PyClical.cpp

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  #define __Pyx_PyUnicode_Concat(a, b)      PyUnicode_Concat(a, b)
  #define __Pyx_PyUnicode_ConcatSafe(a, b)  ((unlikely((a) == Py_None) || unlikely((b) == Py_None)) ?\
      PyNumber_Add(a, b) : __Pyx_PyUnicode_Concat(a, b))
#endif
#if CYTHON_COMPILING_IN_PYPY && !defined(PyUnicode_Contains)
  #define PyUnicode_Contains(u, s)  PySequence_Contains(u, s)
#endif
#if CYTHON_COMPILING_IN_PYPY && !defined(PyByteArray_Check)
  #define PyByteArray_Check(obj)  PyObject_TypeCheck(obj, &PyByteArray_Type)
#endif
#if CYTHON_COMPILING_IN_PYPY && !defined(PyObject_Format)
  #define PyObject_Format(obj, fmt)  PyObject_CallMethod(obj, "__format__", "O", fmt)
#endif
#define __Pyx_PyString_FormatSafe(a, b)   ((unlikely((a) == Py_None || (PyString_Check(b) && !PyString_CheckExact(b)))) ? PyNumber_Remainder(a, b) : __Pyx_PyString_Format(a, b))
#define __Pyx_PyUnicode_FormatSafe(a, b)  ((unlikely((a) == Py_None || (PyUnicode_Check(b) && !PyUnicode_CheckExact(b)))) ? PyNumber_Remainder(a, b) : PyUnicode_Format(a, b))
#if PY_MAJOR_VERSION >= 3
  #define __Pyx_PyString_Format(a, b)  PyUnicode_Format(a, b)
#else
  #define __Pyx_PyString_Format(a, b)  PyString_Format(a, b)
#endif
#if PY_MAJOR_VERSION < 3 && !defined(PyObject_ASCII)
  #define PyObject_ASCII(o)            PyObject_Repr(o)
#endif
#if PY_MAJOR_VERSION >= 3
  #define PyBaseString_Type            PyUnicode_Type
  #define PyStringObject               PyUnicodeObject
  #define PyString_Type                PyUnicode_Type
  #define PyString_Check               PyUnicode_Check
  #define PyString_CheckExact          PyUnicode_CheckExact
#ifndef PyObject_Unicode
  #define PyObject_Unicode             PyObject_Str
#endif
#endif
#if PY_MAJOR_VERSION >= 3
  #define __Pyx_PyBaseString_Check(obj) PyUnicode_Check(obj)
  #define __Pyx_PyBaseString_CheckExact(obj) PyUnicode_CheckExact(obj)
#else
  #define __Pyx_PyBaseString_Check(obj) (PyString_Check(obj) || PyUnicode_Check(obj))
  #define __Pyx_PyBaseString_CheckExact(obj) (PyString_CheckExact(obj) || PyUnicode_CheckExact(obj))
#endif
#ifndef PySet_CheckExact
  #define PySet_CheckExact(obj)        (Py_TYPE(obj) == &PySet_Type)
#endif
#if PY_VERSION_HEX >= 0x030900A4
  #define __Pyx_SET_REFCNT(obj, refcnt) Py_SET_REFCNT(obj, refcnt)
  #define __Pyx_SET_SIZE(obj, size) Py_SET_SIZE(obj, size)
#else
  #define __Pyx_SET_REFCNT(obj, refcnt) Py_REFCNT(obj) = (refcnt)
  #define __Pyx_SET_SIZE(obj, size) Py_SIZE(obj) = (size)
#endif
#if CYTHON_ASSUME_SAFE_MACROS
  #define __Pyx_PySequence_SIZE(seq)  Py_SIZE(seq)
#else
  #define __Pyx_PySequence_SIZE(seq)  PySequence_Size(seq)
#endif
#if PY_MAJOR_VERSION >= 3
  #define PyIntObject                  PyLongObject
  #define PyInt_Type                   PyLong_Type
  #define PyInt_Check(op)              PyLong_Check(op)
  #define PyInt_CheckExact(op)         PyLong_CheckExact(op)
  #define PyInt_FromString             PyLong_FromString
  #define PyInt_FromUnicode            PyLong_FromUnicode
  #define PyInt_FromLong               PyLong_FromLong
  #define PyInt_FromSize_t             PyLong_FromSize_t
  #define PyInt_FromSsize_t            PyLong_FromSsize_t
  #define PyInt_AsLong                 PyLong_AsLong
  #define PyInt_AS_LONG                PyLong_AS_LONG
  #define PyInt_AsSsize_t              PyLong_AsSsize_t
  #define PyInt_AsUnsignedLongMask     PyLong_AsUnsignedLongMask
  #define PyInt_AsUnsignedLongLongMask PyLong_AsUnsignedLongLongMask
  #define PyNumber_Int                 PyNumber_Long
#endif
#if PY_MAJOR_VERSION >= 3
  #define PyBoolObject                 PyLongObject
#endif
#if PY_MAJOR_VERSION >= 3 && CYTHON_COMPILING_IN_PYPY
  #ifndef PyUnicode_InternFromString
    #define PyUnicode_InternFromString(s) PyUnicode_FromString(s)
  #endif
#endif
#if PY_VERSION_HEX < 0x030200A4
  typedef long Py_hash_t;
  #define __Pyx_PyInt_FromHash_t PyInt_FromLong
  #define __Pyx_PyInt_AsHash_t   PyInt_AsLong
#else
  #define __Pyx_PyInt_FromHash_t PyInt_FromSsize_t
  #define __Pyx_PyInt_AsHash_t   PyInt_AsSsize_t
#endif
#if PY_MAJOR_VERSION >= 3
  #define __Pyx_PyMethod_New(func, self, klass) ((self) ? ((void)(klass), PyMethod_New(func, self)) : __Pyx_NewRef(func))
#else
  #define __Pyx_PyMethod_New(func, self, klass) PyMethod_New(func, self, klass)
#endif
#if CYTHON_USE_ASYNC_SLOTS
  #if PY_VERSION_HEX >= 0x030500B1
    #define __Pyx_PyAsyncMethodsStruct PyAsyncMethods
    #define __Pyx_PyType_AsAsync(obj) (Py_TYPE(obj)->tp_as_async)
  #else
    #define __Pyx_PyType_AsAsync(obj) ((__Pyx_PyAsyncMethodsStruct*) (Py_TYPE(obj)->tp_reserved))
  #endif
#else
  #define __Pyx_PyType_AsAsync(obj) NULL
#endif
#ifndef __Pyx_PyAsyncMethodsStruct
    typedef struct {
        unaryfunc am_await;
        unaryfunc am_aiter;
        unaryfunc am_anext;
    } __Pyx_PyAsyncMethodsStruct;
#endif
 
#if defined(WIN32) || defined(MS_WINDOWS)
  #define _USE_MATH_DEFINES
#endif
#include <math.h>
#ifdef NAN
#define __PYX_NAN() ((float) NAN)
#else
static CYTHON_INLINE float __PYX_NAN() {
  float value;
  memset(&value, 0xFF, sizeof(value));
  return value;
}
#endif
#if defined(__CYGWIN__) && defined(_LDBL_EQ_DBL)
#define __Pyx_truncl trunc
#else
#define __Pyx_truncl truncl
#endif
 
#define __PYX_MARK_ERR_POS(f_index, lineno) \
    { __pyx_filename = __pyx_f[f_index]; (void)__pyx_filename; __pyx_lineno = lineno; (void)__pyx_lineno; __pyx_clineno = __LINE__; (void)__pyx_clineno; }
#define __PYX_ERR(f_index, lineno, Ln_error) \
    { __PYX_MARK_ERR_POS(f_index, lineno) goto Ln_error; }
 
#ifndef __PYX_EXTERN_C
  #ifdef __cplusplus
    #define __PYX_EXTERN_C extern "C"
  #else
    #define __PYX_EXTERN_C extern
  #endif
#endif
 
#define __PYX_HAVE__PyClical
#define __PYX_HAVE_API__PyClical
/* Early includes */
#include "ios"
#include "new"
#include "stdexcept"
#include "typeinfo"
#include <vector>
#include "PyClical.h"
#include <string.h>
#include <string>
#ifdef _OPENMP
#include <omp.h>
#endif /* _OPENMP */
 
#if defined(PYREX_WITHOUT_ASSERTIONS) && !defined(CYTHON_WITHOUT_ASSERTIONS)
#define CYTHON_WITHOUT_ASSERTIONS
#endif
 
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_UTF8 0
#define __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT (PY_MAJOR_VERSION >= 3 && __PYX_DEFAULT_STRING_ENCODING_IS_UTF8)
#define __PYX_DEFAULT_STRING_ENCODING ""
#define __Pyx_PyObject_FromString __Pyx_PyBytes_FromString
#define __Pyx_PyObject_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
#define __Pyx_uchar_cast(c) ((unsigned char)c)
#define __Pyx_long_cast(x) ((long)x)
#define __Pyx_fits_Py_ssize_t(v, type, is_signed)  (\
    (sizeof(type) < sizeof(Py_ssize_t))  ||\
    (sizeof(type) > sizeof(Py_ssize_t) &&\
          likely(v < (type)PY_SSIZE_T_MAX ||\
                 v == (type)PY_SSIZE_T_MAX)  &&\
          (!is_signed || likely(v > (type)PY_SSIZE_T_MIN ||\
                                v == (type)PY_SSIZE_T_MIN)))  ||\
    (sizeof(type) == sizeof(Py_ssize_t) &&\
          (is_signed || likely(v < (type)PY_SSIZE_T_MAX ||\
                               v == (type)PY_SSIZE_T_MAX)))  )
static CYTHON_INLINE int __Pyx_is_valid_index(Py_ssize_t i, Py_ssize_t limit) {
    return (size_t) i < (size_t) limit;
}
#if defined (__cplusplus) && __cplusplus >= 201103L
    #include <cstdlib>
    #define __Pyx_sst_abs(value) std::abs(value)
#elif SIZEOF_INT >= SIZEOF_SIZE_T
    #define __Pyx_sst_abs(value) abs(value)
#elif SIZEOF_LONG >= SIZEOF_SIZE_T
    #define __Pyx_sst_abs(value) labs(value)
#elif defined (_MSC_VER)
    #define __Pyx_sst_abs(value) ((Py_ssize_t)_abs64(value))
#elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
    #define __Pyx_sst_abs(value) llabs(value)
#elif defined (__GNUC__)
    #define __Pyx_sst_abs(value) __builtin_llabs(value)
#else
    #define __Pyx_sst_abs(value) ((value<0) ? -value : value)
#endif
static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject*);
static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject*, Py_ssize_t* length);
#define __Pyx_PyByteArray_FromString(s) PyByteArray_FromStringAndSize((const char*)s, strlen((const char*)s))
#define __Pyx_PyByteArray_FromStringAndSize(s, l) PyByteArray_FromStringAndSize((const char*)s, l)
#define __Pyx_PyBytes_FromString        PyBytes_FromString
#define __Pyx_PyBytes_FromStringAndSize PyBytes_FromStringAndSize
static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char*);
#if PY_MAJOR_VERSION < 3
    #define __Pyx_PyStr_FromString        __Pyx_PyBytes_FromString
    #define __Pyx_PyStr_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
#else
    #define __Pyx_PyStr_FromString        __Pyx_PyUnicode_FromString
    #define __Pyx_PyStr_FromStringAndSize __Pyx_PyUnicode_FromStringAndSize
#endif
#define __Pyx_PyBytes_AsWritableString(s)     ((char*) PyBytes_AS_STRING(s))
#define __Pyx_PyBytes_AsWritableSString(s)    ((signed char*) PyBytes_AS_STRING(s))
#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))
#define __Pyx_PyObject_AsWritableSString(s)    ((signed char*) __Pyx_PyObject_AsString(s))
#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)
#define __Pyx_PyUnicode_FromCString(s) __Pyx_PyUnicode_FromString((const char*)s)
static CYTHON_INLINE size_t __Pyx_Py_UNICODE_strlen(const Py_UNICODE *u) {
    const Py_UNICODE *u_end = u;
    while (*u_end++) ;
    return (size_t)(u_end - u - 1);
}
#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 int __Pyx_PyObject_IsTrueAndDecref(PyObject*);
static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x);
#define __Pyx_PySequence_Tuple(obj)\
    (likely(PyTuple_CheckExact(obj)) ? __Pyx_NewRef(obj) : PySequence_Tuple(obj))
static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject*);
static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t);
#if CYTHON_ASSUME_SAFE_MACROS
#define __pyx_PyFloat_AsDouble(x) (PyFloat_CheckExact(x) ? PyFloat_AS_DOUBLE(x) : PyFloat_AsDouble(x))
#else
#define __pyx_PyFloat_AsDouble(x) PyFloat_AsDouble(x)
#endif
#define __pyx_PyFloat_AsFloat(x) ((float) __pyx_PyFloat_AsDouble(x))
#if PY_MAJOR_VERSION >= 3
#define __Pyx_PyNumber_Int(x) (PyLong_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Long(x))
#else
#define __Pyx_PyNumber_Int(x) (PyInt_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Int(x))
#endif
#define __Pyx_PyNumber_Float(x) (PyFloat_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Float(x))
#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
static int __Pyx_sys_getdefaultencoding_not_ascii;
static int __Pyx_init_sys_getdefaultencoding_params(void) {
    PyObject* sys;
    PyObject* default_encoding = NULL;
    PyObject* ascii_chars_u = NULL;
    PyObject* ascii_chars_b = NULL;
    const char* default_encoding_c;
    sys = PyImport_ImportModule("sys");
    if (!sys) goto bad;
    default_encoding = PyObject_CallMethod(sys, (char*) "getdefaultencoding", NULL);
    Py_DECREF(sys);
    if (!default_encoding) goto bad;
    default_encoding_c = PyBytes_AsString(default_encoding);
    if (!default_encoding_c) goto bad;
    if (strcmp(default_encoding_c, "ascii") == 0) {
        __Pyx_sys_getdefaultencoding_not_ascii = 0;
    } else {
        char ascii_chars[128];
        int c;
        for (c = 0; c < 128; c++) {
            ascii_chars[c] = c;
        }
        __Pyx_sys_getdefaultencoding_not_ascii = 1;
        ascii_chars_u = PyUnicode_DecodeASCII(ascii_chars, 128, NULL);
        if (!ascii_chars_u) goto bad;
        ascii_chars_b = PyUnicode_AsEncodedString(ascii_chars_u, default_encoding_c, NULL);
        if (!ascii_chars_b || !PyBytes_Check(ascii_chars_b) || memcmp(ascii_chars, PyBytes_AS_STRING(ascii_chars_b), 128) != 0) {
            PyErr_Format(
                PyExc_ValueError,
                "This module compiled with c_string_encoding=ascii, but default encoding '%.200s' is not a superset of ascii.",
                default_encoding_c);
            goto bad;
        }
        Py_DECREF(ascii_chars_u);
        Py_DECREF(ascii_chars_b);
    }
    Py_DECREF(default_encoding);
    return 0;
bad:
    Py_XDECREF(default_encoding);
    Py_XDECREF(ascii_chars_u);
    Py_XDECREF(ascii_chars_b);
    return -1;
}
#endif
#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT && PY_MAJOR_VERSION >= 3
#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_DecodeUTF8(c_str, size, NULL)
#else
#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_Decode(c_str, size, __PYX_DEFAULT_STRING_ENCODING, NULL)
#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
static char* __PYX_DEFAULT_STRING_ENCODING;
static int __Pyx_init_sys_getdefaultencoding_params(void) {
    PyObject* sys;
    PyObject* default_encoding = NULL;
    char* default_encoding_c;
    sys = PyImport_ImportModule("sys");
    if (!sys) goto bad;
    default_encoding = PyObject_CallMethod(sys, (char*) (const char*) "getdefaultencoding", NULL);
    Py_DECREF(sys);
    if (!default_encoding) goto bad;
    default_encoding_c = PyBytes_AsString(default_encoding);
    if (!default_encoding_c) goto bad;
    __PYX_DEFAULT_STRING_ENCODING = (char*) malloc(strlen(default_encoding_c) + 1);
    if (!__PYX_DEFAULT_STRING_ENCODING) goto bad;
    strcpy(__PYX_DEFAULT_STRING_ENCODING, default_encoding_c);
    Py_DECREF(default_encoding);
    return 0;
bad:
    Py_XDECREF(default_encoding);
    return -1;
}
#endif
#endif
 
 
/* Test for GCC > 2.95 */
#if defined(__GNUC__)     && (__GNUC__ > 2 || (__GNUC__ == 2 && (__GNUC_MINOR__ > 95)))
  #define likely(x)   __builtin_expect(!!(x), 1)
  #define unlikely(x) __builtin_expect(!!(x), 0)
#else /* !__GNUC__ or GCC < 2.95 */
  #define likely(x)   (x)
  #define unlikely(x) (x)
#endif /* __GNUC__ */
static 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;
 
 
static const char *__pyx_f[] = {
  "PyClical.pyx",
  "stringsource",
};
 
/*--- Type declarations ---*/
struct __pyx_obj_8PyClical_index_set;
struct __pyx_obj_8PyClical_clifford;
struct __pyx_obj_8PyClical___pyx_scope_struct____iter__;
struct __pyx_opt_args_8PyClical_sqrt;
struct __pyx_opt_args_8PyClical_log;
struct __pyx_opt_args_8PyClical_cos;
struct __pyx_opt_args_8PyClical_acos;
struct __pyx_opt_args_8PyClical_acosh;
struct __pyx_opt_args_8PyClical_sin;
struct __pyx_opt_args_8PyClical_asin;
struct __pyx_opt_args_8PyClical_asinh;
struct __pyx_opt_args_8PyClical_tan;
struct __pyx_opt_args_8PyClical_atan;
struct __pyx_opt_args_8PyClical_atanh;
struct __pyx_opt_args_8PyClical_random_clifford;
 
/* "PyClical.pyx":1541
 *     return clifford().wrap( glucat.complexifier(toClifford(obj)) )
 * 
 * cpdef inline sqrt(obj, i = None):             # <<<<<<<<<<<<<<
 *     """
 *     Square root of multivector with optional complexifier.
 */
struct __pyx_opt_args_8PyClical_sqrt {
  int __pyx_n;
  PyObject *i;
};
 
/* "PyClical.pyx":1578
 *         return clifford().wrap( glucat.exp(toClifford(obj)) )
 * 
 * cpdef inline log(obj,i = None):             # <<<<<<<<<<<<<<
 *     """
 *     Natural logarithm of multivector with optional complexifier.
 */
struct __pyx_opt_args_8PyClical_log {
  int __pyx_n;
  PyObject *i;
};
 
/* "PyClical.pyx":1601
 *             return clifford().wrap( glucat.log(toClifford(obj)) )
 * 
 * cpdef inline cos(obj,i = None):             # <<<<<<<<<<<<<<
 *     """
 *     Cosine of multivector with optional complexifier.
 */
struct __pyx_opt_args_8PyClical_cos {
  int __pyx_n;
  PyObject *i;
};
 
/* "PyClical.pyx":1618
 *             return clifford().wrap( glucat.cos(toClifford(obj)) )
 * 
 * cpdef inline acos(obj,i = None):             # <<<<<<<<<<<<<<
 *     """
 *     Inverse cosine of multivector with optional complexifier.
 */
struct __pyx_opt_args_8PyClical_acos {
  int __pyx_n;
  PyObject *i;
};
 
/* "PyClical.pyx":1655
 *         return clifford().wrap( glucat.cosh(toClifford(obj)) )
 * 
 * cpdef inline acosh(obj,i = None):             # <<<<<<<<<<<<<<
 *     """
 *     Inverse hyperbolic cosine of multivector with optional complexifier.
 */
struct __pyx_opt_args_8PyClical_acosh {
  int __pyx_n;
  PyObject *i;
};
 
/* "PyClical.pyx":1678
 *             return clifford().wrap( glucat.acosh(toClifford(obj)) )
 * 
 * cpdef inline sin(obj,i = None):             # <<<<<<<<<<<<<<
 *     """
 *     Sine of multivector with optional complexifier.
 */
struct __pyx_opt_args_8PyClical_sin {
  int __pyx_n;
  PyObject *i;
};
 
/* "PyClical.pyx":1697
 *             return clifford().wrap( glucat.sin(toClifford(obj)) )
 * 
 * cpdef inline asin(obj,i = None):             # <<<<<<<<<<<<<<
 *     """
 *     Inverse sine of multivector with optional complexifier.
 */
struct __pyx_opt_args_8PyClical_asin {
  int __pyx_n;
  PyObject *i;
};
 
/* "PyClical.pyx":1732
 *         return clifford().wrap( glucat.sinh(toClifford(obj)) )
 * 
 * cpdef inline asinh(obj,i = None):             # <<<<<<<<<<<<<<
 *     """
 *     Inverse hyperbolic sine of multivector with optional complexifier.
 */
struct __pyx_opt_args_8PyClical_asinh {
  int __pyx_n;
  PyObject *i;
};
 
/* "PyClical.pyx":1751
 *             return clifford().wrap( glucat.asinh(toClifford(obj)) )
 * 
 * cpdef inline tan(obj,i = None):             # <<<<<<<<<<<<<<
 *     """
 *     Tangent of multivector with optional complexifier.
 */
struct __pyx_opt_args_8PyClical_tan {
  int __pyx_n;
  PyObject *i;
};
 
/* "PyClical.pyx":1768
 *             return clifford().wrap( glucat.tan(toClifford(obj)) )
 * 
 * cpdef inline atan(obj,i = None):             # <<<<<<<<<<<<<<
 *     """
 *     Inverse tangent of multivector with optional complexifier.
 */
struct __pyx_opt_args_8PyClical_atan {
  int __pyx_n;
  PyObject *i;
};
 
/* "PyClical.pyx":1797
 *         return clifford().wrap( glucat.tanh(toClifford(obj)) )
 * 
 * cpdef inline atanh(obj,i = None):             # <<<<<<<<<<<<<<
 *     """
 *     Inverse hyperbolic tangent of multivector with optional complexifier.
 */
struct __pyx_opt_args_8PyClical_atanh {
  int __pyx_n;
  PyObject *i;
};
 
/* "PyClical.pyx":1814
 *             return clifford().wrap( glucat.atanh(toClifford(obj)) )
 * 
 * cpdef inline random_clifford(index_set ixt, fill = 1.0):             # <<<<<<<<<<<<<<
 *     """
 *     Random multivector within a frame.
 */
struct __pyx_opt_args_8PyClical_random_clifford {
  int __pyx_n;
  PyObject *fill;
};
 
/* "PyClical.pyx":38
 * 
 * # Forward reference
 * cdef class index_set             # <<<<<<<<<<<<<<
 * 
 * cdef inline IndexSet toIndexSet(obj):
 */
struct __pyx_obj_8PyClical_index_set {
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  struct __pyx_vtabstruct_8PyClical_index_set *__pyx_vtab;
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/* "PyClical.pyx":532
 * 
 * # Forward reference.
 * cdef class clifford             # <<<<<<<<<<<<<<
 * 
 * cdef inline Clifford toClifford(obj):
 */
struct __pyx_obj_8PyClical_clifford {
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/* "PyClical.pyx":229
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 *     def __iter__(self):             # <<<<<<<<<<<<<<
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struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ {
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/* "PyClical.pyx":46
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 * 
 * cdef class index_set:             # <<<<<<<<<<<<<<
 *     """
 *     Python class index_set wraps C++ class IndexSet.
 */
 
struct __pyx_vtabstruct_8PyClical_index_set {
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static CYTHON_INLINE IndexSet __pyx_f_8PyClical_9index_set_unwrap(struct __pyx_obj_8PyClical_index_set *);
 
 
/* "PyClical.pyx":537
 *     return clifford(obj).instance[0]
 * 
 * cdef class clifford:             # <<<<<<<<<<<<<<
 *     """
 *     Python class clifford wraps C++ class Clifford.
 */
 
struct __pyx_vtabstruct_8PyClical_clifford {
  PyObject *(*wrap)(struct __pyx_obj_8PyClical_clifford *, Clifford);
  Clifford (*unwrap)(struct __pyx_obj_8PyClical_clifford *);
  PyObject *(*copy)(struct __pyx_obj_8PyClical_clifford *, int __pyx_skip_dispatch);
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static struct __pyx_vtabstruct_8PyClical_clifford *__pyx_vtabptr_8PyClical_clifford;
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_8clifford_wrap(struct __pyx_obj_8PyClical_clifford *, Clifford);
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  #define __Pyx_GIVEREF(r)
  #define __Pyx_XINCREF(r) Py_XINCREF(r)
  #define __Pyx_XDECREF(r) Py_XDECREF(r)
  #define __Pyx_XGOTREF(r)
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#define __Pyx_PyObject_GetAttrStr(o,n) PyObject_GetAttr(o,n)
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/* GetBuiltinName.proto */
static PyObject *__Pyx_GetBuiltinName(PyObject *name);
 
/* PyCFunctionFastCall.proto */
#if CYTHON_FAST_PYCCALL
static CYTHON_INLINE PyObject *__Pyx_PyCFunction_FastCall(PyObject *func, PyObject **args, Py_ssize_t nargs);
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#define __Pyx_PyCFunction_FastCall(func, args, nargs)  (assert(0), NULL)
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/* PyFunctionFastCall.proto */
#if CYTHON_FAST_PYCALL
#define __Pyx_PyFunction_FastCall(func, args, nargs)\
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static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, Py_ssize_t nargs, PyObject *kwargs);
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#define __Pyx_PyFunction_FastCallDict(func, args, nargs, kwargs) _PyFunction_FastCallDict(func, args, nargs, kwargs)
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#define __Pyx_BUILD_ASSERT_EXPR(cond)\
    (sizeof(char [1 - 2*!(cond)]) - 1)
#ifndef Py_MEMBER_SIZE
#define Py_MEMBER_SIZE(type, member) sizeof(((type *)0)->member)
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  static size_t __pyx_pyframe_localsplus_offset = 0;
  #include "frameobject.h"
  #define __Pxy_PyFrame_Initialize_Offsets()\
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/* PyObjectCall.proto */
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static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw);
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#define __Pyx_PyObject_Call(func, arg, kw) PyObject_Call(func, arg, kw)
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/* PyObjectCallMethO.proto */
#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg);
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/* PyObjectCallOneArg.proto */
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg);
 
/* PyThreadStateGet.proto */
#if CYTHON_FAST_THREAD_STATE
#define __Pyx_PyThreadState_declare  PyThreadState *__pyx_tstate;
#define __Pyx_PyThreadState_assign  __pyx_tstate = __Pyx_PyThreadState_Current;
#define __Pyx_PyErr_Occurred()  __pyx_tstate->curexc_type
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#define __Pyx_PyThreadState_declare
#define __Pyx_PyThreadState_assign
#define __Pyx_PyErr_Occurred()  PyErr_Occurred()
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/* PyErrFetchRestore.proto */
#if CYTHON_FAST_THREAD_STATE
#define __Pyx_PyErr_Clear() __Pyx_ErrRestore(NULL, NULL, NULL)
#define __Pyx_ErrRestoreWithState(type, value, tb)  __Pyx_ErrRestoreInState(PyThreadState_GET(), type, value, tb)
#define __Pyx_ErrFetchWithState(type, value, tb)    __Pyx_ErrFetchInState(PyThreadState_GET(), type, value, tb)
#define __Pyx_ErrRestore(type, value, tb)  __Pyx_ErrRestoreInState(__pyx_tstate, type, value, tb)
#define __Pyx_ErrFetch(type, value, tb)    __Pyx_ErrFetchInState(__pyx_tstate, type, value, tb)
static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb);
static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
#if CYTHON_COMPILING_IN_CPYTHON
#define __Pyx_PyErr_SetNone(exc) (Py_INCREF(exc), __Pyx_ErrRestore((exc), NULL, NULL))
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#define __Pyx_PyErr_SetNone(exc) PyErr_SetNone(exc)
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#define __Pyx_PyErr_Clear() PyErr_Clear()
#define __Pyx_PyErr_SetNone(exc) PyErr_SetNone(exc)
#define __Pyx_ErrRestoreWithState(type, value, tb)  PyErr_Restore(type, value, tb)
#define __Pyx_ErrFetchWithState(type, value, tb)  PyErr_Fetch(type, value, tb)
#define __Pyx_ErrRestoreInState(tstate, type, value, tb)  PyErr_Restore(type, value, tb)
#define __Pyx_ErrFetchInState(tstate, type, value, tb)  PyErr_Fetch(type, value, tb)
#define __Pyx_ErrRestore(type, value, tb)  PyErr_Restore(type, value, tb)
#define __Pyx_ErrFetch(type, value, tb)  PyErr_Fetch(type, value, tb)
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/* WriteUnraisableException.proto */
static void __Pyx_WriteUnraisable(const char *name, int clineno,
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/* PyDictVersioning.proto */
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#define __PYX_DICT_VERSION_INIT  ((PY_UINT64_T) -1)
#define __PYX_GET_DICT_VERSION(dict)  (((PyDictObject*)(dict))->ma_version_tag)
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static CYTHON_INLINE PY_UINT64_T __Pyx_get_tp_dict_version(PyObject *obj);
static CYTHON_INLINE PY_UINT64_T __Pyx_get_object_dict_version(PyObject *obj);
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#define __PYX_GET_DICT_VERSION(dict)  (0)
#define __PYX_UPDATE_DICT_CACHE(dict, value, cache_var, version_var)
#define __PYX_PY_DICT_LOOKUP_IF_MODIFIED(VAR, DICT, LOOKUP)  (VAR) = (LOOKUP);
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/* PyObjectCallNoArg.proto */
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static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func);
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/* RaiseDoubleKeywords.proto */
static void __Pyx_RaiseDoubleKeywordsError(const char* func_name, PyObject* kw_name);
 
/* ParseKeywords.proto */
static int __Pyx_ParseOptionalKeywords(PyObject *kwds, PyObject **argnames[],\
    PyObject *kwds2, PyObject *values[], Py_ssize_t num_pos_args,\
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/* RaiseArgTupleInvalid.proto */
static void __Pyx_RaiseArgtupleInvalid(const char* func_name, int exact,
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/* GetModuleGlobalName.proto */
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#define __Pyx_GetModuleGlobalName(var, name)  {\
    static PY_UINT64_T __pyx_dict_version = 0;\
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    PY_UINT64_T __pyx_dict_version;\
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static PyObject *__Pyx__GetModuleGlobalName(PyObject *name, PY_UINT64_T *dict_version, PyObject **dict_cached_value);
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#define __Pyx_GetModuleGlobalName(var, name)  (var) = __Pyx__GetModuleGlobalName(name)
#define __Pyx_GetModuleGlobalNameUncached(var, name)  (var) = __Pyx__GetModuleGlobalName(name)
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/* GetTopmostException.proto */
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static _PyErr_StackItem * __Pyx_PyErr_GetTopmostException(PyThreadState *tstate);
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/* SaveResetException.proto */
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#define __Pyx_ExceptionSave(type, value, tb)  __Pyx__ExceptionSave(__pyx_tstate, type, value, tb)
static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
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/* PyErrExceptionMatches.proto */
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/* GetException.proto */
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#define __Pyx_GetException(type, value, tb)  __Pyx__GetException(__pyx_tstate, type, value, tb)
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static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb);
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/* RaiseException.proto */
static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause);
 
/* PyObjectCall2Args.proto */
static CYTHON_UNUSED PyObject* __Pyx_PyObject_Call2Args(PyObject* function, PyObject* arg1, PyObject* arg2);
 
/* PyIntBinop.proto */
#if !CYTHON_COMPILING_IN_PYPY
static PyObject* __Pyx_PyInt_AddObjC(PyObject *op1, PyObject *op2, long intval, int inplace, int zerodivision_check);
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#define __Pyx_PyInt_AddObjC(op1, op2, intval, inplace, zerodivision_check)\
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/* PySequenceContains.proto */
static CYTHON_INLINE int __Pyx_PySequence_ContainsTF(PyObject* item, PyObject* seq, int eq) {
    int result = PySequence_Contains(seq, item);
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/* IncludeCppStringH.proto */
#include <string>
 
/* decode_c_string_utf16.proto */
static CYTHON_INLINE PyObject *__Pyx_PyUnicode_DecodeUTF16(const char *s, Py_ssize_t size, const char *errors) {
    int byteorder = 0;
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static CYTHON_INLINE PyObject *__Pyx_PyUnicode_DecodeUTF16LE(const char *s, Py_ssize_t size, const char *errors) {
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static CYTHON_INLINE PyObject *__Pyx_PyUnicode_DecodeUTF16BE(const char *s, Py_ssize_t size, const char *errors) {
    int byteorder = 1;
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}
 
/* decode_c_bytes.proto */
static CYTHON_INLINE PyObject* __Pyx_decode_c_bytes(
         const char* cstring, Py_ssize_t length, Py_ssize_t start, Py_ssize_t stop,
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         PyObject* (*decode_func)(const char *s, Py_ssize_t size, const char *errors));
 
/* decode_cpp_string.proto */
static CYTHON_INLINE PyObject* __Pyx_decode_cpp_string(
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         const char* encoding, const char* errors,
         PyObject* (*decode_func)(const char *s, Py_ssize_t size, const char *errors)) {
    return __Pyx_decode_c_bytes(
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/* SwapException.proto */
#if CYTHON_FAST_THREAD_STATE
#define __Pyx_ExceptionSwap(type, value, tb)  __Pyx__ExceptionSwap(__pyx_tstate, type, value, tb)
static CYTHON_INLINE void __Pyx__ExceptionSwap(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
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static CYTHON_INLINE void __Pyx_ExceptionSwap(PyObject **type, PyObject **value, PyObject **tb);
#endif
 
/* SetItemInt.proto */
#define __Pyx_SetItemInt(o, i, v, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
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    __Pyx_SetItemInt_Fast(o, (Py_ssize_t)i, v, is_list, wraparound, boundscheck) :\
    (is_list ? (PyErr_SetString(PyExc_IndexError, "list assignment index out of range"), -1) :\
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static int __Pyx_SetItemInt_Generic(PyObject *o, PyObject *j, PyObject *v);
static CYTHON_INLINE int __Pyx_SetItemInt_Fast(PyObject *o, Py_ssize_t i, PyObject *v,
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/* ArgTypeTest.proto */
#define __Pyx_ArgTypeTest(obj, type, none_allowed, name, exact)\
    ((likely((Py_TYPE(obj) == type) | (none_allowed && (obj == Py_None)))) ? 1 :\
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static int __Pyx__ArgTypeTest(PyObject *obj, PyTypeObject *type, const char *name, int exact);
 
/* Import.proto */
static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level);
 
/* IncludeStringH.proto */
#include <string.h>
 
/* PyObject_GenericGetAttrNoDict.proto */
#if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000
static CYTHON_INLINE PyObject* __Pyx_PyObject_GenericGetAttrNoDict(PyObject* obj, PyObject* attr_name);
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#define __Pyx_PyObject_GenericGetAttrNoDict PyObject_GenericGetAttr
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/* PyObject_GenericGetAttr.proto */
#if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000
static PyObject* __Pyx_PyObject_GenericGetAttr(PyObject* obj, PyObject* attr_name);
#else
#define __Pyx_PyObject_GenericGetAttr PyObject_GenericGetAttr
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/* SetVTable.proto */
static int __Pyx_SetVtable(PyObject *dict, void *vtable);
 
/* PyObjectGetAttrStrNoError.proto */
static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStrNoError(PyObject* obj, PyObject* attr_name);
 
/* SetupReduce.proto */
static int __Pyx_setup_reduce(PyObject* type_obj);
 
/* BytesEquals.proto */
static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals);
 
/* UnicodeEquals.proto */
static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals);
 
/* CLineInTraceback.proto */
#ifdef CYTHON_CLINE_IN_TRACEBACK
#define __Pyx_CLineForTraceback(tstate, c_line)  (((CYTHON_CLINE_IN_TRACEBACK)) ? c_line : 0)
#else
static int __Pyx_CLineForTraceback(PyThreadState *tstate, int c_line);
#endif
 
/* CodeObjectCache.proto */
typedef struct {
    PyCodeObject* code_object;
    int code_line;
} __Pyx_CodeObjectCacheEntry;
struct __Pyx_CodeObjectCache {
    int count;
    int max_count;
    __Pyx_CodeObjectCacheEntry* entries;
};
static struct __Pyx_CodeObjectCache __pyx_code_cache = {0,0,NULL};
static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line);
static PyCodeObject *__pyx_find_code_object(int code_line);
static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object);
 
/* AddTraceback.proto */
static void __Pyx_AddTraceback(const char *funcname, int c_line,
                               int py_line, const char *filename);
 
/* CppExceptionConversion.proto */
#ifndef __Pyx_CppExn2PyErr
#include <new>
#include <typeinfo>
#include <stdexcept>
#include <ios>
static void __Pyx_CppExn2PyErr() {
  try {
    if (PyErr_Occurred())
      ; // let the latest Python exn pass through and ignore the current one
    else
      throw;
  } catch (const std::bad_alloc& exn) {
    PyErr_SetString(PyExc_MemoryError, exn.what());
  } catch (const std::bad_cast& exn) {
    PyErr_SetString(PyExc_TypeError, exn.what());
  } catch (const std::bad_typeid& exn) {
    PyErr_SetString(PyExc_TypeError, exn.what());
  } catch (const std::domain_error& exn) {
    PyErr_SetString(PyExc_ValueError, exn.what());
  } catch (const std::invalid_argument& exn) {
    PyErr_SetString(PyExc_ValueError, exn.what());
  } catch (const std::ios_base::failure& exn) {
    PyErr_SetString(PyExc_IOError, exn.what());
  } catch (const std::out_of_range& exn) {
    PyErr_SetString(PyExc_IndexError, exn.what());
  } catch (const std::overflow_error& exn) {
    PyErr_SetString(PyExc_OverflowError, exn.what());
  } catch (const std::range_error& exn) {
    PyErr_SetString(PyExc_ArithmeticError, exn.what());
  } catch (const std::underflow_error& exn) {
    PyErr_SetString(PyExc_ArithmeticError, exn.what());
  } catch (const std::exception& exn) {
    PyErr_SetString(PyExc_RuntimeError, exn.what());
  }
  catch (...)
  {
    PyErr_SetString(PyExc_RuntimeError, "Unknown exception");
  }
}
#endif
 
/* CIntToPy.proto */
static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value);
 
/* CIntFromPy.proto */
static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *);
 
/* CIntToPy.proto */
static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value);
 
/* CIntFromPy.proto */
static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *);
 
/* FastTypeChecks.proto */
#if CYTHON_COMPILING_IN_CPYTHON
#define __Pyx_TypeCheck(obj, type) __Pyx_IsSubtype(Py_TYPE(obj), (PyTypeObject *)type)
static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b);
static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject *type);
static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *type1, PyObject *type2);
#else
#define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type)
#define __Pyx_PyErr_GivenExceptionMatches(err, type) PyErr_GivenExceptionMatches(err, type)
#define __Pyx_PyErr_GivenExceptionMatches2(err, type1, type2) (PyErr_GivenExceptionMatches(err, type1) || PyErr_GivenExceptionMatches(err, type2))
#endif
#define __Pyx_PyException_Check(obj) __Pyx_TypeCheck(obj, PyExc_Exception)
 
/* FetchCommonType.proto */
static PyTypeObject* __Pyx_FetchCommonType(PyTypeObject* type);
 
/* PyObjectGetMethod.proto */
static int __Pyx_PyObject_GetMethod(PyObject *obj, PyObject *name, PyObject **method);
 
/* PyObjectCallMethod1.proto */
static PyObject* __Pyx_PyObject_CallMethod1(PyObject* obj, PyObject* method_name, PyObject* arg);
 
/* CoroutineBase.proto */
typedef PyObject *(*__pyx_coroutine_body_t)(PyObject *, PyThreadState *, PyObject *);
#if CYTHON_USE_EXC_INFO_STACK
#define __Pyx_ExcInfoStruct  _PyErr_StackItem
#else
typedef struct {
    PyObject *exc_type;
    PyObject *exc_value;
    PyObject *exc_traceback;
} __Pyx_ExcInfoStruct;
#endif
typedef struct {
    PyObject_HEAD
    __pyx_coroutine_body_t body;
    PyObject *closure;
    __Pyx_ExcInfoStruct gi_exc_state;
    PyObject *gi_weakreflist;
    PyObject *classobj;
    PyObject *yieldfrom;
    PyObject *gi_name;
    PyObject *gi_qualname;
    PyObject *gi_modulename;
    PyObject *gi_code;
    int resume_label;
    char is_running;
} __pyx_CoroutineObject;
static __pyx_CoroutineObject *__Pyx__Coroutine_New(
    PyTypeObject *type, __pyx_coroutine_body_t body, PyObject *code, PyObject *closure,
    PyObject *name, PyObject *qualname, PyObject *module_name);
static __pyx_CoroutineObject *__Pyx__Coroutine_NewInit(
            __pyx_CoroutineObject *gen, __pyx_coroutine_body_t body, PyObject *code, PyObject *closure,
            PyObject *name, PyObject *qualname, PyObject *module_name);
static CYTHON_INLINE void __Pyx_Coroutine_ExceptionClear(__Pyx_ExcInfoStruct *self);
static int __Pyx_Coroutine_clear(PyObject *self);
static PyObject *__Pyx_Coroutine_Send(PyObject *self, PyObject *value);
static PyObject *__Pyx_Coroutine_Close(PyObject *self);
static PyObject *__Pyx_Coroutine_Throw(PyObject *gen, PyObject *args);
#if CYTHON_USE_EXC_INFO_STACK
#define __Pyx_Coroutine_SwapException(self)
#define __Pyx_Coroutine_ResetAndClearException(self)  __Pyx_Coroutine_ExceptionClear(&(self)->gi_exc_state)
#else
#define __Pyx_Coroutine_SwapException(self) {\
    __Pyx_ExceptionSwap(&(self)->gi_exc_state.exc_type, &(self)->gi_exc_state.exc_value, &(self)->gi_exc_state.exc_traceback);\
    __Pyx_Coroutine_ResetFrameBackpointer(&(self)->gi_exc_state);\
    }
#define __Pyx_Coroutine_ResetAndClearException(self) {\
    __Pyx_ExceptionReset((self)->gi_exc_state.exc_type, (self)->gi_exc_state.exc_value, (self)->gi_exc_state.exc_traceback);\
    (self)->gi_exc_state.exc_type = (self)->gi_exc_state.exc_value = (self)->gi_exc_state.exc_traceback = NULL;\
    }
#endif
#if CYTHON_FAST_THREAD_STATE
#define __Pyx_PyGen_FetchStopIterationValue(pvalue)\
    __Pyx_PyGen__FetchStopIterationValue(__pyx_tstate, pvalue)
#else
#define __Pyx_PyGen_FetchStopIterationValue(pvalue)\
    __Pyx_PyGen__FetchStopIterationValue(__Pyx_PyThreadState_Current, pvalue)
#endif
static int __Pyx_PyGen__FetchStopIterationValue(PyThreadState *tstate, PyObject **pvalue);
static CYTHON_INLINE void __Pyx_Coroutine_ResetFrameBackpointer(__Pyx_ExcInfoStruct *exc_state);
 
/* PatchModuleWithCoroutine.proto */
static PyObject* __Pyx_Coroutine_patch_module(PyObject* module, const char* py_code);
 
/* PatchGeneratorABC.proto */
static int __Pyx_patch_abc(void);
 
/* Generator.proto */
#define __Pyx_Generator_USED
static PyTypeObject *__pyx_GeneratorType = 0;
#define __Pyx_Generator_CheckExact(obj) (Py_TYPE(obj) == __pyx_GeneratorType)
#define __Pyx_Generator_New(body, code, closure, name, qualname, module_name)\
    __Pyx__Coroutine_New(__pyx_GeneratorType, body, code, closure, name, qualname, module_name)
static PyObject *__Pyx_Generator_Next(PyObject *self);
static int __pyx_Generator_init(void);
 
/* CheckBinaryVersion.proto */
static int __Pyx_check_binary_version(void);
 
/* InitStrings.proto */
static int __Pyx_InitStrings(__Pyx_StringTabEntry *t);
 
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_9index_set_wrap(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, IndexSet __pyx_v_other); /* proto*/
static CYTHON_INLINE IndexSet __pyx_f_8PyClical_9index_set_unwrap(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto*/
static PyObject *__pyx_f_8PyClical_9index_set_copy(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, int __pyx_skip_dispatch); /* proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_8clifford_wrap(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, Clifford __pyx_v_other); /* proto*/
static CYTHON_INLINE Clifford __pyx_f_8PyClical_8clifford_unwrap(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto*/
static PyObject *__pyx_f_8PyClical_8clifford_copy(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, int __pyx_skip_dispatch); /* proto*/
 
/* Module declarations from 'libcpp.vector' */
 
/* Module declarations from 'glucat' */
 
/* Module declarations from 'libc.string' */
 
/* Module declarations from 'libcpp.string' */
 
/* Module declarations from 'PyClical' */
static PyTypeObject *__pyx_ptype_8PyClical_index_set = 0;
static PyTypeObject *__pyx_ptype_8PyClical_clifford = 0;
static PyTypeObject *__pyx_ptype_8PyClical___pyx_scope_struct____iter__ = 0;
static CYTHON_INLINE IndexSet __pyx_f_8PyClical_toIndexSet(PyObject *); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_compare(PyObject *, PyObject *, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_min_neg(PyObject *, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_max_pos(PyObject *, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE std::vector<scalar_t>  __pyx_f_8PyClical_list_to_vector(PyObject *); /*proto*/
static CYTHON_INLINE Clifford __pyx_f_8PyClical_toClifford(PyObject *); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_inv(PyObject *, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_scalar(PyObject *, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_real(PyObject *, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_imag(PyObject *, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_pure(PyObject *, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_even(PyObject *, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_odd(PyObject *, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_involute(PyObject *, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_reverse(PyObject *, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_conj(PyObject *, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_quad(PyObject *, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_norm(PyObject *, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_abs(PyObject *, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_max_abs(PyObject *, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_pow(PyObject *, PyObject *, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_outer_pow(PyObject *, PyObject *, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_complexifier(PyObject *, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_sqrt(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_sqrt *__pyx_optional_args); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_exp(PyObject *, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_log(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_log *__pyx_optional_args); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_cos(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_cos *__pyx_optional_args); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_acos(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_acos *__pyx_optional_args); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_cosh(PyObject *, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_acosh(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_acosh *__pyx_optional_args); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_sin(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_sin *__pyx_optional_args); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_asin(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_asin *__pyx_optional_args); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_sinh(PyObject *, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_asinh(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_asinh *__pyx_optional_args); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_tan(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_tan *__pyx_optional_args); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_atan(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_atan *__pyx_optional_args); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_tanh(PyObject *, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_atanh(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_atanh *__pyx_optional_args); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_random_clifford(struct __pyx_obj_8PyClical_index_set *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_random_clifford *__pyx_optional_args); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_cga3(PyObject *, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_cga3std(PyObject *, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE PyObject *__pyx_f_8PyClical_agc3(PyObject *, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE PyObject *__pyx_convert_PyObject_string_to_py_std__in_string(std::string const &); /*proto*/
static CYTHON_INLINE PyObject *__pyx_convert_PyUnicode_string_to_py_std__in_string(std::string const &); /*proto*/
static CYTHON_INLINE PyObject *__pyx_convert_PyStr_string_to_py_std__in_string(std::string const &); /*proto*/
static CYTHON_INLINE PyObject *__pyx_convert_PyBytes_string_to_py_std__in_string(std::string const &); /*proto*/
static CYTHON_INLINE PyObject *__pyx_convert_PyByteArray_string_to_py_std__in_string(std::string const &); /*proto*/
#define __Pyx_MODULE_NAME "PyClical"
extern int __pyx_module_is_main_PyClical;
int __pyx_module_is_main_PyClical = 0;
 
/* Implementation of 'PyClical' */
static PyObject *__pyx_builtin_IndexError;
static PyObject *__pyx_builtin_RuntimeError;
static PyObject *__pyx_builtin_TypeError;
static PyObject *__pyx_builtin_ValueError;
static PyObject *__pyx_builtin_NotImplemented;
static PyObject *__pyx_builtin_range;
static PyObject *__pyx_builtin_xrange;
static const char __pyx_k_[] = ".";
static const char __pyx_k_e[] = "e";
static const char __pyx_k_i[] = "i";
static const char __pyx_k_m[] = "m";
static const char __pyx_k_p[] = "p";
static const char __pyx_k_q[] = "q";
static const char __pyx_k__2[] = " ";
static const char __pyx_k__5[] = ":";
static const char __pyx_k__6[] = "\n\t";
static const char __pyx_k__7[] = " (";
static const char __pyx_k__8[] = ", ";
static const char __pyx_k__9[] = ").";
static const char __pyx_k_cl[] = "cl";
static const char __pyx_k_pi[] = "pi";
static const char __pyx_k_abc[] = "abc";
static const char __pyx_k_cos[] = "cos";
static const char __pyx_k_exp[] = "exp";
static const char __pyx_k_frm[] = "frm";
static const char __pyx_k_inv[] = "inv";
static const char __pyx_k_ist[] = "ist";
static const char __pyx_k_ixt[] = "ixt";
static const char __pyx_k_lhs[] = "lhs";
static const char __pyx_k_log[] = "log";
static const char __pyx_k_max[] = "max";
static const char __pyx_k_min[] = "min";
static const char __pyx_k_obj[] = "obj";
static const char __pyx_k_odd[] = "odd";
static const char __pyx_k_pow[] = "pow";
static const char __pyx_k_rhs[] = "rhs";
static const char __pyx_k_sin[] = "sin";
static const char __pyx_k_tan[] = "tan";
static const char __pyx_k_tau[] = "tau";
static const char __pyx_k_Real[] = "Real";
static const char __pyx_k_acos[] = "acos";
static const char __pyx_k_args[] = "args";
static const char __pyx_k_asin[] = "asin";
static const char __pyx_k_atan[] = "atan";
static const char __pyx_k_conj[] = "conj";
static const char __pyx_k_copy[] = "copy";
static const char __pyx_k_cosh[] = "cosh";
static const char __pyx_k_even[] = "even";
static const char __pyx_k_fill[] = "fill";
static const char __pyx_k_from[] = " from ";
static const char __pyx_k_iter[] = "__iter__";
static const char __pyx_k_main[] = "__main__";
static const char __pyx_k_math[] = "math";
static const char __pyx_k_name[] = "__name__";
static const char __pyx_k_norm[] = "norm";
static const char __pyx_k_pure[] = "pure";
static const char __pyx_k_quad[] = "quad";
static const char __pyx_k_send[] = "send";
static const char __pyx_k_sinh[] = "sinh";
static const char __pyx_k_sqrt[] = "sqrt";
static const char __pyx_k_tanh[] = "tanh";
static const char __pyx_k_test[] = "_test";
static const char __pyx_k_0_8_4[] = "0.8.4";
static const char __pyx_k_UTF_8[] = "UTF-8";
static const char __pyx_k_acosh[] = "acosh";
static const char __pyx_k_asinh[] = "asinh";
static const char __pyx_k_atanh[] = "atanh";
static const char __pyx_k_close[] = "close";
static const char __pyx_k_grade[] = "grade";
static const char __pyx_k_istpq[] = "istpq";
static const char __pyx_k_nbar3[] = "nbar3";
static const char __pyx_k_ninf3[] = "ninf3";
static const char __pyx_k_other[] = "other";
static const char __pyx_k_range[] = "range";
static const char __pyx_k_throw[] = "throw";
static const char __pyx_k_using[] = " using (";
static const char __pyx_k_value[] = " value ";
static const char __pyx_k_encode[] = "encode";
static const char __pyx_k_import[] = "__import__";
static const char __pyx_k_reduce[] = "__reduce__";
static const char __pyx_k_scalar[] = "scalar";
static const char __pyx_k_test_2[] = "__test__";
static const char __pyx_k_xrange[] = "xrange";
static const char __pyx_k_doctest[] = "doctest";
static const char __pyx_k_invalid[] = " invalid ";
static const char __pyx_k_numbers[] = "numbers";
static const char __pyx_k_reverse[] = "reverse";
static const char __pyx_k_testmod[] = "testmod";
static const char __pyx_k_version[] = "__version__";
static const char __pyx_k_Integral[] = "Integral";
static const char __pyx_k_PyClical[] = "PyClical";
static const char __pyx_k_Sequence[] = "Sequence";
static const char __pyx_k_as_frame[] = " as frame:\n\t";
static const char __pyx_k_clifford[] = "clifford";
static const char __pyx_k_getstate[] = "__getstate__";
static const char __pyx_k_involute[] = "involute";
static const char __pyx_k_setstate[] = "__setstate__";
static const char __pyx_k_to_frame[] = " to frame ";
static const char __pyx_k_TypeError[] = "TypeError";
static const char __pyx_k_index_set[] = "index_set";
static const char __pyx_k_outer_pow[] = "outer_pow";
static const char __pyx_k_reduce_ex[] = "__reduce_ex__";
static const char __pyx_k_IndexError[] = "IndexError";
static const char __pyx_k_ValueError[] = "ValueError";
static const char __pyx_k_pyx_vtable[] = "__pyx_vtable__";
static const char __pyx_k_collections[] = "collections";
static const char __pyx_k_e_line_1886[] = "e (line 1886)";
static const char __pyx_k_PyClical_pyx[] = "PyClical.pyx";
static const char __pyx_k_RuntimeError[] = "RuntimeError";
static const char __pyx_k_abs_line_1472[] = "abs (line 1472)";
static const char __pyx_k_cos_line_1601[] = "cos (line 1601)";
static const char __pyx_k_exp_line_1564[] = "exp (line 1564)";
static const char __pyx_k_inv_line_1328[] = "inv (line 1328)";
static const char __pyx_k_log_line_1578[] = "log (line 1578)";
static const char __pyx_k_odd_line_1396[] = "odd (line 1396)";
static const char __pyx_k_pow_line_1493[] = "pow (line 1493)";
static const char __pyx_k_reduce_cython[] = "__reduce_cython__";
static const char __pyx_k_sin_line_1678[] = "sin (line 1678)";
static const char __pyx_k_tan_line_1751[] = "tan (line 1751)";
static const char __pyx_k_using_invalid[] = " using invalid ";
static const char __pyx_k_Cannot_reframe[] = "Cannot reframe";
static const char __pyx_k_NotImplemented[] = "NotImplemented";
static const char __pyx_k_Not_applicable[] = "Not applicable.";
static const char __pyx_k_acos_line_1618[] = "acos (line 1618)";
static const char __pyx_k_agc3_line_1843[] = "agc3 (line 1843)";
static const char __pyx_k_asin_line_1697[] = "asin (line 1697)";
static const char __pyx_k_atan_line_1768[] = "atan (line 1768)";
static const char __pyx_k_cga3_line_1823[] = "cga3 (line 1823)";
static const char __pyx_k_conj_line_1435[] = "conj (line 1435)";
static const char __pyx_k_cosh_line_1639[] = "cosh (line 1639)";
static const char __pyx_k_even_line_1387[] = "even (line 1387)";
static const char __pyx_k_imag_line_1365[] = "imag (line 1365)";
static const char __pyx_k_invalid_string[] = " invalid string ";
static const char __pyx_k_norm_line_1461[] = "norm (line 1461)";
static const char __pyx_k_pure_line_1376[] = "pure (line 1376)";
static const char __pyx_k_quad_line_1450[] = "quad (line 1450)";
static const char __pyx_k_real_line_1354[] = "real (line 1354)";
static const char __pyx_k_scalar_epsilon[] = "scalar_epsilon";
static const char __pyx_k_sinh_line_1718[] = "sinh (line 1718)";
static const char __pyx_k_sqrt_line_1541[] = "sqrt (line 1541)";
static const char __pyx_k_tanh_line_1785[] = "tanh (line 1785)";
static const char __pyx_k_acosh_line_1655[] = "acosh (line 1655)";
static const char __pyx_k_asinh_line_1732[] = "asinh (line 1732)";
static const char __pyx_k_atanh_line_1797[] = "atanh (line 1797)";
static const char __pyx_k_istpq_line_1899[] = "istpq (line 1899)";
static const char __pyx_k_setstate_cython[] = "__setstate_cython__";
static const char __pyx_k_compare_line_492[] = "compare (line 492)";
static const char __pyx_k_index_set___iter[] = "index_set.__iter__";
static const char __pyx_k_max_pos_line_513[] = "max_pos (line 513)";
static const char __pyx_k_min_neg_line_504[] = "min_neg (line 504)";
static const char __pyx_k_scalar_line_1343[] = "scalar (line 1343)";
static const char __pyx_k_cga3std_line_1832[] = "cga3std (line 1832)";
static const char __pyx_k_max_abs_line_1481[] = "max_abs (line 1481)";
static const char __pyx_k_reverse_line_1420[] = "reverse (line 1420)";
static const char __pyx_k_cline_in_traceback[] = "cline_in_traceback";
static const char __pyx_k_involute_line_1405[] = "involute (line 1405)";
static const char __pyx_k_outer_pow_line_1517[] = "outer_pow (line 1517)";
static const char __pyx_k_clifford_inv_line_926[] = "clifford.inv (line 926)";
static const char __pyx_k_clifford_pow_line_980[] = "clifford.pow (line 980)";
static const char __pyx_k_clifford_abs_line_1175[] = "clifford.abs (line 1175)";
static const char __pyx_k_clifford_copy_line_556[] = "clifford.copy (line 556)";
static const char __pyx_k_clifford_odd_line_1070[] = "clifford.odd (line 1070)";
static const char __pyx_k_complexifier_line_1526[] = "complexifier (line 1526)";
static const char __pyx_k_index_set_copy_line_65[] = "index_set.copy (line 65)";
static const char __pyx_k_index_set_max_line_351[] = "index_set.max (line 351)";
static const char __pyx_k_index_set_min_line_342[] = "index_set.min (line 342)";
static const char __pyx_k_clifford_conj_line_1138[] = "clifford.conj (line 1138)";
static const char __pyx_k_clifford_even_line_1061[] = "clifford.even (line 1061)";
static const char __pyx_k_clifford_norm_line_1164[] = "clifford.norm (line 1164)";
static const char __pyx_k_clifford_pure_line_1050[] = "clifford.pure (line 1050)";
static const char __pyx_k_clifford_quad_line_1153[] = "clifford.quad (line 1153)";
static const char __pyx_k_Unary_print_clifford_1_1[] = "\n        Unary -.\n\n        >>> print(-clifford(\"{1}\"))\n        -{1}\n        ";
static const char __pyx_k_clifford___or___line_939[] = "clifford.__or__ (line 939)";
static const char __pyx_k_clifford_frame_line_1215[] = "clifford.frame (line 1215)";
static const char __pyx_k_clifford_hidden_doctests[] = "clifford_hidden_doctests";
static const char __pyx_k_clifford_isnan_line_1206[] = "clifford.isnan (line 1206)";
static const char __pyx_k_index_set_count_line_315[] = "index_set.count (line 315)";
static const char __pyx_k_clifford___add___line_740[] = "clifford.__add__ (line 740)";
static const char __pyx_k_clifford___and___line_836[] = "clifford.__and__ (line 836)";
static const char __pyx_k_clifford___ior___line_950[] = "clifford.__ior__ (line 950)";
static const char __pyx_k_clifford___mod___line_806[] = "clifford.__mod__ (line 806)";
static const char __pyx_k_clifford___mul___line_780[] = "clifford.__mul__ (line 780)";
static const char __pyx_k_clifford___neg___line_722[] = "clifford.__neg__ (line 722)";
static const char __pyx_k_clifford___pos___line_731[] = "clifford.__pos__ (line 731)";
static const char __pyx_k_clifford___pow___line_961[] = "clifford.__pow__ (line 961)";
static const char __pyx_k_clifford___sub___line_760[] = "clifford.__sub__ (line 760)";
static const char __pyx_k_clifford___xor___line_866[] = "clifford.__xor__ (line 866)";
static const char __pyx_k_clifford_reframe_line_649[] = "clifford.reframe (line 649)";
static const char __pyx_k_clifford_scalar_line_1039[] = "clifford.scalar (line 1039)";
static const char __pyx_k_index_set___or___line_293[] = "index_set.__or__ (line 293)";
static const char __pyx_k_index_set_hidden_doctests[] = "index_set_hidden_doctests";
static const char __pyx_k_random_clifford_line_1814[] = "random_clifford (line 1814)";
static const char __pyx_k_Cannot_take_vector_part_of[] = "Cannot take vector part of ";
static const char __pyx_k_Unary_print_clifford_1_1_2[] = "\n        Unary +.\n\n        >>> print(+clifford(\"{1}\"))\n        {1}\n        ";
static const char __pyx_k_clifford___iadd___line_751[] = "clifford.__iadd__ (line 751)";
static const char __pyx_k_clifford___iand___line_851[] = "clifford.__iand__ (line 851)";
static const char __pyx_k_clifford___idiv___line_911[] = "clifford.__idiv__ (line 911)";
static const char __pyx_k_clifford___imod___line_821[] = "clifford.__imod__ (line 821)";
static const char __pyx_k_clifford___imul___line_793[] = "clifford.__imul__ (line 793)";
static const char __pyx_k_clifford___isub___line_771[] = "clifford.__isub__ (line 771)";
static const char __pyx_k_clifford___iter___line_638[] = "clifford.__iter__ (line 638)";
static const char __pyx_k_clifford___ixor___line_881[] = "clifford.__ixor__ (line 881)";
static const char __pyx_k_clifford___str___line_1235[] = "clifford.__str__ (line 1235)";
static const char __pyx_k_clifford_max_abs_line_1184[] = "clifford.max_abs (line 1184)";
static const char __pyx_k_clifford_reverse_line_1123[] = "clifford.reverse (line 1123)";
static const char __pyx_k_index_set___and___line_271[] = "index_set.__and__ (line 271)";
static const char __pyx_k_index_set___ior___line_304[] = "index_set.__ior__ (line 304)";
static const char __pyx_k_index_set___str___line_395[] = "index_set.__str__ (line 395)";
static const char __pyx_k_index_set___xor___line_249[] = "index_set.__xor__ (line 249)";
static const char __pyx_k_clifford___call___line_1020[] = "clifford.__call__ (line 1020)";
static const char __pyx_k_clifford___repr___line_1226[] = "clifford.__repr__ (line 1226)";
static const char __pyx_k_clifford_involute_line_1107[] = "clifford.involute (line 1107)";
static const char __pyx_k_index_set___iand___line_282[] = "index_set.__iand__ (line 282)";
static const char __pyx_k_index_set___iter___line_229[] = "index_set.__iter__ (line 229)";
static const char __pyx_k_index_set___ixor___line_260[] = "index_set.__ixor__ (line 260)";
static const char __pyx_k_index_set___repr___line_384[] = "index_set.__repr__ (line 384)";
static const char __pyx_k_clifford_outer_pow_line_1004[] = "clifford.outer_pow (line 1004)";
static const char __pyx_k_clifford_truncated_line_1195[] = "clifford.truncated (line 1195)";
static const char __pyx_k_index_set_count_neg_line_324[] = "index_set.count_neg (line 324)";
static const char __pyx_k_index_set_count_pos_line_333[] = "index_set.count_pos (line 333)";
static const char __pyx_k_clifford___getitem___line_707[] = "clifford.__getitem__ (line 707)";
static const char __pyx_k_clifford___truediv___line_896[] = "clifford.__truediv__ (line 896)";
static const char __pyx_k_index_set___invert___line_240[] = "index_set.__invert__ (line 240)";
static const char __pyx_k_Abbreviation_for_index_set_q_p[] = "\n    Abbreviation for index_set({-q,...p}).\n\n    >>> print(istpq(2,3))\n    {-3,-2,-1,1,2}\n    ";
static const char __pyx_k_Conjugation_reverse_o_involute[] = "\n        Conjugation, reverse o involute == involute o reverse.\n\n        >>> print((clifford(\"{1}\")).conj())\n        -{1}\n        >>> print((clifford(\"{2}\") * clifford(\"{1}\")).conj())\n        {1,2}\n        >>> print((clifford(\"{1}\") * clifford(\"{2}\")).conj())\n        -{1,2}\n        >>> print(clifford(\"1+{1}+{1,2}\").conj())\n        1-{1}-{1,2}\n        ";
static const char __pyx_k_Geometric_product_x_clifford_2[] = "\n        Geometric product.\n\n        >>> x = clifford(2); x *= clifford(\"{2}\"); print(x)\n        2{2}\n        >>> x = clifford(\"{1}\"); x *= clifford(\"{2}\"); print(x)\n        {1,2}\n        >>> x = clifford(\"{1}\"); x *= clifford(\"{1,2}\"); print(x)\n        {2}\n        ";
static const char __pyx_k_Geometric_sum_print_clifford_1[] = "\n        Geometric sum.\n\n        >>> print(clifford(1) + clifford(\"{2}\"))\n        1+{2}\n        >>> print(clifford(\"{1}\") + clifford(\"{2}\"))\n        {1}+{2}\n        ";
static const char __pyx_k_Hyperbolic_sine_of_multivector[] = "\n    Hyperbolic sine of multivector.\n\n    >>> x=clifford(\"{1,2}\") * pi/2; print(sinh(x))\n    {1,2}\n    >>> x=clifford(\"{1,2}\") * pi/6; print(sinh(x))\n    0.5{1,2}\n    ";
static const char __pyx_k_Inner_product_print_clifford_1[] = "\n        Inner product.\n\n        >>> print(clifford(\"{1}\") & clifford(\"{2}\"))\n        0\n        >>> print(clifford(2) & clifford(\"{2}\"))\n        0\n        >>> print(clifford(\"{1}\") & clifford(\"{1}\"))\n        1\n        >>> print(clifford(\"{1}\") & clifford(\"{1,2}\"))\n        {2}\n        ";
static const char __pyx_k_Inverse_tangent_of_multivector[] = "\n    Inverse tangent of multivector with optional complexifier.\n\n    >>> s=index_set({1,2,3}); x=clifford(\"{1}\"); print(tan(atan(x,s),s))\n    {1}\n    >>> x=clifford(\"{1}\"); print(tan(atan(x)))\n    {1}\n    ";
static const char __pyx_k_Iterate_over_the_indices_of_an[] = "\n        Iterate over the indices of an index_set.\n\n        >>> for i in index_set({-3,4,7}):print(i, end=\",\")\n        -3,4,7,\n        ";
static const char __pyx_k_Maximum_member_index_set_1_1_2[] = "\n        Maximum member.\n\n        >>> index_set({-1,1,2}).max()\n        2\n        ";
static const char __pyx_k_Maximum_positive_index_or_0_if[] = "\n    Maximum positive index, or 0 if none.\n\n    >>> max_pos(index_set({1,2}))\n    2\n    ";
static const char __pyx_k_Minimum_member_index_set_1_1_2[] = "\n        Minimum member.\n\n        >>> index_set({-1,1,2}).min()\n        -1\n        ";
static const char __pyx_k_Minimum_negative_index_or_0_if[] = "\n    Minimum negative index, or 0 if none.\n\n    >>> min_neg(index_set({1,2}))\n    0\n    ";
static const char __pyx_k_Odd_part_of_multivector_sum_of[] = "\n        Odd part of multivector, sum of odd grade terms.\n\n        >>> print(clifford(\"1+{1}+{1,2}\").odd())\n        {1}\n        ";
static const char __pyx_k_Outer_product_power_x_clifford[] = "\n        Outer product power.\n\n        >>> x=clifford(\"2+{1}\"); print(x.outer_pow(0))\n        1\n        >>> x=clifford(\"2+{1}\"); print(x.outer_pow(1))\n        2+{1}\n        >>> x=clifford(\"2+{1}\"); print(x.outer_pow(2))\n        4+4{1}\n        >>> print(clifford(\"1+{1}+{1,2}\").outer_pow(3))\n        1+3{1}+3{1,2}\n\n        ";
static const char __pyx_k_Outer_product_print_clifford_1[] = "\n        Outer product.\n\n        >>> print(clifford(\"{1}\") ^ clifford(\"{2}\"))\n        {1,2}\n        >>> print(clifford(2) ^ clifford(\"{2}\"))\n        2{2}\n        >>> print(clifford(\"{1}\") ^ clifford(\"{1}\"))\n        0\n        >>> print(clifford(\"{1}\") ^ clifford(\"{1,2}\"))\n        0\n        ";
static const char __pyx_k_Power_self_to_the_m_x_clifford[] = "\n        Power: self to the m.\n\n        >>> x=clifford(\"{1}\"); print(x ** 2)\n        1\n        >>> x=clifford(\"2\"); print(x ** 2)\n        4\n        >>> x=clifford(\"2+{1}\"); print(x ** 0)\n        1\n        >>> x=clifford(\"2+{1}\"); print(x ** 1)\n        2+{1}\n        >>> x=clifford(\"2+{1}\"); print(x ** 2)\n        5+4{1}\n        >>> i=clifford(\"{1,2}\"); print(exp(pi/2) * (i ** i))\n        1\n        ";
static const char __pyx_k_Pure_part_print_clifford_1_1_1[] = "\n        Pure part.\n\n        >>> print(clifford(\"1+{1}+{1,2}\").pure())\n        {1}+{1,2}\n        >>> print(clifford(\"{1,2}\").pure())\n        {1,2}\n        ";
static const char __pyx_k_Quadratic_form_rev_x_x_0_print[] = "\n        Quadratic form == (rev(x)*x)(0).\n\n        >>> print(clifford(\"1+{1}+{1,2}\").quad())\n        3.0\n        >>> print(clifford(\"1+{-1}+{1,2}+{1,2,3}\").quad())\n        2.0\n        ";
static const char __pyx_k_Set_complement_not_print_index[] = "\n        Set complement: not.\n\n        >>> print(~index_set({-16,-15,-14,-13,-12,-11,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16}))\n        {-32,-31,-30,-29,-28,-27,-26,-25,-24,-23,-22,-21,-20,-19,-18,-17,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32}\n        ";
static const char __pyx_k_Set_union_or_print_index_set_1[] = "\n        Set union: or.\n\n        >>> print(index_set({1}) | index_set({2}))\n        {1,2}\n        >>> print(index_set({1,2}) | index_set({2}))\n        {1,2}\n        ";
static const char __pyx_k_Transform_left_hand_side_using[] = "\n        Transform left hand side, using right hand side as a transformation.\n\n        >>> x=clifford(\"{1,2}\") * pi/2; y=clifford(\"{1}\"); print(y|x)\n        -{1}\n        >>> x=clifford(\"{1,2}\") * pi/2; y=clifford(\"{1}\"); print(y|exp(x))\n        -{1}\n        ";
static const char __pyx_k_clifford_vector_part_line_1079[] = "clifford.vector_part (line 1079)";
static const char __pyx_k_index_set___getitem___line_191[] = "index_set.__getitem__ (line 191)";
static const char __pyx_k_index_set___setitem___line_179[] = "index_set.__setitem__ (line 179)";
static const char __pyx_k_lexicographic_compare_eg_3_4_5[] = "\n    \"lexicographic compare\" eg. {3,4,5} is less than {3,7,8};\n    -1 if a<b, +1 if a>b, 0 if a==b.\n\n    >>> compare(index_set({1,2}),index_set({-1,3}))\n    -1\n    >>> compare(index_set({-1,4}),index_set({-1,3}))\n    1\n    ";
static const char __pyx_k_Abbreviation_for_clifford_index[] = "\n    Abbreviation for clifford(index_set(obj)).\n\n    >>> print(e(1))\n    {1}\n    >>> print(e(-1))\n    {-1}\n    >>> print(e(0))\n    1\n    ";
static const char __pyx_k_Absolute_value_of_multivector_m[] = "\n    Absolute value of multivector: multivector 2-norm.\n\n    >>> abs(clifford(\"1+{-1}+{1,2}+{1,2,3}\"))\n    2.0\n    ";
static const char __pyx_k_Absolute_value_square_root_of_n[] = "\n        Absolute value: square root of norm.\n\n        >>> clifford(\"1+{-1}+{1,2}+{1,2,3}\").abs()\n        2.0\n        ";
static const char __pyx_k_Cardinality_Number_of_indices_i[] = "\n        Cardinality: Number of indices included in set.\n\n        >>> index_set({-1,1,2}).count()\n        3\n        ";
static const char __pyx_k_Check_if_a_multivector_contains[] = "\n        Check if a multivector contains any IEEE NaN values.\n\n        >>> clifford().isnan()\n        False\n        ";
static const char __pyx_k_Contraction_print_clifford_1_cl[] = "\n        Contraction.\n\n        >>> print(clifford(\"{1}\") % clifford(\"{2}\"))\n        0\n        >>> print(clifford(2) % clifford(\"{2}\"))\n        2{2}\n        >>> print(clifford(\"{1}\") % clifford(\"{1}\"))\n        1\n        >>> print(clifford(\"{1}\") % clifford(\"{1,2}\"))\n        {2}\n        ";
static const char __pyx_k_Contraction_x_clifford_1_x_clif[] = "\n        Contraction.\n\n        >>> x = clifford(\"{1}\"); x %= clifford(\"{2}\"); print(x)\n        0\n        >>> x = clifford(2); x %= clifford(\"{2}\"); print(x)\n        2{2}\n        >>> x = clifford(\"{1}\"); x %= clifford(\"{1}\"); print(x)\n        1\n        >>> x = clifford(\"{1}\"); x %= clifford(\"{1,2}\"); print(x)\n        {2}\n        ";
static const char __pyx_k_Convert_CGA3_null_vector_to_Euc[] = "\n    Convert CGA3 null vector to Euclidean 3D vector using Doran and Lasenby definition.\n\n    >>> x=clifford(\"2{1}+9{2}+{3}\"); print(agc3(cga3(x)))\n    2{1}+9{2}+{3}\n    >>> x=clifford(\"2{1}+9{2}+{3}\"); print(agc3(cga3(x))-x)\n    0\n    ";
static const char __pyx_k_Convert_CGA3_null_vector_to_sta[] = "\n    Convert CGA3 null vector to standard conformal null vector using Doran and Lasenby definition.\n\n    >>> x=clifford(\"2{1}+9{2}+{3}\"); print(cga3std(cga3(x)))\n    87{-1}+4{1}+18{2}+2{3}+85{4}\n    >>> x=clifford(\"2{1}+9{2}+{3}\"); print(cga3std(cga3(x))-cga3(x))\n    0\n    ";
static const char __pyx_k_Convert_Euclidean_3D_multivecto[] = "\n    Convert Euclidean 3D multivector to Conformal Geometric Algebra using Doran and Lasenby definition.\n\n    >>> x=clifford(\"2{1}+9{2}+{3}\"); print(cga3(x))\n    87{-1}+4{1}+18{2}+2{3}+85{4}\n    ";
static const char __pyx_k_Copy_this_clifford_object_x_cli[] = "\n        Copy this clifford object.\n\n        >>> x=clifford(\"1{2}\"); y=x.copy(); print(y)\n        {2}\n        ";
static const char __pyx_k_Copy_this_index_set_object_s_in[] = "\n        Copy this index_set object.\n\n        >>> s=index_set(1); t=s.copy(); print(t)\n        {1}\n        ";
static const char __pyx_k_Cosine_of_multivector_with_opti[] = "\n    Cosine of multivector with optional complexifier.\n\n    >>> x=clifford(\"{1,2}\"); print(cos(acos(x),\"{1,2,3}\"))\n    {1,2}\n    >>> x=clifford(\"{1,2}\"); print(cos(acos(x)))\n    {1,2}\n    ";
static const char __pyx_k_Even_part_of_multivector_sum_of[] = "\n        Even part of multivector, sum of even grade terms.\n\n        >>> print(clifford(\"1+{1}+{1,2}\").even())\n        1+{1,2}\n        ";
static const char __pyx_k_Exponential_of_multivector_x_cl[] = "\n    Exponential of multivector.\n\n    >>> x=clifford(\"{1,2}\") * pi/4; print(exp(x))\n    0.7071+0.7071{1,2}\n    >>> x=clifford(\"{1,2}\") * pi/2; print(exp(x))\n    {1,2}\n    ";
static const char __pyx_k_Geometric_difference_print_clif[] = "\n        Geometric difference.\n\n        >>> print(clifford(1) - clifford(\"{2}\"))\n        1-{2}\n        >>> print(clifford(\"{1}\") - clifford(\"{2}\"))\n        {1}-{2}\n        ";
static const char __pyx_k_Geometric_difference_x_clifford[] = "\n        Geometric difference.\n\n        >>> x = clifford(1); x -= clifford(\"{2}\"); print(x)\n        1-{2}\n        ";
static const char __pyx_k_Geometric_multiplicative_invers[] = "\n        Geometric multiplicative inverse.\n\n        >>> x = clifford(\"{1}\"); print(x.inv())\n        {1}\n        >>> x = clifford(2); print(x.inv())\n        0.5\n        >>> x = clifford(\"{1,2}\"); print(x.inv())\n        -{1,2}\n        ";
static const char __pyx_k_Geometric_product_print_cliffor[] = "\n        Geometric product.\n\n        >>> print(clifford(\"{1}\") * clifford(\"{2}\"))\n        {1,2}\n        >>> print(clifford(2) * clifford(\"{2}\"))\n        2{2}\n        >>> print(clifford(\"{1}\") * clifford(\"{1,2}\"))\n        {2}\n        ";
static const char __pyx_k_Geometric_quotient_print_cliffo[] = "\n        Geometric quotient.\n\n        >>> print(clifford(\"{1}\") / clifford(\"{2}\"))\n        {1,2}\n        >>> print(clifford(2) / clifford(\"{2}\"))\n        2{2}\n        >>> print(clifford(\"{1}\") / clifford(\"{1}\"))\n        1\n        >>> print(clifford(\"{1}\") / clifford(\"{1,2}\"))\n        -{2}\n        ";
static const char __pyx_k_Geometric_quotient_x_clifford_1[] = "\n        Geometric quotient.\n\n        >>> x = clifford(\"{1}\"); x /= clifford(\"{2}\"); print(x)\n        {1,2}\n        >>> x = clifford(2); x /= clifford(\"{2}\"); print(x)\n        2{2}\n        >>> x = clifford(\"{1}\"); x /= clifford(\"{1}\"); print(x)\n        1\n        >>> x = clifford(\"{1}\"); x /= clifford(\"{1,2}\"); print(x)\n        -{2}\n        ";
static const char __pyx_k_Geometric_sum_x_clifford_1_x_cl[] = "\n        Geometric sum.\n\n        >>> x = clifford(1); x += clifford(\"{2}\"); print(x)\n        1+{2}\n        ";
static const char __pyx_k_Get_the_value_of_an_index_set_o[] = "\n        Get the value of an index_set object at an index.\n\n        >>> index_set({1})[1]\n        True\n        >>> index_set({1})[2]\n        False\n        >>> index_set({2})[-1]\n        False\n        >>> index_set({2})[1]\n        False\n        >>> index_set({2})[2]\n        True\n        >>> index_set({2})[33]\n        False\n        ";
static const char __pyx_k_Hyperbolic_cosine_of_multivecto[] = "\n    Hyperbolic cosine of multivector.\n\n    >>> x=clifford(\"{1,2}\") * pi; print(cosh(x))\n    -1\n    >>> x=clifford(\"{1,2,3}\"); print(cosh(acosh(x)))\n    {1,2,3}\n    >>> x=clifford(\"{1,2}\"); print(cosh(acosh(x)))\n    {1,2}\n    ";
static const char __pyx_k_Hyperbolic_tangent_of_multivect[] = "\n    Hyperbolic tangent of multivector.\n\n    >>> x=clifford(\"{1,2}\") * pi/4; print(tanh(x))\n    {1,2}\n    ";
static const char __pyx_k_Imaginary_part_deprecated_alway[] = "\n    Imaginary part: deprecated (always 0).\n\n    >>> imag(clifford(\"1+{1}+{1,2}\"))\n    0.0\n    >>> imag(clifford(\"{1,2}\"))\n    0.0\n    ";
static const char __pyx_k_Inner_product_x_clifford_1_x_cl[] = "\n        Inner product.\n\n        >>> x = clifford(\"{1}\"); x &= clifford(\"{2}\"); print(x)\n        0\n        >>> x = clifford(2); x &= clifford(\"{2}\"); print(x)\n        0\n        >>> x = clifford(\"{1}\"); x &= clifford(\"{1}\"); print(x)\n        1\n        >>> x = clifford(\"{1}\"); x &= clifford(\"{1,2}\"); print(x)\n        {2}\n        ";
static const char __pyx_k_Integer_power_of_multivector_ob[] = "\n    Integer power of multivector: obj to the m.\n\n    >>> x=clifford(\"{1}\"); print(pow(x,2))\n    1\n    >>> x=clifford(\"2\"); print(pow(x,2))\n    4\n    >>> x=clifford(\"2+{1}\"); print(pow(x,0))\n    1\n    >>> x=clifford(\"2+{1}\"); print(pow(x,1))\n    2+{1}\n    >>> x=clifford(\"2+{1}\"); print(pow(x,2))\n    5+4{1}\n    >>> print(pow(clifford(\"1+{1}+{1,2}\"),3))\n    1+3{1}+3{1,2}\n    >>> i=clifford(\"{1,2}\"); print(exp(pi/2) * pow(i, i))\n    1\n    ";
static const char __pyx_k_Inverse_cosine_of_multivector_w[] = "\n    Inverse cosine of multivector with optional complexifier.\n\n    >>> x=clifford(\"{1,2}\"); print(cos(acos(x),\"{1,2,3}\"))\n    {1,2}\n    >>> x=clifford(\"{1,2}\"); print(cos(acos(x),\"{-1,1,2,3,4}\"))\n    {1,2}\n    >>> print(acos(0) / pi)\n    0.5\n    >>> x=clifford(\"{1,2}\"); print(cos(acos(x)))\n    {1,2}\n    ";
static const char __pyx_k_Inverse_hyperbolic_cosine_of_mu[] = "\n    Inverse hyperbolic cosine of multivector with optional complexifier.\n\n    >>> print(acosh(0,\"{-2,-1,1}\"))\n    1.571{-2,-1,1}\n    >>> x=clifford(\"{1,2,3}\"); print(cosh(acosh(x,\"{-1,1,2,3,4}\")))\n    {1,2,3}\n    >>> print(acosh(0))\n    1.571{-1}\n    >>> x=clifford(\"{1,2,3}\"); print(cosh(acosh(x)))\n    {1,2,3}\n    >>> x=clifford(\"{1,2}\"); print(cosh(acosh(x)))\n    {1,2}\n    ";
static const char __pyx_k_Inverse_hyperbolic_sine_of_mult[] = "\n    Inverse hyperbolic sine of multivector with optional complexifier.\n\n    >>> x=clifford(\"{1,2}\"); print(asinh(x,\"{1,2,3}\") * 2/pi)\n    {1,2}\n    >>> x=clifford(\"{1,2}\"); print(asinh(x) * 2/pi)\n    {1,2}\n    >>> x=clifford(\"{1,2}\") / 2; print(asinh(x) * 6/pi)\n    {1,2}\n    ";
static const char __pyx_k_Inverse_hyperbolic_tangent_of_m[] = "\n    Inverse hyperbolic tangent of multivector with optional complexifier.\n\n    >>> s=index_set({1,2,3}); x=clifford(\"{1,2}\"); print(tanh(atanh(x,s)))\n    {1,2}\n    >>> x=clifford(\"{1,2}\"); print(tanh(atanh(x)))\n    {1,2}\n    ";
static const char __pyx_k_Inverse_sine_of_multivector_wit[] = "\n    Inverse sine of multivector with optional complexifier.\n\n    >>> s=\"{-1}\"; x=clifford(s); print(asin(sin(x,s),s))\n    {-1}\n    >>> s=\"{-1}\"; x=clifford(s); print(asin(sin(x,s),\"{-2,-1,1}\"))\n    {-1}\n    >>> print(asin(1) / pi)\n    0.5\n    >>> x=clifford(\"{1,2,3}\"); print(asin(sin(x)))\n    {1,2,3}\n    ";
static const char __pyx_k_Main_involution_each_i_is_repla[] = "\n        Main involution, each {i} is replaced by -{i} in each term,\n        eg. clifford(\"{1}\") -> -clifford(\"{1}\").\n\n        >>> print(clifford(\"{1}\").involute())\n        -{1}\n        >>> print((clifford(\"{2}\") * clifford(\"{1}\")).involute())\n        -{1,2}\n        >>> print((clifford(\"{1}\") * clifford(\"{2}\")).involute())\n        {1,2}\n        >>> print(clifford(\"1+{1}+{1,2}\").involute())\n        1-{1}+{1,2}\n        ";
static const char __pyx_k_Maximum_absolute_value_of_coord[] = "\n    Maximum absolute value of coordinates multivector: multivector infinity-norm.\n\n    >>> max_abs(clifford(\"1+{-1}+{1,2}+{1,2,3}\"))\n    1.0\n    >>> max_abs(clifford(\"3+2{1}+{1,2}\"))\n    3.0\n\n    ";
static const char __pyx_k_Maximum_of_absolute_values_of_c[] = "\n        Maximum of absolute values of components of multivector: multivector infinity norm.\n\n        >>> clifford(\"1+{-1}+{1,2}+{1,2,3}\").max_abs()\n        1.0\n        >>> clifford(\"3+2{1}+{1,2}\").max_abs()\n        3.0\n        ";
static const char __pyx_k_Natural_logarithm_of_multivecto[] = "\n    Natural logarithm of multivector with optional complexifier.\n\n    >>> x=clifford(\"{-1}\"); print((log(x,\"{-1}\") * 2/pi))\n    {-1}\n    >>> x=clifford(\"{1,2}\"); print((log(x,\"{1,2,3}\") * 2/pi))\n    {1,2}\n    >>> x=clifford(\"{1,2}\"); print((log(x) * 2/pi))\n    {1,2}\n    >>> x=clifford(\"{1,2}\"); print((log(x,\"{1,2}\") * 2/pi))\n    Traceback (most recent call last):\n    ...\n    RuntimeError: check_complex(val, i): i is not a valid complexifier for val\n    ";
static const char __pyx_k_Norm_sum_of_squares_of_coordina[] = "\n        Norm == sum of squares of coordinates.\n\n        >>> clifford(\"1+{1}+{1,2}\").norm()\n        3.0\n        >>> clifford(\"1+{-1}+{1,2}+{1,2,3}\").norm()\n        4.0\n        ";
static const char __pyx_k_Not_applicable_for_a_in_cliffor[] = "\n        Not applicable.\n\n        >>> for a in clifford(index_set({-3,4,7})):print(a, end=\",\")\n        Traceback (most recent call last):\n          ...\n        TypeError: Not applicable.\n        ";
static const char __pyx_k_Number_of_negative_indices_incl[] = "\n        Number of negative indices included in set.\n\n        >>> index_set({-1,1,2}).count_neg()\n        1\n        ";
static const char __pyx_k_Number_of_positive_indices_incl[] = "\n        Number of positive indices included in set.\n\n        >>> index_set({-1,1,2}).count_pos()\n        2\n        ";
static const char __pyx_k_Outer_product_power_of_multivec[] = "\n    Outer product power of multivector.\n\n    >>> print(outer_pow(clifford(\"1+{1}+{1,2}\"),3))\n    1+3{1}+3{1,2}\n    ";
static const char __pyx_k_Outer_product_x_clifford_1_x_cl[] = "\n        Outer product.\n\n        >>> x = clifford(\"{1}\"); x ^= clifford(\"{2}\"); print(x)\n        {1,2}\n        >>> x = clifford(2); x ^= clifford(\"{2}\"); print(x)\n        2{2}\n        >>> x = clifford(\"{1}\"); x ^= clifford(\"{1}\"); print(x)\n        0\n        >>> x = clifford(\"{1}\"); x ^= clifford(\"{1,2}\"); print(x)\n        0\n        ";
static const char __pyx_k_Pure_grade_vector_part_print_cl[] = "\n        Pure grade-vector part.\n\n        >>> print(clifford(\"{1}\")(1))\n        {1}\n        >>> print(clifford(\"{1}\")(0))\n        0\n        >>> print(clifford(\"1+{1}+{1,2}\")(0))\n        1\n        >>> print(clifford(\"1+{1}+{1,2}\")(1))\n        {1}\n        >>> print(clifford(\"1+{1}+{1,2}\")(2))\n        {1,2}\n        >>> print(clifford(\"1+{1}+{1,2}\")(3))\n        0\n        ";
static const char __pyx_k_Pure_part_print_pure_clifford_1[] = "\n    Pure part\n\n    >>> print(pure(clifford(\"1+{1}+{1,2}\")))\n    {1}+{1,2}\n    >>> print(pure(clifford(\"{1,2}\")))\n    {1,2}\n    ";
static const char __pyx_k_Put_self_into_a_larger_frame_co[] = "\n        Put self into a larger frame, containing the union of self.frame() and index set ixt.\n        This can be used to make multiplication faster, by multiplying within a common frame.\n\n        >>> clifford(\"2+3{1}\").reframe(index_set({1,2,3}))\n        clifford(\"2+3{1}\")\n        >>> s=index_set({1,2,3});t=index_set({-3,-2,-1});x=random_clifford(s); x.reframe(t).frame() == (s|t);\n        True\n        ";
static const char __pyx_k_Random_multivector_within_a_fra[] = "\n    Random multivector within a frame.\n\n    >>> print(random_clifford(index_set({-3,-1,2})).frame())\n    {-3,-1,2}\n    ";
static const char __pyx_k_Real_part_synonym_for_scalar_pa[] = "\n    Real part: synonym for scalar part.\n\n    >>> real(clifford(\"1+{1}+{1,2}\"))\n    1.0\n    >>> real(clifford(\"{1,2}\"))\n    0.0\n    ";
static const char __pyx_k_Remove_all_terms_of_self_with_r[] = "\n        Remove all terms of self with relative size smaller than limit.\n\n        >>> clifford(\"1e8+{1}+1e-8{1,2}\").truncated(1.0e-6)\n        clifford(\"100000000\")\n        >>> clifford(\"1e4+{1}+1e-4{1,2}\").truncated(1.0e-6)\n        clifford(\"10000+{1}\")\n        ";
static const char __pyx_k_Reversion_eg_1_2_2_1_print_reve[] = "\n    Reversion, eg. {1}*{2} -> {2}*{1}\n\n    >>> print(reverse(clifford(\"{1}\")))\n    {1}\n    >>> print(reverse(clifford(\"{2}\") * clifford(\"{1}\")))\n    {1,2}\n    >>> print(reverse(clifford(\"{1}\") * clifford(\"{2}\")))\n    -{1,2}\n    >>> print(reverse(clifford(\"1+{1}+{1,2}\")))\n    1+{1}-{1,2}\n    ";
static const char __pyx_k_Reversion_eg_clifford_1_cliffor[] = "\n        Reversion, eg. clifford(\"{1}\")*clifford(\"{2}\") -> clifford(\"{2}\")*clifford(\"{1}\").\n\n        >>> print(clifford(\"{1}\").reverse())\n        {1}\n        >>> print((clifford(\"{2}\") * clifford(\"{1}\")).reverse())\n        {1,2}\n        >>> print((clifford(\"{1}\") * clifford(\"{2}\")).reverse())\n        -{1,2}\n        >>> print(clifford(\"1+{1}+{1,2}\").reverse())\n        1+{1}-{1,2}\n        ";
static const char __pyx_k_Scalar_part_clifford_1_1_1_2_sc[] = "\n        Scalar part.\n\n        >>> clifford(\"1+{1}+{1,2}\").scalar()\n        1.0\n        >>> clifford(\"{1,2}\").scalar()\n        0.0\n        ";
static const char __pyx_k_Scalar_part_scalar_clifford_1_1[] = "\n    Scalar part.\n\n    >>> scalar(clifford(\"1+{1}+{1,2}\"))\n    1.0\n    >>> scalar(clifford(\"{1,2}\"))\n    0.0\n    ";
static const char __pyx_k_Set_intersection_and_print_inde[] = "\n        Set intersection: and.\n\n        >>> print(index_set({1}) & index_set({2}))\n        {}\n        >>> print(index_set({1,2}) & index_set({2}))\n        {2}\n        ";
static const char __pyx_k_Set_intersection_and_x_index_se[] = "\n        Set intersection: and.\n\n        >>> x = index_set({1}); x &= index_set({2}); print(x)\n        {}\n        >>> x = index_set({1,2}); x &= index_set({2}); print(x)\n        {2}\n        ";
static const char __pyx_k_Set_the_value_of_an_index_set_o[] = "\n        Set the value of an index_set object at index idx to value val.\n\n        >>> s=index_set({1}); s[2] = True; print(s)\n        {1,2}\n        >>> s=index_set({1,2}); s[1] = False; print(s)\n        {2}\n        ";
static const char __pyx_k_Set_union_or_x_index_set_1_x_in[] = "\n        Set union: or.\n\n        >>> x = index_set({1}); x |= index_set({2}); print(x)\n        {1,2}\n        >>> x = index_set({1,2}); x |= index_set({2}); print(x)\n        {1,2}\n        ";
static const char __pyx_k_Sign_of_geometric_product_of_tw[] = "\n        Sign of geometric product of two Clifford basis elements.\n\n        >>> s = index_set({1,2}); t=index_set({-1}); s.sign_of_mult(t)\n        1\n        ";
static const char __pyx_k_Sign_of_geometric_square_of_a_C[] = "\n        Sign of geometric square of a Clifford basis element.\n\n        >>> s = index_set({1,2}); s.sign_of_square()\n        -1\n        ";
static const char __pyx_k_Sine_of_multivector_with_option[] = "\n    Sine of multivector with optional complexifier.\n\n    >>> s=\"{-1}\"; x=clifford(s); print(asin(sin(x,s),s))\n    {-1}\n    >>> s=\"{-1}\"; x=clifford(s); print(asin(sin(x,s),\"{-2,-1,1}\"))\n    {-1}\n    >>> x=clifford(\"{1,2,3}\"); print(asin(sin(x)))\n    {1,2,3}\n    ";
static const char __pyx_k_Square_root_of_1_which_commutes[] = "\n    Square root of -1 which commutes with all members of the frame of the given multivector.\n\n    >>> print(complexifier(clifford(index_set({1}))))\n    {1,2,3}\n    >>> print(complexifier(clifford(index_set({-1}))))\n    {-1}\n    >>> print(complexifier(index_set({1})))\n    {1,2,3}\n    >>> print(complexifier(index_set({-1})))\n    {-1}\n    ";
static const char __pyx_k_Square_root_of_multivector_with[] = "\n    Square root of multivector with optional complexifier.\n\n    >>> print(sqrt(-1))\n    {-1}\n    >>> print(sqrt(clifford(\"2{-1}\")))\n    1+{-1}\n    >>> j=sqrt(-1,complexifier(index_set({1}))); print(j); print(j*j)\n    {1,2,3}\n    -1\n    >>> j=sqrt(-1,\"{1,2,3}\"); print(j); print(j*j)\n    {1,2,3}\n    -1\n    ";
static const char __pyx_k_Subalgebra_generated_by_all_gen[] = "\n        Subalgebra generated by all generators of terms of given multivector.\n\n        >>> print(clifford(\"1+3{-1}+2{1,2}+4{-2,7}\").frame())\n        {-2,-1,1,2,7}\n        >>> s=clifford(\"1+3{-1}+2{1,2}+4{-2,7}\").frame(); type(s)\n        <class 'PyClical.index_set'>\n        ";
static const char __pyx_k_Subscripting_map_from_index_set[] = "\n        Subscripting: map from index set to scalar coordinate.\n\n        >>> clifford(\"{1}\")[index_set(1)]\n        1.0\n        >>> clifford(\"{1}\")[index_set({1})]\n        1.0\n        >>> clifford(\"{1}\")[index_set({1,2})]\n        0.0\n        >>> clifford(\"2{1,2}\")[index_set({1,2})]\n        2.0\n        ";
static const char __pyx_k_Symmetric_set_difference_exclus[] = "\n        Symmetric set difference: exclusive or.\n\n        >>> print(index_set({1}) ^ index_set({2}))\n        {1,2}\n        >>> print(index_set({1,2}) ^ index_set({2}))\n        {1}\n        ";
static const char __pyx_k_Tangent_of_multivector_with_opt[] = "\n    Tangent of multivector with optional complexifier.\n\n    >>> x=clifford(\"{1,2}\"); print(tan(x,\"{1,2,3}\"))\n    0.7616{1,2}\n    >>> x=clifford(\"{1,2}\"); print(tan(x))\n    0.7616{1,2}\n    ";
static const char __pyx_k_Tests_for_functions_that_Doctes[] = "\n    Tests for functions that Doctest cannot see.\n\n    For index_set.__cinit__: Construct index_set.\n\n    >>> print(index_set(1))\n    {1}\n    >>> print(index_set({1,2}))\n    {1,2}\n    >>> print(index_set(index_set({1,2})))\n    {1,2}\n    >>> print(index_set({1,2}))\n    {1,2}\n    >>> print(index_set({1,2,1}))\n    {1,2}\n    >>> print(index_set({1,2,1}))\n    {1,2}\n    >>> print(index_set(\"\"))\n    {}\n    >>> print(index_set(\"{\"))\n    Traceback (most recent call last):\n    ...\n    ValueError: Cannot initialize index_set object from invalid string '{'.\n    >>> print(index_set(\"{1\"))\n    Traceback (most recent call last):\n    ...\n    ValueError: Cannot initialize index_set object from invalid string '{1'.\n    >>> print(index_set(\"{1,2,100}\"))\n    Traceback (most recent call last):\n    ...\n    ValueError: Cannot initialize index_set object from invalid string '{1,2,100}'.\n    >>> print(index_set({1,2,100}))\n    Traceback (most recent call last):\n    ...\n    IndexError: Cannot initialize index_set object from invalid {1, 2, 100}.\n    >>> print(index_set([1,2]))\n    Traceback (most recent call last):\n    ...\n    TypeError: Cannot initialize index_set object from <class 'list'>.\n\n    For index_set.__richcmp__: Compare two objects of class index_set.\n\n    >>> index_set(1) == index_set({1})\n    True\n    >>> index_set({1}) != index_set({1})\n    False\n    >>> index_set({1}) != index_set({2})\n    True\n    >>> index_set({1}) == index_set({2})\n    False\n    >>> index_set({1}) < index_set({2})\n    True\n    >>> index_set({1}) <= index_set({2})\n    True\n    >>> index_set({1}) > index_set({2})\n    False\n    >>> index_set({1}) >= index_set({2})\n    False\n    >>> None == index_set({1,2})\n    False\n    >>> None != index_set({1,2})\n    True\n    >>> None < index_set({1,2})\n    False\n    >>> None <= index_set({1,2})\n    False\n    >>> None > index_set({1,2})\n    False\n    >>> None >= index_set({1,2})\n    False\n    >>> ""index_set({1,2}) == None\n    False\n    >>> index_set({1,2}) != None\n    True\n    >>> index_set({1,2}) < None\n    False\n    >>> index_set({1,2}) <= None\n    False\n    >>> index_set({1,2}) > None\n    False\n    >>> index_set({1,2}) >= None\n    False\n    ";
        static const char __pyx_k_The_informal_string_representat[] = "\n        The \342\200\234informal\342\200\235 string representation of self.\n\n        >>> index_set({1,2}).__str__()\n        '{1,2}'\n        >>> str(index_set({1,2}))\n        '{1,2}'\n        ";
        static const char __pyx_k_The_official_string_representat[] = "\n        The \342\200\234official\342\200\235 string representation of self.\n\n        >>> index_set({1,2}).__repr__()\n        'index_set({1,2})'\n        >>> repr(index_set({1,2}))\n        'index_set({1,2})'\n        ";
        static const char __pyx_k_This_comparison_operator_is_not[] = "This comparison operator is not implemented for ";
        static const char __pyx_k_Vector_part_of_multivector_as_a[] = "\n        Vector part of multivector, as a Python list, with respect to frm.\n\n        >>> print(clifford(\"1+2{1}+3{2}+4{1,2}\").vector_part())\n        [2.0, 3.0]\n        >>> print(clifford(\"1+2{1}+3{2}+4{1,2}\").vector_part(index_set({-1,1,2})))\n        [0.0, 2.0, 3.0]\n        ";
        static const char __pyx_k_index_set_sign_of_mult_line_366[] = "index_set.sign_of_mult (line 366)";
        static const char __pyx_k_norm_sum_of_squares_of_coordina[] = "\n    norm == sum of squares of coordinates.\n\n    >>> norm(clifford(\"1+{1}+{1,2}\"))\n    3.0\n    >>> norm(clifford(\"1+{-1}+{1,2}+{1,2,3}\"))\n    4.0\n    ";
        static const char __pyx_k_Cannot_initialize_clifford_objec[] = "Cannot initialize clifford object from";
        static const char __pyx_k_Cannot_initialize_index_set_obje[] = "Cannot initialize index_set object from";
        static const char __pyx_k_Conjugation_reverse_o_involute_2[] = "\n    Conjugation, reverse o involute == involute o reverse.\n\n    >>> print(conj(clifford(\"{1}\")))\n    -{1}\n    >>> print(conj(clifford(\"{2}\") * clifford(\"{1}\")))\n    {1,2}\n    >>> print(conj(clifford(\"{1}\") * clifford(\"{2}\")))\n    -{1,2}\n    >>> print(conj(clifford(\"1+{1}+{1,2}\")))\n    1-{1}-{1,2}\n    ";
        static const char __pyx_k_Odd_part_of_multivector_sum_of_2[] = "\n    Odd part of multivector, sum of odd grade terms.\n\n    >>> print(odd(clifford(\"1+{1}+{1,2}\")))\n    {1}\n    ";
        static const char __pyx_k_Power_self_to_the_m_x_clifford_2[] = "\n        Power: self to the m.\n\n        >>> x=clifford(\"{1}\"); print(x.pow(2))\n        1\n        >>> x=clifford(\"2\"); print(x.pow(2))\n        4\n        >>> x=clifford(\"2+{1}\"); print(x.pow(0))\n        1\n        >>> x=clifford(\"2+{1}\"); print(x.pow(1))\n        2+{1}\n        >>> x=clifford(\"2+{1}\"); print(x.pow(2))\n        5+4{1}\n        >>> print(clifford(\"1+{1}+{1,2}\").pow(3))\n        1+3{1}+3{1,2}\n        >>> i=clifford(\"{1,2}\"); print(exp(pi/2) * i.pow(i))\n        1\n        ";
        static const char __pyx_k_Quadratic_form_rev_x_x_0_print_2[] = "\n    Quadratic form == (rev(x)*x)(0).\n\n    >>> print(quad(clifford(\"1+{1}+{1,2}\")))\n    3.0\n    >>> print(quad(clifford(\"1+{-1}+{1,2}+{1,2,3}\")))\n    2.0\n    ";
        static const char __pyx_k_Transform_left_hand_side_using_2[] = "\n        Transform left hand side, using right hand side as a transformation.\n\n        >>> x=clifford(\"{1,2}\") * pi/2; y=clifford(\"{1}\"); y|=x; print(y)\n        -{1}\n        >>> x=clifford(\"{1,2}\") * pi/2; y=clifford(\"{1}\"); y|=exp(x); print(y)\n        -{1}\n        ";
        static const char __pyx_k_clifford_hidden_doctests_line_12[] = "clifford_hidden_doctests (line 1244)";
        static const char __pyx_k_index_set_hidden_doctests_line_4[] = "index_set_hidden_doctests (line 406)";
        static const char __pyx_k_index_set_sign_of_square_line_37[] = "index_set.sign_of_square (line 375)";
        static const char __pyx_k_no_default___reduce___due_to_non[] = "no default __reduce__ due to non-trivial __cinit__";
        static const char __pyx_k_Even_part_of_multivector_sum_of_2[] = "\n    Even part of multivector, sum of even grade terms.\n\n    >>> print(even(clifford(\"1+{1}+{1,2}\")))\n    1+{1,2}\n    ";
        static const char __pyx_k_Geometric_multiplicative_invers_2[] = "\n    Geometric multiplicative inverse.\n\n    >>> print(inv(clifford(\"{1}\")))\n    {1}\n    >>> print(inv(clifford(\"{-1}\")))\n    -{-1}\n    >>> print(inv(clifford(\"{-2,-1}\")))\n    -{-2,-1}\n    >>> print(inv(clifford(\"{-1}+{1}\")))\n    nan\n    ";
        static const char __pyx_k_Main_involution_each_i_is_repla_2[] = "\n    Main involution, each {i} is replaced by -{i} in each term, eg. {1}*{2} -> (-{2})*(-{1})\n\n    >>> print(involute(clifford(\"{1}\")))\n    -{1}\n    >>> print(involute(clifford(\"{2}\") * clifford(\"{1}\")))\n    -{1,2}\n    >>> print(involute(clifford(\"{1}\") * clifford(\"{2}\")))\n    {1,2}\n    >>> print(involute(clifford(\"1+{1}+{1,2}\")))\n    1-{1}+{1,2}\n    ";
        static const char __pyx_k_Symmetric_set_difference_exclus_2[] = "\n        Symmetric set difference: exclusive or.\n\n        >>> x = index_set({1}); x ^= index_set({2}); print(x)\n        {1,2}\n        >>> x = index_set({1,2}); x ^= index_set({2}); print(x)\n        {1}\n        ";
        static const char __pyx_k_Tests_for_functions_that_Doctes_2[] = "\n    Tests for functions that Doctest cannot see.\n\n    For clifford.__cinit__: Construct an object of type clifford.\n\n    >>> print(clifford(2))\n    2\n    >>> print(clifford(2.0))\n    2\n    >>> print(clifford(1.0e-1))\n    0.1\n    >>> print(clifford(\"2\"))\n    2\n    >>> print(clifford(\"2{1,2,3}\"))\n    2{1,2,3}\n    >>> print(clifford(clifford(\"2{1,2,3}\")))\n    2{1,2,3}\n    >>> print(clifford(\"-{1}\"))\n    -{1}\n    >>> print(clifford(2,index_set({1,2})))\n    2{1,2}\n    >>> print(clifford([2,3],index_set({1,2})))\n    2{1}+3{2}\n    >>> print(clifford([1,2]))\n    Traceback (most recent call last):\n      ...\n    TypeError: Cannot initialize clifford object from <class 'list'>.\n    >>> print(clifford(None))\n    Traceback (most recent call last):\n      ...\n    TypeError: Cannot initialize clifford object from <class 'NoneType'>.\n    >>> print(clifford(None,[1,2]))\n    Traceback (most recent call last):\n      ...\n    TypeError: Cannot initialize clifford object from (<class 'NoneType'>, <class 'list'>).\n    >>> print(clifford([1,2],[1,2]))\n    Traceback (most recent call last):\n      ...\n    TypeError: Cannot initialize clifford object from (<class 'list'>, <class 'list'>).\n    >>> print(clifford(\"\"))\n    Traceback (most recent call last):\n      ...\n    ValueError: Cannot initialize clifford object from invalid string ''.\n    >>> print(clifford(\"{\"))\n    Traceback (most recent call last):\n      ...\n    ValueError: Cannot initialize clifford object from invalid string '{'.\n    >>> print(clifford(\"{1\"))\n    Traceback (most recent call last):\n      ...\n    ValueError: Cannot initialize clifford object from invalid string '{1'.\n    >>> print(clifford(\"+\"))\n    Traceback (most recent call last):\n      ...\n    ValueError: Cannot initialize clifford object from invalid string '+'.\n    >>> print(clifford(\"-\"))\n    Traceback (most recent call last):\n      ...\n    ValueError: Cannot initialize clifford object fro""m invalid string '-'.\n    >>> print(clifford(\"{1}+\"))\n    Traceback (most recent call last):\n      ...\n    ValueError: Cannot initialize clifford object from invalid string '{1}+'.\n\n    For clifford.__richcmp__: Compare objects of type clifford.\n\n    >>> clifford(\"{1}\") == clifford(\"1{1}\")\n    True\n    >>> clifford(\"{1}\") != clifford(\"1.0{1}\")\n    False\n    >>> clifford(\"{1}\") != clifford(\"1.0\")\n    True\n    >>> clifford(\"{1,2}\") == None\n    False\n    >>> clifford(\"{1,2}\") != None\n    True\n    >>> None == clifford(\"{1,2}\")\n    False\n    >>> None != clifford(\"{1,2}\")\n    True\n    ";
                static const char __pyx_k_The_informal_string_representat_2[] = "\n        The \342\200\234informal\342\200\235 string representation of self.\n\n        >>> clifford(\"1+3{-1}+2{1,2}+4{-2,7}\").__str__()\n        '1+3{-1}+2{1,2}+4{-2,7}'\n        ";
                static const char __pyx_k_The_official_string_representat_2[] = "\n        The \342\200\234official\342\200\235 string representation of self.\n\n        >>> clifford(\"1+3{-1}+2{1,2}+4{-2,7}\").__repr__()\n        'clifford(\"1+3{-1}+2{1,2}+4{-2,7}\")'\n        ";
                static PyObject *__pyx_kp_u_;
                static PyObject *__pyx_kp_u_0_8_4;
                static PyObject *__pyx_kp_u_Abbreviation_for_clifford_index;
                static PyObject *__pyx_kp_u_Abbreviation_for_index_set_q_p;
                static PyObject *__pyx_kp_u_Absolute_value_of_multivector_m;
                static PyObject *__pyx_kp_u_Absolute_value_square_root_of_n;
                static PyObject *__pyx_kp_u_Cannot_initialize_clifford_objec;
                static PyObject *__pyx_kp_u_Cannot_initialize_index_set_obje;
                static PyObject *__pyx_kp_u_Cannot_reframe;
                static PyObject *__pyx_kp_u_Cannot_take_vector_part_of;
                static PyObject *__pyx_kp_u_Cardinality_Number_of_indices_i;
                static PyObject *__pyx_kp_u_Check_if_a_multivector_contains;
                static PyObject *__pyx_kp_u_Conjugation_reverse_o_involute;
                static PyObject *__pyx_kp_u_Conjugation_reverse_o_involute_2;
                static PyObject *__pyx_kp_u_Contraction_print_clifford_1_cl;
                static PyObject *__pyx_kp_u_Contraction_x_clifford_1_x_clif;
                static PyObject *__pyx_kp_u_Convert_CGA3_null_vector_to_Euc;
                static PyObject *__pyx_kp_u_Convert_CGA3_null_vector_to_sta;
                static PyObject *__pyx_kp_u_Convert_Euclidean_3D_multivecto;
                static PyObject *__pyx_kp_u_Copy_this_clifford_object_x_cli;
                static PyObject *__pyx_kp_u_Copy_this_index_set_object_s_in;
                static PyObject *__pyx_kp_u_Cosine_of_multivector_with_opti;
                static PyObject *__pyx_kp_u_Even_part_of_multivector_sum_of;
                static PyObject *__pyx_kp_u_Even_part_of_multivector_sum_of_2;
                static PyObject *__pyx_kp_u_Exponential_of_multivector_x_cl;
                static PyObject *__pyx_kp_u_Geometric_difference_print_clif;
                static PyObject *__pyx_kp_u_Geometric_difference_x_clifford;
                static PyObject *__pyx_kp_u_Geometric_multiplicative_invers;
                static PyObject *__pyx_kp_u_Geometric_multiplicative_invers_2;
                static PyObject *__pyx_kp_u_Geometric_product_print_cliffor;
                static PyObject *__pyx_kp_u_Geometric_product_x_clifford_2;
                static PyObject *__pyx_kp_u_Geometric_quotient_print_cliffo;
                static PyObject *__pyx_kp_u_Geometric_quotient_x_clifford_1;
                static PyObject *__pyx_kp_u_Geometric_sum_print_clifford_1;
                static PyObject *__pyx_kp_u_Geometric_sum_x_clifford_1_x_cl;
                static PyObject *__pyx_kp_u_Get_the_value_of_an_index_set_o;
                static PyObject *__pyx_kp_u_Hyperbolic_cosine_of_multivecto;
                static PyObject *__pyx_kp_u_Hyperbolic_sine_of_multivector;
                static PyObject *__pyx_kp_u_Hyperbolic_tangent_of_multivect;
                static PyObject *__pyx_kp_u_Imaginary_part_deprecated_alway;
                static PyObject *__pyx_n_s_IndexError;
                static PyObject *__pyx_kp_u_Inner_product_print_clifford_1;
                static PyObject *__pyx_kp_u_Inner_product_x_clifford_1_x_cl;
                static PyObject *__pyx_kp_u_Integer_power_of_multivector_ob;
                static PyObject *__pyx_n_s_Integral;
                static PyObject *__pyx_kp_u_Inverse_cosine_of_multivector_w;
                static PyObject *__pyx_kp_u_Inverse_hyperbolic_cosine_of_mu;
                static PyObject *__pyx_kp_u_Inverse_hyperbolic_sine_of_mult;
                static PyObject *__pyx_kp_u_Inverse_hyperbolic_tangent_of_m;
                static PyObject *__pyx_kp_u_Inverse_sine_of_multivector_wit;
                static PyObject *__pyx_kp_u_Inverse_tangent_of_multivector;
                static PyObject *__pyx_kp_u_Iterate_over_the_indices_of_an;
                static PyObject *__pyx_kp_u_Main_involution_each_i_is_repla;
                static PyObject *__pyx_kp_u_Main_involution_each_i_is_repla_2;
                static PyObject *__pyx_kp_u_Maximum_absolute_value_of_coord;
                static PyObject *__pyx_kp_u_Maximum_member_index_set_1_1_2;
                static PyObject *__pyx_kp_u_Maximum_of_absolute_values_of_c;
                static PyObject *__pyx_kp_u_Maximum_positive_index_or_0_if;
                static PyObject *__pyx_kp_u_Minimum_member_index_set_1_1_2;
                static PyObject *__pyx_kp_u_Minimum_negative_index_or_0_if;
                static PyObject *__pyx_kp_u_Natural_logarithm_of_multivecto;
                static PyObject *__pyx_kp_u_Norm_sum_of_squares_of_coordina;
                static PyObject *__pyx_n_s_NotImplemented;
                static PyObject *__pyx_kp_u_Not_applicable;
                static PyObject *__pyx_kp_u_Not_applicable_for_a_in_cliffor;
                static PyObject *__pyx_kp_u_Number_of_negative_indices_incl;
                static PyObject *__pyx_kp_u_Number_of_positive_indices_incl;
                static PyObject *__pyx_kp_u_Odd_part_of_multivector_sum_of;
                static PyObject *__pyx_kp_u_Odd_part_of_multivector_sum_of_2;
                static PyObject *__pyx_kp_u_Outer_product_power_of_multivec;
                static PyObject *__pyx_kp_u_Outer_product_power_x_clifford;
                static PyObject *__pyx_kp_u_Outer_product_print_clifford_1;
                static PyObject *__pyx_kp_u_Outer_product_x_clifford_1_x_cl;
                static PyObject *__pyx_kp_u_Power_self_to_the_m_x_clifford;
                static PyObject *__pyx_kp_u_Power_self_to_the_m_x_clifford_2;
                static PyObject *__pyx_kp_u_Pure_grade_vector_part_print_cl;
                static PyObject *__pyx_kp_u_Pure_part_print_clifford_1_1_1;
                static PyObject *__pyx_kp_u_Pure_part_print_pure_clifford_1;
                static PyObject *__pyx_kp_u_Put_self_into_a_larger_frame_co;
                static PyObject *__pyx_n_s_PyClical;
                static PyObject *__pyx_kp_s_PyClical_pyx;
                static PyObject *__pyx_kp_u_Quadratic_form_rev_x_x_0_print;
                static PyObject *__pyx_kp_u_Quadratic_form_rev_x_x_0_print_2;
                static PyObject *__pyx_kp_u_Random_multivector_within_a_fra;
                static PyObject *__pyx_n_s_Real;
                static PyObject *__pyx_kp_u_Real_part_synonym_for_scalar_pa;
                static PyObject *__pyx_kp_u_Remove_all_terms_of_self_with_r;
                static PyObject *__pyx_kp_u_Reversion_eg_1_2_2_1_print_reve;
                static PyObject *__pyx_kp_u_Reversion_eg_clifford_1_cliffor;
                static PyObject *__pyx_n_s_RuntimeError;
                static PyObject *__pyx_kp_u_Scalar_part_clifford_1_1_1_2_sc;
                static PyObject *__pyx_kp_u_Scalar_part_scalar_clifford_1_1;
                static PyObject *__pyx_n_s_Sequence;
                static PyObject *__pyx_kp_u_Set_complement_not_print_index;
                static PyObject *__pyx_kp_u_Set_intersection_and_print_inde;
                static PyObject *__pyx_kp_u_Set_intersection_and_x_index_se;
                static PyObject *__pyx_kp_u_Set_the_value_of_an_index_set_o;
                static PyObject *__pyx_kp_u_Set_union_or_print_index_set_1;
                static PyObject *__pyx_kp_u_Set_union_or_x_index_set_1_x_in;
                static PyObject *__pyx_kp_u_Sign_of_geometric_product_of_tw;
                static PyObject *__pyx_kp_u_Sign_of_geometric_square_of_a_C;
                static PyObject *__pyx_kp_u_Sine_of_multivector_with_option;
                static PyObject *__pyx_kp_u_Square_root_of_1_which_commutes;
                static PyObject *__pyx_kp_u_Square_root_of_multivector_with;
                static PyObject *__pyx_kp_u_Subalgebra_generated_by_all_gen;
                static PyObject *__pyx_kp_u_Subscripting_map_from_index_set;
                static PyObject *__pyx_kp_u_Symmetric_set_difference_exclus;
                static PyObject *__pyx_kp_u_Symmetric_set_difference_exclus_2;
                static PyObject *__pyx_kp_u_Tangent_of_multivector_with_opt;
                static PyObject *__pyx_kp_u_Tests_for_functions_that_Doctes;
                static PyObject *__pyx_kp_u_Tests_for_functions_that_Doctes_2;
                static PyObject *__pyx_kp_u_The_informal_string_representat;
                static PyObject *__pyx_kp_u_The_informal_string_representat_2;
                static PyObject *__pyx_kp_u_The_official_string_representat;
                static PyObject *__pyx_kp_u_The_official_string_representat_2;
                static PyObject *__pyx_kp_u_This_comparison_operator_is_not;
                static PyObject *__pyx_kp_u_Transform_left_hand_side_using;
                static PyObject *__pyx_kp_u_Transform_left_hand_side_using_2;
                static PyObject *__pyx_n_s_TypeError;
                static PyObject *__pyx_kp_u_UTF_8;
                static PyObject *__pyx_kp_u_Unary_print_clifford_1_1;
                static PyObject *__pyx_kp_u_Unary_print_clifford_1_1_2;
                static PyObject *__pyx_n_s_ValueError;
                static PyObject *__pyx_kp_u_Vector_part_of_multivector_as_a;
                static PyObject *__pyx_kp_u__2;
                static PyObject *__pyx_kp_u__5;
                static PyObject *__pyx_kp_u__6;
                static PyObject *__pyx_kp_u__7;
                static PyObject *__pyx_kp_u__8;
                static PyObject *__pyx_kp_u__9;
                static PyObject *__pyx_n_s_abc;
                static PyObject *__pyx_kp_u_abs_line_1472;
                static PyObject *__pyx_n_s_acos;
                static PyObject *__pyx_kp_u_acos_line_1618;
                static PyObject *__pyx_n_s_acosh;
                static PyObject *__pyx_kp_u_acosh_line_1655;
                static PyObject *__pyx_kp_u_agc3_line_1843;
                static PyObject *__pyx_n_s_args;
                static PyObject *__pyx_kp_u_as_frame;
                static PyObject *__pyx_n_s_asin;
                static PyObject *__pyx_kp_u_asin_line_1697;
                static PyObject *__pyx_n_s_asinh;
                static PyObject *__pyx_kp_u_asinh_line_1732;
                static PyObject *__pyx_n_s_atan;
                static PyObject *__pyx_kp_u_atan_line_1768;
                static PyObject *__pyx_n_s_atanh;
                static PyObject *__pyx_kp_u_atanh_line_1797;
                static PyObject *__pyx_kp_u_cga3_line_1823;
                static PyObject *__pyx_kp_u_cga3std_line_1832;
                static PyObject *__pyx_n_s_cl;
                static PyObject *__pyx_n_s_clifford;
                static PyObject *__pyx_kp_u_clifford___add___line_740;
                static PyObject *__pyx_kp_u_clifford___and___line_836;
                static PyObject *__pyx_kp_u_clifford___call___line_1020;
                static PyObject *__pyx_kp_u_clifford___getitem___line_707;
                static PyObject *__pyx_kp_u_clifford___iadd___line_751;
                static PyObject *__pyx_kp_u_clifford___iand___line_851;
                static PyObject *__pyx_kp_u_clifford___idiv___line_911;
                static PyObject *__pyx_kp_u_clifford___imod___line_821;
                static PyObject *__pyx_kp_u_clifford___imul___line_793;
                static PyObject *__pyx_kp_u_clifford___ior___line_950;
                static PyObject *__pyx_kp_u_clifford___isub___line_771;
                static PyObject *__pyx_kp_u_clifford___iter___line_638;
                static PyObject *__pyx_kp_u_clifford___ixor___line_881;
                static PyObject *__pyx_kp_u_clifford___mod___line_806;
                static PyObject *__pyx_kp_u_clifford___mul___line_780;
                static PyObject *__pyx_kp_u_clifford___neg___line_722;
                static PyObject *__pyx_kp_u_clifford___or___line_939;
                static PyObject *__pyx_kp_u_clifford___pos___line_731;
                static PyObject *__pyx_kp_u_clifford___pow___line_961;
                static PyObject *__pyx_kp_u_clifford___repr___line_1226;
                static PyObject *__pyx_kp_u_clifford___str___line_1235;
                static PyObject *__pyx_kp_u_clifford___sub___line_760;
                static PyObject *__pyx_kp_u_clifford___truediv___line_896;
                static PyObject *__pyx_kp_u_clifford___xor___line_866;
                static PyObject *__pyx_kp_u_clifford_abs_line_1175;
                static PyObject *__pyx_kp_u_clifford_conj_line_1138;
                static PyObject *__pyx_kp_u_clifford_copy_line_556;
                static PyObject *__pyx_kp_u_clifford_even_line_1061;
                static PyObject *__pyx_kp_u_clifford_frame_line_1215;
                static PyObject *__pyx_n_s_clifford_hidden_doctests;
                static PyObject *__pyx_kp_u_clifford_hidden_doctests_line_12;
                static PyObject *__pyx_kp_u_clifford_inv_line_926;
                static PyObject *__pyx_kp_u_clifford_involute_line_1107;
                static PyObject *__pyx_kp_u_clifford_isnan_line_1206;
                static PyObject *__pyx_kp_u_clifford_max_abs_line_1184;
                static PyObject *__pyx_kp_u_clifford_norm_line_1164;
                static PyObject *__pyx_kp_u_clifford_odd_line_1070;
                static PyObject *__pyx_kp_u_clifford_outer_pow_line_1004;
                static PyObject *__pyx_kp_u_clifford_pow_line_980;
                static PyObject *__pyx_kp_u_clifford_pure_line_1050;
                static PyObject *__pyx_kp_u_clifford_quad_line_1153;
                static PyObject *__pyx_kp_u_clifford_reframe_line_649;
                static PyObject *__pyx_kp_u_clifford_reverse_line_1123;
                static PyObject *__pyx_kp_u_clifford_scalar_line_1039;
                static PyObject *__pyx_kp_u_clifford_truncated_line_1195;
                static PyObject *__pyx_kp_u_clifford_vector_part_line_1079;
                static PyObject *__pyx_n_s_cline_in_traceback;
                static PyObject *__pyx_n_s_close;
                static PyObject *__pyx_n_s_collections;
                static PyObject *__pyx_kp_u_compare_line_492;
                static PyObject *__pyx_kp_u_complexifier_line_1526;
                static PyObject *__pyx_n_s_conj;
                static PyObject *__pyx_kp_u_conj_line_1435;
                static PyObject *__pyx_n_s_copy;
                static PyObject *__pyx_n_s_cos;
                static PyObject *__pyx_kp_u_cos_line_1601;
                static PyObject *__pyx_n_s_cosh;
                static PyObject *__pyx_kp_u_cosh_line_1639;
                static PyObject *__pyx_n_s_doctest;
                static PyObject *__pyx_n_s_e;
                static PyObject *__pyx_kp_u_e_line_1886;
                static PyObject *__pyx_n_s_encode;
                static PyObject *__pyx_n_s_even;
                static PyObject *__pyx_kp_u_even_line_1387;
                static PyObject *__pyx_n_s_exp;
                static PyObject *__pyx_kp_u_exp_line_1564;
                static PyObject *__pyx_n_s_fill;
                static PyObject *__pyx_n_s_frm;
                static PyObject *__pyx_kp_u_from;
                static PyObject *__pyx_n_s_getstate;
                static PyObject *__pyx_n_s_grade;
                static PyObject *__pyx_n_s_i;
                static PyObject *__pyx_kp_u_imag_line_1365;
                static PyObject *__pyx_n_s_import;
                static PyObject *__pyx_n_s_index_set;
                static PyObject *__pyx_kp_u_index_set___and___line_271;
                static PyObject *__pyx_kp_u_index_set___getitem___line_191;
                static PyObject *__pyx_kp_u_index_set___iand___line_282;
                static PyObject *__pyx_kp_u_index_set___invert___line_240;
                static PyObject *__pyx_kp_u_index_set___ior___line_304;
                static PyObject *__pyx_n_s_index_set___iter;
                static PyObject *__pyx_kp_u_index_set___iter___line_229;
                static PyObject *__pyx_kp_u_index_set___ixor___line_260;
                static PyObject *__pyx_kp_u_index_set___or___line_293;
                static PyObject *__pyx_kp_u_index_set___repr___line_384;
                static PyObject *__pyx_kp_u_index_set___setitem___line_179;
                static PyObject *__pyx_kp_u_index_set___str___line_395;
                static PyObject *__pyx_kp_u_index_set___xor___line_249;
                static PyObject *__pyx_kp_u_index_set_copy_line_65;
                static PyObject *__pyx_kp_u_index_set_count_line_315;
                static PyObject *__pyx_kp_u_index_set_count_neg_line_324;
                static PyObject *__pyx_kp_u_index_set_count_pos_line_333;
                static PyObject *__pyx_n_s_index_set_hidden_doctests;
                static PyObject *__pyx_kp_u_index_set_hidden_doctests_line_4;
                static PyObject *__pyx_kp_u_index_set_max_line_351;
                static PyObject *__pyx_kp_u_index_set_min_line_342;
                static PyObject *__pyx_kp_u_index_set_sign_of_mult_line_366;
                static PyObject *__pyx_kp_u_index_set_sign_of_square_line_37;
                static PyObject *__pyx_n_s_inv;
                static PyObject *__pyx_kp_u_inv_line_1328;
                static PyObject *__pyx_kp_u_invalid;
                static PyObject *__pyx_kp_u_invalid_string;
                static PyObject *__pyx_n_s_involute;
                static PyObject *__pyx_kp_u_involute_line_1405;
                static PyObject *__pyx_n_s_ist;
                static PyObject *__pyx_n_s_istpq;
                static PyObject *__pyx_kp_u_istpq_line_1899;
                static PyObject *__pyx_n_s_iter;
                static PyObject *__pyx_n_s_ixt;
                static PyObject *__pyx_kp_u_lexicographic_compare_eg_3_4_5;
                static PyObject *__pyx_n_s_lhs;
                static PyObject *__pyx_n_s_log;
                static PyObject *__pyx_kp_u_log_line_1578;
                static PyObject *__pyx_n_s_m;
                static PyObject *__pyx_n_s_main;
                static PyObject *__pyx_n_u_main;
                static PyObject *__pyx_n_s_math;
                static PyObject *__pyx_n_s_max;
                static PyObject *__pyx_kp_u_max_abs_line_1481;
                static PyObject *__pyx_kp_u_max_pos_line_513;
                static PyObject *__pyx_n_s_min;
                static PyObject *__pyx_kp_u_min_neg_line_504;
                static PyObject *__pyx_n_s_name;
                static PyObject *__pyx_n_s_nbar3;
                static PyObject *__pyx_n_s_ninf3;
                static PyObject *__pyx_kp_s_no_default___reduce___due_to_non;
                static PyObject *__pyx_n_s_norm;
                static PyObject *__pyx_kp_u_norm_line_1461;
                static PyObject *__pyx_kp_u_norm_sum_of_squares_of_coordina;
                static PyObject *__pyx_n_s_numbers;
                static PyObject *__pyx_n_s_obj;
                static PyObject *__pyx_n_s_odd;
                static PyObject *__pyx_kp_u_odd_line_1396;
                static PyObject *__pyx_n_s_other;
                static PyObject *__pyx_n_s_outer_pow;
                static PyObject *__pyx_kp_u_outer_pow_line_1517;
                static PyObject *__pyx_n_s_p;
                static PyObject *__pyx_n_s_pi;
                static PyObject *__pyx_n_s_pow;
                static PyObject *__pyx_kp_u_pow_line_1493;
                static PyObject *__pyx_n_s_pure;
                static PyObject *__pyx_kp_u_pure_line_1376;
                static PyObject *__pyx_n_s_pyx_vtable;
                static PyObject *__pyx_n_s_q;
                static PyObject *__pyx_n_s_quad;
                static PyObject *__pyx_kp_u_quad_line_1450;
                static PyObject *__pyx_kp_u_random_clifford_line_1814;
                static PyObject *__pyx_n_s_range;
                static PyObject *__pyx_kp_u_real_line_1354;
                static PyObject *__pyx_n_s_reduce;
                static PyObject *__pyx_n_s_reduce_cython;
                static PyObject *__pyx_n_s_reduce_ex;
                static PyObject *__pyx_n_s_reverse;
                static PyObject *__pyx_kp_u_reverse_line_1420;
                static PyObject *__pyx_n_s_rhs;
                static PyObject *__pyx_n_s_scalar;
                static PyObject *__pyx_n_s_scalar_epsilon;
                static PyObject *__pyx_kp_u_scalar_line_1343;
                static PyObject *__pyx_n_s_send;
                static PyObject *__pyx_n_s_setstate;
                static PyObject *__pyx_n_s_setstate_cython;
                static PyObject *__pyx_n_s_sin;
                static PyObject *__pyx_kp_u_sin_line_1678;
                static PyObject *__pyx_n_s_sinh;
                static PyObject *__pyx_kp_u_sinh_line_1718;
                static PyObject *__pyx_n_s_sqrt;
                static PyObject *__pyx_kp_u_sqrt_line_1541;
                static PyObject *__pyx_n_s_tan;
                static PyObject *__pyx_kp_u_tan_line_1751;
                static PyObject *__pyx_n_s_tanh;
                static PyObject *__pyx_kp_u_tanh_line_1785;
                static PyObject *__pyx_n_s_tau;
                static PyObject *__pyx_n_s_test;
                static PyObject *__pyx_n_s_test_2;
                static PyObject *__pyx_n_s_testmod;
                static PyObject *__pyx_n_s_throw;
                static PyObject *__pyx_kp_u_to_frame;
                static PyObject *__pyx_kp_u_using;
                static PyObject *__pyx_kp_u_using_invalid;
                static PyObject *__pyx_kp_u_value;
                static PyObject *__pyx_n_s_version;
                static PyObject *__pyx_n_s_xrange;
static PyObject *__pyx_pf_8PyClical_9index_set_copy(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
static int __pyx_pf_8PyClical_9index_set_2__cinit__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_other); /* proto */
static void __pyx_pf_8PyClical_9index_set_4__dealloc__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_9index_set_6__richcmp__(struct __pyx_obj_8PyClical_index_set *__pyx_v_lhs, PyObject *__pyx_v_rhs, int __pyx_v_op); /* proto */
static int __pyx_pf_8PyClical_9index_set_8__setitem__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_idx, PyObject *__pyx_v_val); /* proto */
static PyObject *__pyx_pf_8PyClical_9index_set_10__getitem__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_idx); /* proto */
static int __pyx_pf_8PyClical_9index_set_12__contains__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_idx); /* proto */
static PyObject *__pyx_pf_8PyClical_9index_set_14__iter__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_9index_set_17__invert__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_9index_set_19__xor__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
static PyObject *__pyx_pf_8PyClical_9index_set_21__ixor__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
static PyObject *__pyx_pf_8PyClical_9index_set_23__and__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
static PyObject *__pyx_pf_8PyClical_9index_set_25__iand__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
static PyObject *__pyx_pf_8PyClical_9index_set_27__or__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
static PyObject *__pyx_pf_8PyClical_9index_set_29__ior__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
static PyObject *__pyx_pf_8PyClical_9index_set_31count(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_9index_set_33count_neg(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_9index_set_35count_pos(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_9index_set_37min(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_9index_set_39max(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_9index_set_41hash_fn(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_9index_set_43sign_of_mult(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
static PyObject *__pyx_pf_8PyClical_9index_set_45sign_of_square(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_9index_set_47__repr__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_9index_set_49__str__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_9index_set_51__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_9index_set_53__setstate_cython__(CYTHON_UNUSED struct __pyx_obj_8PyClical_index_set *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* proto */
static PyObject *__pyx_pf_8PyClical_index_set_hidden_doctests(CYTHON_UNUSED PyObject *__pyx_self); /* proto */
static PyObject *__pyx_pf_8PyClical_2compare(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
static PyObject *__pyx_pf_8PyClical_4min_neg(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
static PyObject *__pyx_pf_8PyClical_6max_pos(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_copy(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
static int __pyx_pf_8PyClical_8clifford_2__cinit__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_other, PyObject *__pyx_v_ixt); /* proto */
static void __pyx_pf_8PyClical_8clifford_4__dealloc__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
static int __pyx_pf_8PyClical_8clifford_6__contains__(CYTHON_UNUSED struct __pyx_obj_8PyClical_clifford *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v_x); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_8__iter__(CYTHON_UNUSED struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_10reframe(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_ixt); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_12__richcmp__(struct __pyx_obj_8PyClical_clifford *__pyx_v_lhs, PyObject *__pyx_v_rhs, int __pyx_v_op); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_14__getitem__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_ixt); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_16__neg__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_18__pos__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_20__add__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_22__iadd__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_24__sub__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_26__isub__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_28__mul__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_30__imul__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_32__mod__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_34__imod__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_36__and__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_38__iand__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_40__xor__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_42__ixor__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_44__truediv__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
#if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
static PyObject *__pyx_pf_8PyClical_8clifford_46__idiv__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
#endif
static PyObject *__pyx_pf_8PyClical_8clifford_48inv(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_50__or__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_52__ior__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_54__pow__(PyObject *__pyx_v_self, PyObject *__pyx_v_m, CYTHON_UNUSED PyObject *__pyx_v_dummy); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_56pow(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_m); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_58outer_pow(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_m); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_60__call__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_grade); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_62scalar(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_64pure(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_66even(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_68odd(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_70vector_part(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_frm); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_72involute(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_74reverse(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_76conj(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_78quad(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_80norm(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_82abs(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_84max_abs(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_86truncated(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_limit); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_88isnan(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_90frame(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_92__repr__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_94__str__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_96__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_98__setstate_cython__(CYTHON_UNUSED struct __pyx_obj_8PyClical_clifford *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* proto */
static PyObject *__pyx_pf_8PyClical_8clifford_hidden_doctests(CYTHON_UNUSED PyObject *__pyx_self); /* proto */
static PyObject *__pyx_pf_8PyClical_10inv(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
static PyObject *__pyx_pf_8PyClical_12scalar(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
static PyObject *__pyx_pf_8PyClical_14real(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
static PyObject *__pyx_pf_8PyClical_16imag(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
static PyObject *__pyx_pf_8PyClical_18pure(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
static PyObject *__pyx_pf_8PyClical_20even(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
static PyObject *__pyx_pf_8PyClical_22odd(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
static PyObject *__pyx_pf_8PyClical_24involute(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
static PyObject *__pyx_pf_8PyClical_26reverse(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
static PyObject *__pyx_pf_8PyClical_28conj(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
static PyObject *__pyx_pf_8PyClical_30quad(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
static PyObject *__pyx_pf_8PyClical_32norm(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
static PyObject *__pyx_pf_8PyClical_34abs(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
static PyObject *__pyx_pf_8PyClical_36max_abs(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
static PyObject *__pyx_pf_8PyClical_38pow(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_m); /* proto */
static PyObject *__pyx_pf_8PyClical_40outer_pow(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_m); /* proto */
static PyObject *__pyx_pf_8PyClical_42complexifier(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
static PyObject *__pyx_pf_8PyClical_44sqrt(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
static PyObject *__pyx_pf_8PyClical_46exp(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
static PyObject *__pyx_pf_8PyClical_48log(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
static PyObject *__pyx_pf_8PyClical_50cos(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
static PyObject *__pyx_pf_8PyClical_52acos(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
static PyObject *__pyx_pf_8PyClical_54cosh(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
static PyObject *__pyx_pf_8PyClical_56acosh(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
static PyObject *__pyx_pf_8PyClical_58sin(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
static PyObject *__pyx_pf_8PyClical_60asin(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
static PyObject *__pyx_pf_8PyClical_62sinh(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
static PyObject *__pyx_pf_8PyClical_64asinh(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
static PyObject *__pyx_pf_8PyClical_66tan(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
static PyObject *__pyx_pf_8PyClical_68atan(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
static PyObject *__pyx_pf_8PyClical_70tanh(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
static PyObject *__pyx_pf_8PyClical_72atanh(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
static PyObject *__pyx_pf_8PyClical_74random_clifford(CYTHON_UNUSED PyObject *__pyx_self, struct __pyx_obj_8PyClical_index_set *__pyx_v_ixt, PyObject *__pyx_v_fill); /* proto */
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 *     return __Pyx_PyByteArray_FromStringAndSize(s.data(), s.size())
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 */
 
                static CYTHON_INLINE PyObject *__pyx_convert_PyByteArray_string_to_py_std__in_string(std::string const &__pyx_v_s) {
                  PyObject *__pyx_r = NULL;
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 * cdef inline object __pyx_convert_PyByteArray_string_to_py_std__in_string(const string& s):
 *     return __Pyx_PyByteArray_FromStringAndSize(s.data(), s.size())             # <<<<<<<<<<<<<<
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 */
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                  /* "string.to_py":55
 * 
 * @cname("__pyx_convert_PyByteArray_string_to_py_std__in_string")
 * cdef inline object __pyx_convert_PyByteArray_string_to_py_std__in_string(const string& s):             # <<<<<<<<<<<<<<
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                  /* function exit code */
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                static struct __pyx_vtabstruct_8PyClical_index_set __pyx_vtable_8PyClical_index_set;
 
                static PyObject *__pyx_tp_new_8PyClical_index_set(PyTypeObject *t, PyObject *a, PyObject *k) {
                  struct __pyx_obj_8PyClical_index_set *p;
                  PyObject *o;
                  if (likely((t->tp_flags & Py_TPFLAGS_IS_ABSTRACT) == 0)) {
                    o = (*t->tp_alloc)(t, 0);
                  } else {
                    o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_empty_tuple, 0);
                  }
                  if (unlikely(!o)) return 0;
                  p = ((struct __pyx_obj_8PyClical_index_set *)o);
                  p->__pyx_vtab = __pyx_vtabptr_8PyClical_index_set;
                  if (unlikely(__pyx_pw_8PyClical_9index_set_3__cinit__(o, a, k) < 0)) goto bad;
                  return o;
                  bad:
                  Py_DECREF(o); o = 0;
                  return NULL;
                }
 
                static void __pyx_tp_dealloc_8PyClical_index_set(PyObject *o) {
                  #if CYTHON_USE_TP_FINALIZE
                  if (unlikely(PyType_HasFeature(Py_TYPE(o), Py_TPFLAGS_HAVE_FINALIZE) && Py_TYPE(o)->tp_finalize) && (!PyType_IS_GC(Py_TYPE(o)) || !_PyGC_FINALIZED(o))) {
                    if (PyObject_CallFinalizerFromDealloc(o)) return;
                  }
                  #endif
                  {
                    PyObject *etype, *eval, *etb;
                    PyErr_Fetch(&etype, &eval, &etb);
                    __Pyx_SET_REFCNT(o, Py_REFCNT(o) + 1);
                    __pyx_pw_8PyClical_9index_set_5__dealloc__(o);
                    __Pyx_SET_REFCNT(o, Py_REFCNT(o) - 1);
                    PyErr_Restore(etype, eval, etb);
                  }
                  (*Py_TYPE(o)->tp_free)(o);
                }
                static PyObject *__pyx_sq_item_8PyClical_index_set(PyObject *o, Py_ssize_t i) {
                  PyObject *r;
                  PyObject *x = PyInt_FromSsize_t(i); if(!x) return 0;
                  r = Py_TYPE(o)->tp_as_mapping->mp_subscript(o, x);
                  Py_DECREF(x);
                  return r;
                }
 
                static int __pyx_mp_ass_subscript_8PyClical_index_set(PyObject *o, PyObject *i, PyObject *v) {
                  if (v) {
                    return __pyx_pw_8PyClical_9index_set_9__setitem__(o, i, v);
                  }
                  else {
                    PyErr_Format(PyExc_NotImplementedError,
                      "Subscript deletion not supported by %.200s", Py_TYPE(o)->tp_name);
                    return -1;
                  }
                }
 
                static PyMethodDef __pyx_methods_8PyClical_index_set[] = {
                  {"copy", (PyCFunction)__pyx_pw_8PyClical_9index_set_1copy, METH_NOARGS, __pyx_doc_8PyClical_9index_set_copy},
                  {"count", (PyCFunction)__pyx_pw_8PyClical_9index_set_32count, METH_NOARGS, __pyx_doc_8PyClical_9index_set_31count},
                  {"count_neg", (PyCFunction)__pyx_pw_8PyClical_9index_set_34count_neg, METH_NOARGS, __pyx_doc_8PyClical_9index_set_33count_neg},
                  {"count_pos", (PyCFunction)__pyx_pw_8PyClical_9index_set_36count_pos, METH_NOARGS, __pyx_doc_8PyClical_9index_set_35count_pos},
                  {"min", (PyCFunction)__pyx_pw_8PyClical_9index_set_38min, METH_NOARGS, __pyx_doc_8PyClical_9index_set_37min},
                  {"max", (PyCFunction)__pyx_pw_8PyClical_9index_set_40max, METH_NOARGS, __pyx_doc_8PyClical_9index_set_39max},
                  {"hash_fn", (PyCFunction)__pyx_pw_8PyClical_9index_set_42hash_fn, METH_NOARGS, __pyx_doc_8PyClical_9index_set_41hash_fn},
                  {"sign_of_mult", (PyCFunction)__pyx_pw_8PyClical_9index_set_44sign_of_mult, METH_O, __pyx_doc_8PyClical_9index_set_43sign_of_mult},
                  {"sign_of_square", (PyCFunction)__pyx_pw_8PyClical_9index_set_46sign_of_square, METH_NOARGS, __pyx_doc_8PyClical_9index_set_45sign_of_square},
                  {"__reduce_cython__", (PyCFunction)__pyx_pw_8PyClical_9index_set_52__reduce_cython__, METH_NOARGS, 0},
                  {"__setstate_cython__", (PyCFunction)__pyx_pw_8PyClical_9index_set_54__setstate_cython__, METH_O, 0},
                  {0, 0, 0, 0}
                };
 
                static PyNumberMethods __pyx_tp_as_number_index_set = {
                  0, /*nb_add*/
                  0, /*nb_subtract*/
                  0, /*nb_multiply*/
                  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
                  0, /*nb_divide*/
                  #endif
                  0, /*nb_remainder*/
                  0, /*nb_divmod*/
                  0, /*nb_power*/
                  0, /*nb_negative*/
                  0, /*nb_positive*/
                  0, /*nb_absolute*/
                  0, /*nb_nonzero*/
                  __pyx_pw_8PyClical_9index_set_18__invert__, /*nb_invert*/
                  0, /*nb_lshift*/
                  0, /*nb_rshift*/
                  __pyx_pw_8PyClical_9index_set_24__and__, /*nb_and*/
                  __pyx_pw_8PyClical_9index_set_20__xor__, /*nb_xor*/
                  __pyx_pw_8PyClical_9index_set_28__or__, /*nb_or*/
                  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
                  0, /*nb_coerce*/
                  #endif
                  0, /*nb_int*/
                  #if PY_MAJOR_VERSION < 3
                  0, /*nb_long*/
                  #else
                  0, /*reserved*/
                  #endif
                  0, /*nb_float*/
                  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
                  0, /*nb_oct*/
                  #endif
                  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
                  0, /*nb_hex*/
                  #endif
                  0, /*nb_inplace_add*/
                  0, /*nb_inplace_subtract*/
                  0, /*nb_inplace_multiply*/
                  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
                  0, /*nb_inplace_divide*/
                  #endif
                  0, /*nb_inplace_remainder*/
                  0, /*nb_inplace_power*/
                  0, /*nb_inplace_lshift*/
                  0, /*nb_inplace_rshift*/
                  __pyx_pw_8PyClical_9index_set_26__iand__, /*nb_inplace_and*/
                  __pyx_pw_8PyClical_9index_set_22__ixor__, /*nb_inplace_xor*/
                  __pyx_pw_8PyClical_9index_set_30__ior__, /*nb_inplace_or*/
                  0, /*nb_floor_divide*/
                  0, /*nb_true_divide*/
                  0, /*nb_inplace_floor_divide*/
                  0, /*nb_inplace_true_divide*/
                  0, /*nb_index*/
                  #if PY_VERSION_HEX >= 0x03050000
                  0, /*nb_matrix_multiply*/
                  #endif
                  #if PY_VERSION_HEX >= 0x03050000
                  0, /*nb_inplace_matrix_multiply*/
                  #endif
                };
 
                static PySequenceMethods __pyx_tp_as_sequence_index_set = {
                  0, /*sq_length*/
                  0, /*sq_concat*/
                  0, /*sq_repeat*/
                  __pyx_sq_item_8PyClical_index_set, /*sq_item*/
                  0, /*sq_slice*/
                  0, /*sq_ass_item*/
                  0, /*sq_ass_slice*/
                  __pyx_pw_8PyClical_9index_set_13__contains__, /*sq_contains*/
                  0, /*sq_inplace_concat*/
                  0, /*sq_inplace_repeat*/
                };
 
                static PyMappingMethods __pyx_tp_as_mapping_index_set = {
                  0, /*mp_length*/
                  __pyx_pw_8PyClical_9index_set_11__getitem__, /*mp_subscript*/
                  __pyx_mp_ass_subscript_8PyClical_index_set, /*mp_ass_subscript*/
                };
 
                static PyTypeObject __pyx_type_8PyClical_index_set = {
                  PyVarObject_HEAD_INIT(0, 0)
                  "PyClical.index_set", /*tp_name*/
                  sizeof(struct __pyx_obj_8PyClical_index_set), /*tp_basicsize*/
                  0, /*tp_itemsize*/
                  __pyx_tp_dealloc_8PyClical_index_set, /*tp_dealloc*/
                  #if PY_VERSION_HEX < 0x030800b4
                  0, /*tp_print*/
                  #endif
                  #if PY_VERSION_HEX >= 0x030800b4
                  0, /*tp_vectorcall_offset*/
                  #endif
                  0, /*tp_getattr*/
                  0, /*tp_setattr*/
                  #if PY_MAJOR_VERSION < 3
                  0, /*tp_compare*/
                  #endif
                  #if PY_MAJOR_VERSION >= 3
                  0, /*tp_as_async*/
                  #endif
                  __pyx_pw_8PyClical_9index_set_48__repr__, /*tp_repr*/
                  &__pyx_tp_as_number_index_set, /*tp_as_number*/
                  &__pyx_tp_as_sequence_index_set, /*tp_as_sequence*/
                  &__pyx_tp_as_mapping_index_set, /*tp_as_mapping*/
                  0, /*tp_hash*/
                  0, /*tp_call*/
                  __pyx_pw_8PyClical_9index_set_50__str__, /*tp_str*/
                  0, /*tp_getattro*/
                  0, /*tp_setattro*/
                  0, /*tp_as_buffer*/
                  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE, /*tp_flags*/
                  "\n    Python class index_set wraps C++ class IndexSet.\n    ", /*tp_doc*/
                  0, /*tp_traverse*/
                  0, /*tp_clear*/
                  __pyx_pw_8PyClical_9index_set_7__richcmp__, /*tp_richcompare*/
                  0, /*tp_weaklistoffset*/
                  __pyx_pw_8PyClical_9index_set_15__iter__, /*tp_iter*/
                  0, /*tp_iternext*/
                  __pyx_methods_8PyClical_index_set, /*tp_methods*/
                  0, /*tp_members*/
                  0, /*tp_getset*/
                  0, /*tp_base*/
                  0, /*tp_dict*/
                  0, /*tp_descr_get*/
                  0, /*tp_descr_set*/
                  0, /*tp_dictoffset*/
                  0, /*tp_init*/
                  0, /*tp_alloc*/
                  __pyx_tp_new_8PyClical_index_set, /*tp_new*/
                  0, /*tp_free*/
                  0, /*tp_is_gc*/
                  0, /*tp_bases*/
                  0, /*tp_mro*/
                  0, /*tp_cache*/
                  0, /*tp_subclasses*/
                  0, /*tp_weaklist*/
                  0, /*tp_del*/
                  0, /*tp_version_tag*/
                  #if PY_VERSION_HEX >= 0x030400a1
                  0, /*tp_finalize*/
                  #endif
                  #if PY_VERSION_HEX >= 0x030800b1
                  0, /*tp_vectorcall*/
                  #endif
                  #if PY_VERSION_HEX >= 0x030800b4 && PY_VERSION_HEX < 0x03090000
                  0, /*tp_print*/
                  #endif
                };
                static struct __pyx_vtabstruct_8PyClical_clifford __pyx_vtable_8PyClical_clifford;
 
                static PyObject *__pyx_tp_new_8PyClical_clifford(PyTypeObject *t, PyObject *a, PyObject *k) {
                  struct __pyx_obj_8PyClical_clifford *p;
                  PyObject *o;
                  if (likely((t->tp_flags & Py_TPFLAGS_IS_ABSTRACT) == 0)) {
                    o = (*t->tp_alloc)(t, 0);
                  } else {
                    o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_empty_tuple, 0);
                  }
                  if (unlikely(!o)) return 0;
                  p = ((struct __pyx_obj_8PyClical_clifford *)o);
                  p->__pyx_vtab = __pyx_vtabptr_8PyClical_clifford;
                  if (unlikely(__pyx_pw_8PyClical_8clifford_3__cinit__(o, a, k) < 0)) goto bad;
                  return o;
                  bad:
                  Py_DECREF(o); o = 0;
                  return NULL;
                }
 
                static void __pyx_tp_dealloc_8PyClical_clifford(PyObject *o) {
                  #if CYTHON_USE_TP_FINALIZE
                  if (unlikely(PyType_HasFeature(Py_TYPE(o), Py_TPFLAGS_HAVE_FINALIZE) && Py_TYPE(o)->tp_finalize) && (!PyType_IS_GC(Py_TYPE(o)) || !_PyGC_FINALIZED(o))) {
                    if (PyObject_CallFinalizerFromDealloc(o)) return;
                  }
                  #endif
                  {
                    PyObject *etype, *eval, *etb;
                    PyErr_Fetch(&etype, &eval, &etb);
                    __Pyx_SET_REFCNT(o, Py_REFCNT(o) + 1);
                    __pyx_pw_8PyClical_8clifford_5__dealloc__(o);
                    __Pyx_SET_REFCNT(o, Py_REFCNT(o) - 1);
                    PyErr_Restore(etype, eval, etb);
                  }
                  (*Py_TYPE(o)->tp_free)(o);
                }
                static PyObject *__pyx_sq_item_8PyClical_clifford(PyObject *o, Py_ssize_t i) {
                  PyObject *r;
                  PyObject *x = PyInt_FromSsize_t(i); if(!x) return 0;
                  r = Py_TYPE(o)->tp_as_mapping->mp_subscript(o, x);
                  Py_DECREF(x);
                  return r;
                }
 
                static PyMethodDef __pyx_methods_8PyClical_clifford[] = {
                  {"copy", (PyCFunction)__pyx_pw_8PyClical_8clifford_1copy, METH_NOARGS, __pyx_doc_8PyClical_8clifford_copy},
                  {"reframe", (PyCFunction)__pyx_pw_8PyClical_8clifford_11reframe, METH_O, __pyx_doc_8PyClical_8clifford_10reframe},
                  {"inv", (PyCFunction)__pyx_pw_8PyClical_8clifford_49inv, METH_NOARGS, __pyx_doc_8PyClical_8clifford_48inv},
                  {"pow", (PyCFunction)__pyx_pw_8PyClical_8clifford_57pow, METH_O, __pyx_doc_8PyClical_8clifford_56pow},
                  {"outer_pow", (PyCFunction)__pyx_pw_8PyClical_8clifford_59outer_pow, METH_O, __pyx_doc_8PyClical_8clifford_58outer_pow},
                  {"scalar", (PyCFunction)__pyx_pw_8PyClical_8clifford_63scalar, METH_NOARGS, __pyx_doc_8PyClical_8clifford_62scalar},
                  {"pure", (PyCFunction)__pyx_pw_8PyClical_8clifford_65pure, METH_NOARGS, __pyx_doc_8PyClical_8clifford_64pure},
                  {"even", (PyCFunction)__pyx_pw_8PyClical_8clifford_67even, METH_NOARGS, __pyx_doc_8PyClical_8clifford_66even},
                  {"odd", (PyCFunction)__pyx_pw_8PyClical_8clifford_69odd, METH_NOARGS, __pyx_doc_8PyClical_8clifford_68odd},
                  {"vector_part", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_8clifford_71vector_part, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_8clifford_70vector_part},
                  {"involute", (PyCFunction)__pyx_pw_8PyClical_8clifford_73involute, METH_NOARGS, __pyx_doc_8PyClical_8clifford_72involute},
                  {"reverse", (PyCFunction)__pyx_pw_8PyClical_8clifford_75reverse, METH_NOARGS, __pyx_doc_8PyClical_8clifford_74reverse},
                  {"conj", (PyCFunction)__pyx_pw_8PyClical_8clifford_77conj, METH_NOARGS, __pyx_doc_8PyClical_8clifford_76conj},
                  {"quad", (PyCFunction)__pyx_pw_8PyClical_8clifford_79quad, METH_NOARGS, __pyx_doc_8PyClical_8clifford_78quad},
                  {"norm", (PyCFunction)__pyx_pw_8PyClical_8clifford_81norm, METH_NOARGS, __pyx_doc_8PyClical_8clifford_80norm},
                  {"abs", (PyCFunction)__pyx_pw_8PyClical_8clifford_83abs, METH_NOARGS, __pyx_doc_8PyClical_8clifford_82abs},
                  {"max_abs", (PyCFunction)__pyx_pw_8PyClical_8clifford_85max_abs, METH_NOARGS, __pyx_doc_8PyClical_8clifford_84max_abs},
                  {"truncated", (PyCFunction)__pyx_pw_8PyClical_8clifford_87truncated, METH_O, __pyx_doc_8PyClical_8clifford_86truncated},
                  {"isnan", (PyCFunction)__pyx_pw_8PyClical_8clifford_89isnan, METH_NOARGS, __pyx_doc_8PyClical_8clifford_88isnan},
                  {"frame", (PyCFunction)__pyx_pw_8PyClical_8clifford_91frame, METH_NOARGS, __pyx_doc_8PyClical_8clifford_90frame},
                  {"__reduce_cython__", (PyCFunction)__pyx_pw_8PyClical_8clifford_97__reduce_cython__, METH_NOARGS, 0},
                  {"__setstate_cython__", (PyCFunction)__pyx_pw_8PyClical_8clifford_99__setstate_cython__, METH_O, 0},
                  {0, 0, 0, 0}
                };
 
                static PyNumberMethods __pyx_tp_as_number_clifford = {
                  __pyx_pw_8PyClical_8clifford_21__add__, /*nb_add*/
                  __pyx_pw_8PyClical_8clifford_25__sub__, /*nb_subtract*/
                  __pyx_pw_8PyClical_8clifford_29__mul__, /*nb_multiply*/
                  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
                  0, /*nb_divide*/
                  #endif
                  __pyx_pw_8PyClical_8clifford_33__mod__, /*nb_remainder*/
                  0, /*nb_divmod*/
                  __pyx_pw_8PyClical_8clifford_55__pow__, /*nb_power*/
                  __pyx_pw_8PyClical_8clifford_17__neg__, /*nb_negative*/
                  __pyx_pw_8PyClical_8clifford_19__pos__, /*nb_positive*/
                  0, /*nb_absolute*/
                  0, /*nb_nonzero*/
                  0, /*nb_invert*/
                  0, /*nb_lshift*/
                  0, /*nb_rshift*/
                  __pyx_pw_8PyClical_8clifford_37__and__, /*nb_and*/
                  __pyx_pw_8PyClical_8clifford_41__xor__, /*nb_xor*/
                  __pyx_pw_8PyClical_8clifford_51__or__, /*nb_or*/
                  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
                  0, /*nb_coerce*/
                  #endif
                  0, /*nb_int*/
                  #if PY_MAJOR_VERSION < 3
                  0, /*nb_long*/
                  #else
                  0, /*reserved*/
                  #endif
                  0, /*nb_float*/
                  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
                  0, /*nb_oct*/
                  #endif
                  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
                  0, /*nb_hex*/
                  #endif
                  __pyx_pw_8PyClical_8clifford_23__iadd__, /*nb_inplace_add*/
                  __pyx_pw_8PyClical_8clifford_27__isub__, /*nb_inplace_subtract*/
                  __pyx_pw_8PyClical_8clifford_31__imul__, /*nb_inplace_multiply*/
                  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
                  __pyx_pw_8PyClical_8clifford_47__idiv__, /*nb_inplace_divide*/
                  #endif
                  __pyx_pw_8PyClical_8clifford_35__imod__, /*nb_inplace_remainder*/
                  0, /*nb_inplace_power*/
                  0, /*nb_inplace_lshift*/
                  0, /*nb_inplace_rshift*/
                  __pyx_pw_8PyClical_8clifford_39__iand__, /*nb_inplace_and*/
                  __pyx_pw_8PyClical_8clifford_43__ixor__, /*nb_inplace_xor*/
                  __pyx_pw_8PyClical_8clifford_53__ior__, /*nb_inplace_or*/
                  0, /*nb_floor_divide*/
                  __pyx_pw_8PyClical_8clifford_45__truediv__, /*nb_true_divide*/
                  0, /*nb_inplace_floor_divide*/
                  0, /*nb_inplace_true_divide*/
                  0, /*nb_index*/
                  #if PY_VERSION_HEX >= 0x03050000
                  0, /*nb_matrix_multiply*/
                  #endif
                  #if PY_VERSION_HEX >= 0x03050000
                  0, /*nb_inplace_matrix_multiply*/
                  #endif
                };
 
                static PySequenceMethods __pyx_tp_as_sequence_clifford = {
                  0, /*sq_length*/
                  0, /*sq_concat*/
                  0, /*sq_repeat*/
                  __pyx_sq_item_8PyClical_clifford, /*sq_item*/
                  0, /*sq_slice*/
                  0, /*sq_ass_item*/
                  0, /*sq_ass_slice*/
                  __pyx_pw_8PyClical_8clifford_7__contains__, /*sq_contains*/
                  0, /*sq_inplace_concat*/
                  0, /*sq_inplace_repeat*/
                };
 
                static PyMappingMethods __pyx_tp_as_mapping_clifford = {
                  0, /*mp_length*/
                  __pyx_pw_8PyClical_8clifford_15__getitem__, /*mp_subscript*/
                  0, /*mp_ass_subscript*/
                };
 
                static PyTypeObject __pyx_type_8PyClical_clifford = {
                  PyVarObject_HEAD_INIT(0, 0)
                  "PyClical.clifford", /*tp_name*/
                  sizeof(struct __pyx_obj_8PyClical_clifford), /*tp_basicsize*/
                  0, /*tp_itemsize*/
                  __pyx_tp_dealloc_8PyClical_clifford, /*tp_dealloc*/
                  #if PY_VERSION_HEX < 0x030800b4
                  0, /*tp_print*/
                  #endif
                  #if PY_VERSION_HEX >= 0x030800b4
                  0, /*tp_vectorcall_offset*/
                  #endif
                  0, /*tp_getattr*/
                  0, /*tp_setattr*/
                  #if PY_MAJOR_VERSION < 3
                  0, /*tp_compare*/
                  #endif
                  #if PY_MAJOR_VERSION >= 3
                  0, /*tp_as_async*/
                  #endif
                  __pyx_pw_8PyClical_8clifford_93__repr__, /*tp_repr*/
                  &__pyx_tp_as_number_clifford, /*tp_as_number*/
                  &__pyx_tp_as_sequence_clifford, /*tp_as_sequence*/
                  &__pyx_tp_as_mapping_clifford, /*tp_as_mapping*/
                  0, /*tp_hash*/
                  __pyx_pw_8PyClical_8clifford_61__call__, /*tp_call*/
                  __pyx_pw_8PyClical_8clifford_95__str__, /*tp_str*/
                  0, /*tp_getattro*/
                  0, /*tp_setattro*/
                  0, /*tp_as_buffer*/
                  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE, /*tp_flags*/
                  "\n    Python class clifford wraps C++ class Clifford.\n    ", /*tp_doc*/
                  0, /*tp_traverse*/
                  0, /*tp_clear*/
                  __pyx_pw_8PyClical_8clifford_13__richcmp__, /*tp_richcompare*/
                  0, /*tp_weaklistoffset*/
                  __pyx_pw_8PyClical_8clifford_9__iter__, /*tp_iter*/
                  0, /*tp_iternext*/
                  __pyx_methods_8PyClical_clifford, /*tp_methods*/
                  0, /*tp_members*/
                  0, /*tp_getset*/
                  0, /*tp_base*/
                  0, /*tp_dict*/
                  0, /*tp_descr_get*/
                  0, /*tp_descr_set*/
                  0, /*tp_dictoffset*/
                  0, /*tp_init*/
                  0, /*tp_alloc*/
                  __pyx_tp_new_8PyClical_clifford, /*tp_new*/
                  0, /*tp_free*/
                  0, /*tp_is_gc*/
                  0, /*tp_bases*/
                  0, /*tp_mro*/
                  0, /*tp_cache*/
                  0, /*tp_subclasses*/
                  0, /*tp_weaklist*/
                  0, /*tp_del*/
                  0, /*tp_version_tag*/
                  #if PY_VERSION_HEX >= 0x030400a1
                  0, /*tp_finalize*/
                  #endif
                  #if PY_VERSION_HEX >= 0x030800b1
                  0, /*tp_vectorcall*/
                  #endif
                  #if PY_VERSION_HEX >= 0x030800b4 && PY_VERSION_HEX < 0x03090000
                  0, /*tp_print*/
                  #endif
                };
 
                static struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *__pyx_freelist_8PyClical___pyx_scope_struct____iter__[8];
                static int __pyx_freecount_8PyClical___pyx_scope_struct____iter__ = 0;
 
                static PyObject *__pyx_tp_new_8PyClical___pyx_scope_struct____iter__(PyTypeObject *t, CYTHON_UNUSED PyObject *a, CYTHON_UNUSED PyObject *k) {
                  PyObject *o;
                  if (CYTHON_COMPILING_IN_CPYTHON && likely((__pyx_freecount_8PyClical___pyx_scope_struct____iter__ > 0) & (t->tp_basicsize == sizeof(struct __pyx_obj_8PyClical___pyx_scope_struct____iter__)))) {
                    o = (PyObject*)__pyx_freelist_8PyClical___pyx_scope_struct____iter__[--__pyx_freecount_8PyClical___pyx_scope_struct____iter__];
                    memset(o, 0, sizeof(struct __pyx_obj_8PyClical___pyx_scope_struct____iter__));
                    (void) PyObject_INIT(o, t);
                    PyObject_GC_Track(o);
                  } else {
                    o = (*t->tp_alloc)(t, 0);
                    if (unlikely(!o)) return 0;
                  }
                  return o;
                }
 
                static void __pyx_tp_dealloc_8PyClical___pyx_scope_struct____iter__(PyObject *o) {
                  struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *p = (struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *)o;
                  PyObject_GC_UnTrack(o);
                  Py_CLEAR(p->__pyx_v_idx);
                  Py_CLEAR(p->__pyx_v_self);
                  Py_CLEAR(p->__pyx_t_0);
                  if (CYTHON_COMPILING_IN_CPYTHON && ((__pyx_freecount_8PyClical___pyx_scope_struct____iter__ < 8) & (Py_TYPE(o)->tp_basicsize == sizeof(struct __pyx_obj_8PyClical___pyx_scope_struct____iter__)))) {
                    __pyx_freelist_8PyClical___pyx_scope_struct____iter__[__pyx_freecount_8PyClical___pyx_scope_struct____iter__++] = ((struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *)o);
                  } else {
                    (*Py_TYPE(o)->tp_free)(o);
                  }
                }
 
                static int __pyx_tp_traverse_8PyClical___pyx_scope_struct____iter__(PyObject *o, visitproc v, void *a) {
                  int e;
                  struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *p = (struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *)o;
                  if (p->__pyx_v_idx) {
                    e = (*v)(p->__pyx_v_idx, a); if (e) return e;
                  }
                  if (p->__pyx_v_self) {
                    e = (*v)(((PyObject *)p->__pyx_v_self), a); if (e) return e;
                  }
                  if (p->__pyx_t_0) {
                    e = (*v)(p->__pyx_t_0, a); if (e) return e;
                  }
                  return 0;
                }
 
                static PyTypeObject __pyx_type_8PyClical___pyx_scope_struct____iter__ = {
                  PyVarObject_HEAD_INIT(0, 0)
                  "PyClical.__pyx_scope_struct____iter__", /*tp_name*/
                  sizeof(struct __pyx_obj_8PyClical___pyx_scope_struct____iter__), /*tp_basicsize*/
                  0, /*tp_itemsize*/
                  __pyx_tp_dealloc_8PyClical___pyx_scope_struct____iter__, /*tp_dealloc*/
                  #if PY_VERSION_HEX < 0x030800b4
                  0, /*tp_print*/
                  #endif
                  #if PY_VERSION_HEX >= 0x030800b4
                  0, /*tp_vectorcall_offset*/
                  #endif
                  0, /*tp_getattr*/
                  0, /*tp_setattr*/
                  #if PY_MAJOR_VERSION < 3
                  0, /*tp_compare*/
                  #endif
                  #if PY_MAJOR_VERSION >= 3
                  0, /*tp_as_async*/
                  #endif
                  0, /*tp_repr*/
                  0, /*tp_as_number*/
                  0, /*tp_as_sequence*/
                  0, /*tp_as_mapping*/
                  0, /*tp_hash*/
                  0, /*tp_call*/
                  0, /*tp_str*/
                  0, /*tp_getattro*/
                  0, /*tp_setattro*/
                  0, /*tp_as_buffer*/
                  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_HAVE_GC, /*tp_flags*/
                  0, /*tp_doc*/
                  __pyx_tp_traverse_8PyClical___pyx_scope_struct____iter__, /*tp_traverse*/
                  0, /*tp_clear*/
                  0, /*tp_richcompare*/
                  0, /*tp_weaklistoffset*/
                  0, /*tp_iter*/
                  0, /*tp_iternext*/
                  0, /*tp_methods*/
                  0, /*tp_members*/
                  0, /*tp_getset*/
                  0, /*tp_base*/
                  0, /*tp_dict*/
                  0, /*tp_descr_get*/
                  0, /*tp_descr_set*/
                  0, /*tp_dictoffset*/
                  0, /*tp_init*/
                  0, /*tp_alloc*/
                  __pyx_tp_new_8PyClical___pyx_scope_struct____iter__, /*tp_new*/
                  0, /*tp_free*/
                  0, /*tp_is_gc*/
                  0, /*tp_bases*/
                  0, /*tp_mro*/
                  0, /*tp_cache*/
                  0, /*tp_subclasses*/
                  0, /*tp_weaklist*/
                  0, /*tp_del*/
                  0, /*tp_version_tag*/
                  #if PY_VERSION_HEX >= 0x030400a1
                  0, /*tp_finalize*/
                  #endif
                  #if PY_VERSION_HEX >= 0x030800b1
                  0, /*tp_vectorcall*/
                  #endif
                  #if PY_VERSION_HEX >= 0x030800b4 && PY_VERSION_HEX < 0x03090000
                  0, /*tp_print*/
                  #endif
                };
 
                static PyMethodDef __pyx_methods[] = {
                  {"compare", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_3compare, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_2compare},
                  {"min_neg", (PyCFunction)__pyx_pw_8PyClical_5min_neg, METH_O, __pyx_doc_8PyClical_4min_neg},
                  {"max_pos", (PyCFunction)__pyx_pw_8PyClical_7max_pos, METH_O, __pyx_doc_8PyClical_6max_pos},
                  {"inv", (PyCFunction)__pyx_pw_8PyClical_11inv, METH_O, __pyx_doc_8PyClical_10inv},
                  {"scalar", (PyCFunction)__pyx_pw_8PyClical_13scalar, METH_O, __pyx_doc_8PyClical_12scalar},
                  {"real", (PyCFunction)__pyx_pw_8PyClical_15real, METH_O, __pyx_doc_8PyClical_14real},
                  {"imag", (PyCFunction)__pyx_pw_8PyClical_17imag, METH_O, __pyx_doc_8PyClical_16imag},
                  {"pure", (PyCFunction)__pyx_pw_8PyClical_19pure, METH_O, __pyx_doc_8PyClical_18pure},
                  {"even", (PyCFunction)__pyx_pw_8PyClical_21even, METH_O, __pyx_doc_8PyClical_20even},
                  {"odd", (PyCFunction)__pyx_pw_8PyClical_23odd, METH_O, __pyx_doc_8PyClical_22odd},
                  {"involute", (PyCFunction)__pyx_pw_8PyClical_25involute, METH_O, __pyx_doc_8PyClical_24involute},
                  {"reverse", (PyCFunction)__pyx_pw_8PyClical_27reverse, METH_O, __pyx_doc_8PyClical_26reverse},
                  {"conj", (PyCFunction)__pyx_pw_8PyClical_29conj, METH_O, __pyx_doc_8PyClical_28conj},
                  {"quad", (PyCFunction)__pyx_pw_8PyClical_31quad, METH_O, __pyx_doc_8PyClical_30quad},
                  {"norm", (PyCFunction)__pyx_pw_8PyClical_33norm, METH_O, __pyx_doc_8PyClical_32norm},
                  {"abs", (PyCFunction)__pyx_pw_8PyClical_35abs, METH_O, __pyx_doc_8PyClical_34abs},
                  {"max_abs", (PyCFunction)__pyx_pw_8PyClical_37max_abs, METH_O, __pyx_doc_8PyClical_36max_abs},
                  {"pow", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_39pow, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_38pow},
                  {"outer_pow", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_41outer_pow, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_40outer_pow},
                  {"complexifier", (PyCFunction)__pyx_pw_8PyClical_43complexifier, METH_O, __pyx_doc_8PyClical_42complexifier},
                  {"sqrt", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_45sqrt, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_44sqrt},
                  {"exp", (PyCFunction)__pyx_pw_8PyClical_47exp, METH_O, __pyx_doc_8PyClical_46exp},
                  {"log", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_49log, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_48log},
                  {"cos", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_51cos, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_50cos},
                  {"acos", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_53acos, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_52acos},
                  {"cosh", (PyCFunction)__pyx_pw_8PyClical_55cosh, METH_O, __pyx_doc_8PyClical_54cosh},
                  {"acosh", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_57acosh, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_56acosh},
                  {"sin", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_59sin, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_58sin},
                  {"asin", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_61asin, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_60asin},
                  {"sinh", (PyCFunction)__pyx_pw_8PyClical_63sinh, METH_O, __pyx_doc_8PyClical_62sinh},
                  {"asinh", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_65asinh, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_64asinh},
                  {"tan", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_67tan, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_66tan},
                  {"atan", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_69atan, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_68atan},
                  {"tanh", (PyCFunction)__pyx_pw_8PyClical_71tanh, METH_O, __pyx_doc_8PyClical_70tanh},
                  {"atanh", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_73atanh, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_72atanh},
                  {"random_clifford", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_75random_clifford, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_74random_clifford},
                  {"cga3", (PyCFunction)__pyx_pw_8PyClical_77cga3, METH_O, __pyx_doc_8PyClical_76cga3},
                  {"cga3std", (PyCFunction)__pyx_pw_8PyClical_79cga3std, METH_O, __pyx_doc_8PyClical_78cga3std},
                  {"agc3", (PyCFunction)__pyx_pw_8PyClical_81agc3, METH_O, __pyx_doc_8PyClical_80agc3},
                  {0, 0, 0, 0}
                };
 
                #if PY_MAJOR_VERSION >= 3
                #if CYTHON_PEP489_MULTI_PHASE_INIT
                static PyObject* __pyx_pymod_create(PyObject *spec, PyModuleDef *def); /*proto*/
                static int __pyx_pymod_exec_PyClical(PyObject* module); /*proto*/
                static PyModuleDef_Slot __pyx_moduledef_slots[] = {
                  {Py_mod_create, (void*)__pyx_pymod_create},
                  {Py_mod_exec, (void*)__pyx_pymod_exec_PyClical},
                  {0, NULL}
                };
                #endif
 
                static struct PyModuleDef __pyx_moduledef = {
                    PyModuleDef_HEAD_INIT,
                    "PyClical",
                    0, /* m_doc */
                  #if CYTHON_PEP489_MULTI_PHASE_INIT
                    0, /* m_size */
                  #else
                    -1, /* m_size */
                  #endif
                    __pyx_methods /* m_methods */,
                  #if CYTHON_PEP489_MULTI_PHASE_INIT
                    __pyx_moduledef_slots, /* m_slots */
                  #else
                    NULL, /* m_reload */
                  #endif
                    NULL, /* m_traverse */
                    NULL, /* m_clear */
                    NULL /* m_free */
                };
                #endif
                #ifndef CYTHON_SMALL_CODE
#if defined(__clang__)
    #define CYTHON_SMALL_CODE
#elif defined(__GNUC__) && (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 3))
    #define CYTHON_SMALL_CODE __attribute__((cold))
#else
    #define CYTHON_SMALL_CODE
#endif
#endif
 
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    Py_ssize_t offset = Py_TYPE(obj)->tp_dictoffset;
    if (offset) {
#if CYTHON_COMPILING_IN_CPYTHON
        dictptr = (likely(offset > 0)) ? (PyObject **) ((char *)obj + offset) : _PyObject_GetDictPtr(obj);
#else
        dictptr = _PyObject_GetDictPtr(obj);
#endif
    }
    return (dictptr && *dictptr) ? __PYX_GET_DICT_VERSION(*dictptr) : 0;
}
static CYTHON_INLINE int __Pyx_object_dict_version_matches(PyObject* obj, PY_UINT64_T tp_dict_version, PY_UINT64_T obj_dict_version) {
    PyObject *dict = Py_TYPE(obj)->tp_dict;
    if (unlikely(!dict) || unlikely(tp_dict_version != __PYX_GET_DICT_VERSION(dict)))
        return 0;
    return obj_dict_version == __Pyx_get_object_dict_version(obj);
}
#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_CyFunction_Check(func)))
#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
 
/* RaiseDoubleKeywords */
static void __Pyx_RaiseDoubleKeywordsError(
    const char* func_name,
    PyObject* kw_name)
{
    PyErr_Format(PyExc_TypeError,
        #if PY_MAJOR_VERSION >= 3
        "%s() got multiple values for keyword argument '%U'", func_name, kw_name);
        #else
        "%s() got multiple values for keyword argument '%s'", func_name,
        PyString_AsString(kw_name));
        #endif
}
 
/* ParseKeywords */
static int __Pyx_ParseOptionalKeywords(
    PyObject *kwds,
    PyObject **argnames[],
    PyObject *kwds2,
    PyObject *values[],
    Py_ssize_t num_pos_args,
    const char* function_name)
{
    PyObject *key = 0, *value = 0;
    Py_ssize_t pos = 0;
    PyObject*** name;
    PyObject*** first_kw_arg = argnames + num_pos_args;
    while (PyDict_Next(kwds, &pos, &key, &value)) {
        name = first_kw_arg;
        while (*name && (**name != key)) name++;
        if (*name) {
            values[name-argnames] = value;
            continue;
        }
        name = first_kw_arg;
        #if PY_MAJOR_VERSION < 3
        if (likely(PyString_Check(key))) {
            while (*name) {
                if ((CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**name) == PyString_GET_SIZE(key))
                        && _PyString_Eq(**name, key)) {
                    values[name-argnames] = value;
                    break;
                }
                name++;
            }
            if (*name) continue;
            else {
                PyObject*** argname = argnames;
                while (argname != first_kw_arg) {
                    if ((**argname == key) || (
                            (CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**argname) == PyString_GET_SIZE(key))
                             && _PyString_Eq(**argname, key))) {
                        goto arg_passed_twice;
                    }
                    argname++;
                }
            }
        } else
        #endif
        if (likely(PyUnicode_Check(key))) {
            while (*name) {
                int cmp = (**name == key) ? 0 :
                #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
                    (__Pyx_PyUnicode_GET_LENGTH(**name) != __Pyx_PyUnicode_GET_LENGTH(key)) ? 1 :
                #endif
                    PyUnicode_Compare(**name, key);
                if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
                if (cmp == 0) {
                    values[name-argnames] = value;
                    break;
                }
                name++;
            }
            if (*name) continue;
            else {
                PyObject*** argname = argnames;
                while (argname != first_kw_arg) {
                    int cmp = (**argname == key) ? 0 :
                    #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
                        (__Pyx_PyUnicode_GET_LENGTH(**argname) != __Pyx_PyUnicode_GET_LENGTH(key)) ? 1 :
                    #endif
                        PyUnicode_Compare(**argname, key);
                    if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
                    if (cmp == 0) goto arg_passed_twice;
                    argname++;
                }
            }
        } else
            goto invalid_keyword_type;
        if (kwds2) {
            if (unlikely(PyDict_SetItem(kwds2, key, value))) goto bad;
        } else {
            goto invalid_keyword;
        }
    }
    return 0;
arg_passed_twice:
    __Pyx_RaiseDoubleKeywordsError(function_name, key);
    goto bad;
invalid_keyword_type:
    PyErr_Format(PyExc_TypeError,
        "%.200s() keywords must be strings", function_name);
    goto bad;
invalid_keyword:
    PyErr_Format(PyExc_TypeError,
    #if PY_MAJOR_VERSION < 3
        "%.200s() got an unexpected keyword argument '%.200s'",
        function_name, PyString_AsString(key));
    #else
        "%s() got an unexpected keyword argument '%U'",
        function_name, key);
    #endif
bad:
    return -1;
}
 
/* RaiseArgTupleInvalid */
static void __Pyx_RaiseArgtupleInvalid(
    const char* func_name,
    int exact,
    Py_ssize_t num_min,
    Py_ssize_t num_max,
    Py_ssize_t num_found)
{
    Py_ssize_t num_expected;
    const char *more_or_less;
    if (num_found < num_min) {
        num_expected = num_min;
        more_or_less = "at least";
    } else {
        num_expected = num_max;
        more_or_less = "at most";
    }
    if (exact) {
        more_or_less = "exactly";
    }
    PyErr_Format(PyExc_TypeError,
                 "%.200s() takes %.8s %" CYTHON_FORMAT_SSIZE_T "d positional argument%.1s (%" CYTHON_FORMAT_SSIZE_T "d given)",
                 func_name, more_or_less, num_expected,
                 (num_expected == 1) ? "" : "s", num_found);
}
 
/* GetModuleGlobalName */
#if CYTHON_USE_DICT_VERSIONS
static PyObject *__Pyx__GetModuleGlobalName(PyObject *name, PY_UINT64_T *dict_version, PyObject **dict_cached_value)
#else
static CYTHON_INLINE PyObject *__Pyx__GetModuleGlobalName(PyObject *name)
#endif
{
    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);
    __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version)
    if (likely(result)) {
        return __Pyx_NewRef(result);
    } else if (unlikely(PyErr_Occurred())) {
        return NULL;
    }
#else
    result = PyDict_GetItem(__pyx_d, name);
    __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version)
    if (likely(result)) {
        return __Pyx_NewRef(result);
    }
#endif
#else
    result = PyObject_GetItem(__pyx_d, name);
    __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version)
    if (likely(result)) {
        return __Pyx_NewRef(result);
    }
    PyErr_Clear();
#endif
    return __Pyx_GetBuiltinName(name);
}
 
/* GetTopmostException */
#if CYTHON_USE_EXC_INFO_STACK
static _PyErr_StackItem *
__Pyx_PyErr_GetTopmostException(PyThreadState *tstate)
{
    _PyErr_StackItem *exc_info = tstate->exc_info;
    while ((exc_info->exc_type == NULL || exc_info->exc_type == Py_None) &&
           exc_info->previous_item != NULL)
    {
        exc_info = exc_info->previous_item;
    }
    return exc_info;
}
#endif
 
/* SaveResetException */
#if CYTHON_FAST_THREAD_STATE
static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
    #if CYTHON_USE_EXC_INFO_STACK
    _PyErr_StackItem *exc_info = __Pyx_PyErr_GetTopmostException(tstate);
    *type = exc_info->exc_type;
    *value = exc_info->exc_value;
    *tb = exc_info->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 CYTHON_USE_EXC_INFO_STACK
    _PyErr_StackItem *exc_info = tstate->exc_info;
    tmp_type = exc_info->exc_type;
    tmp_value = exc_info->exc_value;
    tmp_tb = exc_info->exc_traceback;
    exc_info->exc_type = type;
    exc_info->exc_value = value;
    exc_info->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 CYTHON_USE_EXC_INFO_STACK
    {
        _PyErr_StackItem *exc_info = tstate->exc_info;
        tmp_type = exc_info->exc_type;
        tmp_value = exc_info->exc_value;
        tmp_tb = exc_info->exc_traceback;
        exc_info->exc_type = local_type;
        exc_info->exc_value = local_value;
        exc_info->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;
}
 
/* 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
 
/* PyObjectCall2Args */
static CYTHON_UNUSED PyObject* __Pyx_PyObject_Call2Args(PyObject* function, PyObject* arg1, PyObject* arg2) {
    PyObject *args, *result = NULL;
    #if CYTHON_FAST_PYCALL
    if (PyFunction_Check(function)) {
        PyObject *args[2] = {arg1, arg2};
        return __Pyx_PyFunction_FastCall(function, args, 2);
    }
    #endif
    #if CYTHON_FAST_PYCCALL
    if (__Pyx_PyFastCFunction_Check(function)) {
        PyObject *args[2] = {arg1, arg2};
        return __Pyx_PyCFunction_FastCall(function, args, 2);
    }
    #endif
    args = PyTuple_New(2);
    if (unlikely(!args)) goto done;
    Py_INCREF(arg1);
    PyTuple_SET_ITEM(args, 0, arg1);
    Py_INCREF(arg2);
    PyTuple_SET_ITEM(args, 1, arg2);
    Py_INCREF(function);
    result = __Pyx_PyObject_Call(function, args, NULL);
    Py_DECREF(args);
    Py_DECREF(function);
done:
    return result;
}
 
/* PyIntBinop */
#if !CYTHON_COMPILING_IN_PYPY
static PyObject* __Pyx_PyInt_AddObjC(PyObject *op1, PyObject *op2, CYTHON_UNUSED long intval, int inplace, int zerodivision_check) {
    (void)inplace;
    (void)zerodivision_check;
    #if PY_MAJOR_VERSION < 3
    if (likely(PyInt_CheckExact(op1))) {
        const long b = intval;
        long x;
        long a = PyInt_AS_LONG(op1);
            x = (long)((unsigned long)a + b);
            if (likely((x^a) >= 0 || (x^b) >= 0))
                return PyInt_FromLong(x);
            return PyLong_Type.tp_as_number->nb_add(op1, op2);
    }
    #endif
    #if CYTHON_USE_PYLONG_INTERNALS
    if (likely(PyLong_CheckExact(op1))) {
        const long b = intval;
        long a, x;
#ifdef HAVE_LONG_LONG
        const PY_LONG_LONG llb = intval;
        PY_LONG_LONG lla, llx;
#endif
        const digit* digits = ((PyLongObject*)op1)->ob_digit;
        const Py_ssize_t size = Py_SIZE(op1);
        if (likely(__Pyx_sst_abs(size) <= 1)) {
            a = likely(size) ? digits[0] : 0;
            if (size == -1) a = -a;
        } else {
            switch (size) {
                case -2:
                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                        a = -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
#ifdef HAVE_LONG_LONG
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
                        lla = -(PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
#endif
                    }
                    CYTHON_FALLTHROUGH;
                case 2:
                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                        a = (long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
#ifdef HAVE_LONG_LONG
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
                        lla = (PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
#endif
                    }
                    CYTHON_FALLTHROUGH;
                case -3:
                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                        a = -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
#ifdef HAVE_LONG_LONG
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
                        lla = -(PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
#endif
                    }
                    CYTHON_FALLTHROUGH;
                case 3:
                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                        a = (long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
#ifdef HAVE_LONG_LONG
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
                        lla = (PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
#endif
                    }
                    CYTHON_FALLTHROUGH;
                case -4:
                    if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                        a = -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
#ifdef HAVE_LONG_LONG
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
                        lla = -(PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
#endif
                    }
                    CYTHON_FALLTHROUGH;
                case 4:
                    if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                        a = (long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
#ifdef HAVE_LONG_LONG
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
                        lla = (PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
#endif
                    }
                    CYTHON_FALLTHROUGH;
                default: return PyLong_Type.tp_as_number->nb_add(op1, op2);
            }
        }
                x = a + b;
            return PyLong_FromLong(x);
#ifdef HAVE_LONG_LONG
        long_long:
                llx = lla + llb;
            return PyLong_FromLongLong(llx);
#endif
        
        
    }
    #endif
    if (PyFloat_CheckExact(op1)) {
        const long b = intval;
        double a = PyFloat_AS_DOUBLE(op1);
            double result;
            PyFPE_START_PROTECT("add", return NULL)
            result = ((double)a) + (double)b;
            PyFPE_END_PROTECT(result)
            return PyFloat_FromDouble(result);
    }
    return (inplace ? PyNumber_InPlaceAdd : PyNumber_Add)(op1, op2);
}
#endif
 
/* decode_c_bytes */
static CYTHON_INLINE PyObject* __Pyx_decode_c_bytes(
         const char* cstring, Py_ssize_t length, Py_ssize_t start, Py_ssize_t stop,
         const char* encoding, const char* errors,
         PyObject* (*decode_func)(const char *s, Py_ssize_t size, const char *errors)) {
    if (unlikely((start < 0) | (stop < 0))) {
        if (start < 0) {
            start += length;
            if (start < 0)
                start = 0;
        }
        if (stop < 0)
            stop += length;
    }
    if (stop > length)
        stop = length;
    if (unlikely(stop <= start))
        return __Pyx_NewRef(__pyx_empty_unicode);
    length = stop - start;
    cstring += start;
    if (decode_func) {
        return decode_func(cstring, length, errors);
    } else {
        return PyUnicode_Decode(cstring, length, encoding, errors);
    }
}
 
/* SwapException */
#if CYTHON_FAST_THREAD_STATE
static CYTHON_INLINE void __Pyx__ExceptionSwap(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    #if CYTHON_USE_EXC_INFO_STACK
    _PyErr_StackItem *exc_info = tstate->exc_info;
    tmp_type = exc_info->exc_type;
    tmp_value = exc_info->exc_value;
    tmp_tb = exc_info->exc_traceback;
    exc_info->exc_type = *type;
    exc_info->exc_value = *value;
    exc_info->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
    *type = tmp_type;
    *value = tmp_value;
    *tb = tmp_tb;
}
#else
static CYTHON_INLINE void __Pyx_ExceptionSwap(PyObject **type, PyObject **value, PyObject **tb) {
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    PyErr_GetExcInfo(&tmp_type, &tmp_value, &tmp_tb);
    PyErr_SetExcInfo(*type, *value, *tb);
    *type = tmp_type;
    *value = tmp_value;
    *tb = tmp_tb;
}
#endif
 
/* SetItemInt */
static int __Pyx_SetItemInt_Generic(PyObject *o, PyObject *j, PyObject *v) {
    int r;
    if (!j) return -1;
    r = PyObject_SetItem(o, j, v);
    Py_DECREF(j);
    return r;
}
static CYTHON_INLINE int __Pyx_SetItemInt_Fast(PyObject *o, Py_ssize_t i, PyObject *v, int is_list,
                                               CYTHON_NCP_UNUSED int wraparound, CYTHON_NCP_UNUSED int boundscheck) {
#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS && CYTHON_USE_TYPE_SLOTS
    if (is_list || PyList_CheckExact(o)) {
        Py_ssize_t n = (!wraparound) ? i : ((likely(i >= 0)) ? i : i + PyList_GET_SIZE(o));
        if ((!boundscheck) || likely(__Pyx_is_valid_index(n, PyList_GET_SIZE(o)))) {
            PyObject* old = PyList_GET_ITEM(o, n);
            Py_INCREF(v);
            PyList_SET_ITEM(o, n, v);
            Py_DECREF(old);
            return 1;
        }
    } else {
        PySequenceMethods *m = Py_TYPE(o)->tp_as_sequence;
        if (likely(m && m->sq_ass_item)) {
            if (wraparound && unlikely(i < 0) && likely(m->sq_length)) {
                Py_ssize_t l = m->sq_length(o);
                if (likely(l >= 0)) {
                    i += l;
                } else {
                    if (!PyErr_ExceptionMatches(PyExc_OverflowError))
                        return -1;
                    PyErr_Clear();
                }
            }
            return m->sq_ass_item(o, i, v);
        }
    }
#else
#if CYTHON_COMPILING_IN_PYPY
    if (is_list || (PySequence_Check(o) && !PyDict_Check(o)))
#else
    if (is_list || PySequence_Check(o))
#endif
    {
        return PySequence_SetItem(o, i, v);
    }
#endif
    return __Pyx_SetItemInt_Generic(o, PyInt_FromSsize_t(i), v);
}
 
/* ArgTypeTest */
static int __Pyx__ArgTypeTest(PyObject *obj, PyTypeObject *type, const char *name, int exact)
{
    if (unlikely(!type)) {
        PyErr_SetString(PyExc_SystemError, "Missing type object");
        return 0;
    }
    else if (exact) {
        #if PY_MAJOR_VERSION == 2
        if ((type == &PyBaseString_Type) && likely(__Pyx_PyBaseString_CheckExact(obj))) return 1;
        #endif
    }
    else {
        if (likely(__Pyx_TypeCheck(obj, type))) return 1;
    }
    PyErr_Format(PyExc_TypeError,
        "Argument '%.200s' has incorrect type (expected %.200s, got %.200s)",
        name, type->tp_name, Py_TYPE(obj)->tp_name);
    return 0;
}
 
/* 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 ((1) && (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, (PyObject *)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;
}
 
/* 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;
}
 
/* PyObjectGetAttrStrNoError */
static void __Pyx_PyObject_GetAttrStr_ClearAttributeError(void) {
    __Pyx_PyThreadState_declare
    __Pyx_PyThreadState_assign
    if (likely(__Pyx_PyErr_ExceptionMatches(PyExc_AttributeError)))
        __Pyx_PyErr_Clear();
}
static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStrNoError(PyObject* obj, PyObject* attr_name) {
    PyObject *result;
#if CYTHON_COMPILING_IN_CPYTHON && CYTHON_USE_TYPE_SLOTS && PY_VERSION_HEX >= 0x030700B1
    PyTypeObject* tp = Py_TYPE(obj);
    if (likely(tp->tp_getattro == PyObject_GenericGetAttr)) {
        return _PyObject_GenericGetAttrWithDict(obj, attr_name, NULL, 1);
    }
#endif
    result = __Pyx_PyObject_GetAttrStr(obj, attr_name);
    if (unlikely(!result)) {
        __Pyx_PyObject_GetAttrStr_ClearAttributeError();
    }
    return result;
}
 
/* SetupReduce */
static int __Pyx_setup_reduce_is_named(PyObject* meth, PyObject* name) {
  int ret;
  PyObject *name_attr;
  name_attr = __Pyx_PyObject_GetAttrStr(meth, __pyx_n_s_name);
  if (likely(name_attr)) {
      ret = PyObject_RichCompareBool(name_attr, name, Py_EQ);
  } else {
      ret = -1;
  }
  if (unlikely(ret < 0)) {
      PyErr_Clear();
      ret = 0;
  }
  Py_XDECREF(name_attr);
  return ret;
}
static int __Pyx_setup_reduce(PyObject* type_obj) {
    int ret = 0;
    PyObject *object_reduce = NULL;
    PyObject *object_reduce_ex = NULL;
    PyObject *reduce = NULL;
    PyObject *reduce_ex = NULL;
    PyObject *reduce_cython = NULL;
    PyObject *setstate = NULL;
    PyObject *setstate_cython = NULL;
#if CYTHON_USE_PYTYPE_LOOKUP
    if (_PyType_Lookup((PyTypeObject*)type_obj, __pyx_n_s_getstate)) goto __PYX_GOOD;
#else
    if (PyObject_HasAttr(type_obj, __pyx_n_s_getstate)) goto __PYX_GOOD;
#endif
#if CYTHON_USE_PYTYPE_LOOKUP
    object_reduce_ex = _PyType_Lookup(&PyBaseObject_Type, __pyx_n_s_reduce_ex); if (!object_reduce_ex) goto __PYX_BAD;
#else
    object_reduce_ex = __Pyx_PyObject_GetAttrStr((PyObject*)&PyBaseObject_Type, __pyx_n_s_reduce_ex); if (!object_reduce_ex) goto __PYX_BAD;
#endif
    reduce_ex = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_n_s_reduce_ex); if (unlikely(!reduce_ex)) goto __PYX_BAD;
    if (reduce_ex == object_reduce_ex) {
#if CYTHON_USE_PYTYPE_LOOKUP
        object_reduce = _PyType_Lookup(&PyBaseObject_Type, __pyx_n_s_reduce); if (!object_reduce) goto __PYX_BAD;
#else
        object_reduce = __Pyx_PyObject_GetAttrStr((PyObject*)&PyBaseObject_Type, __pyx_n_s_reduce); if (!object_reduce) goto __PYX_BAD;
#endif
        reduce = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_n_s_reduce); if (unlikely(!reduce)) goto __PYX_BAD;
        if (reduce == object_reduce || __Pyx_setup_reduce_is_named(reduce, __pyx_n_s_reduce_cython)) {
            reduce_cython = __Pyx_PyObject_GetAttrStrNoError(type_obj, __pyx_n_s_reduce_cython);
            if (likely(reduce_cython)) {
                ret = PyDict_SetItem(((PyTypeObject*)type_obj)->tp_dict, __pyx_n_s_reduce, reduce_cython); if (unlikely(ret < 0)) goto __PYX_BAD;
                ret = PyDict_DelItem(((PyTypeObject*)type_obj)->tp_dict, __pyx_n_s_reduce_cython); if (unlikely(ret < 0)) goto __PYX_BAD;
            } else if (reduce == object_reduce || PyErr_Occurred()) {
                goto __PYX_BAD;
            }
            setstate = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_n_s_setstate);
            if (!setstate) PyErr_Clear();
            if (!setstate || __Pyx_setup_reduce_is_named(setstate, __pyx_n_s_setstate_cython)) {
                setstate_cython = __Pyx_PyObject_GetAttrStrNoError(type_obj, __pyx_n_s_setstate_cython);
                if (likely(setstate_cython)) {
                    ret = PyDict_SetItem(((PyTypeObject*)type_obj)->tp_dict, __pyx_n_s_setstate, setstate_cython); if (unlikely(ret < 0)) goto __PYX_BAD;
                    ret = PyDict_DelItem(((PyTypeObject*)type_obj)->tp_dict, __pyx_n_s_setstate_cython); if (unlikely(ret < 0)) goto __PYX_BAD;
                } else if (!setstate || PyErr_Occurred()) {
                    goto __PYX_BAD;
                }
            }
            PyType_Modified((PyTypeObject*)type_obj);
        }
    }
    goto __PYX_GOOD;
__PYX_BAD:
    if (!PyErr_Occurred())
        PyErr_Format(PyExc_RuntimeError, "Unable to initialize pickling for %s", ((PyTypeObject*)type_obj)->tp_name);
    ret = -1;
__PYX_GOOD:
#if !CYTHON_USE_PYTYPE_LOOKUP
    Py_XDECREF(object_reduce);
    Py_XDECREF(object_reduce_ex);
#endif
    Py_XDECREF(reduce);
    Py_XDECREF(reduce_ex);
    Py_XDECREF(reduce_cython);
    Py_XDECREF(setstate);
    Py_XDECREF(setstate_cython);
    return ret;
}
 
/* 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_MAJOR_VERSION < 3
        Py_XDECREF(owned_ref);
        #endif
        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
}
 
/* CLineInTraceback */
#ifndef CYTHON_CLINE_IN_TRACEBACK
static int __Pyx_CLineForTraceback(CYTHON_NCP_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)) {
        __PYX_PY_DICT_LOOKUP_IF_MODIFIED(
            use_cline, *cython_runtime_dict,
            __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 (use_cline == Py_False || (use_cline != Py_True && 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);
}
 
/* 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) ((int) 0 - (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);
    }
}
 
/* CIntFromPy */
static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) {
    const int neg_one = (int) ((int) 0 - (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;
}
 
/* CIntToPy */
static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) {
    const long neg_one = (long) ((long) 0 - (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);
    }
}
 
/* CIntFromPy */
static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *x) {
    const long neg_one = (long) ((long) 0 - (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
 
/* FetchCommonType */
static PyTypeObject* __Pyx_FetchCommonType(PyTypeObject* type) {
    PyObject* fake_module;
    PyTypeObject* cached_type = NULL;
    fake_module = PyImport_AddModule((char*) "_cython_" CYTHON_ABI);
    if (!fake_module) return NULL;
    Py_INCREF(fake_module);
    cached_type = (PyTypeObject*) PyObject_GetAttrString(fake_module, type->tp_name);
    if (cached_type) {
        if (!PyType_Check((PyObject*)cached_type)) {
            PyErr_Format(PyExc_TypeError,
                "Shared Cython type %.200s is not a type object",
                type->tp_name);
            goto bad;
        }
        if (cached_type->tp_basicsize != type->tp_basicsize) {
            PyErr_Format(PyExc_TypeError,
                "Shared Cython type %.200s has the wrong size, try recompiling",
                type->tp_name);
            goto bad;
        }
    } else {
        if (!PyErr_ExceptionMatches(PyExc_AttributeError)) goto bad;
        PyErr_Clear();
        if (PyType_Ready(type) < 0) goto bad;
        if (PyObject_SetAttrString(fake_module, type->tp_name, (PyObject*) type) < 0)
            goto bad;
        Py_INCREF(type);
        cached_type = type;
    }
done:
    Py_DECREF(fake_module);
    return cached_type;
bad:
    Py_XDECREF(cached_type);
    cached_type = NULL;
    goto done;
}
 
/* PyObjectGetMethod */
static int __Pyx_PyObject_GetMethod(PyObject *obj, PyObject *name, PyObject **method) {
    PyObject *attr;
#if CYTHON_UNPACK_METHODS && CYTHON_COMPILING_IN_CPYTHON && CYTHON_USE_PYTYPE_LOOKUP
    PyTypeObject *tp = Py_TYPE(obj);
    PyObject *descr;
    descrgetfunc f = NULL;
    PyObject **dictptr, *dict;
    int meth_found = 0;
    assert (*method == NULL);
    if (unlikely(tp->tp_getattro != PyObject_GenericGetAttr)) {
        attr = __Pyx_PyObject_GetAttrStr(obj, name);
        goto try_unpack;
    }
    if (unlikely(tp->tp_dict == NULL) && unlikely(PyType_Ready(tp) < 0)) {
        return 0;
    }
    descr = _PyType_Lookup(tp, name);
    if (likely(descr != NULL)) {
        Py_INCREF(descr);
#if PY_MAJOR_VERSION >= 3
        #ifdef __Pyx_CyFunction_USED
        if (likely(PyFunction_Check(descr) || (Py_TYPE(descr) == &PyMethodDescr_Type) || __Pyx_CyFunction_Check(descr)))
        #else
        if (likely(PyFunction_Check(descr) || (Py_TYPE(descr) == &PyMethodDescr_Type)))
        #endif
#else
        #ifdef __Pyx_CyFunction_USED
        if (likely(PyFunction_Check(descr) || __Pyx_CyFunction_Check(descr)))
        #else
        if (likely(PyFunction_Check(descr)))
        #endif
#endif
        {
            meth_found = 1;
        } else {
            f = Py_TYPE(descr)->tp_descr_get;
            if (f != NULL && PyDescr_IsData(descr)) {
                attr = f(descr, obj, (PyObject *)Py_TYPE(obj));
                Py_DECREF(descr);
                goto try_unpack;
            }
        }
    }
    dictptr = _PyObject_GetDictPtr(obj);
    if (dictptr != NULL && (dict = *dictptr) != NULL) {
        Py_INCREF(dict);
        attr = __Pyx_PyDict_GetItemStr(dict, name);
        if (attr != NULL) {
            Py_INCREF(attr);
            Py_DECREF(dict);
            Py_XDECREF(descr);
            goto try_unpack;
        }
        Py_DECREF(dict);
    }
    if (meth_found) {
        *method = descr;
        return 1;
    }
    if (f != NULL) {
        attr = f(descr, obj, (PyObject *)Py_TYPE(obj));
        Py_DECREF(descr);
        goto try_unpack;
    }
    if (descr != NULL) {
        *method = descr;
        return 0;
    }
    PyErr_Format(PyExc_AttributeError,
#if PY_MAJOR_VERSION >= 3
                 "'%.50s' object has no attribute '%U'",
                 tp->tp_name, name);
#else
                 "'%.50s' object has no attribute '%.400s'",
                 tp->tp_name, PyString_AS_STRING(name));
#endif
    return 0;
#else
    attr = __Pyx_PyObject_GetAttrStr(obj, name);
    goto try_unpack;
#endif
try_unpack:
#if CYTHON_UNPACK_METHODS
    if (likely(attr) && PyMethod_Check(attr) && likely(PyMethod_GET_SELF(attr) == obj)) {
        PyObject *function = PyMethod_GET_FUNCTION(attr);
        Py_INCREF(function);
        Py_DECREF(attr);
        *method = function;
        return 1;
    }
#endif
    *method = attr;
    return 0;
}
 
/* PyObjectCallMethod1 */
static PyObject* __Pyx__PyObject_CallMethod1(PyObject* method, PyObject* arg) {
    PyObject *result = __Pyx_PyObject_CallOneArg(method, arg);
    Py_DECREF(method);
    return result;
}
static PyObject* __Pyx_PyObject_CallMethod1(PyObject* obj, PyObject* method_name, PyObject* arg) {
    PyObject *method = NULL, *result;
    int is_method = __Pyx_PyObject_GetMethod(obj, method_name, &method);
    if (likely(is_method)) {
        result = __Pyx_PyObject_Call2Args(method, obj, arg);
        Py_DECREF(method);
        return result;
    }
    if (unlikely(!method)) return NULL;
    return __Pyx__PyObject_CallMethod1(method, arg);
}
 
/* CoroutineBase */
#include <structmember.h>
#include <frameobject.h>
#define __Pyx_Coroutine_Undelegate(gen) Py_CLEAR((gen)->yieldfrom)
static int __Pyx_PyGen__FetchStopIterationValue(CYTHON_UNUSED PyThreadState *__pyx_tstate, PyObject **pvalue) {
    PyObject *et, *ev, *tb;
    PyObject *value = NULL;
    __Pyx_ErrFetch(&et, &ev, &tb);
    if (!et) {
        Py_XDECREF(tb);
        Py_XDECREF(ev);
        Py_INCREF(Py_None);
        *pvalue = Py_None;
        return 0;
    }
    if (likely(et == PyExc_StopIteration)) {
        if (!ev) {
            Py_INCREF(Py_None);
            value = Py_None;
        }
#if PY_VERSION_HEX >= 0x030300A0
        else if (Py_TYPE(ev) == (PyTypeObject*)PyExc_StopIteration) {
            value = ((PyStopIterationObject *)ev)->value;
            Py_INCREF(value);
            Py_DECREF(ev);
        }
#endif
        else if (unlikely(PyTuple_Check(ev))) {
            if (PyTuple_GET_SIZE(ev) >= 1) {
#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
                value = PyTuple_GET_ITEM(ev, 0);
                Py_INCREF(value);
#else
                value = PySequence_ITEM(ev, 0);
#endif
            } else {
                Py_INCREF(Py_None);
                value = Py_None;
            }
            Py_DECREF(ev);
        }
        else if (!__Pyx_TypeCheck(ev, (PyTypeObject*)PyExc_StopIteration)) {
            value = ev;
        }
        if (likely(value)) {
            Py_XDECREF(tb);
            Py_DECREF(et);
            *pvalue = value;
            return 0;
        }
    } else if (!__Pyx_PyErr_GivenExceptionMatches(et, PyExc_StopIteration)) {
        __Pyx_ErrRestore(et, ev, tb);
        return -1;
    }
    PyErr_NormalizeException(&et, &ev, &tb);
    if (unlikely(!PyObject_TypeCheck(ev, (PyTypeObject*)PyExc_StopIteration))) {
        __Pyx_ErrRestore(et, ev, tb);
        return -1;
    }
    Py_XDECREF(tb);
    Py_DECREF(et);
#if PY_VERSION_HEX >= 0x030300A0
    value = ((PyStopIterationObject *)ev)->value;
    Py_INCREF(value);
    Py_DECREF(ev);
#else
    {
        PyObject* args = __Pyx_PyObject_GetAttrStr(ev, __pyx_n_s_args);
        Py_DECREF(ev);
        if (likely(args)) {
            value = PySequence_GetItem(args, 0);
            Py_DECREF(args);
        }
        if (unlikely(!value)) {
            __Pyx_ErrRestore(NULL, NULL, NULL);
            Py_INCREF(Py_None);
            value = Py_None;
        }
    }
#endif
    *pvalue = value;
    return 0;
}
static CYTHON_INLINE
void __Pyx_Coroutine_ExceptionClear(__Pyx_ExcInfoStruct *exc_state) {
    PyObject *t, *v, *tb;
    t = exc_state->exc_type;
    v = exc_state->exc_value;
    tb = exc_state->exc_traceback;
    exc_state->exc_type = NULL;
    exc_state->exc_value = NULL;
    exc_state->exc_traceback = NULL;
    Py_XDECREF(t);
    Py_XDECREF(v);
    Py_XDECREF(tb);
}
#define __Pyx_Coroutine_AlreadyRunningError(gen)  (__Pyx__Coroutine_AlreadyRunningError(gen), (PyObject*)NULL)
static void __Pyx__Coroutine_AlreadyRunningError(CYTHON_UNUSED __pyx_CoroutineObject *gen) {
    const char *msg;
    if ((0)) {
    #ifdef __Pyx_Coroutine_USED
    } else if (__Pyx_Coroutine_Check((PyObject*)gen)) {
        msg = "coroutine already executing";
    #endif
    #ifdef __Pyx_AsyncGen_USED
    } else if (__Pyx_AsyncGen_CheckExact((PyObject*)gen)) {
        msg = "async generator already executing";
    #endif
    } else {
        msg = "generator already executing";
    }
    PyErr_SetString(PyExc_ValueError, msg);
}
#define __Pyx_Coroutine_NotStartedError(gen)  (__Pyx__Coroutine_NotStartedError(gen), (PyObject*)NULL)
static void __Pyx__Coroutine_NotStartedError(CYTHON_UNUSED PyObject *gen) {
    const char *msg;
    if ((0)) {
    #ifdef __Pyx_Coroutine_USED
    } else if (__Pyx_Coroutine_Check(gen)) {
        msg = "can't send non-None value to a just-started coroutine";
    #endif
    #ifdef __Pyx_AsyncGen_USED
    } else if (__Pyx_AsyncGen_CheckExact(gen)) {
        msg = "can't send non-None value to a just-started async generator";
    #endif
    } else {
        msg = "can't send non-None value to a just-started generator";
    }
    PyErr_SetString(PyExc_TypeError, msg);
}
#define __Pyx_Coroutine_AlreadyTerminatedError(gen, value, closing)  (__Pyx__Coroutine_AlreadyTerminatedError(gen, value, closing), (PyObject*)NULL)
static void __Pyx__Coroutine_AlreadyTerminatedError(CYTHON_UNUSED PyObject *gen, PyObject *value, CYTHON_UNUSED int closing) {
    #ifdef __Pyx_Coroutine_USED
    if (!closing && __Pyx_Coroutine_Check(gen)) {
        PyErr_SetString(PyExc_RuntimeError, "cannot reuse already awaited coroutine");
    } else
    #endif
    if (value) {
        #ifdef __Pyx_AsyncGen_USED
        if (__Pyx_AsyncGen_CheckExact(gen))
            PyErr_SetNone(__Pyx_PyExc_StopAsyncIteration);
        else
        #endif
        PyErr_SetNone(PyExc_StopIteration);
    }
}
static
PyObject *__Pyx_Coroutine_SendEx(__pyx_CoroutineObject *self, PyObject *value, int closing) {
    __Pyx_PyThreadState_declare
    PyThreadState *tstate;
    __Pyx_ExcInfoStruct *exc_state;
    PyObject *retval;
    assert(!self->is_running);
    if (unlikely(self->resume_label == 0)) {
        if (unlikely(value && value != Py_None)) {
            return __Pyx_Coroutine_NotStartedError((PyObject*)self);
        }
    }
    if (unlikely(self->resume_label == -1)) {
        return __Pyx_Coroutine_AlreadyTerminatedError((PyObject*)self, value, closing);
    }
#if CYTHON_FAST_THREAD_STATE
    __Pyx_PyThreadState_assign
    tstate = __pyx_tstate;
#else
    tstate = __Pyx_PyThreadState_Current;
#endif
    exc_state = &self->gi_exc_state;
    if (exc_state->exc_type) {
        #if CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_PYSTON
        #else
        if (exc_state->exc_traceback) {
            PyTracebackObject *tb = (PyTracebackObject *) exc_state->exc_traceback;
            PyFrameObject *f = tb->tb_frame;
            Py_XINCREF(tstate->frame);
            assert(f->f_back == NULL);
            f->f_back = tstate->frame;
        }
        #endif
    }
#if CYTHON_USE_EXC_INFO_STACK
    exc_state->previous_item = tstate->exc_info;
    tstate->exc_info = exc_state;
#else
    if (exc_state->exc_type) {
        __Pyx_ExceptionSwap(&exc_state->exc_type, &exc_state->exc_value, &exc_state->exc_traceback);
    } else {
        __Pyx_Coroutine_ExceptionClear(exc_state);
        __Pyx_ExceptionSave(&exc_state->exc_type, &exc_state->exc_value, &exc_state->exc_traceback);
    }
#endif
    self->is_running = 1;
    retval = self->body((PyObject *) self, tstate, value);
    self->is_running = 0;
#if CYTHON_USE_EXC_INFO_STACK
    exc_state = &self->gi_exc_state;
    tstate->exc_info = exc_state->previous_item;
    exc_state->previous_item = NULL;
    __Pyx_Coroutine_ResetFrameBackpointer(exc_state);
#endif
    return retval;
}
static CYTHON_INLINE void __Pyx_Coroutine_ResetFrameBackpointer(__Pyx_ExcInfoStruct *exc_state) {
    PyObject *exc_tb = exc_state->exc_traceback;
    if (likely(exc_tb)) {
#if CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_PYSTON
#else
        PyTracebackObject *tb = (PyTracebackObject *) exc_tb;
        PyFrameObject *f = tb->tb_frame;
        Py_CLEAR(f->f_back);
#endif
    }
}
static CYTHON_INLINE
PyObject *__Pyx_Coroutine_MethodReturn(CYTHON_UNUSED PyObject* gen, PyObject *retval) {
    if (unlikely(!retval)) {
        __Pyx_PyThreadState_declare
        __Pyx_PyThreadState_assign
        if (!__Pyx_PyErr_Occurred()) {
            PyObject *exc = PyExc_StopIteration;
            #ifdef __Pyx_AsyncGen_USED
            if (__Pyx_AsyncGen_CheckExact(gen))
                exc = __Pyx_PyExc_StopAsyncIteration;
            #endif
            __Pyx_PyErr_SetNone(exc);
        }
    }
    return retval;
}
static CYTHON_INLINE
PyObject *__Pyx_Coroutine_FinishDelegation(__pyx_CoroutineObject *gen) {
    PyObject *ret;
    PyObject *val = NULL;
    __Pyx_Coroutine_Undelegate(gen);
    __Pyx_PyGen__FetchStopIterationValue(__Pyx_PyThreadState_Current, &val);
    ret = __Pyx_Coroutine_SendEx(gen, val, 0);
    Py_XDECREF(val);
    return ret;
}
static PyObject *__Pyx_Coroutine_Send(PyObject *self, PyObject *value) {
    PyObject *retval;
    __pyx_CoroutineObject *gen = (__pyx_CoroutineObject*) self;
    PyObject *yf = gen->yieldfrom;
    if (unlikely(gen->is_running))
        return __Pyx_Coroutine_AlreadyRunningError(gen);
    if (yf) {
        PyObject *ret;
        gen->is_running = 1;
        #ifdef __Pyx_Generator_USED
        if (__Pyx_Generator_CheckExact(yf)) {
            ret = __Pyx_Coroutine_Send(yf, value);
        } else
        #endif
        #ifdef __Pyx_Coroutine_USED
        if (__Pyx_Coroutine_Check(yf)) {
            ret = __Pyx_Coroutine_Send(yf, value);
        } else
        #endif
        #ifdef __Pyx_AsyncGen_USED
        if (__pyx_PyAsyncGenASend_CheckExact(yf)) {
            ret = __Pyx_async_gen_asend_send(yf, value);
        } else
        #endif
        #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x03030000 && (defined(__linux__) || PY_VERSION_HEX >= 0x030600B3)
        if (PyGen_CheckExact(yf)) {
            ret = _PyGen_Send((PyGenObject*)yf, value == Py_None ? NULL : value);
        } else
        #endif
        #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x03050000 && defined(PyCoro_CheckExact) && (defined(__linux__) || PY_VERSION_HEX >= 0x030600B3)
        if (PyCoro_CheckExact(yf)) {
            ret = _PyGen_Send((PyGenObject*)yf, value == Py_None ? NULL : value);
        } else
        #endif
        {
            if (value == Py_None)
                ret = Py_TYPE(yf)->tp_iternext(yf);
            else
                ret = __Pyx_PyObject_CallMethod1(yf, __pyx_n_s_send, value);
        }
        gen->is_running = 0;
        if (likely(ret)) {
            return ret;
        }
        retval = __Pyx_Coroutine_FinishDelegation(gen);
    } else {
        retval = __Pyx_Coroutine_SendEx(gen, value, 0);
    }
    return __Pyx_Coroutine_MethodReturn(self, retval);
}
static int __Pyx_Coroutine_CloseIter(__pyx_CoroutineObject *gen, PyObject *yf) {
    PyObject *retval = NULL;
    int err = 0;
    #ifdef __Pyx_Generator_USED
    if (__Pyx_Generator_CheckExact(yf)) {
        retval = __Pyx_Coroutine_Close(yf);
        if (!retval)
            return -1;
    } else
    #endif
    #ifdef __Pyx_Coroutine_USED
    if (__Pyx_Coroutine_Check(yf)) {
        retval = __Pyx_Coroutine_Close(yf);
        if (!retval)
            return -1;
    } else
    if (__Pyx_CoroutineAwait_CheckExact(yf)) {
        retval = __Pyx_CoroutineAwait_Close((__pyx_CoroutineAwaitObject*)yf, NULL);
        if (!retval)
            return -1;
    } else
    #endif
    #ifdef __Pyx_AsyncGen_USED
    if (__pyx_PyAsyncGenASend_CheckExact(yf)) {
        retval = __Pyx_async_gen_asend_close(yf, NULL);
    } else
    if (__pyx_PyAsyncGenAThrow_CheckExact(yf)) {
        retval = __Pyx_async_gen_athrow_close(yf, NULL);
    } else
    #endif
    {
        PyObject *meth;
        gen->is_running = 1;
        meth = __Pyx_PyObject_GetAttrStr(yf, __pyx_n_s_close);
        if (unlikely(!meth)) {
            if (!PyErr_ExceptionMatches(PyExc_AttributeError)) {
                PyErr_WriteUnraisable(yf);
            }
            PyErr_Clear();
        } else {
            retval = PyObject_CallFunction(meth, NULL);
            Py_DECREF(meth);
            if (!retval)
                err = -1;
        }
        gen->is_running = 0;
    }
    Py_XDECREF(retval);
    return err;
}
static PyObject *__Pyx_Generator_Next(PyObject *self) {
    __pyx_CoroutineObject *gen = (__pyx_CoroutineObject*) self;
    PyObject *yf = gen->yieldfrom;
    if (unlikely(gen->is_running))
        return __Pyx_Coroutine_AlreadyRunningError(gen);
    if (yf) {
        PyObject *ret;
        gen->is_running = 1;
        #ifdef __Pyx_Generator_USED
        if (__Pyx_Generator_CheckExact(yf)) {
            ret = __Pyx_Generator_Next(yf);
        } else
        #endif
        #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x03030000 && (defined(__linux__) || PY_VERSION_HEX >= 0x030600B3)
        if (PyGen_CheckExact(yf)) {
            ret = _PyGen_Send((PyGenObject*)yf, NULL);
        } else
        #endif
        #ifdef __Pyx_Coroutine_USED
        if (__Pyx_Coroutine_Check(yf)) {
            ret = __Pyx_Coroutine_Send(yf, Py_None);
        } else
        #endif
            ret = Py_TYPE(yf)->tp_iternext(yf);
        gen->is_running = 0;
        if (likely(ret)) {
            return ret;
        }
        return __Pyx_Coroutine_FinishDelegation(gen);
    }
    return __Pyx_Coroutine_SendEx(gen, Py_None, 0);
}
static PyObject *__Pyx_Coroutine_Close_Method(PyObject *self, CYTHON_UNUSED PyObject *arg) {
    return __Pyx_Coroutine_Close(self);
}
static PyObject *__Pyx_Coroutine_Close(PyObject *self) {
    __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
    PyObject *retval, *raised_exception;
    PyObject *yf = gen->yieldfrom;
    int err = 0;
    if (unlikely(gen->is_running))
        return __Pyx_Coroutine_AlreadyRunningError(gen);
    if (yf) {
        Py_INCREF(yf);
        err = __Pyx_Coroutine_CloseIter(gen, yf);
        __Pyx_Coroutine_Undelegate(gen);
        Py_DECREF(yf);
    }
    if (err == 0)
        PyErr_SetNone(PyExc_GeneratorExit);
    retval = __Pyx_Coroutine_SendEx(gen, NULL, 1);
    if (unlikely(retval)) {
        const char *msg;
        Py_DECREF(retval);
        if ((0)) {
        #ifdef __Pyx_Coroutine_USED
        } else if (__Pyx_Coroutine_Check(self)) {
            msg = "coroutine ignored GeneratorExit";
        #endif
        #ifdef __Pyx_AsyncGen_USED
        } else if (__Pyx_AsyncGen_CheckExact(self)) {
#if PY_VERSION_HEX < 0x03060000
            msg = "async generator ignored GeneratorExit - might require Python 3.6+ finalisation (PEP 525)";
#else
            msg = "async generator ignored GeneratorExit";
#endif
        #endif
        } else {
            msg = "generator ignored GeneratorExit";
        }
        PyErr_SetString(PyExc_RuntimeError, msg);
        return NULL;
    }
    raised_exception = PyErr_Occurred();
    if (likely(!raised_exception || __Pyx_PyErr_GivenExceptionMatches2(raised_exception, PyExc_GeneratorExit, PyExc_StopIteration))) {
        if (raised_exception) PyErr_Clear();
        Py_INCREF(Py_None);
        return Py_None;
    }
    return NULL;
}
static PyObject *__Pyx__Coroutine_Throw(PyObject *self, PyObject *typ, PyObject *val, PyObject *tb,
                                        PyObject *args, int close_on_genexit) {
    __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
    PyObject *yf = gen->yieldfrom;
    if (unlikely(gen->is_running))
        return __Pyx_Coroutine_AlreadyRunningError(gen);
    if (yf) {
        PyObject *ret;
        Py_INCREF(yf);
        if (__Pyx_PyErr_GivenExceptionMatches(typ, PyExc_GeneratorExit) && close_on_genexit) {
            int err = __Pyx_Coroutine_CloseIter(gen, yf);
            Py_DECREF(yf);
            __Pyx_Coroutine_Undelegate(gen);
            if (err < 0)
                return __Pyx_Coroutine_MethodReturn(self, __Pyx_Coroutine_SendEx(gen, NULL, 0));
            goto throw_here;
        }
        gen->is_running = 1;
        if (0
        #ifdef __Pyx_Generator_USED
            || __Pyx_Generator_CheckExact(yf)
        #endif
        #ifdef __Pyx_Coroutine_USED
            || __Pyx_Coroutine_Check(yf)
        #endif
            ) {
            ret = __Pyx__Coroutine_Throw(yf, typ, val, tb, args, close_on_genexit);
        #ifdef __Pyx_Coroutine_USED
        } else if (__Pyx_CoroutineAwait_CheckExact(yf)) {
            ret = __Pyx__Coroutine_Throw(((__pyx_CoroutineAwaitObject*)yf)->coroutine, typ, val, tb, args, close_on_genexit);
        #endif
        } else {
            PyObject *meth = __Pyx_PyObject_GetAttrStr(yf, __pyx_n_s_throw);
            if (unlikely(!meth)) {
                Py_DECREF(yf);
                if (!PyErr_ExceptionMatches(PyExc_AttributeError)) {
                    gen->is_running = 0;
                    return NULL;
                }
                PyErr_Clear();
                __Pyx_Coroutine_Undelegate(gen);
                gen->is_running = 0;
                goto throw_here;
            }
            if (likely(args)) {
                ret = PyObject_CallObject(meth, args);
            } else {
                ret = PyObject_CallFunctionObjArgs(meth, typ, val, tb, NULL);
            }
            Py_DECREF(meth);
        }
        gen->is_running = 0;
        Py_DECREF(yf);
        if (!ret) {
            ret = __Pyx_Coroutine_FinishDelegation(gen);
        }
        return __Pyx_Coroutine_MethodReturn(self, ret);
    }
throw_here:
    __Pyx_Raise(typ, val, tb, NULL);
    return __Pyx_Coroutine_MethodReturn(self, __Pyx_Coroutine_SendEx(gen, NULL, 0));
}
static PyObject *__Pyx_Coroutine_Throw(PyObject *self, PyObject *args) {
    PyObject *typ;
    PyObject *val = NULL;
    PyObject *tb = NULL;
    if (!PyArg_UnpackTuple(args, (char *)"throw", 1, 3, &typ, &val, &tb))
        return NULL;
    return __Pyx__Coroutine_Throw(self, typ, val, tb, args, 1);
}
static CYTHON_INLINE int __Pyx_Coroutine_traverse_excstate(__Pyx_ExcInfoStruct *exc_state, visitproc visit, void *arg) {
    Py_VISIT(exc_state->exc_type);
    Py_VISIT(exc_state->exc_value);
    Py_VISIT(exc_state->exc_traceback);
    return 0;
}
static int __Pyx_Coroutine_traverse(__pyx_CoroutineObject *gen, visitproc visit, void *arg) {
    Py_VISIT(gen->closure);
    Py_VISIT(gen->classobj);
    Py_VISIT(gen->yieldfrom);
    return __Pyx_Coroutine_traverse_excstate(&gen->gi_exc_state, visit, arg);
}
static int __Pyx_Coroutine_clear(PyObject *self) {
    __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
    Py_CLEAR(gen->closure);
    Py_CLEAR(gen->classobj);
    Py_CLEAR(gen->yieldfrom);
    __Pyx_Coroutine_ExceptionClear(&gen->gi_exc_state);
#ifdef __Pyx_AsyncGen_USED
    if (__Pyx_AsyncGen_CheckExact(self)) {
        Py_CLEAR(((__pyx_PyAsyncGenObject*)gen)->ag_finalizer);
    }
#endif
    Py_CLEAR(gen->gi_code);
    Py_CLEAR(gen->gi_name);
    Py_CLEAR(gen->gi_qualname);
    Py_CLEAR(gen->gi_modulename);
    return 0;
}
static void __Pyx_Coroutine_dealloc(PyObject *self) {
    __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
    PyObject_GC_UnTrack(gen);
    if (gen->gi_weakreflist != NULL)
        PyObject_ClearWeakRefs(self);
    if (gen->resume_label >= 0) {
        PyObject_GC_Track(self);
#if PY_VERSION_HEX >= 0x030400a1 && CYTHON_USE_TP_FINALIZE
        if (PyObject_CallFinalizerFromDealloc(self))
#else
        Py_TYPE(gen)->tp_del(self);
        if (self->ob_refcnt > 0)
#endif
        {
            return;
        }
        PyObject_GC_UnTrack(self);
    }
#ifdef __Pyx_AsyncGen_USED
    if (__Pyx_AsyncGen_CheckExact(self)) {
        /* We have to handle this case for asynchronous generators
           right here, because this code has to be between UNTRACK
           and GC_Del. */
        Py_CLEAR(((__pyx_PyAsyncGenObject*)self)->ag_finalizer);
    }
#endif
    __Pyx_Coroutine_clear(self);
    PyObject_GC_Del(gen);
}
static void __Pyx_Coroutine_del(PyObject *self) {
    PyObject *error_type, *error_value, *error_traceback;
    __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
    __Pyx_PyThreadState_declare
    if (gen->resume_label < 0) {
        return;
    }
#if !CYTHON_USE_TP_FINALIZE
    assert(self->ob_refcnt == 0);
    self->ob_refcnt = 1;
#endif
    __Pyx_PyThreadState_assign
    __Pyx_ErrFetch(&error_type, &error_value, &error_traceback);
#ifdef __Pyx_AsyncGen_USED
    if (__Pyx_AsyncGen_CheckExact(self)) {
        __pyx_PyAsyncGenObject *agen = (__pyx_PyAsyncGenObject*)self;
        PyObject *finalizer = agen->ag_finalizer;
        if (finalizer && !agen->ag_closed) {
            PyObject *res = __Pyx_PyObject_CallOneArg(finalizer, self);
            if (unlikely(!res)) {
                PyErr_WriteUnraisable(self);
            } else {
                Py_DECREF(res);
            }
            __Pyx_ErrRestore(error_type, error_value, error_traceback);
            return;
        }
    }
#endif
    if (unlikely(gen->resume_label == 0 && !error_value)) {
#ifdef __Pyx_Coroutine_USED
#ifdef __Pyx_Generator_USED
    if (!__Pyx_Generator_CheckExact(self))
#endif
        {
        PyObject_GC_UnTrack(self);
#if PY_MAJOR_VERSION >= 3  || defined(PyErr_WarnFormat)
        if (unlikely(PyErr_WarnFormat(PyExc_RuntimeWarning, 1, "coroutine '%.50S' was never awaited", gen->gi_qualname) < 0))
            PyErr_WriteUnraisable(self);
#else
        {PyObject *msg;
        char *cmsg;
        #if CYTHON_COMPILING_IN_PYPY
        msg = NULL;
        cmsg = (char*) "coroutine was never awaited";
        #else
        char *cname;
        PyObject *qualname;
        qualname = gen->gi_qualname;
        cname = PyString_AS_STRING(qualname);
        msg = PyString_FromFormat("coroutine '%.50s' was never awaited", cname);
        if (unlikely(!msg)) {
            PyErr_Clear();
            cmsg = (char*) "coroutine was never awaited";
        } else {
            cmsg = PyString_AS_STRING(msg);
        }
        #endif
        if (unlikely(PyErr_WarnEx(PyExc_RuntimeWarning, cmsg, 1) < 0))
            PyErr_WriteUnraisable(self);
        Py_XDECREF(msg);}
#endif
        PyObject_GC_Track(self);
        }
#endif
    } else {
        PyObject *res = __Pyx_Coroutine_Close(self);
        if (unlikely(!res)) {
            if (PyErr_Occurred())
                PyErr_WriteUnraisable(self);
        } else {
            Py_DECREF(res);
        }
    }
    __Pyx_ErrRestore(error_type, error_value, error_traceback);
#if !CYTHON_USE_TP_FINALIZE
    assert(self->ob_refcnt > 0);
    if (--self->ob_refcnt == 0) {
        return;
    }
    {
        Py_ssize_t refcnt = self->ob_refcnt;
        _Py_NewReference(self);
        self->ob_refcnt = refcnt;
    }
#if CYTHON_COMPILING_IN_CPYTHON
    assert(PyType_IS_GC(self->ob_type) &&
           _Py_AS_GC(self)->gc.gc_refs != _PyGC_REFS_UNTRACKED);
    _Py_DEC_REFTOTAL;
#endif
#ifdef COUNT_ALLOCS
    --Py_TYPE(self)->tp_frees;
    --Py_TYPE(self)->tp_allocs;
#endif
#endif
}
static PyObject *
__Pyx_Coroutine_get_name(__pyx_CoroutineObject *self, CYTHON_UNUSED void *context)
{
    PyObject *name = self->gi_name;
    if (unlikely(!name)) name = Py_None;
    Py_INCREF(name);
    return name;
}
static int
__Pyx_Coroutine_set_name(__pyx_CoroutineObject *self, PyObject *value, CYTHON_UNUSED void *context)
{
    PyObject *tmp;
#if PY_MAJOR_VERSION >= 3
    if (unlikely(value == NULL || !PyUnicode_Check(value)))
#else
    if (unlikely(value == NULL || !PyString_Check(value)))
#endif
    {
        PyErr_SetString(PyExc_TypeError,
                        "__name__ must be set to a string object");
        return -1;
    }
    tmp = self->gi_name;
    Py_INCREF(value);
    self->gi_name = value;
    Py_XDECREF(tmp);
    return 0;
}
static PyObject *
__Pyx_Coroutine_get_qualname(__pyx_CoroutineObject *self, CYTHON_UNUSED void *context)
{
    PyObject *name = self->gi_qualname;
    if (unlikely(!name)) name = Py_None;
    Py_INCREF(name);
    return name;
}
static int
__Pyx_Coroutine_set_qualname(__pyx_CoroutineObject *self, PyObject *value, CYTHON_UNUSED void *context)
{
    PyObject *tmp;
#if PY_MAJOR_VERSION >= 3
    if (unlikely(value == NULL || !PyUnicode_Check(value)))
#else
    if (unlikely(value == NULL || !PyString_Check(value)))
#endif
    {
        PyErr_SetString(PyExc_TypeError,
                        "__qualname__ must be set to a string object");
        return -1;
    }
    tmp = self->gi_qualname;
    Py_INCREF(value);
    self->gi_qualname = value;
    Py_XDECREF(tmp);
    return 0;
}
static __pyx_CoroutineObject *__Pyx__Coroutine_New(
            PyTypeObject* type, __pyx_coroutine_body_t body, PyObject *code, PyObject *closure,
            PyObject *name, PyObject *qualname, PyObject *module_name) {
    __pyx_CoroutineObject *gen = PyObject_GC_New(__pyx_CoroutineObject, type);
    if (unlikely(!gen))
        return NULL;
    return __Pyx__Coroutine_NewInit(gen, body, code, closure, name, qualname, module_name);
}
static __pyx_CoroutineObject *__Pyx__Coroutine_NewInit(
            __pyx_CoroutineObject *gen, __pyx_coroutine_body_t body, PyObject *code, PyObject *closure,
            PyObject *name, PyObject *qualname, PyObject *module_name) {
    gen->body = body;
    gen->closure = closure;
    Py_XINCREF(closure);
    gen->is_running = 0;
    gen->resume_label = 0;
    gen->classobj = NULL;
    gen->yieldfrom = NULL;
    gen->gi_exc_state.exc_type = NULL;
    gen->gi_exc_state.exc_value = NULL;
    gen->gi_exc_state.exc_traceback = NULL;
#if CYTHON_USE_EXC_INFO_STACK
    gen->gi_exc_state.previous_item = NULL;
#endif
    gen->gi_weakreflist = NULL;
    Py_XINCREF(qualname);
    gen->gi_qualname = qualname;
    Py_XINCREF(name);
    gen->gi_name = name;
    Py_XINCREF(module_name);
    gen->gi_modulename = module_name;
    Py_XINCREF(code);
    gen->gi_code = code;
    PyObject_GC_Track(gen);
    return gen;
}
 
/* PatchModuleWithCoroutine */
static PyObject* __Pyx_Coroutine_patch_module(PyObject* module, const char* py_code) {
#if defined(__Pyx_Generator_USED) || defined(__Pyx_Coroutine_USED)
    int result;
    PyObject *globals, *result_obj;
    globals = PyDict_New();  if (unlikely(!globals)) goto ignore;
    result = PyDict_SetItemString(globals, "_cython_coroutine_type",
    #ifdef __Pyx_Coroutine_USED
        (PyObject*)__pyx_CoroutineType);
    #else
        Py_None);
    #endif
    if (unlikely(result < 0)) goto ignore;
    result = PyDict_SetItemString(globals, "_cython_generator_type",
    #ifdef __Pyx_Generator_USED
        (PyObject*)__pyx_GeneratorType);
    #else
        Py_None);
    #endif
    if (unlikely(result < 0)) goto ignore;
    if (unlikely(PyDict_SetItemString(globals, "_module", module) < 0)) goto ignore;
    if (unlikely(PyDict_SetItemString(globals, "__builtins__", __pyx_b) < 0)) goto ignore;
    result_obj = PyRun_String(py_code, Py_file_input, globals, globals);
    if (unlikely(!result_obj)) goto ignore;
    Py_DECREF(result_obj);
    Py_DECREF(globals);
    return module;
ignore:
    Py_XDECREF(globals);
    PyErr_WriteUnraisable(module);
    if (unlikely(PyErr_WarnEx(PyExc_RuntimeWarning, "Cython module failed to patch module with custom type", 1) < 0)) {
        Py_DECREF(module);
        module = NULL;
    }
#else
    py_code++;
#endif
    return module;
}
 
/* PatchGeneratorABC */
#ifndef CYTHON_REGISTER_ABCS
#define CYTHON_REGISTER_ABCS 1
#endif
#if defined(__Pyx_Generator_USED) || defined(__Pyx_Coroutine_USED)
static PyObject* __Pyx_patch_abc_module(PyObject *module);
static PyObject* __Pyx_patch_abc_module(PyObject *module) {
    module = __Pyx_Coroutine_patch_module(
        module, ""
"if _cython_generator_type is not None:\n"
"    try: Generator = _module.Generator\n"
"    except AttributeError: pass\n"
"    else: Generator.register(_cython_generator_type)\n"
"if _cython_coroutine_type is not None:\n"
"    try: Coroutine = _module.Coroutine\n"
"    except AttributeError: pass\n"
"    else: Coroutine.register(_cython_coroutine_type)\n"
    );
    return module;
}
#endif
static int __Pyx_patch_abc(void) {
#if defined(__Pyx_Generator_USED) || defined(__Pyx_Coroutine_USED)
    static int abc_patched = 0;
    if (CYTHON_REGISTER_ABCS && !abc_patched) {
        PyObject *module;
        module = PyImport_ImportModule((PY_MAJOR_VERSION >= 3) ? "collections.abc" : "collections");
        if (!module) {
            PyErr_WriteUnraisable(NULL);
            if (unlikely(PyErr_WarnEx(PyExc_RuntimeWarning,
                    ((PY_MAJOR_VERSION >= 3) ?
                        "Cython module failed to register with collections.abc module" :
                        "Cython module failed to register with collections module"), 1) < 0)) {
                return -1;
            }
        } else {
            module = __Pyx_patch_abc_module(module);
            abc_patched = 1;
            if (unlikely(!module))
                return -1;
            Py_DECREF(module);
        }
        module = PyImport_ImportModule("backports_abc");
        if (module) {
            module = __Pyx_patch_abc_module(module);
            Py_XDECREF(module);
        }
        if (!module) {
            PyErr_Clear();
        }
    }
#else
    if ((0)) __Pyx_Coroutine_patch_module(NULL, NULL);
#endif
    return 0;
}
 
/* Generator */
static PyMethodDef __pyx_Generator_methods[] = {
    {"send", (PyCFunction) __Pyx_Coroutine_Send, METH_O,
     (char*) PyDoc_STR("send(arg) -> send 'arg' into generator,\nreturn next yielded value or raise StopIteration.")},
    {"throw", (PyCFunction) __Pyx_Coroutine_Throw, METH_VARARGS,
     (char*) PyDoc_STR("throw(typ[,val[,tb]]) -> raise exception in generator,\nreturn next yielded value or raise StopIteration.")},
    {"close", (PyCFunction) __Pyx_Coroutine_Close_Method, METH_NOARGS,
     (char*) PyDoc_STR("close() -> raise GeneratorExit inside generator.")},
    {0, 0, 0, 0}
};
static PyMemberDef __pyx_Generator_memberlist[] = {
    {(char *) "gi_running", T_BOOL, offsetof(__pyx_CoroutineObject, is_running), READONLY, NULL},
    {(char*) "gi_yieldfrom", T_OBJECT, offsetof(__pyx_CoroutineObject, yieldfrom), READONLY,
     (char*) PyDoc_STR("object being iterated by 'yield from', or None")},
    {(char*) "gi_code", T_OBJECT, offsetof(__pyx_CoroutineObject, gi_code), READONLY, NULL},
    {0, 0, 0, 0, 0}
};
static PyGetSetDef __pyx_Generator_getsets[] = {
    {(char *) "__name__", (getter)__Pyx_Coroutine_get_name, (setter)__Pyx_Coroutine_set_name,
     (char*) PyDoc_STR("name of the generator"), 0},
    {(char *) "__qualname__", (getter)__Pyx_Coroutine_get_qualname, (setter)__Pyx_Coroutine_set_qualname,
     (char*) PyDoc_STR("qualified name of the generator"), 0},
    {0, 0, 0, 0, 0}
};
static PyTypeObject __pyx_GeneratorType_type = {
    PyVarObject_HEAD_INIT(0, 0)
    "generator",
    sizeof(__pyx_CoroutineObject),
    0,
    (destructor) __Pyx_Coroutine_dealloc,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC | Py_TPFLAGS_HAVE_FINALIZE,
    0,
    (traverseproc) __Pyx_Coroutine_traverse,
    0,
    0,
    offsetof(__pyx_CoroutineObject, gi_weakreflist),
    0,
    (iternextfunc) __Pyx_Generator_Next,
    __pyx_Generator_methods,
    __pyx_Generator_memberlist,
    __pyx_Generator_getsets,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
#if CYTHON_USE_TP_FINALIZE
    0,
#else
    __Pyx_Coroutine_del,
#endif
    0,
#if CYTHON_USE_TP_FINALIZE
    __Pyx_Coroutine_del,
#elif PY_VERSION_HEX >= 0x030400a1
    0,
#endif
#if PY_VERSION_HEX >= 0x030800b1
    0,
#endif
#if PY_VERSION_HEX >= 0x030800b4 && PY_VERSION_HEX < 0x03090000
    0,
#endif
};
static int __pyx_Generator_init(void) {
    __pyx_GeneratorType_type.tp_getattro = __Pyx_PyObject_GenericGetAttrNoDict;
    __pyx_GeneratorType_type.tp_iter = PyObject_SelfIter;
    __pyx_GeneratorType = __Pyx_FetchCommonType(&__pyx_GeneratorType_type);
    if (unlikely(!__pyx_GeneratorType)) {
        return -1;
    }
    return 0;
}
 
/* 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;
}
 
/* 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 CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject* x) {
    int retval;
    if (unlikely(!x)) return -1;
    retval = __Pyx_PyObject_IsTrue(x);
    Py_DECREF(x);
    return retval;
}
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(b);
  }
#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 */