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typedef struct {
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#define __Pyx_void_to_None(void_result) ((void)(void_result), Py_INCREF(Py_None), Py_None)

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    #define __PYX_EXTERN_C extern
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#define __PYX_HAVE__pandas___period
#define __PYX_HAVE_API__pandas___period
#include "string.h"
#include "stdio.h"
#include "pythread.h"
#include "stdlib.h"
#include "numpy/arrayobject.h"
#include "numpy/ufuncobject.h"
#include "datetime_helper.h"
#include "headers/stdint.h"
#include "datetime.h"
#include "numpy/ndarrayobject.h"
#include "numpy_helper.h"
#include "numpy/npy_common.h"
#include "datetime/np_datetime.h"
#include "datetime/np_datetime_strings.h"
#include "period_helper.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
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#ifndef CYTHON_NCP_UNUSED
# if CYTHON_COMPILING_IN_CPYTHON
#  define CYTHON_NCP_UNUSED
# else
#  define CYTHON_NCP_UNUSED CYTHON_UNUSED
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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_uchar_cast(c) ((unsigned char)c)
#define __Pyx_long_cast(x) ((long)x)
#define __Pyx_fits_Py_ssize_t(v, type, is_signed)  (\
    (sizeof(type) < sizeof(Py_ssize_t))  ||\
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          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)))  )
#if defined (__cplusplus) && __cplusplus >= 201103L
    #include <cstdlib>
    #define __Pyx_sst_abs(value) std::abs(value)
#elif SIZEOF_INT >= SIZEOF_SIZE_T
    #define __Pyx_sst_abs(value) abs(value)
#elif SIZEOF_LONG >= SIZEOF_SIZE_T
    #define __Pyx_sst_abs(value) labs(value)
#elif defined (_MSC_VER) && defined (_M_X64)
    #define __Pyx_sst_abs(value) _abs64(value)
#elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
    #define __Pyx_sst_abs(value) llabs(value)
#elif defined (__GNUC__)
    #define __Pyx_sst_abs(value) __builtin_llabs(value)
#else
    #define __Pyx_sst_abs(value) ((value<0) ? -value : value)
#endif
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_FromCString(s)  __Pyx_PyObject_FromString((const char*)s)
#define __Pyx_PyBytes_FromCString(s)   __Pyx_PyBytes_FromString((const char*)s)
#define __Pyx_PyByteArray_FromCString(s)   __Pyx_PyByteArray_FromString((const char*)s)
#define __Pyx_PyStr_FromCString(s)     __Pyx_PyStr_FromString((const char*)s)
#define __Pyx_PyUnicode_FromCString(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_NewRef(obj) (Py_INCREF(obj), obj)
#define __Pyx_Owned_Py_None(b) __Pyx_NewRef(Py_None)
#define __Pyx_PyBool_FromLong(b) ((b) ? __Pyx_NewRef(Py_True) : __Pyx_NewRef(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*) "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[] = {
  "pandas/src/period.pyx",
  "pandas/src/datetime.pxd",
  "pandas/src/util.pxd",
  "pandas/src/numpy.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;


/* "numpy.pxd":726
 * # in Cython to enable them only on the right systems.
 * 
 * ctypedef npy_int8       int8_t             # <<<<<<<<<<<<<<
 * ctypedef npy_int16      int16_t
 * ctypedef npy_int32      int32_t
 */
typedef npy_int8 __pyx_t_5numpy_int8_t;

/* "numpy.pxd":727
 * 
 * ctypedef npy_int8       int8_t
 * ctypedef npy_int16      int16_t             # <<<<<<<<<<<<<<
 * ctypedef npy_int32      int32_t
 * ctypedef npy_int64      int64_t
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typedef npy_int16 __pyx_t_5numpy_int16_t;

/* "numpy.pxd":728
 * ctypedef npy_int8       int8_t
 * ctypedef npy_int16      int16_t
 * ctypedef npy_int32      int32_t             # <<<<<<<<<<<<<<
 * ctypedef npy_int64      int64_t
 * #ctypedef npy_int96      int96_t
 */
typedef npy_int32 __pyx_t_5numpy_int32_t;

/* "numpy.pxd":729
 * ctypedef npy_int16      int16_t
 * ctypedef npy_int32      int32_t
 * ctypedef npy_int64      int64_t             # <<<<<<<<<<<<<<
 * #ctypedef npy_int96      int96_t
 * #ctypedef npy_int128     int128_t
 */
typedef npy_int64 __pyx_t_5numpy_int64_t;

/* "numpy.pxd":733
 * #ctypedef npy_int128     int128_t
 * 
 * ctypedef npy_uint8      uint8_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uint16     uint16_t
 * ctypedef npy_uint32     uint32_t
 */
typedef npy_uint8 __pyx_t_5numpy_uint8_t;

/* "numpy.pxd":734
 * 
 * ctypedef npy_uint8      uint8_t
 * ctypedef npy_uint16     uint16_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uint32     uint32_t
 * ctypedef npy_uint64     uint64_t
 */
typedef npy_uint16 __pyx_t_5numpy_uint16_t;

/* "numpy.pxd":735
 * ctypedef npy_uint8      uint8_t
 * ctypedef npy_uint16     uint16_t
 * ctypedef npy_uint32     uint32_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uint64     uint64_t
 * #ctypedef npy_uint96     uint96_t
 */
typedef npy_uint32 __pyx_t_5numpy_uint32_t;

/* "numpy.pxd":736
 * ctypedef npy_uint16     uint16_t
 * ctypedef npy_uint32     uint32_t
 * ctypedef npy_uint64     uint64_t             # <<<<<<<<<<<<<<
 * #ctypedef npy_uint96     uint96_t
 * #ctypedef npy_uint128    uint128_t
 */
typedef npy_uint64 __pyx_t_5numpy_uint64_t;

/* "numpy.pxd":740
 * #ctypedef npy_uint128    uint128_t
 * 
 * ctypedef npy_float16    float16_t             # <<<<<<<<<<<<<<
 * ctypedef npy_float32    float32_t
 * ctypedef npy_float64    float64_t
 */
typedef npy_float16 __pyx_t_5numpy_float16_t;

/* "numpy.pxd":741
 * 
 * ctypedef npy_float16    float16_t
 * ctypedef npy_float32    float32_t             # <<<<<<<<<<<<<<
 * ctypedef npy_float64    float64_t
 * #ctypedef npy_float80    float80_t
 */
typedef npy_float32 __pyx_t_5numpy_float32_t;

/* "numpy.pxd":742
 * ctypedef npy_float16    float16_t
 * ctypedef npy_float32    float32_t
 * ctypedef npy_float64    float64_t             # <<<<<<<<<<<<<<
 * #ctypedef npy_float80    float80_t
 * #ctypedef npy_float128   float128_t
 */
typedef npy_float64 __pyx_t_5numpy_float64_t;

/* "numpy.pxd":751
 * # The int types are mapped a bit surprising --
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 * ctypedef npy_long       int_t             # <<<<<<<<<<<<<<
 * ctypedef npy_longlong   long_t
 * ctypedef npy_longlong   longlong_t
 */
typedef npy_long __pyx_t_5numpy_int_t;

/* "numpy.pxd":752
 * # numpy.int corresponds to 'l' and numpy.long to 'q'
 * ctypedef npy_long       int_t
 * ctypedef npy_longlong   long_t             # <<<<<<<<<<<<<<
 * ctypedef npy_longlong   longlong_t
 * 
 */
typedef npy_longlong __pyx_t_5numpy_long_t;

/* "numpy.pxd":753
 * ctypedef npy_long       int_t
 * ctypedef npy_longlong   long_t
 * ctypedef npy_longlong   longlong_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_ulong      uint_t
 */
typedef npy_longlong __pyx_t_5numpy_longlong_t;

/* "numpy.pxd":755
 * ctypedef npy_longlong   longlong_t
 * 
 * ctypedef npy_ulong      uint_t             # <<<<<<<<<<<<<<
 * ctypedef npy_ulonglong  ulong_t
 * ctypedef npy_ulonglong  ulonglong_t
 */
typedef npy_ulong __pyx_t_5numpy_uint_t;

/* "numpy.pxd":756
 * 
 * ctypedef npy_ulong      uint_t
 * ctypedef npy_ulonglong  ulong_t             # <<<<<<<<<<<<<<
 * ctypedef npy_ulonglong  ulonglong_t
 * 
 */
typedef npy_ulonglong __pyx_t_5numpy_ulong_t;

/* "numpy.pxd":757
 * ctypedef npy_ulong      uint_t
 * ctypedef npy_ulonglong  ulong_t
 * ctypedef npy_ulonglong  ulonglong_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_intp       intp_t
 */
typedef npy_ulonglong __pyx_t_5numpy_ulonglong_t;

/* "numpy.pxd":759
 * ctypedef npy_ulonglong  ulonglong_t
 * 
 * ctypedef npy_intp       intp_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uintp      uintp_t
 * 
 */
typedef npy_intp __pyx_t_5numpy_intp_t;

/* "numpy.pxd":760
 * 
 * ctypedef npy_intp       intp_t
 * ctypedef npy_uintp      uintp_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_double     float_t
 */
typedef npy_uintp __pyx_t_5numpy_uintp_t;

/* "numpy.pxd":762
 * ctypedef npy_uintp      uintp_t
 * 
 * ctypedef npy_double     float_t             # <<<<<<<<<<<<<<
 * ctypedef npy_double     double_t
 * ctypedef npy_longdouble longdouble_t
 */
typedef npy_double __pyx_t_5numpy_float_t;

/* "numpy.pxd":763
 * 
 * ctypedef npy_double     float_t
 * ctypedef npy_double     double_t             # <<<<<<<<<<<<<<
 * ctypedef npy_longdouble longdouble_t
 * 
 */
typedef npy_double __pyx_t_5numpy_double_t;

/* "numpy.pxd":764
 * ctypedef npy_double     float_t
 * ctypedef npy_double     double_t
 * ctypedef npy_longdouble longdouble_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_cfloat      cfloat_t
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typedef npy_longdouble __pyx_t_5numpy_longdouble_t;
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#if CYTHON_CCOMPLEX
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/*--- Type declarations ---*/
struct __pyx_obj_6pandas_7_period_Period;

/* "numpy.pxd":766
 * ctypedef npy_longdouble longdouble_t
 * 
 * ctypedef npy_cfloat      cfloat_t             # <<<<<<<<<<<<<<
 * ctypedef npy_cdouble     cdouble_t
 * ctypedef npy_clongdouble clongdouble_t
 */
typedef npy_cfloat __pyx_t_5numpy_cfloat_t;

/* "numpy.pxd":767
 * 
 * ctypedef npy_cfloat      cfloat_t
 * ctypedef npy_cdouble     cdouble_t             # <<<<<<<<<<<<<<
 * ctypedef npy_clongdouble clongdouble_t
 * 
 */
typedef npy_cdouble __pyx_t_5numpy_cdouble_t;

/* "numpy.pxd":768
 * ctypedef npy_cfloat      cfloat_t
 * ctypedef npy_cdouble     cdouble_t
 * ctypedef npy_clongdouble clongdouble_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_cdouble     complex_t
 */
typedef npy_clongdouble __pyx_t_5numpy_clongdouble_t;

/* "numpy.pxd":770
 * ctypedef npy_clongdouble clongdouble_t
 * 
 * ctypedef npy_cdouble     complex_t             # <<<<<<<<<<<<<<
 * 
 * cdef inline object PyArray_MultiIterNew1(a):
 */
typedef npy_cdouble __pyx_t_5numpy_complex_t;
struct __pyx_opt_args_6pandas_7_period_resolution;

/* "pandas/src/period.pyx":390
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 * 
 * ctypedef int (*accessor)(int64_t ordinal, int freq) except INT32_MIN             # <<<<<<<<<<<<<<
 * 
 * def get_period_field(int code, int64_t value, int freq):
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typedef int (*__pyx_t_6pandas_7_period_accessor)(__pyx_t_5numpy_int64_t, int);

/* "pandas/src/period.pyx":468
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 * 
 * cpdef resolution(ndarray[int64_t] stamps, tz=None):             # <<<<<<<<<<<<<<
 *     cdef:
 *         Py_ssize_t i, n = len(stamps)
 */
struct __pyx_opt_args_6pandas_7_period_resolution {
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  PyObject *tz;
};

/* "pandas/src/period.pyx":638
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 * cdef class Period(object):             # <<<<<<<<<<<<<<
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 */
struct __pyx_obj_6pandas_7_period_Period {
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  struct __pyx_vtabstruct_6pandas_7_period_Period *__pyx_vtab;
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  PyObject *freq;
};



struct __pyx_vtabstruct_6pandas_7_period_Period {
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static struct __pyx_vtabstruct_6pandas_7_period_Period *__pyx_vtabptr_6pandas_7_period_Period;

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static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStr(PyObject* obj, PyObject* attr_name) {
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#define __Pyx_PyObject_GetAttrStr(o,n) PyObject_GetAttr(o,n)
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static PyObject *__Pyx_GetBuiltinName(PyObject *name);

static CYTHON_INLINE __pyx_t_5numpy_int64_t __Pyx_div___pyx_t_5numpy_int64_t(__pyx_t_5numpy_int64_t, __pyx_t_5numpy_int64_t);

#define UNARY_NEG_WOULD_OVERFLOW(x)\
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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_WriteUnraisable(const char *name, int clineno,
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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 int  __Pyx_GetBufferAndValidate(Py_buffer* buf, PyObject* obj,
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static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info);

static CYTHON_INLINE PyObject *__Pyx_GetModuleGlobalName(PyObject *name);

#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw);
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#define __Pyx_PyObject_Call(func, arg, kw) PyObject_Call(func, arg, kw)
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static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type);

static void __Pyx_RaiseBufferFallbackError(void);

#define __Pyx_BufPtrStrided1d(type, buf, i0, s0) (type)((char*)buf + i0 * s0)
static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause);

#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);

#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func);
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#define __Pyx_PyObject_CallNoArg(func) __Pyx_PyObject_Call(func, __pyx_empty_tuple, NULL)
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static void __Pyx_RaiseBufferIndexError(int axis);

static CYTHON_INLINE long __Pyx_div_long(long, long);

static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level);

#define __Pyx_GetItemInt(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
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    __Pyx_GetItemInt_Fast(o, (Py_ssize_t)i, is_list, wraparound, boundscheck) :\
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#define __Pyx_GetItemInt_List(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
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static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i,
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#define __Pyx_GetItemInt_Tuple(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
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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 int __Pyx_PySequence_ContainsTF(PyObject* item, PyObject* seq, int eq) {
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#define __Pyx_SetItemInt(o, i, v, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
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static CYTHON_INLINE long __Pyx_mod_long(long, long);

static CYTHON_INLINE __pyx_t_5numpy_int64_t __Pyx_mod___pyx_t_5numpy_int64_t(__pyx_t_5numpy_int64_t, __pyx_t_5numpy_int64_t);

static CYTHON_INLINE void __Pyx_RaiseUnboundLocalError(const char *varname);

static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected);

static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index);

static CYTHON_INLINE int __Pyx_IterFinish(void);

static int __Pyx_IternextUnpackEndCheck(PyObject *retval, Py_ssize_t expected);

#if CYTHON_COMPILING_IN_CPYTHON
static PyObject* __Pyx_PyInt_SubtractObjC(PyObject *op1, PyObject *op2, long intval, int inplace);
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static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals);

static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals);

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#define __Pyx_PyObject_DelAttrStr(o,n) __Pyx_PyObject_SetAttrStr(o,n,NULL)
static CYTHON_INLINE int __Pyx_PyObject_SetAttrStr(PyObject* obj, PyObject* attr_name, PyObject* value) {
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static CYTHON_INLINE void __Pyx_ExceptionSave(PyObject **type, PyObject **value, PyObject **tb);
static void __Pyx_ExceptionReset(PyObject *type, PyObject *value, PyObject *tb);

static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb);

#if CYTHON_COMPILING_IN_CPYTHON
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static PyObject* __Pyx_PyInt_AddObjC(PyObject *op1, PyObject *op2, long intval, int inplace);
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static PyObject *__Pyx_ImportModule(const char *name);

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

static int __Pyx_ImportVoidPtr(PyObject *module, const char *name, void **p, const char *sig);

static int __Pyx_ImportFunction(PyObject *module, const char *funcname, void (**f)(void), const char *sig);

static int __Pyx_InitStrings(__Pyx_StringTabEntry *t);

static PyObject *__pyx_f_6pandas_7_period_6Period__field(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self, PyObject *__pyx_v_alias); /* proto*/

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

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

/* Module declarations from 'cpython' */

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/* Module declarations from 'datetime' */

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static CYTHON_INLINE PyObject *__pyx_f_8datetime__dts_to_pydatetime(pandas_datetimestruct *); /*proto*/

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/* Module declarations from 'pandas.lib' */
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static int (*__pyx_f_6pandas_5tslib__is_utc)(PyObject *); /*proto*/
static int (*__pyx_f_6pandas_5tslib__is_tzlocal)(PyObject *); /*proto*/
static PyObject *(*__pyx_f_6pandas_5tslib__get_dst_info)(PyObject *); /*proto*/

/* Module declarations from 'pandas._period' */
static PyTypeObject *__pyx_ptype_6pandas_7_period_Period = 0;
static int __pyx_v_6pandas_7_period_PY2;
static __pyx_t_5numpy_int64_t __pyx_v_6pandas_7_period_NPY_NAT;
static int __pyx_v_6pandas_7_period_US_RESO;
static int __pyx_v_6pandas_7_period_MS_RESO;
static int __pyx_v_6pandas_7_period_S_RESO;
static int __pyx_v_6pandas_7_period_T_RESO;
static int __pyx_v_6pandas_7_period_H_RESO;
static int __pyx_v_6pandas_7_period_D_RESO;
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static char __pyx_v_6pandas_7_period_END;
static PyObject *__pyx_v_6pandas_7_period_extra_fmts = 0;
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static __pyx_t_5numpy_int64_t __pyx_f_6pandas_7_period_period_ordinal_to_dt64(__pyx_t_5numpy_int64_t, int, int __pyx_skip_dispatch); /*proto*/
static PyObject *__pyx_f_6pandas_7_period__period_strftime(__pyx_t_5numpy_int64_t, int, PyObject *); /*proto*/
static __pyx_t_6pandas_7_period_accessor __pyx_f_6pandas_7_period__get_accessor_func(int); /*proto*/
static PyObject *__pyx_f_6pandas_7_period_resolution(PyArrayObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_6pandas_7_period_resolution *__pyx_optional_args); /*proto*/
static CYTHON_INLINE int __pyx_f_6pandas_7_period__reso_stamp(pandas_datetimestruct *); /*proto*/
static PyObject *__pyx_f_6pandas_7_period__reso_local(PyArrayObject *, PyObject *); /*proto*/
static PyArrayObject *__pyx_f_6pandas_7_period_localize_dt64arr_to_period(PyArrayObject *, int, PyObject *); /*proto*/
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static __Pyx_TypeInfo __Pyx_TypeInfo_object = { "Python object", NULL, sizeof(PyObject *), { 0 }, 0, 'O', 0, 0 };
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int __pyx_module_is_main_pandas___period = 0;

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static PyObject *__pyx_builtin_Exception;
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static char __pyx_k_i[] = "i";
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static char __pyx_k_n[] = "n";
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static char __pyx_k_Zg[] = "Zg";
static char __pyx_k_i8[] = "i8";
static char __pyx_k_np[] = "np";
static char __pyx_k_ps[] = "ps";
static char __pyx_k_sz[] = "sz";
static char __pyx_k_tz[] = "tz";
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static char __pyx_k_03d[] = "%03d";
static char __pyx_k_06d[] = "%06d";
static char __pyx_k_09d[] = "%09d";
static char __pyx_k_END[] = "END";
static char __pyx_k_NaT[] = "NaT";
static char __pyx_k_Y_m[] = "%Y-%m";
static char __pyx_k_any[] = "any";
static char __pyx_k_arr[] = "arr";
static char __pyx_k_d_2[] = "%d";
static char __pyx_k_day[] = "day";
static char __pyx_k_doc[] = "__doc__";
static char __pyx_k_dts[] = "dts";
static char __pyx_k_end[] = "end";
static char __pyx_k_f_2[] = "%f";
static char __pyx_k_fmt[] = "fmt";
static char __pyx_k_get[] = "get";
static char __pyx_k_how[] = "how";
static char __pyx_k_inf[] = "inf";
static char __pyx_k_l_2[] = "%l";
static char __pyx_k_lib[] = "lib";
static char __pyx_k_min[] = "min";
static char __pyx_k_msg[] = "msg";
static char __pyx_k_n_2[] = "%n";
static char __pyx_k_nan[] = "nan";
static char __pyx_k_new[] = "__new__";
static char __pyx_k_now[] = "now";
static char __pyx_k_out[] = "out";
static char __pyx_k_q_2[] = "%q";
static char __pyx_k_s_2[] = "%s";
static char __pyx_k_s_s[] = "%s/%s";
static char __pyx_k_sys[] = "sys";
static char __pyx_k_typ[] = "_typ";
static char __pyx_k_val[] = "val";
static char __pyx_k_FQ_q[] = "%FQ%q";
static char __pyx_k_Tick[] = "Tick";
static char __pyx_k_base[] = "base";
static char __pyx_k_code[] = "code";
static char __pyx_k_date[] = "date";
static char __pyx_k_freq[] = "freq";
static char __pyx_k_func[] = "func";
static char __pyx_k_hour[] = "hour";
static char __pyx_k_iNaT[] = "iNaT";
static char __pyx_k_left[] = "left";
static char __pyx_k_main[] = "__main__";
static char __pyx_k_mask[] = "mask";
static char __pyx_k_mnum[] = "mnum";
static char __pyx_k_mult[] = "mult";
static char __pyx_k_name[] = "__name__";
static char __pyx_k_pytz[] = "pytz";
static char __pyx_k_side[] = "side";
static char __pyx_k_test[] = "__test__";
static char __pyx_k_year[] = "year";
static char __pyx_k_BEGIN[] = "BEGIN";
static char __pyx_k_START[] = "START";
static char __pyx_k_Y_m_d[] = "%Y-%m-%d";
static char __pyx_k_dtarr[] = "dtarr";
static char __pyx_k_dtype[] = "dtype";
static char __pyx_k_empty[] = "empty";
static char __pyx_k_finfo[] = "finfo";
static char __pyx_k_freq1[] = "freq1";
static char __pyx_k_freq2[] = "freq2";
static char __pyx_k_int64[] = "int64";
static char __pyx_k_month[] = "month";
static char __pyx_k_numpy[] = "numpy";
static char __pyx_k_range[] = "range";
static char __pyx_k_right[] = "right";
static char __pyx_k_start[] = "start";
static char __pyx_k_tslib[] = "tslib";
static char __pyx_k_upper[] = "upper";
static char __pyx_k_utf_8[] = "utf-8";
static char __pyx_k_value[] = "value";
static char __pyx_k_D_RESO[] = "D_RESO";
static char __pyx_k_FINISH[] = "FINISH";
static char __pyx_k_H_RESO[] = "H_RESO";
static char __pyx_k_S_RESO[] = "S_RESO";
static char __pyx_k_T_RESO[] = "T_RESO";
static char __pyx_k_asfreq[] = "asfreq";
static char __pyx_k_astype[] = "astype";
static char __pyx_k_compat[] = "compat";
static char __pyx_k_decode[] = "decode";
static char __pyx_k_encode[] = "encode";
static char __pyx_k_format[] = "format";
static char __pyx_k_ignore[] = "ignore";
static char __pyx_k_import[] = "__import__";
static char __pyx_k_minute[] = "minute";
static char __pyx_k_module[] = "__module__";
static char __pyx_k_name_2[] = "name";
static char __pyx_k_pandas[] = "pandas";
static char __pyx_k_period[] = "period";
static char __pyx_k_result[] = "result";
static char __pyx_k_second[] = "second";
static char __pyx_k_stamps[] = "stamps";
static char __pyx_k_values[] = "values";
static char __pyx_k_MS_RESO[] = "MS_RESO";
static char __pyx_k_US_RESO[] = "US_RESO";
static char __pyx_k_freqstr[] = "freqstr";
static char __pyx_k_offsets[] = "offsets";
static char __pyx_k_ordinal[] = "ordinal";
static char __pyx_k_prepare[] = "__prepare__";
static char __pyx_k_quarter[] = "quarter";
static char __pyx_k_replace[] = "replace";
static char __pyx_k_unicode[] = "__unicode__";
static char __pyx_k_KeyError[] = "KeyError";
static char __pyx_k_datetime[] = "datetime";
static char __pyx_k_dateutil[] = "dateutil";
static char __pyx_k_end_time[] = "end_time";
static char __pyx_k_get_freq[] = "get_freq";
static char __pyx_k_how_dict[] = "how_dict";
static char __pyx_k_operator[] = "operator";
static char __pyx_k_ordinals[] = "ordinals";
static char __pyx_k_property[] = "property";
static char __pyx_k_qualname[] = "__qualname__";
static char __pyx_k_relation[] = "relation";
static char __pyx_k_Exception[] = "Exception";
static char __pyx_k_Timedelta[] = "Timedelta";
static char __pyx_k_Timestamp[] = "Timestamp";
static char __pyx_k_TypeError[] = "TypeError";
static char __pyx_k_Y_m_d_H_M[] = "%Y-%m-%d %H:%M";
static char __pyx_k_add_delta[] = "_add_delta";
static char __pyx_k_dayofweek[] = "dayofweek";
static char __pyx_k_have_pytz[] = "have_pytz";
static char __pyx_k_metaclass[] = "__metaclass__";
static char __pyx_k_periodarr[] = "periodarr";
static char __pyx_k_rule_code[] = "rule_code";
static char __pyx_k_timedelta[] = "timedelta";
static char __pyx_k_to_offset[] = "to_offset";
static char __pyx_k_DateOffset[] = "DateOffset";
static char __pyx_k_IndexError[] = "IndexError";
static char __pyx_k_Period_s_s[] = "Period('%s', '%s')";
static char __pyx_k_Resolution[] = "Resolution";
static char __pyx_k_ValueError[] = "ValueError";
static char __pyx_k_Y_m_d_H_00[] = "%Y-%m-%d %H:00";
static char __pyx_k_datetime64[] = "datetime64";
static char __pyx_k_freq_group[] = "freq_group";
static char __pyx_k_is_integer[] = "is_integer";
static char __pyx_k_pyx_vtable[] = "__pyx_vtable__";
static char __pyx_k_start_time[] = "start_time";
static char __pyx_k_weekofyear[] = "weekofyear";
static char __pyx_k_Y_m_d_H_M_S[] = "%Y-%m-%d %H:%M:%S";
static char __pyx_k_comparables[] = "_comparables";
static char __pyx_k_frequencies[] = "frequencies";
static char __pyx_k_microsecond[] = "microsecond";
static char __pyx_k_nat_strings[] = "_nat_strings";
static char __pyx_k_timedelta64[] = "timedelta64";
static char __pyx_k_RuntimeError[] = "RuntimeError";
static char __pyx_k_from_ordinal[] = "_from_ordinal";
static char __pyx_k_get_freq_str[] = "_get_freq_str";
static char __pyx_k_searchsorted[] = "searchsorted";
static char __pyx_k_string_types[] = "string_types";
static char __pyx_k_to_timestamp[] = "to_timestamp";
static char __pyx_k_version_info[] = "version_info";
static char __pyx_k_Y_m_d_H_M_S_l[] = "%Y-%m-%d %H:%M:%S.%l";
static char __pyx_k_Y_m_d_H_M_S_n[] = "%Y-%m-%d %H:%M:%S.%n";
static char __pyx_k_Y_m_d_H_M_S_u[] = "%Y-%m-%d %H:%M:%S.%u";
static char __pyx_k_days_in_month[] = "days_in_month";
static char __pyx_k_get_freq_code[] = "get_freq_code";
static char __pyx_k_get_utcoffset[] = "_get_utcoffset";
static char __pyx_k_month_numbers[] = "_month_numbers";
static char __pyx_k_period_format[] = "period_format";
static char __pyx_k_DIFFERENT_FREQ[] = "_DIFFERENT_FREQ";
static char __pyx_k_NotImplemented[] = "NotImplemented";
static char __pyx_k_Unknown_freq_d[] = "Unknown freq: %d";
static char __pyx_k_get_base_alias[] = "get_base_alias";
static char __pyx_k_get_rule_month[] = "_get_rule_month";
static char __pyx_k_pandas__period[] = "pandas._period";
static char __pyx_k_pandas_tseries[] = "pandas.tseries";
static char __pyx_k_period_ordinal[] = "period_ordinal";
static char __pyx_k_extract_ordinals[] = "extract_ordinals";
static char __pyx_k_get_period_field[] = "get_period_field";
static char __pyx_k_quarter_to_myear[] = "_quarter_to_myear";
static char __pyx_k_Unable_to_parse_s[] = "Unable to parse %s";
static char __pyx_k_get_standard_freq[] = "get_standard_freq";
static char __pyx_k_parse_time_string[] = "parse_time_string";
static char __pyx_k_period_alias_dict[] = "_period_alias_dict";
static char __pyx_k_period_asfreq_arr[] = "period_asfreq_arr";
static char __pyx_k_maybe_convert_freq[] = "_maybe_convert_freq";
static char __pyx_k_validate_end_alias[] = "_validate_end_alias";
static char __pyx_k_index_out_of_bounds[] = "index out of bounds";
static char __pyx_k_ordinal_from_fields[] = "_ordinal_from_fields";
static char __pyx_k_DIFFERENT_FREQ_INDEX[] = "_DIFFERENT_FREQ_INDEX";
static char __pyx_k_delta_to_nanoseconds[] = "_delta_to_nanoseconds";
static char __pyx_k_dt64arr_to_periodarr[] = "dt64arr_to_periodarr";
static char __pyx_k_get_period_field_arr[] = "get_period_field_arr";
static char __pyx_k_pandas_tseries_tools[] = "pandas.tseries.tools";
static char __pyx_k_periodarr_to_dt64arr[] = "periodarr_to_dt64arr";
static char __pyx_k_IncompatibleFrequency[] = "IncompatibleFrequency";
static char __pyx_k_Quarter_must_be_1_q_4[] = "Quarter must be 1 <= q <= 4";
static char __pyx_k_get_to_timestamp_base[] = "get_to_timestamp_base";
static char __pyx_k_How_must_be_one_of_S_or_E[] = "How must be one of S or E";
static char __pyx_k_Period_strftime_line_1012[] = "Period.strftime (line 1012)";
static char __pyx_k_Could_not_find_pytz_module[] = "Could not find pytz module";
static char __pyx_k_Ordinal_must_be_an_integer[] = "Ordinal must be an integer";
static char __pyx_k_Unrecognized_period_code_d[] = "Unrecognized period code: %d";
static char __pyx_k_Frequency_conversion_failed[] = "Frequency conversion failed";
static char __pyx_k_ndarray_is_not_C_contiguous[] = "ndarray is not C contiguous";
static char __pyx_k_Unable_to_get_quarter_and_year[] = "Unable to get quarter and year";
static char __pyx_k_Cannot_compare_type_r_with_type[] = "Cannot compare type %r with type %r";
static char __pyx_k_If_value_is_None_freq_cannot_be[] = "If value is None, freq cannot be None";
static char __pyx_k_Input_has_different_freq_1_from[] = "Input has different freq={1} from Period(freq={0})";
static char __pyx_k_Returns_the_string_representati[] = "\n        Returns the string representation of the :class:`Period`, depending\n        on the selected :keyword:`format`. :keyword:`format` must be a string\n        containing one or several directives.  The method recognizes the same\n        directives as the :func:`time.strftime` function of the standard Python\n        distribution, as well as the specific additional directives ``%f``,\n        ``%F``, ``%q``. (formatting & docs originally from scikits.timeries)\n\n        +-----------+--------------------------------+-------+\n        | Directive | Meaning                        | Notes |\n        +===========+================================+=======+\n        | ``%a``    | Locale's abbreviated weekday   |       |\n        |           | name.                          |       |\n        +-----------+--------------------------------+-------+\n        | ``%A``    | Locale's full weekday name.    |       |\n        +-----------+--------------------------------+-------+\n        | ``%b``    | Locale's abbreviated month     |       |\n        |           | name.                          |       |\n        +-----------+--------------------------------+-------+\n        | ``%B``    | Locale's full month name.      |       |\n        +-----------+--------------------------------+-------+\n        | ``%c``    | Locale's appropriate date and  |       |\n        |           | time representation.           |       |\n        +-----------+--------------------------------+-------+\n        | ``%d``    | Day of the month as a decimal  |       |\n        |           | number [01,31].                |       |\n        +-----------+--------------------------------+-------+\n        | ``%f``    | 'Fiscal' year without a        | \\(1)  |\n        |           | century  as a decimal number   |       |\n        |           | [00,99]                        |       |\n        +-----------+--------------------------------+-------+\n        | ``%F``    | 'Fiscal' year with a century  "" | \\(2)  |\n        |           | as a decimal number            |       |\n        +-----------+--------------------------------+-------+\n        | ``%H``    | Hour (24-hour clock) as a      |       |\n        |           | decimal number [00,23].        |       |\n        +-----------+--------------------------------+-------+\n        | ``%I``    | Hour (12-hour clock) as a      |       |\n        |           | decimal number [01,12].        |       |\n        +-----------+--------------------------------+-------+\n        | ``%j``    | Day of the year as a decimal   |       |\n        |           | number [001,366].              |       |\n        +-----------+--------------------------------+-------+\n        | ``%m``    | Month as a decimal number      |       |\n        |           | [01,12].                       |       |\n        +-----------+--------------------------------+-------+\n        | ``%M``    | Minute as a decimal number     |       |\n        |           | [00,59].                       |       |\n        +-----------+--------------------------------+-------+\n        | ``%p``    | Locale's equivalent of either  | \\(3)  |\n        |           | AM or PM.                      |       |\n        +-----------+--------------------------------+-------+\n        | ``%q``    | Quarter as a decimal number    |       |\n        |           | [01,04]                        |       |\n        +-----------+--------------------------------+-------+\n        | ``%S``    | Second as a decimal number     | \\(4)  |\n        |           | [00,61].                       |       |\n        +-----------+--------------------------------+-------+\n        | ``%U``    | Week number of the year        | \\(5)  |\n        |           | (Sunday as the first day of    |       |\n        |           | the week) as a decimal number  |       |\n        |           | [00,53].  All days in a new    |       |\n        |           | year preceding the first       |       |""\n        |           | Sunday are considered to be in |       |\n        |           | week 0.                        |       |\n        +-----------+--------------------------------+-------+\n        | ``%w``    | Weekday as a decimal number    |       |\n        |           | [0(Sunday),6].                 |       |\n        +-----------+--------------------------------+-------+\n        | ``%W``    | Week number of the year        | \\(5)  |\n        |           | (Monday as the first day of    |       |\n        |           | the week) as a decimal number  |       |\n        |           | [00,53].  All days in a new    |       |\n        |           | year preceding the first       |       |\n        |           | Monday are considered to be in |       |\n        |           | week 0.                        |       |\n        +-----------+--------------------------------+-------+\n        | ``%x``    | Locale's appropriate date      |       |\n        |           | representation.                |       |\n        +-----------+--------------------------------+-------+\n        | ``%X``    | Locale's appropriate time      |       |\n        |           | representation.                |       |\n        +-----------+--------------------------------+-------+\n        | ``%y``    | Year without century as a      |       |\n        |           | decimal number [00,99].        |       |\n        +-----------+--------------------------------+-------+\n        | ``%Y``    | Year with century as a decimal |       |\n        |           | number.                        |       |\n        +-----------+--------------------------------+-------+\n        | ``%Z``    | Time zone name (no characters  |       |\n        |           | if no time zone exists).       |       |\n        +-----------+--------------------------------+-------+\n        | ``%%``    | A literal ``'%'`` character.   |       |\n        +-----------+--------------------------------+-------+\n\n        .. ""note::\n\n            (1)\n                The ``%f`` directive is the same as ``%y`` if the frequency is\n                not quarterly.\n                Otherwise, it corresponds to the 'fiscal' year, as defined by\n                the :attr:`qyear` attribute.\n\n            (2)\n                The ``%F`` directive is the same as ``%Y`` if the frequency is\n                not quarterly.\n                Otherwise, it corresponds to the 'fiscal' year, as defined by\n                the :attr:`qyear` attribute.\n\n            (3)\n                The ``%p`` directive only affects the output hour field\n                if the ``%I`` directive is used to parse the hour.\n\n            (4)\n                The range really is ``0`` to ``61``; this accounts for leap\n                seconds and the (very rare) double leap seconds.\n\n            (5)\n                The ``%U`` and ``%W`` directives are only used in calculations\n                when the day of the week and the year are specified.\n\n        .. rubric::  Examples\n\n            >>> a = Period(freq='Q@JUL', year=2006, quarter=1)\n            >>> a.strftime('%F-Q%q')\n            '2006-Q1'\n            >>> # Output the last month in the quarter of this date\n            >>> a.strftime('%b-%Y')\n            'Oct-2005'\n            >>>\n            >>> a = Period(freq='D', year=2001, month=1, day=1)\n            >>> a.strftime('%d-%b-%Y')\n            '01-Jan-2006'\n            >>> a.strftime('%b. %d, %Y was a %A')\n            'Jan. 01, 2001 was a Monday'\n        ";
static char __pyx_k_home_yoh_deb_gits_pkg_exppsy_pa[] = "/home/yoh/deb/gits/pkg-exppsy/pandas/pandas/src/period.pyx";
static char __pyx_k_unknown_dtype_code_in_numpy_pxd[] = "unknown dtype code in numpy.pxd (%d)";
static char __pyx_k_Cannot_do_arithmetic_with_non_co[] = "Cannot do arithmetic with non-conforming periods";
static char __pyx_k_Format_string_allocated_too_shor[] = "Format string allocated too short, see comment in numpy.pxd";
static char __pyx_k_Frequency_must_be_positive_becau[] = "Frequency must be positive, because it represents span: {0}";
static char __pyx_k_If_value_is_NaT_freq_cannot_be_N[] = "If value is NaT, freq cannot be None because it cannot be inferred";
static char __pyx_k_Input_cannnot_be_converted_to_Pe[] = "Input cannnot be converted to Period(freq={0})";
static char __pyx_k_Invalid_frequency_or_could_not_i[] = "Invalid frequency or could not infer: %s";
static char __pyx_k_Must_supply_freq_for_datetime_va[] = "Must supply freq for datetime value";
static char __pyx_k_Must_supply_freq_for_ordinal_val[] = "Must supply freq for ordinal value";
static char __pyx_k_Non_native_byte_order_not_suppor[] = "Non-native byte order not supported";
static char __pyx_k_Only_value_or_ordinal_but_not_bo[] = "Only value or ordinal but not both should be given but not both";
static char __pyx_k_Unable_to_convert_to_desired_fre[] = "Unable to convert to desired frequency.";
static char __pyx_k_Value_must_be_Period_string_inte[] = "Value must be Period, string, integer, or datetime";
static char __pyx_k_ndarray_is_not_Fortran_contiguou[] = "ndarray is not Fortran contiguous";
static char __pyx_k_Input_has_different_freq_1_from_2[] = "Input has different freq={1} from PeriodIndex(freq={0})";
static char __pyx_k_Format_string_allocated_too_shor_2[] = "Format string allocated too short.";
static PyObject *__pyx_kp_s_03d;
static PyObject *__pyx_kp_s_06d;
static PyObject *__pyx_kp_s_09d;
static PyObject *__pyx_kp_s_2d;
static PyObject *__pyx_kp_b_AB;
static PyObject *__pyx_kp_s_AB;
static PyObject *__pyx_n_s_BEGIN;
static PyObject *__pyx_kp_b_CD;
static PyObject *__pyx_kp_s_CD;
static PyObject *__pyx_kp_s_Cannot_compare_type_r_with_type;
static PyObject *__pyx_kp_s_Cannot_do_arithmetic_with_non_co;
static PyObject *__pyx_kp_s_Could_not_find_pytz_module;
static PyObject *__pyx_n_s_DIFFERENT_FREQ;
static PyObject *__pyx_n_s_DIFFERENT_FREQ_INDEX;
static PyObject *__pyx_n_s_D_RESO;
static PyObject *__pyx_n_s_DateOffset;
static PyObject *__pyx_n_s_E;
static PyObject *__pyx_kp_b_EF;
static PyObject *__pyx_kp_s_EF;
static PyObject *__pyx_n_s_END;
static PyObject *__pyx_n_s_Exception;
static PyObject *__pyx_kp_b_F;
static PyObject *__pyx_n_s_FINISH;
static PyObject *__pyx_kp_b_FQ_q;
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_Frequency_conversion_failed;
static PyObject *__pyx_kp_s_Frequency_must_be_positive_becau;
static PyObject *__pyx_kp_b_GH;
static PyObject *__pyx_kp_s_GH;
static PyObject *__pyx_n_s_H_RESO;
static PyObject *__pyx_kp_s_How_must_be_one_of_S_or_E;
static PyObject *__pyx_kp_b_IJ;
static PyObject *__pyx_kp_s_IJ;
static PyObject *__pyx_kp_s_If_value_is_NaT_freq_cannot_be_N;
static PyObject *__pyx_kp_s_If_value_is_None_freq_cannot_be;
static PyObject *__pyx_n_s_IncompatibleFrequency;
static PyObject *__pyx_n_s_IndexError;
static PyObject *__pyx_kp_s_Input_cannnot_be_converted_to_Pe;
static PyObject *__pyx_kp_s_Input_has_different_freq_1_from;
static PyObject *__pyx_kp_s_Input_has_different_freq_1_from_2;
static PyObject *__pyx_kp_s_Invalid_frequency_or_could_not_i;
static PyObject *__pyx_kp_b_KL;
static PyObject *__pyx_kp_s_KL;
static PyObject *__pyx_n_s_KeyError;
static PyObject *__pyx_n_s_MS_RESO;
static PyObject *__pyx_kp_s_Must_supply_freq_for_datetime_va;
static PyObject *__pyx_kp_s_Must_supply_freq_for_ordinal_val;
static PyObject *__pyx_n_s_NaT;
static PyObject *__pyx_kp_u_Non_native_byte_order_not_suppor;
static PyObject *__pyx_n_s_NotImplemented;
static PyObject *__pyx_kp_s_Only_value_or_ordinal_but_not_bo;
static PyObject *__pyx_kp_s_Ordinal_must_be_an_integer;
static PyObject *__pyx_kp_s_Period_s_s;
static PyObject *__pyx_kp_u_Period_strftime_line_1012;
static PyObject *__pyx_kp_s_Quarter_must_be_1_q_4;
static PyObject *__pyx_n_s_Resolution;
static PyObject *__pyx_kp_u_Returns_the_string_representati;
static PyObject *__pyx_n_s_RuntimeError;
static PyObject *__pyx_n_s_S;
static PyObject *__pyx_n_s_START;
static PyObject *__pyx_n_s_S_RESO;
static PyObject *__pyx_n_s_T_RESO;
static PyObject *__pyx_n_s_Tick;
static PyObject *__pyx_n_s_Timedelta;
static PyObject *__pyx_n_s_Timestamp;
static PyObject *__pyx_n_s_TypeError;
static PyObject *__pyx_n_s_US_RESO;
static PyObject *__pyx_kp_s_Unable_to_convert_to_desired_fre;
static PyObject *__pyx_kp_s_Unable_to_get_quarter_and_year;
static PyObject *__pyx_kp_s_Unable_to_parse_s;
static PyObject *__pyx_kp_s_Unknown_freq_d;
static PyObject *__pyx_kp_s_Unrecognized_period_code_d;
static PyObject *__pyx_n_s_ValueError;
static PyObject *__pyx_kp_s_Value_must_be_Period_string_inte;
static PyObject *__pyx_kp_b_Y;
static PyObject *__pyx_kp_b_Y_m;
static PyObject *__pyx_kp_b_Y_m_d;
static PyObject *__pyx_kp_b_Y_m_d_H_00;
static PyObject *__pyx_kp_b_Y_m_d_H_M;
static PyObject *__pyx_kp_b_Y_m_d_H_M_S;
static PyObject *__pyx_kp_b_Y_m_d_H_M_S_l;
static PyObject *__pyx_kp_b_Y_m_d_H_M_S_n;
static PyObject *__pyx_kp_b_Y_m_d_H_M_S_u;
static PyObject *__pyx_n_s_add_delta;
static PyObject *__pyx_n_s_any;
static PyObject *__pyx_n_s_arr;
static PyObject *__pyx_n_s_asfreq;
static PyObject *__pyx_n_s_astype;
static PyObject *__pyx_n_s_base;
static PyObject *__pyx_n_s_code;
static PyObject *__pyx_n_s_comparables;
static PyObject *__pyx_n_s_compat;
static PyObject *__pyx_n_s_d;
static PyObject *__pyx_kp_s_d_2;
static PyObject *__pyx_n_s_date;
static PyObject *__pyx_n_s_datetime;
static PyObject *__pyx_n_s_datetime64;
static PyObject *__pyx_n_s_dateutil;
static PyObject *__pyx_n_s_day;
static PyObject *__pyx_n_s_dayofweek;
static PyObject *__pyx_n_s_days_in_month;
static PyObject *__pyx_n_s_decode;
static PyObject *__pyx_n_s_delta_to_nanoseconds;
static PyObject *__pyx_n_s_doc;
static PyObject *__pyx_n_s_dt64arr_to_periodarr;
static PyObject *__pyx_n_s_dtarr;
static PyObject *__pyx_n_s_dts;
static PyObject *__pyx_n_s_dtype;
static PyObject *__pyx_n_s_empty;
static PyObject *__pyx_n_s_encode;
static PyObject *__pyx_n_s_end;
static PyObject *__pyx_n_s_end_time;
static PyObject *__pyx_n_s_extract_ordinals;
static PyObject *__pyx_n_s_f;
static PyObject *__pyx_kp_b_f_2;
static PyObject *__pyx_n_s_finfo;
static PyObject *__pyx_n_s_fmt;
static PyObject *__pyx_n_s_format;
static PyObject *__pyx_n_s_freq;
static PyObject *__pyx_n_s_freq1;
static PyObject *__pyx_n_s_freq2;
static PyObject *__pyx_n_s_freq_group;
static PyObject *__pyx_n_s_freqstr;
static PyObject *__pyx_n_s_frequencies;
static PyObject *__pyx_n_s_from_ordinal;
static PyObject *__pyx_n_s_func;
static PyObject *__pyx_n_s_get;
static PyObject *__pyx_n_s_get_base_alias;
static PyObject *__pyx_n_s_get_freq;
static PyObject *__pyx_n_s_get_freq_code;
static PyObject *__pyx_n_s_get_freq_str;
static PyObject *__pyx_n_s_get_period_field;
static PyObject *__pyx_n_s_get_period_field_arr;
static PyObject *__pyx_n_s_get_rule_month;
static PyObject *__pyx_n_s_get_standard_freq;
static PyObject *__pyx_n_s_get_to_timestamp_base;
static PyObject *__pyx_n_s_get_utcoffset;
static PyObject *__pyx_n_s_h;
static PyObject *__pyx_n_s_have_pytz;
static PyObject *__pyx_kp_s_home_yoh_deb_gits_pkg_exppsy_pa;
static PyObject *__pyx_n_s_hour;
static PyObject *__pyx_n_s_how;
static PyObject *__pyx_n_s_how_dict;
static PyObject *__pyx_n_s_i;
static PyObject *__pyx_n_s_i8;
static PyObject *__pyx_n_s_iNaT;
static PyObject *__pyx_n_s_ignore;
static PyObject *__pyx_n_s_import;
static PyObject *__pyx_kp_s_index_out_of_bounds;
static PyObject *__pyx_n_s_inf;
static PyObject *__pyx_n_s_int64;
static PyObject *__pyx_n_s_is_integer;
static PyObject *__pyx_n_s_l;
static PyObject *__pyx_kp_b_l_2;
static PyObject *__pyx_n_s_left;
static PyObject *__pyx_n_s_lib;
static PyObject *__pyx_n_s_m;
static PyObject *__pyx_n_s_main;
static PyObject *__pyx_n_s_mask;
static PyObject *__pyx_n_s_maybe_convert_freq;
static PyObject *__pyx_n_s_metaclass;
static PyObject *__pyx_n_s_microsecond;
static PyObject *__pyx_n_s_min;
static PyObject *__pyx_n_s_minute;
static PyObject *__pyx_n_s_mnum;
static PyObject *__pyx_n_s_module;
static PyObject *__pyx_n_s_month;
static PyObject *__pyx_n_s_month_numbers;
static PyObject *__pyx_n_s_msg;
static PyObject *__pyx_n_s_mult;
static PyObject *__pyx_n_s_n;
static PyObject *__pyx_kp_b_n_2;
static PyObject *__pyx_n_s_name;
static PyObject *__pyx_n_s_name_2;
static PyObject *__pyx_n_s_nan;
static PyObject *__pyx_n_s_nat_strings;
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_new;
static PyObject *__pyx_n_s_now;
static PyObject *__pyx_n_s_np;
static PyObject *__pyx_n_s_numpy;
static PyObject *__pyx_n_s_offsets;
static PyObject *__pyx_n_s_operator;
static PyObject *__pyx_n_s_ordinal;
static PyObject *__pyx_n_s_ordinal_from_fields;
static PyObject *__pyx_n_s_ordinals;
static PyObject *__pyx_n_s_out;
static PyObject *__pyx_n_s_p;
static PyObject *__pyx_n_s_pandas;
static PyObject *__pyx_n_s_pandas__period;
static PyObject *__pyx_n_s_pandas_tseries;
static PyObject *__pyx_n_s_pandas_tseries_tools;
static PyObject *__pyx_n_s_parse_time_string;
static PyObject *__pyx_n_s_period;
static PyObject *__pyx_n_s_period_alias_dict;
static PyObject *__pyx_n_s_period_asfreq_arr;
static PyObject *__pyx_n_s_period_format;
static PyObject *__pyx_n_s_period_ordinal;
static PyObject *__pyx_n_s_periodarr;
static PyObject *__pyx_n_s_periodarr_to_dt64arr;
static PyObject *__pyx_n_s_prepare;
static PyObject *__pyx_n_s_property;
static PyObject *__pyx_n_s_ps;
static PyObject *__pyx_n_s_pytz;
static PyObject *__pyx_n_s_pyx_vtable;
static PyObject *__pyx_kp_b_q_2;
static PyObject *__pyx_n_s_qualname;
static PyObject *__pyx_n_s_quarter;
static PyObject *__pyx_n_s_quarter_to_myear;
static PyObject *__pyx_n_s_range;
static PyObject *__pyx_n_s_relation;
static PyObject *__pyx_n_s_replace;
static PyObject *__pyx_n_s_result;
static PyObject *__pyx_n_s_right;
static PyObject *__pyx_n_s_rule_code;
static PyObject *__pyx_n_s_s;
static PyObject *__pyx_kp_s_s_2;
static PyObject *__pyx_kp_s_s_s;
static PyObject *__pyx_n_s_searchsorted;
static PyObject *__pyx_n_s_second;
static PyObject *__pyx_n_s_side;
static PyObject *__pyx_n_s_stamps;
static PyObject *__pyx_n_s_start;
static PyObject *__pyx_n_s_start_time;
static PyObject *__pyx_n_s_string_types;
static PyObject *__pyx_n_s_sys;
static PyObject *__pyx_n_s_sz;
static PyObject *__pyx_n_s_test;
static PyObject *__pyx_n_s_timedelta;
static PyObject *__pyx_n_s_timedelta64;
static PyObject *__pyx_n_s_to_offset;
static PyObject *__pyx_n_s_to_timestamp;
static PyObject *__pyx_n_s_tslib;
static PyObject *__pyx_n_s_typ;
static PyObject *__pyx_n_s_tz;
static PyObject *__pyx_kp_b_u;
static PyObject *__pyx_n_s_unicode;
static PyObject *__pyx_kp_u_unknown_dtype_code_in_numpy_pxd;
static PyObject *__pyx_n_s_upper;
static PyObject *__pyx_n_s_us;
static PyObject *__pyx_kp_s_utf_8;
static PyObject *__pyx_n_s_val;
static PyObject *__pyx_n_s_validate_end_alias;
static PyObject *__pyx_n_s_value;
static PyObject *__pyx_n_s_values;
static PyObject *__pyx_n_s_version_info;
static PyObject *__pyx_n_s_weekofyear;
static PyObject *__pyx_n_s_y;
static PyObject *__pyx_n_s_year;
static PyObject *__pyx_pf_6pandas_7_period_dt64arr_to_periodarr(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_dtarr, int __pyx_v_freq, PyObject *__pyx_v_tz); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_2periodarr_to_dt64arr(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_periodarr, int __pyx_v_freq); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_4period_asfreq(CYTHON_UNUSED PyObject *__pyx_self, __pyx_t_5numpy_int64_t __pyx_v_period_ordinal, int __pyx_v_freq1, int __pyx_v_freq2, int __pyx_v_end); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6period_asfreq_arr(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_arr, int __pyx_v_freq1, int __pyx_v_freq2, int __pyx_v_end); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_8period_ordinal(CYTHON_UNUSED PyObject *__pyx_self, int __pyx_v_y, int __pyx_v_m, int __pyx_v_d, int __pyx_v_h, int __pyx_v_min, int __pyx_v_s, int __pyx_v_us, int __pyx_v_ps, int __pyx_v_freq); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_10period_ordinal_to_dt64(CYTHON_UNUSED PyObject *__pyx_self, __pyx_t_5numpy_int64_t __pyx_v_ordinal, int __pyx_v_freq); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_12period_format(CYTHON_UNUSED PyObject *__pyx_self, __pyx_t_5numpy_int64_t __pyx_v_value, int __pyx_v_freq, PyObject *__pyx_v_fmt); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_14get_period_field(CYTHON_UNUSED PyObject *__pyx_self, int __pyx_v_code, __pyx_t_5numpy_int64_t __pyx_v_value, int __pyx_v_freq); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_16get_period_field_arr(CYTHON_UNUSED PyObject *__pyx_self, int __pyx_v_code, PyArrayObject *__pyx_v_arr, int __pyx_v_freq); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_18extract_ordinals(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_values, PyObject *__pyx_v_freq); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_20resolution(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_stamps, PyObject *__pyx_v_tz); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period__maybe_convert_freq(CYTHON_UNUSED PyTypeObject *__pyx_v_cls, PyObject *__pyx_v_freq); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_2_from_ordinal(PyTypeObject *__pyx_v_cls, PyObject *__pyx_v_ordinal, PyObject *__pyx_v_freq); /* proto */
static int __pyx_pf_6pandas_7_period_6Period_4__init__(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self, PyObject *__pyx_v_value, PyObject *__pyx_v_freq, PyObject *__pyx_v_ordinal, PyObject *__pyx_v_year, PyObject *__pyx_v_month, PyObject *__pyx_v_quarter, PyObject *__pyx_v_day, PyObject *__pyx_v_hour, PyObject *__pyx_v_minute, PyObject *__pyx_v_second); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_6__richcmp__(PyObject *__pyx_v_self, PyObject *__pyx_v_other, PyObject *__pyx_v_op); /* proto */
static Py_hash_t __pyx_pf_6pandas_7_period_6Period_8__hash__(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_10_add_delta(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self, PyObject *__pyx_v_other); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_12__add__(PyObject *__pyx_v_self, PyObject *__pyx_v_other); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_14__sub__(PyObject *__pyx_v_self, PyObject *__pyx_v_other); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_16asfreq(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self, PyObject *__pyx_v_freq, PyObject *__pyx_v_how); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_18start_time(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_20end_time(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_22to_timestamp(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self, PyObject *__pyx_v_freq, PyObject *__pyx_v_how, PyObject *__pyx_v_tz); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_4year___get__(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_5month___get__(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_3day___get__(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_4hour___get__(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_6minute___get__(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_6second___get__(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_10weekofyear___get__(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_4week___get__(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_9dayofweek___get__(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_7weekday___get__(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_9dayofyear___get__(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_7quarter___get__(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_5qyear___get__(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_13days_in_month___get__(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_11daysinmonth___get__(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_24now(CYTHON_UNUSED PyTypeObject *__pyx_v_cls, PyObject *__pyx_v_freq); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_26__str__(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_28freqstr(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_30__repr__(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_32__unicode__(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_34__setstate__(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self, PyObject *__pyx_v_state); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_36__reduce__(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_38strftime(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self, PyObject *__pyx_v_fmt); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_7ordinal___get__(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self); /* proto */
static int __pyx_pf_6pandas_7_period_6Period_7ordinal_2__set__(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_6Period_4freq___get__(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self); /* proto */
static int __pyx_pf_6pandas_7_period_6Period_4freq_2__set__(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_6pandas_7_period_6Period_4freq_4__del__(struct __pyx_obj_6pandas_7_period_Period *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_22_ordinal_from_fields(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_year, PyObject *__pyx_v_month, PyObject *__pyx_v_quarter, PyObject *__pyx_v_day, PyObject *__pyx_v_hour, PyObject *__pyx_v_minute, PyObject *__pyx_v_second, PyObject *__pyx_v_freq); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_24_quarter_to_myear(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_year, PyObject *__pyx_v_quarter, PyObject *__pyx_v_freq); /* proto */
static PyObject *__pyx_pf_6pandas_7_period_26_validate_end_alias(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_how); /* 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 PyObject *__pyx_tp_new_6pandas_7_period_Period(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_int_0;
static PyObject *__pyx_int_1;
static PyObject *__pyx_int_2;
static PyObject *__pyx_int_3;
static PyObject *__pyx_int_4;
static PyObject *__pyx_int_5;
static PyObject *__pyx_int_6;
static PyObject *__pyx_int_7;
static PyObject *__pyx_int_8;
static PyObject *__pyx_int_9;
static PyObject *__pyx_int_10;
static PyObject *__pyx_int_11;
static PyObject *__pyx_int_12;
static PyObject *__pyx_int_15;
static PyObject *__pyx_int_6000;
static PyObject *__pyx_int_1000000000;
static PyObject *__pyx_tuple_;
static PyObject *__pyx_tuple__2;
static PyObject *__pyx_tuple__3;
static PyObject *__pyx_tuple__4;
static PyObject *__pyx_tuple__5;
static PyObject *__pyx_tuple__6;
static PyObject *__pyx_tuple__7;
static PyObject *__pyx_tuple__8;
static PyObject *__pyx_tuple__9;
static PyObject *__pyx_tuple__10;
static PyObject *__pyx_tuple__11;
static PyObject *__pyx_tuple__12;
static PyObject *__pyx_tuple__13;
static PyObject *__pyx_tuple__14;
static PyObject *__pyx_tuple__15;
static PyObject *__pyx_tuple__16;
static PyObject *__pyx_tuple__17;
static PyObject *__pyx_tuple__18;
static PyObject *__pyx_tuple__19;
static PyObject *__pyx_tuple__20;
static PyObject *__pyx_tuple__21;
static PyObject *__pyx_tuple__22;
static PyObject *__pyx_tuple__23;
static PyObject *__pyx_tuple__24;
static PyObject *__pyx_tuple__25;
static PyObject *__pyx_tuple__26;
static PyObject *__pyx_tuple__27;
static PyObject *__pyx_tuple__29;
static PyObject *__pyx_tuple__31;
static PyObject *__pyx_tuple__33;
static PyObject *__pyx_tuple__35;
static PyObject *__pyx_tuple__37;
static PyObject *__pyx_tuple__38;
static PyObject *__pyx_tuple__39;
static PyObject *__pyx_tuple__40;
static PyObject *__pyx_tuple__41;
static PyObject *__pyx_tuple__42;
static PyObject *__pyx_tuple__43;
static PyObject *__pyx_tuple__45;
static PyObject *__pyx_tuple__47;
static PyObject *__pyx_tuple__49;
static PyObject *__pyx_tuple__51;
static PyObject *__pyx_tuple__53;
static PyObject *__pyx_codeobj__28;
static PyObject *__pyx_codeobj__30;
static PyObject *__pyx_codeobj__32;
static PyObject *__pyx_codeobj__34;
static PyObject *__pyx_codeobj__36;
static PyObject *__pyx_codeobj__44;
static PyObject *__pyx_codeobj__46;
static PyObject *__pyx_codeobj__48;
static PyObject *__pyx_codeobj__50;
static PyObject *__pyx_codeobj__52;
static PyObject *__pyx_codeobj__54;

/* "pandas/src/period.pyx":116
 * #----------------------------------------------------------------------
 * 
 * cdef inline int64_t apply_mult(int64_t period_ord, int64_t mult):             # <<<<<<<<<<<<<<
 *     """
 *     Get freq+multiple ordinal value from corresponding freq-only ordinal value.
 */

static CYTHON_INLINE __pyx_t_5numpy_int64_t __pyx_f_6pandas_7_period_apply_mult(__pyx_t_5numpy_int64_t __pyx_v_period_ord, __pyx_t_5numpy_int64_t __pyx_v_mult) {
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  /* "pandas/src/period.pyx":122
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 * 
 */
  __pyx_t_1 = ((__pyx_v_mult == 1) != 0);
  if (__pyx_t_1) {

    /* "pandas/src/period.pyx":123
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 * 
 *     return (period_ord - 1) // mult
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    goto __pyx_L0;

    /* "pandas/src/period.pyx":122
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 *         return period_ord
 * 
 */
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  /* "pandas/src/period.pyx":125
 *         return period_ord
 * 
 *     return (period_ord - 1) // mult             # <<<<<<<<<<<<<<
 * 
 * cdef inline int64_t remove_mult(int64_t period_ord_w_mult, int64_t mult):
 */
  __pyx_t_2 = (__pyx_v_period_ord - 1);
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  /* "pandas/src/period.pyx":116
 * #----------------------------------------------------------------------
 * 
 * cdef inline int64_t apply_mult(int64_t period_ord, int64_t mult):             # <<<<<<<<<<<<<<
 *     """
 *     Get freq+multiple ordinal value from corresponding freq-only ordinal value.
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  /* function exit code */
  __pyx_L1_error:;
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/* "pandas/src/period.pyx":127
 *     return (period_ord - 1) // mult
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 * cdef inline int64_t remove_mult(int64_t period_ord_w_mult, int64_t mult):             # <<<<<<<<<<<<<<
 *     """
 *     Get freq-only ordinal value from corresponding freq+multiple ordinal.
 */

static CYTHON_INLINE __pyx_t_5numpy_int64_t __pyx_f_6pandas_7_period_remove_mult(__pyx_t_5numpy_int64_t __pyx_v_period_ord_w_mult, __pyx_t_5numpy_int64_t __pyx_v_mult) {
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  /* "pandas/src/period.pyx":131
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 */
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    /* "pandas/src/period.pyx":132
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 * 
 *     return period_ord_w_mult * mult + 1;
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    /* "pandas/src/period.pyx":131
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All days in a new    |       |\n        |           | year preceding the first       |       |\n        |           | Monday are considered to be in |       |\n        |           | week 0.                        |       |\n        +-----------+--------------------------------+-------+\n        | ``%x``    | Locale's appropriate date      |       |\n        |           | representation.                |       |\n        +-----------+--------------------------------+-------+\n        | ``%X``    | Locale's appropriate time      |       |\n        |           | representation.                |       |\n        +-----------+--------------------------------+-------+\n        | ``%y``    | Year without century as a      |       |\n        |           | decimal number [00,99].        |       |\n        +-----------+--------------------------------+-------+\n        | ``%Y``    | Year with century as a decimal |       |\n        |           | number.                        |       |\n        +-----------+--------------------------------+-------+\n        | ``%Z``    | Time zone name (no characters  |       |\n        |           | if no time zone exists).       |       |\n        +-----------+--------------------------------+-------+\n        | ``%%``    | A literal ``'%'`` character.   |       |\n        +-----------+--------------------------------+-------+\n\n        .. 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  return __pyx_pw_6pandas_7_period_6Period_5month_1__get__(o);
}

static PyObject *__pyx_getprop_6pandas_7_period_6Period_day(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pandas_7_period_6Period_3day_1__get__(o);
}

static PyObject *__pyx_getprop_6pandas_7_period_6Period_hour(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pandas_7_period_6Period_4hour_1__get__(o);
}

static PyObject *__pyx_getprop_6pandas_7_period_6Period_minute(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pandas_7_period_6Period_6minute_1__get__(o);
}

static PyObject *__pyx_getprop_6pandas_7_period_6Period_second(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pandas_7_period_6Period_6second_1__get__(o);
}

static PyObject *__pyx_getprop_6pandas_7_period_6Period_weekofyear(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pandas_7_period_6Period_10weekofyear_1__get__(o);
}

static PyObject *__pyx_getprop_6pandas_7_period_6Period_week(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pandas_7_period_6Period_4week_1__get__(o);
}

static PyObject *__pyx_getprop_6pandas_7_period_6Period_dayofweek(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pandas_7_period_6Period_9dayofweek_1__get__(o);
}

static PyObject *__pyx_getprop_6pandas_7_period_6Period_weekday(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pandas_7_period_6Period_7weekday_1__get__(o);
}

static PyObject *__pyx_getprop_6pandas_7_period_6Period_dayofyear(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pandas_7_period_6Period_9dayofyear_1__get__(o);
}

static PyObject *__pyx_getprop_6pandas_7_period_6Period_quarter(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pandas_7_period_6Period_7quarter_1__get__(o);
}

static PyObject *__pyx_getprop_6pandas_7_period_6Period_qyear(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pandas_7_period_6Period_5qyear_1__get__(o);
}

static PyObject *__pyx_getprop_6pandas_7_period_6Period_days_in_month(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pandas_7_period_6Period_13days_in_month_1__get__(o);
}

static PyObject *__pyx_getprop_6pandas_7_period_6Period_daysinmonth(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pandas_7_period_6Period_11daysinmonth_1__get__(o);
}

static PyObject *__pyx_getprop_6pandas_7_period_6Period_ordinal(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pandas_7_period_6Period_7ordinal_1__get__(o);
}

static int __pyx_setprop_6pandas_7_period_6Period_ordinal(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pandas_7_period_6Period_7ordinal_3__set__(o, v);
  }
  else {
    PyErr_SetString(PyExc_NotImplementedError, "__del__");
    return -1;
  }
}

static PyObject *__pyx_getprop_6pandas_7_period_6Period_freq(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_pw_6pandas_7_period_6Period_4freq_1__get__(o);
}

static int __pyx_setprop_6pandas_7_period_6Period_freq(PyObject *o, PyObject *v, CYTHON_UNUSED void *x) {
  if (v) {
    return __pyx_pw_6pandas_7_period_6Period_4freq_3__set__(o, v);
  }
  else {
    return __pyx_pw_6pandas_7_period_6Period_4freq_5__del__(o);
  }
}

static PyMethodDef __pyx_methods_6pandas_7_period_Period[] = {
  {"_maybe_convert_freq", (PyCFunction)__pyx_pw_6pandas_7_period_6Period_1_maybe_convert_freq, METH_O, 0},
  {"_from_ordinal", (PyCFunction)__pyx_pw_6pandas_7_period_6Period_3_from_ordinal, METH_VARARGS|METH_KEYWORDS, __pyx_doc_6pandas_7_period_6Period_2_from_ordinal},
  {"_add_delta", (PyCFunction)__pyx_pw_6pandas_7_period_6Period_11_add_delta, METH_O, 0},
  {"asfreq", (PyCFunction)__pyx_pw_6pandas_7_period_6Period_17asfreq, METH_VARARGS|METH_KEYWORDS, __pyx_doc_6pandas_7_period_6Period_16asfreq},
  {"start_time", (PyCFunction)__pyx_pw_6pandas_7_period_6Period_19start_time, METH_NOARGS, 0},
  {"end_time", (PyCFunction)__pyx_pw_6pandas_7_period_6Period_21end_time, METH_NOARGS, 0},
  {"to_timestamp", (PyCFunction)__pyx_pw_6pandas_7_period_6Period_23to_timestamp, METH_VARARGS|METH_KEYWORDS, __pyx_doc_6pandas_7_period_6Period_22to_timestamp},
  {"now", (PyCFunction)__pyx_pw_6pandas_7_period_6Period_25now, METH_VARARGS|METH_KEYWORDS, 0},
  {"freqstr", (PyCFunction)__pyx_pw_6pandas_7_period_6Period_29freqstr, METH_NOARGS, 0},
  {"__unicode__", (PyCFunction)__pyx_pw_6pandas_7_period_6Period_33__unicode__, METH_NOARGS, __pyx_doc_6pandas_7_period_6Period_32__unicode__},
  {"__setstate__", (PyCFunction)__pyx_pw_6pandas_7_period_6Period_35__setstate__, METH_O, 0},
  {"__reduce__", (PyCFunction)__pyx_pw_6pandas_7_period_6Period_37__reduce__, METH_NOARGS, 0},
  {"strftime", (PyCFunction)__pyx_pw_6pandas_7_period_6Period_39strftime, METH_O, __pyx_doc_6pandas_7_period_6Period_38strftime},
  {0, 0, 0, 0}
};

static struct PyGetSetDef __pyx_getsets_6pandas_7_period_Period[] = {
  {(char *)"year", __pyx_getprop_6pandas_7_period_6Period_year, 0, 0, 0},
  {(char *)"month", __pyx_getprop_6pandas_7_period_6Period_month, 0, 0, 0},
  {(char *)"day", __pyx_getprop_6pandas_7_period_6Period_day, 0, 0, 0},
  {(char *)"hour", __pyx_getprop_6pandas_7_period_6Period_hour, 0, 0, 0},
  {(char *)"minute", __pyx_getprop_6pandas_7_period_6Period_minute, 0, 0, 0},
  {(char *)"second", __pyx_getprop_6pandas_7_period_6Period_second, 0, 0, 0},
  {(char *)"weekofyear", __pyx_getprop_6pandas_7_period_6Period_weekofyear, 0, 0, 0},
  {(char *)"week", __pyx_getprop_6pandas_7_period_6Period_week, 0, 0, 0},
  {(char *)"dayofweek", __pyx_getprop_6pandas_7_period_6Period_dayofweek, 0, 0, 0},
  {(char *)"weekday", __pyx_getprop_6pandas_7_period_6Period_weekday, 0, 0, 0},
  {(char *)"dayofyear", __pyx_getprop_6pandas_7_period_6Period_dayofyear, 0, 0, 0},
  {(char *)"quarter", __pyx_getprop_6pandas_7_period_6Period_quarter, 0, 0, 0},
  {(char *)"qyear", __pyx_getprop_6pandas_7_period_6Period_qyear, 0, 0, 0},
  {(char *)"days_in_month", __pyx_getprop_6pandas_7_period_6Period_days_in_month, 0, 0, 0},
  {(char *)"daysinmonth", __pyx_getprop_6pandas_7_period_6Period_daysinmonth, 0, 0, 0},
  {(char *)"ordinal", __pyx_getprop_6pandas_7_period_6Period_ordinal, __pyx_setprop_6pandas_7_period_6Period_ordinal, 0, 0},
  {(char *)"freq", __pyx_getprop_6pandas_7_period_6Period_freq, __pyx_setprop_6pandas_7_period_6Period_freq, 0, 0},
  {0, 0, 0, 0, 0}
};

static PyNumberMethods __pyx_tp_as_number_Period = {
  __pyx_pw_6pandas_7_period_6Period_13__add__, /*nb_add*/
  __pyx_pw_6pandas_7_period_6Period_15__sub__, /*nb_subtract*/
  0, /*nb_multiply*/
  #if PY_MAJOR_VERSION < 3 || CYTHON_COMPILING_IN_PYPY
  0, /*nb_divide*/
  #endif
  0, /*nb_remainder*/
  0, /*nb_divmod*/
  0, /*nb_power*/
  0, /*nb_negative*/
  0, /*nb_positive*/
  0, /*nb_absolute*/
  0, /*nb_nonzero*/
  0, /*nb_invert*/
  0, /*nb_lshift*/
  0, /*nb_rshift*/
  0, /*nb_and*/
  0, /*nb_xor*/
  0, /*nb_or*/
  #if PY_MAJOR_VERSION < 3 || CYTHON_COMPILING_IN_PYPY
  0, /*nb_coerce*/
  #endif
  0, /*nb_int*/
  #if PY_MAJOR_VERSION < 3
  0, /*nb_long*/
  #else
  0, /*reserved*/
  #endif
  0, /*nb_float*/
  #if PY_MAJOR_VERSION < 3 || CYTHON_COMPILING_IN_PYPY
  0, /*nb_oct*/
  #endif
  #if PY_MAJOR_VERSION < 3 || CYTHON_COMPILING_IN_PYPY
  0, /*nb_hex*/
  #endif
  0, /*nb_inplace_add*/
  0, /*nb_inplace_subtract*/
  0, /*nb_inplace_multiply*/
  #if PY_MAJOR_VERSION < 3 || CYTHON_COMPILING_IN_PYPY
  0, /*nb_inplace_divide*/
  #endif
  0, /*nb_inplace_remainder*/
  0, /*nb_inplace_power*/
  0, /*nb_inplace_lshift*/
  0, /*nb_inplace_rshift*/
  0, /*nb_inplace_and*/
  0, /*nb_inplace_xor*/
  0, /*nb_inplace_or*/
  0, /*nb_floor_divide*/
  0, /*nb_true_divide*/
  0, /*nb_inplace_floor_divide*/
  0, /*nb_inplace_true_divide*/
  0, /*nb_index*/
  #if PY_VERSION_HEX >= 0x03050000
  0, /*nb_matrix_multiply*/
  #endif
  #if PY_VERSION_HEX >= 0x03050000
  0, /*nb_inplace_matrix_multiply*/
  #endif
};

static PyTypeObject __pyx_type_6pandas_7_period_Period = {
  PyVarObject_HEAD_INIT(0, 0)
  "pandas._period.Period", /*tp_name*/
  sizeof(struct __pyx_obj_6pandas_7_period_Period), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc_6pandas_7_period_Period, /*tp_dealloc*/
  0, /*tp_print*/
  0, /*tp_getattr*/
  0, /*tp_setattr*/
  #if PY_MAJOR_VERSION < 3
  0, /*tp_compare*/
  #endif
  #if PY_MAJOR_VERSION >= 3
  0, /*tp_as_async*/
  #endif
  __pyx_pw_6pandas_7_period_6Period_31__repr__, /*tp_repr*/
  &__pyx_tp_as_number_Period, /*tp_as_number*/
  0, /*tp_as_sequence*/
  0, /*tp_as_mapping*/
  __pyx_pw_6pandas_7_period_6Period_9__hash__, /*tp_hash*/
  0, /*tp_call*/
  __pyx_pw_6pandas_7_period_6Period_27__str__, /*tp_str*/
  0, /*tp_getattro*/
  0, /*tp_setattro*/
  0, /*tp_as_buffer*/
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC, /*tp_flags*/
  "\n    Represents an period of time\n\n    Parameters\n    ----------\n    value : Period or compat.string_types, default None\n        The time period represented (e.g., '4Q2005')\n    freq : str, default None\n        One of pandas period strings or corresponding objects\n    year : int, default None\n    month : int, default 1\n    quarter : int, default None\n    day : int, default 1\n    hour : int, default 0\n    minute : int, default 0\n    second : int, default 0\n    ", /*tp_doc*/
  __pyx_tp_traverse_6pandas_7_period_Period, /*tp_traverse*/
  __pyx_tp_clear_6pandas_7_period_Period, /*tp_clear*/
  __pyx_pw_6pandas_7_period_6Period_7__richcmp__, /*tp_richcompare*/
  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
  0, /*tp_iternext*/
  __pyx_methods_6pandas_7_period_Period, /*tp_methods*/
  0, /*tp_members*/
  __pyx_getsets_6pandas_7_period_Period, /*tp_getset*/
  0, /*tp_base*/
  0, /*tp_dict*/
  0, /*tp_descr_get*/
  0, /*tp_descr_set*/
  0, /*tp_dictoffset*/
  __pyx_pw_6pandas_7_period_6Period_5__init__, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_6pandas_7_period_Period, /*tp_new*/
  0, /*tp_free*/
  0, /*tp_is_gc*/
  0, /*tp_bases*/
  0, /*tp_mro*/
  0, /*tp_cache*/
  0, /*tp_subclasses*/
  0, /*tp_weaklist*/
  0, /*tp_del*/
  0, /*tp_version_tag*/
  #if PY_VERSION_HEX >= 0x030400a1
  0, /*tp_finalize*/
  #endif
};

static PyMethodDef __pyx_methods[] = {
  {"period_asfreq", (PyCFunction)__pyx_pw_6pandas_7_period_5period_asfreq, METH_VARARGS|METH_KEYWORDS, __pyx_doc_6pandas_7_period_4period_asfreq},
  {"period_ordinal_to_dt64", (PyCFunction)__pyx_pw_6pandas_7_period_11period_ordinal_to_dt64, METH_VARARGS|METH_KEYWORDS, 0},
  {"resolution", (PyCFunction)__pyx_pw_6pandas_7_period_21resolution, METH_VARARGS|METH_KEYWORDS, 0},
  {0, 0, 0, 0}
};

#if PY_MAJOR_VERSION >= 3
static struct PyModuleDef __pyx_moduledef = {
  #if PY_VERSION_HEX < 0x03020000
    { PyObject_HEAD_INIT(NULL) NULL, 0, NULL },
  #else
    PyModuleDef_HEAD_INIT,
  #endif
    "_period",
    0, /* m_doc */
    -1, /* m_size */
    __pyx_methods /* m_methods */,
    NULL, /* m_reload */
    NULL, /* m_traverse */
    NULL, /* m_clear */
    NULL /* m_free */
};
#endif

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#if PY_MAJOR_VERSION < 3
PyMODINIT_FUNC init_period(void); /*proto*/
PyMODINIT_FUNC init_period(void)
#else
PyMODINIT_FUNC PyInit__period(void); /*proto*/
PyMODINIT_FUNC PyInit__period(void)
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}
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 CYTHON_INLINE PyObject *__Pyx_GetModuleGlobalName(PyObject *name) {
    PyObject *result;
#if CYTHON_COMPILING_IN_CPYTHON
    result = PyDict_GetItem(__pyx_d, name);
    if (likely(result)) {
        Py_INCREF(result);
    } else {
#else
    result = PyObject_GetItem(__pyx_d, name);
    if (!result) {
        PyErr_Clear();
#endif
        result = __Pyx_GetBuiltinName(name);
    }
    return result;
}

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

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

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

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

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

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

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

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

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;
}

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,
                                                              CYTHON_NCP_UNUSED int wraparound,
                                                              CYTHON_NCP_UNUSED 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);
        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_Tuple_Fast(PyObject *o, Py_ssize_t i,
                                                              CYTHON_NCP_UNUSED int wraparound,
                                                              CYTHON_NCP_UNUSED int boundscheck) {
#if CYTHON_COMPILING_IN_CPYTHON
    if (wraparound & unlikely(i < 0)) i += PyTuple_GET_SIZE(o);
    if ((!boundscheck) || likely((0 <= i) & (i < PyTuple_GET_SIZE(o)))) {
        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, int is_list,
                                                     CYTHON_NCP_UNUSED int wraparound,
                                                     CYTHON_NCP_UNUSED int boundscheck) {
#if CYTHON_COMPILING_IN_CPYTHON
    if (is_list || PyList_CheckExact(o)) {
        Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyList_GET_SIZE(o);
        if ((!boundscheck) || (likely((n >= 0) & (n < PyList_GET_SIZE(o))))) {
            PyObject *r = PyList_GET_ITEM(o, n);
            Py_INCREF(r);
            return r;
        }
    }
    else if (PyTuple_CheckExact(o)) {
        Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyTuple_GET_SIZE(o);
        if ((!boundscheck) || likely((n >= 0) & (n < PyTuple_GET_SIZE(o)))) {
            PyObject *r = PyTuple_GET_ITEM(o, n);
            Py_INCREF(r);
            return r;
        }
    } else {
        PySequenceMethods *m = Py_TYPE(o)->tp_as_sequence;
        if (likely(m && m->sq_item)) {
            if (wraparound && unlikely(i < 0) && likely(m->sq_length)) {
                Py_ssize_t l = m->sq_length(o);
                if (likely(l >= 0)) {
                    i += l;
                } else {
                    if (PyErr_ExceptionMatches(PyExc_OverflowError))
                        PyErr_Clear();
                    else
                        return NULL;
                }
            }
            return m->sq_item(o, i);
        }
    }
#else
    if (is_list || PySequence_Check(o)) {
        return PySequence_GetItem(o, i);
    }
#endif
    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
}

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

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

static CYTHON_INLINE __pyx_t_5numpy_int64_t __Pyx_mod___pyx_t_5numpy_int64_t(__pyx_t_5numpy_int64_t a, __pyx_t_5numpy_int64_t b) {
    __pyx_t_5numpy_int64_t r = a % b;
    r += ((r != 0) & ((r ^ b) < 0)) * b;
    return r;
}

static CYTHON_INLINE void __Pyx_RaiseUnboundLocalError(const char *varname) {
    PyErr_Format(PyExc_UnboundLocalError, "local variable '%s' referenced before assignment", varname);
}

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 int __Pyx_IterFinish(void) {
#if CYTHON_COMPILING_IN_CPYTHON
    PyThreadState *tstate = PyThreadState_GET();
    PyObject* exc_type = tstate->curexc_type;
    if (unlikely(exc_type)) {
        if (likely(exc_type == PyExc_StopIteration) || PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration)) {
            PyObject *exc_value, *exc_tb;
            exc_value = tstate->curexc_value;
            exc_tb = tstate->curexc_traceback;
            tstate->curexc_type = 0;
            tstate->curexc_value = 0;
            tstate->curexc_traceback = 0;
            Py_DECREF(exc_type);
            Py_XDECREF(exc_value);
            Py_XDECREF(exc_tb);
            return 0;
        } else {
            return -1;
        }
    }
    return 0;
#else
    if (unlikely(PyErr_Occurred())) {
        if (likely(PyErr_ExceptionMatches(PyExc_StopIteration))) {
            PyErr_Clear();
            return 0;
        } else {
            return -1;
        }
    }
    return 0;
#endif
}

static int __Pyx_IternextUnpackEndCheck(PyObject *retval, Py_ssize_t expected) {
    if (unlikely(retval)) {
        Py_DECREF(retval);
        __Pyx_RaiseTooManyValuesError(expected);
        return -1;
    } else {
        return __Pyx_IterFinish();
    }
    return 0;
}

#if CYTHON_USE_PYLONG_INTERNALS
  #include "longintrepr.h"
#endif

#if CYTHON_COMPILING_IN_CPYTHON
static PyObject* __Pyx_PyInt_SubtractObjC(PyObject *op1, PyObject *op2, CYTHON_UNUSED long intval, CYTHON_UNUSED int inplace) {
    #if PY_MAJOR_VERSION < 3
    if (likely(PyInt_CheckExact(op1))) {
        const long b = intval;
        long x;
        long a = PyInt_AS_LONG(op1);
            x = (long)((unsigned long)a - b);
            if (likely((x^a) >= 0 || (x^~b) >= 0))
                return PyInt_FromLong(x);
            return PyLong_Type.tp_as_number->nb_subtract(op1, op2);
    }
    #endif
    #if CYTHON_USE_PYLONG_INTERNALS && PY_MAJOR_VERSION >= 3
    if (likely(PyLong_CheckExact(op1))) {
        const long b = intval;
        long a, x;
        const PY_LONG_LONG llb = intval;
        PY_LONG_LONG lla, llx;
        const digit* digits = ((PyLongObject*)op1)->ob_digit;
        const Py_ssize_t size = Py_SIZE(op1);
        if (likely(__Pyx_sst_abs(size) <= 1)) {
            a = likely(size) ? digits[0] : 0;
            if (size == -1) a = -a;
        } else {
            switch (size) {
                case -2:
                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                        a = -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
                        lla = -(PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
                    }
                case 2:
                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                        a = (long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
                        lla = (PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
                    }
                case -3:
                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                        a = -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
                        lla = -(PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
                    }
                case 3:
                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                        a = (long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
                        lla = (PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
                    }
                case -4:
                    if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                        a = -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
                        lla = -(PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
                    }
                case 4:
                    if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                        a = (long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
                        lla = (PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
                    }
                default: return PyLong_Type.tp_as_number->nb_subtract(op1, op2);
            }
        }
                x = a - b;
            return PyLong_FromLong(x);
        long_long:
                llx = lla - llb;
            return PyLong_FromLongLong(llx);
    }
    #endif
    if (PyFloat_CheckExact(op1)) {
        const long b = intval;
        double a = PyFloat_AS_DOUBLE(op1);
            double result;
            PyFPE_START_PROTECT("subtract", return NULL)
            result = ((double)a) - (double)b;
            PyFPE_END_PROTECT(result)
            return PyFloat_FromDouble(result);
    }
    return (inplace ? PyNumber_InPlaceSubtract : PyNumber_Subtract)(op1, op2);
}
#endif

static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals) {
#if CYTHON_COMPILING_IN_PYPY
    return PyObject_RichCompareBool(s1, s2, equals);
#else
    if (s1 == s2) {
        return (equals == Py_EQ);
    } else if (PyBytes_CheckExact(s1) & PyBytes_CheckExact(s2)) {
        const char *ps1, *ps2;
        Py_ssize_t length = PyBytes_GET_SIZE(s1);
        if (length != PyBytes_GET_SIZE(s2))
            return (equals == Py_NE);
        ps1 = PyBytes_AS_STRING(s1);
        ps2 = PyBytes_AS_STRING(s2);
        if (ps1[0] != ps2[0]) {
            return (equals == Py_NE);
        } else if (length == 1) {
            return (equals == Py_EQ);
        } else {
            int result = memcmp(ps1, ps2, (size_t)length);
            return (equals == Py_EQ) ? (result == 0) : (result != 0);
        }
    } else if ((s1 == Py_None) & PyBytes_CheckExact(s2)) {
        return (equals == Py_NE);
    } else if ((s2 == Py_None) & PyBytes_CheckExact(s1)) {
        return (equals == Py_NE);
    } else {
        int result;
        PyObject* py_result = PyObject_RichCompare(s1, s2, equals);
        if (!py_result)
            return -1;
        result = __Pyx_PyObject_IsTrue(py_result);
        Py_DECREF(py_result);
        return result;
    }
#endif
}

static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals) {
#if CYTHON_COMPILING_IN_PYPY
    return PyObject_RichCompareBool(s1, s2, equals);
#else
#if PY_MAJOR_VERSION < 3
    PyObject* owned_ref = NULL;
#endif
    int s1_is_unicode, s2_is_unicode;
    if (s1 == s2) {
        goto return_eq;
    }
    s1_is_unicode = PyUnicode_CheckExact(s1);
    s2_is_unicode = PyUnicode_CheckExact(s2);
#if PY_MAJOR_VERSION < 3
    if ((s1_is_unicode & (!s2_is_unicode)) && PyString_CheckExact(s2)) {
        owned_ref = PyUnicode_FromObject(s2);
        if (unlikely(!owned_ref))
            return -1;
        s2 = owned_ref;
        s2_is_unicode = 1;
    } else if ((s2_is_unicode & (!s1_is_unicode)) && PyString_CheckExact(s1)) {
        owned_ref = PyUnicode_FromObject(s1);
        if (unlikely(!owned_ref))
            return -1;
        s1 = owned_ref;
        s1_is_unicode = 1;
    } else if (((!s2_is_unicode) & (!s1_is_unicode))) {
        return __Pyx_PyBytes_Equals(s1, s2, equals);
    }
#endif
    if (s1_is_unicode & s2_is_unicode) {
        Py_ssize_t length;
        int kind;
        void *data1, *data2;
        if (unlikely(__Pyx_PyUnicode_READY(s1) < 0) || unlikely(__Pyx_PyUnicode_READY(s2) < 0))
            return -1;
        length = __Pyx_PyUnicode_GET_LENGTH(s1);
        if (length != __Pyx_PyUnicode_GET_LENGTH(s2)) {
            goto return_ne;
        }
        kind = __Pyx_PyUnicode_KIND(s1);
        if (kind != __Pyx_PyUnicode_KIND(s2)) {
            goto return_ne;
        }
        data1 = __Pyx_PyUnicode_DATA(s1);
        data2 = __Pyx_PyUnicode_DATA(s2);
        if (__Pyx_PyUnicode_READ(kind, data1, 0) != __Pyx_PyUnicode_READ(kind, data2, 0)) {
            goto return_ne;
        } else if (length == 1) {
            goto return_eq;
        } else {
            int result = memcmp(data1, data2, (size_t)(length * kind));
            #if PY_MAJOR_VERSION < 3
            Py_XDECREF(owned_ref);
            #endif
            return (equals == Py_EQ) ? (result == 0) : (result != 0);
        }
    } else if ((s1 == Py_None) & s2_is_unicode) {
        goto return_ne;
    } else if ((s2 == Py_None) & s1_is_unicode) {
        goto return_ne;
    } else {
        int result;
        PyObject* py_result = PyObject_RichCompare(s1, s2, equals);
        if (!py_result)
            return -1;
        result = __Pyx_PyObject_IsTrue(py_result);
        Py_DECREF(py_result);
        return result;
    }
return_eq:
    #if PY_MAJOR_VERSION < 3
    Py_XDECREF(owned_ref);
    #endif
    return (equals == Py_EQ);
return_ne:
    #if PY_MAJOR_VERSION < 3
    Py_XDECREF(owned_ref);
    #endif
    return (equals == Py_NE);
#endif
}

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

static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb) {
    PyObject *local_type, *local_value, *local_tb;
#if CYTHON_COMPILING_IN_CPYTHON
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    PyThreadState *tstate = PyThreadState_GET();
    local_type = tstate->curexc_type;
    local_value = tstate->curexc_value;
    local_tb = tstate->curexc_traceback;
    tstate->curexc_type = 0;
    tstate->curexc_value = 0;
    tstate->curexc_traceback = 0;
#else
    PyErr_Fetch(&local_type, &local_value, &local_tb);
#endif
    PyErr_NormalizeException(&local_type, &local_value, &local_tb);
#if CYTHON_COMPILING_IN_CPYTHON
    if (unlikely(tstate->curexc_type))
#else
    if (unlikely(PyErr_Occurred()))
#endif
        goto bad;
    #if PY_MAJOR_VERSION >= 3
    if (local_tb) {
        if (unlikely(PyException_SetTraceback(local_value, local_tb) < 0))
            goto bad;
    }
    #endif
    Py_XINCREF(local_tb);
    Py_XINCREF(local_type);
    Py_XINCREF(local_value);
    *type = local_type;
    *value = local_value;
    *tb = local_tb;
#if CYTHON_COMPILING_IN_CPYTHON
    tmp_type = tstate->exc_type;
    tmp_value = tstate->exc_value;
    tmp_tb = tstate->exc_traceback;
    tstate->exc_type = local_type;
    tstate->exc_value = local_value;
    tstate->exc_traceback = local_tb;
    Py_XDECREF(tmp_type);
    Py_XDECREF(tmp_value);
    Py_XDECREF(tmp_tb);
#else
    PyErr_SetExcInfo(local_type, local_value, local_tb);
#endif
    return 0;
bad:
    *type = 0;
    *value = 0;
    *tb = 0;
    Py_XDECREF(local_type);
    Py_XDECREF(local_value);
    Py_XDECREF(local_tb);
    return -1;
}

#if CYTHON_COMPILING_IN_CPYTHON
static PyObject* __Pyx_PyInt_EqObjC(PyObject *op1, PyObject *op2, CYTHON_UNUSED long intval, CYTHON_UNUSED int inplace) {
    if (op1 == op2) {
        Py_RETURN_TRUE;
    }
    #if PY_MAJOR_VERSION < 3
    if (likely(PyInt_CheckExact(op1))) {
        const long b = intval;
        long a = PyInt_AS_LONG(op1);
        if (a == b) {
            Py_RETURN_TRUE;
        } else {
            Py_RETURN_FALSE;
        }
    }
    #endif
    #if CYTHON_USE_PYLONG_INTERNALS && PY_MAJOR_VERSION >= 3
    if (likely(PyLong_CheckExact(op1))) {
        const long b = intval;
        long a;
        const digit* digits = ((PyLongObject*)op1)->ob_digit;
        const Py_ssize_t size = Py_SIZE(op1);
        if (likely(__Pyx_sst_abs(size) <= 1)) {
            a = likely(size) ? digits[0] : 0;
            if (size == -1) a = -a;
        } else {
            switch (size) {
                case -2:
                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                        a = -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    }
                case 2:
                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                        a = (long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    }
                case -3:
                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                        a = -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    }
                case 3:
                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                        a = (long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    }
                case -4:
                    if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                        a = -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    }
                case 4:
                    if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                        a = (long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    }
                #if PyLong_SHIFT < 30 && PyLong_SHIFT != 15
                default: return PyLong_Type.tp_richcompare(op1, op2, Py_EQ);
                #else
                default: Py_RETURN_FALSE;
                #endif
            }
        }
            if (a == b) {
                Py_RETURN_TRUE;
            } else {
                Py_RETURN_FALSE;
            }
    }
    #endif
    if (PyFloat_CheckExact(op1)) {
        const long b = intval;
        double a = PyFloat_AS_DOUBLE(op1);
            if ((double)a == (double)b) {
                Py_RETURN_TRUE;
            } else {
                Py_RETURN_FALSE;
            }
    }
    return PyObject_RichCompare(op1, op2, Py_EQ);
}
#endif

#if CYTHON_COMPILING_IN_CPYTHON
static PyObject* __Pyx_PyInt_AddObjC(PyObject *op1, PyObject *op2, CYTHON_UNUSED long intval, CYTHON_UNUSED int inplace) {
    #if PY_MAJOR_VERSION < 3
    if (likely(PyInt_CheckExact(op1))) {
        const long b = intval;
        long x;
        long a = PyInt_AS_LONG(op1);
            x = (long)((unsigned long)a + b);
            if (likely((x^a) >= 0 || (x^b) >= 0))
                return PyInt_FromLong(x);
            return PyLong_Type.tp_as_number->nb_add(op1, op2);
    }
    #endif
    #if CYTHON_USE_PYLONG_INTERNALS && PY_MAJOR_VERSION >= 3
    if (likely(PyLong_CheckExact(op1))) {
        const long b = intval;
        long a, x;
        const PY_LONG_LONG llb = intval;
        PY_LONG_LONG lla, llx;
        const digit* digits = ((PyLongObject*)op1)->ob_digit;
        const Py_ssize_t size = Py_SIZE(op1);
        if (likely(__Pyx_sst_abs(size) <= 1)) {
            a = likely(size) ? digits[0] : 0;
            if (size == -1) a = -a;
        } else {
            switch (size) {
                case -2:
                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                        a = -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
                        lla = -(PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
                    }
                case 2:
                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                        a = (long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
                        lla = (PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
                    }
                case -3:
                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                        a = -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
                        lla = -(PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
                    }
                case 3:
                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                        a = (long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
                        lla = (PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
                    }
                case -4:
                    if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                        a = -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
                        lla = -(PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
                    }
                case 4:
                    if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                        a = (long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
                        lla = (PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
                    }
                default: return PyLong_Type.tp_as_number->nb_add(op1, op2);
            }
        }
                x = a + b;
            return PyLong_FromLong(x);
        long_long:
                llx = lla + llb;
            return PyLong_FromLongLong(llx);
    }
    #endif
    if (PyFloat_CheckExact(op1)) {
        const long b = intval;
        double a = PyFloat_AS_DOUBLE(op1);
            double result;
            PyFPE_START_PROTECT("add", return NULL)
            result = ((double)a) + (double)b;
            PyFPE_END_PROTECT(result)
            return PyFloat_FromDouble(result);
    }
    return (inplace ? PyNumber_InPlaceAdd : PyNumber_Add)(op1, op2);
}
#endif

#if CYTHON_COMPILING_IN_CPYTHON
static PyObject* __Pyx_PyInt_RemainderObjC(PyObject *op1, PyObject *op2, CYTHON_UNUSED long intval, CYTHON_UNUSED int inplace) {
    #if PY_MAJOR_VERSION < 3
    if (likely(PyInt_CheckExact(op1))) {
        const long b = intval;
        long x;
        long a = PyInt_AS_LONG(op1);
            x = a % b;
            x += ((x != 0) & ((x ^ b) < 0)) * b;
            return PyInt_FromLong(x);
    }
    #endif
    #if CYTHON_USE_PYLONG_INTERNALS && PY_MAJOR_VERSION >= 3
    if (likely(PyLong_CheckExact(op1))) {
        const long b = intval;
        long a, x;
        const PY_LONG_LONG llb = intval;
        PY_LONG_LONG lla, llx;
        const digit* digits = ((PyLongObject*)op1)->ob_digit;
        const Py_ssize_t size = Py_SIZE(op1);
        if (likely(__Pyx_sst_abs(size) <= 1)) {
            a = likely(size) ? digits[0] : 0;
            if (size == -1) a = -a;
        } else {
            switch (size) {
                case -2:
                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                        a = -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
                        lla = -(PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
                    }
                case 2:
                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                        a = (long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
                        lla = (PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
                    }
                case -3:
                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                        a = -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
                        lla = -(PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
                    }
                case 3:
                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                        a = (long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
                        lla = (PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
                    }
                case -4:
                    if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                        a = -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
                        lla = -(PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
                    }
                case 4:
                    if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                        a = (long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
                        lla = (PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
                    }
                default: return PyLong_Type.tp_as_number->nb_remainder(op1, op2);
            }
        }
                x = a % b;
                x += ((x != 0) & ((x ^ b) < 0)) * b;
            return PyLong_FromLong(x);
        long_long:
                llx = lla % llb;
                llx += ((llx != 0) & ((llx ^ llb) < 0)) * llb;
            return PyLong_FromLongLong(llx);
    }
    #endif
    return (inplace ? PyNumber_InPlaceRemainder : PyNumber_Remainder)(op1, op2);
}
#endif

static PyObject* __Pyx_PyDict_GetItemDefault(PyObject* d, PyObject* key, PyObject* default_value) {
    PyObject* value;
#if PY_MAJOR_VERSION >= 3 && !CYTHON_COMPILING_IN_PYPY
    value = PyDict_GetItemWithError(d, key);
    if (unlikely(!value)) {
        if (unlikely(PyErr_Occurred()))
            return NULL;
        value = default_value;
    }
    Py_INCREF(value);
#else
    if (PyString_CheckExact(key) || PyUnicode_CheckExact(key) || PyInt_CheckExact(key)) {
        value = PyDict_GetItem(d, key);
        if (unlikely(!value)) {
            value = default_value;
        }
        Py_INCREF(value);
    } else {
        if (default_value == Py_None)
            default_value = NULL;
        value = PyObject_CallMethodObjArgs(
            d, __pyx_n_s_get, key, default_value, NULL);
    }
#endif
    return value;
}

static CYTHON_INLINE PyObject *__Pyx_GetAttr(PyObject *o, PyObject *n) {
#if CYTHON_COMPILING_IN_CPYTHON
#if PY_MAJOR_VERSION >= 3
    if (likely(PyUnicode_Check(n)))
#else
    if (likely(PyString_Check(n)))
#endif
        return __Pyx_PyObject_GetAttrStr(o, n);
#endif
    return PyObject_GetAttr(o, n);
}

static CYTHON_INLINE PyObject *__Pyx_GetAttr3(PyObject *o, PyObject *n, PyObject *d) {
    PyObject *r = __Pyx_GetAttr(o, n);
    if (unlikely(!r)) {
        if (!PyErr_ExceptionMatches(PyExc_AttributeError))
            goto bad;
        PyErr_Clear();
        r = d;
        Py_INCREF(d);
    }
    return r;
bad:
    return NULL;
}

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

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

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 PyObject *__Pyx_CalculateMetaclass(PyTypeObject *metaclass, PyObject *bases) {
    Py_ssize_t i, nbases = PyTuple_GET_SIZE(bases);
    for (i=0; i < nbases; i++) {
        PyTypeObject *tmptype;
        PyObject *tmp = PyTuple_GET_ITEM(bases, i);
        tmptype = Py_TYPE(tmp);
#if PY_MAJOR_VERSION < 3
        if (tmptype == &PyClass_Type)
            continue;
#endif
        if (!metaclass) {
            metaclass = tmptype;
            continue;
        }
        if (PyType_IsSubtype(metaclass, tmptype))
            continue;
        if (PyType_IsSubtype(tmptype, metaclass)) {
            metaclass = tmptype;
            continue;
        }
        PyErr_SetString(PyExc_TypeError,
                        "metaclass conflict: "
                        "the metaclass of a derived class "
                        "must be a (non-strict) subclass "
                        "of the metaclasses of all its bases");
        return NULL;
    }
    if (!metaclass) {
#if PY_MAJOR_VERSION < 3
        metaclass = &PyClass_Type;
#else
        metaclass = &PyType_Type;
#endif
    }
    Py_INCREF((PyObject*) metaclass);
    return (PyObject*) metaclass;
}

static PyObject *__Pyx_Py3MetaclassPrepare(PyObject *metaclass, PyObject *bases, PyObject *name,
                                           PyObject *qualname, PyObject *mkw, PyObject *modname, PyObject *doc) {
    PyObject *ns;
    if (metaclass) {
        PyObject *prep = __Pyx_PyObject_GetAttrStr(metaclass, __pyx_n_s_prepare);
        if (prep) {
            PyObject *pargs = PyTuple_Pack(2, name, bases);
            if (unlikely(!pargs)) {
                Py_DECREF(prep);
                return NULL;
            }
            ns = PyObject_Call(prep, pargs, mkw);
            Py_DECREF(prep);
            Py_DECREF(pargs);
        } else {
            if (unlikely(!PyErr_ExceptionMatches(PyExc_AttributeError)))
                return NULL;
            PyErr_Clear();
            ns = PyDict_New();
        }
    } else {
        ns = PyDict_New();
    }
    if (unlikely(!ns))
        return NULL;
    if (unlikely(PyObject_SetItem(ns, __pyx_n_s_module, modname) < 0)) goto bad;
    if (unlikely(PyObject_SetItem(ns, __pyx_n_s_qualname, qualname) < 0)) goto bad;
    if (unlikely(doc && PyObject_SetItem(ns, __pyx_n_s_doc, doc) < 0)) goto bad;
    return ns;
bad:
    Py_DECREF(ns);
    return NULL;
}
static PyObject *__Pyx_Py3ClassCreate(PyObject *metaclass, PyObject *name, PyObject *bases,
                                      PyObject *dict, PyObject *mkw,
                                      int calculate_metaclass, int allow_py2_metaclass) {
    PyObject *result, *margs;
    PyObject *owned_metaclass = NULL;
    if (allow_py2_metaclass) {
        owned_metaclass = PyObject_GetItem(dict, __pyx_n_s_metaclass);
        if (owned_metaclass) {
            metaclass = owned_metaclass;
        } else if (likely(PyErr_ExceptionMatches(PyExc_KeyError))) {
            PyErr_Clear();
        } else {
            return NULL;
        }
    }
    if (calculate_metaclass && (!metaclass || PyType_Check(metaclass))) {
        metaclass = __Pyx_CalculateMetaclass((PyTypeObject*) metaclass, bases);
        Py_XDECREF(owned_metaclass);
        if (unlikely(!metaclass))
            return NULL;
        owned_metaclass = metaclass;
    }
    margs = PyTuple_Pack(3, name, bases, dict);
    if (unlikely(!margs)) {
        result = NULL;
    } else {
        result = PyObject_Call(metaclass, margs, mkw);
        Py_DECREF(margs);
    }
    Py_XDECREF(owned_metaclass);
    return result;
}

static PyObject *__Pyx_GetNameInClass(PyObject *nmspace, PyObject *name) {
    PyObject *result;
    result = __Pyx_PyObject_GetAttrStr(nmspace, name);
    if (!result)
        result = __Pyx_GetModuleGlobalName(name);
    return result;
}

static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line) {
    int start = 0, mid = 0, end = count - 1;
    if (end >= 0 && code_line > entries[end].code_line) {
        return count;
    }
    while (start < end) {
        mid = start + (end - start) / 2;
        if (code_line < entries[mid].code_line) {
            end = mid;
        } else if (code_line > entries[mid].code_line) {
             start = mid + 1;
        } else {
            return mid;
        }
    }
    if (code_line <= entries[mid].code_line) {
        return mid;
    } else {
        return mid + 1;
    }
}
static 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 CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) {
    const long neg_one = (long) -1, const_zero = (long) 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 PY_LONG_LONG)) {
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
        }
    } else {
        if (sizeof(long) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
            return PyLong_FromLongLong((PY_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);
    }
}

#define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)\
    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 0)
#define __PYX_VERIFY_RETURN_INT_EXC(target_type, func_type, func_value)\
    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 1)
#define __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, exc)\
    {\
        func_type value = func_value;\
        if (sizeof(target_type) < sizeof(func_type)) {\
            if (unlikely(value != (func_type) (target_type) value)) {\
                func_type zero = 0;\
                if (exc && unlikely(value == (func_type)-1 && PyErr_Occurred()))\
                    return (target_type) -1;\
                if (is_unsigned && unlikely(value < zero))\
                    goto raise_neg_overflow;\
                else\
                    goto raise_overflow;\
            }\
        }\
        return (target_type) value;\
    }

static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) {
    const int neg_one = (int) -1, const_zero = (int) 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_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (int) 0;
                case  1: __PYX_VERIFY_RETURN_INT(int, digit, digits[0])
                case 2:
                    if (8 * sizeof(int) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) >= 2 * PyLong_SHIFT) {
                            return (int) (((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(int) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) >= 3 * PyLong_SHIFT) {
                            return (int) (((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(int) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) >= 4 * PyLong_SHIFT) {
                            return (int) (((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
                        }
                    }
                    break;
            }
#endif
#if CYTHON_COMPILING_IN_CPYTHON
            if (unlikely(Py_SIZE(x) < 0)) {
                goto raise_neg_overflow;
            }
#else
            {
                int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
                if (unlikely(result < 0))
                    return (int) -1;
                if (unlikely(result == 1))
                    goto raise_neg_overflow;
            }
#endif
            if (sizeof(int) <= sizeof(unsigned long)) {
                __PYX_VERIFY_RETURN_INT_EXC(int, unsigned long, PyLong_AsUnsignedLong(x))
            } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
            }
        } else {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (int) 0;
                case -1: __PYX_VERIFY_RETURN_INT(int, sdigit, -(sdigit) digits[0])
                case  1: __PYX_VERIFY_RETURN_INT(int,  digit, +digits[0])
                case -2:
                    if (8 * sizeof(int) - 1 > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
                            return (int) (((int)-1)*(((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case 2:
                    if (8 * sizeof(int) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
                            return (int) ((((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case -3:
                    if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
                            return (int) (((int)-1)*(((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(int) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
                            return (int) ((((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case -4:
                    if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) {
                            return (int) (((int)-1)*(((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(int) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) {
                            return (int) ((((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
            }
#endif
            if (sizeof(int) <= sizeof(long)) {
                __PYX_VERIFY_RETURN_INT_EXC(int, long, PyLong_AsLong(x))
            } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(int, PY_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 npy_int64 __Pyx_PyInt_As_npy_int64(PyObject *x) {
    const npy_int64 neg_one = (npy_int64) -1, const_zero = (npy_int64) 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_MAJOR_VERSION < 3
    if (likely(PyInt_Check(x))) {
        if (sizeof(npy_int64) < sizeof(long)) {
            __PYX_VERIFY_RETURN_INT(npy_int64, long, PyInt_AS_LONG(x))
        } else {
            long val = PyInt_AS_LONG(x);
            if (is_unsigned && unlikely(val < 0)) {
                goto raise_neg_overflow;
            }
            return (npy_int64) val;
        }
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (npy_int64) 0;
                case  1: __PYX_VERIFY_RETURN_INT(npy_int64, digit, digits[0])
                case 2:
                    if (8 * sizeof(npy_int64) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(npy_int64, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(npy_int64) >= 2 * PyLong_SHIFT) {
                            return (npy_int64) (((((npy_int64)digits[1]) << PyLong_SHIFT) | (npy_int64)digits[0]));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(npy_int64) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(npy_int64, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(npy_int64) >= 3 * PyLong_SHIFT) {
                            return (npy_int64) (((((((npy_int64)digits[2]) << PyLong_SHIFT) | (npy_int64)digits[1]) << PyLong_SHIFT) | (npy_int64)digits[0]));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(npy_int64) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(npy_int64, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(npy_int64) >= 4 * PyLong_SHIFT) {
                            return (npy_int64) (((((((((npy_int64)digits[3]) << PyLong_SHIFT) | (npy_int64)digits[2]) << PyLong_SHIFT) | (npy_int64)digits[1]) << PyLong_SHIFT) | (npy_int64)digits[0]));
                        }
                    }
                    break;
            }
#endif
#if CYTHON_COMPILING_IN_CPYTHON
            if (unlikely(Py_SIZE(x) < 0)) {
                goto raise_neg_overflow;
            }
#else
            {
                int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
                if (unlikely(result < 0))
                    return (npy_int64) -1;
                if (unlikely(result == 1))
                    goto raise_neg_overflow;
            }
#endif
            if (sizeof(npy_int64) <= sizeof(unsigned long)) {
                __PYX_VERIFY_RETURN_INT_EXC(npy_int64, unsigned long, PyLong_AsUnsignedLong(x))
            } else if (sizeof(npy_int64) <= sizeof(unsigned PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(npy_int64, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
            }
        } else {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (npy_int64) 0;
                case -1: __PYX_VERIFY_RETURN_INT(npy_int64, sdigit, -(sdigit) digits[0])
                case  1: __PYX_VERIFY_RETURN_INT(npy_int64,  digit, +digits[0])
                case -2:
                    if (8 * sizeof(npy_int64) - 1 > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(npy_int64, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(npy_int64) - 1 > 2 * PyLong_SHIFT) {
                            return (npy_int64) (((npy_int64)-1)*(((((npy_int64)digits[1]) << PyLong_SHIFT) | (npy_int64)digits[0])));
                        }
                    }
                    break;
                case 2:
                    if (8 * sizeof(npy_int64) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(npy_int64, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(npy_int64) - 1 > 2 * PyLong_SHIFT) {
                            return (npy_int64) ((((((npy_int64)digits[1]) << PyLong_SHIFT) | (npy_int64)digits[0])));
                        }
                    }
                    break;
                case -3:
                    if (8 * sizeof(npy_int64) - 1 > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(npy_int64, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(npy_int64) - 1 > 3 * PyLong_SHIFT) {
                            return (npy_int64) (((npy_int64)-1)*(((((((npy_int64)digits[2]) << PyLong_SHIFT) | (npy_int64)digits[1]) << PyLong_SHIFT) | (npy_int64)digits[0])));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(npy_int64) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(npy_int64, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(npy_int64) - 1 > 3 * PyLong_SHIFT) {
                            return (npy_int64) ((((((((npy_int64)digits[2]) << PyLong_SHIFT) | (npy_int64)digits[1]) << PyLong_SHIFT) | (npy_int64)digits[0])));
                        }
                    }
                    break;
                case -4:
                    if (8 * sizeof(npy_int64) - 1 > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(npy_int64, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(npy_int64) - 1 > 4 * PyLong_SHIFT) {
                            return (npy_int64) (((npy_int64)-1)*(((((((((npy_int64)digits[3]) << PyLong_SHIFT) | (npy_int64)digits[2]) << PyLong_SHIFT) | (npy_int64)digits[1]) << PyLong_SHIFT) | (npy_int64)digits[0])));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(npy_int64) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(npy_int64, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(npy_int64) - 1 > 4 * PyLong_SHIFT) {
                            return (npy_int64) ((((((((((npy_int64)digits[3]) << PyLong_SHIFT) | (npy_int64)digits[2]) << PyLong_SHIFT) | (npy_int64)digits[1]) << PyLong_SHIFT) | (npy_int64)digits[0])));
                        }
                    }
                    break;
            }
#endif
            if (sizeof(npy_int64) <= sizeof(long)) {
                __PYX_VERIFY_RETURN_INT_EXC(npy_int64, long, PyLong_AsLong(x))
            } else if (sizeof(npy_int64) <= sizeof(PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(npy_int64, PY_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
            npy_int64 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 (npy_int64) -1;
        }
    } else {
        npy_int64 val;
        PyObject *tmp = __Pyx_PyNumber_Int(x);
        if (!tmp) return (npy_int64) -1;
        val = __Pyx_PyInt_As_npy_int64(tmp);
        Py_DECREF(tmp);
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to npy_int64");
    return (npy_int64) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to npy_int64");
    return (npy_int64) -1;
}

static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value) {
    const int neg_one = (int) -1, const_zero = (int) 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 PY_LONG_LONG)) {
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
        }
    } else {
        if (sizeof(int) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
            return PyLong_FromLongLong((PY_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_npy_int64(npy_int64 value) {
    const npy_int64 neg_one = (npy_int64) -1, const_zero = (npy_int64) 0;
    const int is_unsigned = neg_one > const_zero;
    if (is_unsigned) {
        if (sizeof(npy_int64) < sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(npy_int64) <= sizeof(unsigned long)) {
            return PyLong_FromUnsignedLong((unsigned long) value);
        } else if (sizeof(npy_int64) <= sizeof(unsigned PY_LONG_LONG)) {
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
        }
    } else {
        if (sizeof(npy_int64) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(npy_int64) <= sizeof(PY_LONG_LONG)) {
            return PyLong_FromLongLong((PY_LONG_LONG) value);
        }
    }
    {
        int one = 1; int little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&value;
        return _PyLong_FromByteArray(bytes, sizeof(npy_int64),
                                     little, !is_unsigned);
    }
}

static CYTHON_INLINE npy_int32 __Pyx_PyInt_As_npy_int32(PyObject *x) {
    const npy_int32 neg_one = (npy_int32) -1, const_zero = (npy_int32) 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_MAJOR_VERSION < 3
    if (likely(PyInt_Check(x))) {
        if (sizeof(npy_int32) < sizeof(long)) {
            __PYX_VERIFY_RETURN_INT(npy_int32, long, PyInt_AS_LONG(x))
        } else {
            long val = PyInt_AS_LONG(x);
            if (is_unsigned && unlikely(val < 0)) {
                goto raise_neg_overflow;
            }
            return (npy_int32) val;
        }
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (npy_int32) 0;
                case  1: __PYX_VERIFY_RETURN_INT(npy_int32, digit, digits[0])
                case 2:
                    if (8 * sizeof(npy_int32) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(npy_int32, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(npy_int32) >= 2 * PyLong_SHIFT) {
                            return (npy_int32) (((((npy_int32)digits[1]) << PyLong_SHIFT) | (npy_int32)digits[0]));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(npy_int32) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(npy_int32, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(npy_int32) >= 3 * PyLong_SHIFT) {
                            return (npy_int32) (((((((npy_int32)digits[2]) << PyLong_SHIFT) | (npy_int32)digits[1]) << PyLong_SHIFT) | (npy_int32)digits[0]));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(npy_int32) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(npy_int32, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(npy_int32) >= 4 * PyLong_SHIFT) {
                            return (npy_int32) (((((((((npy_int32)digits[3]) << PyLong_SHIFT) | (npy_int32)digits[2]) << PyLong_SHIFT) | (npy_int32)digits[1]) << PyLong_SHIFT) | (npy_int32)digits[0]));
                        }
                    }
                    break;
            }
#endif
#if CYTHON_COMPILING_IN_CPYTHON
            if (unlikely(Py_SIZE(x) < 0)) {
                goto raise_neg_overflow;
            }
#else
            {
                int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
                if (unlikely(result < 0))
                    return (npy_int32) -1;
                if (unlikely(result == 1))
                    goto raise_neg_overflow;
            }
#endif
            if (sizeof(npy_int32) <= sizeof(unsigned long)) {
                __PYX_VERIFY_RETURN_INT_EXC(npy_int32, unsigned long, PyLong_AsUnsignedLong(x))
            } else if (sizeof(npy_int32) <= sizeof(unsigned PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(npy_int32, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
            }
        } else {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (npy_int32) 0;
                case -1: __PYX_VERIFY_RETURN_INT(npy_int32, sdigit, -(sdigit) digits[0])
                case  1: __PYX_VERIFY_RETURN_INT(npy_int32,  digit, +digits[0])
                case -2:
                    if (8 * sizeof(npy_int32) - 1 > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(npy_int32, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(npy_int32) - 1 > 2 * PyLong_SHIFT) {
                            return (npy_int32) (((npy_int32)-1)*(((((npy_int32)digits[1]) << PyLong_SHIFT) | (npy_int32)digits[0])));
                        }
                    }
                    break;
                case 2:
                    if (8 * sizeof(npy_int32) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(npy_int32, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(npy_int32) - 1 > 2 * PyLong_SHIFT) {
                            return (npy_int32) ((((((npy_int32)digits[1]) << PyLong_SHIFT) | (npy_int32)digits[0])));
                        }
                    }
                    break;
                case -3:
                    if (8 * sizeof(npy_int32) - 1 > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(npy_int32, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(npy_int32) - 1 > 3 * PyLong_SHIFT) {
                            return (npy_int32) (((npy_int32)-1)*(((((((npy_int32)digits[2]) << PyLong_SHIFT) | (npy_int32)digits[1]) << PyLong_SHIFT) | (npy_int32)digits[0])));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(npy_int32) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(npy_int32, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(npy_int32) - 1 > 3 * PyLong_SHIFT) {
                            return (npy_int32) ((((((((npy_int32)digits[2]) << PyLong_SHIFT) | (npy_int32)digits[1]) << PyLong_SHIFT) | (npy_int32)digits[0])));
                        }
                    }
                    break;
                case -4:
                    if (8 * sizeof(npy_int32) - 1 > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(npy_int32, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(npy_int32) - 1 > 4 * PyLong_SHIFT) {
                            return (npy_int32) (((npy_int32)-1)*(((((((((npy_int32)digits[3]) << PyLong_SHIFT) | (npy_int32)digits[2]) << PyLong_SHIFT) | (npy_int32)digits[1]) << PyLong_SHIFT) | (npy_int32)digits[0])));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(npy_int32) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(npy_int32, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(npy_int32) - 1 > 4 * PyLong_SHIFT) {
                            return (npy_int32) ((((((((((npy_int32)digits[3]) << PyLong_SHIFT) | (npy_int32)digits[2]) << PyLong_SHIFT) | (npy_int32)digits[1]) << PyLong_SHIFT) | (npy_int32)digits[0])));
                        }
                    }
                    break;
            }
#endif
            if (sizeof(npy_int32) <= sizeof(long)) {
                __PYX_VERIFY_RETURN_INT_EXC(npy_int32, long, PyLong_AsLong(x))
            } else if (sizeof(npy_int32) <= sizeof(PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(npy_int32, PY_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
            npy_int32 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 (npy_int32) -1;
        }
    } else {
        npy_int32 val;
        PyObject *tmp = __Pyx_PyNumber_Int(x);
        if (!tmp) return (npy_int32) -1;
        val = __Pyx_PyInt_As_npy_int32(tmp);
        Py_DECREF(tmp);
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to npy_int32");
    return (npy_int32) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to npy_int32");
    return (npy_int32) -1;
}

static CYTHON_INLINE PyObject* __Pyx_PyInt_From_npy_int32(npy_int32 value) {
    const npy_int32 neg_one = (npy_int32) -1, const_zero = (npy_int32) 0;
    const int is_unsigned = neg_one > const_zero;
    if (is_unsigned) {
        if (sizeof(npy_int32) < sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(npy_int32) <= sizeof(unsigned long)) {
            return PyLong_FromUnsignedLong((unsigned long) value);
        } else if (sizeof(npy_int32) <= sizeof(unsigned PY_LONG_LONG)) {
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
        }
    } else {
        if (sizeof(npy_int32) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(npy_int32) <= sizeof(PY_LONG_LONG)) {
            return PyLong_FromLongLong((PY_LONG_LONG) value);
        }
    }
    {
        int one = 1; int little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&value;
        return _PyLong_FromByteArray(bytes, sizeof(npy_int32),
                                     little, !is_unsigned);
    }
}

static PyObject* __Pyx_Method_ClassMethod(PyObject *method) {
#if CYTHON_COMPILING_IN_PYPY
    if (PyObject_TypeCheck(method, &PyWrapperDescr_Type)) {
        return PyClassMethod_New(method);
    }
#else
    static PyTypeObject *methoddescr_type = NULL;
    if (methoddescr_type == NULL) {
       PyObject *meth = PyObject_GetAttrString((PyObject*)&PyList_Type, "append");
       if (!meth) return NULL;
       methoddescr_type = Py_TYPE(meth);
       Py_DECREF(meth);
    }
    if (PyObject_TypeCheck(method, methoddescr_type)) {
        PyMethodDescrObject *descr = (PyMethodDescrObject *)method;
        #if PY_VERSION_HEX < 0x03020000
        PyTypeObject *d_type = descr->d_type;
        #else
        PyTypeObject *d_type = descr->d_common.d_type;
        #endif
        return PyDescr_NewClassMethod(d_type, descr->d_method);
    }
#endif
    else if (PyMethod_Check(method)) {
        return PyClassMethod_New(PyMethod_GET_FUNCTION(method));
    }
    else if (PyCFunction_Check(method)) {
        return PyClassMethod_New(method);
    }
#ifdef __Pyx_CyFunction_USED
    else if (PyObject_TypeCheck(method, __pyx_CyFunctionType)) {
        return PyClassMethod_New(method);
    }
#endif
    PyErr_SetString(PyExc_TypeError,
                   "Class-level classmethod() can only be called on "
                   "a method_descriptor or instance method.");
    return NULL;
}

#if CYTHON_CCOMPLEX
  #ifdef __cplusplus
    static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
      return ::std::complex< float >(x, y);
    }
  #else
    static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
      return x + y*(__pyx_t_float_complex)_Complex_I;
    }
  #endif
#else
    static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
      __pyx_t_float_complex z;
      z.real = x;
      z.imag = y;
      return z;
    }
#endif

#if CYTHON_CCOMPLEX
#else
    static CYTHON_INLINE int __Pyx_c_eqf(__pyx_t_float_complex a, __pyx_t_float_complex b) {
       return (a.real == b.real) && (a.imag == b.imag);
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sumf(__pyx_t_float_complex a, __pyx_t_float_complex b) {
        __pyx_t_float_complex z;
        z.real = a.real + b.real;
        z.imag = a.imag + b.imag;
        return z;
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_difff(__pyx_t_float_complex a, __pyx_t_float_complex b) {
        __pyx_t_float_complex z;
        z.real = a.real - b.real;
        z.imag = a.imag - b.imag;
        return z;
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prodf(__pyx_t_float_complex a, __pyx_t_float_complex b) {
        __pyx_t_float_complex z;
        z.real = a.real * b.real - a.imag * b.imag;
        z.imag = a.real * b.imag + a.imag * b.real;
        return z;
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quotf(__pyx_t_float_complex a, __pyx_t_float_complex b) {
        __pyx_t_float_complex z;
        float denom = b.real * b.real + b.imag * b.imag;
        z.real = (a.real * b.real + a.imag * b.imag) / denom;
        z.imag = (a.imag * b.real - a.real * b.imag) / denom;
        return z;
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_negf(__pyx_t_float_complex a) {
        __pyx_t_float_complex z;
        z.real = -a.real;
        z.imag = -a.imag;
        return z;
    }
    static CYTHON_INLINE int __Pyx_c_is_zerof(__pyx_t_float_complex a) {
       return (a.real == 0) && (a.imag == 0);
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conjf(__pyx_t_float_complex a) {
        __pyx_t_float_complex z;
        z.real =  a.real;
        z.imag = -a.imag;
        return z;
    }
    #if 1
        static CYTHON_INLINE float __Pyx_c_absf(__pyx_t_float_complex z) {
          #if !defined(HAVE_HYPOT) || defined(_MSC_VER)
            return sqrtf(z.real*z.real + z.imag*z.imag);
          #else
            return hypotf(z.real, z.imag);
          #endif
        }
        static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_powf(__pyx_t_float_complex a, __pyx_t_float_complex b) {
            __pyx_t_float_complex z;
            float r, lnr, theta, z_r, z_theta;
            if (b.imag == 0 && b.real == (int)b.real) {
                if (b.real < 0) {
                    float denom = a.real * a.real + a.imag * a.imag;
                    a.real = a.real / denom;
                    a.imag = -a.imag / denom;
                    b.real = -b.real;
                }
                switch ((int)b.real) {
                    case 0:
                        z.real = 1;
                        z.imag = 0;
                        return z;
                    case 1:
                        return a;
                    case 2:
                        z = __Pyx_c_prodf(a, a);
                        return __Pyx_c_prodf(a, a);
                    case 3:
                        z = __Pyx_c_prodf(a, a);
                        return __Pyx_c_prodf(z, a);
                    case 4:
                        z = __Pyx_c_prodf(a, a);
                        return __Pyx_c_prodf(z, z);
                }
            }
            if (a.imag == 0) {
                if (a.real == 0) {
                    return a;
                }
                r = a.real;
                theta = 0;
            } else {
                r = __Pyx_c_absf(a);
                theta = atan2f(a.imag, a.real);
            }
            lnr = logf(r);
            z_r = expf(lnr * b.real - theta * b.imag);
            z_theta = theta * b.real + lnr * b.imag;
            z.real = z_r * cosf(z_theta);
            z.imag = z_r * sinf(z_theta);
            return z;
        }
    #endif
#endif

#if CYTHON_CCOMPLEX
  #ifdef __cplusplus
    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
      return ::std::complex< double >(x, y);
    }
  #else
    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
      return x + y*(__pyx_t_double_complex)_Complex_I;
    }
  #endif
#else
    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
      __pyx_t_double_complex z;
      z.real = x;
      z.imag = y;
      return z;
    }
#endif

#if CYTHON_CCOMPLEX
#else
    static CYTHON_INLINE int __Pyx_c_eq(__pyx_t_double_complex a, __pyx_t_double_complex b) {
       return (a.real == b.real) && (a.imag == b.imag);
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        __pyx_t_double_complex z;
        z.real = a.real + b.real;
        z.imag = a.imag + b.imag;
        return z;
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        __pyx_t_double_complex z;
        z.real = a.real - b.real;
        z.imag = a.imag - b.imag;
        return z;
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        __pyx_t_double_complex z;
        z.real = a.real * b.real - a.imag * b.imag;
        z.imag = a.real * b.imag + a.imag * b.real;
        return z;
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        __pyx_t_double_complex z;
        double denom = b.real * b.real + b.imag * b.imag;
        z.real = (a.real * b.real + a.imag * b.imag) / denom;
        z.imag = (a.imag * b.real - a.real * b.imag) / denom;
        return z;
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg(__pyx_t_double_complex a) {
        __pyx_t_double_complex z;
        z.real = -a.real;
        z.imag = -a.imag;
        return z;
    }
    static CYTHON_INLINE int __Pyx_c_is_zero(__pyx_t_double_complex a) {
       return (a.real == 0) && (a.imag == 0);
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj(__pyx_t_double_complex a) {
        __pyx_t_double_complex z;
        z.real =  a.real;
        z.imag = -a.imag;
        return z;
    }
    #if 1
        static CYTHON_INLINE double __Pyx_c_abs(__pyx_t_double_complex z) {
          #if !defined(HAVE_HYPOT) || defined(_MSC_VER)
            return sqrt(z.real*z.real + z.imag*z.imag);
          #else
            return hypot(z.real, z.imag);
          #endif
        }
        static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow(__pyx_t_double_complex a, __pyx_t_double_complex b) {
            __pyx_t_double_complex z;
            double r, lnr, theta, z_r, z_theta;
            if (b.imag == 0 && b.real == (int)b.real) {
                if (b.real < 0) {
                    double denom = a.real * a.real + a.imag * a.imag;
                    a.real = a.real / denom;
                    a.imag = -a.imag / denom;
                    b.real = -b.real;
                }
                switch ((int)b.real) {
                    case 0:
                        z.real = 1;
                        z.imag = 0;
                        return z;
                    case 1:
                        return a;
                    case 2:
                        z = __Pyx_c_prod(a, a);
                        return __Pyx_c_prod(a, a);
                    case 3:
                        z = __Pyx_c_prod(a, a);
                        return __Pyx_c_prod(z, a);
                    case 4:
                        z = __Pyx_c_prod(a, a);
                        return __Pyx_c_prod(z, z);
                }
            }
            if (a.imag == 0) {
                if (a.real == 0) {
                    return a;
                }
                r = a.real;
                theta = 0;
            } else {
                r = __Pyx_c_abs(a);
                theta = atan2(a.imag, a.real);
            }
            lnr = log(r);
            z_r = exp(lnr * b.real - theta * b.imag);
            z_theta = theta * b.real + lnr * b.imag;
            z.real = z_r * cos(z_theta);
            z.imag = z_r * sin(z_theta);
            return z;
        }
    #endif
#endif

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

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

static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *x) {
    const long neg_one = (long) -1, const_zero = (long) 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_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (long) 0;
                case  1: __PYX_VERIFY_RETURN_INT(long, digit, digits[0])
                case 2:
                    if (8 * sizeof(long) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) >= 2 * PyLong_SHIFT) {
                            return (long) (((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(long) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) >= 3 * PyLong_SHIFT) {
                            return (long) (((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(long) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) >= 4 * PyLong_SHIFT) {
                            return (long) (((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
                        }
                    }
                    break;
            }
#endif
#if CYTHON_COMPILING_IN_CPYTHON
            if (unlikely(Py_SIZE(x) < 0)) {
                goto raise_neg_overflow;
            }
#else
            {
                int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
                if (unlikely(result < 0))
                    return (long) -1;
                if (unlikely(result == 1))
                    goto raise_neg_overflow;
            }
#endif
            if (sizeof(long) <= sizeof(unsigned long)) {
                __PYX_VERIFY_RETURN_INT_EXC(long, unsigned long, PyLong_AsUnsignedLong(x))
            } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(long, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
            }
        } else {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (long) 0;
                case -1: __PYX_VERIFY_RETURN_INT(long, sdigit, -(sdigit) digits[0])
                case  1: __PYX_VERIFY_RETURN_INT(long,  digit, +digits[0])
                case -2:
                    if (8 * sizeof(long) - 1 > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                            return (long) (((long)-1)*(((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case 2:
                    if (8 * sizeof(long) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                            return (long) ((((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case -3:
                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                            return (long) (((long)-1)*(((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(long) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                            return (long) ((((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case -4:
                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                            return (long) (((long)-1)*(((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(long) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                            return (long) ((((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
            }
#endif
            if (sizeof(long) <= sizeof(long)) {
                __PYX_VERIFY_RETURN_INT_EXC(long, long, PyLong_AsLong(x))
            } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(long, PY_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

#ifndef __PYX_HAVE_RT_ImportVoidPtr
#define __PYX_HAVE_RT_ImportVoidPtr
static int __Pyx_ImportVoidPtr(PyObject *module, const char *name, void **p, const char *sig) {
    PyObject *d = 0;
    PyObject *cobj = 0;
    d = PyObject_GetAttrString(module, (char *)"__pyx_capi__");
    if (!d)
        goto bad;
    cobj = PyDict_GetItemString(d, name);
    if (!cobj) {
        PyErr_Format(PyExc_ImportError,
            "%.200s does not export expected C variable %.200s",
                PyModule_GetName(module), name);
        goto bad;
    }
#if PY_VERSION_HEX >= 0x02070000
    if (!PyCapsule_IsValid(cobj, sig)) {
        PyErr_Format(PyExc_TypeError,
            "C variable %.200s.%.200s has wrong signature (expected %.500s, got %.500s)",
             PyModule_GetName(module), name, sig, PyCapsule_GetName(cobj));
        goto bad;
    }
    *p = PyCapsule_GetPointer(cobj, sig);
#else
    {const char *desc, *s1, *s2;
    desc = (const char *)PyCObject_GetDesc(cobj);
    if (!desc)
        goto bad;
    s1 = desc; s2 = sig;
    while (*s1 != '\0' && *s1 == *s2) { s1++; s2++; }
    if (*s1 != *s2) {
        PyErr_Format(PyExc_TypeError,
            "C variable %.200s.%.200s has wrong signature (expected %.500s, got %.500s)",
             PyModule_GetName(module), name, sig, desc);
        goto bad;
    }
    *p = PyCObject_AsVoidPtr(cobj);}
#endif
    if (!(*p))
        goto bad;
    Py_DECREF(d);
    return 0;
bad:
    Py_XDECREF(d);
    return -1;
}
#endif

#ifndef __PYX_HAVE_RT_ImportFunction
#define __PYX_HAVE_RT_ImportFunction
static int __Pyx_ImportFunction(PyObject *module, const char *funcname, void (**f)(void), const char *sig) {
    PyObject *d = 0;
    PyObject *cobj = 0;
    union {
        void (*fp)(void);
        void *p;
    } tmp;
    d = PyObject_GetAttrString(module, (char *)"__pyx_capi__");
    if (!d)
        goto bad;
    cobj = PyDict_GetItemString(d, funcname);
    if (!cobj) {
        PyErr_Format(PyExc_ImportError,
            "%.200s does not export expected C function %.200s",
                PyModule_GetName(module), funcname);
        goto bad;
    }
#if PY_VERSION_HEX >= 0x02070000
    if (!PyCapsule_IsValid(cobj, sig)) {
        PyErr_Format(PyExc_TypeError,
            "C function %.200s.%.200s has wrong signature (expected %.500s, got %.500s)",
             PyModule_GetName(module), funcname, sig, PyCapsule_GetName(cobj));
        goto bad;
    }
    tmp.p = PyCapsule_GetPointer(cobj, sig);
#else
    {const char *desc, *s1, *s2;
    desc = (const char *)PyCObject_GetDesc(cobj);
    if (!desc)
        goto bad;
    s1 = desc; s2 = sig;
    while (*s1 != '\0' && *s1 == *s2) { s1++; s2++; }
    if (*s1 != *s2) {
        PyErr_Format(PyExc_TypeError,
            "C function %.200s.%.200s has wrong signature (expected %.500s, got %.500s)",
             PyModule_GetName(module), funcname, sig, desc);
        goto bad;
    }
    tmp.p = PyCObject_AsVoidPtr(cobj);}
#endif
    *f = tmp.fp;
    if (!(*f))
        goto bad;
    Py_DECREF(d);
    return 0;
bad:
    Py_XDECREF(d);
    return -1;
}
#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 CYTHON_COMPILING_IN_CPYTHON && (__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) || (defined(PyByteArray_AS_STRING) && defined(PyByteArray_GET_SIZE))
    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 __Pyx_NewRef(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))) {
    if (sizeof(Py_ssize_t) >= sizeof(long))
        return PyInt_AS_LONG(b);
    else
        return PyInt_AsSsize_t(x);
  }
#endif
  if (likely(PyLong_CheckExact(b))) {
    #if CYTHON_USE_PYLONG_INTERNALS
    const digit* digits = ((PyLongObject*)b)->ob_digit;
    const Py_ssize_t size = Py_SIZE(b);
    if (likely(__Pyx_sst_abs(size) <= 1)) {
        ival = likely(size) ? digits[0] : 0;
        if (size == -1) ival = -ival;
        return ival;
    } else {
      switch (size) {
         case 2:
           if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
             return (Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case -2:
           if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
             return -(Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case 3:
           if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
             return (Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case -3:
           if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
             return -(Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case 4:
           if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
             return (Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case -4:
           if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
             return -(Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
      }
    }
    #endif
    return PyLong_AsSsize_t(b);
  }
  x = PyNumber_Index(b);
  if (!x) return -1;
  ival = 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 */
