_xyz[__pyx_v_i]) = (__pyx_v_index[((__pyx_v_m * 3) + __pyx_v_i)]);
    }

    /* "dipy/tracking/propspeed.pyx":327
 *             xyz[i]=index[m * 3 + i]
 *         # fill qa_tmp and ind_tmp
 *         for j from 0 <= j < peaks:             # <<<<<<<<<<<<<<
 *             xyz[3] = j
 *             off = offset(<cnp.npy_intp*> xyz, strides, 4, 8)
 */
    __pyx_t_3 = __pyx_v_peaks;
    for (__pyx_v_j = 0; __pyx_v_j < __pyx_t_3; __pyx_v_j++) {

      /* "dipy/tracking/propspeed.pyx":328
 *         # fill qa_tmp and ind_tmp
 *         for j from 0 <= j < peaks:
 *             xyz[3] = j             # <<<<<<<<<<<<<<
 *             off = offset(<cnp.npy_intp*> xyz, strides, 4, 8)
 *             qa_tmp[j] = qa[off]
 */
      (__pyx_v_xyz[3]) = __pyx_v_j;

      /* "dipy/tracking/propspeed.pyx":329
 *         for j from 0 <= j < peaks:
 *             xyz[3] = j
 *             off = offset(<cnp.npy_intp*> xyz, strides, 4, 8)             # <<<<<<<<<<<<<<
 *             qa_tmp[j] = qa[off]
 *             ind_tmp[j] = ind[off]
 */
      __pyx_v_off = __pyx_f_4dipy_8tracking_9propspeed_offset(((npy_intp *)__pyx_v_xyz), __pyx_v_strides, 4, 8);

      /* "dipy/tracking/propspeed.pyx":330
 *             xyz[3] = j
 *             off = offset(<cnp.npy_intp*> xyz, strides, 4, 8)
 *             qa_tmp[j] = qa[off]             # <<<<<<<<<<<<<<
 *             ind_tmp[j] = ind[off]
 *         # return the nearest direction by searching in all peaks
 */
      (__pyx_v_qa_tmp[__pyx_v_j]) = (__pyx_v_qa[__pyx_v_off]);

      /* "dipy/tracking/propspeed.pyx":331
 *             off = offset(<cnp.npy_intp*> xyz, strides, 4, 8)
 *             qa_tmp[j] = qa[off]
 *             ind_tmp[j] = ind[off]             # <<<<<<<<<<<<<<
 *         # return the nearest direction by searching in all peaks
 *         delta=_nearest_direction(dx,
 */
      (__pyx_v_ind_tmp[__pyx_v_j]) = (__pyx_v_ind[__pyx_v_off]);
    }

    /* "dipy/tracking/propspeed.pyx":333
 *             ind_tmp[j] = ind[off]
 *         # return the nearest direction by searching in all peaks
 *         delta=_nearest_direction(dx,             # <<<<<<<<<<<<<<
 *                                  qa_tmp,
 *                                  ind_tmp,
 */
    __pyx_v_delta = __pyx_f_4dipy_8tracking_9propspeed__nearest_direction(__pyx_v_dx, __pyx_v_qa_tmp, __pyx_v_ind_tmp, __pyx_v_peaks, __pyx_v_odf_vertices, __pyx_v_qa_thr, __pyx_v_ang_thr, __pyx_v_direction);

    /* "dipy/tracking/propspeed.pyx":344
 *         # (obeying the thresholds) from that neighboring voxel, so this voxel
 *         # is not adding to the total weight
 *         if delta == 0:             # <<<<<<<<<<<<<<
 *             continue
 *         # add in total
 */
    __pyx_t_1 = ((__pyx_v_delta == 0.0) != 0);
    if (__pyx_t_1) {

      /* "dipy/tracking/propspeed.pyx":345
 *         # is not adding to the total weight
 *         if delta == 0:
 *             continue             # <<<<<<<<<<<<<<
 *         # add in total
 *         total_w += w[m]
 */
      goto __pyx_L8_continue;
    }

    /* "dipy/tracking/propspeed.pyx":347
 *             continue
 *         # add in total
 *         total_w += w[m]             # <<<<<<<<<<<<<<
 *         for i from 0 <= i < 3:
 *             new_direction[i] += w[m] * direction[i]
 */
    __pyx_v_total_w = (__pyx_v_total_w + (__pyx_v_w[__pyx_v_m]));

    /* "dipy/tracking/propspeed.pyx":348
 *         # add in total
 *         total_w += w[m]
 *         for i from 0 <= i < 3:             # <<<<<<<<<<<<<<
 *             new_direction[i] += w[m] * direction[i]
 *     # if less than half the volume is time to stop propagating
 */
    for (__pyx_v_i = 0; __pyx_v_i < 3; __pyx_v_i++) {

      /* "dipy/tracking/propspeed.pyx":349
 *         total_w += w[m]
 *         for i from 0 <= i < 3:
 *             new_direction[i] += w[m] * direction[i]             # <<<<<<<<<<<<<<
 *     # if less than half the volume is time to stop propagating
 *     if total_w < total_weight: # termination
 */
      __pyx_t_3 = __pyx_v_i;
      (__pyx_v_new_direction[__pyx_t_3]) = ((__pyx_v_new_direction[__pyx_t_3]) + ((__pyx_v_w[__pyx_v_m]) * (__pyx_v_direction[__pyx_v_i])));
    }
    __pyx_L8_continue:;
  }

  /* "dipy/tracking/propspeed.pyx":351
 *             new_direction[i] += w[m] * direction[i]
 *     # if less than half the volume is time to stop propagating
 *     if total_w < total_weight: # termination             # <<<<<<<<<<<<<<
 *         return 0
 *     # all good return normalized weighted next direction
 */
  __pyx_t_1 = ((__pyx_v_total_w < __pyx_v_total_weight) != 0);
  if (__pyx_t_1) {

    /* "dipy/tracking/propspeed.pyx":352
 *     # if less than half the volume is time to stop propagating
 *     if total_w < total_weight: # termination
 *         return 0             # <<<<<<<<<<<<<<
 *     # all good return normalized weighted next direction
 *     normd = new_direction[0]**2 + new_direction[1]**2 + new_direction[2]**2
 */
    __pyx_r = 0;
    goto __pyx_L0;
  }

  /* "dipy/tracking/propspeed.pyx":354
 *         return 0
 *     # all good return normalized weighted next direction
 *     normd = new_direction[0]**2 + new_direction[1]**2 + new_direction[2]**2             # <<<<<<<<<<<<<<
 *     normd = 1 / sqrt(normd)
 *     for i from 0 <= i < 3:
 */
  __pyx_v_normd = ((pow((__pyx_v_new_direction[0]), 2.0) + pow((__pyx_v_new_direction[1]), 2.0)) + pow((__pyx_v_new_direction[2]), 2.0));

  /* "dipy/tracking/propspeed.pyx":355
 *     # all good return normalized weighted next direction
 *     normd = new_direction[0]**2 + new_direction[1]**2 + new_direction[2]**2
 *     normd = 1 / sqrt(normd)             # <<<<<<<<<<<<<<
 *     for i from 0 <= i < 3:
 *         direction[i] = new_direction[i] * normd
 */
  __pyx_v_normd = (1.0 / sqrt(__pyx_v_normd));

  /* "dipy/tracking/propspeed.pyx":356
 *     normd = new_direction[0]**2 + new_direction[1]**2 + new_direction[2]**2
 *     normd = 1 / sqrt(normd)
 *     for i from 0 <= i < 3:             # <<<<<<<<<<<<<<
 *         direction[i] = new_direction[i] * normd
 *     return 1
 */
  for (__pyx_v_i = 0; __pyx_v_i < 3; __pyx_v_i++) {

    /* "dipy/tracking/propspeed.pyx":357
 *     normd = 1 / sqrt(normd)
 *     for i from 0 <= i < 3:
 *         direction[i] = new_direction[i] * normd             # <<<<<<<<<<<<<<
 *     return 1
 * 
 */
    (__pyx_v_direction[__pyx_v_i]) = ((__pyx_v_new_direction[__pyx_v_i]) * __pyx_v_normd);
  }

  /* "dipy/tracking/propspeed.pyx":358
 *     for i from 0 <= i < 3:
 *         direction[i] = new_direction[i] * normd
 *     return 1             # <<<<<<<<<<<<<<
 * 
 * 
 */
  __pyx_r = 1;
  goto __pyx_L0;

  /* "dipy/tracking/propspeed.pyx":291
 * 
 * @cython.cdivision(True)
 * cdef cnp.npy_intp _propagation_direction(double *point,             # <<<<<<<<<<<<<<
 *                                          double* dx,
 *                                          double* qa,
 */

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

/* "dipy/tracking/propspeed.pyx":361
 * 
 * 
 * cdef cnp.npy_intp _initial_direction(double* seed,double *qa,             # <<<<<<<<<<<<<<
 *                                      double* ind, double* odf_vertices,
 *                                      double qa_thr,
 */

static npy_intp __pyx_f_4dipy_8tracking_9propspeed__initial_direction(double *__pyx_v_seed, double *__pyx_v_qa, double *__pyx_v_ind, double *__pyx_v_odf_vertices, double __pyx_v_qa_thr, npy_intp *__pyx_v_strides, npy_intp __pyx_v_ref, double *__pyx_v_direction) {
  npy_intp __pyx_v_point[4];
  npy_intp __pyx_v_off;
  npy_intp __pyx_v_i;
  double __pyx_v_qa_tmp;
  double __pyx_v_ind_tmp;
  npy_intp __pyx_r;
  int __pyx_t_1;

  /* "dipy/tracking/propspeed.pyx":376
 *     # (grid) for the trilinear interpolation to run smoothly.
 *     # Find the index for qa
 *     for i from 0 <= i < 3:             # <<<<<<<<<<<<<<
 *         point[i] = <cnp.npy_intp>floor(seed[i] + .5)
 *     point[3] = ref
 */
  for (__pyx_v_i = 0; __pyx_v_i < 3; __pyx_v_i++) {

    /* "dipy/tracking/propspeed.pyx":377
 *     # Find the index for qa
 *     for i from 0 <= i < 3:
 *         point[i] = <cnp.npy_intp>floor(seed[i] + .5)             # <<<<<<<<<<<<<<
 *     point[3] = ref
 *     # Find the offcet in memory to access the qa value
 */
    (__pyx_v_point[__pyx_v_i]) = ((npy_intp)floor(((__pyx_v_seed[__pyx_v_i]) + .5)));
  }

  /* "dipy/tracking/propspeed.pyx":378
 *     for i from 0 <= i < 3:
 *         point[i] = <cnp.npy_intp>floor(seed[i] + .5)
 *     point[3] = ref             # <<<<<<<<<<<<<<
 *     # Find the offcet in memory to access the qa value
 *     off = offset(<cnp.npy_intp*>point,strides, 4, 8)
 */
  (__pyx_v_point[3]) = __pyx_v_ref;

  /* "dipy/tracking/propspeed.pyx":380
 *     point[3] = ref
 *     # Find the offcet in memory to access the qa value
 *     off = offset(<cnp.npy_intp*>point,strides, 4, 8)             # <<<<<<<<<<<<<<
 *     qa_tmp = qa[off]
 *     # Check for scalar threshold
 */
  __pyx_v_off = __pyx_f_4dipy_8tracking_9propspeed_offset(((npy_intp *)__pyx_v_point), __pyx_v_strides, 4, 8);

  /* "dipy/tracking/propspeed.pyx":381
 *     # Find the offcet in memory to access the qa value
 *     off = offset(<cnp.npy_intp*>point,strides, 4, 8)
 *     qa_tmp = qa[off]             # <<<<<<<<<<<<<<
 *     # Check for scalar threshold
 *     if qa_tmp < qa_thr:
 */
  __pyx_v_qa_tmp = (__pyx_v_qa[__pyx_v_off]);

  /* "dipy/tracking/propspeed.pyx":383
 *     qa_tmp = qa[off]
 *     # Check for scalar threshold
 *     if qa_tmp < qa_thr:             # <<<<<<<<<<<<<<
 *         return 0
 *     # Find the correct direction from the indices
 */
  __pyx_t_1 = ((__pyx_v_qa_tmp < __pyx_v_qa_thr) != 0);
  if (__pyx_t_1) {

    /* "dipy/tracking/propspeed.pyx":384
 *     # Check for scalar threshold
 *     if qa_tmp < qa_thr:
 *         return 0             # <<<<<<<<<<<<<<
 *     # Find the correct direction from the indices
 *     ind_tmp = ind[off] # similar to ind[point] in numpy syntax
 */
    __pyx_r = 0;
    goto __pyx_L0;
  }

  /* "dipy/tracking/propspeed.pyx":386
 *         return 0
 *     # Find the correct direction from the indices
 *     ind_tmp = ind[off] # similar to ind[point] in numpy syntax             # <<<<<<<<<<<<<<
 *     # Return initial direction through odf_vertices by ind
 *     for i from 0 <= i < 3:
 */
  __pyx_v_ind_tmp = (__pyx_v_ind[__pyx_v_off]);

  /* "dipy/tracking/propspeed.pyx":388
 *     ind_tmp = ind[off] # similar to ind[point] in numpy syntax
 *     # Return initial direction through odf_vertices by ind
 *     for i from 0 <= i < 3:             # <<<<<<<<<<<<<<
 *         direction[i] = odf_vertices[3 * <cnp.npy_intp>ind_tmp + i]
 *     return 1
 */
  for (__pyx_v_i = 0; __pyx_v_i < 3; __pyx_v_i++) {

    /* "dipy/tracking/propspeed.pyx":389
 *     # Return initial direction through odf_vertices by ind
 *     for i from 0 <= i < 3:
 *         direction[i] = odf_vertices[3 * <cnp.npy_intp>ind_tmp + i]             # <<<<<<<<<<<<<<
 *     return 1
 * 
 */
    (__pyx_v_direction[__pyx_v_i]) = (__pyx_v_odf_vertices[((3 * ((npy_intp)__pyx_v_ind_tmp)) + __pyx_v_i)]);
  }

  /* "dipy/tracking/propspeed.pyx":390
 *     for i from 0 <= i < 3:
 *         direction[i] = odf_vertices[3 * <cnp.npy_intp>ind_tmp + i]
 *     return 1             # <<<<<<<<<<<<<<
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/* "dipy/tracking/propspeed.pyx":393
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    const char* t = *ts;
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      return -1;
    } else {
        count = *t++ - '0';
        while (*t >= '0' && *t < '9') {
            count *= 10;
            count += *t++ - '0';
        }
    }
    *ts = t;
    return count;
}
static int __Pyx_BufFmt_ExpectNumber(const char **ts) {
    int number = __Pyx_BufFmt_ParseNumber(ts);
    if (number == -1)
        PyErr_Format(PyExc_ValueError,\
                     "Does not understand character buffer dtype format string ('%c')", **ts);
    return number;
}
static void __Pyx_BufFmt_RaiseUnexpectedChar(char ch) {
  PyErr_Format(PyExc_ValueError,
               "Unexpected format string character: '%c'", ch);
}
static const char* __Pyx_BufFmt_DescribeTypeChar(char ch, int is_complex) {
  switch (ch) {
    case 'c': return "'char'";
    case 'b': return "'signed char'";
    case 'B': return "'unsigned char'";
    case 'h': return "'short'";
    case 'H': return "'unsigned short'";
    case 'i': return "'int'";
    case 'I': return "'unsigned int'";
    case 'l': return "'long'";
    case 'L': return "'unsigned long'";
    case 'q': return "'long long'";
    case 'Q': return "'unsigned long long'";
    case 'f': return (is_complex ? "'complex float'" : "'float'");
    case 'd': return (is_complex ? "'complex double'" : "'double'");
    case 'g': return (is_complex ? "'complex long double'" : "'long double'");
    case 'T': return "a struct";
    case 'O': return "Python object";
    case 'P': return "a pointer";
    case 's': case 'p': return "a string";
    case 0: return "end";
    default: return "unparseable format string";
  }
}
static size_t __Pyx_BufFmt_TypeCharToStandardSize(char ch, int is_complex) {
  switch (ch) {
    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return 2;
    case 'i': case 'I': case 'l': case 'L': return 4;
    case 'q': case 'Q': return 8;
    case 'f': return (is_complex ? 8 : 4);
    case 'd': return (is_complex ? 16 : 8);
    case 'g': {
      PyErr_SetString(PyExc_ValueError, "Python does not define a standard format string size for long double ('g')..");
      return 0;
    }
    case 'O': case 'P': return sizeof(void*);
    default:
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
}
static size_t __Pyx_BufFmt_TypeCharToNativeSize(char ch, int is_complex) {
  switch (ch) {
    case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return sizeof(short);
    case 'i': case 'I': return sizeof(int);
    case 'l': case 'L': return sizeof(long);
    #ifdef HAVE_LONG_LONG
    case 'q': case 'Q': return sizeof(PY_LONG_LONG);
    #endif
    case 'f': return sizeof(float) * (is_complex ? 2 : 1);
    case 'd': return sizeof(double) * (is_complex ? 2 : 1);
    case 'g': return sizeof(long double) * (is_complex ? 2 : 1);
    case 'O': case 'P': return sizeof(void*);
    default: {
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
  }
}
typedef struct { char c; short x; } __Pyx_st_short;
typedef struct { char c; int x; } __Pyx_st_int;
typedef struct { char c; long x; } __Pyx_st_long;
typedef struct { char c; float x; } __Pyx_st_float;
typedef struct { char c; double x; } __Pyx_st_double;
typedef struct { char c; long double x; } __Pyx_st_longdouble;
typedef struct { char c; void *x; } __Pyx_st_void_p;
#ifdef HAVE_LONG_LONG
typedef struct { char c; PY_LONG_LONG x; } __Pyx_st_longlong;
#endif
static size_t __Pyx_BufFmt_TypeCharToAlignment(char ch, CYTHON_UNUSED int is_complex) {
  switch (ch) {
    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return sizeof(__Pyx_st_short) - sizeof(short);
    case 'i': case 'I': return sizeof(__Pyx_st_int) - sizeof(int);
    case 'l': case 'L': return sizeof(__Pyx_st_long) - sizeof(long);
#ifdef HAVE_LONG_LONG
    case 'q': case 'Q': return sizeof(__Pyx_st_longlong) - sizeof(PY_LONG_LONG);
#endif
    case 'f': return sizeof(__Pyx_st_float) - sizeof(float);
    case 'd': return sizeof(__Pyx_st_double) - sizeof(double);
    case 'g': return sizeof(__Pyx_st_longdouble) - sizeof(long double);
    case 'P': case 'O': return sizeof(__Pyx_st_void_p) - sizeof(void*);
    default:
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
}
/* These are for computing the padding at the end of the struct to align
   on the first member of the struct. This will probably the same as above,
   but we don't have any guarantees.
 */
typedef struct { short x; char c; } __Pyx_pad_short;
typedef struct { int x; char c; } __Pyx_pad_int;
typedef struct { long x; char c; } __Pyx_pad_long;
typedef struct { float x; char c; } __Pyx_pad_float;
typedef struct { double x; char c; } __Pyx_pad_double;
typedef struct { long double x; char c; } __Pyx_pad_longdouble;
typedef struct { void *x; char c; } __Pyx_pad_void_p;
#ifdef HAVE_LONG_LONG
typedef struct { PY_LONG_LONG x; char c; } __Pyx_pad_longlong;
#endif
static size_t __Pyx_BufFmt_TypeCharToPadding(char ch, CYTHON_UNUSED int is_complex) {
  switch (ch) {
    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return sizeof(__Pyx_pad_short) - sizeof(short);
    case 'i': case 'I': return sizeof(__Pyx_pad_int) - sizeof(int);
    case 'l': case 'L': return sizeof(__Pyx_pad_long) - sizeof(long);
#ifdef HAVE_LONG_LONG
    case 'q': case 'Q': return sizeof(__Pyx_pad_longlong) - sizeof(PY_LONG_LONG);
#endif
    case 'f': return sizeof(__Pyx_pad_float) - sizeof(float);
    case 'd': return sizeof(__Pyx_pad_double) - sizeof(double);
    case 'g': return sizeof(__Pyx_pad_longdouble) - sizeof(long double);
    case 'P': case 'O': return sizeof(__Pyx_pad_void_p) - sizeof(void*);
    default:
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
}
static char __Pyx_BufFmt_TypeCharToGroup(char ch, int is_complex) {
  switch (ch) {
    case 'c':
        return 'H';
    case 'b': case 'h': case 'i':
    case 'l': case 'q': case 's': case 'p':
        return 'I';
    case '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, arraysize = 1;
  if (ctx->enc_type == 0) return 0;
  if (ctx->head->field->type->arraysize[0]) {
    int i, ndim = 0;
    if (ctx->enc_type == 's' || ctx->enc_type == 'p') {
        ctx->is_valid_array = ctx->head->field->type->ndim == 1;
        ndim = 1;
        if (ctx->enc_count != ctx->head->field->type->arraysize[0]) {
            PyErr_Format(PyExc_ValueError,
                         "Expected a dimension of size %zu, got %zu",
                         ctx->head->field->type->arraysize[0], ctx->enc_count);
            return -1;
        }
    }
    if (!ctx->is_valid_array) {
      PyErr_Format(PyExc_ValueError, "Expected %d dimensions, got %d",
                   ctx->head->field->type->ndim, ndim);
      return -1;
    }
    for (i = 0; i < ctx->head->field->type->ndim; i++) {
      arraysize *= ctx->head->field->type->arraysize[i];
    }
    ctx->is_valid_array = 0;
    ctx->enc_count = 1;
  }
  group = __Pyx_BufFmt_TypeCharToGroup(ctx->enc_type, ctx->is_complex);
  do {
    __Pyx_StructField* field = ctx->head->field;
    __Pyx_TypeInfo* type = field->type;
    if (ctx->enc_packmode == '@' || ctx->enc_packmode == '^') {
      size = __Pyx_BufFmt_TypeCharToNativeSize(ctx->enc_type, ctx->is_complex);
    } else {
      size = __Pyx_BufFmt_TypeCharToStandardSize(ctx->enc_type, ctx->is_complex);
    }
    if (ctx->enc_packmode == '@') {
      size_t align_at = __Pyx_BufFmt_TypeCharToAlignment(ctx->enc_type, ctx->is_complex);
      size_t align_mod_offset;
      if (align_at == 0) return -1;
      align_mod_offset = ctx->fmt_offset % align_at;
      if (align_mod_offset > 0) ctx->fmt_offset += align_at - align_mod_offset;
      if (ctx->struct_alignment == 0)
          ctx->struct_alignment = __Pyx_BufFmt_TypeCharToPadding(ctx->enc_type,
                                                                 ctx->is_complex);
    }
    if (type->size != size || type->typegroup != group) {
      if (type->typegroup == 'C' && type->fields != NULL) {
        size_t parent_offset = ctx->head->parent_offset + field->offset;
        ++ctx->head;
        ctx->head->field = type->fields;
        ctx->head->parent_offset = parent_offset;
        continue;
      }
      if ((type->typegroup == 'H' || group == 'H') && type->size == size) {
      } else {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return -1;
      }
    }
    offset = ctx->head->parent_offset + field->offset;
    if (ctx->fmt_offset != offset) {
      PyErr_Format(PyExc_ValueError,
                   "Buffer dtype mismatch; next field is at offset %" CYTHON_FORMAT_SSIZE_T "d but %" CYTHON_FORMAT_SSIZE_T "d expected",
                   (Py_ssize_t)ctx->fmt_offset, (Py_ssize_t)offset);
      return -1;
    }
    ctx->fmt_offset += size;
    if (arraysize)
      ctx->fmt_offset += (arraysize - 1) * size;
    --ctx->enc_count;
    while (1) {
      if (field == &ctx->root) {
        ctx->head = NULL;
        if (ctx->enc_count != 0) {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return -1;
        }
        break;
      }
      ctx->head->field = ++field;
      if (field->type == NULL) {
        --ctx->head;
        field = ctx->head->field;
        continue;
      } else if (field->type->typegroup == 'S') {
        size_t parent_offset = ctx->head->parent_offset + field->offset;
        if (field->type->fields->type == NULL) continue;
        field = field->type->fields;
        ++ctx->head;
        ctx->head->field = field;
        ctx->head->parent_offset = parent_offset;
        break;
      } else {
        break;
      }
    }
  } while (ctx->enc_count);
  ctx->enc_type = 0;
  ctx->is_complex = 0;
  return 0;
}
static CYTHON_INLINE PyObject *
__pyx_buffmt_parse_array(__Pyx_BufFmt_Context* ctx, const char** tsp)
{
    const char *ts = *tsp;
    int i = 0, number;
    int ndim = ctx->head->field->type->ndim;
;
    ++ts;
    if (ctx->new_count != 1) {
        PyErr_SetString(PyExc_ValueError,
                        "Cannot handle repeated arrays in format string");
        return NULL;
    }
    if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
    while (*ts && *ts != ')') {
        switch (*ts) {
            case ' ': case '\f': case '\r': case '\n': case '\t': case '\v':  continue;
            default:  break;
        }
        number = __Pyx_BufFmt_ExpectNumber(&ts);
        if (number == -1) return NULL;
        if (i < ndim && (size_t) number != ctx->head->field->type->arraysize[i])
            return PyErr_Format(PyExc_ValueError,
                        "Expected a dimension of size %zu, got %d",
                        ctx->head->field->type->arraysize[i], number);
        if (*ts != ',' && *ts != ')')
            return PyErr_Format(PyExc_ValueError,
                                "Expected a comma in format string, got '%c'", *ts);
        if (*ts == ',') ts++;
        i++;
    }
    if (i != ndim)
        return PyErr_Format(PyExc_ValueError, "Expected %d dimension(s), got %d",
                            ctx->head->field->type->ndim, i);
    if (!*ts) {
        PyErr_SetString(PyExc_ValueError,
                        "Unexpected end of format string, expected ')'");
        return NULL;
    }
    ctx->is_valid_array = 1;
    ctx->new_count = 1;
    *tsp = ++ts;
    return Py_None;
}
static const char* __Pyx_BufFmt_CheckString(__Pyx_BufFmt_Context* ctx, const char* ts) {
  int got_Z = 0;
  while (1) {
    switch(*ts) {
      case 0:
        if (ctx->enc_type != 0 && ctx->head == NULL) {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return NULL;
        }
        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
        if (ctx->head != NULL) {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return NULL;
        }
        return ts;
      case ' ':
      case '\r':
      case '\n':
        ++ts;
        break;
      case '<':
        if (!__Pyx_IsLittleEndian()) {
          PyErr_SetString(PyExc_ValueError, "Little-endian buffer not supported on big-endian compiler");
          return NULL;
        }
        ctx->new_packmode = '=';
        ++ts;
        break;
      case '>':
      case '!':
        if (__Pyx_IsLittleEndian()) {
          PyErr_SetString(PyExc_ValueError, "Big-endian buffer not supported on little-endian compiler");
          return NULL;
        }
        ctx->new_packmode = '=';
        ++ts;
        break;
      case '=':
      case '@':
      case '^':
        ctx->new_packmode = *ts++;
        break;
      case 'T':
        {
          const char* ts_after_sub;
          size_t i, struct_count = ctx->new_count;
          size_t struct_alignment = ctx->struct_alignment;
          ctx->new_count = 1;
          ++ts;
          if (*ts != '{') {
            PyErr_SetString(PyExc_ValueError, "Buffer acquisition: Expected '{' after 'T'");
            return NULL;
          }
          if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
          ctx->enc_type = 0;
          ctx->enc_count = 0;
          ctx->struct_alignment = 0;
          ++ts;
          ts_after_sub = ts;
          for (i = 0; i != struct_count; ++i) {
            ts_after_sub = __Pyx_BufFmt_CheckString(ctx, ts);
            if (!ts_after_sub) return NULL;
          }
          ts = ts_after_sub;
          if (struct_alignment) ctx->struct_alignment = struct_alignment;
        }
        break;
      case '}':
        {
          size_t alignment = ctx->struct_alignment;
          ++ts;
          if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
          ctx->enc_type = 0;
          if (alignment && ctx->fmt_offset % alignment) {
            ctx->fmt_offset += alignment - (ctx->fmt_offset % alignment);
          }
        }
        return ts;
      case 'x':
        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
        ctx->fmt_offset += ctx->new_count;
        ctx->new_count = 1;
        ctx->enc_count = 0;
        ctx->enc_type = 0;
        ctx->enc_packmode = ctx->new_packmode;
        ++ts;
        break;
      case 'Z':
        got_Z = 1;
        ++ts;
        if (*ts != 'f' && *ts != 'd' && *ts != 'g') {
          __Pyx_BufFmt_RaiseUnexpectedChar('Z');
          return NULL;
        }
      case 'c': case 'b': case 'B': case 'h': case 'H': case 'i': case 'I':
      case 'l': case 'L': case 'q': case 'Q':
      case 'f': case 'd': case 'g':
      case 'O': case 'p':
        if (ctx->enc_type == *ts && got_Z == ctx->is_complex &&
            ctx->enc_packmode == ctx->new_packmode) {
          ctx->enc_count += ctx->new_count;
          ctx->new_count = 1;
          got_Z = 0;
          ++ts;
          break;
        }
      case 's':
        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
        ctx->enc_count = ctx->new_count;
        ctx->enc_packmode = ctx->new_packmode;
        ctx->enc_type = *ts;
        ctx->is_complex = got_Z;
        ++ts;
        ctx->new_count = 1;
        got_Z = 0;
        break;
      case ':':
        ++ts;
        while(*ts != ':') ++ts;
        ++ts;
        break;
      case '(':
        if (!__pyx_buffmt_parse_array(ctx, &ts)) return NULL;
        break;
      default:
        {
          int number = __Pyx_BufFmt_ExpectNumber(&ts);
          if (number == -1) return NULL;
          ctx->new_count = (size_t)number;
        }
    }
  }
}
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 || obj == NULL) {
    __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 (%" CYTHON_FORMAT_SSIZE_T "d byte%s) does not match size of '%s' (%" CYTHON_FORMAT_SSIZE_T "d byte%s)",
      buf->itemsize, (buf->itemsize > 1) ? "s" : "",
      dtype->name, (Py_ssize_t)dtype->size, (dtype->size > 1) ? "s" : "");
    goto fail;
  }
  if (buf->suboffsets == NULL) buf->suboffsets = __Pyx_minusones;
  return 0;
fail:;
  __Pyx_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);
}

#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw) {
    PyObject *result;
    ternaryfunc call = func->ob_type->tp_call;
    if (unlikely(!call))
        return PyObject_Call(func, arg, kw);
    if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
        return NULL;
    result = (*call)(func, arg, kw);
    Py_LeaveRecursiveCall();
    if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
        PyErr_SetString(
            PyExc_SystemError,
            "NULL result without error in PyObject_Call");
    }
    return result;
}
#endif

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);
    if (!value || value == Py_None)
        value = NULL;
    else
        Py_INCREF(value);
    if (!tb || tb == Py_None)
        tb = NULL;
    else {
        Py_INCREF(tb);
        if (!PyTraceBack_Check(tb)) {
            PyErr_SetString(PyExc_TypeError,
                "raise: arg 3 must be a traceback or None");
            goto raise_error;
        }
    }
    if (PyType_Check(type)) {
#if CYTHON_COMPILING_IN_PYPY
        if (!value) {
            Py_INCREF(Py_None);
            value = Py_None;
        }
#endif
        PyErr_NormalizeException(&type, &value, &tb);
    } else {
        if (value) {
            PyErr_SetString(PyExc_TypeError,
                "instance exception may not have a separate value");
            goto raise_error;
        }
        value = type;
        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;
        }
    }
    __Pyx_ErrRestore(type, value, tb);
    return;
raise_error:
    Py_XDECREF(value);
    Py_XDECREF(type);
    Py_XDECREF(tb);
    return;
}
#else
static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause) {
    PyObject* owned_instance = NULL;
    if (tb == Py_None) {
        tb = 0;
    } else if (tb && !PyTraceBack_Check(tb)) {
        PyErr_SetString(PyExc_TypeError,
            "raise: arg 3 must be a traceback or None");
        goto bad;
    }
    if (value == Py_None)
        value = 0;
    if (PyExceptionInstance_Check(type)) {
        if (value) {
            PyErr_SetString(PyExc_TypeError,
                "instance exception may not have a separate value");
            goto bad;
        }
        value = type;
        type = (PyObject*) Py_TYPE(value);
    } else if (PyExceptionClass_Check(type)) {
        PyObject *instance_class = NULL;
        if (value && PyExceptionInstance_Check(value)) {
            instance_class = (PyObject*) Py_TYPE(value);
            if (instance_class != type) {
                if (PyObject_IsSubclass(instance_class, type)) {
                    type = instance_class;
                } else {
                    instance_class = NULL;
                }
            }
        }
        if (!instance_class) {
            PyObject *args;
            if (!value)
                args = PyTuple_New(0);
            else if (PyTuple_Check(value)) {
                Py_INCREF(value);
                args = value;
            } else
                args = PyTuple_Pack(1, value);
            if (!args)
                goto bad;
            owned_instance = PyObject_Call(type, args, NULL);
            Py_DECREF(args);
            if (!owned_instance)
                goto bad;
            value = owned_instance;
            if (!PyExceptionInstance_Check(value)) {
                PyErr_Format(PyExc_TypeError,
                             "calling %R should have returned an instance of "
                             "BaseException, not %R",
                             type, Py_TYPE(value));
                goto bad;
            }
        }
    } else {
        PyErr_SetString(PyExc_TypeError,
            "raise: exception class must be a subclass of BaseException");
        goto bad;
    }
#if PY_VERSION_HEX >= 0x03030000
    if (cause) {
#else
    if (cause && cause != Py_None) {
#endif
        PyObject *fixed_cause;
        if (cause == Py_None) {
            fixed_cause = NULL;
        } else if (PyExceptionClass_Check(cause)) {
            fixed_cause = PyObject_CallObject(cause, NULL);
            if (fixed_cause == NULL)
                goto bad;
        } else if (PyExceptionInstance_Check(cause)) {
            fixed_cause = cause;
            Py_INCREF(fixed_cause);
        } else {
            PyErr_SetString(PyExc_TypeError,
                            "exception causes must derive from "
                            "BaseException");
            goto bad;
        }
        PyException_SetCause(value, fixed_cause);
    }
    PyErr_SetObject(type, value);
    if (tb) {
#if CYTHON_COMPILING_IN_PYPY
        PyObject *tmp_type, *tmp_value, *tmp_tb;
        PyErr_Fetch(tmp_type, tmp_value, tmp_tb);
        Py_INCREF(tb);
        PyErr_Restore(tmp_type, tmp_value, tb);
        Py_XDECREF(tmp_tb);
#else
        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);
        }
#endif
    }
bad:
    Py_XDECREF(owned_instance);
    return;
}
#endif

#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg) {
    PyObject *self, *result;
    PyCFunction cfunc;
    cfunc = PyCFunction_GET_FUNCTION(func);
    self = PyCFunction_GET_SELF(func);
    if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
        return NULL;
    result = cfunc(self, arg);
    Py_LeaveRecursiveCall();
    if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
        PyErr_SetString(
            PyExc_SystemError,
            "NULL result without error in PyObject_Call");
    }
    return result;
}
#endif

#if CYTHON_COMPILING_IN_CPYTHON
static PyObject* __Pyx__PyObject_CallOneArg(PyObject *func, PyObject *arg) {
    PyObject *result;
    PyObject *args = PyTuple_New(1);
    if (unlikely(!args)) return NULL;
    Py_INCREF(arg);
    PyTuple_SET_ITEM(args, 0, arg);
    result = __Pyx_PyObject_Call(func, args, NULL);
    Py_DECREF(args);
    return result;
}
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
#ifdef __Pyx_CyFunction_USED
    if (likely(PyCFunction_Check(func) || PyObject_TypeCheck(func, __pyx_CyFunctionType))) {
#else
    if (likely(PyCFunction_Check(func))) {
#endif
        if (likely(PyCFunction_GET_FLAGS(func) & METH_O)) {
            return __Pyx_PyObject_CallMethO(func, arg);
        }
    }
    return __Pyx__PyObject_CallOneArg(func, arg);
}
#else
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
    PyObject* args = PyTuple_Pack(1, arg);
    return (likely(args)) ? __Pyx_PyObject_Call(func, args, NULL) : NULL;
}
#endif

#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func) {
#ifdef __Pyx_CyFunction_USED
    if (likely(PyCFunction_Check(func) || PyObject_TypeCheck(func, __pyx_CyFunctionType))) {
#else
    if (likely(PyCFunction_Check(func))) {
#endif
        if (likely(PyCFunction_GET_FLAGS(func) & METH_NOARGS)) {
            return __Pyx_PyObject_CallMethO(func, NULL);
        }
    }
    return __Pyx_PyObject_Call(func, __pyx_empty_tuple, NULL);
}
#endif

static CYTHON_INLINE int __Pyx_SetItemInt_Generic(PyObject *o, PyObject *j, PyObject *v) {
    int r;
    if (!j) return -1;
    r = PyObject_SetItem(o, j, v);
    Py_DECREF(j);
    return r;
}
static CYTHON_INLINE int __Pyx_SetItemInt_Fast(PyObject *o, Py_ssize_t i, PyObject *v,
                                               int is_list, int wraparound, int boundscheck) {
#if CYTHON_COMPILING_IN_CPYTHON
    if (is_list || PyList_CheckExact(o)) {
        Py_ssize_t n = (!wraparound) ? i : ((likely(i >= 0)) ? i : i + PyList_GET_SIZE(o));
        if ((!boundscheck) || likely((n >= 0) & (n < PyList_GET_SIZE(o)))) {
            PyObject* old = PyList_GET_ITEM(o, n);
            Py_INCREF(v);
            PyList_SET_ITEM(o, n, v);
            Py_DECREF(old);
            return 1;
        }
    } else {
        PySequenceMethods *m = Py_TYPE(o)->tp_as_sequence;
        if (likely(m && m->sq_ass_item)) {
            if (wraparound && unlikely(i < 0) && likely(m->sq_length)) {
                Py_ssize_t l = m->sq_length(o);
                if (likely(l >= 0)) {
                    i += l;
                } else {
                    if (PyErr_ExceptionMatches(PyExc_OverflowError))
                        PyErr_Clear();
                    else
                        return -1;
                }
            }
            return m->sq_ass_item(o, i, v);
        }
    }
#else
#if CYTHON_COMPILING_IN_PYPY
    if (is_list || (PySequence_Check(o) && !PyDict_Check(o))) {
#else
    if (is_list || PySequence_Check(o)) {
#endif
        return PySequence_SetItem(o, i, v);
    }
#endif
    return __Pyx_SetItemInt_Generic(o, PyInt_FromSsize_t(i), v);
}

static CYTHON_INLINE PyObject *__Pyx_GetModuleGlobalName(PyObject *name) {
    PyObject *result;
#if CYTHON_COMPILING_IN_CPYTHON
    result = PyDict_GetItem(__pyx_d, name);
    if (likely(result)) {
        Py_INCREF(result);
    } else {
#else
    result = PyObject_GetItem(__pyx_d, name);
    if (!result) {
        PyErr_Clear();
#endif
        result = __Pyx_GetBuiltinName(name);
    }
    return result;
}

static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected) {
    PyErr_Format(PyExc_ValueError,
                 "too many values to unpack (expected %" CYTHON_FORMAT_SSIZE_T "d)", expected);
}

static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index) {
    PyErr_Format(PyExc_ValueError,
                 "need more than %" CYTHON_FORMAT_SSIZE_T "d value%.1s to unpack",
                 index, (index == 1) ? "" : "s");
}

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

static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type) {
    if (unlikely(!type)) {
        PyErr_SetString(PyExc_SystemError, "Missing type object");
        return 0;
    }
    if (likely(PyObject_TypeCheck(obj, type)))
        return 1;
    PyErr_Format(PyExc_TypeError, "Cannot convert %.200s to %.200s",
                 Py_TYPE(obj)->tp_name, type->tp_name);
    return 0;
}

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, (size_t)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,
        0,
        0,
        0,
        0,
        __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,
        __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;
    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_frame = PyFrame_New(
        PyThreadState_GET(), /*PyThreadState *tstate,*/
        py_code,             /*PyCodeObject *code,*/
        __pyx_d,      /*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);
}

#if PY_MAJOR_VERSION < 3
static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags) {
    if (PyObject_CheckBuffer(obj)) return PyObject_GetBuffer(obj, view, flags);
        if (PyObject_TypeCheck(obj, __pyx_ptype_5numpy_ndarray)) return __pyx_pw_5numpy_7ndarray_1__getbuffer__(obj, view, flags);
    PyErr_Format(PyExc_TypeError, "'%.200s' 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) return;
    if (PyObject_CheckBuffer(obj)) {
        PyBuffer_Release(view);
        return;
    }
        if (PyObject_TypeCheck(obj, __pyx_ptype_5numpy_ndarray)) { __pyx_pw_5numpy_7ndarray_3__releasebuffer__(obj, view); return; }
    Py_DECREF(obj);
    view->obj = NULL;
}
#endif


            static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level) {
    PyObject *empty_list = 0;
    PyObject *module = 0;
    PyObject *global_dict = 0;
    PyObject *empty_dict = 0;
    PyObject *list;
    #if PY_VERSION_HEX < 0x03030000
    PyObject *py_import;
    py_import = __Pyx_PyObject_GetAttrStr(__pyx_b, __pyx_n_s_import);
    if (!py_import)
        goto bad;
    #endif
    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_MAJOR_VERSION >= 3
        if (level == -1) {
            if (strchr(__Pyx_MODULE_NAME, '.')) {
                #if PY_VERSION_HEX < 0x03030000
                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);
                #else
                module = PyImport_ImportModuleLevelObject(
                    name, global_dict, empty_dict, list, 1);
                #endif
                if (!module) {
                    if (!PyErr_ExceptionMatches(PyExc_ImportError))
                        goto bad;
                    PyErr_Clear();
                }
            }
            level = 0;
        }
        #endif
        if (!module) {
            #if PY_VERSION_HEX < 0x03030000
            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
            module = PyImport_ImportModuleLevelObject(
                name, global_dict, empty_dict, list, level);
            #endif
        }
    }
bad:
    #if PY_VERSION_HEX < 0x03030000
    Py_XDECREF(py_import);
    #endif
    Py_XDECREF(empty_list);
    Py_XDECREF(empty_dict);
    return module;
}

#define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)       \
    {                                                                     \
        func_type value = func_value;                                     \
        if (sizeof(target_type) < sizeof(func_type)) {                    \
            if (unlikely(value != (func_type) (target_type) value)) {     \
                func_type zero = 0;                                       \
                if (is_unsigned && unlikely(value < zero))                \
                    goto raise_neg_overflow;                              \
                else                                                      \
                    goto raise_overflow;                                  \
            }                                                             \
        }                                                                 \
        return (target_type) value;                                       \
    }

#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
 #if CYTHON_USE_PYLONG_INTERNALS
  #include "longintrepr.h"
 #endif
#endif

static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) {
    const int neg_one = (int) -1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_MAJOR_VERSION < 3
    if (likely(PyInt_Check(x))) {
        if (sizeof(int) < sizeof(long)) {
            __PYX_VERIFY_RETURN_INT(int, long, PyInt_AS_LONG(x))
        } else {
            long val = PyInt_AS_LONG(x);
            if (is_unsigned && unlikely(val < 0)) {
                goto raise_neg_overflow;
            }
            return (int) val;
        }
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
 #if CYTHON_USE_PYLONG_INTERNALS
            switch (Py_SIZE(x)) {
                case  0: return 0;
                case  1: __PYX_VERIFY_RETURN_INT(int, digit, ((PyLongObject*)x)->ob_digit[0]);
            }
 #endif
#endif
            if (unlikely(Py_SIZE(x) < 0)) {
                goto raise_neg_overflow;
            }
            if (sizeof(int) <= sizeof(unsigned long)) {
                __PYX_VERIFY_RETURN_INT(int, unsigned long, PyLong_AsUnsignedLong(x))
            } else if (sizeof(int) <= sizeof(unsigned long long)) {
                __PYX_VERIFY_RETURN_INT(int, unsigned long long, PyLong_AsUnsignedLongLong(x))
            }
        } else {
#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
 #if CYTHON_USE_PYLONG_INTERNALS
            switch (Py_SIZE(x)) {
                case  0: return 0;
                case  1: __PYX_VERIFY_RETURN_INT(int,  digit, +(((PyLongObject*)x)->ob_digit[0]));
                case -1: __PYX_VERIFY_RETURN_INT(int, sdigit, -(sdigit) ((PyLongObject*)x)->ob_digit[0]);
            }
 #endif
#endif
            if (sizeof(int) <= sizeof(long)) {
                __PYX_VERIFY_RETURN_INT(int, long, PyLong_AsLong(x))
            } else if (sizeof(int) <= sizeof(long long)) {
                __PYX_VERIFY_RETURN_INT(int, long long, PyLong_AsLongLong(x))
            }
        }
        {
#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
            PyErr_SetString(PyExc_RuntimeError,
                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
#else
            int val;
            PyObject *v = __Pyx_PyNumber_Int(x);
 #if PY_MAJOR_VERSION < 3
            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;
            }
#endif
            return (int) -1;
        }
    } else {
        int val;
        PyObject *tmp = __Pyx_PyNumber_Int(x);
        if (!tmp) return (int) -1;
        val = __Pyx_PyInt_As_int(tmp);
        Py_DECREF(tmp);
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to int");
    return (int) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to int");
    return (int) -1;
}

static CYTHON_INLINE Py_intptr_t __Pyx_PyInt_As_Py_intptr_t(PyObject *x) {
    const Py_intptr_t neg_one = (Py_intptr_t) -1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_MAJOR_VERSION < 3
    if (likely(PyInt_Check(x))) {
        if (sizeof(Py_intptr_t) < sizeof(long)) {
            __PYX_VERIFY_RETURN_INT(Py_intptr_t, long, PyInt_AS_LONG(x))
        } else {
            long val = PyInt_AS_LONG(x);
            if (is_unsigned && unlikely(val < 0)) {
                goto raise_neg_overflow;
            }
            return (Py_intptr_t) val;
        }
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
 #if CYTHON_USE_PYLONG_INTERNALS
            switch (Py_SIZE(x)) {
                case  0: return 0;
                case  1: __PYX_VERIFY_RETURN_INT(Py_intptr_t, digit, ((PyLongObject*)x)->ob_digit[0]);
            }
 #endif
#endif
            if (unlikely(Py_SIZE(x) < 0)) {
                goto raise_neg_overflow;
            }
            if (sizeof(Py_intptr_t) <= sizeof(unsigned long)) {
                __PYX_VERIFY_RETURN_INT(Py_intptr_t, unsigned long, PyLong_AsUnsignedLong(x))
            } else if (sizeof(Py_intptr_t) <= sizeof(unsigned long long)) {
                __PYX_VERIFY_RETURN_INT(Py_intptr_t, unsigned long long, PyLong_AsUnsignedLongLong(x))
            }
        } else {
#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
 #if CYTHON_USE_PYLONG_INTERNALS
            switch (Py_SIZE(x)) {
                case  0: return 0;
                case  1: __PYX_VERIFY_RETURN_INT(Py_intptr_t,  digit, +(((PyLongObject*)x)->ob_digit[0]));
                case -1: __PYX_VERIFY_RETURN_INT(Py_intptr_t, sdigit, -(sdigit) ((PyLongObject*)x)->ob_digit[0]);
            }
 #endif
#endif
            if (sizeof(Py_intptr_t) <= sizeof(long)) {
                __PYX_VERIFY_RETURN_INT(Py_intptr_t, long, PyLong_AsLong(x))
            } else if (sizeof(Py_intptr_t) <= sizeof(long long)) {
                __PYX_VERIFY_RETURN_INT(Py_intptr_t, long long, PyLong_AsLongLong(x))
            }
        }
        {
#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
            PyErr_SetString(PyExc_RuntimeError,
                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
#else
            Py_intptr_t val;
            PyObject *v = __Pyx_PyNumber_Int(x);
 #if PY_MAJOR_VERSION < 3
            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;
            }
#endif
            return (Py_intptr_t) -1;
        }
    } else {
        Py_intptr_t val;
        PyObject *tmp = __Pyx_PyNumber_Int(x);
        if (!tmp) return (Py_intptr_t) -1;
        val = __Pyx_PyInt_As_Py_intptr_t(tmp);
        Py_DECREF(tmp);
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to Py_intptr_t");
    return (Py_intptr_t) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to Py_intptr_t");
    return (Py_intptr_t) -1;
}

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

#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 PyObject* __Pyx_PyInt_From_int(int value) {
    const int neg_one = (int) -1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
    if (is_unsigned) {
        if (sizeof(int) < sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(int) <= sizeof(unsigned long)) {
            return PyLong_FromUnsignedLong((unsigned long) value);
        } else if (sizeof(int) <= sizeof(unsigned long long)) {
            return PyLong_FromUnsignedLongLong((unsigned long long) value);
        }
    } else {
        if (sizeof(int) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(int) <= sizeof(long long)) {
            return PyLong_FromLongLong((long long) value);
        }
    }
    {
        int one = 1; int little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&value;
        return _PyLong_FromByteArray(bytes, sizeof(int),
                                     little, !is_unsigned);
    }
}

static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) {
    const long neg_one = (long) -1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
    if (is_unsigned) {
        if (sizeof(long) < sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(long) <= sizeof(unsigned long)) {
            return PyLong_FromUnsignedLong((unsigned long) value);
        } else if (sizeof(long) <= sizeof(unsigned long long)) {
            return PyLong_FromUnsignedLongLong((unsigned long long) value);
        }
    } else {
        if (sizeof(long) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(long) <= sizeof(long long)) {
            return PyLong_FromLongLong((long long) value);
        }
    }
    {
        int one = 1; int little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&value;
        return _PyLong_FromByteArray(bytes, sizeof(long),
                                     little, !is_unsigned);
    }
}

static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *x) {
    const long neg_one = (long) -1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_MAJOR_VERSION < 3
    if (likely(PyInt_Check(x))) {
        if (sizeof(long) < sizeof(long)) {
            __PYX_VERIFY_RETURN_INT(long, long, PyInt_AS_LONG(x))
        } else {
            long val = PyInt_AS_LONG(x);
            if (is_unsigned && unlikely(val < 0)) {
                goto raise_neg_overflow;
            }
            return (long) val;
        }
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
 #if CYTHON_USE_PYLONG_INTERNALS
            switch (Py_SIZE(x)) {
                case  0: return 0;
                case  1: __PYX_VERIFY_RETURN_INT(long, digit, ((PyLongObject*)x)->ob_digit[0]);
            }
 #endif
#endif
            if (unlikely(Py_SIZE(x) < 0)) {
                goto raise_neg_overflow;
            }
            if (sizeof(long) <= sizeof(unsigned long)) {
                __PYX_VERIFY_RETURN_INT(long, unsigned long, PyLong_AsUnsignedLong(x))
            } else if (sizeof(long) <= sizeof(unsigned long long)) {
                __PYX_VERIFY_RETURN_INT(long, unsigned long long, PyLong_AsUnsignedLongLong(x))
            }
        } else {
#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
 #if CYTHON_USE_PYLONG_INTERNALS
            switch (Py_SIZE(x)) {
                case  0: return 0;
                case  1: __PYX_VERIFY_RETURN_INT(long,  digit, +(((PyLongObject*)x)->ob_digit[0]));
                case -1: __PYX_VERIFY_RETURN_INT(long, sdigit, -(sdigit) ((PyLongObject*)x)->ob_digit[0]);
            }
 #endif
#endif
            if (sizeof(long) <= sizeof(long)) {
                __PYX_VERIFY_RETURN_INT(long, long, PyLong_AsLong(x))
            } else if (sizeof(long) <= sizeof(long long)) {
                __PYX_VERIFY_RETURN_INT(long, long long, PyLong_AsLongLong(x))
            }
        }
        {
#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
            PyErr_SetString(PyExc_RuntimeError,
                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
#else
            long val;
            PyObject *v = __Pyx_PyNumber_Int(x);
 #if PY_MAJOR_VERSION < 3
            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;
            }
#endif
            return (long) -1;
        }
    } else {
        long val;
        PyObject *tmp = __Pyx_PyNumber_Int(x);
        if (!tmp) return (long) -1;
        val = __Pyx_PyInt_As_long(tmp);
        Py_DECREF(tmp);
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to long");
    return (long) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to long");
    return (long) -1;
}

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);
        return PyErr_WarnEx(NULL, message, 1);
    }
    return 0;
}

static int __Pyx_ExportFunction(const char *name, void (*f)(void), const char *sig) {
    PyObject *d = 0;
    PyObject *cobj = 0;
    union {
        void (*fp)(void);
        void *p;
    } tmp;
    d = PyObject_GetAttrString(__pyx_m, (char *)"__pyx_capi__");
    if (!d) {
        PyErr_Clear();
        d = PyDict_New();
        if (!d)
            goto bad;
        Py_INCREF(d);
        if (PyModule_AddObject(__pyx_m, (char *)"__pyx_capi__", d) < 0)
            goto bad;
    }
    tmp.fp = f;
#if PY_VERSION_HEX >= 0x02070000
    cobj = PyCapsule_New(tmp.p, sig, 0);
#else
    cobj = PyCObject_FromVoidPtrAndDesc(tmp.p, (void *)sig, 0);
#endif
    if (!cobj)
        goto bad;
    if (PyDict_SetItemString(d, name, cobj) < 0)
        goto bad;
    Py_DECREF(cobj);
    Py_DECREF(d);
    return 0;
bad:
    Py_XDECREF(cobj);
    Py_XDECREF(d);
    return -1;
}

#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

#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_ssize_t basicsize;
#ifdef Py_LIMITED_API
    PyObject *py_basicsize;
#endif
    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,
            "%.200s.%.200s is not a type object",
            module_name, class_name);
        goto bad;
    }
#ifndef Py_LIMITED_API
    basicsize = ((PyTypeObject *)result)->tp_basicsize;
#else
    py_basicsize = PyObject_GetAttrString(result, "__basicsize__");
    if (!py_basicsize)
        goto bad;
    basicsize = PyLong_AsSsize_t(py_basicsize);
    Py_DECREF(py_basicsize);
    py_basicsize = 0;
    if (basicsize == (Py_ssize_t)-1 && PyErr_Occurred())
        goto bad;
#endif
    if (!strict && (size_t)basicsize > size) {
        PyOS_snprintf(warning, sizeof(warning),
            "%s.%s size changed, may indicate binary incompatibility",
            module_name, class_name);
        if (PyErr_WarnEx(NULL, warning, 0) < 0) goto bad;
    }
    else if ((size_t)basicsize != size) {
        PyErr_Format(PyExc_ValueError,
            "%.200s.%.200s 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

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
        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;
}

static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char* c_str) {
    return __Pyx_PyUnicode_FromStringAndSize(c_str, (Py_ssize_t)strlen(c_str));
}
static CYTHON_INLINE char* __Pyx_PyObject_AsString(PyObject* o) {
    Py_ssize_t ignore;
    return __Pyx_PyObject_AsStringAndSize(o, &ignore);
}
static CYTHON_INLINE char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
    if (
#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
            __Pyx_sys_getdefaultencoding_not_ascii &&
#endif
            PyUnicode_Check(o)) {
#if PY_VERSION_HEX < 0x03030000
        char* defenc_c;
        PyObject* defenc = _PyUnicode_AsDefaultEncodedString(o, NULL);
        if (!defenc) return NULL;
        defenc_c = PyBytes_AS_STRING(defenc);
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
        {
            char* end = defenc_c + PyBytes_GET_SIZE(defenc);
            char* c;
            for (c = defenc_c; c < end; c++) {
                if ((unsigned char) (*c) >= 128) {
                    PyUnicode_AsASCIIString(o);
                    return NULL;
                }
            }
        }
#endif
        *length = PyBytes_GET_SIZE(defenc);
        return defenc_c;
#else
        if (__Pyx_PyUnicode_READY(o) == -1) return NULL;
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
        if (PyUnicode_IS_ASCII(o)) {
            *length = PyUnicode_GET_LENGTH(o);
            return PyUnicode_AsUTF8(o);
        } else {
            PyUnicode_AsASCIIString(o);
            return NULL;
        }
#else
        return PyUnicode_AsUTF8AndSize(o, length);
#endif
#endif
    } else
#endif
#if !CYTHON_COMPILING_IN_PYPY
    if (PyByteArray_Check(o)) {
        *length = PyByteArray_GET_SIZE(o);
        return PyByteArray_AS_STRING(o);
    } else
#endif
    {
        char* result;
        int r = PyBytes_AsStringAndSize(o, &result, length);
        if (unlikely(r < 0)) {
            return NULL;
        } else {
            return result;
        }
    }
}
static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) {
   int is_true = x == Py_True;
   if (is_true | (x == Py_False) | (x == Py_None)) return is_true;
   else return PyObject_IsTrue(x);
}
static CYTHON_INLINE PyObject* __Pyx_PyNumber_Int(PyObject* x) {
  PyNumberMethods *m;
  const char *name = NULL;
  PyObject *res = NULL;
#if PY_MAJOR_VERSION < 3
  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_MAJOR_VERSION < 3
  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_MAJOR_VERSION < 3
    if (!PyInt_Check(res) && !PyLong_Check(res)) {
#else
    if (!PyLong_Check(res)) {
#endif
      PyErr_Format(PyExc_TypeError,
                   "__%.4s__ returned non-%.4s (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;
#if PY_MAJOR_VERSION < 3
  if (likely(PyInt_CheckExact(b)))
      return PyInt_AS_LONG(b);
#endif
  if (likely(PyLong_CheckExact(b))) {
    #if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
     #if CYTHON_USE_PYLONG_INTERNALS
       switch (Py_SIZE(b)) {
       case -1: return -(sdigit)((PyLongObject*)b)->ob_digit[0];
       case  0: return 0;
       case  1: return ((PyLongObject*)b)->ob_digit[0];
       }
     #endif
    #endif
    return PyLong_AsSsize_t(b);
  }
  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) {
    return PyInt_FromSize_t(ival);
}


#endif /* Py_PYTHON_H */
