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/* BEGIN: Cython Metadata
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END: Cython Metadata */

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#ifndef __Pyx_PyAsyncMethodsStruct
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#define __PYX_HAVE__sklearn__linear_model__sag_fast
#define __PYX_HAVE_API__sklearn__linear_model__sag_fast
/* Early includes */
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#include "numpy/arrayobject.h"
#include "numpy/ufuncobject.h"
#include <math.h>
#include <stddef.h>
#include <time.h>
#include "sgd_fast_helpers.h"
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#if defined(PYREX_WITHOUT_ASSERTIONS) && !defined(CYTHON_WITHOUT_ASSERTIONS)
#define CYTHON_WITHOUT_ASSERTIONS
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typedef struct {PyObject **p; const char *s; const Py_ssize_t n; const char* encoding;
                const char is_unicode; const char is_str; const char intern; } __Pyx_StringTabEntry;

#define __PYX_DEFAULT_STRING_ENCODING_IS_ASCII 0
#define __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT 0
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#define __Pyx_PyObject_FromString __Pyx_PyBytes_FromString
#define __Pyx_PyObject_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
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#define __Pyx_long_cast(x) ((long)x)
#define __Pyx_fits_Py_ssize_t(v, type, is_signed)  (\
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#if defined (__cplusplus) && __cplusplus >= 201103L
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static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject*);
static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject*, Py_ssize_t* length);
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#define __Pyx_PyByteArray_FromStringAndSize(s, l) PyByteArray_FromStringAndSize((const char*)s, l)
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#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
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    #define __Pyx_PyStr_FromString        __Pyx_PyUnicode_FromString
    #define __Pyx_PyStr_FromStringAndSize __Pyx_PyUnicode_FromStringAndSize
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#define __Pyx_PyBytes_AsWritableString(s)     ((char*) PyBytes_AS_STRING(s))
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#define __Pyx_PyBytes_AsWritableUString(s)    ((unsigned char*) PyBytes_AS_STRING(s))
#define __Pyx_PyBytes_AsString(s)     ((const char*) PyBytes_AS_STRING(s))
#define __Pyx_PyBytes_AsSString(s)    ((const signed char*) PyBytes_AS_STRING(s))
#define __Pyx_PyBytes_AsUString(s)    ((const unsigned char*) PyBytes_AS_STRING(s))
#define __Pyx_PyObject_AsWritableString(s)    ((char*) __Pyx_PyObject_AsString(s))
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#define __Pyx_PyObject_AsWritableUString(s)    ((unsigned char*) __Pyx_PyObject_AsString(s))
#define __Pyx_PyObject_AsSString(s)    ((const signed char*) __Pyx_PyObject_AsString(s))
#define __Pyx_PyObject_AsUString(s)    ((const 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)
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static CYTHON_INLINE size_t __Pyx_Py_UNICODE_strlen(const Py_UNICODE *u) {
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}
#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)
static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b);
static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*);
static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x);
#define __Pyx_PySequence_Tuple(obj)\
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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))
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#define __pyx_PyFloat_AsDouble(x) PyFloat_AsDouble(x)
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#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))
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#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;
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        ascii_chars_u = PyUnicode_DecodeASCII(ascii_chars, 128, NULL);
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            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;
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        Py_DECREF(ascii_chars_u);
        Py_DECREF(ascii_chars_b);
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bad:
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#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) {
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    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;
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    return 0;
bad:
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/* Test for GCC > 2.95 */
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#endif /* __GNUC__ */
static CYTHON_INLINE void __Pyx_pretend_to_initialize(void* ptr) { (void)ptr; }

static PyObject *__pyx_m = NULL;
static PyObject *__pyx_d;
static PyObject *__pyx_b;
static PyObject *__pyx_cython_runtime = NULL;
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)
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    #define CYTHON_CCOMPLEX 1
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#endif
#if CYTHON_CCOMPLEX
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#endif
#if CYTHON_CCOMPLEX && !defined(__cplusplus) && defined(__sun__) && defined(__GNUC__)
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  #define _Complex_I 1.0fj
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static const char *__pyx_f[] = {
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/* BufferFormatStructs.proto */
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struct __Pyx_StructField_;
#define __PYX_BUF_FLAGS_PACKED_STRUCT (1 << 0)
typedef struct {
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typedef struct __Pyx_StructField_ {
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typedef struct {
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typedef struct {
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#define __Pyx_PyGILState_Ensure PyGILState_Ensure
#define __Pyx_PyGILState_Release PyGILState_Release
#define __Pyx_FastGIL_Remember()
#define __Pyx_FastGIL_Forget()
#define __Pyx_FastGilFuncInit()

/* ForceInitThreads.proto */
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/* "../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":730
 * # 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/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":731
 * 
 * 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/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":732
 * ctypedef npy_int8       int8_t
 * ctypedef npy_int16      int16_t
 * ctypedef npy_int32      int32_t             # <<<<<<<<<<<<<<
 * ctypedef npy_int64      int64_t
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typedef npy_int32 __pyx_t_5numpy_int32_t;

/* "../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":733
 * ctypedef npy_int16      int16_t
 * ctypedef npy_int32      int32_t
 * ctypedef npy_int64      int64_t             # <<<<<<<<<<<<<<
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typedef npy_int64 __pyx_t_5numpy_int64_t;

/* "../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":737
 * #ctypedef npy_int128     int128_t
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 * ctypedef npy_uint16     uint16_t
 * ctypedef npy_uint32     uint32_t
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typedef npy_uint8 __pyx_t_5numpy_uint8_t;

/* "../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":738
 * 
 * ctypedef npy_uint8      uint8_t
 * ctypedef npy_uint16     uint16_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uint32     uint32_t
 * ctypedef npy_uint64     uint64_t
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typedef npy_uint16 __pyx_t_5numpy_uint16_t;

/* "../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":739
 * 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/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":740
 * 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/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":744
 * #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/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":745
 * 
 * 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/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":754
 * # 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
 */
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/* "../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":755
 * # 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/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":756
 * 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/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":758
 * 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/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":759
 * 
 * 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/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":760
 * 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/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":762
 * 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/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":763
 * 
 * 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/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":765
 * 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/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":766
 * 
 * ctypedef npy_double     float_t
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typedef npy_double __pyx_t_5numpy_double_t;

/* "../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":767
 * 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 */
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/* Declarations.proto */
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static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double, double);


/*--- Type declarations ---*/
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_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_8sag_fast_MultinomialLogLoss;

/* "../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":769
 * 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/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":770
 * 
 * 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/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":771
 * 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/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":773
 * ctypedef npy_clongdouble clongdouble_t
 * 
 * ctypedef npy_cdouble     complex_t             # <<<<<<<<<<<<<<
 * 
 * cdef inline object PyArray_MultiIterNew1(a):
 */
typedef npy_cdouble __pyx_t_5numpy_complex_t;

/* "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;
};


/* "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;
};


/* "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;
};


/* "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;
};


/* "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;
};


/* "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;
};


/* "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;
};


/* "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/sag_fast.pyx":53
 * 
 * 
 * cdef class MultinomialLogLoss:             # <<<<<<<<<<<<<<
 *     cdef double _loss(self, double* prediction, double y, int n_classes,
 *                       double sample_weight) nogil:
 */
struct __pyx_obj_7sklearn_12linear_model_8sag_fast_MultinomialLogLoss {
  PyObject_HEAD
  struct __pyx_vtabstruct_7sklearn_12linear_model_8sag_fast_MultinomialLogLoss *__pyx_vtab;
};



/* "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_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;


/* "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_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;


/* "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_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;


/* "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_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;


/* "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_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;


/* "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 *);
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  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 *);
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static struct __pyx_vtabstruct_7sklearn_5utils_11seq_dataset_SequentialDataset *__pyx_vtabptr_7sklearn_5utils_11seq_dataset_SequentialDataset;


/* "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;


/* "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/sag_fast.pyx":53
 * 
 * 
 * cdef class MultinomialLogLoss:             # <<<<<<<<<<<<<<
 *     cdef double _loss(self, double* prediction, double y, int n_classes,
 *                       double sample_weight) nogil:
 */

struct __pyx_vtabstruct_7sklearn_12linear_model_8sag_fast_MultinomialLogLoss {
  double (*_loss)(struct __pyx_obj_7sklearn_12linear_model_8sag_fast_MultinomialLogLoss *, double *, double, int, double);
  void (*_dloss)(struct __pyx_obj_7sklearn_12linear_model_8sag_fast_MultinomialLogLoss *, double *, double, int, double, double *);
};
static struct __pyx_vtabstruct_7sklearn_12linear_model_8sag_fast_MultinomialLogLoss *__pyx_vtabptr_7sklearn_12linear_model_8sag_fast_MultinomialLogLoss;

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    #define __Pyx_CREAL(z) ((z).real())
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    #define __Pyx_CREAL(z) (__real__(z))
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    #define __Pyx_CREAL(z) ((z).real)
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    #define __Pyx_SET_CREAL(z,x) __Pyx_CREAL(z) = (x)
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    #define __Pyx_c_eq_float(a, b)   ((a)==(b))
    #define __Pyx_c_sum_float(a, b)  ((a)+(b))
    #define __Pyx_c_diff_float(a, b) ((a)-(b))
    #define __Pyx_c_prod_float(a, b) ((a)*(b))
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    #define __Pyx_c_is_zero_float(z) ((z)==(float)0)
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        #define __Pyx_c_abs_float(z)     (::std::abs(z))
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/* Arithmetic.proto */
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    #define __Pyx_c_eq_double(a, b)   ((a)==(b))
    #define __Pyx_c_sum_double(a, b)  ((a)+(b))
    #define __Pyx_c_diff_double(a, b) ((a)-(b))
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    #define __Pyx_c_is_zero_double(z) ((z)==(double)0)
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    static CYTHON_INLINE int __Pyx_c_eq_double(__pyx_t_double_complex, __pyx_t_double_complex);
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/* CIntToPy.proto */
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/* CIntFromPy.proto */
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/* PrintOne.proto */
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/* FastTypeChecks.proto */
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#define __Pyx_TypeCheck(obj, type) __Pyx_IsSubtype(Py_TYPE(obj), (PyTypeObject *)type)
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static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject *type);
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#define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type)
#define __Pyx_PyErr_GivenExceptionMatches(err, type) PyErr_GivenExceptionMatches(err, type)
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/* ModuleImport.proto */
static PyObject *__Pyx_ImportModule(const char *name);

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

/* InitStrings.proto */
static int __Pyx_InitStrings(__Pyx_StringTabEntry *t);

static double __pyx_f_7sklearn_12linear_model_8sag_fast_18MultinomialLogLoss__loss(CYTHON_UNUSED struct __pyx_obj_7sklearn_12linear_model_8sag_fast_MultinomialLogLoss *__pyx_v_self, double *__pyx_v_prediction, double __pyx_v_y, int __pyx_v_n_classes, double __pyx_v_sample_weight); /* proto*/
static void __pyx_f_7sklearn_12linear_model_8sag_fast_18MultinomialLogLoss__dloss(CYTHON_UNUSED struct __pyx_obj_7sklearn_12linear_model_8sag_fast_MultinomialLogLoss *__pyx_v_self, double *__pyx_v_prediction, double __pyx_v_y, int __pyx_v_n_classes, double __pyx_v_sample_weight, double *__pyx_v_gradient_ptr); /* proto*/

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

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

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

/* Module declarations from '__builtin__' */

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

/* Module declarations from 'cpython' */

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

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

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

/* Module declarations from 'numpy' */

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

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

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

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

/* Module declarations from 'sklearn.linear_model.sgd_fast' */
static PyTypeObject *__pyx_ptype_7sklearn_12linear_model_8sgd_fast_LossFunction = 0;
static PyTypeObject *__pyx_ptype_7sklearn_12linear_model_8sgd_fast_Regression = 0;
static PyTypeObject *__pyx_ptype_7sklearn_12linear_model_8sgd_fast_Classification = 0;
static PyTypeObject *__pyx_ptype_7sklearn_12linear_model_8sgd_fast_Log = 0;
static PyTypeObject *__pyx_ptype_7sklearn_12linear_model_8sgd_fast_SquaredLoss = 0;

/* Module declarations from 'sklearn.utils.seq_dataset' */
static PyTypeObject *__pyx_ptype_7sklearn_5utils_11seq_dataset_SequentialDataset = 0;
static PyTypeObject *__pyx_ptype_7sklearn_5utils_11seq_dataset_ArrayDataset = 0;
static PyTypeObject *__pyx_ptype_7sklearn_5utils_11seq_dataset_CSRDataset = 0;

/* Module declarations from 'sklearn.linear_model.sag_fast' */
static PyTypeObject *__pyx_ptype_7sklearn_12linear_model_8sag_fast_MultinomialLogLoss = 0;
static CYTHON_INLINE double __pyx_f_7sklearn_12linear_model_8sag_fast_fmax(double, double); /*proto*/
static double __pyx_f_7sklearn_12linear_model_8sag_fast__logsumexp(double *, int); /*proto*/
static CYTHON_INLINE double __pyx_f_7sklearn_12linear_model_8sag_fast__soft_thresholding(double, double); /*proto*/
static void __pyx_f_7sklearn_12linear_model_8sag_fast_raise_infinite_error(int); /*proto*/
static double __pyx_f_7sklearn_12linear_model_8sag_fast_scale_weights(double *, double, int, int, int, int, double *, double *, int *, int, double *, int); /*proto*/
static void __pyx_f_7sklearn_12linear_model_8sag_fast_lagged_update(double *, double, int, int, int, int, double *, double *, int *, int, double *, int *, int, int); /*proto*/
static void __pyx_f_7sklearn_12linear_model_8sag_fast_predict_sample(double *, int *, int, double *, double, double *, double *, int); /*proto*/
static __Pyx_TypeInfo __Pyx_TypeInfo_double = { "double", NULL, sizeof(double), { 0 }, 0, 'R', 0, 0 };
static __Pyx_TypeInfo __Pyx_TypeInfo_int = { "bint", NULL, sizeof(int), { 0 }, 0, IS_UNSIGNED(int) ? 'U' : 'I', IS_UNSIGNED(int), 0 };
#define __Pyx_MODULE_NAME "sklearn.linear_model.sag_fast"
extern int __pyx_module_is_main_sklearn__linear_model__sag_fast;
int __pyx_module_is_main_sklearn__linear_model__sag_fast = 0;

/* Implementation of 'sklearn.linear_model.sag_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_i[] = "i";
static const char __pyx_k_j[] = "j";
static const char __pyx_k_y[] = "y";
static const char __pyx_k_np[] = "np";
static const char __pyx_k_end[] = "end";
static const char __pyx_k_idx[] = "idx";
static const char __pyx_k_log[] = "log";
static const char __pyx_k_sag[] = "sag";
static const char __pyx_k_tol[] = "tol";
static const char __pyx_k_val[] = "val";
static const char __pyx_k_beta[] = "beta";
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_prox[] = "prox";
static const char __pyx_k_saga[] = "saga";
static const char __pyx_k_seen[] = "seen";
static const char __pyx_k_test[] = "__test__";
static const char __pyx_k_xnnz[] = "xnnz";
static const char __pyx_k_alpha[] = "alpha";
static const char __pyx_k_dtype[] = "dtype";
static const char __pyx_k_empty[] = "empty";
static const char __pyx_k_f_idx[] = "f_idx";
static const char __pyx_k_int32[] = "int32";
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_s_idx[] = "s_idx";
static const char __pyx_k_zeros[] = "zeros";
static const char __pyx_k_double[] = "double";
static const char __pyx_k_import[] = "__import__";
static const char __pyx_k_n_iter[] = "n_iter";
static const char __pyx_k_wscale[] = "wscale";
static const char __pyx_k_cum_sum[] = "cum_sum";
static const char __pyx_k_dataset[] = "dataset";
static const char __pyx_k_squared[] = "squared";
static const char __pyx_k_verbose[] = "verbose";
static const char __pyx_k_weights[] = "weights";
static const char __pyx_k_end_time[] = "end_time";
static const char __pyx_k_gradient[] = "gradient";
static const char __pyx_k_max_iter[] = "max_iter";
static const char __pyx_k_num_seen[] = "num_seen";
static const char __pyx_k_sum_loss[] = "sum_loss";
static const char __pyx_k_class_ind[] = "class_ind";
static const char __pyx_k_intercept[] = "intercept";
static const char __pyx_k_multiloss[] = "multiloss";
static const char __pyx_k_n_classes[] = "n_classes";
static const char __pyx_k_n_samples[] = "n_samples";
static const char __pyx_k_rescaling[] = "rescaling...";
static const char __pyx_k_seen_init[] = "seen_init";
static const char __pyx_k_step_size[] = "step_size";
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_prediction[] = "prediction";
static const char __pyx_k_pyx_vtable[] = "__pyx_vtable__";
static const char __pyx_k_sample_ind[] = "sample_ind";
static const char __pyx_k_sample_itr[] = "sample_itr";
static const char __pyx_k_start_time[] = "start_time";
static const char __pyx_k_x_data_ptr[] = "x_data_ptr";
static const char __pyx_k_ImportError[] = "ImportError";
static const char __pyx_k_feature_ind[] = "feature_ind";
static const char __pyx_k_multinomial[] = "multinomial";
static const char __pyx_k_RuntimeError[] = "RuntimeError";
static const char __pyx_k_feature_hist[] = "feature_hist";
static const char __pyx_k_sum_gradient[] = "sum_gradient";
static const char __pyx_k_fit_intercept[] = "fit_intercept";
static const char __pyx_k_loss_function[] = "loss_function";
static const char __pyx_k_sample_weight[] = "sample_weight";
static const char __pyx_k_weights_array[] = "weights_array";
static const char __pyx_k_wscale_update[] = "wscale_update";
static const char __pyx_k_gradient_array[] = "gradient_array";
static const char __pyx_k_cumulative_sums[] = "cumulative_sums";
static const char __pyx_k_gradient_memory[] = "gradient_memory";
static const char __pyx_k_intercept_array[] = "intercept_array";
static const char __pyx_k_intercept_decay[] = "intercept_decay";
static const char __pyx_k_prediction_array[] = "prediction_array";
static const char __pyx_k_previous_weights[] = "previous_weights";
static const char __pyx_k_sum_gradient_init[] = "sum_gradient_init";
static const char __pyx_k_cline_in_traceback[] = "cline_in_traceback";
static const char __pyx_k_feature_hist_array[] = "feature_hist_array";
static const char __pyx_k_sum_gradient_array[] = "sum_gradient_array";
static const char __pyx_k_gradient_correction[] = "gradient_correction";
static const char __pyx_k_cumulative_sums_prox[] = "cumulative_sums_prox";
static const char __pyx_k_gradient_memory_init[] = "gradient_memory_init";
static const char __pyx_k_cumulative_sums_array[] = "cumulative_sums_array";
static const char __pyx_k_intercept_sum_gradient[] = "intercept_sum_gradient";
static const char __pyx_k_previous_weights_array[] = "previous_weights_array";
static const char __pyx_k_cumulative_sums_prox_array[] = "cumulative_sums_prox_array";
static const char __pyx_k_intercept_sum_gradient_init[] = "intercept_sum_gradient_init";
static const char __pyx_k_ndarray_is_not_C_contiguous[] = "ndarray is not C contiguous";
static const char __pyx_k_sklearn_linear_model_sag_fast[] = "sklearn.linear_model.sag_fast";
static const char __pyx_k_convergence_after_d_epochs_took[] = "convergence after %d epochs took %d seconds";
static const char __pyx_k_multinomial_grad_loss_all_sampl[] = "_multinomial_grad_loss_all_samples";
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. Lowering the step_size or scaling the 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_Invalid_loss_parameter_got_s_ins[] = "Invalid loss parameter: got %s instead of one of ('log', 'squared', 'multinomial')";
static const char __pyx_k_Non_native_byte_order_not_suppor[] = "Non-native byte order not supported";
static const char __pyx_k_max_iter_reached_after_d_seconds[] = "max_iter reached after %d seconds";
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_sklearn_linear_model_sag_fast_py[] = "sklearn/linear_model/sag_fast.pyx";
static const char __pyx_k_Format_string_allocated_too_shor_2[] = "Format string allocated too short.";
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_kp_s_Invalid_loss_parameter_got_s_ins;
static PyObject *__pyx_kp_u_Non_native_byte_order_not_suppor;
static PyObject *__pyx_n_s_RuntimeError;
static PyObject *__pyx_n_s_ValueError;
static PyObject *__pyx_n_s_alpha;
static PyObject *__pyx_n_s_beta;
static PyObject *__pyx_n_s_c;
static PyObject *__pyx_n_s_class_ind;
static PyObject *__pyx_n_s_cline_in_traceback;
static PyObject *__pyx_kp_s_convergence_after_d_epochs_took;
static PyObject *__pyx_n_s_cum_sum;
static PyObject *__pyx_n_s_cumulative_sums;
static PyObject *__pyx_n_s_cumulative_sums_array;
static PyObject *__pyx_n_s_cumulative_sums_prox;
static PyObject *__pyx_n_s_cumulative_sums_prox_array;
static PyObject *__pyx_n_s_dataset;
static PyObject *__pyx_n_s_double;
static PyObject *__pyx_n_s_dtype;
static PyObject *__pyx_n_s_empty;
static PyObject *__pyx_n_s_end;
static PyObject *__pyx_n_s_end_time;
static PyObject *__pyx_n_s_f_idx;
static PyObject *__pyx_n_s_feature_hist;
static PyObject *__pyx_n_s_feature_hist_array;
static PyObject *__pyx_n_s_feature_ind;
static PyObject *__pyx_n_s_file;
static PyObject *__pyx_n_s_fit_intercept;
static PyObject *__pyx_n_s_gradient;
static PyObject *__pyx_n_s_gradient_array;
static PyObject *__pyx_n_s_gradient_correction;
static PyObject *__pyx_n_s_gradient_memory;
static PyObject *__pyx_n_s_gradient_memory_init;
static PyObject *__pyx_n_s_i;
static PyObject *__pyx_n_s_idx;
static PyObject *__pyx_n_s_import;
static PyObject *__pyx_n_s_int32;
static PyObject *__pyx_n_s_intercept;
static PyObject *__pyx_n_s_intercept_array;
static PyObject *__pyx_n_s_intercept_decay;
static PyObject *__pyx_n_s_intercept_sum_gradient;
static PyObject *__pyx_n_s_intercept_sum_gradient_init;
static PyObject *__pyx_n_s_j;
static PyObject *__pyx_n_s_log;
static PyObject *__pyx_n_s_loss;
static PyObject *__pyx_n_s_loss_function;
static PyObject *__pyx_n_s_main;
static PyObject *__pyx_n_s_max_change;
static PyObject *__pyx_n_s_max_iter;
static PyObject *__pyx_kp_s_max_iter_reached_after_d_seconds;
static PyObject *__pyx_n_s_max_weight;
static PyObject *__pyx_n_s_multiloss;
static PyObject *__pyx_n_s_multinomial;
static PyObject *__pyx_n_s_multinomial_grad_loss_all_sampl;
static PyObject *__pyx_n_s_n_classes;
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_np;
static PyObject *__pyx_n_s_num_seen;
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_order;
static PyObject *__pyx_n_s_prediction;
static PyObject *__pyx_n_s_prediction_array;
static PyObject *__pyx_n_s_previous_weights;
static PyObject *__pyx_n_s_previous_weights_array;
static PyObject *__pyx_n_s_print;
static PyObject *__pyx_n_s_prox;
static PyObject *__pyx_n_s_pyx_vtable;
static PyObject *__pyx_n_s_range;
static PyObject *__pyx_kp_s_rescaling;
static PyObject *__pyx_n_s_s_idx;
static PyObject *__pyx_n_s_sag;
static PyObject *__pyx_n_s_saga;
static PyObject *__pyx_n_s_sample_ind;
static PyObject *__pyx_n_s_sample_itr;
static PyObject *__pyx_n_s_sample_weight;
static PyObject *__pyx_n_s_seen;
static PyObject *__pyx_n_s_seen_init;
static PyObject *__pyx_n_s_sklearn_linear_model_sag_fast;
static PyObject *__pyx_kp_s_sklearn_linear_model_sag_fast_py;
static PyObject *__pyx_n_s_squared;
static PyObject *__pyx_n_s_start_time;
static PyObject *__pyx_n_s_step_size;
static PyObject *__pyx_n_s_sum_gradient;
static PyObject *__pyx_n_s_sum_gradient_array;
static PyObject *__pyx_n_s_sum_gradient_init;
static PyObject *__pyx_n_s_sum_loss;
static PyObject *__pyx_n_s_test;
static PyObject *__pyx_n_s_tol;
static PyObject *__pyx_kp_u_unknown_dtype_code_in_numpy_pxd;
static PyObject *__pyx_n_s_val;
static PyObject *__pyx_n_s_verbose;
static PyObject *__pyx_n_s_weights;
static PyObject *__pyx_n_s_weights_array;
static PyObject *__pyx_n_s_wscale;
static PyObject *__pyx_n_s_wscale_update;
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_8sag_fast_18MultinomialLogLoss___reduce__(CYTHON_UNUSED struct __pyx_obj_7sklearn_12linear_model_8sag_fast_MultinomialLogLoss *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_7sklearn_12linear_model_8sag_fast__multinomial_grad_loss_all_samples(CYTHON_UNUSED PyObject *__pyx_self, struct __pyx_obj_7sklearn_5utils_11seq_dataset_SequentialDataset *__pyx_v_dataset, PyArrayObject *__pyx_v_weights_array, PyArrayObject *__pyx_v_intercept_array, int __pyx_v_n_samples, int __pyx_v_n_features, int __pyx_v_n_classes); /* proto */
static PyObject *__pyx_pf_7sklearn_12linear_model_8sag_fast_2sag(CYTHON_UNUSED PyObject *__pyx_self, struct __pyx_obj_7sklearn_5utils_11seq_dataset_SequentialDataset *__pyx_v_dataset, PyArrayObject *__pyx_v_weights_array, PyArrayObject *__pyx_v_intercept_array, int __pyx_v_n_samples, int __pyx_v_n_features, int __pyx_v_n_classes, double __pyx_v_tol, int __pyx_v_max_iter, PyObject *__pyx_v_loss_function, double __pyx_v_step_size, double __pyx_v_alpha, double __pyx_v_beta, PyArrayObject *__pyx_v_sum_gradient_init, PyArrayObject *__pyx_v_gradient_memory_init, PyArrayObject *__pyx_v_seen_init, int __pyx_v_num_seen, int __pyx_v_fit_intercept, PyArrayObject *__pyx_v_intercept_sum_gradient_init, double __pyx_v_intercept_decay, int __pyx_v_saga, int __pyx_v_verbose); /* 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_8sag_fast_MultinomialLogLoss(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tuple_;
static PyObject *__pyx_tuple__2;
static PyObject *__pyx_tuple__3;
static PyObject *__pyx_tuple__4;
static PyObject *__pyx_tuple__5;
static PyObject *__pyx_tuple__6;
static PyObject *__pyx_tuple__7;
static PyObject *__pyx_tuple__8;
static PyObject *__pyx_tuple__9;
static PyObject *__pyx_tuple__10;
static PyObject *__pyx_tuple__12;
static PyObject *__pyx_codeobj__11;
static PyObject *__pyx_codeobj__13;
/* Late includes */

/* "sklearn/linear_model/sag_fast.pyx":25
 * 
 * 
 * cdef inline double fmax(double x, double y) nogil:             # <<<<<<<<<<<<<<
 *     if x > y:
 *         return x
 */

static CYTHON_INLINE double __pyx_f_7sklearn_12linear_model_8sag_fast_fmax(double __pyx_v_x, double __pyx_v_y) {
  double __pyx_r;
  int __pyx_t_1;

  /* "sklearn/linear_model/sag_fast.pyx":26
 * 
 * cdef inline double fmax(double x, double y) nogil:
 *     if x > y:             # <<<<<<<<<<<<<<
 *         return x
 *     return y
 */
  __pyx_t_1 = ((__pyx_v_x > __pyx_v_y) != 0);
  if (__pyx_t_1) {

    /* "sklearn/linear_model/sag_fast.pyx":27
 * cdef inline double fmax(double x, double y) nogil:
 *     if x > y:
 *         return x             # <<<<<<<<<<<<<<
 *     return y
 * 
 */
    __pyx_r = __pyx_v_x;
    goto __pyx_L0;

    /* "sklearn/linear_model/sag_fast.pyx":26
 * 
 * cdef inline double fmax(double x, double y) nogil:
 *     if x > y:             # <<<<<<<<<<<<<<
 *         return x
 *     return y
 */
  }

  /* "sklearn/linear_model/sag_fast.pyx":28
 *     if x > y:
 *         return x
 *     return y             # <<<<<<<<<<<<<<
 * 
 * 
 */
  __pyx_r = __pyx_v_y;
  goto __pyx_L0;

  /* "sklearn/linear_model/sag_fast.pyx":25
 * 
 * 
 * cdef inline double fmax(double x, double y) nogil:             # <<<<<<<<<<<<<<
 *     if x > y:
 *         return x
 */

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

/* "sklearn/linear_model/sag_fast.pyx":31
 * 
 * 
 * cdef double _logsumexp(double* arr, int n_classes) nogil:             # <<<<<<<<<<<<<<
 *     """Computes the sum of arr assuming arr is in the log domain.
 * 
 */

static double __pyx_f_7sklearn_12linear_model_8sag_fast__logsumexp(double *__pyx_v_arr, int __pyx_v_n_classes) {
  double __pyx_v_vmax;
  double __pyx_v_out;
  int __pyx_v_i;
  double __pyx_r;
  int __pyx_t_1;
  int __pyx_t_2;
  int __pyx_t_3;
  int __pyx_t_4;

  /* "sklearn/linear_model/sag_fast.pyx":39
 *     # Use the max to normalize, as with the log this is what accumulates
 *     # the less errors
 *     cdef double vmax = arr[0]             # <<<<<<<<<<<<<<
 *     cdef double out = 0.0
 *     cdef int i
 */
  __pyx_v_vmax = (__pyx_v_arr[0]);

  /* "sklearn/linear_model/sag_fast.pyx":40
 *     # the less errors
 *     cdef double vmax = arr[0]
 *     cdef double out = 0.0             # <<<<<<<<<<<<<<
 *     cdef int i
 * 
 */
  __pyx_v_out = 0.0;

  /* "sklearn/linear_model/sag_fast.pyx":43
 *     cdef int i
 * 
 *     for i in range(1, n_classes):             # <<<<<<<<<<<<<<
 *         if vmax < arr[i]:
 *             vmax = arr[i]
 */
  __pyx_t_1 = __pyx_v_n_classes;
  __pyx_t_2 = __pyx_t_1;
  for (__pyx_t_3 = 1; __pyx_t_3 < __pyx_t_2; __pyx_t_3+=1) {
    __pyx_v_i = __pyx_t_3;

    /* "sklearn/linear_model/sag_fast.pyx":44
 * 
 *     for i in range(1, n_classes):
 *         if vmax < arr[i]:             # <<<<<<<<<<<<<<
 *             vmax = arr[i]
 * 
 */
    __pyx_t_4 = ((__pyx_v_vmax < (__pyx_v_arr[__pyx_v_i])) != 0);
    if (__pyx_t_4) {

      /* "sklearn/linear_model/sag_fast.pyx":45
 *     for i in range(1, n_classes):
 *         if vmax < arr[i]:
 *             vmax = arr[i]             # <<<<<<<<<<<<<<
 * 
 *     for i in range(n_classes):
 */
      __pyx_v_vmax = (__pyx_v_arr[__pyx_v_i]);

      /* "sklearn/linear_model/sag_fast.pyx":44
 * 
 *     for i in range(1, n_classes):
 *         if vmax < arr[i]:             # <<<<<<<<<<<<<<
 *             vmax = arr[i]
 * 
 */
    }
  }

  /* "sklearn/linear_model/sag_fast.pyx":47
 *             vmax = arr[i]
 * 
 *     for i in range(n_classes):             # <<<<<<<<<<<<<<
 *         out += exp(arr[i] - vmax)
 * 
 */
  __pyx_t_1 = __pyx_v_n_classes;
  __pyx_t_2 = __pyx_t_1;
  for (__pyx_t_3 = 0; __pyx_t_3 < __pyx_t_2; __pyx_t_3+=1) {
    __pyx_v_i = __pyx_t_3;

    /* "sklearn/linear_model/sag_fast.pyx":48
 * 
 *     for i in range(n_classes):
 *         out += exp(arr[i] - vmax)             # <<<<<<<<<<<<<<
 * 
 *     return log(out) + vmax
 */
    __pyx_v_out = (__pyx_v_out + exp(((__pyx_v_arr[__pyx_v_i]) - __pyx_v_vmax)));
  }

  /* "sklearn/linear_model/sag_fast.pyx":50
 *         out += exp(arr[i] - vmax)
 * 
 *     return log(out) + vmax             # <<<<<<<<<<<<<<
 * 
 * 
 */
  __pyx_r = (log(__pyx_v_out) + __pyx_v_vmax);
  goto __pyx_L0;

  /* "sklearn/linear_model/sag_fast.pyx":31
 * 
 * 
 * cdef double _logsumexp(double* arr, int n_classes) nogil:             # <<<<<<<<<<<<<<
 *     """Computes the sum of arr assuming arr is in the log domain.
 * 
 */

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

/* "sklearn/linear_model/sag_fast.pyx":54
 * 
 * cdef class MultinomialLogLoss:
 *     cdef double _loss(self, double* prediction, double y, int n_classes,             # <<<<<<<<<<<<<<
 *                       double sample_weight) nogil:
 *         """Multinomial Logistic regression loss.
 */

static double __pyx_f_7sklearn_12linear_model_8sag_fast_18MultinomialLogLoss__loss(CYTHON_UNUSED struct __pyx_obj_7sklearn_12linear_model_8sag_fast_MultinomialLogLoss *__pyx_v_self, double *__pyx_v_prediction, double __pyx_v_y, int __pyx_v_n_classes, double __pyx_v_sample_weight) {
  double __pyx_v_logsumexp_prediction;
  double __pyx_v_loss;
  double __pyx_r;

  /* "sklearn/linear_model/sag_fast.pyx":91
 *         Springer. (Chapter 4.3.4)
 *         """
 *         cdef double logsumexp_prediction = _logsumexp(prediction, n_classes)             # <<<<<<<<<<<<<<
 *         cdef double loss
 * 
 */
  __pyx_v_logsumexp_prediction = __pyx_f_7sklearn_12linear_model_8sag_fast__logsumexp(__pyx_v_prediction, __pyx_v_n_classes);

  /* "sklearn/linear_model/sag_fast.pyx":95
 * 
 *         # y is the indice of the correct class of current sample.
 *         loss = (logsumexp_prediction - prediction[int(y)]) * sample_weight             # <<<<<<<<<<<<<<
 *         return loss
 * 
 */
  __pyx_v_loss = ((__pyx_v_logsumexp_prediction - (__pyx_v_prediction[((Py_ssize_t)__pyx_v_y)])) * __pyx_v_sample_weight);

  /* "sklearn/linear_model/sag_fast.pyx":96
 *         # y is the indice of the correct class of current sample.
 *         loss = (logsumexp_prediction - prediction[int(y)]) * sample_weight
 *         return loss             # <<<<<<<<<<<<<<
 * 
 *     cdef void _dloss(self, double* prediction, double y, int n_classes,
 */
  __pyx_r = __pyx_v_loss;
  goto __pyx_L0;

  /* "sklearn/linear_model/sag_fast.pyx":54
 * 
 * cdef class MultinomialLogLoss:
 *     cdef double _loss(self, double* prediction, double y, int n_classes,             # <<<<<<<<<<<<<<
 *                       double sample_weight) nogil:
 *         """Multinomial Logistic regression loss.
 */

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

/* "sklearn/linear_model/sag_fast.pyx":98
 *         return loss
 * 
 *     cdef void _dloss(self, double* prediction, double y, int n_classes,             # <<<<<<<<<<<<<<
 *                      double sample_weight, double* gradient_ptr) nogil:
 *         """Multinomial Logistic regression gradient of the loss.
 */

static void __pyx_f_7sklearn_12linear_model_8sag_fast_18MultinomialLogLoss__dloss(CYTHON_UNUSED struct __pyx_obj_7sklearn_12linear_model_8sag_fast_MultinomialLogLoss *__pyx_v_self, double *__pyx_v_prediction, double __pyx_v_y, int __pyx_v_n_classes, double __pyx_v_sample_weight, double *__pyx_v_gradient_ptr) {
  double __pyx_v_logsumexp_prediction;
  int __pyx_v_class_ind;
  int __pyx_t_1;
  int __pyx_t_2;
  int __pyx_t_3;
  int __pyx_t_4;
  int __pyx_t_5;

  /* "sklearn/linear_model/sag_fast.pyx":137
 *         Springer. (Chapter 4.3.4)
 *         """
 *         cdef double logsumexp_prediction = _logsumexp(prediction, n_classes)             # <<<<<<<<<<<<<<
 *         cdef int class_ind
 * 
 */
  __pyx_v_logsumexp_prediction = __pyx_f_7sklearn_12linear_model_8sag_fast__logsumexp(__pyx_v_prediction, __pyx_v_n_classes);

  /* "sklearn/linear_model/sag_fast.pyx":140
 *         cdef int class_ind
 * 
 *         for class_ind in range(n_classes):             # <<<<<<<<<<<<<<
 *             gradient_ptr[class_ind] = exp(prediction[class_ind] -
 *                                           logsumexp_prediction)
 */
  __pyx_t_1 = __pyx_v_n_classes;
  __pyx_t_2 = __pyx_t_1;
  for (__pyx_t_3 = 0; __pyx_t_3 < __pyx_t_2; __pyx_t_3+=1) {
    __pyx_v_class_ind = __pyx_t_3;

    /* "sklearn/linear_model/sag_fast.pyx":141
 * 
 *         for class_ind in range(n_classes):
 *             gradient_ptr[class_ind] = exp(prediction[class_ind] -             # <<<<<<<<<<<<<<
 *                                           logsumexp_prediction)
 * 
 */
    (__pyx_v_gradient_ptr[__pyx_v_class_ind]) = exp(((__pyx_v_prediction[__pyx_v_class_ind]) - __pyx_v_logsumexp_prediction));

    /* "sklearn/linear_model/sag_fast.pyx":145
 * 
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 *         start_time = time(NULL)
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 */
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 *                 # update the number of samples seen and the seen array
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 *                     seen[sample_ind] = 1
 * 
 */
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 * 
 *                 # make the weight updates
 */
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 * 
 *                 # update the number of samples seen and the seen array
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 *                     num_seen += 1
 *                     seen[sample_ind] = 1
 */
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 * 
 *                 # make the weight updates
 *                 if sample_itr > 0:             # <<<<<<<<<<<<<<
 *                    lagged_update(weights, wscale, xnnz,
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 */
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 *                 # make the weight updates
 *                 if sample_itr > 0:
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 *                           n_samples, n_classes, sample_itr,
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 * 
 *                 # make the weight updates
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 *                           n_samples, n_classes, sample_itr,
 */
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 *                                      gradient)
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 *                 # compute the gradient for this sample, given the prediction
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 *                     multiloss._dloss(prediction, y, n_classes, sample_weight,             # <<<<<<<<<<<<<<
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 *                 else:
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 *                 if multinomial:
 *                     multiloss._dloss(prediction, y, n_classes, sample_weight,
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 *                 else:
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 * 
 *                 # compute the gradient for this sample, given the prediction
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 *                                      gradient)
 */
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 *                                      gradient)
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 * 
 *                 # L2 regularization by simply rescaling the weights
 */
            /*else*/ {
              if (unlikely(!__pyx_v_loss)) { __Pyx_RaiseUnboundLocalError("loss"); __PYX_ERR(0, 415, __pyx_L8_error) }
              (__pyx_v_gradient[0]) = (((struct __pyx_vtabstruct_7sklearn_12linear_model_8sgd_fast_LossFunction *)__pyx_v_loss->__pyx_vtab)->_dloss(__pyx_v_loss, (__pyx_v_prediction[0]), __pyx_v_y) * __pyx_v_sample_weight);
            }
            __pyx_L16:;

            /* "sklearn/linear_model/sag_fast.pyx":418
 * 
 *                 # L2 regularization by simply rescaling the weights
 *                 wscale *= wscale_update             # <<<<<<<<<<<<<<
 * 
 *                 # make the updates to the sum of gradients
 */
            __pyx_v_wscale = (__pyx_v_wscale * __pyx_v_wscale_update);

            /* "sklearn/linear_model/sag_fast.pyx":421
 * 
 *                 # make the updates to the sum of gradients
 *                 for j in range(xnnz):             # <<<<<<<<<<<<<<
 *                     feature_ind = x_ind_ptr[j]
 *                     val = x_data_ptr[j]
 */
            __pyx_t_23 = __pyx_v_xnnz;
            __pyx_t_24 = __pyx_t_23;
            for (__pyx_t_25 = 0; __pyx_t_25 < __pyx_t_24; __pyx_t_25+=1) {
              __pyx_v_j = __pyx_t_25;

              /* "sklearn/linear_model/sag_fast.pyx":422
 *                 # make the updates to the sum of gradients
 *                 for j in range(xnnz):
 *                     feature_ind = x_ind_ptr[j]             # <<<<<<<<<<<<<<
 *                     val = x_data_ptr[j]
 *                     f_idx = feature_ind * n_classes
 */
              __pyx_v_feature_ind = (__pyx_v_x_ind_ptr[__pyx_v_j]);

              /* "sklearn/linear_model/sag_fast.pyx":423
 *                 for j in range(xnnz):
 *                     feature_ind = x_ind_ptr[j]
 *                     val = x_data_ptr[j]             # <<<<<<<<<<<<<<
 *                     f_idx = feature_ind * n_classes
 *                     for class_ind in range(n_classes):
 */
              __pyx_v_val = (__pyx_v_x_data_ptr[__pyx_v_j]);

              /* "sklearn/linear_model/sag_fast.pyx":424
 *                     feature_ind = x_ind_ptr[j]
 *                     val = x_data_ptr[j]
 *                     f_idx = feature_ind * n_classes             # <<<<<<<<<<<<<<
 *                     for class_ind in range(n_classes):
 *                         gradient_correction = \
 */
              __pyx_v_f_idx = (__pyx_v_feature_ind * __pyx_v_n_classes);

              /* "sklearn/linear_model/sag_fast.pyx":425
 *                     val = x_data_ptr[j]
 *                     f_idx = feature_ind * n_classes
 *                     for class_ind in range(n_classes):             # <<<<<<<<<<<<<<
 *                         gradient_correction = \
 *                             val * (gradient[class_ind] -
 */
              __pyx_t_26 = __pyx_v_n_classes;
              __pyx_t_27 = __pyx_t_26;
              for (__pyx_t_28 = 0; __pyx_t_28 < __pyx_t_27; __pyx_t_28+=1) {
                __pyx_v_class_ind = __pyx_t_28;

                /* "sklearn/linear_model/sag_fast.pyx":427
 *                     for class_ind in range(n_classes):
 *                         gradient_correction = \
 *                             val * (gradient[class_ind] -             # <<<<<<<<<<<<<<
 *                                    gradient_memory[s_idx + class_ind])
 *                         if saga:
 */
                __pyx_v_gradient_correction = (__pyx_v_val * ((__pyx_v_gradient[__pyx_v_class_ind]) - (__pyx_v_gradient_memory[(__pyx_v_s_idx + __pyx_v_class_ind)])));

                /* "sklearn/linear_model/sag_fast.pyx":429
 *                             val * (gradient[class_ind] -
 *                                    gradient_memory[s_idx + class_ind])
 *                         if saga:             # <<<<<<<<<<<<<<
 *                             weights[f_idx + class_ind] -= \
 *                                 (gradient_correction * step_size
 */
                __pyx_t_12 = (__pyx_v_saga != 0);
                if (__pyx_t_12) {

                  /* "sklearn/linear_model/sag_fast.pyx":430
 *                                    gradient_memory[s_idx + class_ind])
 *                         if saga:
 *                             weights[f_idx + class_ind] -= \             # <<<<<<<<<<<<<<
 *                                 (gradient_correction * step_size
 *                                  * (1 - 1. / num_seen) / wscale)
 */
                  __pyx_t_29 = (__pyx_v_f_idx + __pyx_v_class_ind);

                  /* "sklearn/linear_model/sag_fast.pyx":432
 *                             weights[f_idx + class_ind] -= \
 *                                 (gradient_correction * step_size
 *                                  * (1 - 1. / num_seen) / wscale)             # <<<<<<<<<<<<<<
 *                         sum_gradient[f_idx + class_ind] += gradient_correction
 * 
 */
                  (__pyx_v_weights[__pyx_t_29]) = ((__pyx_v_weights[__pyx_t_29]) - (((__pyx_v_gradient_correction * __pyx_v_step_size) * (1.0 - (1. / __pyx_v_num_seen))) / __pyx_v_wscale));

                  /* "sklearn/linear_model/sag_fast.pyx":429
 *                             val * (gradient[class_ind] -
 *                                    gradient_memory[s_idx + class_ind])
 *                         if saga:             # <<<<<<<<<<<<<<
 *                             weights[f_idx + class_ind] -= \
 *                                 (gradient_correction * step_size
 */
                }

                /* "sklearn/linear_model/sag_fast.pyx":433
 *                                 (gradient_correction * step_size
 *                                  * (1 - 1. / num_seen) / wscale)
 *                         sum_gradient[f_idx + class_ind] += gradient_correction             # <<<<<<<<<<<<<<
 * 
 *                 # fit the intercept
 */
                __pyx_t_29 = (__pyx_v_f_idx + __pyx_v_class_ind);
                (__pyx_v_sum_gradient[__pyx_t_29]) = ((__pyx_v_sum_gradient[__pyx_t_29]) + __pyx_v_gradient_correction);
              }
            }

            /* "sklearn/linear_model/sag_fast.pyx":436
 * 
 *                 # fit the intercept
 *                 if fit_intercept:             # <<<<<<<<<<<<<<
 *                     for class_ind in range(n_classes):
 *                         gradient_correction = (gradient[class_ind] -
 */
            __pyx_t_12 = (__pyx_v_fit_intercept != 0);
            if (__pyx_t_12) {

              /* "sklearn/linear_model/sag_fast.pyx":437
 *                 # fit the intercept
 *                 if fit_intercept:
 *                     for class_ind in range(n_classes):             # <<<<<<<<<<<<<<
 *                         gradient_correction = (gradient[class_ind] -
 *                                                gradient_memory[s_idx + class_ind])
 */
              __pyx_t_23 = __pyx_v_n_classes;
              __pyx_t_24 = __pyx_t_23;
              for (__pyx_t_25 = 0; __pyx_t_25 < __pyx_t_24; __pyx_t_25+=1) {
                __pyx_v_class_ind = __pyx_t_25;

                /* "sklearn/linear_model/sag_fast.pyx":438
 *                 if fit_intercept:
 *                     for class_ind in range(n_classes):
 *                         gradient_correction = (gradient[class_ind] -             # <<<<<<<<<<<<<<
 *                                                gradient_memory[s_idx + class_ind])
 *                         intercept_sum_gradient[class_ind] += gradient_correction
 */
                __pyx_v_gradient_correction = ((__pyx_v_gradient[__pyx_v_class_ind]) - (__pyx_v_gradient_memory[(__pyx_v_s_idx + __pyx_v_class_ind)]));

                /* "sklearn/linear_model/sag_fast.pyx":440
 *                         gradient_correction = (gradient[class_ind] -
 *                                                gradient_memory[s_idx + class_ind])
 *                         intercept_sum_gradient[class_ind] += gradient_correction             # <<<<<<<<<<<<<<
 *                         gradient_correction *= step_size * (1. - 1. / num_seen)
 *                         if saga:
 */
                __pyx_t_26 = __pyx_v_class_ind;
                (__pyx_v_intercept_sum_gradient[__pyx_t_26]) = ((__pyx_v_intercept_sum_gradient[__pyx_t_26]) + __pyx_v_gradient_correction);

                /* "sklearn/linear_model/sag_fast.pyx":441
 *                                                gradient_memory[s_idx + class_ind])
 *                         intercept_sum_gradient[class_ind] += gradient_correction
 *                         gradient_correction *= step_size * (1. - 1. / num_seen)             # <<<<<<<<<<<<<<
 *                         if saga:
 *                             intercept[class_ind] -= \
 */
                __pyx_v_gradient_correction = (__pyx_v_gradient_correction * (__pyx_v_step_size * (1. - (1. / __pyx_v_num_seen))));

                /* "sklearn/linear_model/sag_fast.pyx":442
 *                         intercept_sum_gradient[class_ind] += gradient_correction
 *                         gradient_correction *= step_size * (1. - 1. / num_seen)
 *                         if saga:             # <<<<<<<<<<<<<<
 *                             intercept[class_ind] -= \
 *                                 (step_size * intercept_sum_gradient[class_ind] /
 */
                __pyx_t_12 = (__pyx_v_saga != 0);
                if (__pyx_t_12) {

                  /* "sklearn/linear_model/sag_fast.pyx":443
 *                         gradient_correction *= step_size * (1. - 1. / num_seen)
 *                         if saga:
 *                             intercept[class_ind] -= \             # <<<<<<<<<<<<<<
 *                                 (step_size * intercept_sum_gradient[class_ind] /
 *                                  num_seen * intercept_decay) + gradient_correction
 */
                  __pyx_t_26 = __pyx_v_class_ind;

                  /* "sklearn/linear_model/sag_fast.pyx":445
 *                             intercept[class_ind] -= \
 *                                 (step_size * intercept_sum_gradient[class_ind] /
 *                                  num_seen * intercept_decay) + gradient_correction             # <<<<<<<<<<<<<<
 *                         else:
 *                             intercept[class_ind] -= \
 */
                  (__pyx_v_intercept[__pyx_t_26]) = ((__pyx_v_intercept[__pyx_t_26]) - ((((__pyx_v_step_size * (__pyx_v_intercept_sum_gradient[__pyx_v_class_ind])) / __pyx_v_num_seen) * __pyx_v_intercept_decay) + __pyx_v_gradient_correction));

                  /* "sklearn/linear_model/sag_fast.pyx":442
 *                         intercept_sum_gradient[class_ind] += gradient_correction
 *                         gradient_correction *= step_size * (1. - 1. / num_seen)
 *                         if saga:             # <<<<<<<<<<<<<<
 *                             intercept[class_ind] -= \
 *                                 (step_size * intercept_sum_gradient[class_ind] /
 */
                  goto __pyx_L25;
                }

                /* "sklearn/linear_model/sag_fast.pyx":447
 *                                  num_seen * intercept_decay) + gradient_correction
 *                         else:
 *                             intercept[class_ind] -= \             # <<<<<<<<<<<<<<
 *                                 (step_size * intercept_sum_gradient[class_ind] /
 *                                  num_seen * intercept_decay)
 */
                /*else*/ {
                  __pyx_t_26 = __pyx_v_class_ind;

                  /* "sklearn/linear_model/sag_fast.pyx":449
 *                             intercept[class_ind] -= \
 *                                 (step_size * intercept_sum_gradient[class_ind] /
 *                                  num_seen * intercept_decay)             # <<<<<<<<<<<<<<
 * 
 *                         # check to see that the intercept is not inf or NaN
 */
                  (__pyx_v_intercept[__pyx_t_26]) = ((__pyx_v_intercept[__pyx_t_26]) - (((__pyx_v_step_size * (__pyx_v_intercept_sum_gradient[__pyx_v_class_ind])) / __pyx_v_num_seen) * __pyx_v_intercept_decay));
                }
                __pyx_L25:;

                /* "sklearn/linear_model/sag_fast.pyx":452
 * 
 *                         # check to see that the intercept is not inf or NaN
 *                         if not skl_isfinite(intercept[class_ind]):             # <<<<<<<<<<<<<<
 *                             with gil:
 *                                 raise_infinite_error(n_iter)
 */
                __pyx_t_12 = ((!(skl_isfinite((__pyx_v_intercept[__pyx_v_class_ind])) != 0)) != 0);
                if (__pyx_t_12) {

                  /* "sklearn/linear_model/sag_fast.pyx":453
 *                         # check to see that the intercept is not inf or NaN
 *                         if not skl_isfinite(intercept[class_ind]):
 *                             with gil:             # <<<<<<<<<<<<<<
 *                                 raise_infinite_error(n_iter)
 * 
 */
                  {
                      #ifdef WITH_THREAD
                      PyGILState_STATE __pyx_gilstate_save = __Pyx_PyGILState_Ensure();
                      #endif
                      /*try:*/ {

                        /* "sklearn/linear_model/sag_fast.pyx":454
 *                         if not skl_isfinite(intercept[class_ind]):
 *                             with gil:
 *                                 raise_infinite_error(n_iter)             # <<<<<<<<<<<<<<
 * 
 *                 # update the gradient memory for this sample
 */
                        __pyx_f_7sklearn_12linear_model_8sag_fast_raise_infinite_error(__pyx_v_n_iter);
                      }

                      /* "sklearn/linear_model/sag_fast.pyx":453
 *                         # check to see that the intercept is not inf or NaN
 *                         if not skl_isfinite(intercept[class_ind]):
 *                             with gil:             # <<<<<<<<<<<<<<
 *                                 raise_infinite_error(n_iter)
 * 
 */
                      /*finally:*/ {
                        /*normal exit:*/{
                          #ifdef WITH_THREAD
                          __Pyx_PyGILState_Release(__pyx_gilstate_save);
                          #endif
                          goto __pyx_L31;
                        }
                        __pyx_L31:;
                      }
                  }

                  /* "sklearn/linear_model/sag_fast.pyx":452
 * 
 *                         # check to see that the intercept is not inf or NaN
 *                         if not skl_isfinite(intercept[class_ind]):             # <<<<<<<<<<<<<<
 *                             with gil:
 *                                 raise_infinite_error(n_iter)
 */
                }
              }

              /* "sklearn/linear_model/sag_fast.pyx":436
 * 
 *                 # fit the intercept
 *                 if fit_intercept:             # <<<<<<<<<<<<<<
 *                     for class_ind in range(n_classes):
 *                         gradient_correction = (gradient[class_ind] -
 */
            }

            /* "sklearn/linear_model/sag_fast.pyx":457
 * 
 *                 # update the gradient memory for this sample
 *                 for class_ind in range(n_classes):             # <<<<<<<<<<<<<<
 *                     gradient_memory[s_idx + class_ind] = gradient[class_ind]
 * 
 */
            __pyx_t_23 = __pyx_v_n_classes;
            __pyx_t_24 = __pyx_t_23;
            for (__pyx_t_25 = 0; __pyx_t_25 < __pyx_t_24; __pyx_t_25+=1) {
              __pyx_v_class_ind = __pyx_t_25;

              /* "sklearn/linear_model/sag_fast.pyx":458
 *                 # update the gradient memory for this sample
 *                 for class_ind in range(n_classes):
 *                     gradient_memory[s_idx + class_ind] = gradient[class_ind]             # <<<<<<<<<<<<<<
 * 
 *                 if sample_itr == 0:
 */
              (__pyx_v_gradient_memory[(__pyx_v_s_idx + __pyx_v_class_ind)]) = (__pyx_v_gradient[__pyx_v_class_ind]);
            }

            /* "sklearn/linear_model/sag_fast.pyx":460
 *                     gradient_memory[s_idx + class_ind] = gradient[class_ind]
 * 
 *                 if sample_itr == 0:             # <<<<<<<<<<<<<<
 *                     cumulative_sums[0] = step_size / (wscale * num_seen)
 *                     if prox:
 */
            __pyx_t_12 = ((__pyx_v_sample_itr == 0) != 0);
            if (__pyx_t_12) {

              /* "sklearn/linear_model/sag_fast.pyx":461
 * 
 *                 if sample_itr == 0:
 *                     cumulative_sums[0] = step_size / (wscale * num_seen)             # <<<<<<<<<<<<<<
 *                     if prox:
 *                         cumulative_sums_prox[0] = step_size * beta / wscale
 */
              (__pyx_v_cumulative_sums[0]) = (__pyx_v_step_size / (__pyx_v_wscale * __pyx_v_num_seen));

              /* "sklearn/linear_model/sag_fast.pyx":462
 *                 if sample_itr == 0:
 *                     cumulative_sums[0] = step_size / (wscale * num_seen)
 *                     if prox:             # <<<<<<<<<<<<<<
 *                         cumulative_sums_prox[0] = step_size * beta / wscale
 *                 else:
 */
              __pyx_t_12 = (__pyx_v_prox != 0);
              if (__pyx_t_12) {

                /* "sklearn/linear_model/sag_fast.pyx":463
 *                     cumulative_sums[0] = step_size / (wscale * num_seen)
 *                     if prox:
 *                         cumulative_sums_prox[0] = step_size * beta / wscale             # <<<<<<<<<<<<<<
 *                 else:
 *                     cumulative_sums[sample_itr] = \
 */
                (__pyx_v_cumulative_sums_prox[0]) = ((__pyx_v_step_size * __pyx_v_beta) / __pyx_v_wscale);

                /* "sklearn/linear_model/sag_fast.pyx":462
 *                 if sample_itr == 0:
 *                     cumulative_sums[0] = step_size / (wscale * num_seen)
 *                     if prox:             # <<<<<<<<<<<<<<
 *                         cumulative_sums_prox[0] = step_size * beta / wscale
 *                 else:
 */
              }

              /* "sklearn/linear_model/sag_fast.pyx":460
 *                     gradient_memory[s_idx + class_ind] = gradient[class_ind]
 * 
 *                 if sample_itr == 0:             # <<<<<<<<<<<<<<
 *                     cumulative_sums[0] = step_size / (wscale * num_seen)
 *                     if prox:
 */
              goto __pyx_L34;
            }

            /* "sklearn/linear_model/sag_fast.pyx":465
 *                         cumulative_sums_prox[0] = step_size * beta / wscale
 *                 else:
 *                     cumulative_sums[sample_itr] = \             # <<<<<<<<<<<<<<
 *                         (cumulative_sums[sample_itr - 1] +
 *                          step_size / (wscale * num_seen))
 */
            /*else*/ {

              /* "sklearn/linear_model/sag_fast.pyx":466
 *                 else:
 *                     cumulative_sums[sample_itr] = \
 *                         (cumulative_sums[sample_itr - 1] +             # <<<<<<<<<<<<<<
 *                          step_size / (wscale * num_seen))
 *                     if prox:
 */
              (__pyx_v_cumulative_sums[__pyx_v_sample_itr]) = ((__pyx_v_cumulative_sums[(__pyx_v_sample_itr - 1)]) + (__pyx_v_step_size / (__pyx_v_wscale * __pyx_v_num_seen)));

              /* "sklearn/linear_model/sag_fast.pyx":468
 *                         (cumulative_sums[sample_itr - 1] +
 *                          step_size / (wscale * num_seen))
 *                     if prox:             # <<<<<<<<<<<<<<
 *                         cumulative_sums_prox[sample_itr] = \
 *                         (cumulative_sums_prox[sample_itr - 1] +
 */
              __pyx_t_12 = (__pyx_v_prox != 0);
              if (__pyx_t_12) {

                /* "sklearn/linear_model/sag_fast.pyx":469
 *                          step_size / (wscale * num_seen))
 *                     if prox:
 *                         cumulative_sums_prox[sample_itr] = \             # <<<<<<<<<<<<<<
 *                         (cumulative_sums_prox[sample_itr - 1] +
 *                              step_size * beta / wscale)
 */
                (__pyx_v_cumulative_sums_prox[__pyx_v_sample_itr]) = ((__pyx_v_cumulative_sums_prox[(__pyx_v_sample_itr - 1)]) + ((__pyx_v_step_size * __pyx_v_beta) / __pyx_v_wscale));

                /* "sklearn/linear_model/sag_fast.pyx":468
 *                         (cumulative_sums[sample_itr - 1] +
 *                          step_size / (wscale * num_seen))
 *                     if prox:             # <<<<<<<<<<<<<<
 *                         cumulative_sums_prox[sample_itr] = \
 *                         (cumulative_sums_prox[sample_itr - 1] +
 */
              }
            }
            __pyx_L34:;

            /* "sklearn/linear_model/sag_fast.pyx":473
 *                              step_size * beta / wscale)
 *                 # If wscale gets too small, we need to reset the scale.
 *                 if wscale < 1e-9:             # <<<<<<<<<<<<<<
 *                     if verbose:
 *                         with gil:
 */
            __pyx_t_12 = ((__pyx_v_wscale < 1e-9) != 0);
            if (__pyx_t_12) {

              /* "sklearn/linear_model/sag_fast.pyx":474
 *                 # If wscale gets too small, we need to reset the scale.
 *                 if wscale < 1e-9:
 *                     if verbose:             # <<<<<<<<<<<<<<
 *                         with gil:
 *                             print("rescaling...")
 */
              __pyx_t_12 = (__pyx_v_verbose != 0);
              if (__pyx_t_12) {

                /* "sklearn/linear_model/sag_fast.pyx":475
 *                 if wscale < 1e-9:
 *                     if verbose:
 *                         with gil:             # <<<<<<<<<<<<<<
 *                             print("rescaling...")
 *                     wscale = scale_weights(
 */
                {
                    #ifdef WITH_THREAD
                    PyGILState_STATE __pyx_gilstate_save = __Pyx_PyGILState_Ensure();
                    #endif
                    /*try:*/ {

                      /* "sklearn/linear_model/sag_fast.pyx":476
 *                     if verbose:
 *                         with gil:
 *                             print("rescaling...")             # <<<<<<<<<<<<<<
 *                     wscale = scale_weights(
 *                         weights, wscale, n_features, n_samples, n_classes,
 */
                      if (__Pyx_PrintOne(0, __pyx_kp_s_rescaling) < 0) __PYX_ERR(0, 476, __pyx_L42_error)
                    }

                    /* "sklearn/linear_model/sag_fast.pyx":475
 *                 if wscale < 1e-9:
 *                     if verbose:
 *                         with gil:             # <<<<<<<<<<<<<<
 *                             print("rescaling...")
 *                     wscale = scale_weights(
 */
                    /*finally:*/ {
                      /*normal exit:*/{
                        #ifdef WITH_THREAD
                        __Pyx_PyGILState_Release(__pyx_gilstate_save);
                        #endif
                        goto __pyx_L43;
                      }
                      __pyx_L42_error: {
                        #ifdef WITH_THREAD
                        __Pyx_PyGILState_Release(__pyx_gilstate_save);
                        #endif
                        goto __pyx_L8_error;
                      }
                      __pyx_L43:;
                    }
                }

                /* "sklearn/linear_model/sag_fast.pyx":474
 *                 # If wscale gets too small, we need to reset the scale.
 *                 if wscale < 1e-9:
 *                     if verbose:             # <<<<<<<<<<<<<<
 *                         with gil:
 *                             print("rescaling...")
 */
              }

              /* "sklearn/linear_model/sag_fast.pyx":477
 *                         with gil:
 *                             print("rescaling...")
 *                     wscale = scale_weights(             # <<<<<<<<<<<<<<
 *                         weights, wscale, n_features, n_samples, n_classes,
 *                         sample_itr, cumulative_sums,
 */
              __pyx_v_wscale = __pyx_f_7sklearn_12linear_model_8sag_fast_scale_weights(__pyx_v_weights, __pyx_v_wscale, __pyx_v_n_features, __pyx_v_n_samples, __pyx_v_n_classes, __pyx_v_sample_itr, __pyx_v_cumulative_sums, __pyx_v_cumulative_sums_prox, __pyx_v_feature_hist, __pyx_v_prox, __pyx_v_sum_gradient, __pyx_v_n_iter);

              /* "sklearn/linear_model/sag_fast.pyx":473
 *                              step_size * beta / wscale)
 *                 # If wscale gets too small, we need to reset the scale.
 *                 if wscale < 1e-9:             # <<<<<<<<<<<<<<
 *                     if verbose:
 *                         with gil:
 */
            }
          }

          /* "sklearn/linear_model/sag_fast.pyx":486
 *             # we scale the weights every n_samples iterations and reset the
 *             # just-in-time update system for numerical stability.
 *             wscale = scale_weights(weights, wscale, n_features, n_samples,             # <<<<<<<<<<<<<<
 *                                    n_classes, n_samples - 1, cumulative_sums,
 *                                    cumulative_sums_prox,
 */
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/* "sklearn/linear_model/sag_fast.pyx":529
 * 
 * 
 * cdef double scale_weights(double* weights, double wscale, int n_features,             # <<<<<<<<<<<<<<
 *                           int n_samples, int n_classes, int sample_itr,
 *                           double* cumulative_sums,
 */

static double __pyx_f_7sklearn_12linear_model_8sag_fast_scale_weights(double *__pyx_v_weights, double __pyx_v_wscale, int __pyx_v_n_features, int __pyx_v_n_samples, int __pyx_v_n_classes, int __pyx_v_sample_itr, double *__pyx_v_cumulative_sums, double *__pyx_v_cumulative_sums_prox, int *__pyx_v_feature_hist, int __pyx_v_prox, double *__pyx_v_sum_gradient, int __pyx_v_n_iter) {
  double __pyx_r;

  /* "sklearn/linear_model/sag_fast.pyx":546
 *     """
 * 
 *     lagged_update(weights, wscale, n_features,             # <<<<<<<<<<<<<<
 *                           n_samples, n_classes, sample_itr + 1,
 *                           cumulative_sums,
 */
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  /* "sklearn/linear_model/sag_fast.pyx":557
 *                           n_iter)
 *     # reset wscale to 1.0
 *     return 1.0             # <<<<<<<<<<<<<<
 * 
 * 
 */
  __pyx_r = 1.0;
  goto __pyx_L0;

  /* "sklearn/linear_model/sag_fast.pyx":529
 * 
 * 
 * cdef double scale_weights(double* weights, double wscale, int n_features,             # <<<<<<<<<<<<<<
 *                           int n_samples, int n_classes, int sample_itr,
 *                           double* cumulative_sums,
 */

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

/* "sklearn/linear_model/sag_fast.pyx":560
 * 
 * 
 * cdef void lagged_update(double* weights, double wscale, int xnnz,             # <<<<<<<<<<<<<<
 *                           int n_samples, int n_classes, int sample_itr,
 *                           double* cumulative_sums,
 */

static void __pyx_f_7sklearn_12linear_model_8sag_fast_lagged_update(double *__pyx_v_weights, double __pyx_v_wscale, int __pyx_v_xnnz, int __pyx_v_n_samples, int __pyx_v_n_classes, int __pyx_v_sample_itr, double *__pyx_v_cumulative_sums, double *__pyx_v_cumulative_sums_prox, int *__pyx_v_feature_hist, int __pyx_v_prox, double *__pyx_v_sum_gradient, int *__pyx_v_x_ind_ptr, int __pyx_v_reset, int __pyx_v_n_iter) {
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  int __pyx_v_class_ind;
  int __pyx_v_idx;
  int __pyx_v_f_idx;
  int __pyx_v_lagged_ind;
  int __pyx_v_last_update_ind;
  double __pyx_v_cum_sum;
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  double __pyx_v_cum_sum_prox;
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  int __pyx_t_6;
  int __pyx_t_7;
  int __pyx_t_8;
  long __pyx_t_9;
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 *                           bint reset,
 *                           int n_iter) nogil:
 *     """Hard perform the JIT updates for non-zero features of present sample.             # <<<<<<<<<<<<<<
 * 
 *     The updates that awaits are kept in memory using cumulative_sums,
 */
  /*try:*/ {

    /* "sklearn/linear_model/sag_fast.pyx":579
 *     cdef int feature_ind, class_ind, idx, f_idx, lagged_ind, last_update_ind
 *     cdef double cum_sum, grad_step, prox_step
 *     for feature_ind in range(xnnz):             # <<<<<<<<<<<<<<
 *         if not reset:
 *             feature_ind = x_ind_ptr[feature_ind]
 */
    __pyx_t_1 = __pyx_v_xnnz;
    __pyx_t_2 = __pyx_t_1;
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      __pyx_v_feature_ind = __pyx_t_3;

      /* "sklearn/linear_model/sag_fast.pyx":580
 *     cdef double cum_sum, grad_step, prox_step
 *     for feature_ind in range(xnnz):
 *         if not reset:             # <<<<<<<<<<<<<<
 *             feature_ind = x_ind_ptr[feature_ind]
 *         f_idx = feature_ind * n_classes
 */
      __pyx_t_4 = ((!(__pyx_v_reset != 0)) != 0);
      if (__pyx_t_4) {

        /* "sklearn/linear_model/sag_fast.pyx":581
 *     for feature_ind in range(xnnz):
 *         if not reset:
 *             feature_ind = x_ind_ptr[feature_ind]             # <<<<<<<<<<<<<<
 *         f_idx = feature_ind * n_classes
 * 
 */
        __pyx_v_feature_ind = (__pyx_v_x_ind_ptr[__pyx_v_feature_ind]);

        /* "sklearn/linear_model/sag_fast.pyx":580
 *     cdef double cum_sum, grad_step, prox_step
 *     for feature_ind in range(xnnz):
 *         if not reset:             # <<<<<<<<<<<<<<
 *             feature_ind = x_ind_ptr[feature_ind]
 *         f_idx = feature_ind * n_classes
 */
      }

      /* "sklearn/linear_model/sag_fast.pyx":582
 *         if not reset:
 *             feature_ind = x_ind_ptr[feature_ind]
 *         f_idx = feature_ind * n_classes             # <<<<<<<<<<<<<<
 * 
 *         cum_sum = cumulative_sums[sample_itr - 1]
 */
      __pyx_v_f_idx = (__pyx_v_feature_ind * __pyx_v_n_classes);

      /* "sklearn/linear_model/sag_fast.pyx":584
 *         f_idx = feature_ind * n_classes
 * 
 *         cum_sum = cumulative_sums[sample_itr - 1]             # <<<<<<<<<<<<<<
 *         if prox:
 *             cum_sum_prox = cumulative_sums_prox[sample_itr - 1]
 */
      __pyx_v_cum_sum = (__pyx_v_cumulative_sums[(__pyx_v_sample_itr - 1)]);

      /* "sklearn/linear_model/sag_fast.pyx":585
 * 
 *         cum_sum = cumulative_sums[sample_itr - 1]
 *         if prox:             # <<<<<<<<<<<<<<
 *             cum_sum_prox = cumulative_sums_prox[sample_itr - 1]
 *         if feature_hist[feature_ind] != 0:
 */
      __pyx_t_4 = (__pyx_v_prox != 0);
      if (__pyx_t_4) {

        /* "sklearn/linear_model/sag_fast.pyx":586
 *         cum_sum = cumulative_sums[sample_itr - 1]
 *         if prox:
 *             cum_sum_prox = cumulative_sums_prox[sample_itr - 1]             # <<<<<<<<<<<<<<
 *         if feature_hist[feature_ind] != 0:
 *             cum_sum -= cumulative_sums[feature_hist[feature_ind] - 1]
 */
        __pyx_v_cum_sum_prox = (__pyx_v_cumulative_sums_prox[(__pyx_v_sample_itr - 1)]);

        /* "sklearn/linear_model/sag_fast.pyx":585
 * 
 *         cum_sum = cumulative_sums[sample_itr - 1]
 *         if prox:             # <<<<<<<<<<<<<<
 *             cum_sum_prox = cumulative_sums_prox[sample_itr - 1]
 *         if feature_hist[feature_ind] != 0:
 */
      }

      /* "sklearn/linear_model/sag_fast.pyx":587
 *         if prox:
 *             cum_sum_prox = cumulative_sums_prox[sample_itr - 1]
 *         if feature_hist[feature_ind] != 0:             # <<<<<<<<<<<<<<
 *             cum_sum -= cumulative_sums[feature_hist[feature_ind] - 1]
 *             if prox:
 */
      __pyx_t_4 = (((__pyx_v_feature_hist[__pyx_v_feature_ind]) != 0) != 0);
      if (__pyx_t_4) {

        /* "sklearn/linear_model/sag_fast.pyx":588
 *             cum_sum_prox = cumulative_sums_prox[sample_itr - 1]
 *         if feature_hist[feature_ind] != 0:
 *             cum_sum -= cumulative_sums[feature_hist[feature_ind] - 1]             # <<<<<<<<<<<<<<
 *             if prox:
 *                 cum_sum_prox -= cumulative_sums_prox[feature_hist[feature_ind] - 1]
 */
        __pyx_v_cum_sum = (__pyx_v_cum_sum - (__pyx_v_cumulative_sums[((__pyx_v_feature_hist[__pyx_v_feature_ind]) - 1)]));

        /* "sklearn/linear_model/sag_fast.pyx":589
 *         if feature_hist[feature_ind] != 0:
 *             cum_sum -= cumulative_sums[feature_hist[feature_ind] - 1]
 *             if prox:             # <<<<<<<<<<<<<<
 *                 cum_sum_prox -= cumulative_sums_prox[feature_hist[feature_ind] - 1]
 *         if not prox:
 */
        __pyx_t_4 = (__pyx_v_prox != 0);
        if (__pyx_t_4) {

          /* "sklearn/linear_model/sag_fast.pyx":590
 *             cum_sum -= cumulative_sums[feature_hist[feature_ind] - 1]
 *             if prox:
 *                 cum_sum_prox -= cumulative_sums_prox[feature_hist[feature_ind] - 1]             # <<<<<<<<<<<<<<
 *         if not prox:
 *             for class_ind in range(n_classes):
 */
          __pyx_v_cum_sum_prox = (__pyx_v_cum_sum_prox - (__pyx_v_cumulative_sums_prox[((__pyx_v_feature_hist[__pyx_v_feature_ind]) - 1)]));

          /* "sklearn/linear_model/sag_fast.pyx":589
 *         if feature_hist[feature_ind] != 0:
 *             cum_sum -= cumulative_sums[feature_hist[feature_ind] - 1]
 *             if prox:             # <<<<<<<<<<<<<<
 *                 cum_sum_prox -= cumulative_sums_prox[feature_hist[feature_ind] - 1]
 *         if not prox:
 */
        }

        /* "sklearn/linear_model/sag_fast.pyx":587
 *         if prox:
 *             cum_sum_prox = cumulative_sums_prox[sample_itr - 1]
 *         if feature_hist[feature_ind] != 0:             # <<<<<<<<<<<<<<
 *             cum_sum -= cumulative_sums[feature_hist[feature_ind] - 1]
 *             if prox:
 */
      }

      /* "sklearn/linear_model/sag_fast.pyx":591
 *             if prox:
 *                 cum_sum_prox -= cumulative_sums_prox[feature_hist[feature_ind] - 1]
 *         if not prox:             # <<<<<<<<<<<<<<
 *             for class_ind in range(n_classes):
 *                 idx = f_idx + class_ind
 */
      __pyx_t_4 = ((!(__pyx_v_prox != 0)) != 0);
      if (__pyx_t_4) {

        /* "sklearn/linear_model/sag_fast.pyx":592
 *                 cum_sum_prox -= cumulative_sums_prox[feature_hist[feature_ind] - 1]
 *         if not prox:
 *             for class_ind in range(n_classes):             # <<<<<<<<<<<<<<
 *                 idx = f_idx + class_ind
 *                 weights[idx] -= cum_sum * sum_gradient[idx]
 */
        __pyx_t_5 = __pyx_v_n_classes;
        __pyx_t_6 = __pyx_t_5;
        for (__pyx_t_7 = 0; __pyx_t_7 < __pyx_t_6; __pyx_t_7+=1) {
          __pyx_v_class_ind = __pyx_t_7;

          /* "sklearn/linear_model/sag_fast.pyx":593
 *         if not prox:
 *             for class_ind in range(n_classes):
 *                 idx = f_idx + class_ind             # <<<<<<<<<<<<<<
 *                 weights[idx] -= cum_sum * sum_gradient[idx]
 *                 if reset:
 */
          __pyx_v_idx = (__pyx_v_f_idx + __pyx_v_class_ind);

          /* "sklearn/linear_model/sag_fast.pyx":594
 *             for class_ind in range(n_classes):
 *                 idx = f_idx + class_ind
 *                 weights[idx] -= cum_sum * sum_gradient[idx]             # <<<<<<<<<<<<<<
 *                 if reset:
 *                     weights[idx] *= wscale
 */
          __pyx_t_8 = __pyx_v_idx;
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          /* "sklearn/linear_model/sag_fast.pyx":595
 *                 idx = f_idx + class_ind
 *                 weights[idx] -= cum_sum * sum_gradient[idx]
 *                 if reset:             # <<<<<<<<<<<<<<
 *                     weights[idx] *= wscale
 *                     if not skl_isfinite(weights[idx]):
 */
          __pyx_t_4 = (__pyx_v_reset != 0);
          if (__pyx_t_4) {

            /* "sklearn/linear_model/sag_fast.pyx":596
 *                 weights[idx] -= cum_sum * sum_gradient[idx]
 *                 if reset:
 *                     weights[idx] *= wscale             # <<<<<<<<<<<<<<
 *                     if not skl_isfinite(weights[idx]):
 *                         with gil:
 */
            __pyx_t_8 = __pyx_v_idx;
            (__pyx_v_weights[__pyx_t_8]) = ((__pyx_v_weights[__pyx_t_8]) * __pyx_v_wscale);

            /* "sklearn/linear_model/sag_fast.pyx":597
 *                 if reset:
 *                     weights[idx] *= wscale
 *                     if not skl_isfinite(weights[idx]):             # <<<<<<<<<<<<<<
 *                         with gil:
 *                             raise_infinite_error(n_iter)
 */
            __pyx_t_4 = ((!(skl_isfinite((__pyx_v_weights[__pyx_v_idx])) != 0)) != 0);
            if (__pyx_t_4) {

              /* "sklearn/linear_model/sag_fast.pyx":598
 *                     weights[idx] *= wscale
 *                     if not skl_isfinite(weights[idx]):
 *                         with gil:             # <<<<<<<<<<<<<<
 *                             raise_infinite_error(n_iter)
 *         else:
 */
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                  PyGILState_STATE __pyx_gilstate_save = __Pyx_PyGILState_Ensure();
                  #endif
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                    /* "sklearn/linear_model/sag_fast.pyx":599
 *                     if not skl_isfinite(weights[idx]):
 *                         with gil:
 *                             raise_infinite_error(n_iter)             # <<<<<<<<<<<<<<
 *         else:
 *             for class_ind in range(n_classes):
 */
                    __pyx_f_7sklearn_12linear_model_8sag_fast_raise_infinite_error(__pyx_v_n_iter);
                  }

                  /* "sklearn/linear_model/sag_fast.pyx":598
 *                     weights[idx] *= wscale
 *                     if not skl_isfinite(weights[idx]):
 *                         with gil:             # <<<<<<<<<<<<<<
 *                             raise_infinite_error(n_iter)
 *         else:
 */
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                      __Pyx_PyGILState_Release(__pyx_gilstate_save);
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                      goto __pyx_L21;
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                    __pyx_L21:;
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              /* "sklearn/linear_model/sag_fast.pyx":597
 *                 if reset:
 *                     weights[idx] *= wscale
 *                     if not skl_isfinite(weights[idx]):             # <<<<<<<<<<<<<<
 *                         with gil:
 *                             raise_infinite_error(n_iter)
 */
            }

            /* "sklearn/linear_model/sag_fast.pyx":595
 *                 idx = f_idx + class_ind
 *                 weights[idx] -= cum_sum * sum_gradient[idx]
 *                 if reset:             # <<<<<<<<<<<<<<
 *                     weights[idx] *= wscale
 *                     if not skl_isfinite(weights[idx]):
 */
          }
        }

        /* "sklearn/linear_model/sag_fast.pyx":591
 *             if prox:
 *                 cum_sum_prox -= cumulative_sums_prox[feature_hist[feature_ind] - 1]
 *         if not prox:             # <<<<<<<<<<<<<<
 *             for class_ind in range(n_classes):
 *                 idx = f_idx + class_ind
 */
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      }

      /* "sklearn/linear_model/sag_fast.pyx":601
 *                             raise_infinite_error(n_iter)
 *         else:
 *             for class_ind in range(n_classes):             # <<<<<<<<<<<<<<
 *                 idx = f_idx + class_ind
 *                 if fabs(sum_gradient[idx] * cum_sum) < cum_sum_prox:
 */
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          /* "sklearn/linear_model/sag_fast.pyx":602
 *         else:
 *             for class_ind in range(n_classes):
 *                 idx = f_idx + class_ind             # <<<<<<<<<<<<<<
 *                 if fabs(sum_gradient[idx] * cum_sum) < cum_sum_prox:
 *                     # In this case, we can perform all the gradient steps and
 */
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          /* "sklearn/linear_model/sag_fast.pyx":603
 *             for class_ind in range(n_classes):
 *                 idx = f_idx + class_ind
 *                 if fabs(sum_gradient[idx] * cum_sum) < cum_sum_prox:             # <<<<<<<<<<<<<<
 *                     # In this case, we can perform all the gradient steps and
 *                     # all the proximal steps in this order, which is more
 */
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            /* "sklearn/linear_model/sag_fast.pyx":608
 *                     # efficient than unrolling all the lagged updates.
 *                     # Idea taken from scikit-learn-contrib/lightning.
 *                     weights[idx] -= cum_sum * sum_gradient[idx]             # <<<<<<<<<<<<<<
 *                     weights[idx] = _soft_thresholding(weights[idx],
 *                                                       cum_sum_prox)
 */
            __pyx_t_8 = __pyx_v_idx;
            (__pyx_v_weights[__pyx_t_8]) = ((__pyx_v_weights[__pyx_t_8]) - (__pyx_v_cum_sum * (__pyx_v_sum_gradient[__pyx_v_idx])));

            /* "sklearn/linear_model/sag_fast.pyx":609
 *                     # Idea taken from scikit-learn-contrib/lightning.
 *                     weights[idx] -= cum_sum * sum_gradient[idx]
 *                     weights[idx] = _soft_thresholding(weights[idx],             # <<<<<<<<<<<<<<
 *                                                       cum_sum_prox)
 *                 else:
 */
            (__pyx_v_weights[__pyx_v_idx]) = __pyx_f_7sklearn_12linear_model_8sag_fast__soft_thresholding((__pyx_v_weights[__pyx_v_idx]), __pyx_v_cum_sum_prox);

            /* "sklearn/linear_model/sag_fast.pyx":603
 *             for class_ind in range(n_classes):
 *                 idx = f_idx + class_ind
 *                 if fabs(sum_gradient[idx] * cum_sum) < cum_sum_prox:             # <<<<<<<<<<<<<<
 *                     # In this case, we can perform all the gradient steps and
 *                     # all the proximal steps in this order, which is more
 */
            goto __pyx_L24;
          }

          /* "sklearn/linear_model/sag_fast.pyx":612
 *                                                       cum_sum_prox)
 *                 else:
 *                     last_update_ind = feature_hist[feature_ind] - 1             # <<<<<<<<<<<<<<
 *                     if last_update_ind == -1:
 *                         last_update_ind = sample_itr - 1
 */
          /*else*/ {
            __pyx_v_last_update_ind = ((__pyx_v_feature_hist[__pyx_v_feature_ind]) - 1);

            /* "sklearn/linear_model/sag_fast.pyx":613
 *                 else:
 *                     last_update_ind = feature_hist[feature_ind] - 1
 *                     if last_update_ind == -1:             # <<<<<<<<<<<<<<
 *                         last_update_ind = sample_itr - 1
 *                     for lagged_ind in range(sample_itr - 1,
 */
            __pyx_t_4 = ((__pyx_v_last_update_ind == -1L) != 0);
            if (__pyx_t_4) {

              /* "sklearn/linear_model/sag_fast.pyx":614
 *                     last_update_ind = feature_hist[feature_ind] - 1
 *                     if last_update_ind == -1:
 *                         last_update_ind = sample_itr - 1             # <<<<<<<<<<<<<<
 *                     for lagged_ind in range(sample_itr - 1,
 *                                    last_update_ind - 1, -1):
 */
              __pyx_v_last_update_ind = (__pyx_v_sample_itr - 1);

              /* "sklearn/linear_model/sag_fast.pyx":613
 *                 else:
 *                     last_update_ind = feature_hist[feature_ind] - 1
 *                     if last_update_ind == -1:             # <<<<<<<<<<<<<<
 *                         last_update_ind = sample_itr - 1
 *                     for lagged_ind in range(sample_itr - 1,
 */
            }

            /* "sklearn/linear_model/sag_fast.pyx":616
 *                         last_update_ind = sample_itr - 1
 *                     for lagged_ind in range(sample_itr - 1,
 *                                    last_update_ind - 1, -1):             # <<<<<<<<<<<<<<
 *                         if lagged_ind > 0:
 *                             grad_step = (cumulative_sums[lagged_ind]
 */
            __pyx_t_9 = (__pyx_v_last_update_ind - 1);

            /* "sklearn/linear_model/sag_fast.pyx":615
 *                     if last_update_ind == -1:
 *                         last_update_ind = sample_itr - 1
 *                     for lagged_ind in range(sample_itr - 1,             # <<<<<<<<<<<<<<
 *                                    last_update_ind - 1, -1):
 *                         if lagged_ind > 0:
 */
            __pyx_t_10 = __pyx_t_9;
            for (__pyx_t_8 = (__pyx_v_sample_itr - 1); __pyx_t_8 > __pyx_t_10; __pyx_t_8-=1) {
              __pyx_v_lagged_ind = __pyx_t_8;

              /* "sklearn/linear_model/sag_fast.pyx":617
 *                     for lagged_ind in range(sample_itr - 1,
 *                                    last_update_ind - 1, -1):
 *                         if lagged_ind > 0:             # <<<<<<<<<<<<<<
 *                             grad_step = (cumulative_sums[lagged_ind]
 *                                - cumulative_sums[lagged_ind - 1])
 */
              __pyx_t_4 = ((__pyx_v_lagged_ind > 0) != 0);
              if (__pyx_t_4) {

                /* "sklearn/linear_model/sag_fast.pyx":619
 *                         if lagged_ind > 0:
 *                             grad_step = (cumulative_sums[lagged_ind]
 *                                - cumulative_sums[lagged_ind - 1])             # <<<<<<<<<<<<<<
 *                             prox_step = (cumulative_sums_prox[lagged_ind]
 *                                - cumulative_sums_prox[lagged_ind - 1])
 */
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                /* "sklearn/linear_model/sag_fast.pyx":621
 *                                - cumulative_sums[lagged_ind - 1])
 *                             prox_step = (cumulative_sums_prox[lagged_ind]
 *                                - cumulative_sums_prox[lagged_ind - 1])             # <<<<<<<<<<<<<<
 *                         else:
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 *                                - cumulative_sums_prox[lagged_ind - 1])
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 *                             grad_step = cumulative_sums[lagged_ind]
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{
  union {
    uint32_t u32;
    uint8_t u8[4];
  } S;
  S.u32 = 0x01020304;
  return S.u8[0] == 4;
}

/* BufferFormatCheck */
static void __Pyx_BufFmt_Init(__Pyx_BufFmt_Context* ctx,
                              __Pyx_BufFmt_StackElem* stack,
                              __Pyx_TypeInfo* type) {
  stack[0].field = &ctx->root;
  stack[0].parent_offset = 0;
  ctx->root.type = type;
  ctx->root.name = "buffer dtype";
  ctx->root.offset = 0;
  ctx->head = stack;
  ctx->head->field = &ctx->root;
  ctx->fmt_offset = 0;
  ctx->head->parent_offset = 0;
  ctx->new_packmode = '@';
  ctx->enc_packmode = '@';
  ctx->new_count = 1;
  ctx->enc_count = 0;
  ctx->enc_type = 0;
  ctx->is_complex = 0;
  ctx->is_valid_array = 0;
  ctx->struct_alignment = 0;
  while (type->typegroup == 'S') {
    ++ctx->head;
    ctx->head->field = type->fields;
    ctx->head->parent_offset = 0;
    type = type->fields->type;
  }
}
static int __Pyx_BufFmt_ParseNumber(const char** ts) {
    int count;
    const char* t = *ts;
    if (*t < '0' || *t > '9') {
      return -1;
    } else {
        count = *t++ - '0';
        while (*t >= '0' && *t < '9') {
            count *= 10;
            count += *t++ - '0';
        }
    }
    *ts = t;
    return count;
}
static int __Pyx_BufFmt_ExpectNumber(const char **ts) {
    int number = __Pyx_BufFmt_ParseNumber(ts);
    if (number == -1)
        PyErr_Format(PyExc_ValueError,\
                     "Does not understand character buffer dtype format string ('%c')", **ts);
    return number;
}
static void __Pyx_BufFmt_RaiseUnexpectedChar(char ch) {
  PyErr_Format(PyExc_ValueError,
               "Unexpected format string character: '%c'", ch);
}
static const char* __Pyx_BufFmt_DescribeTypeChar(char ch, int is_complex) {
  switch (ch) {
    case 'c': return "'char'";
    case 'b': return "'signed char'";
    case 'B': return "'unsigned char'";
    case 'h': return "'short'";
    case 'H': return "'unsigned short'";
    case 'i': return "'int'";
    case 'I': return "'unsigned int'";
    case 'l': return "'long'";
    case 'L': return "'unsigned long'";
    case 'q': return "'long long'";
    case 'Q': return "'unsigned long long'";
    case 'f': return (is_complex ? "'complex float'" : "'float'");
    case 'd': return (is_complex ? "'complex double'" : "'double'");
    case 'g': return (is_complex ? "'complex long double'" : "'long double'");
    case 'T': return "a struct";
    case 'O': return "Python object";
    case 'P': return "a pointer";
    case 's': case 'p': return "a string";
    case 0: return "end";
    default: return "unparseable format string";
  }
}
static size_t __Pyx_BufFmt_TypeCharToStandardSize(char ch, int is_complex) {
  switch (ch) {
    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return 2;
    case 'i': case 'I': case 'l': case 'L': return 4;
    case 'q': case 'Q': return 8;
    case 'f': return (is_complex ? 8 : 4);
    case 'd': return (is_complex ? 16 : 8);
    case 'g': {
      PyErr_SetString(PyExc_ValueError, "Python does not define a standard format string size for long double ('g')..");
      return 0;
    }
    case 'O': case 'P': return sizeof(void*);
    default:
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
}
static size_t __Pyx_BufFmt_TypeCharToNativeSize(char ch, int is_complex) {
  switch (ch) {
    case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return sizeof(short);
    case 'i': case 'I': return sizeof(int);
    case 'l': case 'L': return sizeof(long);
    #ifdef HAVE_LONG_LONG
    case 'q': case 'Q': return sizeof(PY_LONG_LONG);
    #endif
    case 'f': return sizeof(float) * (is_complex ? 2 : 1);
    case 'd': return sizeof(double) * (is_complex ? 2 : 1);
    case 'g': return sizeof(long double) * (is_complex ? 2 : 1);
    case 'O': case 'P': return sizeof(void*);
    default: {
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
  }
}
typedef struct { char c; short x; } __Pyx_st_short;
typedef struct { char c; int x; } __Pyx_st_int;
typedef struct { char c; long x; } __Pyx_st_long;
typedef struct { char c; float x; } __Pyx_st_float;
typedef struct { char c; double x; } __Pyx_st_double;
typedef struct { char c; long double x; } __Pyx_st_longdouble;
typedef struct { char c; void *x; } __Pyx_st_void_p;
#ifdef HAVE_LONG_LONG
typedef struct { char c; PY_LONG_LONG x; } __Pyx_st_longlong;
#endif
static size_t __Pyx_BufFmt_TypeCharToAlignment(char ch, CYTHON_UNUSED int is_complex) {
  switch (ch) {
    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return sizeof(__Pyx_st_short) - sizeof(short);
    case 'i': case 'I': return sizeof(__Pyx_st_int) - sizeof(int);
    case 'l': case 'L': return sizeof(__Pyx_st_long) - sizeof(long);
#ifdef HAVE_LONG_LONG
    case 'q': case 'Q': return sizeof(__Pyx_st_longlong) - sizeof(PY_LONG_LONG);
#endif
    case 'f': return sizeof(__Pyx_st_float) - sizeof(float);
    case 'd': return sizeof(__Pyx_st_double) - sizeof(double);
    case 'g': return sizeof(__Pyx_st_longdouble) - sizeof(long double);
    case 'P': case 'O': return sizeof(__Pyx_st_void_p) - sizeof(void*);
    default:
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
}
/* These are for computing the padding at the end of the struct to align
   on the first member of the struct. This will probably the same as above,
   but we don't have any guarantees.
 */
typedef struct { short x; char c; } __Pyx_pad_short;
typedef struct { int x; char c; } __Pyx_pad_int;
typedef struct { long x; char c; } __Pyx_pad_long;
typedef struct { float x; char c; } __Pyx_pad_float;
typedef struct { double x; char c; } __Pyx_pad_double;
typedef struct { long double x; char c; } __Pyx_pad_longdouble;
typedef struct { void *x; char c; } __Pyx_pad_void_p;
#ifdef HAVE_LONG_LONG
typedef struct { PY_LONG_LONG x; char c; } __Pyx_pad_longlong;
#endif
static size_t __Pyx_BufFmt_TypeCharToPadding(char ch, CYTHON_UNUSED int is_complex) {
  switch (ch) {
    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return sizeof(__Pyx_pad_short) - sizeof(short);
    case 'i': case 'I': return sizeof(__Pyx_pad_int) - sizeof(int);
    case 'l': case 'L': return sizeof(__Pyx_pad_long) - sizeof(long);
#ifdef HAVE_LONG_LONG
    case 'q': case 'Q': return sizeof(__Pyx_pad_longlong) - sizeof(PY_LONG_LONG);
#endif
    case 'f': return sizeof(__Pyx_pad_float) - sizeof(float);
    case 'd': return sizeof(__Pyx_pad_double) - sizeof(double);
    case 'g': return sizeof(__Pyx_pad_longdouble) - sizeof(long double);
    case 'P': case 'O': return sizeof(__Pyx_pad_void_p) - sizeof(void*);
    default:
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
}
static char __Pyx_BufFmt_TypeCharToGroup(char ch, int is_complex) {
  switch (ch) {
    case 'c':
        return 'H';
    case 'b': case 'h': case 'i':
    case 'l': case 'q': case 's': case 'p':
        return 'I';
    case 'B': case 'H': case 'I': case 'L': case 'Q':
        return 'U';
    case 'f': case 'd': case 'g':
        return (is_complex ? 'C' : 'R');
    case 'O':
        return 'O';
    case 'P':
        return 'P';
    default: {
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
  }
}
static void __Pyx_BufFmt_RaiseExpected(__Pyx_BufFmt_Context* ctx) {
  if (ctx->head == NULL || ctx->head->field == &ctx->root) {
    const char* expected;
    const char* quote;
    if (ctx->head == NULL) {
      expected = "end";
      quote = "";
    } else {
      expected = ctx->head->field->type->name;
      quote = "'";
    }
    PyErr_Format(PyExc_ValueError,
                 "Buffer dtype mismatch, expected %s%s%s but got %s",
                 quote, expected, quote,
                 __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex));
  } else {
    __Pyx_StructField* field = ctx->head->field;
    __Pyx_StructField* parent = (ctx->head - 1)->field;
    PyErr_Format(PyExc_ValueError,
                 "Buffer dtype mismatch, expected '%s' but got %s in '%s.%s'",
                 field->type->name, __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex),
                 parent->type->name, field->name);
  }
}
static int __Pyx_BufFmt_ProcessTypeChunk(__Pyx_BufFmt_Context* ctx) {
  char group;
  size_t size, offset, arraysize = 1;
  if (ctx->enc_type == 0) return 0;
  if (ctx->head->field->type->arraysize[0]) {
    int i, ndim = 0;
    if (ctx->enc_type == 's' || ctx->enc_type == 'p') {
        ctx->is_valid_array = ctx->head->field->type->ndim == 1;
        ndim = 1;
        if (ctx->enc_count != ctx->head->field->type->arraysize[0]) {
            PyErr_Format(PyExc_ValueError,
                         "Expected a dimension of size %zu, got %zu",
                         ctx->head->field->type->arraysize[0], ctx->enc_count);
            return -1;
        }
    }
    if (!ctx->is_valid_array) {
      PyErr_Format(PyExc_ValueError, "Expected %d dimensions, got %d",
                   ctx->head->field->type->ndim, ndim);
      return -1;
    }
    for (i = 0; i < ctx->head->field->type->ndim; i++) {
      arraysize *= ctx->head->field->type->arraysize[i];
    }
    ctx->is_valid_array = 0;
    ctx->enc_count = 1;
  }
  group = __Pyx_BufFmt_TypeCharToGroup(ctx->enc_type, ctx->is_complex);
  do {
    __Pyx_StructField* field = ctx->head->field;
    __Pyx_TypeInfo* type = field->type;
    if (ctx->enc_packmode == '@' || ctx->enc_packmode == '^') {
      size = __Pyx_BufFmt_TypeCharToNativeSize(ctx->enc_type, ctx->is_complex);
    } else {
      size = __Pyx_BufFmt_TypeCharToStandardSize(ctx->enc_type, ctx->is_complex);
    }
    if (ctx->enc_packmode == '@') {
      size_t align_at = __Pyx_BufFmt_TypeCharToAlignment(ctx->enc_type, ctx->is_complex);
      size_t align_mod_offset;
      if (align_at == 0) return -1;
      align_mod_offset = ctx->fmt_offset % align_at;
      if (align_mod_offset > 0) ctx->fmt_offset += align_at - align_mod_offset;
      if (ctx->struct_alignment == 0)
          ctx->struct_alignment = __Pyx_BufFmt_TypeCharToPadding(ctx->enc_type,
                                                                 ctx->is_complex);
    }
    if (type->size != size || type->typegroup != group) {
      if (type->typegroup == 'C' && type->fields != NULL) {
        size_t parent_offset = ctx->head->parent_offset + field->offset;
        ++ctx->head;
        ctx->head->field = type->fields;
        ctx->head->parent_offset = parent_offset;
        continue;
      }
      if ((type->typegroup == 'H' || group == 'H') && type->size == size) {
      } else {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return -1;
      }
    }
    offset = ctx->head->parent_offset + field->offset;
    if (ctx->fmt_offset != offset) {
      PyErr_Format(PyExc_ValueError,
                   "Buffer dtype mismatch; next field is at offset %" CYTHON_FORMAT_SSIZE_T "d but %" CYTHON_FORMAT_SSIZE_T "d expected",
                   (Py_ssize_t)ctx->fmt_offset, (Py_ssize_t)offset);
      return -1;
    }
    ctx->fmt_offset += size;
    if (arraysize)
      ctx->fmt_offset += (arraysize - 1) * size;
    --ctx->enc_count;
    while (1) {
      if (field == &ctx->root) {
        ctx->head = NULL;
        if (ctx->enc_count != 0) {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return -1;
        }
        break;
      }
      ctx->head->field = ++field;
      if (field->type == NULL) {
        --ctx->head;
        field = ctx->head->field;
        continue;
      } else if (field->type->typegroup == 'S') {
        size_t parent_offset = ctx->head->parent_offset + field->offset;
        if (field->type->fields->type == NULL) continue;
        field = field->type->fields;
        ++ctx->head;
        ctx->head->field = field;
        ctx->head->parent_offset = parent_offset;
        break;
      } else {
        break;
      }
    }
  } while (ctx->enc_count);
  ctx->enc_type = 0;
  ctx->is_complex = 0;
  return 0;
}
static 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_Is_Little_Endian()) {
          PyErr_SetString(PyExc_ValueError, "Little-endian buffer not supported on big-endian compiler");
          return NULL;
        }
        ctx->new_packmode = '=';
        ++ts;
        break;
      case '>':
      case '!':
        if (__Pyx_Is_Little_Endian()) {
          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;
        }
        CYTHON_FALLTHROUGH;
      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;
        }
        CYTHON_FALLTHROUGH;
      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;
        }
    }
  }
}

/* BufferGetAndValidate */
  static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info) {
  if (unlikely(info->buf == NULL)) return;
  if (info->suboffsets == __Pyx_minusones) info->suboffsets = NULL;
  __Pyx_ReleaseBuffer(info);
}
static 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 int __Pyx__GetBufferAndValidate(
        Py_buffer* buf, PyObject* obj,  __Pyx_TypeInfo* dtype, int flags,
        int nd, int cast, __Pyx_BufFmt_StackElem* stack)
{
  buf->buf = NULL;
  if (unlikely(__Pyx_GetBuffer(obj, buf, flags) == -1)) {
    __Pyx_ZeroBuffer(buf);
    return -1;
  }
  if (unlikely(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 (unlikely((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_SafeReleaseBuffer(buf);
  return -1;
}

/* 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 = __Pyx_PyThreadState_Current;
    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
#endif

/* 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

/* 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

/* 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) || __Pyx_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

/* GetModuleGlobalName */
    static CYTHON_INLINE PyObject *__Pyx_GetModuleGlobalName(PyObject *name) {
    PyObject *result;
#if !CYTHON_AVOID_BORROWED_REFS
#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030500A1
    result = _PyDict_GetItem_KnownHash(__pyx_d, name, ((PyASCIIObject *) name)->hash);
    if (likely(result)) {
        Py_INCREF(result);
    } else if (unlikely(PyErr_Occurred())) {
        result = NULL;
    } else {
#else
    result = PyDict_GetItem(__pyx_d, name);
    if (likely(result)) {
        Py_INCREF(result);
    } else {
#endif
#else
    result = PyObject_GetItem(__pyx_d, name);
    if (!result) {
        PyErr_Clear();
#endif
        result = __Pyx_GetBuiltinName(name);
    }
    return result;
}

/* 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(__Pyx_TypeCheck(obj, type)))
        return 1;
    PyErr_Format(PyExc_TypeError, "Cannot convert %.200s to %.200s",
                 Py_TYPE(obj)->tp_name, type->tp_name);
    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

/* BytesEquals */
        static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals) {
#if CYTHON_COMPILING_IN_PYPY
    return PyObject_RichCompareBool(s1, s2, equals);
#else
    if (s1 == s2) {
        return (equals == Py_EQ);
    } else if (PyBytes_CheckExact(s1) & PyBytes_CheckExact(s2)) {
        const char *ps1, *ps2;
        Py_ssize_t length = PyBytes_GET_SIZE(s1);
        if (length != PyBytes_GET_SIZE(s2))
            return (equals == Py_NE);
        ps1 = PyBytes_AS_STRING(s1);
        ps2 = PyBytes_AS_STRING(s2);
        if (ps1[0] != ps2[0]) {
            return (equals == Py_NE);
        } else if (length == 1) {
            return (equals == Py_EQ);
        } else {
            int result;
#if CYTHON_USE_UNICODE_INTERNALS
            Py_hash_t hash1, hash2;
            hash1 = ((PyBytesObject*)s1)->ob_shash;
            hash2 = ((PyBytesObject*)s2)->ob_shash;
            if (hash1 != hash2 && hash1 != -1 && hash2 != -1) {
                return (equals == Py_NE);
            }
#endif
            result = memcmp(ps1, ps2, (size_t)length);
            return (equals == Py_EQ) ? (result == 0) : (result != 0);
        }
    } else if ((s1 == Py_None) & PyBytes_CheckExact(s2)) {
        return (equals == Py_NE);
    } else if ((s2 == Py_None) & PyBytes_CheckExact(s1)) {
        return (equals == Py_NE);
    } else {
        int result;
        PyObject* py_result = PyObject_RichCompare(s1, s2, equals);
        if (!py_result)
            return -1;
        result = __Pyx_PyObject_IsTrue(py_result);
        Py_DECREF(py_result);
        return result;
    }
#endif
}

/* UnicodeEquals */
        static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals) {
#if CYTHON_COMPILING_IN_PYPY
    return PyObject_RichCompareBool(s1, s2, equals);
#else
#if PY_MAJOR_VERSION < 3
    PyObject* owned_ref = NULL;
#endif
    int s1_is_unicode, s2_is_unicode;
    if (s1 == s2) {
        goto return_eq;
    }
    s1_is_unicode = PyUnicode_CheckExact(s1);
    s2_is_unicode = PyUnicode_CheckExact(s2);
#if PY_MAJOR_VERSION < 3
    if ((s1_is_unicode & (!s2_is_unicode)) && PyString_CheckExact(s2)) {
        owned_ref = PyUnicode_FromObject(s2);
        if (unlikely(!owned_ref))
            return -1;
        s2 = owned_ref;
        s2_is_unicode = 1;
    } else if ((s2_is_unicode & (!s1_is_unicode)) && PyString_CheckExact(s1)) {
        owned_ref = PyUnicode_FromObject(s1);
        if (unlikely(!owned_ref))
            return -1;
        s1 = owned_ref;
        s1_is_unicode = 1;
    } else if (((!s2_is_unicode) & (!s1_is_unicode))) {
        return __Pyx_PyBytes_Equals(s1, s2, equals);
    }
#endif
    if (s1_is_unicode & s2_is_unicode) {
        Py_ssize_t length;
        int kind;
        void *data1, *data2;
        if (unlikely(__Pyx_PyUnicode_READY(s1) < 0) || unlikely(__Pyx_PyUnicode_READY(s2) < 0))
            return -1;
        length = __Pyx_PyUnicode_GET_LENGTH(s1);
        if (length != __Pyx_PyUnicode_GET_LENGTH(s2)) {
            goto return_ne;
        }
#if CYTHON_USE_UNICODE_INTERNALS
        {
            Py_hash_t hash1, hash2;
        #if CYTHON_PEP393_ENABLED
            hash1 = ((PyASCIIObject*)s1)->hash;
            hash2 = ((PyASCIIObject*)s2)->hash;
        #else
            hash1 = ((PyUnicodeObject*)s1)->hash;
            hash2 = ((PyUnicodeObject*)s2)->hash;
        #endif
            if (hash1 != hash2 && hash1 != -1 && hash2 != -1) {
                goto return_ne;
            }
        }
#endif
        kind = __Pyx_PyUnicode_KIND(s1);
        if (kind != __Pyx_PyUnicode_KIND(s2)) {
            goto return_ne;
        }
        data1 = __Pyx_PyUnicode_DATA(s1);
        data2 = __Pyx_PyUnicode_DATA(s2);
        if (__Pyx_PyUnicode_READ(kind, data1, 0) != __Pyx_PyUnicode_READ(kind, data2, 0)) {
            goto return_ne;
        } else if (length == 1) {
            goto return_eq;
        } else {
            int result = memcmp(data1, data2, (size_t)(length * kind));
            #if PY_MAJOR_VERSION < 3
            Py_XDECREF(owned_ref);
            #endif
            return (equals == Py_EQ) ? (result == 0) : (result != 0);
        }
    } else if ((s1 == Py_None) & s2_is_unicode) {
        goto return_ne;
    } else if ((s2 == Py_None) & s1_is_unicode) {
        goto return_ne;
    } else {
        int result;
        PyObject* py_result = PyObject_RichCompare(s1, s2, equals);
        if (!py_result)
            return -1;
        result = __Pyx_PyObject_IsTrue(py_result);
        Py_DECREF(py_result);
        return result;
    }
return_eq:
    #if PY_MAJOR_VERSION < 3
    Py_XDECREF(owned_ref);
    #endif
    return (equals == Py_EQ);
return_ne:
    #if PY_MAJOR_VERSION < 3
    Py_XDECREF(owned_ref);
    #endif
    return (equals == Py_NE);
#endif
}

/* 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);
    int flags = PyCFunction_GET_FLAGS(func);
    assert(PyCFunction_Check(func));
    assert(METH_FASTCALL == (flags & ~(METH_CLASS | METH_STATIC | METH_COEXIST | METH_KEYWORDS)));
    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());
    if ((PY_VERSION_HEX < 0x030700A0) || unlikely(flags & METH_KEYWORDS)) {
        return (*((__Pyx_PyCFunctionFastWithKeywords)meth)) (self, args, nargs, NULL);
    } else {
        return (*((__Pyx_PyCFunctionFast)meth)) (self, args, nargs);
    }
}
#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
    if (likely(PyCFunction_Check(func))) {
        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

/* 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 (cause) {
        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 = __Pyx_PyThreadState_Current;
        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

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

/* None */
        static CYTHON_INLINE void __Pyx_RaiseUnboundLocalError(const char *varname) {
    PyErr_Format(PyExc_UnboundLocalError, "local variable '%s' referenced before assignment", varname);
}

/* WriteUnraisableException */
        static void __Pyx_WriteUnraisable(const char *name, CYTHON_UNUSED int clineno,
                                  CYTHON_UNUSED int lineno, CYTHON_UNUSED const char *filename,
                                  int full_traceback, CYTHON_UNUSED int nogil) {
    PyObject *old_exc, *old_val, *old_tb;
    PyObject *ctx;
    __Pyx_PyThreadState_declare
#ifdef WITH_THREAD
    PyGILState_STATE state;
    if (nogil)
        state = PyGILState_Ensure();
#ifdef _MSC_VER
    else state = (PyGILState_STATE)-1;
#endif
#endif
    __Pyx_PyThreadState_assign
    __Pyx_ErrFetch(&old_exc, &old_val, &old_tb);
    if (full_traceback) {
        Py_XINCREF(old_exc);
        Py_XINCREF(old_val);
        Py_XINCREF(old_tb);
        __Pyx_ErrRestore(old_exc, old_val, old_tb);
        PyErr_PrintEx(1);
    }
    #if PY_MAJOR_VERSION < 3
    ctx = PyString_FromString(name);
    #else
    ctx = PyUnicode_FromString(name);
    #endif
    __Pyx_ErrRestore(old_exc, old_val, old_tb);
    if (!ctx) {
        PyErr_WriteUnraisable(Py_None);
    } else {
        PyErr_WriteUnraisable(ctx);
        Py_DECREF(ctx);
    }
#ifdef WITH_THREAD
    if (nogil)
        PyGILState_Release(state);
#endif
}

/* DictGetItem */
        #if PY_MAJOR_VERSION >= 3 && !CYTHON_COMPILING_IN_PYPY
static PyObject *__Pyx_PyDict_GetItem(PyObject *d, PyObject* key) {
    PyObject *value;
    value = PyDict_GetItemWithError(d, key);
    if (unlikely(!value)) {
        if (!PyErr_Occurred()) {
            PyObject* args = PyTuple_Pack(1, key);
            if (likely(args))
                PyErr_SetObject(PyExc_KeyError, args);
            Py_XDECREF(args);
        }
        return NULL;
    }
    Py_INCREF(value);
    return value;
}
#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");
}

/* 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) {
    #if PY_VERSION_HEX >= 0x030700A3
    *type = tstate->exc_state.exc_type;
    *value = tstate->exc_state.exc_value;
    *tb = tstate->exc_state.exc_traceback;
    #else
    *type = tstate->exc_type;
    *value = tstate->exc_value;
    *tb = tstate->exc_traceback;
    #endif
    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;
    #if PY_VERSION_HEX >= 0x030700A3
    tmp_type = tstate->exc_state.exc_type;
    tmp_value = tstate->exc_state.exc_value;
    tmp_tb = tstate->exc_state.exc_traceback;
    tstate->exc_state.exc_type = type;
    tstate->exc_state.exc_value = value;
    tstate->exc_state.exc_traceback = tb;
    #else
    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;
    #endif
    Py_XDECREF(tmp_type);
    Py_XDECREF(tmp_value);
    Py_XDECREF(tmp_tb);
}
#endif

/* PyErrExceptionMatches */
        #if CYTHON_FAST_THREAD_STATE
static int __Pyx_PyErr_ExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) {
    Py_ssize_t i, n;
    n = PyTuple_GET_SIZE(tuple);
#if PY_MAJOR_VERSION >= 3
    for (i=0; i<n; i++) {
        if (exc_type == PyTuple_GET_ITEM(tuple, i)) return 1;
    }
#endif
    for (i=0; i<n; i++) {
        if (__Pyx_PyErr_GivenExceptionMatches(exc_type, PyTuple_GET_ITEM(tuple, i))) return 1;
    }
    return 0;
}
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;
    if (unlikely(PyTuple_Check(err)))
        return __Pyx_PyErr_ExceptionMatchesTuple(exc_type, err);
    return __Pyx_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
    #if PY_VERSION_HEX >= 0x030700A3
    tmp_type = tstate->exc_state.exc_type;
    tmp_value = tstate->exc_state.exc_value;
    tmp_tb = tstate->exc_state.exc_traceback;
    tstate->exc_state.exc_type = local_type;
    tstate->exc_state.exc_value = local_value;
    tstate->exc_state.exc_traceback = local_tb;
    #else
    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;
    #endif
    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;
}

/* PyObject_GenericGetAttrNoDict */
          #if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000
static PyObject *__Pyx_RaiseGenericGetAttributeError(PyTypeObject *tp, PyObject *attr_name) {
    PyErr_Format(PyExc_AttributeError,
#if PY_MAJOR_VERSION >= 3
                 "'%.50s' object has no attribute '%U'",
                 tp->tp_name, attr_name);
#else
                 "'%.50s' object has no attribute '%.400s'",
                 tp->tp_name, PyString_AS_STRING(attr_name));
#endif
    return NULL;
}
static CYTHON_INLINE PyObject* __Pyx_PyObject_GenericGetAttrNoDict(PyObject* obj, PyObject* attr_name) {
    PyObject *descr;
    PyTypeObject *tp = Py_TYPE(obj);
    if (unlikely(!PyString_Check(attr_name))) {
        return PyObject_GenericGetAttr(obj, attr_name);
    }
    assert(!tp->tp_dictoffset);
    descr = _PyType_Lookup(tp, attr_name);
    if (unlikely(!descr)) {
        return __Pyx_RaiseGenericGetAttributeError(tp, attr_name);
    }
    Py_INCREF(descr);
    #if PY_MAJOR_VERSION < 3
    if (likely(PyType_HasFeature(Py_TYPE(descr), Py_TPFLAGS_HAVE_CLASS)))
    #endif
    {
        descrgetfunc f = Py_TYPE(descr)->tp_descr_get;
        if (unlikely(f)) {
            PyObject *res = f(descr, obj, (PyObject *)tp);
            Py_DECREF(descr);
            return res;
        }
    }
    return descr;
}
#endif

/* PyObject_GenericGetAttr */
          #if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000
static PyObject* __Pyx_PyObject_GenericGetAttr(PyObject* obj, PyObject* attr_name) {
    if (unlikely(Py_TYPE(obj)->tp_dictoffset)) {
        return PyObject_GenericGetAttr(obj, attr_name);
    }
    return __Pyx_PyObject_GenericGetAttrNoDict(obj, attr_name);
}
#endif

/* 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_MAJOR_VERSION < 3
    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, '.')) {
                module = PyImport_ImportModuleLevelObject(
                    name, global_dict, empty_dict, list, 1);
                if (!module) {
                    if (!PyErr_ExceptionMatches(PyExc_ImportError))
                        goto bad;
                    PyErr_Clear();
                }
            }
            level = 0;
        }
        #endif
        if (!module) {
            #if PY_MAJOR_VERSION < 3
            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_MAJOR_VERSION < 3
    Py_XDECREF(py_import);
    #endif
    Py_XDECREF(empty_list);
    Py_XDECREF(empty_dict);
    return module;
}

/* CLineInTraceback */
          #ifndef CYTHON_CLINE_IN_TRACEBACK
static int __Pyx_CLineForTraceback(CYTHON_UNUSED PyThreadState *tstate, int c_line) {
    PyObject *use_cline;
    PyObject *ptype, *pvalue, *ptraceback;
#if CYTHON_COMPILING_IN_CPYTHON
    PyObject **cython_runtime_dict;
#endif
    if (unlikely(!__pyx_cython_runtime)) {
        return c_line;
    }
    __Pyx_ErrFetchInState(tstate, &ptype, &pvalue, &ptraceback);
#if CYTHON_COMPILING_IN_CPYTHON
    cython_runtime_dict = _PyObject_GetDictPtr(__pyx_cython_runtime);
    if (likely(cython_runtime_dict)) {
      use_cline = __Pyx_PyDict_GetItemStr(*cython_runtime_dict, __pyx_n_s_cline_in_traceback);
    } else
#endif
    {
      PyObject *use_cline_obj = __Pyx_PyObject_GetAttrStr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback);
      if (use_cline_obj) {
        use_cline = PyObject_Not(use_cline_obj) ? Py_False : Py_True;
        Py_DECREF(use_cline_obj);
      } else {
        PyErr_Clear();
        use_cline = NULL;
      }
    }
    if (!use_cline) {
        c_line = 0;
        PyObject_SetAttr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback, Py_False);
    }
    else if (PyObject_Not(use_cline) != 0) {
        c_line = 0;
    }
    __Pyx_ErrRestoreInState(tstate, ptype, pvalue, ptraceback);
    return c_line;
}
#endif

/* 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;
    PyThreadState *tstate = __Pyx_PyThreadState_Current;
    if (c_line) {
        c_line = __Pyx_CLineForTraceback(tstate, c_line);
    }
    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(
        tstate,            /*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 (__Pyx_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 ((0)) {}
        else if (__Pyx_TypeCheck(obj, __pyx_ptype_5numpy_ndarray)) __pyx_pw_5numpy_7ndarray_3__releasebuffer__(obj, view);
    view->obj = NULL;
    Py_DECREF(obj);
}
#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);
    }
}

/* 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_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);
    }
}

/* CIntToPy */
          static CYTHON_INLINE PyObject* __Pyx_PyInt_From_time_t(time_t value) {
    const time_t neg_one = (time_t) -1, const_zero = (time_t) 0;
    const int is_unsigned = neg_one > const_zero;
    if (is_unsigned) {
        if (sizeof(time_t) < sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(time_t) <= sizeof(unsigned long)) {
            return PyLong_FromUnsignedLong((unsigned long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(time_t) <= sizeof(unsigned PY_LONG_LONG)) {
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
#endif
        }
    } else {
        if (sizeof(time_t) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(time_t) <= 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(time_t),
                                     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;
}

/* 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;
}

/* FastTypeChecks */
          #if CYTHON_COMPILING_IN_CPYTHON
static int __Pyx_InBases(PyTypeObject *a, PyTypeObject *b) {
    while (a) {
        a = a->tp_base;
        if (a == b)
            return 1;
    }
    return b == &PyBaseObject_Type;
}
static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b) {
    PyObject *mro;
    if (a == b) return 1;
    mro = a->tp_mro;
    if (likely(mro)) {
        Py_ssize_t i, n;
        n = PyTuple_GET_SIZE(mro);
        for (i = 0; i < n; i++) {
            if (PyTuple_GET_ITEM(mro, i) == (PyObject *)b)
                return 1;
        }
        return 0;
    }
    return __Pyx_InBases(a, b);
}
#if PY_MAJOR_VERSION == 2
static int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject* exc_type2) {
    PyObject *exception, *value, *tb;
    int res;
    __Pyx_PyThreadState_declare
    __Pyx_PyThreadState_assign
    __Pyx_ErrFetch(&exception, &value, &tb);
    res = exc_type1 ? PyObject_IsSubclass(err, exc_type1) : 0;
    if (unlikely(res == -1)) {
        PyErr_WriteUnraisable(err);
        res = 0;
    }
    if (!res) {
        res = PyObject_IsSubclass(err, exc_type2);
        if (unlikely(res == -1)) {
            PyErr_WriteUnraisable(err);
            res = 0;
        }
    }
    __Pyx_ErrRestore(exception, value, tb);
    return res;
}
#else
static CYTHON_INLINE int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject *exc_type2) {
    int res = exc_type1 ? __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type1) : 0;
    if (!res) {
        res = __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type2);
    }
    return res;
}
#endif
static int __Pyx_PyErr_GivenExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) {
    Py_ssize_t i, n;
    assert(PyExceptionClass_Check(exc_type));
    n = PyTuple_GET_SIZE(tuple);
#if PY_MAJOR_VERSION >= 3
    for (i=0; i<n; i++) {
        if (exc_type == PyTuple_GET_ITEM(tuple, i)) return 1;
    }
#endif
    for (i=0; i<n; i++) {
        PyObject *t = PyTuple_GET_ITEM(tuple, i);
        #if PY_MAJOR_VERSION < 3
        if (likely(exc_type == t)) return 1;
        #endif
        if (likely(PyExceptionClass_Check(t))) {
            if (__Pyx_inner_PyErr_GivenExceptionMatches2(exc_type, NULL, t)) return 1;
        } else {
        }
    }
    return 0;
}
static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject* exc_type) {
    if (likely(err == exc_type)) return 1;
    if (likely(PyExceptionClass_Check(err))) {
        if (likely(PyExceptionClass_Check(exc_type))) {
            return __Pyx_inner_PyErr_GivenExceptionMatches2(err, NULL, exc_type);
        } else if (likely(PyTuple_Check(exc_type))) {
            return __Pyx_PyErr_GivenExceptionMatchesTuple(err, exc_type);
        } else {
        }
    }
    return PyErr_GivenExceptionMatches(err, exc_type);
}
static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *exc_type1, PyObject *exc_type2) {
    assert(PyExceptionClass_Check(exc_type1));
    assert(PyExceptionClass_Check(exc_type2));
    if (likely(err == exc_type1 || err == exc_type2)) return 1;
    if (likely(PyExceptionClass_Check(err))) {
        return __Pyx_inner_PyErr_GivenExceptionMatches2(err, exc_type1, exc_type2);
    }
    return (PyErr_GivenExceptionMatches(err, exc_type1) || PyErr_GivenExceptionMatches(err, exc_type2));
}
#endif

/* 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;
        if (PyObject_Hash(*t->p) == -1)
            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 const char* __Pyx_PyObject_AsString(PyObject* o) {
    Py_ssize_t ignore;
    return __Pyx_PyObject_AsStringAndSize(o, &ignore);
}
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
#if !CYTHON_PEP393_ENABLED
static const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
    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
static CYTHON_INLINE const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
    if (unlikely(__Pyx_PyUnicode_READY(o) == -1)) return NULL;
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
    if (likely(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
#endif
static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
    if (
#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
            __Pyx_sys_getdefaultencoding_not_ascii &&
#endif
            PyUnicode_Check(o)) {
        return __Pyx_PyUnicode_AsStringAndSize(o, length);
    } 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 PyObject* __Pyx_PyNumber_IntOrLongWrongResultType(PyObject* result, const char* type_name) {
#if PY_MAJOR_VERSION >= 3
    if (PyLong_Check(result)) {
        if (PyErr_WarnFormat(PyExc_DeprecationWarning, 1,
                "__int__ returned non-int (type %.200s).  "
                "The ability to return an instance of a strict subclass of int "
                "is deprecated, and may be removed in a future version of Python.",
                Py_TYPE(result)->tp_name)) {
            Py_DECREF(result);
            return NULL;
        }
        return result;
    }
#endif
    PyErr_Format(PyExc_TypeError,
                 "__%.4s__ returned non-%.4s (type %.200s)",
                 type_name, type_name, Py_TYPE(result)->tp_name);
    Py_DECREF(result);
    return NULL;
}
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 (likely(PyInt_Check(x) || PyLong_Check(x)))
#else
  if (likely(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 = m->nb_int(x);
  }
  else if (m && m->nb_long) {
    name = "long";
    res = m->nb_long(x);
  }
  #else
  if (likely(m && m->nb_int)) {
    name = "int";
    res = m->nb_int(x);
  }
  #endif
#else
  if (!PyBytes_CheckExact(x) && !PyUnicode_CheckExact(x)) {
    res = PyNumber_Int(x);
  }
#endif
  if (likely(res)) {
#if PY_MAJOR_VERSION < 3
    if (unlikely(!PyInt_Check(res) && !PyLong_Check(res))) {
#else
    if (unlikely(!PyLong_CheckExact(res))) {
#endif
        return __Pyx_PyNumber_IntOrLongWrongResultType(res, name);
    }
  }
  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_PyBool_FromLong(long b) {
  return b ? __Pyx_NewRef(Py_True) : __Pyx_NewRef(Py_False);
}
static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) {
    return PyInt_FromSize_t(ival);
}


#endif /* Py_PYTHON_H */
