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/* BEGIN: Cython Metadata
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#define __PYX_HAVE__sklearn__linear_model__sgd_fast
#define __PYX_HAVE_API__sklearn__linear_model__sgd_fast
#include <math.h>
#include <string.h>
#include <stdio.h>
#include <stdlib.h>
#include "numpy/arrayobject.h"
#include "numpy/ufuncobject.h"
#include "numpy/npy_math.h"
#include "sgd_fast_helpers.h"
#include "math.h"
#ifdef _OPENMP
#include <omp.h>
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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_IntOrLong(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_ASSUME_SAFE_MACROS
#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
#define __Pyx_PyNumber_Int(x) (PyLong_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Long(x))
#else
#define __Pyx_PyNumber_Int(x) (PyInt_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Int(x))
#endif
#define __Pyx_PyNumber_Float(x) (PyFloat_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Float(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 PyObject *__pyx_empty_unicode;
static int __pyx_lineno;
static int __pyx_clineno = 0;
static const char * __pyx_cfilenm= __FILE__;
static const char *__pyx_filename;

/* Header.proto */
#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[] = {
  "sklearn/linear_model/sgd_fast.pyx",
  "__init__.pxd",
  "type.pxd",
  "sklearn/utils/weight_vector.pxd",
  "sklearn/utils/seq_dataset.pxd",
};
/* BufferFormatStructs.proto */
#define IS_UNSIGNED(type) (((type) -1) > 0)
struct __Pyx_StructField_;
#define __PYX_BUF_FLAGS_PACKED_STRUCT (1 << 0)
typedef struct {
  const char* name;
  struct __Pyx_StructField_* fields;
  size_t size;
  size_t arraysize[8];
  int ndim;
  char typegroup;
  char is_unsigned;
  int flags;
} __Pyx_TypeInfo;
typedef struct __Pyx_StructField_ {
  __Pyx_TypeInfo* type;
  const char* name;
  size_t offset;
} __Pyx_StructField;
typedef struct {
  __Pyx_StructField* field;
  size_t parent_offset;
} __Pyx_BufFmt_StackElem;
typedef struct {
  __Pyx_StructField root;
  __Pyx_BufFmt_StackElem* head;
  size_t fmt_offset;
  size_t new_count, enc_count;
  size_t struct_alignment;
  int is_complex;
  char enc_type;
  char new_packmode;
  char enc_packmode;
  char is_valid_array;
} __Pyx_BufFmt_Context;


/* "../../../../../usr/lib/python3/dist-packages/Cython/Includes/numpy/__init__.pxd":725
 * # in Cython to enable them only on the right systems.
 * 
 * ctypedef npy_int8       int8_t             # <<<<<<<<<<<<<<
 * ctypedef npy_int16      int16_t
 * ctypedef npy_int32      int32_t
 */
typedef npy_int8 __pyx_t_5numpy_int8_t;

/* "../../../../../usr/lib/python3/dist-packages/Cython/Includes/numpy/__init__.pxd":726
 * 
 * ctypedef npy_int8       int8_t
 * ctypedef npy_int16      int16_t             # <<<<<<<<<<<<<<
 * ctypedef npy_int32      int32_t
 * ctypedef npy_int64      int64_t
 */
typedef npy_int16 __pyx_t_5numpy_int16_t;

/* "../../../../../usr/lib/python3/dist-packages/Cython/Includes/numpy/__init__.pxd":727
 * ctypedef npy_int8       int8_t
 * ctypedef npy_int16      int16_t
 * ctypedef npy_int32      int32_t             # <<<<<<<<<<<<<<
 * ctypedef npy_int64      int64_t
 * #ctypedef npy_int96      int96_t
 */
typedef npy_int32 __pyx_t_5numpy_int32_t;

/* "../../../../../usr/lib/python3/dist-packages/Cython/Includes/numpy/__init__.pxd":728
 * ctypedef npy_int16      int16_t
 * ctypedef npy_int32      int32_t
 * ctypedef npy_int64      int64_t             # <<<<<<<<<<<<<<
 * #ctypedef npy_int96      int96_t
 * #ctypedef npy_int128     int128_t
 */
typedef npy_int64 __pyx_t_5numpy_int64_t;

/* "../../../../../usr/lib/python3/dist-packages/Cython/Includes/numpy/__init__.pxd":732
 * #ctypedef npy_int128     int128_t
 * 
 * ctypedef npy_uint8      uint8_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uint16     uint16_t
 * ctypedef npy_uint32     uint32_t
 */
typedef npy_uint8 __pyx_t_5numpy_uint8_t;

/* "../../../../../usr/lib/python3/dist-packages/Cython/Includes/numpy/__init__.pxd":733
 * 
 * ctypedef npy_uint8      uint8_t
 * ctypedef npy_uint16     uint16_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uint32     uint32_t
 * ctypedef npy_uint64     uint64_t
 */
typedef npy_uint16 __pyx_t_5numpy_uint16_t;

/* "../../../../../usr/lib/python3/dist-packages/Cython/Includes/numpy/__init__.pxd":734
 * 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;

/* "../../../../../usr/lib/python3/dist-packages/Cython/Includes/numpy/__init__.pxd":735
 * 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;

/* "../../../../../usr/lib/python3/dist-packages/Cython/Includes/numpy/__init__.pxd":739
 * #ctypedef npy_uint128    uint128_t
 * 
 * ctypedef npy_float32    float32_t             # <<<<<<<<<<<<<<
 * ctypedef npy_float64    float64_t
 * #ctypedef npy_float80    float80_t
 */
typedef npy_float32 __pyx_t_5numpy_float32_t;

/* "../../../../../usr/lib/python3/dist-packages/Cython/Includes/numpy/__init__.pxd":740
 * 
 * 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;

/* "../../../../../usr/lib/python3/dist-packages/Cython/Includes/numpy/__init__.pxd":749
 * # The int types are mapped a bit surprising --
 * # numpy.int corresponds to 'l' and numpy.long to 'q'
 * ctypedef npy_long       int_t             # <<<<<<<<<<<<<<
 * ctypedef npy_longlong   long_t
 * ctypedef npy_longlong   longlong_t
 */
typedef npy_long __pyx_t_5numpy_int_t;

/* "../../../../../usr/lib/python3/dist-packages/Cython/Includes/numpy/__init__.pxd":750
 * # 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;

/* "../../../../../usr/lib/python3/dist-packages/Cython/Includes/numpy/__init__.pxd":751
 * 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;

/* "../../../../../usr/lib/python3/dist-packages/Cython/Includes/numpy/__init__.pxd":753
 * 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;

/* "../../../../../usr/lib/python3/dist-packages/Cython/Includes/numpy/__init__.pxd":754
 * 
 * ctypedef npy_ulong      uint_t
 * ctypedef npy_ulonglong  ulong_t             # <<<<<<<<<<<<<<
 * ctypedef npy_ulonglong  ulonglong_t
 * 
 */
typedef npy_ulonglong __pyx_t_5numpy_ulong_t;

/* "../../../../../usr/lib/python3/dist-packages/Cython/Includes/numpy/__init__.pxd":755
 * 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;

/* "../../../../../usr/lib/python3/dist-packages/Cython/Includes/numpy/__init__.pxd":757
 * ctypedef npy_ulonglong  ulonglong_t
 * 
 * ctypedef npy_intp       intp_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uintp      uintp_t
 * 
 */
typedef npy_intp __pyx_t_5numpy_intp_t;

/* "../../../../../usr/lib/python3/dist-packages/Cython/Includes/numpy/__init__.pxd":758
 * 
 * ctypedef npy_intp       intp_t
 * ctypedef npy_uintp      uintp_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_double     float_t
 */
typedef npy_uintp __pyx_t_5numpy_uintp_t;

/* "../../../../../usr/lib/python3/dist-packages/Cython/Includes/numpy/__init__.pxd":760
 * 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;

/* "../../../../../usr/lib/python3/dist-packages/Cython/Includes/numpy/__init__.pxd":761
 * 
 * ctypedef npy_double     float_t
 * ctypedef npy_double     double_t             # <<<<<<<<<<<<<<
 * ctypedef npy_longdouble longdouble_t
 * 
 */
typedef npy_double __pyx_t_5numpy_double_t;

/* "../../../../../usr/lib/python3/dist-packages/Cython/Includes/numpy/__init__.pxd":762
 * ctypedef npy_double     float_t
 * ctypedef npy_double     double_t
 * ctypedef npy_longdouble longdouble_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_cfloat      cfloat_t
 */
typedef npy_longdouble __pyx_t_5numpy_longdouble_t;
/* Declarations.proto */
#if CYTHON_CCOMPLEX
  #ifdef __cplusplus
    typedef ::std::complex< float > __pyx_t_float_complex;
  #else
    typedef float _Complex __pyx_t_float_complex;
  #endif
#else
    typedef struct { float real, imag; } __pyx_t_float_complex;
#endif
static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float, float);

/* Declarations.proto */
#if CYTHON_CCOMPLEX
  #ifdef __cplusplus
    typedef ::std::complex< double > __pyx_t_double_complex;
  #else
    typedef double _Complex __pyx_t_double_complex;
  #endif
#else
    typedef struct { double real, imag; } __pyx_t_double_complex;
#endif
static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double, double);


/*--- Type declarations ---*/
struct __pyx_obj_7sklearn_5utils_13weight_vector_WeightVector;
struct __pyx_obj_7sklearn_5utils_11seq_dataset_SequentialDataset;
struct __pyx_obj_7sklearn_5utils_11seq_dataset_ArrayDataset;
struct __pyx_obj_7sklearn_5utils_11seq_dataset_CSRDataset;
struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_LossFunction;
struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Regression;
struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Classification;
struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Log;
struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_SquaredLoss;
struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_ModifiedHuber;
struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Hinge;
struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_SquaredHinge;
struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Huber;
struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_EpsilonInsensitive;
struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_SquaredEpsilonInsensitive;

/* "../../../../../usr/lib/python3/dist-packages/Cython/Includes/numpy/__init__.pxd":764
 * 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;

/* "../../../../../usr/lib/python3/dist-packages/Cython/Includes/numpy/__init__.pxd":765
 * 
 * ctypedef npy_cfloat      cfloat_t
 * ctypedef npy_cdouble     cdouble_t             # <<<<<<<<<<<<<<
 * ctypedef npy_clongdouble clongdouble_t
 * 
 */
typedef npy_cdouble __pyx_t_5numpy_cdouble_t;

/* "../../../../../usr/lib/python3/dist-packages/Cython/Includes/numpy/__init__.pxd":766
 * 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;

/* "../../../../../usr/lib/python3/dist-packages/Cython/Includes/numpy/__init__.pxd":768
 * ctypedef npy_clongdouble clongdouble_t
 * 
 * ctypedef npy_cdouble     complex_t             # <<<<<<<<<<<<<<
 * 
 * cdef inline object PyArray_MultiIterNew1(a):
 */
typedef npy_cdouble __pyx_t_5numpy_complex_t;

/* "sklearn/utils/weight_vector.pxd":10
 * 
 * 
 * cdef class WeightVector(object):             # <<<<<<<<<<<<<<
 *     cdef np.ndarray w
 *     cdef np.ndarray aw
 */
struct __pyx_obj_7sklearn_5utils_13weight_vector_WeightVector {
  PyObject_HEAD
  struct __pyx_vtabstruct_7sklearn_5utils_13weight_vector_WeightVector *__pyx_vtab;
  PyArrayObject *w;
  PyArrayObject *aw;
  double *w_data_ptr;
  double *aw_data_ptr;
  double wscale;
  double average_a;
  double average_b;
  int n_features;
  double sq_norm;
};


/* "sklearn/utils/seq_dataset.pxd":8
 * # iterators over the rows of a matrix X and corresponding target values y.
 * 
 * cdef class SequentialDataset:             # <<<<<<<<<<<<<<
 *     cdef int current_index
 *     cdef np.ndarray index
 */
struct __pyx_obj_7sklearn_5utils_11seq_dataset_SequentialDataset {
  PyObject_HEAD
  struct __pyx_vtabstruct_7sklearn_5utils_11seq_dataset_SequentialDataset *__pyx_vtab;
  int current_index;
  PyArrayObject *index;
  int *index_data_ptr;
  Py_ssize_t n_samples;
  __pyx_t_5numpy_uint32_t seed;
};


/* "sklearn/utils/seq_dataset.pxd":28
 * 
 * 
 * cdef class ArrayDataset(SequentialDataset):             # <<<<<<<<<<<<<<
 *     cdef np.ndarray X
 *     cdef np.ndarray Y
 */
struct __pyx_obj_7sklearn_5utils_11seq_dataset_ArrayDataset {
  struct __pyx_obj_7sklearn_5utils_11seq_dataset_SequentialDataset __pyx_base;
  PyArrayObject *X;
  PyArrayObject *Y;
  PyArrayObject *sample_weights;
  Py_ssize_t n_features;
  npy_intp X_stride;
  double *X_data_ptr;
  double *Y_data_ptr;
  PyArrayObject *feature_indices;
  int *feature_indices_ptr;
  double *sample_weight_data;
};


/* "sklearn/utils/seq_dataset.pxd":41
 * 
 * 
 * cdef class CSRDataset(SequentialDataset):             # <<<<<<<<<<<<<<
 *     cdef np.ndarray X_data
 *     cdef np.ndarray X_indptr
 */
struct __pyx_obj_7sklearn_5utils_11seq_dataset_CSRDataset {
  struct __pyx_obj_7sklearn_5utils_11seq_dataset_SequentialDataset __pyx_base;
  PyArrayObject *X_data;
  PyArrayObject *X_indptr;
  PyArrayObject *X_indices;
  PyArrayObject *Y;
  PyArrayObject *sample_weights;
  double *X_data_ptr;
  int *X_indptr_ptr;
  int *X_indices_ptr;
  double *Y_data_ptr;
  double *sample_weight_data;
};


/* "sklearn/linear_model/sgd_fast.pxd":4
 * # License: BSD 3 clause
 * 
 * cdef class LossFunction:             # <<<<<<<<<<<<<<
 *     cdef double loss(self, double p, double y) nogil
 *     cdef double _dloss(self, double p, double y) nogil
 */
struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_LossFunction {
  PyObject_HEAD
  struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_LossFunction *__pyx_vtab;
};


/* "sklearn/linear_model/sgd_fast.pxd":9
 * 
 * 
 * cdef class Regression(LossFunction):             # <<<<<<<<<<<<<<
 *     cdef double loss(self, double p, double y) nogil
 *     cdef double _dloss(self, double p, double y) nogil
 */
struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Regression {
  struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_LossFunction __pyx_base;
};


/* "sklearn/linear_model/sgd_fast.pxd":14
 * 
 * 
 * cdef class Classification(LossFunction):             # <<<<<<<<<<<<<<
 *     cdef double loss(self, double p, double y) nogil
 *     cdef double _dloss(self, double p, double y) nogil
 */
struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Classification {
  struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_LossFunction __pyx_base;
};


/* "sklearn/linear_model/sgd_fast.pxd":19
 * 
 * 
 * cdef class Log(Classification):             # <<<<<<<<<<<<<<
 *     cdef double loss(self, double p, double y) nogil
 *     cdef double _dloss(self, double p, double y) nogil
 */
struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Log {
  struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Classification __pyx_base;
};


/* "sklearn/linear_model/sgd_fast.pxd":24
 * 
 * 
 * cdef class SquaredLoss(Regression):             # <<<<<<<<<<<<<<
 *     cdef double loss(self, double p, double y) nogil
 *     cdef double _dloss(self, double p, double y) nogil
 */
struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_SquaredLoss {
  struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Regression __pyx_base;
};


/* "sklearn/linear_model/sgd_fast.pyx":110
 * 
 * 
 * cdef class ModifiedHuber(Classification):             # <<<<<<<<<<<<<<
 *     """Modified Huber loss for binary classification with y in {-1, 1}
 * 
 */
struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_ModifiedHuber {
  struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Classification __pyx_base;
};


/* "sklearn/linear_model/sgd_fast.pyx":140
 * 
 * 
 * cdef class Hinge(Classification):             # <<<<<<<<<<<<<<
 *     """Hinge loss for binary classification tasks with y in {-1,1}
 * 
 */
struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Hinge {
  struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Classification __pyx_base;
  double threshold;
};


/* "sklearn/linear_model/sgd_fast.pyx":172
 * 
 * 
 * cdef class SquaredHinge(Classification):             # <<<<<<<<<<<<<<
 *     """Squared Hinge loss for binary classification tasks with y in {-1,1}
 * 
 */
struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_SquaredHinge {
  struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Classification __pyx_base;
  double threshold;
};


/* "sklearn/linear_model/sgd_fast.pyx":241
 * 
 * 
 * cdef class Huber(Regression):             # <<<<<<<<<<<<<<
 *     """Huber regression loss
 * 
 */
struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Huber {
  struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Regression __pyx_base;
  double c;
};


/* "sklearn/linear_model/sgd_fast.pyx":277
 * 
 * 
 * cdef class EpsilonInsensitive(Regression):             # <<<<<<<<<<<<<<
 *     """Epsilon-Insensitive loss (used by SVR).
 * 
 */
struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_EpsilonInsensitive {
  struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Regression __pyx_base;
  double epsilon;
};


/* "sklearn/linear_model/sgd_fast.pyx":304
 * 
 * 
 * cdef class SquaredEpsilonInsensitive(Regression):             # <<<<<<<<<<<<<<
 *     """Epsilon-Insensitive loss.
 * 
 */
struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_SquaredEpsilonInsensitive {
  struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Regression __pyx_base;
  double epsilon;
};



/* "sklearn/utils/weight_vector.pxd":10
 * 
 * 
 * cdef class WeightVector(object):             # <<<<<<<<<<<<<<
 *     cdef np.ndarray w
 *     cdef np.ndarray aw
 */

struct __pyx_vtabstruct_7sklearn_5utils_13weight_vector_WeightVector {
  void (*add)(struct __pyx_obj_7sklearn_5utils_13weight_vector_WeightVector *, double *, int *, int, double);
  void (*add_average)(struct __pyx_obj_7sklearn_5utils_13weight_vector_WeightVector *, double *, int *, int, double, double);
  double (*dot)(struct __pyx_obj_7sklearn_5utils_13weight_vector_WeightVector *, double *, int *, int);
  void (*scale)(struct __pyx_obj_7sklearn_5utils_13weight_vector_WeightVector *, double);
  void (*reset_wscale)(struct __pyx_obj_7sklearn_5utils_13weight_vector_WeightVector *);
  double (*norm)(struct __pyx_obj_7sklearn_5utils_13weight_vector_WeightVector *);
};
static struct __pyx_vtabstruct_7sklearn_5utils_13weight_vector_WeightVector *__pyx_vtabptr_7sklearn_5utils_13weight_vector_WeightVector;


/* "sklearn/utils/seq_dataset.pxd":8
 * # iterators over the rows of a matrix X and corresponding target values y.
 * 
 * cdef class SequentialDataset:             # <<<<<<<<<<<<<<
 *     cdef int current_index
 *     cdef np.ndarray index
 */

struct __pyx_vtabstruct_7sklearn_5utils_11seq_dataset_SequentialDataset {
  void (*shuffle)(struct __pyx_obj_7sklearn_5utils_11seq_dataset_SequentialDataset *, __pyx_t_5numpy_uint32_t);
  int (*_get_next_index)(struct __pyx_obj_7sklearn_5utils_11seq_dataset_SequentialDataset *);
  int (*_get_random_index)(struct __pyx_obj_7sklearn_5utils_11seq_dataset_SequentialDataset *);
  void (*_sample)(struct __pyx_obj_7sklearn_5utils_11seq_dataset_SequentialDataset *, double **, int **, int *, double *, double *, int);
  void (*next)(struct __pyx_obj_7sklearn_5utils_11seq_dataset_SequentialDataset *, double **, int **, int *, double *, double *);
  int (*random)(struct __pyx_obj_7sklearn_5utils_11seq_dataset_SequentialDataset *, double **, int **, int *, double *, double *);
};
static struct __pyx_vtabstruct_7sklearn_5utils_11seq_dataset_SequentialDataset *__pyx_vtabptr_7sklearn_5utils_11seq_dataset_SequentialDataset;


/* "sklearn/utils/seq_dataset.pxd":28
 * 
 * 
 * cdef class ArrayDataset(SequentialDataset):             # <<<<<<<<<<<<<<
 *     cdef np.ndarray X
 *     cdef np.ndarray Y
 */

struct __pyx_vtabstruct_7sklearn_5utils_11seq_dataset_ArrayDataset {
  struct __pyx_vtabstruct_7sklearn_5utils_11seq_dataset_SequentialDataset __pyx_base;
};
static struct __pyx_vtabstruct_7sklearn_5utils_11seq_dataset_ArrayDataset *__pyx_vtabptr_7sklearn_5utils_11seq_dataset_ArrayDataset;


/* "sklearn/utils/seq_dataset.pxd":41
 * 
 * 
 * cdef class CSRDataset(SequentialDataset):             # <<<<<<<<<<<<<<
 *     cdef np.ndarray X_data
 *     cdef np.ndarray X_indptr
 */

struct __pyx_vtabstruct_7sklearn_5utils_11seq_dataset_CSRDataset {
  struct __pyx_vtabstruct_7sklearn_5utils_11seq_dataset_SequentialDataset __pyx_base;
};
static struct __pyx_vtabstruct_7sklearn_5utils_11seq_dataset_CSRDataset *__pyx_vtabptr_7sklearn_5utils_11seq_dataset_CSRDataset;


/* "sklearn/linear_model/sgd_fast.pyx":47
 * # ----------------------------------------
 * 
 * cdef class LossFunction:             # <<<<<<<<<<<<<<
 *     """Base class for convex loss functions"""
 * 
 */

struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_LossFunction {
  double (*loss)(struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_LossFunction *, double, double);
  double (*_dloss)(struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_LossFunction *, double, double);
};
static struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_LossFunction *__pyx_vtabptr_7sklearn_12linear_model_8sgd_fast_LossFunction;


/* "sklearn/linear_model/sgd_fast.pyx":90
 * 
 * 
 * cdef class Regression(LossFunction):             # <<<<<<<<<<<<<<
 *     """Base class for loss functions for regression"""
 * 
 */

struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_Regression {
  struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_LossFunction __pyx_base;
};
static struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_Regression *__pyx_vtabptr_7sklearn_12linear_model_8sgd_fast_Regression;


/* "sklearn/linear_model/sgd_fast.pyx":100
 * 
 * 
 * cdef class Classification(LossFunction):             # <<<<<<<<<<<<<<
 *     """Base class for loss functions for classification"""
 * 
 */

struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_Classification {
  struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_LossFunction __pyx_base;
};
static struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_Classification *__pyx_vtabptr_7sklearn_12linear_model_8sgd_fast_Classification;


/* "sklearn/linear_model/sgd_fast.pyx":204
 * 
 * 
 * cdef class Log(Classification):             # <<<<<<<<<<<<<<
 *     """Logistic regression loss for binary classification with y in {-1, 1}"""
 * 
 */

struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_Log {
  struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_Classification __pyx_base;
};
static struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_Log *__pyx_vtabptr_7sklearn_12linear_model_8sgd_fast_Log;


/* "sklearn/linear_model/sgd_fast.pyx":229
 * 
 * 
 * cdef class SquaredLoss(Regression):             # <<<<<<<<<<<<<<
 *     """Squared loss traditional used in linear regression."""
 *     cdef double loss(self, double p, double y) nogil:
 */

struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_SquaredLoss {
  struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_Regression __pyx_base;
};
static struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_SquaredLoss *__pyx_vtabptr_7sklearn_12linear_model_8sgd_fast_SquaredLoss;


/* "sklearn/linear_model/sgd_fast.pyx":110
 * 
 * 
 * cdef class ModifiedHuber(Classification):             # <<<<<<<<<<<<<<
 *     """Modified Huber loss for binary classification with y in {-1, 1}
 * 
 */

struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_ModifiedHuber {
  struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_Classification __pyx_base;
};
static struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_ModifiedHuber *__pyx_vtabptr_7sklearn_12linear_model_8sgd_fast_ModifiedHuber;


/* "sklearn/linear_model/sgd_fast.pyx":140
 * 
 * 
 * cdef class Hinge(Classification):             # <<<<<<<<<<<<<<
 *     """Hinge loss for binary classification tasks with y in {-1,1}
 * 
 */

struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_Hinge {
  struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_Classification __pyx_base;
};
static struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_Hinge *__pyx_vtabptr_7sklearn_12linear_model_8sgd_fast_Hinge;


/* "sklearn/linear_model/sgd_fast.pyx":172
 * 
 * 
 * cdef class SquaredHinge(Classification):             # <<<<<<<<<<<<<<
 *     """Squared Hinge loss for binary classification tasks with y in {-1,1}
 * 
 */

struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_SquaredHinge {
  struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_Classification __pyx_base;
};
static struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_SquaredHinge *__pyx_vtabptr_7sklearn_12linear_model_8sgd_fast_SquaredHinge;


/* "sklearn/linear_model/sgd_fast.pyx":241
 * 
 * 
 * cdef class Huber(Regression):             # <<<<<<<<<<<<<<
 *     """Huber regression loss
 * 
 */

struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_Huber {
  struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_Regression __pyx_base;
};
static struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_Huber *__pyx_vtabptr_7sklearn_12linear_model_8sgd_fast_Huber;


/* "sklearn/linear_model/sgd_fast.pyx":277
 * 
 * 
 * cdef class EpsilonInsensitive(Regression):             # <<<<<<<<<<<<<<
 *     """Epsilon-Insensitive loss (used by SVR).
 * 
 */

struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_EpsilonInsensitive {
  struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_Regression __pyx_base;
};
static struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_EpsilonInsensitive *__pyx_vtabptr_7sklearn_12linear_model_8sgd_fast_EpsilonInsensitive;


/* "sklearn/linear_model/sgd_fast.pyx":304
 * 
 * 
 * cdef class SquaredEpsilonInsensitive(Regression):             # <<<<<<<<<<<<<<
 *     """Epsilon-Insensitive loss.
 * 
 */

struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_SquaredEpsilonInsensitive {
  struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_Regression __pyx_base;
};
static struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_SquaredEpsilonInsensitive *__pyx_vtabptr_7sklearn_12linear_model_8sgd_fast_SquaredEpsilonInsensitive;

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static double __pyx_f_7sklearn_12linear_model_8sgd_fast_12LossFunction_loss(CYTHON_UNUSED struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_LossFunction *__pyx_v_self, CYTHON_UNUSED double __pyx_v_p, CYTHON_UNUSED double __pyx_v_y); /* proto*/
static double __pyx_f_7sklearn_12linear_model_8sgd_fast_12LossFunction__dloss(CYTHON_UNUSED struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_LossFunction *__pyx_v_self, CYTHON_UNUSED double __pyx_v_p, CYTHON_UNUSED double __pyx_v_y); /* proto*/
static double __pyx_f_7sklearn_12linear_model_8sgd_fast_10Regression_loss(CYTHON_UNUSED struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Regression *__pyx_v_self, CYTHON_UNUSED double __pyx_v_p, CYTHON_UNUSED double __pyx_v_y); /* proto*/
static double __pyx_f_7sklearn_12linear_model_8sgd_fast_10Regression__dloss(CYTHON_UNUSED struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Regression *__pyx_v_self, CYTHON_UNUSED double __pyx_v_p, CYTHON_UNUSED double __pyx_v_y); /* proto*/
static double __pyx_f_7sklearn_12linear_model_8sgd_fast_14Classification_loss(CYTHON_UNUSED struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Classification *__pyx_v_self, CYTHON_UNUSED double __pyx_v_p, CYTHON_UNUSED double __pyx_v_y); /* proto*/
static double __pyx_f_7sklearn_12linear_model_8sgd_fast_14Classification__dloss(CYTHON_UNUSED struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Classification *__pyx_v_self, CYTHON_UNUSED double __pyx_v_p, CYTHON_UNUSED double __pyx_v_y); /* proto*/
static double __pyx_f_7sklearn_12linear_model_8sgd_fast_13ModifiedHuber_loss(CYTHON_UNUSED struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_ModifiedHuber *__pyx_v_self, double __pyx_v_p, double __pyx_v_y); /* proto*/
static double __pyx_f_7sklearn_12linear_model_8sgd_fast_13ModifiedHuber__dloss(CYTHON_UNUSED struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_ModifiedHuber *__pyx_v_self, double __pyx_v_p, double __pyx_v_y); /* proto*/
static double __pyx_f_7sklearn_12linear_model_8sgd_fast_5Hinge_loss(struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Hinge *__pyx_v_self, double __pyx_v_p, double __pyx_v_y); /* proto*/
static double __pyx_f_7sklearn_12linear_model_8sgd_fast_5Hinge__dloss(struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Hinge *__pyx_v_self, double __pyx_v_p, double __pyx_v_y); /* proto*/
static double __pyx_f_7sklearn_12linear_model_8sgd_fast_12SquaredHinge_loss(struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_SquaredHinge *__pyx_v_self, double __pyx_v_p, double __pyx_v_y); /* proto*/
static double __pyx_f_7sklearn_12linear_model_8sgd_fast_12SquaredHinge__dloss(struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_SquaredHinge *__pyx_v_self, double __pyx_v_p, double __pyx_v_y); /* proto*/
static double __pyx_f_7sklearn_12linear_model_8sgd_fast_3Log_loss(CYTHON_UNUSED struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Log *__pyx_v_self, double __pyx_v_p, double __pyx_v_y); /* proto*/
static double __pyx_f_7sklearn_12linear_model_8sgd_fast_3Log__dloss(CYTHON_UNUSED struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Log *__pyx_v_self, double __pyx_v_p, double __pyx_v_y); /* proto*/
static double __pyx_f_7sklearn_12linear_model_8sgd_fast_11SquaredLoss_loss(CYTHON_UNUSED struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_SquaredLoss *__pyx_v_self, double __pyx_v_p, double __pyx_v_y); /* proto*/
static double __pyx_f_7sklearn_12linear_model_8sgd_fast_11SquaredLoss__dloss(CYTHON_UNUSED struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_SquaredLoss *__pyx_v_self, double __pyx_v_p, double __pyx_v_y); /* proto*/
static double __pyx_f_7sklearn_12linear_model_8sgd_fast_5Huber_loss(struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Huber *__pyx_v_self, double __pyx_v_p, double __pyx_v_y); /* proto*/
static double __pyx_f_7sklearn_12linear_model_8sgd_fast_5Huber__dloss(struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Huber *__pyx_v_self, double __pyx_v_p, double __pyx_v_y); /* proto*/
static double __pyx_f_7sklearn_12linear_model_8sgd_fast_18EpsilonInsensitive_loss(struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_EpsilonInsensitive *__pyx_v_self, double __pyx_v_p, double __pyx_v_y); /* proto*/
static double __pyx_f_7sklearn_12linear_model_8sgd_fast_18EpsilonInsensitive__dloss(struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_EpsilonInsensitive *__pyx_v_self, double __pyx_v_p, double __pyx_v_y); /* proto*/
static double __pyx_f_7sklearn_12linear_model_8sgd_fast_25SquaredEpsilonInsensitive_loss(struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_SquaredEpsilonInsensitive *__pyx_v_self, double __pyx_v_p, double __pyx_v_y); /* proto*/
static double __pyx_f_7sklearn_12linear_model_8sgd_fast_25SquaredEpsilonInsensitive__dloss(struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_SquaredEpsilonInsensitive *__pyx_v_self, double __pyx_v_p, double __pyx_v_y); /* proto*/

/* Module declarations from 'cython' */

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

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

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static PyTypeObject *__pyx_ptype_7sklearn_12linear_model_8sgd_fast_EpsilonInsensitive = 0;
static PyTypeObject *__pyx_ptype_7sklearn_12linear_model_8sgd_fast_SquaredEpsilonInsensitive = 0;
static int __pyx_f_7sklearn_12linear_model_8sgd_fast_any_nonfinite(double *, int); /*proto*/
static double __pyx_f_7sklearn_12linear_model_8sgd_fast_sqnorm(double *, int *, int); /*proto*/
static void __pyx_f_7sklearn_12linear_model_8sgd_fast_l1penalty(struct __pyx_obj_7sklearn_5utils_13weight_vector_WeightVector *, double *, int *, int, double); /*proto*/
static __Pyx_TypeInfo __Pyx_TypeInfo_double = { "double", NULL, sizeof(double), { 0 }, 0, 'R', 0, 0 };
#define __Pyx_MODULE_NAME "sklearn.linear_model.sgd_fast"
int __pyx_module_is_main_sklearn__linear_model__sgd_fast = 0;

/* Implementation of 'sklearn.linear_model.sgd_fast' */
static PyObject *__pyx_builtin_range;
static PyObject *__pyx_builtin_ValueError;
static PyObject *__pyx_builtin_RuntimeError;
static PyObject *__pyx_builtin_ImportError;
static const char __pyx_k_C[] = "C";
static const char __pyx_k_c[] = "c";
static const char __pyx_k_i[] = "i";
static const char __pyx_k_p[] = "p";
static const char __pyx_k_q[] = "q";
static const char __pyx_k_t[] = "t";
static const char __pyx_k_u[] = "u";
static const char __pyx_k_w[] = "w";
static const char __pyx_k_y[] = "y";
static const char __pyx_k_np[] = "np";
static const char __pyx_k__10[] = "_";
static const char __pyx_k_end[] = "end";
static const char __pyx_k_eta[] = "eta";
static const char __pyx_k_inf[] = "inf";
static const char __pyx_k_sys[] = "sys";
static const char __pyx_k_tol[] = "tol";
static const char __pyx_k_eta0[] = "eta0";
static const char __pyx_k_file[] = "file";
static const char __pyx_k_loss[] = "loss";
static const char __pyx_k_main[] = "__main__";
static const char __pyx_k_seed[] = "seed";
static const char __pyx_k_sqrt[] = "sqrt";
static const char __pyx_k_test[] = "__test__";
static const char __pyx_k_time[] = "time";
static const char __pyx_k_typw[] = "typw";
static const char __pyx_k_xnnz[] = "xnnz";
static const char __pyx_k_alpha[] = "alpha";
static const char __pyx_k_count[] = "count";
static const char __pyx_k_dloss[] = "dloss";
static const char __pyx_k_dtype[] = "dtype";
static const char __pyx_k_epoch[] = "epoch";
static const char __pyx_k_numpy[] = "numpy";
static const char __pyx_k_order[] = "order";
static const char __pyx_k_print[] = "print";
static const char __pyx_k_range[] = "range";
static const char __pyx_k_shape[] = "shape";
static const char __pyx_k_w_ptr[] = "w_ptr";
static const char __pyx_k_zeros[] = "zeros";
static const char __pyx_k_import[] = "__import__";
static const char __pyx_k_n_iter[] = "n_iter_";
static const char __pyx_k_ps_ptr[] = "ps_ptr";
static const char __pyx_k_update[] = "update";
static const char __pyx_k_Epoch_d[] = "-- Epoch %d";
static const char __pyx_k_average[] = "average";
static const char __pyx_k_dataset[] = "dataset";
static const char __pyx_k_epsilon[] = "epsilon";
static const char __pyx_k_float64[] = "float64";
static const char __pyx_k_nonzero[] = "nonzero";
static const char __pyx_k_power_t[] = "power_t";
static const char __pyx_k_shuffle[] = "shuffle";
static const char __pyx_k_sumloss[] = "sumloss";
static const char __pyx_k_t_start[] = "t_start";
static const char __pyx_k_verbose[] = "verbose";
static const char __pyx_k_weights[] = "weights";
static const char __pyx_k_infinity[] = "infinity";
static const char __pyx_k_is_hinge[] = "is_hinge";
static const char __pyx_k_l1_ratio[] = "l1_ratio";
static const char __pyx_k_max_iter[] = "max_iter";
static const char __pyx_k_MAX_DLOSS[] = "MAX_DLOSS";
static const char __pyx_k_intercept[] = "intercept";
static const char __pyx_k_n_samples[] = "n_samples";
static const char __pyx_k_plain_sgd[] = "_plain_sgd";
static const char __pyx_k_threshold[] = "threshold";
static const char __pyx_k_x_ind_ptr[] = "x_ind_ptr";
static const char __pyx_k_ValueError[] = "ValueError";
static const char __pyx_k_max_change[] = "max_change";
static const char __pyx_k_max_weight[] = "max_weight";
static const char __pyx_k_n_features[] = "n_features";
static const char __pyx_k_pyx_vtable[] = "__pyx_vtable__";
static const char __pyx_k_q_data_ptr[] = "q_data_ptr";
static const char __pyx_k_weight_neg[] = "weight_neg";
static const char __pyx_k_weight_pos[] = "weight_pos";
static const char __pyx_k_x_data_ptr[] = "x_data_ptr";
static const char __pyx_k_ImportError[] = "ImportError";
static const char __pyx_k_average_sgd[] = "average_sgd";
static const char __pyx_k_plain_sgd_2[] = "plain_sgd";
static const char __pyx_k_RuntimeError[] = "RuntimeError";
static const char __pyx_k_class_weight[] = "class_weight";
static const char __pyx_k_initial_eta0[] = "initial_eta0";
static const char __pyx_k_optimal_init[] = "optimal_init";
static const char __pyx_k_penalty_type[] = "penalty_type";
static const char __pyx_k_fit_intercept[] = "fit_intercept";
static const char __pyx_k_learning_rate[] = "learning_rate";
static const char __pyx_k_previous_loss[] = "previous_loss";
static const char __pyx_k_sample_weight[] = "sample_weight";
static const char __pyx_k_average_weights[] = "average_weights";
static const char __pyx_k_intercept_decay[] = "intercept_decay";
static const char __pyx_k_standard_weights[] = "standard_weights";
static const char __pyx_k_average_intercept[] = "average_intercept";
static const char __pyx_k_standard_intercept[] = "standard_intercept";
static const char __pyx_k_ndarray_is_not_C_contiguous[] = "ndarray is not C contiguous";
static const char __pyx_k_sklearn_linear_model_sgd_fast[] = "sklearn.linear_model.sgd_fast";
static const char __pyx_k_Total_training_time_2f_seconds[] = "Total training time: %.2f seconds.";
static const char __pyx_k_home_yoh_deb_gits_scikit_learn[] = "/home/yoh/deb/gits/scikit-learn/sklearn/linear_model/sgd_fast.pyx";
static const char __pyx_k_Convergence_after_d_epochs_took[] = "Convergence after %d epochs took %.2f seconds";
static const char __pyx_k_numpy_core_multiarray_failed_to[] = "numpy.core.multiarray failed to import";
static const char __pyx_k_unknown_dtype_code_in_numpy_pxd[] = "unknown dtype code in numpy.pxd (%d)";
static const char __pyx_k_Floating_point_under_overflow_oc[] = "Floating-point under-/overflow occurred at epoch #%d. Scaling input data with StandardScaler or MinMaxScaler might help.";
static const char __pyx_k_Format_string_allocated_too_shor[] = "Format string allocated too short, see comment in numpy.pxd";
static const char __pyx_k_Non_native_byte_order_not_suppor[] = "Non-native byte order not supported";
static const char __pyx_k_Norm_2f_NNZs_d_Bias_6f_T_d_Avg_l[] = "Norm: %.2f, NNZs: %d, Bias: %.6f, T: %d, Avg. loss: %f";
static const char __pyx_k_ndarray_is_not_Fortran_contiguou[] = "ndarray is not Fortran contiguous";
static const char __pyx_k_numpy_core_umath_failed_to_impor[] = "numpy.core.umath failed to import";
static const char __pyx_k_Format_string_allocated_too_shor_2[] = "Format string allocated too short.";
static PyObject *__pyx_n_s_C;
static PyObject *__pyx_kp_s_Convergence_after_d_epochs_took;
static PyObject *__pyx_kp_s_Epoch_d;
static PyObject *__pyx_kp_s_Floating_point_under_overflow_oc;
static PyObject *__pyx_kp_u_Format_string_allocated_too_shor;
static PyObject *__pyx_kp_u_Format_string_allocated_too_shor_2;
static PyObject *__pyx_n_s_ImportError;
static PyObject *__pyx_n_s_MAX_DLOSS;
static PyObject *__pyx_kp_u_Non_native_byte_order_not_suppor;
static PyObject *__pyx_kp_s_Norm_2f_NNZs_d_Bias_6f_T_d_Avg_l;
static PyObject *__pyx_n_s_RuntimeError;
static PyObject *__pyx_kp_s_Total_training_time_2f_seconds;
static PyObject *__pyx_n_s_ValueError;
static PyObject *__pyx_n_s__10;
static PyObject *__pyx_n_s_alpha;
static PyObject *__pyx_n_s_average;
static PyObject *__pyx_n_s_average_intercept;
static PyObject *__pyx_n_s_average_sgd;
static PyObject *__pyx_n_s_average_weights;
static PyObject *__pyx_n_s_c;
static PyObject *__pyx_n_s_class_weight;
static PyObject *__pyx_n_s_count;
static PyObject *__pyx_n_s_dataset;
static PyObject *__pyx_n_s_dloss;
static PyObject *__pyx_n_s_dtype;
static PyObject *__pyx_n_s_end;
static PyObject *__pyx_n_s_epoch;
static PyObject *__pyx_n_s_epsilon;
static PyObject *__pyx_n_s_eta;
static PyObject *__pyx_n_s_eta0;
static PyObject *__pyx_n_s_file;
static PyObject *__pyx_n_s_fit_intercept;
static PyObject *__pyx_n_s_float64;
static PyObject *__pyx_kp_s_home_yoh_deb_gits_scikit_learn;
static PyObject *__pyx_n_s_i;
static PyObject *__pyx_n_s_import;
static PyObject *__pyx_n_s_inf;
static PyObject *__pyx_n_s_infinity;
static PyObject *__pyx_n_s_initial_eta0;
static PyObject *__pyx_n_s_intercept;
static PyObject *__pyx_n_s_intercept_decay;
static PyObject *__pyx_n_s_is_hinge;
static PyObject *__pyx_n_s_l1_ratio;
static PyObject *__pyx_n_s_learning_rate;
static PyObject *__pyx_n_s_loss;
static PyObject *__pyx_n_s_main;
static PyObject *__pyx_n_s_max_change;
static PyObject *__pyx_n_s_max_iter;
static PyObject *__pyx_n_s_max_weight;
static PyObject *__pyx_n_s_n_features;
static PyObject *__pyx_n_s_n_iter;
static PyObject *__pyx_n_s_n_samples;
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_nonzero;
static PyObject *__pyx_n_s_np;
static PyObject *__pyx_n_s_numpy;
static PyObject *__pyx_kp_s_numpy_core_multiarray_failed_to;
static PyObject *__pyx_kp_s_numpy_core_umath_failed_to_impor;
static PyObject *__pyx_n_s_optimal_init;
static PyObject *__pyx_n_s_order;
static PyObject *__pyx_n_s_p;
static PyObject *__pyx_n_s_penalty_type;
static PyObject *__pyx_n_s_plain_sgd;
static PyObject *__pyx_n_s_plain_sgd_2;
static PyObject *__pyx_n_s_power_t;
static PyObject *__pyx_n_s_previous_loss;
static PyObject *__pyx_n_s_print;
static PyObject *__pyx_n_s_ps_ptr;
static PyObject *__pyx_n_s_pyx_vtable;
static PyObject *__pyx_n_s_q;
static PyObject *__pyx_n_s_q_data_ptr;
static PyObject *__pyx_n_s_range;
static PyObject *__pyx_n_s_sample_weight;
static PyObject *__pyx_n_s_seed;
static PyObject *__pyx_n_s_shape;
static PyObject *__pyx_n_s_shuffle;
static PyObject *__pyx_n_s_sklearn_linear_model_sgd_fast;
static PyObject *__pyx_n_s_sqrt;
static PyObject *__pyx_n_s_standard_intercept;
static PyObject *__pyx_n_s_standard_weights;
static PyObject *__pyx_n_s_sumloss;
static PyObject *__pyx_n_s_sys;
static PyObject *__pyx_n_s_t;
static PyObject *__pyx_n_s_t_start;
static PyObject *__pyx_n_s_test;
static PyObject *__pyx_n_s_threshold;
static PyObject *__pyx_n_s_time;
static PyObject *__pyx_n_s_tol;
static PyObject *__pyx_n_s_typw;
static PyObject *__pyx_n_s_u;
static PyObject *__pyx_kp_u_unknown_dtype_code_in_numpy_pxd;
static PyObject *__pyx_n_s_update;
static PyObject *__pyx_n_s_verbose;
static PyObject *__pyx_n_s_w;
static PyObject *__pyx_n_s_w_ptr;
static PyObject *__pyx_n_s_weight_neg;
static PyObject *__pyx_n_s_weight_pos;
static PyObject *__pyx_n_s_weights;
static PyObject *__pyx_n_s_x_data_ptr;
static PyObject *__pyx_n_s_x_ind_ptr;
static PyObject *__pyx_n_s_xnnz;
static PyObject *__pyx_n_s_y;
static PyObject *__pyx_n_s_zeros;
static PyObject *__pyx_pf_7sklearn_12linear_model_8sgd_fast_12LossFunction_dloss(struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_LossFunction *__pyx_v_self, double __pyx_v_p, double __pyx_v_y); /* proto */
static PyObject *__pyx_pf_7sklearn_12linear_model_8sgd_fast_13ModifiedHuber___reduce__(CYTHON_UNUSED struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_ModifiedHuber *__pyx_v_self); /* proto */
static int __pyx_pf_7sklearn_12linear_model_8sgd_fast_5Hinge___init__(struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Hinge *__pyx_v_self, double __pyx_v_threshold); /* proto */
static PyObject *__pyx_pf_7sklearn_12linear_model_8sgd_fast_5Hinge_2__reduce__(struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Hinge *__pyx_v_self); /* proto */
static int __pyx_pf_7sklearn_12linear_model_8sgd_fast_12SquaredHinge___init__(struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_SquaredHinge *__pyx_v_self, double __pyx_v_threshold); /* proto */
static PyObject *__pyx_pf_7sklearn_12linear_model_8sgd_fast_12SquaredHinge_2__reduce__(struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_SquaredHinge *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_7sklearn_12linear_model_8sgd_fast_3Log___reduce__(CYTHON_UNUSED struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Log *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_7sklearn_12linear_model_8sgd_fast_11SquaredLoss___reduce__(CYTHON_UNUSED struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_SquaredLoss *__pyx_v_self); /* proto */
static int __pyx_pf_7sklearn_12linear_model_8sgd_fast_5Huber___init__(struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Huber *__pyx_v_self, double __pyx_v_c); /* proto */
static PyObject *__pyx_pf_7sklearn_12linear_model_8sgd_fast_5Huber_2__reduce__(struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Huber *__pyx_v_self); /* proto */
static int __pyx_pf_7sklearn_12linear_model_8sgd_fast_18EpsilonInsensitive___init__(struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_EpsilonInsensitive *__pyx_v_self, double __pyx_v_epsilon); /* proto */
static PyObject *__pyx_pf_7sklearn_12linear_model_8sgd_fast_18EpsilonInsensitive_2__reduce__(struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_EpsilonInsensitive *__pyx_v_self); /* proto */
static int __pyx_pf_7sklearn_12linear_model_8sgd_fast_25SquaredEpsilonInsensitive___init__(struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_SquaredEpsilonInsensitive *__pyx_v_self, double __pyx_v_epsilon); /* proto */
static PyObject *__pyx_pf_7sklearn_12linear_model_8sgd_fast_25SquaredEpsilonInsensitive_2__reduce__(struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_SquaredEpsilonInsensitive *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_7sklearn_12linear_model_8sgd_fast_plain_sgd(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_weights, double __pyx_v_intercept, struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_LossFunction *__pyx_v_loss, int __pyx_v_penalty_type, double __pyx_v_alpha, double __pyx_v_C, double __pyx_v_l1_ratio, struct __pyx_obj_7sklearn_5utils_11seq_dataset_SequentialDataset *__pyx_v_dataset, int __pyx_v_max_iter, double __pyx_v_tol, int __pyx_v_fit_intercept, int __pyx_v_verbose, int __pyx_v_shuffle, __pyx_t_5numpy_uint32_t __pyx_v_seed, double __pyx_v_weight_pos, double __pyx_v_weight_neg, int __pyx_v_learning_rate, double __pyx_v_eta0, double __pyx_v_power_t, double __pyx_v_t, double __pyx_v_intercept_decay); /* proto */
static PyObject *__pyx_pf_7sklearn_12linear_model_8sgd_fast_2average_sgd(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_weights, double __pyx_v_intercept, PyArrayObject *__pyx_v_average_weights, double __pyx_v_average_intercept, struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_LossFunction *__pyx_v_loss, int __pyx_v_penalty_type, double __pyx_v_alpha, double __pyx_v_C, double __pyx_v_l1_ratio, struct __pyx_obj_7sklearn_5utils_11seq_dataset_SequentialDataset *__pyx_v_dataset, int __pyx_v_max_iter, double __pyx_v_tol, int __pyx_v_fit_intercept, int __pyx_v_verbose, int __pyx_v_shuffle, __pyx_t_5numpy_uint32_t __pyx_v_seed, double __pyx_v_weight_pos, double __pyx_v_weight_neg, int __pyx_v_learning_rate, double __pyx_v_eta0, double __pyx_v_power_t, double __pyx_v_t, double __pyx_v_intercept_decay, int __pyx_v_average); /* proto */
static PyObject *__pyx_pf_7sklearn_12linear_model_8sgd_fast_4_plain_sgd(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_weights, double __pyx_v_intercept, PyArrayObject *__pyx_v_average_weights, double __pyx_v_average_intercept, struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_LossFunction *__pyx_v_loss, int __pyx_v_penalty_type, double __pyx_v_alpha, double __pyx_v_C, double __pyx_v_l1_ratio, struct __pyx_obj_7sklearn_5utils_11seq_dataset_SequentialDataset *__pyx_v_dataset, int __pyx_v_max_iter, double __pyx_v_tol, int __pyx_v_fit_intercept, int __pyx_v_verbose, int __pyx_v_shuffle, __pyx_t_5numpy_uint32_t __pyx_v_seed, double __pyx_v_weight_pos, double __pyx_v_weight_neg, int __pyx_v_learning_rate, double __pyx_v_eta0, double __pyx_v_power_t, double __pyx_v_t, double __pyx_v_intercept_decay, int __pyx_v_average); /* 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_7sklearn_12linear_model_8sgd_fast_LossFunction(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_7sklearn_12linear_model_8sgd_fast_Regression(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_7sklearn_12linear_model_8sgd_fast_Classification(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_7sklearn_12linear_model_8sgd_fast_Log(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_7sklearn_12linear_model_8sgd_fast_SquaredLoss(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_7sklearn_12linear_model_8sgd_fast_ModifiedHuber(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_7sklearn_12linear_model_8sgd_fast_Hinge(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_7sklearn_12linear_model_8sgd_fast_SquaredHinge(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_7sklearn_12linear_model_8sgd_fast_Huber(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_7sklearn_12linear_model_8sgd_fast_EpsilonInsensitive(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_7sklearn_12linear_model_8sgd_fast_SquaredEpsilonInsensitive(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_float_1_0;
static PyObject *__pyx_int_0;
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__11;
static PyObject *__pyx_tuple__13;
static PyObject *__pyx_tuple__15;
static PyObject *__pyx_codeobj__12;
static PyObject *__pyx_codeobj__14;
static PyObject *__pyx_codeobj__16;

/* "sklearn/linear_model/sgd_fast.pyx":50
 *     """Base class for convex loss functions"""
 * 
 *     cdef double loss(self, double p, double y) nogil:             # <<<<<<<<<<<<<<
 *         """Evaluate the loss function.
 * 
 */

static double __pyx_f_7sklearn_12linear_model_8sgd_fast_12LossFunction_loss(CYTHON_UNUSED struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_LossFunction *__pyx_v_self, CYTHON_UNUSED double __pyx_v_p, CYTHON_UNUSED double __pyx_v_y) {
  double __pyx_r;

  /* "sklearn/linear_model/sgd_fast.pyx":65
 *             The loss evaluated at `p` and `y`.
 *         """
 *         return 0.             # <<<<<<<<<<<<<<
 * 
 *     def dloss(self, double p, double y):
 */
  __pyx_r = 0.;
  goto __pyx_L0;

  /* "sklearn/linear_model/sgd_fast.pyx":50
 *     """Base class for convex loss functions"""
 * 
 *     cdef double loss(self, double p, double y) nogil:             # <<<<<<<<<<<<<<
 *         """Evaluate the loss function.
 * 
 */

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

/* "sklearn/linear_model/sgd_fast.pyx":67
 *         return 0.
 * 
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 *                 dataset.next(&x_data_ptr, &x_ind_ptr, &xnnz,
 */
            ((struct __pyx_vtabstruct_7sklearn_5utils_11seq_dataset_SequentialDataset *)__pyx_v_dataset->__pyx_vtab)->shuffle(__pyx_v_dataset, __pyx_v_seed);

            /* "sklearn/linear_model/sgd_fast.pyx":617
 *                 with gil:
 *                     print("-- Epoch %d" % (epoch + 1))
 *             if shuffle:             # <<<<<<<<<<<<<<
 *                 dataset.shuffle(seed)
 *             for i in range(n_samples):
 */
          }

          /* "sklearn/linear_model/sgd_fast.pyx":619
 *             if shuffle:
 *                 dataset.shuffle(seed)
 *             for i in range(n_samples):             # <<<<<<<<<<<<<<
 *                 dataset.next(&x_data_ptr, &x_ind_ptr, &xnnz,
 *                              &y, &sample_weight)
 */
          __pyx_t_1 = __pyx_v_n_samples;
          for (__pyx_t_18 = 0; __pyx_t_18 < __pyx_t_1; __pyx_t_18+=1) {
            __pyx_v_i = __pyx_t_18;

            /* "sklearn/linear_model/sgd_fast.pyx":620
 *                 dataset.shuffle(seed)
 *             for i in range(n_samples):
 *                 dataset.next(&x_data_ptr, &x_ind_ptr, &xnnz,             # <<<<<<<<<<<<<<
 *                              &y, &sample_weight)
 * 
 */
            ((struct __pyx_vtabstruct_7sklearn_5utils_11seq_dataset_SequentialDataset *)__pyx_v_dataset->__pyx_vtab)->next(__pyx_v_dataset, (&__pyx_v_x_data_ptr), (&__pyx_v_x_ind_ptr), (&__pyx_v_xnnz), (&__pyx_v_y), (&__pyx_v_sample_weight));

            /* "sklearn/linear_model/sgd_fast.pyx":623
 *                              &y, &sample_weight)
 * 
 *                 p = w.dot(x_data_ptr, x_ind_ptr, xnnz) + intercept             # <<<<<<<<<<<<<<
 *                 if learning_rate == OPTIMAL:
 *                     eta = 1.0 / (alpha * (optimal_init + t - 1))
 */
            __pyx_v_p = (((struct __pyx_vtabstruct_7sklearn_5utils_13weight_vector_WeightVector *)__pyx_v_w->__pyx_vtab)->dot(__pyx_v_w, __pyx_v_x_data_ptr, __pyx_v_x_ind_ptr, __pyx_v_xnnz) + __pyx_v_intercept);

            /* "sklearn/linear_model/sgd_fast.pyx":624
 * 
 *                 p = w.dot(x_data_ptr, x_ind_ptr, xnnz) + intercept
 *                 if learning_rate == OPTIMAL:             # <<<<<<<<<<<<<<
 *                     eta = 1.0 / (alpha * (optimal_init + t - 1))
 *                 elif learning_rate == INVSCALING:
 */
            switch (__pyx_v_learning_rate) {
              case 2:

              /* "sklearn/linear_model/sgd_fast.pyx":625
 *                 p = w.dot(x_data_ptr, x_ind_ptr, xnnz) + intercept
 *                 if learning_rate == OPTIMAL:
 *                     eta = 1.0 / (alpha * (optimal_init + t - 1))             # <<<<<<<<<<<<<<
 *                 elif learning_rate == INVSCALING:
 *                     eta = eta0 / pow(t, power_t)
 */
              __pyx_v_eta = (1.0 / (__pyx_v_alpha * ((__pyx_v_optimal_init + __pyx_v_t) - 1.0)));

              /* "sklearn/linear_model/sgd_fast.pyx":624
 * 
 *                 p = w.dot(x_data_ptr, x_ind_ptr, xnnz) + intercept
 *                 if learning_rate == OPTIMAL:             # <<<<<<<<<<<<<<
 *                     eta = 1.0 / (alpha * (optimal_init + t - 1))
 *                 elif learning_rate == INVSCALING:
 */
              break;

              /* "sklearn/linear_model/sgd_fast.pyx":626
 *                 if learning_rate == OPTIMAL:
 *                     eta = 1.0 / (alpha * (optimal_init + t - 1))
 *                 elif learning_rate == INVSCALING:             # <<<<<<<<<<<<<<
 *                     eta = eta0 / pow(t, power_t)
 * 
 */
              case 3:

              /* "sklearn/linear_model/sgd_fast.pyx":627
 *                     eta = 1.0 / (alpha * (optimal_init + t - 1))
 *                 elif learning_rate == INVSCALING:
 *                     eta = eta0 / pow(t, power_t)             # <<<<<<<<<<<<<<
 * 
 *                 sumloss += loss.loss(p, y)
 */
              __pyx_v_eta = (__pyx_v_eta0 / pow(__pyx_v_t, __pyx_v_power_t));

              /* "sklearn/linear_model/sgd_fast.pyx":626
 *                 if learning_rate == OPTIMAL:
 *                     eta = 1.0 / (alpha * (optimal_init + t - 1))
 *                 elif learning_rate == INVSCALING:             # <<<<<<<<<<<<<<
 *                     eta = eta0 / pow(t, power_t)
 * 
 */
              break;
              default: break;
            }

            /* "sklearn/linear_model/sgd_fast.pyx":629
 *                     eta = eta0 / pow(t, power_t)
 * 
 *                 sumloss += loss.loss(p, y)             # <<<<<<<<<<<<<<
 * 
 *                 if y > 0.0:
 */
            __pyx_v_sumloss = (__pyx_v_sumloss + ((struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_LossFunction *)__pyx_v_loss->__pyx_vtab)->loss(__pyx_v_loss, __pyx_v_p, __pyx_v_y));

            /* "sklearn/linear_model/sgd_fast.pyx":631
 *                 sumloss += loss.loss(p, y)
 * 
 *                 if y > 0.0:             # <<<<<<<<<<<<<<
 *                     class_weight = weight_pos
 *                 else:
 */
            __pyx_t_6 = ((__pyx_v_y > 0.0) != 0);
            if (__pyx_t_6) {

              /* "sklearn/linear_model/sgd_fast.pyx":632
 * 
 *                 if y > 0.0:
 *                     class_weight = weight_pos             # <<<<<<<<<<<<<<
 *                 else:
 *                     class_weight = weight_neg
 */
              __pyx_v_class_weight = __pyx_v_weight_pos;

              /* "sklearn/linear_model/sgd_fast.pyx":631
 *                 sumloss += loss.loss(p, y)
 * 
 *                 if y > 0.0:             # <<<<<<<<<<<<<<
 *                     class_weight = weight_pos
 *                 else:
 */
              goto __pyx_L18;
            }

            /* "sklearn/linear_model/sgd_fast.pyx":634
 *                     class_weight = weight_pos
 *                 else:
 *                     class_weight = weight_neg             # <<<<<<<<<<<<<<
 * 
 *                 if learning_rate == PA1:
 */
            /*else*/ {
              __pyx_v_class_weight = __pyx_v_weight_neg;
            }
            __pyx_L18:;

            /* "sklearn/linear_model/sgd_fast.pyx":636
 *                     class_weight = weight_neg
 * 
 *                 if learning_rate == PA1:             # <<<<<<<<<<<<<<
 *                     update = sqnorm(x_data_ptr, x_ind_ptr, xnnz)
 *                     if update == 0:
 */
            switch (__pyx_v_learning_rate) {
              case 4:

              /* "sklearn/linear_model/sgd_fast.pyx":637
 * 
 *                 if learning_rate == PA1:
 *                     update = sqnorm(x_data_ptr, x_ind_ptr, xnnz)             # <<<<<<<<<<<<<<
 *                     if update == 0:
 *                         continue
 */
              __pyx_v_update = __pyx_f_7sklearn_12linear_model_8sgd_fast_sqnorm(__pyx_v_x_data_ptr, __pyx_v_x_ind_ptr, __pyx_v_xnnz);

              /* "sklearn/linear_model/sgd_fast.pyx":638
 *                 if learning_rate == PA1:
 *                     update = sqnorm(x_data_ptr, x_ind_ptr, xnnz)
 *                     if update == 0:             # <<<<<<<<<<<<<<
 *                         continue
 *                     update = min(C, loss.loss(p, y) / update)
 */
              __pyx_t_6 = ((__pyx_v_update == 0.0) != 0);
              if (__pyx_t_6) {

                /* "sklearn/linear_model/sgd_fast.pyx":639
 *                     update = sqnorm(x_data_ptr, x_ind_ptr, xnnz)
 *                     if update == 0:
 *                         continue             # <<<<<<<<<<<<<<
 *                     update = min(C, loss.loss(p, y) / update)
 *                 elif learning_rate == PA2:
 */
                goto __pyx_L16_continue;

                /* "sklearn/linear_model/sgd_fast.pyx":638
 *                 if learning_rate == PA1:
 *                     update = sqnorm(x_data_ptr, x_ind_ptr, xnnz)
 *                     if update == 0:             # <<<<<<<<<<<<<<
 *                         continue
 *                     update = min(C, loss.loss(p, y) / update)
 */
              }

              /* "sklearn/linear_model/sgd_fast.pyx":640
 *                     if update == 0:
 *                         continue
 *                     update = min(C, loss.loss(p, y) / update)             # <<<<<<<<<<<<<<
 *                 elif learning_rate == PA2:
 *                     update = sqnorm(x_data_ptr, x_ind_ptr, xnnz)
 */
              __pyx_t_5 = (((struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_LossFunction *)__pyx_v_loss->__pyx_vtab)->loss(__pyx_v_loss, __pyx_v_p, __pyx_v_y) / __pyx_v_update);
              __pyx_t_19 = __pyx_v_C;
              if (((__pyx_t_5 < __pyx_t_19) != 0)) {
                __pyx_t_20 = __pyx_t_5;
              } else {
                __pyx_t_20 = __pyx_t_19;
              }
              __pyx_v_update = __pyx_t_20;

              /* "sklearn/linear_model/sgd_fast.pyx":636
 *                     class_weight = weight_neg
 * 
 *                 if learning_rate == PA1:             # <<<<<<<<<<<<<<
 *                     update = sqnorm(x_data_ptr, x_ind_ptr, xnnz)
 *                     if update == 0:
 */
              break;

              /* "sklearn/linear_model/sgd_fast.pyx":641
 *                         continue
 *                     update = min(C, loss.loss(p, y) / update)
 *                 elif learning_rate == PA2:             # <<<<<<<<<<<<<<
 *                     update = sqnorm(x_data_ptr, x_ind_ptr, xnnz)
 *                     update = loss.loss(p, y) / (update + 0.5 / C)
 */
              case 5:

              /* "sklearn/linear_model/sgd_fast.pyx":642
 *                     update = min(C, loss.loss(p, y) / update)
 *                 elif learning_rate == PA2:
 *                     update = sqnorm(x_data_ptr, x_ind_ptr, xnnz)             # <<<<<<<<<<<<<<
 *                     update = loss.loss(p, y) / (update + 0.5 / C)
 *                 else:
 */
              __pyx_v_update = __pyx_f_7sklearn_12linear_model_8sgd_fast_sqnorm(__pyx_v_x_data_ptr, __pyx_v_x_ind_ptr, __pyx_v_xnnz);

              /* "sklearn/linear_model/sgd_fast.pyx":643
 *                 elif learning_rate == PA2:
 *                     update = sqnorm(x_data_ptr, x_ind_ptr, xnnz)
 *                     update = loss.loss(p, y) / (update + 0.5 / C)             # <<<<<<<<<<<<<<
 *                 else:
 *                     dloss = loss._dloss(p, y)
 */
              __pyx_v_update = (((struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_LossFunction *)__pyx_v_loss->__pyx_vtab)->loss(__pyx_v_loss, __pyx_v_p, __pyx_v_y) / (__pyx_v_update + (0.5 / __pyx_v_C)));

              /* "sklearn/linear_model/sgd_fast.pyx":641
 *                         continue
 *                     update = min(C, loss.loss(p, y) / update)
 *                 elif learning_rate == PA2:             # <<<<<<<<<<<<<<
 *                     update = sqnorm(x_data_ptr, x_ind_ptr, xnnz)
 *                     update = loss.loss(p, y) / (update + 0.5 / C)
 */
              break;
              default:

              /* "sklearn/linear_model/sgd_fast.pyx":645
 *                     update = loss.loss(p, y) / (update + 0.5 / C)
 *                 else:
 *                     dloss = loss._dloss(p, y)             # <<<<<<<<<<<<<<
 *                     # clip dloss with large values to avoid numerical
 *                     # instabilities
 */
              __pyx_v_dloss = ((struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_LossFunction *)__pyx_v_loss->__pyx_vtab)->_dloss(__pyx_v_loss, __pyx_v_p, __pyx_v_y);

              /* "sklearn/linear_model/sgd_fast.pyx":648
 *                     # clip dloss with large values to avoid numerical
 *                     # instabilities
 *                     if dloss < -MAX_DLOSS:             # <<<<<<<<<<<<<<
 *                         dloss = -MAX_DLOSS
 *                     elif dloss > MAX_DLOSS:
 */
              __pyx_t_6 = ((__pyx_v_dloss < (-__pyx_v_MAX_DLOSS)) != 0);
              if (__pyx_t_6) {

                /* "sklearn/linear_model/sgd_fast.pyx":649
 *                     # instabilities
 *                     if dloss < -MAX_DLOSS:
 *                         dloss = -MAX_DLOSS             # <<<<<<<<<<<<<<
 *                     elif dloss > MAX_DLOSS:
 *                         dloss = MAX_DLOSS
 */
                __pyx_v_dloss = (-__pyx_v_MAX_DLOSS);

                /* "sklearn/linear_model/sgd_fast.pyx":648
 *                     # clip dloss with large values to avoid numerical
 *                     # instabilities
 *                     if dloss < -MAX_DLOSS:             # <<<<<<<<<<<<<<
 *                         dloss = -MAX_DLOSS
 *                     elif dloss > MAX_DLOSS:
 */
                goto __pyx_L20;
              }

              /* "sklearn/linear_model/sgd_fast.pyx":650
 *                     if dloss < -MAX_DLOSS:
 *                         dloss = -MAX_DLOSS
 *                     elif dloss > MAX_DLOSS:             # <<<<<<<<<<<<<<
 *                         dloss = MAX_DLOSS
 *                     update = -eta * dloss
 */
              __pyx_t_6 = ((__pyx_v_dloss > __pyx_v_MAX_DLOSS) != 0);
              if (__pyx_t_6) {

                /* "sklearn/linear_model/sgd_fast.pyx":651
 *                         dloss = -MAX_DLOSS
 *                     elif dloss > MAX_DLOSS:
 *                         dloss = MAX_DLOSS             # <<<<<<<<<<<<<<
 *                     update = -eta * dloss
 * 
 */
                __pyx_v_dloss = __pyx_v_MAX_DLOSS;

                /* "sklearn/linear_model/sgd_fast.pyx":650
 *                     if dloss < -MAX_DLOSS:
 *                         dloss = -MAX_DLOSS
 *                     elif dloss > MAX_DLOSS:             # <<<<<<<<<<<<<<
 *                         dloss = MAX_DLOSS
 *                     update = -eta * dloss
 */
              }
              __pyx_L20:;

              /* "sklearn/linear_model/sgd_fast.pyx":652
 *                     elif dloss > MAX_DLOSS:
 *                         dloss = MAX_DLOSS
 *                     update = -eta * dloss             # <<<<<<<<<<<<<<
 * 
 *                 if learning_rate >= PA1:
 */
              __pyx_v_update = ((-__pyx_v_eta) * __pyx_v_dloss);
              break;
            }

            /* "sklearn/linear_model/sgd_fast.pyx":654
 *                     update = -eta * dloss
 * 
 *                 if learning_rate >= PA1:             # <<<<<<<<<<<<<<
 *                     if is_hinge:
 *                         # classification
 */
            __pyx_t_6 = ((__pyx_v_learning_rate >= 4) != 0);
            if (__pyx_t_6) {

              /* "sklearn/linear_model/sgd_fast.pyx":655
 * 
 *                 if learning_rate >= PA1:
 *                     if is_hinge:             # <<<<<<<<<<<<<<
 *                         # classification
 *                         update *= y
 */
              __pyx_t_6 = (__pyx_v_is_hinge != 0);
              if (__pyx_t_6) {

                /* "sklearn/linear_model/sgd_fast.pyx":657
 *                     if is_hinge:
 *                         # classification
 *                         update *= y             # <<<<<<<<<<<<<<
 *                     elif y - p < 0:
 *                         # regression
 */
                __pyx_v_update = (__pyx_v_update * __pyx_v_y);

                /* "sklearn/linear_model/sgd_fast.pyx":655
 * 
 *                 if learning_rate >= PA1:
 *                     if is_hinge:             # <<<<<<<<<<<<<<
 *                         # classification
 *                         update *= y
 */
                goto __pyx_L22;
              }

              /* "sklearn/linear_model/sgd_fast.pyx":658
 *                         # classification
 *                         update *= y
 *                     elif y - p < 0:             # <<<<<<<<<<<<<<
 *                         # regression
 *                         update *= -1
 */
              __pyx_t_6 = (((__pyx_v_y - __pyx_v_p) < 0.0) != 0);
              if (__pyx_t_6) {

                /* "sklearn/linear_model/sgd_fast.pyx":660
 *                     elif y - p < 0:
 *                         # regression
 *                         update *= -1             # <<<<<<<<<<<<<<
 * 
 *                 update *= class_weight * sample_weight
 */
                __pyx_v_update = (__pyx_v_update * -1.0);

                /* "sklearn/linear_model/sgd_fast.pyx":658
 *                         # classification
 *                         update *= y
 *                     elif y - p < 0:             # <<<<<<<<<<<<<<
 *                         # regression
 *                         update *= -1
 */
              }
              __pyx_L22:;

              /* "sklearn/linear_model/sgd_fast.pyx":654
 *                     update = -eta * dloss
 * 
 *                 if learning_rate >= PA1:             # <<<<<<<<<<<<<<
 *                     if is_hinge:
 *                         # classification
 */
            }

            /* "sklearn/linear_model/sgd_fast.pyx":662
 *                         update *= -1
 * 
 *                 update *= class_weight * sample_weight             # <<<<<<<<<<<<<<
 * 
 *                 if penalty_type >= L2:
 */
            __pyx_v_update = (__pyx_v_update * (__pyx_v_class_weight * __pyx_v_sample_weight));

            /* "sklearn/linear_model/sgd_fast.pyx":664
 *                 update *= class_weight * sample_weight
 * 
 *                 if penalty_type >= L2:             # <<<<<<<<<<<<<<
 *                     # do not scale to negative values when eta or alpha are too
 *                     # big: instead set the weights to zero
 */
            __pyx_t_6 = ((__pyx_v_penalty_type >= 2) != 0);
            if (__pyx_t_6) {

              /* "sklearn/linear_model/sgd_fast.pyx":667
 *                     # do not scale to negative values when eta or alpha are too
 *                     # big: instead set the weights to zero
 *                     w.scale(max(0, 1.0 - ((1.0 - l1_ratio) * eta * alpha)))             # <<<<<<<<<<<<<<
 *                 if update != 0.0:
 *                     w.add(x_data_ptr, x_ind_ptr, xnnz, update)
 */
              __pyx_t_20 = (1.0 - (((1.0 - __pyx_v_l1_ratio) * __pyx_v_eta) * __pyx_v_alpha));
              __pyx_t_21 = 0;
              if (((__pyx_t_20 > __pyx_t_21) != 0)) {
                __pyx_t_5 = __pyx_t_20;
              } else {
                __pyx_t_5 = __pyx_t_21;
              }
              ((struct __pyx_vtabstruct_7sklearn_5utils_13weight_vector_WeightVector *)__pyx_v_w->__pyx_vtab)->scale(__pyx_v_w, __pyx_t_5);

              /* "sklearn/linear_model/sgd_fast.pyx":664
 *                 update *= class_weight * sample_weight
 * 
 *                 if penalty_type >= L2:             # <<<<<<<<<<<<<<
 *                     # do not scale to negative values when eta or alpha are too
 *                     # big: instead set the weights to zero
 */
            }

            /* "sklearn/linear_model/sgd_fast.pyx":668
 *                     # big: instead set the weights to zero
 *                     w.scale(max(0, 1.0 - ((1.0 - l1_ratio) * eta * alpha)))
 *                 if update != 0.0:             # <<<<<<<<<<<<<<
 *                     w.add(x_data_ptr, x_ind_ptr, xnnz, update)
 *                     if fit_intercept == 1:
 */
            __pyx_t_6 = ((__pyx_v_update != 0.0) != 0);
            if (__pyx_t_6) {

              /* "sklearn/linear_model/sgd_fast.pyx":669
 *                     w.scale(max(0, 1.0 - ((1.0 - l1_ratio) * eta * alpha)))
 *                 if update != 0.0:
 *                     w.add(x_data_ptr, x_ind_ptr, xnnz, update)             # <<<<<<<<<<<<<<
 *                     if fit_intercept == 1:
 *                         intercept += update * intercept_decay
 */
              ((struct __pyx_vtabstruct_7sklearn_5utils_13weight_vector_WeightVector *)__pyx_v_w->__pyx_vtab)->add(__pyx_v_w, __pyx_v_x_data_ptr, __pyx_v_x_ind_ptr, __pyx_v_xnnz, __pyx_v_update);

              /* "sklearn/linear_model/sgd_fast.pyx":670
 *                 if update != 0.0:
 *                     w.add(x_data_ptr, x_ind_ptr, xnnz, update)
 *                     if fit_intercept == 1:             # <<<<<<<<<<<<<<
 *                         intercept += update * intercept_decay
 * 
 */
              __pyx_t_6 = ((__pyx_v_fit_intercept == 1) != 0);
              if (__pyx_t_6) {

                /* "sklearn/linear_model/sgd_fast.pyx":671
 *                     w.add(x_data_ptr, x_ind_ptr, xnnz, update)
 *                     if fit_intercept == 1:
 *                         intercept += update * intercept_decay             # <<<<<<<<<<<<<<
 * 
 *                 if 0 < average <= t:
 */
                __pyx_v_intercept = (__pyx_v_intercept + (__pyx_v_update * __pyx_v_intercept_decay));

                /* "sklearn/linear_model/sgd_fast.pyx":670
 *                 if update != 0.0:
 *                     w.add(x_data_ptr, x_ind_ptr, xnnz, update)
 *                     if fit_intercept == 1:             # <<<<<<<<<<<<<<
 *                         intercept += update * intercept_decay
 * 
 */
              }

              /* "sklearn/linear_model/sgd_fast.pyx":668
 *                     # big: instead set the weights to zero
 *                     w.scale(max(0, 1.0 - ((1.0 - l1_ratio) * eta * alpha)))
 *                 if update != 0.0:             # <<<<<<<<<<<<<<
 *                     w.add(x_data_ptr, x_ind_ptr, xnnz, update)
 *                     if fit_intercept == 1:
 */
            }

            /* "sklearn/linear_model/sgd_fast.pyx":673
 *                         intercept += update * intercept_decay
 * 
 *                 if 0 < average <= t:             # <<<<<<<<<<<<<<
 *                     # compute the average for the intercept and update the
 *                     # average weights, this is done regardless as to whether
 */
            __pyx_t_6 = (0.0 < __pyx_v_average);
            if (__pyx_t_6) {
              __pyx_t_6 = (__pyx_v_average <= __pyx_v_t);
            }
            __pyx_t_22 = (__pyx_t_6 != 0);
            if (__pyx_t_22) {

              /* "sklearn/linear_model/sgd_fast.pyx":678
 *                     # the update is 0
 * 
 *                     w.add_average(x_data_ptr, x_ind_ptr, xnnz,             # <<<<<<<<<<<<<<
 *                                   update, (t - average + 1))
 *                     average_intercept += ((intercept - average_intercept) /
 */
              ((struct __pyx_vtabstruct_7sklearn_5utils_13weight_vector_WeightVector *)__pyx_v_w->__pyx_vtab)->add_average(__pyx_v_w, __pyx_v_x_data_ptr, __pyx_v_x_ind_ptr, __pyx_v_xnnz, __pyx_v_update, ((__pyx_v_t - __pyx_v_average) + 1.0));

              /* "sklearn/linear_model/sgd_fast.pyx":680
 *                     w.add_average(x_data_ptr, x_ind_ptr, xnnz,
 *                                   update, (t - average + 1))
 *                     average_intercept += ((intercept - average_intercept) /             # <<<<<<<<<<<<<<
 *                                           (t - average + 1))
 * 
 */
              __pyx_v_average_intercept = (__pyx_v_average_intercept + ((__pyx_v_intercept - __pyx_v_average_intercept) / ((__pyx_v_t - __pyx_v_average) + 1.0)));

              /* "sklearn/linear_model/sgd_fast.pyx":673
 *                         intercept += update * intercept_decay
 * 
 *                 if 0 < average <= t:             # <<<<<<<<<<<<<<
 *                     # compute the average for the intercept and update the
 *                     # average weights, this is done regardless as to whether
 */
            }

            /* "sklearn/linear_model/sgd_fast.pyx":683
 *                                           (t - average + 1))
 * 
 *                 if penalty_type == L1 or penalty_type == ELASTICNET:             # <<<<<<<<<<<<<<
 *                     u += (l1_ratio * eta * alpha)
 *                     l1penalty(w, q_data_ptr, x_ind_ptr, xnnz, u)
 */
            switch (__pyx_v_penalty_type) {
              case 1:
              case 3:

              /* "sklearn/linear_model/sgd_fast.pyx":684
 * 
 *                 if penalty_type == L1 or penalty_type == ELASTICNET:
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static struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_SquaredLoss __pyx_vtable_7sklearn_12linear_model_8sgd_fast_SquaredLoss;

static PyObject *__pyx_tp_new_7sklearn_12linear_model_8sgd_fast_SquaredLoss(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_SquaredLoss *p;
  PyObject *o = __pyx_tp_new_7sklearn_12linear_model_8sgd_fast_Regression(t, a, k);
  if (unlikely(!o)) return 0;
  p = ((struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_SquaredLoss *)o);
  p->__pyx_base.__pyx_base.__pyx_vtab = (struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_LossFunction*)__pyx_vtabptr_7sklearn_12linear_model_8sgd_fast_SquaredLoss;
  return o;
}

static PyMethodDef __pyx_methods_7sklearn_12linear_model_8sgd_fast_SquaredLoss[] = {
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  {0, 0, 0, 0}
};

static PyTypeObject __pyx_type_7sklearn_12linear_model_8sgd_fast_SquaredLoss = {
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static struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_ModifiedHuber __pyx_vtable_7sklearn_12linear_model_8sgd_fast_ModifiedHuber;

static PyObject *__pyx_tp_new_7sklearn_12linear_model_8sgd_fast_ModifiedHuber(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_ModifiedHuber *p;
  PyObject *o = __pyx_tp_new_7sklearn_12linear_model_8sgd_fast_Classification(t, a, k);
  if (unlikely(!o)) return 0;
  p = ((struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_ModifiedHuber *)o);
  p->__pyx_base.__pyx_base.__pyx_vtab = (struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_LossFunction*)__pyx_vtabptr_7sklearn_12linear_model_8sgd_fast_ModifiedHuber;
  return o;
}

static PyMethodDef __pyx_methods_7sklearn_12linear_model_8sgd_fast_ModifiedHuber[] = {
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};

static PyTypeObject __pyx_type_7sklearn_12linear_model_8sgd_fast_ModifiedHuber = {
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  "Modified Huber loss for binary classification with y in {-1, 1}\n\n    This is equivalent to quadratically smoothed SVM with gamma = 2.\n\n    See T. Zhang 'Solving Large Scale Linear Prediction Problems Using\n    Stochastic Gradient Descent', ICML'04.\n    ", /*tp_doc*/
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static struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_Hinge __pyx_vtable_7sklearn_12linear_model_8sgd_fast_Hinge;

static PyObject *__pyx_tp_new_7sklearn_12linear_model_8sgd_fast_Hinge(PyTypeObject *t, PyObject *a, PyObject *k) {
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  p = ((struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Hinge *)o);
  p->__pyx_base.__pyx_base.__pyx_vtab = (struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_LossFunction*)__pyx_vtabptr_7sklearn_12linear_model_8sgd_fast_Hinge;
  return o;
}

static PyMethodDef __pyx_methods_7sklearn_12linear_model_8sgd_fast_Hinge[] = {
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static PyTypeObject __pyx_type_7sklearn_12linear_model_8sgd_fast_Hinge = {
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static struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_SquaredHinge __pyx_vtable_7sklearn_12linear_model_8sgd_fast_SquaredHinge;

static PyObject *__pyx_tp_new_7sklearn_12linear_model_8sgd_fast_SquaredHinge(PyTypeObject *t, PyObject *a, PyObject *k) {
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  if (unlikely(!o)) return 0;
  p = ((struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_SquaredHinge *)o);
  p->__pyx_base.__pyx_base.__pyx_vtab = (struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_LossFunction*)__pyx_vtabptr_7sklearn_12linear_model_8sgd_fast_SquaredHinge;
  return o;
}

static PyMethodDef __pyx_methods_7sklearn_12linear_model_8sgd_fast_SquaredHinge[] = {
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static PyTypeObject __pyx_type_7sklearn_12linear_model_8sgd_fast_SquaredHinge = {
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static struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_Huber __pyx_vtable_7sklearn_12linear_model_8sgd_fast_Huber;

static PyObject *__pyx_tp_new_7sklearn_12linear_model_8sgd_fast_Huber(PyTypeObject *t, PyObject *a, PyObject *k) {
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  PyObject *o = __pyx_tp_new_7sklearn_12linear_model_8sgd_fast_Regression(t, a, k);
  if (unlikely(!o)) return 0;
  p = ((struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_Huber *)o);
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  return o;
}

static PyMethodDef __pyx_methods_7sklearn_12linear_model_8sgd_fast_Huber[] = {
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static PyTypeObject __pyx_type_7sklearn_12linear_model_8sgd_fast_Huber = {
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static struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_EpsilonInsensitive __pyx_vtable_7sklearn_12linear_model_8sgd_fast_EpsilonInsensitive;

static PyObject *__pyx_tp_new_7sklearn_12linear_model_8sgd_fast_EpsilonInsensitive(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_EpsilonInsensitive *p;
  PyObject *o = __pyx_tp_new_7sklearn_12linear_model_8sgd_fast_Regression(t, a, k);
  if (unlikely(!o)) return 0;
  p = ((struct __pyx_obj_7sklearn_12linear_model_8sgd_fast_EpsilonInsensitive *)o);
  p->__pyx_base.__pyx_base.__pyx_vtab = (struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_LossFunction*)__pyx_vtabptr_7sklearn_12linear_model_8sgd_fast_EpsilonInsensitive;
  return o;
}

static PyMethodDef __pyx_methods_7sklearn_12linear_model_8sgd_fast_EpsilonInsensitive[] = {
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static PyTypeObject __pyx_type_7sklearn_12linear_model_8sgd_fast_EpsilonInsensitive = {
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static struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_SquaredEpsilonInsensitive __pyx_vtable_7sklearn_12linear_model_8sgd_fast_SquaredEpsilonInsensitive;

static PyObject *__pyx_tp_new_7sklearn_12linear_model_8sgd_fast_SquaredEpsilonInsensitive(PyTypeObject *t, PyObject *a, PyObject *k) {
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  /* "../../../../../usr/lib/python3/dist-packages/Cython/Includes/numpy/__init__.pxd":997
 *         raise ImportError("numpy.core.umath failed to import")
 * 
 * cdef inline int import_ufunc() except -1:             # <<<<<<<<<<<<<<
 *     try:
 *         _import_umath()
 */

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

  goto __pyx_L0;
  __pyx_L1_error:;
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  if (__pyx_m) {
    if (__pyx_d) {
      __Pyx_AddTraceback("init sklearn.linear_model.sgd_fast", __pyx_clineno, __pyx_lineno, __pyx_filename);
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    Py_DECREF(__pyx_m); __pyx_m = 0;
  } else if (!PyErr_Occurred()) {
    PyErr_SetString(PyExc_ImportError, "init sklearn.linear_model.sgd_fast");
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  __pyx_L0:;
  __Pyx_RefNannyFinishContext();
  #if PY_MAJOR_VERSION < 3
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/* --- Runtime support code --- */
/* Refnanny */
#if CYTHON_REFNANNY
static __Pyx_RefNannyAPIStruct *__Pyx_RefNannyImportAPI(const char *modname) {
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    void *r = NULL;
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    p = PyObject_GetAttrString(m, (char *)"RefNannyAPI");
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/* GetBuiltinName */
static PyObject *__Pyx_GetBuiltinName(PyObject *name) {
    PyObject* result = __Pyx_PyObject_GetAttrStr(__pyx_b, name);
    if (unlikely(!result)) {
        PyErr_Format(PyExc_NameError,
#if PY_MAJOR_VERSION >= 3
            "name '%U' is not defined", name);
#else
            "name '%.200s' is not defined", PyString_AS_STRING(name));
#endif
    }
    return result;
}

/* RaiseArgTupleInvalid */
static void __Pyx_RaiseArgtupleInvalid(
    const char* func_name,
    int exact,
    Py_ssize_t num_min,
    Py_ssize_t num_max,
    Py_ssize_t num_found)
{
    Py_ssize_t num_expected;
    const char *more_or_less;
    if (num_found < num_min) {
        num_expected = num_min;
        more_or_less = "at least";
    } else {
        num_expected = num_max;
        more_or_less = "at most";
    }
    if (exact) {
        more_or_less = "exactly";
    }
    PyErr_Format(PyExc_TypeError,
                 "%.200s() takes %.8s %" CYTHON_FORMAT_SSIZE_T "d positional argument%.1s (%" CYTHON_FORMAT_SSIZE_T "d given)",
                 func_name, more_or_less, num_expected,
                 (num_expected == 1) ? "" : "s", num_found);
}

/* RaiseDoubleKeywords */
static void __Pyx_RaiseDoubleKeywordsError(
    const char* func_name,
    PyObject* kw_name)
{
    PyErr_Format(PyExc_TypeError,
        #if PY_MAJOR_VERSION >= 3
        "%s() got multiple values for keyword argument '%U'", func_name, kw_name);
        #else
        "%s() got multiple values for keyword argument '%s'", func_name,
        PyString_AsString(kw_name));
        #endif
}

/* ParseKeywords */
static int __Pyx_ParseOptionalKeywords(
    PyObject *kwds,
    PyObject **argnames[],
    PyObject *kwds2,
    PyObject *values[],
    Py_ssize_t num_pos_args,
    const char* function_name)
{
    PyObject *key = 0, *value = 0;
    Py_ssize_t pos = 0;
    PyObject*** name;
    PyObject*** first_kw_arg = argnames + num_pos_args;
    while (PyDict_Next(kwds, &pos, &key, &value)) {
        name = first_kw_arg;
        while (*name && (**name != key)) name++;
        if (*name) {
            values[name-argnames] = value;
            continue;
        }
        name = first_kw_arg;
        #if PY_MAJOR_VERSION < 3
        if (likely(PyString_CheckExact(key)) || likely(PyString_Check(key))) {
            while (*name) {
                if ((CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**name) == PyString_GET_SIZE(key))
                        && _PyString_Eq(**name, key)) {
                    values[name-argnames] = value;
                    break;
                }
                name++;
            }
            if (*name) continue;
            else {
                PyObject*** argname = argnames;
                while (argname != first_kw_arg) {
                    if ((**argname == key) || (
                            (CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**argname) == PyString_GET_SIZE(key))
                             && _PyString_Eq(**argname, key))) {
                        goto arg_passed_twice;
                    }
                    argname++;
                }
            }
        } else
        #endif
        if (likely(PyUnicode_Check(key))) {
            while (*name) {
                int cmp = (**name == key) ? 0 :
                #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
                    (PyUnicode_GET_SIZE(**name) != PyUnicode_GET_SIZE(key)) ? 1 :
                #endif
                    PyUnicode_Compare(**name, key);
                if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
                if (cmp == 0) {
                    values[name-argnames] = value;
                    break;
                }
                name++;
            }
            if (*name) continue;
            else {
                PyObject*** argname = argnames;
                while (argname != first_kw_arg) {
                    int cmp = (**argname == key) ? 0 :
                    #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
                        (PyUnicode_GET_SIZE(**argname) != PyUnicode_GET_SIZE(key)) ? 1 :
                    #endif
                        PyUnicode_Compare(**argname, key);
                    if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
                    if (cmp == 0) goto arg_passed_twice;
                    argname++;
                }
            }
        } else
            goto invalid_keyword_type;
        if (kwds2) {
            if (unlikely(PyDict_SetItem(kwds2, key, value))) goto bad;
        } else {
            goto invalid_keyword;
        }
    }
    return 0;
arg_passed_twice:
    __Pyx_RaiseDoubleKeywordsError(function_name, key);
    goto bad;
invalid_keyword_type:
    PyErr_Format(PyExc_TypeError,
        "%.200s() keywords must be strings", function_name);
    goto bad;
invalid_keyword:
    PyErr_Format(PyExc_TypeError,
    #if PY_MAJOR_VERSION < 3
        "%.200s() got an unexpected keyword argument '%.200s'",
        function_name, PyString_AsString(key));
    #else
        "%s() got an unexpected keyword argument '%U'",
        function_name, key);
    #endif
bad:
    return -1;
}

/* ArgTypeTest */
static void __Pyx_RaiseArgumentTypeInvalid(const char* name, PyObject *obj, PyTypeObject *type) {
    PyErr_Format(PyExc_TypeError,
        "Argument '%.200s' has incorrect type (expected %.200s, got %.200s)",
        name, type->tp_name, Py_TYPE(obj)->tp_name);
}
static CYTHON_INLINE int __Pyx_ArgTypeTest(PyObject *obj, PyTypeObject *type, int none_allowed,
    const char *name, int exact)
{
    if (unlikely(!type)) {
        PyErr_SetString(PyExc_SystemError, "Missing type object");
        return 0;
    }
    if (none_allowed && obj == Py_None) return 1;
    else if (exact) {
        if (likely(Py_TYPE(obj) == type)) return 1;
        #if PY_MAJOR_VERSION == 2
        else if ((type == &PyBaseString_Type) && likely(__Pyx_PyBaseString_CheckExact(obj))) return 1;
        #endif
    }
    else {
        if (likely(PyObject_TypeCheck(obj, type))) return 1;
    }
    __Pyx_RaiseArgumentTypeInvalid(name, obj, type);
    return 0;
}

/* BufferFormatCheck */
static CYTHON_INLINE int __Pyx_IsLittleEndian(void) {
  unsigned int n = 1;
  return *(unsigned char*)(&n) != 0;
}
static void __Pyx_BufFmt_Init(__Pyx_BufFmt_Context* ctx,
                              __Pyx_BufFmt_StackElem* stack,
                              __Pyx_TypeInfo* type) {
  stack[0].field = &ctx->root;
  stack[0].parent_offset = 0;
  ctx->root.type = type;
  ctx->root.name = "buffer dtype";
  ctx->root.offset = 0;
  ctx->head = stack;
  ctx->head->field = &ctx->root;
  ctx->fmt_offset = 0;
  ctx->head->parent_offset = 0;
  ctx->new_packmode = '@';
  ctx->enc_packmode = '@';
  ctx->new_count = 1;
  ctx->enc_count = 0;
  ctx->enc_type = 0;
  ctx->is_complex = 0;
  ctx->is_valid_array = 0;
  ctx->struct_alignment = 0;
  while (type->typegroup == 'S') {
    ++ctx->head;
    ctx->head->field = type->fields;
    ctx->head->parent_offset = 0;
    type = type->fields->type;
  }
}
static int __Pyx_BufFmt_ParseNumber(const char** ts) {
    int count;
    const char* t = *ts;
    if (*t < '0' || *t > '9') {
      return -1;
    } else {
        count = *t++ - '0';
        while (*t >= '0' && *t < '9') {
            count *= 10;
            count += *t++ - '0';
        }
    }
    *ts = t;
    return count;
}
static int __Pyx_BufFmt_ExpectNumber(const char **ts) {
    int number = __Pyx_BufFmt_ParseNumber(ts);
    if (number == -1)
        PyErr_Format(PyExc_ValueError,\
                     "Does not understand character buffer dtype format string ('%c')", **ts);
    return number;
}
static void __Pyx_BufFmt_RaiseUnexpectedChar(char ch) {
  PyErr_Format(PyExc_ValueError,
               "Unexpected format string character: '%c'", ch);
}
static const char* __Pyx_BufFmt_DescribeTypeChar(char ch, int is_complex) {
  switch (ch) {
    case 'c': return "'char'";
    case 'b': return "'signed char'";
    case 'B': return "'unsigned char'";
    case 'h': return "'short'";
    case 'H': return "'unsigned short'";
    case 'i': return "'int'";
    case 'I': return "'unsigned int'";
    case 'l': return "'long'";
    case 'L': return "'unsigned long'";
    case 'q': return "'long long'";
    case 'Q': return "'unsigned long long'";
    case 'f': return (is_complex ? "'complex float'" : "'float'");
    case 'd': return (is_complex ? "'complex double'" : "'double'");
    case 'g': return (is_complex ? "'complex long double'" : "'long double'");
    case 'T': return "a struct";
    case 'O': return "Python object";
    case 'P': return "a pointer";
    case 's': case 'p': return "a string";
    case 0: return "end";
    default: return "unparseable format string";
  }
}
static size_t __Pyx_BufFmt_TypeCharToStandardSize(char ch, int is_complex) {
  switch (ch) {
    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return 2;
    case 'i': case 'I': case 'l': case 'L': return 4;
    case 'q': case 'Q': return 8;
    case 'f': return (is_complex ? 8 : 4);
    case 'd': return (is_complex ? 16 : 8);
    case 'g': {
      PyErr_SetString(PyExc_ValueError, "Python does not define a standard format string size for long double ('g')..");
      return 0;
    }
    case 'O': case 'P': return sizeof(void*);
    default:
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
}
static size_t __Pyx_BufFmt_TypeCharToNativeSize(char ch, int is_complex) {
  switch (ch) {
    case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return sizeof(short);
    case 'i': case 'I': return sizeof(int);
    case 'l': case 'L': return sizeof(long);
    #ifdef HAVE_LONG_LONG
    case 'q': case 'Q': return sizeof(PY_LONG_LONG);
    #endif
    case 'f': return sizeof(float) * (is_complex ? 2 : 1);
    case 'd': return sizeof(double) * (is_complex ? 2 : 1);
    case 'g': return sizeof(long double) * (is_complex ? 2 : 1);
    case 'O': case 'P': return sizeof(void*);
    default: {
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
  }
}
typedef struct { char c; short x; } __Pyx_st_short;
typedef struct { char c; int x; } __Pyx_st_int;
typedef struct { char c; long x; } __Pyx_st_long;
typedef struct { char c; float x; } __Pyx_st_float;
typedef struct { char c; double x; } __Pyx_st_double;
typedef struct { char c; long double x; } __Pyx_st_longdouble;
typedef struct { char c; void *x; } __Pyx_st_void_p;
#ifdef HAVE_LONG_LONG
typedef struct { char c; PY_LONG_LONG x; } __Pyx_st_longlong;
#endif
static size_t __Pyx_BufFmt_TypeCharToAlignment(char ch, CYTHON_UNUSED int is_complex) {
  switch (ch) {
    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return sizeof(__Pyx_st_short) - sizeof(short);
    case 'i': case 'I': return sizeof(__Pyx_st_int) - sizeof(int);
    case 'l': case 'L': return sizeof(__Pyx_st_long) - sizeof(long);
#ifdef HAVE_LONG_LONG
    case 'q': case 'Q': return sizeof(__Pyx_st_longlong) - sizeof(PY_LONG_LONG);
#endif
    case 'f': return sizeof(__Pyx_st_float) - sizeof(float);
    case 'd': return sizeof(__Pyx_st_double) - sizeof(double);
    case 'g': return sizeof(__Pyx_st_longdouble) - sizeof(long double);
    case 'P': case 'O': return sizeof(__Pyx_st_void_p) - sizeof(void*);
    default:
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
}
/* These are for computing the padding at the end of the struct to align
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 */
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;
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}
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');
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        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);
}

/* GetModuleGlobalName */
  static CYTHON_INLINE PyObject *__Pyx_GetModuleGlobalName(PyObject *name) {
    PyObject *result;
#if !CYTHON_AVOID_BORROWED_REFS
    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;
}

/* PyFunctionFastCall */
    #if CYTHON_FAST_PYCALL
#include "frameobject.h"
static PyObject* __Pyx_PyFunction_FastCallNoKw(PyCodeObject *co, PyObject **args, Py_ssize_t na,
                                               PyObject *globals) {
    PyFrameObject *f;
    PyThreadState *tstate = PyThreadState_GET();
    PyObject **fastlocals;
    Py_ssize_t i;
    PyObject *result;
    assert(globals != NULL);
    /* XXX Perhaps we should create a specialized
       PyFrame_New() that doesn't take locals, but does
       take builtins without sanity checking them.
       */
    assert(tstate != NULL);
    f = PyFrame_New(tstate, co, globals, NULL);
    if (f == NULL) {
        return NULL;
    }
    fastlocals = f->f_localsplus;
    for (i = 0; i < na; i++) {
        Py_INCREF(*args);
        fastlocals[i] = *args++;
    }
    result = PyEval_EvalFrameEx(f,0);
    ++tstate->recursion_depth;
    Py_DECREF(f);
    --tstate->recursion_depth;
    return result;
}
#if 1 || PY_VERSION_HEX < 0x030600B1
static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, int nargs, PyObject *kwargs) {
    PyCodeObject *co = (PyCodeObject *)PyFunction_GET_CODE(func);
    PyObject *globals = PyFunction_GET_GLOBALS(func);
    PyObject *argdefs = PyFunction_GET_DEFAULTS(func);
    PyObject *closure;
#if PY_MAJOR_VERSION >= 3
    PyObject *kwdefs;
#endif
    PyObject *kwtuple, **k;
    PyObject **d;
    Py_ssize_t nd;
    Py_ssize_t nk;
    PyObject *result;
    assert(kwargs == NULL || PyDict_Check(kwargs));
    nk = kwargs ? PyDict_Size(kwargs) : 0;
    if (Py_EnterRecursiveCall((char*)" while calling a Python object")) {
        return NULL;
    }
    if (
#if PY_MAJOR_VERSION >= 3
            co->co_kwonlyargcount == 0 &&
#endif
            likely(kwargs == NULL || nk == 0) &&
            co->co_flags == (CO_OPTIMIZED | CO_NEWLOCALS | CO_NOFREE)) {
        if (argdefs == NULL && co->co_argcount == nargs) {
            result = __Pyx_PyFunction_FastCallNoKw(co, args, nargs, globals);
            goto done;
        }
        else if (nargs == 0 && argdefs != NULL
                 && co->co_argcount == Py_SIZE(argdefs)) {
            /* function called with no arguments, but all parameters have
               a default value: use default values as arguments .*/
            args = &PyTuple_GET_ITEM(argdefs, 0);
            result =__Pyx_PyFunction_FastCallNoKw(co, args, Py_SIZE(argdefs), globals);
            goto done;
        }
    }
    if (kwargs != NULL) {
        Py_ssize_t pos, i;
        kwtuple = PyTuple_New(2 * nk);
        if (kwtuple == NULL) {
            result = NULL;
            goto done;
        }
        k = &PyTuple_GET_ITEM(kwtuple, 0);
        pos = i = 0;
        while (PyDict_Next(kwargs, &pos, &k[i], &k[i+1])) {
            Py_INCREF(k[i]);
            Py_INCREF(k[i+1]);
            i += 2;
        }
        nk = i / 2;
    }
    else {
        kwtuple = NULL;
        k = NULL;
    }
    closure = PyFunction_GET_CLOSURE(func);
#if PY_MAJOR_VERSION >= 3
    kwdefs = PyFunction_GET_KW_DEFAULTS(func);
#endif
    if (argdefs != NULL) {
        d = &PyTuple_GET_ITEM(argdefs, 0);
        nd = Py_SIZE(argdefs);
    }
    else {
        d = NULL;
        nd = 0;
    }
#if PY_MAJOR_VERSION >= 3
    result = PyEval_EvalCodeEx((PyObject*)co, globals, (PyObject *)NULL,
                               args, nargs,
                               k, (int)nk,
                               d, (int)nd, kwdefs, closure);
#else
    result = PyEval_EvalCodeEx(co, globals, (PyObject *)NULL,
                               args, nargs,
                               k, (int)nk,
                               d, (int)nd, closure);
#endif
    Py_XDECREF(kwtuple);
done:
    Py_LeaveRecursiveCall();
    return result;
}
#endif  // CPython < 3.6
#endif  // CYTHON_FAST_PYCALL

/* PyCFunctionFastCall */
    #if CYTHON_FAST_PYCCALL
static CYTHON_INLINE PyObject * __Pyx_PyCFunction_FastCall(PyObject *func_obj, PyObject **args, Py_ssize_t nargs) {
    PyCFunctionObject *func = (PyCFunctionObject*)func_obj;
    PyCFunction meth = PyCFunction_GET_FUNCTION(func);
    PyObject *self = PyCFunction_GET_SELF(func);
    assert(PyCFunction_Check(func));
    assert(METH_FASTCALL == (PyCFunction_GET_FLAGS(func) & ~(METH_CLASS | METH_STATIC | METH_COEXIST)));
    assert(nargs >= 0);
    assert(nargs == 0 || args != NULL);
    /* _PyCFunction_FastCallDict() must not be called with an exception set,
       because it may clear it (directly or indirectly) and so the
       caller loses its exception */
    assert(!PyErr_Occurred());
    return (*((__Pyx_PyCFunctionFast)meth)) (self, args, nargs, NULL);
}
#endif  // CYTHON_FAST_PYCCALL

/* PyObjectCall */
    #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

/* RaiseTooManyValuesToUnpack */
    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);
}

/* RaiseNeedMoreValuesToUnpack */
    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");
}

/* IterFinish */
    static CYTHON_INLINE int __Pyx_IterFinish(void) {
#if CYTHON_FAST_THREAD_STATE
    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
}

/* UnpackItemEndCheck */
    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;
}

/* PyErrFetchRestore */
    #if CYTHON_FAST_THREAD_STATE
static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    tmp_type = tstate->curexc_type;
    tmp_value = tstate->curexc_value;
    tmp_tb = tstate->curexc_traceback;
    tstate->curexc_type = type;
    tstate->curexc_value = value;
    tstate->curexc_traceback = tb;
    Py_XDECREF(tmp_type);
    Py_XDECREF(tmp_value);
    Py_XDECREF(tmp_tb);
}
static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
    *type = tstate->curexc_type;
    *value = tstate->curexc_value;
    *tb = tstate->curexc_traceback;
    tstate->curexc_type = 0;
    tstate->curexc_value = 0;
    tstate->curexc_traceback = 0;
}
#endif

/* ExtTypeTest */
    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;
}

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

/* PyFloatBinop */
    #if !CYTHON_COMPILING_IN_PYPY
static PyObject* __Pyx_PyFloat_DivideCObj(PyObject *op1, PyObject *op2, double floatval, CYTHON_UNUSED int inplace) {
    const double a = floatval;
    double b, result;
    if (likely(PyFloat_CheckExact(op2))) {
        b = PyFloat_AS_DOUBLE(op2);
    } else
    #if PY_MAJOR_VERSION < 3
    if (likely(PyInt_CheckExact(op2))) {
        b = (double) PyInt_AS_LONG(op2);
    } else
    #endif
    if (likely(PyLong_CheckExact(op2))) {
        #if CYTHON_USE_PYLONG_INTERNALS
        const digit* digits = ((PyLongObject*)op2)->ob_digit;
        const Py_ssize_t size = Py_SIZE(op2);
        switch (size) {
            case  0: b = 0.0; break;
            case -1: b = -(double) digits[0]; break;
            case  1: b = (double) digits[0]; break;
            case -2:
            case 2:
                if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (1 * PyLong_SHIFT < 53))) {
                    b = (double) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    if ((8 * sizeof(unsigned long) < 53) || (2 * PyLong_SHIFT < 53) || (b < (double) (1L<<53))) {
                        if (size == -2)
                            b = -b;
                        break;
                    }
                }
            case -3:
            case 3:
                if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (2 * PyLong_SHIFT < 53))) {
                    b = (double) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    if ((8 * sizeof(unsigned long) < 53) || (3 * PyLong_SHIFT < 53) || (b < (double) (1L<<53))) {
                        if (size == -3)
                            b = -b;
                        break;
                    }
                }
            case -4:
            case 4:
                if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (3 * PyLong_SHIFT < 53))) {
                    b = (double) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                    if ((8 * sizeof(unsigned long) < 53) || (4 * PyLong_SHIFT < 53) || (b < (double) (1L<<53))) {
                        if (size == -4)
                            b = -b;
                        break;
                    }
                }
            default:
        #else
        {
        #endif
            b = PyLong_AsDouble(op2);
            if (unlikely(b == -1.0 && PyErr_Occurred())) return NULL;
        }
    } else {
        return (inplace ? __Pyx_PyNumber_InPlaceDivide(op1, op2) : __Pyx_PyNumber_Divide(op1, op2));
    }
        PyFPE_START_PROTECT("divide", return NULL)
        result = a / b;
        PyFPE_END_PROTECT(result)
        return PyFloat_FromDouble(result);
}
#endif

/* PyObjectCallMethO */
      #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

/* PyObjectCallOneArg */
      #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) {
#if CYTHON_FAST_PYCALL
    if (PyFunction_Check(func)) {
        return __Pyx_PyFunction_FastCall(func, &arg, 1);
    }
#endif
#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);
#if CYTHON_FAST_PYCCALL
        } else if (PyCFunction_GET_FLAGS(func) & METH_FASTCALL) {
            return __Pyx_PyCFunction_FastCall(func, &arg, 1);
#endif
        }
    }
    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

/* PyObjectCallNoArg */
        #if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func) {
#if CYTHON_FAST_PYCALL
    if (PyFunction_Check(func)) {
        return __Pyx_PyFunction_FastCall(func, NULL, 0);
    }
#endif
#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

/* GetItemInt */
          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_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
    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_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
    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_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS && CYTHON_USE_TYPE_SLOTS
    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))
                        return NULL;
                    PyErr_Clear();
                }
            }
            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));
}

/* RaiseException */
          #if PY_MAJOR_VERSION < 3
static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb,
                        CYTHON_UNUSED PyObject *cause) {
    __Pyx_PyThreadState_declare
    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_PyThreadState_assign
    __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

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

/* SaveResetException */
            #if CYTHON_FAST_THREAD_STATE
static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
    *type = tstate->exc_type;
    *value = tstate->exc_value;
    *tb = tstate->exc_traceback;
    Py_XINCREF(*type);
    Py_XINCREF(*value);
    Py_XINCREF(*tb);
}
static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    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);
}
#endif

/* PyErrExceptionMatches */
            #if CYTHON_FAST_THREAD_STATE
static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err) {
    PyObject *exc_type = tstate->curexc_type;
    if (exc_type == err) return 1;
    if (unlikely(!exc_type)) return 0;
    return PyErr_GivenExceptionMatches(exc_type, err);
}
#endif

/* GetException */
            #if CYTHON_FAST_THREAD_STATE
static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
#else
static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb) {
#endif
    PyObject *local_type, *local_value, *local_tb;
#if CYTHON_FAST_THREAD_STATE
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    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_FAST_THREAD_STATE
    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_FAST_THREAD_STATE
    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;
}

/* SetVTable */
              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;
}

/* GetVTable */
              static void* __Pyx_GetVtable(PyObject *dict) {
    void* ptr;
    PyObject *ob = PyObject_GetItem(dict, __pyx_n_s_pyx_vtable);
    if (!ob)
        goto bad;
#if PY_VERSION_HEX >= 0x02070000
    ptr = PyCapsule_GetPointer(ob, 0);
#else
    ptr = PyCObject_AsVoidPtr(ob);
#endif
    if (!ptr && !PyErr_Occurred())
        PyErr_SetString(PyExc_RuntimeError, "invalid vtable found for imported type");
    Py_DECREF(ob);
    return ptr;
bad:
    Py_XDECREF(ob);
    return NULL;
}

/* Import */
              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;
}

/* ImportFrom */
              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;
}

/* CodeObjectCache */
              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);
}

/* AddTraceback */
              #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;
    __Pyx_PyFrame_SetLineNumber(py_frame, 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


              /* CIntFromPyVerify */
              #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;\
    }

/* CIntToPy */
              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);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
#endif
        }
    } else {
        if (sizeof(int) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
            return PyLong_FromLongLong((PY_LONG_LONG) value);
#endif
        }
    }
    {
        int one = 1; int little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&value;
        return _PyLong_FromByteArray(bytes, sizeof(int),
                                     little, !is_unsigned);
    }
}

/* CIntToPy */
              static CYTHON_INLINE PyObject* __Pyx_PyInt_From_npy_uint32(npy_uint32 value) {
    const npy_uint32 neg_one = (npy_uint32) -1, const_zero = (npy_uint32) 0;
    const int is_unsigned = neg_one > const_zero;
    if (is_unsigned) {
        if (sizeof(npy_uint32) < sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(npy_uint32) <= sizeof(unsigned long)) {
            return PyLong_FromUnsignedLong((unsigned long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(npy_uint32) <= sizeof(unsigned PY_LONG_LONG)) {
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
#endif
        }
    } else {
        if (sizeof(npy_uint32) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(npy_uint32) <= sizeof(PY_LONG_LONG)) {
            return PyLong_FromLongLong((PY_LONG_LONG) value);
#endif
        }
    }
    {
        int one = 1; int little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&value;
        return _PyLong_FromByteArray(bytes, sizeof(npy_uint32),
                                     little, !is_unsigned);
    }
}

/* CIntToPy */
              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);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
#endif
        }
    } else {
        if (sizeof(long) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
            return PyLong_FromLongLong((PY_LONG_LONG) value);
#endif
        }
    }
    {
        int one = 1; int little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&value;
        return _PyLong_FromByteArray(bytes, sizeof(long),
                                     little, !is_unsigned);
    }
}

/* Print */
              #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION < 3
static PyObject *__Pyx_GetStdout(void) {
    PyObject *f = PySys_GetObject((char *)"stdout");
    if (!f) {
        PyErr_SetString(PyExc_RuntimeError, "lost sys.stdout");
    }
    return f;
}
static int __Pyx_Print(PyObject* f, PyObject *arg_tuple, int newline) {
    int i;
    if (!f) {
        if (!(f = __Pyx_GetStdout()))
            return -1;
    }
    Py_INCREF(f);
    for (i=0; i < PyTuple_GET_SIZE(arg_tuple); i++) {
        PyObject* v;
        if (PyFile_SoftSpace(f, 1)) {
            if (PyFile_WriteString(" ", f) < 0)
                goto error;
        }
        v = PyTuple_GET_ITEM(arg_tuple, i);
        if (PyFile_WriteObject(v, f, Py_PRINT_RAW) < 0)
            goto error;
        if (PyString_Check(v)) {
            char *s = PyString_AsString(v);
            Py_ssize_t len = PyString_Size(v);
            if (len > 0) {
                switch (s[len-1]) {
                    case ' ': break;
                    case '\f': case '\r': case '\n': case '\t': case '\v':
                        PyFile_SoftSpace(f, 0);
                        break;
                    default:  break;
                }
            }
        }
    }
    if (newline) {
        if (PyFile_WriteString("\n", f) < 0)
            goto error;
        PyFile_SoftSpace(f, 0);
    }
    Py_DECREF(f);
    return 0;
error:
    Py_DECREF(f);
    return -1;
}
#else
static int __Pyx_Print(PyObject* stream, PyObject *arg_tuple, int newline) {
    PyObject* kwargs = 0;
    PyObject* result = 0;
    PyObject* end_string;
    if (unlikely(!__pyx_print)) {
        __pyx_print = PyObject_GetAttr(__pyx_b, __pyx_n_s_print);
        if (!__pyx_print)
            return -1;
    }
    if (stream) {
        kwargs = PyDict_New();
        if (unlikely(!kwargs))
            return -1;
        if (unlikely(PyDict_SetItem(kwargs, __pyx_n_s_file, stream) < 0))
            goto bad;
        if (!newline) {
            end_string = PyUnicode_FromStringAndSize(" ", 1);
            if (unlikely(!end_string))
                goto bad;
            if (PyDict_SetItem(kwargs, __pyx_n_s_end, end_string) < 0) {
                Py_DECREF(end_string);
                goto bad;
            }
            Py_DECREF(end_string);
        }
    } else if (!newline) {
        if (unlikely(!__pyx_print_kwargs)) {
            __pyx_print_kwargs = PyDict_New();
            if (unlikely(!__pyx_print_kwargs))
                return -1;
            end_string = PyUnicode_FromStringAndSize(" ", 1);
            if (unlikely(!end_string))
                return -1;
            if (PyDict_SetItem(__pyx_print_kwargs, __pyx_n_s_end, end_string) < 0) {
                Py_DECREF(end_string);
                return -1;
            }
            Py_DECREF(end_string);
        }
        kwargs = __pyx_print_kwargs;
    }
    result = PyObject_Call(__pyx_print, arg_tuple, kwargs);
    if (unlikely(kwargs) && (kwargs != __pyx_print_kwargs))
        Py_DECREF(kwargs);
    if (!result)
        return -1;
    Py_DECREF(result);
    return 0;
bad:
    if (kwargs != __pyx_print_kwargs)
        Py_XDECREF(kwargs);
    return -1;
}
#endif

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

/* Declarations */
              #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

/* Arithmetic */
              #if CYTHON_CCOMPLEX
#else
    static CYTHON_INLINE int __Pyx_c_eq_float(__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_sum_float(__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_diff_float(__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_prod_float(__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;
    }
    #if 1
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
        if (b.imag == 0) {
            return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.real);
        } else if (fabsf(b.real) >= fabsf(b.imag)) {
            if (b.real == 0 && b.imag == 0) {
                return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.imag);
            } else {
                float r = b.imag / b.real;
                float s = 1.0 / (b.real + b.imag * r);
                return __pyx_t_float_complex_from_parts(
                    (a.real + a.imag * r) * s, (a.imag - a.real * r) * s);
            }
        } else {
            float r = b.real / b.imag;
            float s = 1.0 / (b.imag + b.real * r);
            return __pyx_t_float_complex_from_parts(
                (a.real * r + a.imag) * s, (a.imag * r - a.real) * s);
        }
    }
    #else
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
        if (b.imag == 0) {
            return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.real);
        } else {
            float denom = b.real * b.real + b.imag * b.imag;
            return __pyx_t_float_complex_from_parts(
                (a.real * b.real + a.imag * b.imag) / denom,
                (a.imag * b.real - a.real * b.imag) / denom);
        }
    }
    #endif
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_neg_float(__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_zero_float(__pyx_t_float_complex a) {
       return (a.real == 0) && (a.imag == 0);
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conj_float(__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_abs_float(__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_pow_float(__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_prod_float(a, a);
                        return __Pyx_c_prod_float(a, a);
                    case 3:
                        z = __Pyx_c_prod_float(a, a);
                        return __Pyx_c_prod_float(z, a);
                    case 4:
                        z = __Pyx_c_prod_float(a, a);
                        return __Pyx_c_prod_float(z, z);
                }
            }
            if (a.imag == 0) {
                if (a.real == 0) {
                    return a;
                } else if (b.imag == 0) {
                    z.real = powf(a.real, b.real);
                    z.imag = 0;
                    return z;
                } else if (a.real > 0) {
                    r = a.real;
                    theta = 0;
                } else {
                    r = -a.real;
                    theta = atan2f(0, -1);
                }
            } else {
                r = __Pyx_c_abs_float(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

/* Declarations */
              #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

/* Arithmetic */
              #if CYTHON_CCOMPLEX
#else
    static CYTHON_INLINE int __Pyx_c_eq_double(__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_double(__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_double(__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_double(__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;
    }
    #if 1
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        if (b.imag == 0) {
            return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real);
        } else if (fabs(b.real) >= fabs(b.imag)) {
            if (b.real == 0 && b.imag == 0) {
                return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.imag);
            } else {
                double r = b.imag / b.real;
                double s = 1.0 / (b.real + b.imag * r);
                return __pyx_t_double_complex_from_parts(
                    (a.real + a.imag * r) * s, (a.imag - a.real * r) * s);
            }
        } else {
            double r = b.real / b.imag;
            double s = 1.0 / (b.imag + b.real * r);
            return __pyx_t_double_complex_from_parts(
                (a.real * r + a.imag) * s, (a.imag * r - a.real) * s);
        }
    }
    #else
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        if (b.imag == 0) {
            return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real);
        } else {
            double denom = b.real * b.real + b.imag * b.imag;
            return __pyx_t_double_complex_from_parts(
                (a.real * b.real + a.imag * b.imag) / denom,
                (a.imag * b.real - a.real * b.imag) / denom);
        }
    }
    #endif
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__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_double(__pyx_t_double_complex a) {
       return (a.real == 0) && (a.imag == 0);
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__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_double(__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_double(__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_double(a, a);
                        return __Pyx_c_prod_double(a, a);
                    case 3:
                        z = __Pyx_c_prod_double(a, a);
                        return __Pyx_c_prod_double(z, a);
                    case 4:
                        z = __Pyx_c_prod_double(a, a);
                        return __Pyx_c_prod_double(z, z);
                }
            }
            if (a.imag == 0) {
                if (a.real == 0) {
                    return a;
                } else if (b.imag == 0) {
                    z.real = pow(a.real, b.real);
                    z.imag = 0;
                    return z;
                } else if (a.real > 0) {
                    r = a.real;
                    theta = 0;
                } else {
                    r = -a.real;
                    theta = atan2(0, -1);
                }
            } else {
                r = __Pyx_c_abs_double(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

/* CIntToPy */
              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);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(enum NPY_TYPES) <= sizeof(unsigned PY_LONG_LONG)) {
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
#endif
        }
    } else {
        if (sizeof(enum NPY_TYPES) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(enum NPY_TYPES) <= sizeof(PY_LONG_LONG)) {
            return PyLong_FromLongLong((PY_LONG_LONG) value);
#endif
        }
    }
    {
        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);
    }
}

/* CIntFromPy */
              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))
#ifdef HAVE_LONG_LONG
            } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
#endif
            }
        } 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) (-(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))
#ifdef HAVE_LONG_LONG
            } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(int, PY_LONG_LONG, PyLong_AsLongLong(x))
#endif
            }
        }
        {
#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_IntOrLong(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_IntOrLong(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;
}

/* CIntFromPy */
              static CYTHON_INLINE npy_uint32 __Pyx_PyInt_As_npy_uint32(PyObject *x) {
    const npy_uint32 neg_one = (npy_uint32) -1, const_zero = (npy_uint32) 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_MAJOR_VERSION < 3
    if (likely(PyInt_Check(x))) {
        if (sizeof(npy_uint32) < sizeof(long)) {
            __PYX_VERIFY_RETURN_INT(npy_uint32, long, PyInt_AS_LONG(x))
        } else {
            long val = PyInt_AS_LONG(x);
            if (is_unsigned && unlikely(val < 0)) {
                goto raise_neg_overflow;
            }
            return (npy_uint32) 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_uint32) 0;
                case  1: __PYX_VERIFY_RETURN_INT(npy_uint32, digit, digits[0])
                case 2:
                    if (8 * sizeof(npy_uint32) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(npy_uint32, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(npy_uint32) >= 2 * PyLong_SHIFT) {
                            return (npy_uint32) (((((npy_uint32)digits[1]) << PyLong_SHIFT) | (npy_uint32)digits[0]));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(npy_uint32) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(npy_uint32, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(npy_uint32) >= 3 * PyLong_SHIFT) {
                            return (npy_uint32) (((((((npy_uint32)digits[2]) << PyLong_SHIFT) | (npy_uint32)digits[1]) << PyLong_SHIFT) | (npy_uint32)digits[0]));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(npy_uint32) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(npy_uint32, 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_uint32) >= 4 * PyLong_SHIFT) {
                            return (npy_uint32) (((((((((npy_uint32)digits[3]) << PyLong_SHIFT) | (npy_uint32)digits[2]) << PyLong_SHIFT) | (npy_uint32)digits[1]) << PyLong_SHIFT) | (npy_uint32)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_uint32) -1;
                if (unlikely(result == 1))
                    goto raise_neg_overflow;
            }
#endif
            if (sizeof(npy_uint32) <= sizeof(unsigned long)) {
                __PYX_VERIFY_RETURN_INT_EXC(npy_uint32, unsigned long, PyLong_AsUnsignedLong(x))
#ifdef HAVE_LONG_LONG
            } else if (sizeof(npy_uint32) <= sizeof(unsigned PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(npy_uint32, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
#endif
            }
        } else {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (npy_uint32) 0;
                case -1: __PYX_VERIFY_RETURN_INT(npy_uint32, sdigit, (sdigit) (-(sdigit)digits[0]))
                case  1: __PYX_VERIFY_RETURN_INT(npy_uint32,  digit, +digits[0])
                case -2:
                    if (8 * sizeof(npy_uint32) - 1 > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(npy_uint32, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(npy_uint32) - 1 > 2 * PyLong_SHIFT) {
                            return (npy_uint32) (((npy_uint32)-1)*(((((npy_uint32)digits[1]) << PyLong_SHIFT) | (npy_uint32)digits[0])));
                        }
                    }
                    break;
                case 2:
                    if (8 * sizeof(npy_uint32) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(npy_uint32, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(npy_uint32) - 1 > 2 * PyLong_SHIFT) {
                            return (npy_uint32) ((((((npy_uint32)digits[1]) << PyLong_SHIFT) | (npy_uint32)digits[0])));
                        }
                    }
                    break;
                case -3:
                    if (8 * sizeof(npy_uint32) - 1 > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(npy_uint32, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(npy_uint32) - 1 > 3 * PyLong_SHIFT) {
                            return (npy_uint32) (((npy_uint32)-1)*(((((((npy_uint32)digits[2]) << PyLong_SHIFT) | (npy_uint32)digits[1]) << PyLong_SHIFT) | (npy_uint32)digits[0])));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(npy_uint32) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(npy_uint32, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(npy_uint32) - 1 > 3 * PyLong_SHIFT) {
                            return (npy_uint32) ((((((((npy_uint32)digits[2]) << PyLong_SHIFT) | (npy_uint32)digits[1]) << PyLong_SHIFT) | (npy_uint32)digits[0])));
                        }
                    }
                    break;
                case -4:
                    if (8 * sizeof(npy_uint32) - 1 > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(npy_uint32, 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_uint32) - 1 > 4 * PyLong_SHIFT) {
                            return (npy_uint32) (((npy_uint32)-1)*(((((((((npy_uint32)digits[3]) << PyLong_SHIFT) | (npy_uint32)digits[2]) << PyLong_SHIFT) | (npy_uint32)digits[1]) << PyLong_SHIFT) | (npy_uint32)digits[0])));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(npy_uint32) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(npy_uint32, 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_uint32) - 1 > 4 * PyLong_SHIFT) {
                            return (npy_uint32) ((((((((((npy_uint32)digits[3]) << PyLong_SHIFT) | (npy_uint32)digits[2]) << PyLong_SHIFT) | (npy_uint32)digits[1]) << PyLong_SHIFT) | (npy_uint32)digits[0])));
                        }
                    }
                    break;
            }
#endif
            if (sizeof(npy_uint32) <= sizeof(long)) {
                __PYX_VERIFY_RETURN_INT_EXC(npy_uint32, long, PyLong_AsLong(x))
#ifdef HAVE_LONG_LONG
            } else if (sizeof(npy_uint32) <= sizeof(PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(npy_uint32, PY_LONG_LONG, PyLong_AsLongLong(x))
#endif
            }
        }
        {
#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
            PyErr_SetString(PyExc_RuntimeError,
                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
#else
            npy_uint32 val;
            PyObject *v = __Pyx_PyNumber_IntOrLong(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_uint32) -1;
        }
    } else {
        npy_uint32 val;
        PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
        if (!tmp) return (npy_uint32) -1;
        val = __Pyx_PyInt_As_npy_uint32(tmp);
        Py_DECREF(tmp);
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to npy_uint32");
    return (npy_uint32) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to npy_uint32");
    return (npy_uint32) -1;
}

/* CIntFromPy */
              static CYTHON_INLINE unsigned int __Pyx_PyInt_As_unsigned_int(PyObject *x) {
    const unsigned int neg_one = (unsigned int) -1, const_zero = (unsigned int) 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_MAJOR_VERSION < 3
    if (likely(PyInt_Check(x))) {
        if (sizeof(unsigned int) < sizeof(long)) {
            __PYX_VERIFY_RETURN_INT(unsigned int, long, PyInt_AS_LONG(x))
        } else {
            long val = PyInt_AS_LONG(x);
            if (is_unsigned && unlikely(val < 0)) {
                goto raise_neg_overflow;
            }
            return (unsigned 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 (unsigned int) 0;
                case  1: __PYX_VERIFY_RETURN_INT(unsigned int, digit, digits[0])
                case 2:
                    if (8 * sizeof(unsigned int) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(unsigned int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(unsigned int) >= 2 * PyLong_SHIFT) {
                            return (unsigned int) (((((unsigned int)digits[1]) << PyLong_SHIFT) | (unsigned int)digits[0]));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(unsigned int) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(unsigned int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(unsigned int) >= 3 * PyLong_SHIFT) {
                            return (unsigned int) (((((((unsigned int)digits[2]) << PyLong_SHIFT) | (unsigned int)digits[1]) << PyLong_SHIFT) | (unsigned int)digits[0]));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(unsigned int) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(unsigned 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(unsigned int) >= 4 * PyLong_SHIFT) {
                            return (unsigned int) (((((((((unsigned int)digits[3]) << PyLong_SHIFT) | (unsigned int)digits[2]) << PyLong_SHIFT) | (unsigned int)digits[1]) << PyLong_SHIFT) | (unsigned 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 (unsigned int) -1;
                if (unlikely(result == 1))
                    goto raise_neg_overflow;
            }
#endif
            if (sizeof(unsigned int) <= sizeof(unsigned long)) {
                __PYX_VERIFY_RETURN_INT_EXC(unsigned int, unsigned long, PyLong_AsUnsignedLong(x))
#ifdef HAVE_LONG_LONG
            } else if (sizeof(unsigned int) <= sizeof(unsigned PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(unsigned int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
#endif
            }
        } else {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (unsigned int) 0;
                case -1: __PYX_VERIFY_RETURN_INT(unsigned int, sdigit, (sdigit) (-(sdigit)digits[0]))
                case  1: __PYX_VERIFY_RETURN_INT(unsigned int,  digit, +digits[0])
                case -2:
                    if (8 * sizeof(unsigned int) - 1 > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(unsigned int, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(unsigned int) - 1 > 2 * PyLong_SHIFT) {
                            return (unsigned int) (((unsigned int)-1)*(((((unsigned int)digits[1]) << PyLong_SHIFT) | (unsigned int)digits[0])));
                        }
                    }
                    break;
                case 2:
                    if (8 * sizeof(unsigned int) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(unsigned int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(unsigned int) - 1 > 2 * PyLong_SHIFT) {
                            return (unsigned int) ((((((unsigned int)digits[1]) << PyLong_SHIFT) | (unsigned int)digits[0])));
                        }
                    }
                    break;
                case -3:
                    if (8 * sizeof(unsigned int) - 1 > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(unsigned int, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(unsigned int) - 1 > 3 * PyLong_SHIFT) {
                            return (unsigned int) (((unsigned int)-1)*(((((((unsigned int)digits[2]) << PyLong_SHIFT) | (unsigned int)digits[1]) << PyLong_SHIFT) | (unsigned int)digits[0])));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(unsigned int) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(unsigned int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(unsigned int) - 1 > 3 * PyLong_SHIFT) {
                            return (unsigned int) ((((((((unsigned int)digits[2]) << PyLong_SHIFT) | (unsigned int)digits[1]) << PyLong_SHIFT) | (unsigned int)digits[0])));
                        }
                    }
                    break;
                case -4:
                    if (8 * sizeof(unsigned int) - 1 > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(unsigned 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(unsigned int) - 1 > 4 * PyLong_SHIFT) {
                            return (unsigned int) (((unsigned int)-1)*(((((((((unsigned int)digits[3]) << PyLong_SHIFT) | (unsigned int)digits[2]) << PyLong_SHIFT) | (unsigned int)digits[1]) << PyLong_SHIFT) | (unsigned int)digits[0])));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(unsigned int) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(unsigned 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(unsigned int) - 1 > 4 * PyLong_SHIFT) {
                            return (unsigned int) ((((((((((unsigned int)digits[3]) << PyLong_SHIFT) | (unsigned int)digits[2]) << PyLong_SHIFT) | (unsigned int)digits[1]) << PyLong_SHIFT) | (unsigned int)digits[0])));
                        }
                    }
                    break;
            }
#endif
            if (sizeof(unsigned int) <= sizeof(long)) {
                __PYX_VERIFY_RETURN_INT_EXC(unsigned int, long, PyLong_AsLong(x))
#ifdef HAVE_LONG_LONG
            } else if (sizeof(unsigned int) <= sizeof(PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(unsigned int, PY_LONG_LONG, PyLong_AsLongLong(x))
#endif
            }
        }
        {
#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
            PyErr_SetString(PyExc_RuntimeError,
                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
#else
            unsigned int val;
            PyObject *v = __Pyx_PyNumber_IntOrLong(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 (unsigned int) -1;
        }
    } else {
        unsigned int val;
        PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
        if (!tmp) return (unsigned int) -1;
        val = __Pyx_PyInt_As_unsigned_int(tmp);
        Py_DECREF(tmp);
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to unsigned int");
    return (unsigned int) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to unsigned int");
    return (unsigned int) -1;
}

/* PrintOne */
              #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION < 3
static int __Pyx_PrintOne(PyObject* f, PyObject *o) {
    if (!f) {
        if (!(f = __Pyx_GetStdout()))
            return -1;
    }
    Py_INCREF(f);
    if (PyFile_SoftSpace(f, 0)) {
        if (PyFile_WriteString(" ", f) < 0)
            goto error;
    }
    if (PyFile_WriteObject(o, f, Py_PRINT_RAW) < 0)
        goto error;
    if (PyFile_WriteString("\n", f) < 0)
        goto error;
    Py_DECREF(f);
    return 0;
error:
    Py_DECREF(f);
    return -1;
    /* the line below is just to avoid C compiler
     * warnings about unused functions */
    return __Pyx_Print(f, NULL, 0);
}
#else
static int __Pyx_PrintOne(PyObject* stream, PyObject *o) {
    int res;
    PyObject* arg_tuple = PyTuple_Pack(1, o);
    if (unlikely(!arg_tuple))
        return -1;
    res = __Pyx_Print(stream, arg_tuple, 1);
    Py_DECREF(arg_tuple);
    return res;
}
#endif

/* CIntFromPy */
              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))
#ifdef HAVE_LONG_LONG
            } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(long, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
#endif
            }
        } 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) (-(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))
#ifdef HAVE_LONG_LONG
            } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(long, PY_LONG_LONG, PyLong_AsLongLong(x))
#endif
            }
        }
        {
#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_IntOrLong(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_IntOrLong(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;
}

/* CheckBinaryVersion */
              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;
}

/* ModuleImport */
              #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

/* TypeImport */
              #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. Expected %zd, got %zd",
            module_name, class_name, basicsize, size);
        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. Expected %zd, got %zd",
            module_name, class_name, basicsize, size);
        goto bad;
    }
    return (PyTypeObject *)result;
bad:
    Py_XDECREF(py_module);
    Py_XDECREF(result);
    return NULL;
}
#endif

/* InitStrings */
              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_IntOrLong(PyObject* x) {
#if CYTHON_USE_TYPE_SLOTS
  PyNumberMethods *m;
#endif
  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);
#if CYTHON_USE_TYPE_SLOTS
  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
#else
  res = PyNumber_Int(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 */
