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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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#define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type)
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  #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
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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___rmsd
#define __PYX_HAVE_API___rmsd
#include "string.h"
#include "stdio.h"
#include "stdlib.h"
#include "numpy/arrayobject.h"
#include "numpy/ufuncobject.h"
#include "pythread.h"
#include "center.h"
#include "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[] = {
  "_rmsd.pyx",
  "__init__.pxd",
  "type.pxd",
  "bool.pxd",
  "complex.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;


/* "../../miniconda/envs/3.4.2/lib/python3.4/site-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;

/* "../../miniconda/envs/3.4.2/lib/python3.4/site-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;

/* "../../miniconda/envs/3.4.2/lib/python3.4/site-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;

/* "../../miniconda/envs/3.4.2/lib/python3.4/site-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;

/* "../../miniconda/envs/3.4.2/lib/python3.4/site-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;

/* "../../miniconda/envs/3.4.2/lib/python3.4/site-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
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typedef npy_uint16 __pyx_t_5numpy_uint16_t;

/* "../../miniconda/envs/3.4.2/lib/python3.4/site-packages/Cython/Includes/numpy/__init__.pxd":732
 * ctypedef npy_uint8      uint8_t
 * ctypedef npy_uint16     uint16_t
 * ctypedef npy_uint32     uint32_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uint64     uint64_t
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 */
typedef npy_uint32 __pyx_t_5numpy_uint32_t;

/* "../../miniconda/envs/3.4.2/lib/python3.4/site-packages/Cython/Includes/numpy/__init__.pxd":733
 * ctypedef npy_uint16     uint16_t
 * ctypedef npy_uint32     uint32_t
 * ctypedef npy_uint64     uint64_t             # <<<<<<<<<<<<<<
 * #ctypedef npy_uint96     uint96_t
 * #ctypedef npy_uint128    uint128_t
 */
typedef npy_uint64 __pyx_t_5numpy_uint64_t;

/* "../../miniconda/envs/3.4.2/lib/python3.4/site-packages/Cython/Includes/numpy/__init__.pxd":737
 * #ctypedef npy_uint128    uint128_t
 * 
 * ctypedef npy_float32    float32_t             # <<<<<<<<<<<<<<
 * ctypedef npy_float64    float64_t
 * #ctypedef npy_float80    float80_t
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typedef npy_float32 __pyx_t_5numpy_float32_t;

/* "../../miniconda/envs/3.4.2/lib/python3.4/site-packages/Cython/Includes/numpy/__init__.pxd":738
 * 
 * ctypedef npy_float32    float32_t
 * ctypedef npy_float64    float64_t             # <<<<<<<<<<<<<<
 * #ctypedef npy_float80    float80_t
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typedef npy_float64 __pyx_t_5numpy_float64_t;

/* "../../miniconda/envs/3.4.2/lib/python3.4/site-packages/Cython/Includes/numpy/__init__.pxd":747
 * # The int types are mapped a bit surprising --
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 * ctypedef npy_longlong   long_t
 * ctypedef npy_longlong   longlong_t
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typedef npy_long __pyx_t_5numpy_int_t;

/* "../../miniconda/envs/3.4.2/lib/python3.4/site-packages/Cython/Includes/numpy/__init__.pxd":748
 * # numpy.int corresponds to 'l' and numpy.long to 'q'
 * ctypedef npy_long       int_t
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 * ctypedef npy_longlong   longlong_t
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 */
typedef npy_longlong __pyx_t_5numpy_long_t;

/* "../../miniconda/envs/3.4.2/lib/python3.4/site-packages/Cython/Includes/numpy/__init__.pxd":749
 * ctypedef npy_long       int_t
 * ctypedef npy_longlong   long_t
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typedef npy_longlong __pyx_t_5numpy_longlong_t;

/* "../../miniconda/envs/3.4.2/lib/python3.4/site-packages/Cython/Includes/numpy/__init__.pxd":751
 * ctypedef npy_longlong   longlong_t
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 * ctypedef npy_ulonglong  ulong_t
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typedef npy_ulong __pyx_t_5numpy_uint_t;

/* "../../miniconda/envs/3.4.2/lib/python3.4/site-packages/Cython/Includes/numpy/__init__.pxd":752
 * 
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typedef npy_ulonglong __pyx_t_5numpy_ulong_t;

/* "../../miniconda/envs/3.4.2/lib/python3.4/site-packages/Cython/Includes/numpy/__init__.pxd":753
 * ctypedef npy_ulong      uint_t
 * ctypedef npy_ulonglong  ulong_t
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typedef npy_ulonglong __pyx_t_5numpy_ulonglong_t;

/* "../../miniconda/envs/3.4.2/lib/python3.4/site-packages/Cython/Includes/numpy/__init__.pxd":755
 * ctypedef npy_ulonglong  ulonglong_t
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typedef npy_intp __pyx_t_5numpy_intp_t;

/* "../../miniconda/envs/3.4.2/lib/python3.4/site-packages/Cython/Includes/numpy/__init__.pxd":756
 * 
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typedef npy_uintp __pyx_t_5numpy_uintp_t;

/* "../../miniconda/envs/3.4.2/lib/python3.4/site-packages/Cython/Includes/numpy/__init__.pxd":758
 * ctypedef npy_uintp      uintp_t
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 */
typedef npy_double __pyx_t_5numpy_float_t;

/* "../../miniconda/envs/3.4.2/lib/python3.4/site-packages/Cython/Includes/numpy/__init__.pxd":759
 * 
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typedef npy_double __pyx_t_5numpy_double_t;

/* "../../miniconda/envs/3.4.2/lib/python3.4/site-packages/Cython/Includes/numpy/__init__.pxd":760
 * ctypedef npy_double     float_t
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/* "../../miniconda/envs/3.4.2/lib/python3.4/site-packages/Cython/Includes/numpy/__init__.pxd":762
 * ctypedef npy_longdouble longdouble_t
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typedef npy_cfloat __pyx_t_5numpy_cfloat_t;

/* "../../miniconda/envs/3.4.2/lib/python3.4/site-packages/Cython/Includes/numpy/__init__.pxd":763
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typedef npy_cdouble __pyx_t_5numpy_cdouble_t;

/* "../../miniconda/envs/3.4.2/lib/python3.4/site-packages/Cython/Includes/numpy/__init__.pxd":764
 * ctypedef npy_cfloat      cfloat_t
 * ctypedef npy_cdouble     cdouble_t
 * ctypedef npy_clongdouble clongdouble_t             # <<<<<<<<<<<<<<
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typedef npy_clongdouble __pyx_t_5numpy_clongdouble_t;

/* "../../miniconda/envs/3.4.2/lib/python3.4/site-packages/Cython/Includes/numpy/__init__.pxd":766
 * ctypedef npy_clongdouble clongdouble_t
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typedef npy_cdouble __pyx_t_5numpy_complex_t;
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static void __Pyx_RaiseArgtupleInvalid(const char* func_name, int exact,
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static void __Pyx_RaiseDoubleKeywordsError(const char* func_name, PyObject* kw_name);

static int __Pyx_ParseOptionalKeywords(PyObject *kwds, PyObject **argnames[], \
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static CYTHON_INLINE int __Pyx_ArgTypeTest(PyObject *obj, PyTypeObject *type, int none_allowed,
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static CYTHON_INLINE PyObject *__Pyx_GetModuleGlobalName(PyObject *name);

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static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw);
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#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg);
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static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg);

#define __Pyx_GetItemInt(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck) \
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static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i,
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static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j);
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i,
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static CYTHON_INLINE void __Pyx_ErrRestore(PyObject *type, PyObject *value, PyObject *tb);
static CYTHON_INLINE void __Pyx_ErrFetch(PyObject **type, PyObject **value, PyObject **tb);

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

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

static CYTHON_INLINE int  __Pyx_GetBufferAndValidate(Py_buffer* buf, PyObject* obj,
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static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info);

static void __Pyx_RaiseBufferFallbackError(void);

static void __Pyx_RaiseBufferIndexError(int axis);

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#define __Pyx_BufPtrCContig3d(type, buf, i0, s0, i1, s1, i2, s2) ((type)((char*)buf + i0 * s0 + i1 * s1) + i2)
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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);

static PyObject* __Pyx_ImportFrom(PyObject* module, PyObject* name);

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static PyObject *__Pyx_ImportModule(const char *name);

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/* Module declarations from 'cython' */

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

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

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

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

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

/* Module declarations from '__builtin__' */

/* 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 'cpython.version' */

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

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

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

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

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

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

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

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

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

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

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/* Module declarations from 'cpython.bool' */
static PyTypeObject *__pyx_ptype_7cpython_4bool_bool = 0;

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static PyTypeObject *__pyx_ptype_7cpython_7complex_complex = 0;

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

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

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

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

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

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

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

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

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

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

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

/* Module declarations from 'cpython' */

/* Module declarations from '_rmsd' */
__PYX_EXTERN_C DL_IMPORT(float) msd_axis_major(int, int, int, float *, float *, float, float); /*proto*/
__PYX_EXTERN_C DL_IMPORT(float) msd_atom_major(int, int, float *, float *, float, float, int, float *); /*proto*/
__PYX_EXTERN_C DL_IMPORT(float) rot_msd_atom_major(int const , int const , float const *, float const *, float const *); /*proto*/
__PYX_EXTERN_C DL_IMPORT(float) rot_atom_major(int const , float *, float const *); /*proto*/
static __Pyx_TypeInfo __Pyx_TypeInfo_nn___pyx_t_5numpy_float32_t = { "float32_t", NULL, sizeof(__pyx_t_5numpy_float32_t), { 0 }, 0, 'R', 0, 0 };
#define __Pyx_MODULE_NAME "_rmsd"
int __pyx_module_is_main__rmsd = 0;

/* Implementation of '_rmsd' */
static PyObject *__pyx_builtin_ValueError;
static PyObject *__pyx_builtin_range;
static PyObject *__pyx_builtin_RuntimeError;
static PyObject *__pyx_pf_5_rmsd_rmsd(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_target, PyObject *__pyx_v_reference, int __pyx_v_frame, PyObject *__pyx_v_atom_indices, PyBoolObject *__pyx_v_parallel, PyBoolObject *__pyx_v_precentered); /* proto */
static PyObject *__pyx_pf_5_rmsd_2_center_inplace_atom_major(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_xyz); /* proto */
static PyObject *__pyx_pf_5_rmsd_4getMultipleRMSDs_axis_major(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_xyz1, PyArrayObject *__pyx_v_xyz2, PyArrayObject *__pyx_v_g1, PyArrayObject *__pyx_v_g2, int __pyx_v_frame, PyBoolObject *__pyx_v_parallel); /* proto */
static PyObject *__pyx_pf_5_rmsd_6getMultipleRMSDs_atom_major(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_xyz1, PyArrayObject *__pyx_v_xyz2, PyArrayObject *__pyx_v_g1, PyArrayObject *__pyx_v_g2, int __pyx_v_frame, PyBoolObject *__pyx_v_parallel); /* proto */
static PyObject *__pyx_pf_5_rmsd_8superpose_atom_major(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_xyz_align_target, PyArrayObject *__pyx_v_xyz_align_mobile, PyArrayObject *__pyx_v_g_target, PyArrayObject *__pyx_v_g_mobile, PyArrayObject *__pyx_v_xyz_displace_mobile, int __pyx_v_target_frame, PyBoolObject *__pyx_v_parallel); /* proto */
static PyObject *__pyx_pf_5_rmsd_10getMultipleAlignDisplaceRMSDs_atom_major(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_xyz_align1, PyArrayObject *__pyx_v_xyz_align2, PyArrayObject *__pyx_v_g_align1, PyArrayObject *__pyx_v_g_align2, PyArrayObject *__pyx_v_xyz_displ1, PyArrayObject *__pyx_v_xyz_displ2, int __pyx_v_n_atoms_align, int __pyx_v_n_atoms_displ, int __pyx_v_frame, PyBoolObject *__pyx_v_parallel); /* 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_C[] = "C";
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_l[] = "l";
static char __pyx_k_q[] = "q";
static char __pyx_k_Zd[] = "Zd";
static char __pyx_k_Zf[] = "Zf";
static char __pyx_k_Zg[] = "Zg";
static char __pyx_k_g1[] = "g1";
static char __pyx_k_g2[] = "g2";
static char __pyx_k_np[] = "np";
static char __pyx_k_all[] = "all";
static char __pyx_k_int[] = "int";
static char __pyx_k_msd[] = "msd";
static char __pyx_k_rot[] = "rot";
static char __pyx_k_xyz[] = "xyz";
static char __pyx_k_main[] = "__main__";
static char __pyx_k_name[] = "name";
static char __pyx_k_ndim[] = "ndim";
static char __pyx_k_rmsd[] = "rmsd";
static char __pyx_k_test[] = "__test__";
static char __pyx_k_xyz1[] = "xyz1";
static char __pyx_k_xyz2[] = "xyz2";
static char __pyx_k_dtype[] = "dtype";
static char __pyx_k_empty[] = "empty";
static char __pyx_k_flags[] = "flags";
static char __pyx_k_frame[] = "frame";
static char __pyx_k_numpy[] = "numpy";
static char __pyx_k_order[] = "order";
static char __pyx_k_range[] = "range";
static char __pyx_k_ref_g[] = "ref_g";
static char __pyx_k_shape[] = "shape";
static char __pyx_k_zeros[] = "zeros";
static char __pyx_k_import[] = "__import__";
static char __pyx_k_rmsd_2[] = "_rmsd";
static char __pyx_k_target[] = "target";
static char __pyx_k_traces[] = "traces";
static char __pyx_k_asarray[] = "asarray";
static char __pyx_k_float32[] = "float32";
static char __pyx_k_n_atoms[] = "n_atoms";
static char __pyx_k_g_align1[] = "g_align1";
static char __pyx_k_g_align2[] = "g_align2";
static char __pyx_k_g_mobile[] = "g_mobile";
static char __pyx_k_g_target[] = "g_target";
static char __pyx_k_n_frames[] = "n_frames";
static char __pyx_k_parallel[] = "parallel";
static char __pyx_k_target_g[] = "target_g";
static char __pyx_k_distances[] = "distances";
static char __pyx_k_reference[] = "reference";
static char __pyx_k_writeable[] = "writeable";
static char __pyx_k_ValueError[] = "ValueError";
static char __pyx_k_target_xyz[] = "target_xyz";
static char __pyx_k_xyz_align1[] = "xyz_align1";
static char __pyx_k_xyz_align2[] = "xyz_align2";
static char __pyx_k_xyz_displ1[] = "xyz_displ1";
static char __pyx_k_xyz_displ2[] = "xyz_displ2";
static char __pyx_k_ensure_type[] = "ensure_type";
static char __pyx_k_precentered[] = "precentered";
static char __pyx_k_rmsd_traces[] = "_rmsd_traces";
static char __pyx_k_RuntimeError[] = "RuntimeError";
static char __pyx_k_atom_indices[] = "atom_indices";
static char __pyx_k_mdtraj_utils[] = "mdtraj.utils";
static char __pyx_k_rmsd_line_60[] = "rmsd (line 60)";
static char __pyx_k_target_frame[] = "target_frame";
static char __pyx_k_n_atoms_align[] = "n_atoms_align";
static char __pyx_k_n_atoms_displ[] = "n_atoms_displ";
static char __pyx_k_ref_xyz_frame[] = "ref_xyz_frame";
static char __pyx_k_target_n_frames[] = "target_n_frames";
static char __pyx_k_n_atoms_displace[] = "n_atoms_displace";
static char __pyx_k_xyz_align_mobile[] = "xyz_align_mobile";
static char __pyx_k_xyz_align_target[] = "xyz_align_target";
static char __pyx_k_xyz_displace_mobile[] = "xyz_displace_mobile";
static char __pyx_k_n_align_atoms_padded[] = "n_align_atoms_padded";
static char __pyx_k_n_displ_atoms_padded[] = "n_displ_atoms_padded";
static char __pyx_k_superpose_atom_major[] = "superpose_atom_major";
static char __pyx_k_xyz_is_not_writeable[] = "xyz is not writeable";
static char __pyx_k_center_inplace_atom_major[] = "_center_inplace_atom_major";
static char __pyx_k_getMultipleRMSDs_atom_major[] = "getMultipleRMSDs_atom_major";
static char __pyx_k_getMultipleRMSDs_axis_major[] = "getMultipleRMSDs_axis_major";
static char __pyx_k_ndarray_is_not_C_contiguous[] = "ndarray is not C contiguous";
static char __pyx_k_target_xyz_is_not_writeable[] = "target_xyz is not writeable";
static char __pyx_k_home_rmcgibbo_local_mdtraj_mdtr[] = "/home/rmcgibbo/local/mdtraj/mdtraj/rmsd/_rmsd.pyx";
static char __pyx_k_unknown_dtype_code_in_numpy_pxd[] = "unknown dtype code in numpy.pxd (%d)";
static char __pyx_k_Cannot_calculate_RMSD_of_frame_d[] = "Cannot calculate RMSD of frame %d: reference has only %d frames.";
static char __pyx_k_Format_string_allocated_too_shor[] = "Format string allocated too short, see comment in numpy.pxd";
static char __pyx_k_Input_arrays_must_have_middle_di[] = "Input arrays must have middle dimension of 4*n, found %d and %d.";
static char __pyx_k_Input_arrays_must_have_same_numb[] = "Input arrays must have same number of atoms. found %d and %d.";
static char __pyx_k_Input_trajectories_must_have_sam[] = "Input trajectories must have same number of atoms. found %d and %d.";
static char __pyx_k_Non_native_byte_order_not_suppor[] = "Non-native byte order not supported";
static char __pyx_k_atom_indices_must_be_valid_posit[] = "atom_indices must be valid positive indices";
static char __pyx_k_getMultipleAlignDisplaceRMSDs_at[] = "getMultipleAlignDisplaceRMSDs_atom_major";
static char __pyx_k_ndarray_is_not_Fortran_contiguou[] = "ndarray is not Fortran contiguous";
static char __pyx_k_rmsd_target_reference_frame_0_at[] = "rmsd(target, reference, frame=0, atom_indices=None, parallel=True, precentered=False)\n\n    Compute RMSD of all conformations in target to a reference conformation.\n    Note, this will center the conformations in place.\n\n    Parameters\n    ----------\n    target : md.Trajectory\n        For each conformation in this trajectory, compute the RMSD to\n        a particular 'reference' conformation in another trajectory\n        object.\n    reference : md.Trajectory\n        The object containing the reference conformation to measure distances\n        to.\n    frame : int\n        The index of the conformation in `reference` to measure\n        distances to.\n    atom_indices : array_like, or None\n        The indices of the atoms to use in the RMSD calculation. If not\n        supplied, all atoms will be used.\n    parallel : bool\n        Use OpenMP to calculate each of the RMSDs in parallel over\n        multiple cores.\n    precentered : bool, default=False\n        Assume that the conformations are already centered at the origin, and that\n        the \"rmsd_traces\" have been computed, as is done by\n        `Trajectory.center_coordinates`. The \"rmsd_traces\" are intermediate\n        calculations needed for the RMSD calculation which can be computed\n        independently on each trajectory. Note that this has the potential to\n        be unsafe; if you use Trajectory.center_coordinates and then modify\n        the trajectory's coordinates, the center and traces will be out of\n        date and the RMSDs will be incorrect.\n\n    Examples\n    --------\n    >>> import mdtraj as md                                      # doctest: +SKIP\n    >>> rmsds = md.rmsd(trajectory, trajectory, 0)               # doctest: +SKIP\n    >>> print rmdsds                                             # doctest: +SKIP\n    array([ 0.0,  0.03076187,  0.02549562, ...,  0.06230228,\n        0.00666826,  0.24364147])\n\n    The calculation is slightly faster if you precenter the tr""ajectory\n\n    >>> trajectory.center_coordinates()\n    >>> rmsds = md.rmsd(trajectory, trajectory, 0, precentered=True)\n\n    See Also\n    --------\n    Trajectory.center_coordinates\n\n    Notes\n    -----\n    This function uses OpenMP to parallelize the calculation across\n    multiple cores. To control the number of threads launched by OpenMP,\n    you can set the environment variable ``OMP_NUM_THREADS``.\n\n    Returns\n    -------\n    rmsds : np.ndarray, shape=(target.n_frames,)\n        A 1-D numpy array of the optimal root-mean-square deviations from\n        the `frame`-th conformation in reference to each of the conformations\n        in target.\n    ";
static char __pyx_k_xyz_align1_and_xyz_displ1_must_c[] = "xyz_align1 and xyz_displ1 must contain the same number of frames";
static char __pyx_k_xyz_align2_and_xyz_displ2_must_c[] = "xyz_align2 and xyz_displ2 must contain the same number of frames";
static char __pyx_k_xyz_align_mobile_and_xyz_displac[] = "xyz_align_mobile and xyz_displace_mobile must contain the same number of frames";
static char __pyx_k_Cannot_calculate_RMSD_of_frame_d_2[] = "Cannot calculate RMSD of frame %d: xyz1 has only %d frames.";
static char __pyx_k_Format_string_allocated_too_shor_2[] = "Format string allocated too short.";
static PyObject *__pyx_n_s_C;
static PyObject *__pyx_kp_s_Cannot_calculate_RMSD_of_frame_d;
static PyObject *__pyx_kp_s_Cannot_calculate_RMSD_of_frame_d_2;
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_s_Input_arrays_must_have_middle_di;
static PyObject *__pyx_kp_s_Input_arrays_must_have_same_numb;
static PyObject *__pyx_kp_s_Input_trajectories_must_have_sam;
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_all;
static PyObject *__pyx_n_s_asarray;
static PyObject *__pyx_n_s_atom_indices;
static PyObject *__pyx_kp_s_atom_indices_must_be_valid_posit;
static PyObject *__pyx_n_s_center_inplace_atom_major;
static PyObject *__pyx_n_s_distances;
static PyObject *__pyx_n_s_dtype;
static PyObject *__pyx_n_s_empty;
static PyObject *__pyx_n_s_ensure_type;
static PyObject *__pyx_n_s_flags;
static PyObject *__pyx_n_s_float32;
static PyObject *__pyx_n_s_frame;
static PyObject *__pyx_n_s_g1;
static PyObject *__pyx_n_s_g2;
static PyObject *__pyx_n_s_g_align1;
static PyObject *__pyx_n_s_g_align2;
static PyObject *__pyx_n_s_g_mobile;
static PyObject *__pyx_n_s_g_target;
static PyObject *__pyx_n_s_getMultipleAlignDisplaceRMSDs_at;
static PyObject *__pyx_n_s_getMultipleRMSDs_atom_major;
static PyObject *__pyx_n_s_getMultipleRMSDs_axis_major;
static PyObject *__pyx_kp_s_home_rmcgibbo_local_mdtraj_mdtr;
static PyObject *__pyx_n_s_i;
static PyObject *__pyx_n_s_import;
static PyObject *__pyx_n_s_int;
static PyObject *__pyx_n_s_main;
static PyObject *__pyx_n_s_mdtraj_utils;
static PyObject *__pyx_n_s_msd;
static PyObject *__pyx_n_s_n_align_atoms_padded;
static PyObject *__pyx_n_s_n_atoms;
static PyObject *__pyx_n_s_n_atoms_align;
static PyObject *__pyx_n_s_n_atoms_displ;
static PyObject *__pyx_n_s_n_atoms_displace;
static PyObject *__pyx_n_s_n_displ_atoms_padded;
static PyObject *__pyx_n_s_n_frames;
static PyObject *__pyx_n_s_name;
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_ndim;
static PyObject *__pyx_n_s_np;
static PyObject *__pyx_n_s_numpy;
static PyObject *__pyx_n_s_order;
static PyObject *__pyx_n_s_parallel;
static PyObject *__pyx_n_s_precentered;
static PyObject *__pyx_n_s_range;
static PyObject *__pyx_n_s_ref_g;
static PyObject *__pyx_n_s_ref_xyz_frame;
static PyObject *__pyx_n_s_reference;
static PyObject *__pyx_n_s_rmsd;
static PyObject *__pyx_n_s_rmsd_2;
static PyObject *__pyx_kp_u_rmsd_line_60;
static PyObject *__pyx_kp_u_rmsd_target_reference_frame_0_at;
static PyObject *__pyx_n_s_rmsd_traces;
static PyObject *__pyx_n_s_rot;
static PyObject *__pyx_n_s_shape;
static PyObject *__pyx_n_s_superpose_atom_major;
static PyObject *__pyx_n_s_target;
static PyObject *__pyx_n_s_target_frame;
static PyObject *__pyx_n_s_target_g;
static PyObject *__pyx_n_s_target_n_frames;
static PyObject *__pyx_n_s_target_xyz;
static PyObject *__pyx_kp_s_target_xyz_is_not_writeable;
static PyObject *__pyx_n_s_test;
static PyObject *__pyx_n_s_traces;
static PyObject *__pyx_kp_u_unknown_dtype_code_in_numpy_pxd;
static PyObject *__pyx_n_s_writeable;
static PyObject *__pyx_n_s_xyz;
static PyObject *__pyx_n_s_xyz1;
static PyObject *__pyx_n_s_xyz2;
static PyObject *__pyx_n_s_xyz_align1;
static PyObject *__pyx_kp_s_xyz_align1_and_xyz_displ1_must_c;
static PyObject *__pyx_n_s_xyz_align2;
static PyObject *__pyx_kp_s_xyz_align2_and_xyz_displ2_must_c;
static PyObject *__pyx_n_s_xyz_align_mobile;
static PyObject *__pyx_kp_s_xyz_align_mobile_and_xyz_displac;
static PyObject *__pyx_n_s_xyz_align_target;
static PyObject *__pyx_n_s_xyz_displ1;
static PyObject *__pyx_n_s_xyz_displ2;
static PyObject *__pyx_n_s_xyz_displace_mobile;
static PyObject *__pyx_kp_s_xyz_is_not_writeable;
static PyObject *__pyx_n_s_zeros;
static PyObject *__pyx_int_0;
static PyObject *__pyx_int_1;
static PyObject *__pyx_int_3;
static PyObject *__pyx_slice_;
static PyObject *__pyx_slice__3;
static PyObject *__pyx_slice__4;
static PyObject *__pyx_slice__5;
static PyObject *__pyx_slice__6;
static PyObject *__pyx_slice__7;
static PyObject *__pyx_tuple__2;
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/* "_rmsd.pyx":60
 * ##############################################################################
 * 
 * def rmsd(target, reference, int frame=0, atom_indices=None, bool parallel=True, bool precentered=False):             # <<<<<<<<<<<<<<
 *     """rmsd(target, reference, frame=0, atom_indices=None, parallel=True, precentered=False)
 * 
 */

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static char __pyx_doc_5_rmsd_rmsd[] = "rmsd(target, reference, frame=0, atom_indices=None, parallel=True, precentered=False)\n\n    Compute RMSD of all conformations in target to a reference conformation.\n    Note, this will center the conformations in place.\n\n    Parameters\n    ----------\n    target : md.Trajectory\n        For each conformation in this trajectory, compute the RMSD to\n        a particular 'reference' conformation in another trajectory\n        object.\n    reference : md.Trajectory\n        The object containing the reference conformation to measure distances\n        to.\n    frame : int\n        The index of the conformation in `reference` to measure\n        distances to.\n    atom_indices : array_like, or None\n        The indices of the atoms to use in the RMSD calculation. If not\n        supplied, all atoms will be used.\n    parallel : bool\n        Use OpenMP to calculate each of the RMSDs in parallel over\n        multiple cores.\n    precentered : bool, default=False\n        Assume that the conformations are already centered at the origin, and that\n        the \"rmsd_traces\" have been computed, as is done by\n        `Trajectory.center_coordinates`. The \"rmsd_traces\" are intermediate\n        calculations needed for the RMSD calculation which can be computed\n        independently on each trajectory. Note that this has the potential to\n        be unsafe; if you use Trajectory.center_coordinates and then modify\n        the trajectory's coordinates, the center and traces will be out of\n        date and the RMSDs will be incorrect.\n\n    Examples\n    --------\n    >>> import mdtraj as md                                      # doctest: +SKIP\n    >>> rmsds = md.rmsd(trajectory, trajectory, 0)               # doctest: +SKIP\n    >>> print rmdsds                                             # doctest: +SKIP\n    array([ 0.0,  0.03076187,  0.02549562, ...,  0.06230228,\n        0.00666826,  0.24364147])\n\n    The calculation is slightly faster if you precenter the tr""ajectory\n\n    >>> trajectory.center_coordinates()\n    >>> rmsds = md.rmsd(trajectory, trajectory, 0, precentered=True)\n\n    See Also\n    --------\n    Trajectory.center_coordinates\n\n    Notes\n    -----\n    This function uses OpenMP to parallelize the calculation across\n    multiple cores. To control the number of threads launched by OpenMP,\n    you can set the environment variable ``OMP_NUM_THREADS``.\n\n    Returns\n    -------\n    rmsds : np.ndarray, shape=(target.n_frames,)\n        A 1-D numpy array of the optimal root-mean-square deviations from\n        the `frame`-th conformation in reference to each of the conformations\n        in target.\n    ";
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/* "_rmsd.pyx":264
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/* "_rmsd.pyx":328
 * @cython.boundscheck(False)
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 * np.ndarray[np.float32_t, ndim=3, mode="c"] xyz_align_target not None,
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                              /* "_rmsd.pyx":374
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 *     if parallel == True:
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/* "_rmsd.pyx":385
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 * np.ndarray[np.float32_t, ndim=3, mode="c"] xyz_align2 not None,
 */

/* Python wrapper */
static PyObject *__pyx_pw_5_rmsd_11getMultipleAlignDisplaceRMSDs_atom_major(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/
static char __pyx_doc_5_rmsd_10getMultipleAlignDisplaceRMSDs_atom_major[] = "getMultipleAlignDisplaceRMSDs_atom_major(xyz_align1, xyz_align2, g_align1, g_align2, xyz_displ1, xyz_displ2, n_atoms_align, n_atoms_displ, frame, parallel=True)\n\n    Calculate the RMSD of several frames to a single frame, with the\n    coordinates laid out in atom-major orders, where alignments are computed\n    by determining the optimal rotation matrix to align `xyz_align1` against\n    `xyz_align2`, and then using this rotation matrix displace `xyz_displ1`,\n    and computing its mean-squared-displacement with respect to `xyz_displ2`.\n\n    Parameters\n    ----------\n    xyz_align1 : np.ndarray, shape=(n_frames, n_atoms_align_padded, 3), dtype=float32\n        Alignment coordinates of reference frame.\n    xyz_align2 : np.ndarray, shape=(n_frames, n_atoms_align_padded, 3), dtype=float32\n        Alignment coordinates of frames to iterate over.\n    g_align1 : np.ndarray, shape = (n_frames), dtype=float32\n        Pre-calculated G factors (traces) for each frame in xyz1\n    g_align2 : np.ndarray, shape = (n_frames), dtype=float32\n        Pre-calculated G factors (traces) for each frame in xyz2\n    xyz_displ1 : np.ndarray, shape=(n_frames, n_atoms_displ_padded, 3), dtype=float32\n        Displacement coordinates of reference frame.\n    xyz_displ2 : np.ndarray, shape=(n_frames, n_atoms_displ_padded, 3), dtype=float32\n        Displacement coordinates of frames to iterate over.\n    n_atoms_align : int\n        The number of true atoms in the alignment coordinates\n    n_atoms_displ : int\n        The number of true atoms in the displacement coordinates\n    frame : int\n        Index of the desired reference frame in xyz_align1 / xyz_displ1.\n    parallel : bool, default True\n        If True, use OpenMP parallelization.\n\n    Returns\n    -------\n    rmsds: np.ndarray, shape=(len(xyz2),)\n        RMSDs between xyz_displ1[frame] and all of xyz_displ2, after the alignment that maximizes\n        the overlap between xyz_align1[frame] and all of xyz_align2""\n    rotations: np.ndarray, shape=(len(xyz2), 3, 3)\n        The rotation matrix for each of the alignments\n    ";
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 */
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  /* "../../miniconda/envs/3.4.2/lib/python3.4/site-packages/Cython/Includes/numpy/__init__.pxd":976
 *      arr.base = baseptr
 * 
 * cdef inline object get_array_base(ndarray arr):             # <<<<<<<<<<<<<<
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 */

  /*--- Wrapped vars code ---*/

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    Py_DECREF(__pyx_m); __pyx_m = 0;
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static __Pyx_RefNannyAPIStruct *__Pyx_RefNannyImportAPI(const char *modname) {
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        PyErr_Format(PyExc_NameError,
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static void __Pyx_RaiseArgtupleInvalid(
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{
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        "%s() got multiple values for keyword argument '%s'", func_name,
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        #endif
}

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        #if PY_MAJOR_VERSION < 3
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        #endif
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                #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
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                    int cmp = (**argname == key) ? 0 :
                    #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
                        (PyUnicode_GET_SIZE(**argname) != PyUnicode_GET_SIZE(key)) ? 1 :
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                        PyUnicode_Compare(**argname, key);
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arg_passed_twice:
    __Pyx_RaiseDoubleKeywordsError(function_name, key);
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invalid_keyword_type:
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    goto bad;
invalid_keyword:
    PyErr_Format(PyExc_TypeError,
    #if PY_MAJOR_VERSION < 3
        "%.200s() got an unexpected keyword argument '%.200s'",
        function_name, PyString_AsString(key));
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        "%s() got an unexpected keyword argument '%U'",
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bad:
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static void __Pyx_RaiseArgumentTypeInvalid(const char* name, PyObject *obj, PyTypeObject *type) {
    PyErr_Format(PyExc_TypeError,
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static CYTHON_INLINE int __Pyx_ArgTypeTest(PyObject *obj, PyTypeObject *type, int none_allowed,
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        #if PY_MAJOR_VERSION == 2
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        #endif
    }
    else {
        if (likely(PyObject_TypeCheck(obj, type))) return 1;
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    __Pyx_RaiseArgumentTypeInvalid(name, obj, type);
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}

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

#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,
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#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg) {
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    Py_LeaveRecursiveCall();
    if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
        PyErr_SetString(
            PyExc_SystemError,
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}
#endif

#if CYTHON_COMPILING_IN_CPYTHON
static PyObject* __Pyx__PyObject_CallOneArg(PyObject *func, PyObject *arg) {
    PyObject *result;
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    PyTuple_SET_ITEM(args, 0, arg);
    result = __Pyx_PyObject_Call(func, args, NULL);
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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) {
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}
#endif

static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j) {
    PyObject *r;
    if (!j) return NULL;
    r = PyObject_GetItem(o, j);
    Py_DECREF(j);
    return r;
}
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i,
                                                              int wraparound, int boundscheck) {
#if CYTHON_COMPILING_IN_CPYTHON
    if (wraparound & unlikely(i < 0)) i += PyList_GET_SIZE(o);
    if ((!boundscheck) || likely((0 <= i) & (i < PyList_GET_SIZE(o)))) {
        PyObject *r = PyList_GET_ITEM(o, i);
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        return r;
    }
    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
#else
    return PySequence_GetItem(o, i);
#endif
}
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i,
                                                              int wraparound, int boundscheck) {
#if CYTHON_COMPILING_IN_CPYTHON
    if (wraparound & unlikely(i < 0)) i += PyTuple_GET_SIZE(o);
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        PyObject *r = PyTuple_GET_ITEM(o, i);
        Py_INCREF(r);
        return r;
    }
    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
#else
    return PySequence_GetItem(o, i);
#endif
}
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i,
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            PyObject *r = PyList_GET_ITEM(o, n);
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    else if (PyTuple_CheckExact(o)) {
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            return r;
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#else
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#if PY_MAJOR_VERSION < 3
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        Py_INCREF(value);
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        Py_INCREF(tb);
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            PyErr_SetString(PyExc_TypeError,
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#if CYTHON_COMPILING_IN_PYPY
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            Py_INCREF(Py_None);
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            PyErr_SetString(PyExc_TypeError,
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    } 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

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 CYTHON_INLINE int __Pyx_IsLittleEndian(void) {
  unsigned int n = 1;
  return *(unsigned char*)(&n) != 0;
}
static void __Pyx_BufFmt_Init(__Pyx_BufFmt_Context* ctx,
                              __Pyx_BufFmt_StackElem* stack,
                              __Pyx_TypeInfo* type) {
  stack[0].field = &ctx->root;
  stack[0].parent_offset = 0;
  ctx->root.type = type;
  ctx->root.name = "buffer dtype";
  ctx->root.offset = 0;
  ctx->head = stack;
  ctx->head->field = &ctx->root;
  ctx->fmt_offset = 0;
  ctx->head->parent_offset = 0;
  ctx->new_packmode = '@';
  ctx->enc_packmode = '@';
  ctx->new_count = 1;
  ctx->enc_count = 0;
  ctx->enc_type = 0;
  ctx->is_complex = 0;
  ctx->is_valid_array = 0;
  ctx->struct_alignment = 0;
  while (type->typegroup == 'S') {
    ++ctx->head;
    ctx->head->field = type->fields;
    ctx->head->parent_offset = 0;
    type = type->fields->type;
  }
}
static int __Pyx_BufFmt_ParseNumber(const char** ts) {
    int count;
    const char* t = *ts;
    if (*t < '0' || *t > '9') {
      return -1;
    } else {
        count = *t++ - '0';
        while (*t >= '0' && *t < '9') {
            count *= 10;
            count += *t++ - '0';
        }
    }
    *ts = t;
    return count;
}
static int __Pyx_BufFmt_ExpectNumber(const char **ts) {
    int number = __Pyx_BufFmt_ParseNumber(ts);
    if (number == -1)
        PyErr_Format(PyExc_ValueError,\
                     "Does not understand character buffer dtype format string ('%c')", **ts);
    return number;
}
static void __Pyx_BufFmt_RaiseUnexpectedChar(char ch) {
  PyErr_Format(PyExc_ValueError,
               "Unexpected format string character: '%c'", ch);
}
static const char* __Pyx_BufFmt_DescribeTypeChar(char ch, int is_complex) {
  switch (ch) {
    case '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);
}

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

static void __Pyx_RaiseBufferIndexError(int axis) {
  PyErr_Format(PyExc_IndexError,
     "Out of bounds on buffer access (axis %d)", axis);
}

static void __Pyx_RaiseBufferIndexErrorNogil(int axis) {
    #ifdef WITH_THREAD
    PyGILState_STATE gilstate = PyGILState_Ensure();
    #endif
    __Pyx_RaiseBufferIndexError(axis);
    #ifdef WITH_THREAD
    PyGILState_Release(gilstate);
    #endif
}

static CYTHON_INLINE long __Pyx_mod_long(long a, long b) {
    long r = a % b;
    r += ((r != 0) & ((r ^ b) < 0)) * b;
    return r;
}

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 PyObject* __Pyx_ImportFrom(PyObject* module, PyObject* name) {
    PyObject* value = __Pyx_PyObject_GetAttrStr(module, name);
    if (unlikely(!value) && PyErr_ExceptionMatches(PyExc_AttributeError)) {
        PyErr_Format(PyExc_ImportError,
        #if PY_MAJOR_VERSION < 3
            "cannot import name %.230s", PyString_AS_STRING(name));
        #else
            "cannot import name %S", name);
        #endif
    }
    return value;
}

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 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 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_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 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;
}

#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 */
