glucat  0.8.2
PyClical.cpp
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1 /* Generated by Cython 0.29.6 */
2 
3 /* BEGIN: Cython Metadata
4 {
5  "distutils": {
6  "depends": [
7  "PyClical.h"
8  ],
9  "extra_compile_args": [
10  "-I.",
11  "-I..",
12  "-fno-strict-aliasing",
13  "-Wno-unused",
14  "-Wall",
15  "-std=c++11",
16  "-g",
17  "-O3",
18  "-O2",
19  "-Wall",
20  "-D_FORTIFY_SOURCE=2",
21  "-fstack-protector-strong",
22  "-funwind-tables",
23  "-fasynchronous-unwind-tables",
24  "-fstack-clash-protection",
25  "-g",
26  "-finline-limit=4000",
27  "--param",
28  "inline-unit-growth=200",
29  "-funroll-loops",
30  "-fvariable-expansion-in-unroller",
31  "-DNDEBUG",
32  "-DHAVE_BITS_WORDSIZE_H",
33  "-D_GLUCAT_USE_STD_UNORDERED_MAP",
34  "-D_GLUCAT_USE_DENSE_MATRICES",
35  "-D_GLUCAT_CHECK_ISNAN",
36  "-Wno-unused-local-typedefs",
37  "-Wno-misleading-indentation",
38  "-fno-check-new",
39  "-fexceptions"
40  ],
41  "include_dirs": [
42  ".",
43  ".."
44  ],
45  "language": "c++",
46  "name": "PyClical",
47  "sources": [
48  "PyClical.pyx"
49  ]
50  },
51  "module_name": "PyClical"
52 }
53 END: Cython Metadata */
54 
55 #define PY_SSIZE_T_CLEAN
56 #include "Python.h"
57 #ifndef Py_PYTHON_H
58  #error Python headers needed to compile C extensions, please install development version of Python.
59 #elif PY_VERSION_HEX < 0x02060000 || (0x03000000 <= PY_VERSION_HEX && PY_VERSION_HEX < 0x03030000)
60  #error Cython requires Python 2.6+ or Python 3.3+.
61 #else
62 #define CYTHON_ABI "0_29_6"
63 #define CYTHON_HEX_VERSION 0x001D06F0
64 #define CYTHON_FUTURE_DIVISION 0
65 #include <stddef.h>
66 #ifndef offsetof
67  #define offsetof(type, member) ( (size_t) & ((type*)0) -> member )
68 #endif
69 #if !defined(WIN32) && !defined(MS_WINDOWS)
70  #ifndef __stdcall
71  #define __stdcall
72  #endif
73  #ifndef __cdecl
74  #define __cdecl
75  #endif
76  #ifndef __fastcall
77  #define __fastcall
78  #endif
79 #endif
80 #ifndef DL_IMPORT
81  #define DL_IMPORT(t) t
82 #endif
83 #ifndef DL_EXPORT
84  #define DL_EXPORT(t) t
85 #endif
86 #define __PYX_COMMA ,
87 #ifndef HAVE_LONG_LONG
88  #if PY_VERSION_HEX >= 0x02070000
89  #define HAVE_LONG_LONG
90  #endif
91 #endif
92 #ifndef PY_LONG_LONG
93  #define PY_LONG_LONG LONG_LONG
94 #endif
95 #ifndef Py_HUGE_VAL
96  #define Py_HUGE_VAL HUGE_VAL
97 #endif
98 #ifdef PYPY_VERSION
99  #define CYTHON_COMPILING_IN_PYPY 1
100  #define CYTHON_COMPILING_IN_PYSTON 0
101  #define CYTHON_COMPILING_IN_CPYTHON 0
102  #undef CYTHON_USE_TYPE_SLOTS
103  #define CYTHON_USE_TYPE_SLOTS 0
104  #undef CYTHON_USE_PYTYPE_LOOKUP
105  #define CYTHON_USE_PYTYPE_LOOKUP 0
106  #if PY_VERSION_HEX < 0x03050000
107  #undef CYTHON_USE_ASYNC_SLOTS
108  #define CYTHON_USE_ASYNC_SLOTS 0
109  #elif !defined(CYTHON_USE_ASYNC_SLOTS)
110  #define CYTHON_USE_ASYNC_SLOTS 1
111  #endif
112  #undef CYTHON_USE_PYLIST_INTERNALS
113  #define CYTHON_USE_PYLIST_INTERNALS 0
114  #undef CYTHON_USE_UNICODE_INTERNALS
115  #define CYTHON_USE_UNICODE_INTERNALS 0
116  #undef CYTHON_USE_UNICODE_WRITER
117  #define CYTHON_USE_UNICODE_WRITER 0
118  #undef CYTHON_USE_PYLONG_INTERNALS
119  #define CYTHON_USE_PYLONG_INTERNALS 0
120  #undef CYTHON_AVOID_BORROWED_REFS
121  #define CYTHON_AVOID_BORROWED_REFS 1
122  #undef CYTHON_ASSUME_SAFE_MACROS
123  #define CYTHON_ASSUME_SAFE_MACROS 0
124  #undef CYTHON_UNPACK_METHODS
125  #define CYTHON_UNPACK_METHODS 0
126  #undef CYTHON_FAST_THREAD_STATE
127  #define CYTHON_FAST_THREAD_STATE 0
128  #undef CYTHON_FAST_PYCALL
129  #define CYTHON_FAST_PYCALL 0
130  #undef CYTHON_PEP489_MULTI_PHASE_INIT
131  #define CYTHON_PEP489_MULTI_PHASE_INIT 0
132  #undef CYTHON_USE_TP_FINALIZE
133  #define CYTHON_USE_TP_FINALIZE 0
134  #undef CYTHON_USE_DICT_VERSIONS
135  #define CYTHON_USE_DICT_VERSIONS 0
136  #undef CYTHON_USE_EXC_INFO_STACK
137  #define CYTHON_USE_EXC_INFO_STACK 0
138 #elif defined(PYSTON_VERSION)
139  #define CYTHON_COMPILING_IN_PYPY 0
140  #define CYTHON_COMPILING_IN_PYSTON 1
141  #define CYTHON_COMPILING_IN_CPYTHON 0
142  #ifndef CYTHON_USE_TYPE_SLOTS
143  #define CYTHON_USE_TYPE_SLOTS 1
144  #endif
145  #undef CYTHON_USE_PYTYPE_LOOKUP
146  #define CYTHON_USE_PYTYPE_LOOKUP 0
147  #undef CYTHON_USE_ASYNC_SLOTS
148  #define CYTHON_USE_ASYNC_SLOTS 0
149  #undef CYTHON_USE_PYLIST_INTERNALS
150  #define CYTHON_USE_PYLIST_INTERNALS 0
151  #ifndef CYTHON_USE_UNICODE_INTERNALS
152  #define CYTHON_USE_UNICODE_INTERNALS 1
153  #endif
154  #undef CYTHON_USE_UNICODE_WRITER
155  #define CYTHON_USE_UNICODE_WRITER 0
156  #undef CYTHON_USE_PYLONG_INTERNALS
157  #define CYTHON_USE_PYLONG_INTERNALS 0
158  #ifndef CYTHON_AVOID_BORROWED_REFS
159  #define CYTHON_AVOID_BORROWED_REFS 0
160  #endif
161  #ifndef CYTHON_ASSUME_SAFE_MACROS
162  #define CYTHON_ASSUME_SAFE_MACROS 1
163  #endif
164  #ifndef CYTHON_UNPACK_METHODS
165  #define CYTHON_UNPACK_METHODS 1
166  #endif
167  #undef CYTHON_FAST_THREAD_STATE
168  #define CYTHON_FAST_THREAD_STATE 0
169  #undef CYTHON_FAST_PYCALL
170  #define CYTHON_FAST_PYCALL 0
171  #undef CYTHON_PEP489_MULTI_PHASE_INIT
172  #define CYTHON_PEP489_MULTI_PHASE_INIT 0
173  #undef CYTHON_USE_TP_FINALIZE
174  #define CYTHON_USE_TP_FINALIZE 0
175  #undef CYTHON_USE_DICT_VERSIONS
176  #define CYTHON_USE_DICT_VERSIONS 0
177  #undef CYTHON_USE_EXC_INFO_STACK
178  #define CYTHON_USE_EXC_INFO_STACK 0
179 #else
180  #define CYTHON_COMPILING_IN_PYPY 0
181  #define CYTHON_COMPILING_IN_PYSTON 0
182  #define CYTHON_COMPILING_IN_CPYTHON 1
183  #ifndef CYTHON_USE_TYPE_SLOTS
184  #define CYTHON_USE_TYPE_SLOTS 1
185  #endif
186  #if PY_VERSION_HEX < 0x02070000
187  #undef CYTHON_USE_PYTYPE_LOOKUP
188  #define CYTHON_USE_PYTYPE_LOOKUP 0
189  #elif !defined(CYTHON_USE_PYTYPE_LOOKUP)
190  #define CYTHON_USE_PYTYPE_LOOKUP 1
191  #endif
192  #if PY_MAJOR_VERSION < 3
193  #undef CYTHON_USE_ASYNC_SLOTS
194  #define CYTHON_USE_ASYNC_SLOTS 0
195  #elif !defined(CYTHON_USE_ASYNC_SLOTS)
196  #define CYTHON_USE_ASYNC_SLOTS 1
197  #endif
198  #if PY_VERSION_HEX < 0x02070000
199  #undef CYTHON_USE_PYLONG_INTERNALS
200  #define CYTHON_USE_PYLONG_INTERNALS 0
201  #elif !defined(CYTHON_USE_PYLONG_INTERNALS)
202  #define CYTHON_USE_PYLONG_INTERNALS 1
203  #endif
204  #ifndef CYTHON_USE_PYLIST_INTERNALS
205  #define CYTHON_USE_PYLIST_INTERNALS 1
206  #endif
207  #ifndef CYTHON_USE_UNICODE_INTERNALS
208  #define CYTHON_USE_UNICODE_INTERNALS 1
209  #endif
210  #if PY_VERSION_HEX < 0x030300F0
211  #undef CYTHON_USE_UNICODE_WRITER
212  #define CYTHON_USE_UNICODE_WRITER 0
213  #elif !defined(CYTHON_USE_UNICODE_WRITER)
214  #define CYTHON_USE_UNICODE_WRITER 1
215  #endif
216  #ifndef CYTHON_AVOID_BORROWED_REFS
217  #define CYTHON_AVOID_BORROWED_REFS 0
218  #endif
219  #ifndef CYTHON_ASSUME_SAFE_MACROS
220  #define CYTHON_ASSUME_SAFE_MACROS 1
221  #endif
222  #ifndef CYTHON_UNPACK_METHODS
223  #define CYTHON_UNPACK_METHODS 1
224  #endif
225  #ifndef CYTHON_FAST_THREAD_STATE
226  #define CYTHON_FAST_THREAD_STATE 1
227  #endif
228  #ifndef CYTHON_FAST_PYCALL
229  #define CYTHON_FAST_PYCALL 1
230  #endif
231  #ifndef CYTHON_PEP489_MULTI_PHASE_INIT
232  #define CYTHON_PEP489_MULTI_PHASE_INIT (PY_VERSION_HEX >= 0x03050000)
233  #endif
234  #ifndef CYTHON_USE_TP_FINALIZE
235  #define CYTHON_USE_TP_FINALIZE (PY_VERSION_HEX >= 0x030400a1)
236  #endif
237  #ifndef CYTHON_USE_DICT_VERSIONS
238  #define CYTHON_USE_DICT_VERSIONS (PY_VERSION_HEX >= 0x030600B1)
239  #endif
240  #ifndef CYTHON_USE_EXC_INFO_STACK
241  #define CYTHON_USE_EXC_INFO_STACK (PY_VERSION_HEX >= 0x030700A3)
242  #endif
243 #endif
244 #if !defined(CYTHON_FAST_PYCCALL)
245 #define CYTHON_FAST_PYCCALL (CYTHON_FAST_PYCALL && PY_VERSION_HEX >= 0x030600B1)
246 #endif
247 #if CYTHON_USE_PYLONG_INTERNALS
248  #include "longintrepr.h"
249  #undef SHIFT
250  #undef BASE
251  #undef MASK
252  #ifdef SIZEOF_VOID_P
253  enum { __pyx_check_sizeof_voidp = 1 / (int)(SIZEOF_VOID_P == sizeof(void*)) };
254  #endif
255 #endif
256 #ifndef __has_attribute
257  #define __has_attribute(x) 0
258 #endif
259 #ifndef __has_cpp_attribute
260  #define __has_cpp_attribute(x) 0
261 #endif
262 #ifndef CYTHON_RESTRICT
263  #if defined(__GNUC__)
264  #define CYTHON_RESTRICT __restrict__
265  #elif defined(_MSC_VER) && _MSC_VER >= 1400
266  #define CYTHON_RESTRICT __restrict
267  #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
268  #define CYTHON_RESTRICT restrict
269  #else
270  #define CYTHON_RESTRICT
271  #endif
272 #endif
273 #ifndef CYTHON_UNUSED
274 # if defined(__GNUC__)
275 # if !(defined(__cplusplus)) || (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 4))
276 # define CYTHON_UNUSED __attribute__ ((__unused__))
277 # else
278 # define CYTHON_UNUSED
279 # endif
280 # elif defined(__ICC) || (defined(__INTEL_COMPILER) && !defined(_MSC_VER))
281 # define CYTHON_UNUSED __attribute__ ((__unused__))
282 # else
283 # define CYTHON_UNUSED
284 # endif
285 #endif
286 #ifndef CYTHON_MAYBE_UNUSED_VAR
287 # if defined(__cplusplus)
288  template<class T> void CYTHON_MAYBE_UNUSED_VAR( const T& ) { }
289 # else
290 # define CYTHON_MAYBE_UNUSED_VAR(x) (void)(x)
291 # endif
292 #endif
293 #ifndef CYTHON_NCP_UNUSED
294 # if CYTHON_COMPILING_IN_CPYTHON
295 # define CYTHON_NCP_UNUSED
296 # else
297 # define CYTHON_NCP_UNUSED CYTHON_UNUSED
298 # endif
299 #endif
300 #define __Pyx_void_to_None(void_result) ((void)(void_result), Py_INCREF(Py_None), Py_None)
301 #ifdef _MSC_VER
302  #ifndef _MSC_STDINT_H_
303  #if _MSC_VER < 1300
304  typedef unsigned char uint8_t;
305  typedef unsigned int uint32_t;
306  #else
307  typedef unsigned __int8 uint8_t;
308  typedef unsigned __int32 uint32_t;
309  #endif
310  #endif
311 #else
312  #include <stdint.h>
313 #endif
314 #ifndef CYTHON_FALLTHROUGH
315  #if defined(__cplusplus) && __cplusplus >= 201103L
316  #if __has_cpp_attribute(fallthrough)
317  #define CYTHON_FALLTHROUGH [[fallthrough]]
318  #elif __has_cpp_attribute(clang::fallthrough)
319  #define CYTHON_FALLTHROUGH [[clang::fallthrough]]
320  #elif __has_cpp_attribute(gnu::fallthrough)
321  #define CYTHON_FALLTHROUGH [[gnu::fallthrough]]
322  #endif
323  #endif
324  #ifndef CYTHON_FALLTHROUGH
325  #if __has_attribute(fallthrough)
326  #define CYTHON_FALLTHROUGH __attribute__((fallthrough))
327  #else
328  #define CYTHON_FALLTHROUGH
329  #endif
330  #endif
331  #if defined(__clang__ ) && defined(__apple_build_version__)
332  #if __apple_build_version__ < 7000000
333  #undef CYTHON_FALLTHROUGH
334  #define CYTHON_FALLTHROUGH
335  #endif
336  #endif
337 #endif
338 
339 #ifndef __cplusplus
340  #error "Cython files generated with the C++ option must be compiled with a C++ compiler."
341 #endif
342 #ifndef CYTHON_INLINE
343  #if defined(__clang__)
344  #define CYTHON_INLINE __inline__ __attribute__ ((__unused__))
345  #else
346  #define CYTHON_INLINE inline
347  #endif
348 #endif
349 template<typename T>
350 void __Pyx_call_destructor(T& x) {
351  x.~T();
352 }
353 template<typename T>
354 class __Pyx_FakeReference {
355  public:
356  __Pyx_FakeReference() : ptr(NULL) { }
357  __Pyx_FakeReference(const T& ref) : ptr(const_cast<T*>(&ref)) { }
358  T *operator->() { return ptr; }
359  T *operator&() { return ptr; }
360  operator T&() { return *ptr; }
361  template<typename U> bool operator ==(U other) { return *ptr == other; }
362  template<typename U> bool operator !=(U other) { return *ptr != other; }
363  private:
364  T *ptr;
365 };
366 
367 #if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x02070600 && !defined(Py_OptimizeFlag)
368  #define Py_OptimizeFlag 0
369 #endif
370 #define __PYX_BUILD_PY_SSIZE_T "n"
371 #define CYTHON_FORMAT_SSIZE_T "z"
372 #if PY_MAJOR_VERSION < 3
373  #define __Pyx_BUILTIN_MODULE_NAME "__builtin__"
374  #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
375  PyCode_New(a+k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)
376  #define __Pyx_DefaultClassType PyClass_Type
377 #else
378  #define __Pyx_BUILTIN_MODULE_NAME "builtins"
379  #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
380  PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)
381  #define __Pyx_DefaultClassType PyType_Type
382 #endif
383 #ifndef Py_TPFLAGS_CHECKTYPES
384  #define Py_TPFLAGS_CHECKTYPES 0
385 #endif
386 #ifndef Py_TPFLAGS_HAVE_INDEX
387  #define Py_TPFLAGS_HAVE_INDEX 0
388 #endif
389 #ifndef Py_TPFLAGS_HAVE_NEWBUFFER
390  #define Py_TPFLAGS_HAVE_NEWBUFFER 0
391 #endif
392 #ifndef Py_TPFLAGS_HAVE_FINALIZE
393  #define Py_TPFLAGS_HAVE_FINALIZE 0
394 #endif
395 #ifndef METH_STACKLESS
396  #define METH_STACKLESS 0
397 #endif
398 #if PY_VERSION_HEX <= 0x030700A3 || !defined(METH_FASTCALL)
399  #ifndef METH_FASTCALL
400  #define METH_FASTCALL 0x80
401  #endif
402  typedef PyObject *(*__Pyx_PyCFunctionFast) (PyObject *self, PyObject *const *args, Py_ssize_t nargs);
403  typedef PyObject *(*__Pyx_PyCFunctionFastWithKeywords) (PyObject *self, PyObject *const *args,
404  Py_ssize_t nargs, PyObject *kwnames);
405 #else
406  #define __Pyx_PyCFunctionFast _PyCFunctionFast
407  #define __Pyx_PyCFunctionFastWithKeywords _PyCFunctionFastWithKeywords
408 #endif
409 #if CYTHON_FAST_PYCCALL
410 #define __Pyx_PyFastCFunction_Check(func)\
411  ((PyCFunction_Check(func) && (METH_FASTCALL == (PyCFunction_GET_FLAGS(func) & ~(METH_CLASS | METH_STATIC | METH_COEXIST | METH_KEYWORDS | METH_STACKLESS)))))
412 #else
413 #define __Pyx_PyFastCFunction_Check(func) 0
414 #endif
415 #if CYTHON_COMPILING_IN_PYPY && !defined(PyObject_Malloc)
416  #define PyObject_Malloc(s) PyMem_Malloc(s)
417  #define PyObject_Free(p) PyMem_Free(p)
418  #define PyObject_Realloc(p) PyMem_Realloc(p)
419 #endif
420 #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX < 0x030400A1
421  #define PyMem_RawMalloc(n) PyMem_Malloc(n)
422  #define PyMem_RawRealloc(p, n) PyMem_Realloc(p, n)
423  #define PyMem_RawFree(p) PyMem_Free(p)
424 #endif
425 #if CYTHON_COMPILING_IN_PYSTON
426  #define __Pyx_PyCode_HasFreeVars(co) PyCode_HasFreeVars(co)
427  #define __Pyx_PyFrame_SetLineNumber(frame, lineno) PyFrame_SetLineNumber(frame, lineno)
428 #else
429  #define __Pyx_PyCode_HasFreeVars(co) (PyCode_GetNumFree(co) > 0)
430  #define __Pyx_PyFrame_SetLineNumber(frame, lineno) (frame)->f_lineno = (lineno)
431 #endif
432 #if !CYTHON_FAST_THREAD_STATE || PY_VERSION_HEX < 0x02070000
433  #define __Pyx_PyThreadState_Current PyThreadState_GET()
434 #elif PY_VERSION_HEX >= 0x03060000
435  #define __Pyx_PyThreadState_Current _PyThreadState_UncheckedGet()
436 #elif PY_VERSION_HEX >= 0x03000000
437  #define __Pyx_PyThreadState_Current PyThreadState_GET()
438 #else
439  #define __Pyx_PyThreadState_Current _PyThreadState_Current
440 #endif
441 #if PY_VERSION_HEX < 0x030700A2 && !defined(PyThread_tss_create) && !defined(Py_tss_NEEDS_INIT)
442 #include "pythread.h"
443 #define Py_tss_NEEDS_INIT 0
444 typedef int Py_tss_t;
445 static CYTHON_INLINE int PyThread_tss_create(Py_tss_t *key) {
446  *key = PyThread_create_key();
447  return 0;
448 }
449 static CYTHON_INLINE Py_tss_t * PyThread_tss_alloc(void) {
450  Py_tss_t *key = (Py_tss_t *)PyObject_Malloc(sizeof(Py_tss_t));
451  *key = Py_tss_NEEDS_INIT;
452  return key;
453 }
454 static CYTHON_INLINE void PyThread_tss_free(Py_tss_t *key) {
455  PyObject_Free(key);
456 }
457 static CYTHON_INLINE int PyThread_tss_is_created(Py_tss_t *key) {
458  return *key != Py_tss_NEEDS_INIT;
459 }
460 static CYTHON_INLINE void PyThread_tss_delete(Py_tss_t *key) {
461  PyThread_delete_key(*key);
462  *key = Py_tss_NEEDS_INIT;
463 }
464 static CYTHON_INLINE int PyThread_tss_set(Py_tss_t *key, void *value) {
465  return PyThread_set_key_value(*key, value);
466 }
467 static CYTHON_INLINE void * PyThread_tss_get(Py_tss_t *key) {
468  return PyThread_get_key_value(*key);
469 }
470 #endif
471 #if CYTHON_COMPILING_IN_CPYTHON || defined(_PyDict_NewPresized)
472 #define __Pyx_PyDict_NewPresized(n) ((n <= 8) ? PyDict_New() : _PyDict_NewPresized(n))
473 #else
474 #define __Pyx_PyDict_NewPresized(n) PyDict_New()
475 #endif
476 #if PY_MAJOR_VERSION >= 3 || CYTHON_FUTURE_DIVISION
477  #define __Pyx_PyNumber_Divide(x,y) PyNumber_TrueDivide(x,y)
478  #define __Pyx_PyNumber_InPlaceDivide(x,y) PyNumber_InPlaceTrueDivide(x,y)
479 #else
480  #define __Pyx_PyNumber_Divide(x,y) PyNumber_Divide(x,y)
481  #define __Pyx_PyNumber_InPlaceDivide(x,y) PyNumber_InPlaceDivide(x,y)
482 #endif
483 #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030500A1 && CYTHON_USE_UNICODE_INTERNALS
484 #define __Pyx_PyDict_GetItemStr(dict, name) _PyDict_GetItem_KnownHash(dict, name, ((PyASCIIObject *) name)->hash)
485 #else
486 #define __Pyx_PyDict_GetItemStr(dict, name) PyDict_GetItem(dict, name)
487 #endif
488 #if PY_VERSION_HEX > 0x03030000 && defined(PyUnicode_KIND)
489  #define CYTHON_PEP393_ENABLED 1
490  #define __Pyx_PyUnicode_READY(op) (likely(PyUnicode_IS_READY(op)) ?\
491  0 : _PyUnicode_Ready((PyObject *)(op)))
492  #define __Pyx_PyUnicode_GET_LENGTH(u) PyUnicode_GET_LENGTH(u)
493  #define __Pyx_PyUnicode_READ_CHAR(u, i) PyUnicode_READ_CHAR(u, i)
494  #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u) PyUnicode_MAX_CHAR_VALUE(u)
495  #define __Pyx_PyUnicode_KIND(u) PyUnicode_KIND(u)
496  #define __Pyx_PyUnicode_DATA(u) PyUnicode_DATA(u)
497  #define __Pyx_PyUnicode_READ(k, d, i) PyUnicode_READ(k, d, i)
498  #define __Pyx_PyUnicode_WRITE(k, d, i, ch) PyUnicode_WRITE(k, d, i, ch)
499  #define __Pyx_PyUnicode_IS_TRUE(u) (0 != (likely(PyUnicode_IS_READY(u)) ? PyUnicode_GET_LENGTH(u) : PyUnicode_GET_SIZE(u)))
500 #else
501  #define CYTHON_PEP393_ENABLED 0
502  #define PyUnicode_1BYTE_KIND 1
503  #define PyUnicode_2BYTE_KIND 2
504  #define PyUnicode_4BYTE_KIND 4
505  #define __Pyx_PyUnicode_READY(op) (0)
506  #define __Pyx_PyUnicode_GET_LENGTH(u) PyUnicode_GET_SIZE(u)
507  #define __Pyx_PyUnicode_READ_CHAR(u, i) ((Py_UCS4)(PyUnicode_AS_UNICODE(u)[i]))
508  #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u) ((sizeof(Py_UNICODE) == 2) ? 65535 : 1114111)
509  #define __Pyx_PyUnicode_KIND(u) (sizeof(Py_UNICODE))
510  #define __Pyx_PyUnicode_DATA(u) ((void*)PyUnicode_AS_UNICODE(u))
511  #define __Pyx_PyUnicode_READ(k, d, i) ((void)(k), (Py_UCS4)(((Py_UNICODE*)d)[i]))
512  #define __Pyx_PyUnicode_WRITE(k, d, i, ch) (((void)(k)), ((Py_UNICODE*)d)[i] = ch)
513  #define __Pyx_PyUnicode_IS_TRUE(u) (0 != PyUnicode_GET_SIZE(u))
514 #endif
515 #if CYTHON_COMPILING_IN_PYPY
516  #define __Pyx_PyUnicode_Concat(a, b) PyNumber_Add(a, b)
517  #define __Pyx_PyUnicode_ConcatSafe(a, b) PyNumber_Add(a, b)
518 #else
519  #define __Pyx_PyUnicode_Concat(a, b) PyUnicode_Concat(a, b)
520  #define __Pyx_PyUnicode_ConcatSafe(a, b) ((unlikely((a) == Py_None) || unlikely((b) == Py_None)) ?\
521  PyNumber_Add(a, b) : __Pyx_PyUnicode_Concat(a, b))
522 #endif
523 #if CYTHON_COMPILING_IN_PYPY && !defined(PyUnicode_Contains)
524  #define PyUnicode_Contains(u, s) PySequence_Contains(u, s)
525 #endif
526 #if CYTHON_COMPILING_IN_PYPY && !defined(PyByteArray_Check)
527  #define PyByteArray_Check(obj) PyObject_TypeCheck(obj, &PyByteArray_Type)
528 #endif
529 #if CYTHON_COMPILING_IN_PYPY && !defined(PyObject_Format)
530  #define PyObject_Format(obj, fmt) PyObject_CallMethod(obj, "__format__", "O", fmt)
531 #endif
532 #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))
533 #define __Pyx_PyUnicode_FormatSafe(a, b) ((unlikely((a) == Py_None || (PyUnicode_Check(b) && !PyUnicode_CheckExact(b)))) ? PyNumber_Remainder(a, b) : PyUnicode_Format(a, b))
534 #if PY_MAJOR_VERSION >= 3
535  #define __Pyx_PyString_Format(a, b) PyUnicode_Format(a, b)
536 #else
537  #define __Pyx_PyString_Format(a, b) PyString_Format(a, b)
538 #endif
539 #if PY_MAJOR_VERSION < 3 && !defined(PyObject_ASCII)
540  #define PyObject_ASCII(o) PyObject_Repr(o)
541 #endif
542 #if PY_MAJOR_VERSION >= 3
543  #define PyBaseString_Type PyUnicode_Type
544  #define PyStringObject PyUnicodeObject
545  #define PyString_Type PyUnicode_Type
546  #define PyString_Check PyUnicode_Check
547  #define PyString_CheckExact PyUnicode_CheckExact
548  #define PyObject_Unicode PyObject_Str
549 #endif
550 #if PY_MAJOR_VERSION >= 3
551  #define __Pyx_PyBaseString_Check(obj) PyUnicode_Check(obj)
552  #define __Pyx_PyBaseString_CheckExact(obj) PyUnicode_CheckExact(obj)
553 #else
554  #define __Pyx_PyBaseString_Check(obj) (PyString_Check(obj) || PyUnicode_Check(obj))
555  #define __Pyx_PyBaseString_CheckExact(obj) (PyString_CheckExact(obj) || PyUnicode_CheckExact(obj))
556 #endif
557 #ifndef PySet_CheckExact
558  #define PySet_CheckExact(obj) (Py_TYPE(obj) == &PySet_Type)
559 #endif
560 #if CYTHON_ASSUME_SAFE_MACROS
561  #define __Pyx_PySequence_SIZE(seq) Py_SIZE(seq)
562 #else
563  #define __Pyx_PySequence_SIZE(seq) PySequence_Size(seq)
564 #endif
565 #if PY_MAJOR_VERSION >= 3
566  #define PyIntObject PyLongObject
567  #define PyInt_Type PyLong_Type
568  #define PyInt_Check(op) PyLong_Check(op)
569  #define PyInt_CheckExact(op) PyLong_CheckExact(op)
570  #define PyInt_FromString PyLong_FromString
571  #define PyInt_FromUnicode PyLong_FromUnicode
572  #define PyInt_FromLong PyLong_FromLong
573  #define PyInt_FromSize_t PyLong_FromSize_t
574  #define PyInt_FromSsize_t PyLong_FromSsize_t
575  #define PyInt_AsLong PyLong_AsLong
576  #define PyInt_AS_LONG PyLong_AS_LONG
577  #define PyInt_AsSsize_t PyLong_AsSsize_t
578  #define PyInt_AsUnsignedLongMask PyLong_AsUnsignedLongMask
579  #define PyInt_AsUnsignedLongLongMask PyLong_AsUnsignedLongLongMask
580  #define PyNumber_Int PyNumber_Long
581 #endif
582 #if PY_MAJOR_VERSION >= 3
583  #define PyBoolObject PyLongObject
584 #endif
585 #if PY_MAJOR_VERSION >= 3 && CYTHON_COMPILING_IN_PYPY
586  #ifndef PyUnicode_InternFromString
587  #define PyUnicode_InternFromString(s) PyUnicode_FromString(s)
588  #endif
589 #endif
590 #if PY_VERSION_HEX < 0x030200A4
591  typedef long Py_hash_t;
592  #define __Pyx_PyInt_FromHash_t PyInt_FromLong
593  #define __Pyx_PyInt_AsHash_t PyInt_AsLong
594 #else
595  #define __Pyx_PyInt_FromHash_t PyInt_FromSsize_t
596  #define __Pyx_PyInt_AsHash_t PyInt_AsSsize_t
597 #endif
598 #if PY_MAJOR_VERSION >= 3
599  #define __Pyx_PyMethod_New(func, self, klass) ((self) ? PyMethod_New(func, self) : (Py_INCREF(func), func))
600 #else
601  #define __Pyx_PyMethod_New(func, self, klass) PyMethod_New(func, self, klass)
602 #endif
603 #if CYTHON_USE_ASYNC_SLOTS
604  #if PY_VERSION_HEX >= 0x030500B1
605  #define __Pyx_PyAsyncMethodsStruct PyAsyncMethods
606  #define __Pyx_PyType_AsAsync(obj) (Py_TYPE(obj)->tp_as_async)
607  #else
608  #define __Pyx_PyType_AsAsync(obj) ((__Pyx_PyAsyncMethodsStruct*) (Py_TYPE(obj)->tp_reserved))
609  #endif
610 #else
611  #define __Pyx_PyType_AsAsync(obj) NULL
612 #endif
613 #ifndef __Pyx_PyAsyncMethodsStruct
614  typedef struct {
615  unaryfunc am_await;
616  unaryfunc am_aiter;
617  unaryfunc am_anext;
618  } __Pyx_PyAsyncMethodsStruct;
619 #endif
620 
621 #if defined(WIN32) || defined(MS_WINDOWS)
622  #define _USE_MATH_DEFINES
623 #endif
624 #include <math.h>
625 #ifdef NAN
626 #define __PYX_NAN() ((float) NAN)
627 #else
628 static CYTHON_INLINE float __PYX_NAN() {
629  float value;
630  memset(&value, 0xFF, sizeof(value));
631  return value;
632 }
633 #endif
634 #if defined(__CYGWIN__) && defined(_LDBL_EQ_DBL)
635 #define __Pyx_truncl trunc
636 #else
637 #define __Pyx_truncl truncl
638 #endif
639 
640 
641 #define __PYX_ERR(f_index, lineno, Ln_error) \
642 { \
643  __pyx_filename = __pyx_f[f_index]; __pyx_lineno = lineno; __pyx_clineno = __LINE__; goto Ln_error; \
644 }
645 
646 #ifndef __PYX_EXTERN_C
647  #ifdef __cplusplus
648  #define __PYX_EXTERN_C extern "C"
649  #else
650  #define __PYX_EXTERN_C extern
651  #endif
652 #endif
653 
654 #define __PYX_HAVE__PyClical
655 #define __PYX_HAVE_API__PyClical
656 /* Early includes */
657 #include "ios"
658 #include "new"
659 #include "stdexcept"
660 #include "typeinfo"
661 #include <vector>
662 #include "PyClical.h"
663 #ifdef _OPENMP
664 #include <omp.h>
665 #endif /* _OPENMP */
666 
667 #if defined(PYREX_WITHOUT_ASSERTIONS) && !defined(CYTHON_WITHOUT_ASSERTIONS)
668 #define CYTHON_WITHOUT_ASSERTIONS
669 #endif
670 
671 typedef struct {PyObject **p; const char *s; const Py_ssize_t n; const char* encoding;
672  const char is_unicode; const char is_str; const char intern; } __Pyx_StringTabEntry;
673 
674 #define __PYX_DEFAULT_STRING_ENCODING_IS_ASCII 0
675 #define __PYX_DEFAULT_STRING_ENCODING_IS_UTF8 0
676 #define __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT (PY_MAJOR_VERSION >= 3 && __PYX_DEFAULT_STRING_ENCODING_IS_UTF8)
677 #define __PYX_DEFAULT_STRING_ENCODING ""
678 #define __Pyx_PyObject_FromString __Pyx_PyBytes_FromString
679 #define __Pyx_PyObject_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
680 #define __Pyx_uchar_cast(c) ((unsigned char)c)
681 #define __Pyx_long_cast(x) ((long)x)
682 #define __Pyx_fits_Py_ssize_t(v, type, is_signed) (\
683  (sizeof(type) < sizeof(Py_ssize_t)) ||\
684  (sizeof(type) > sizeof(Py_ssize_t) &&\
685  likely(v < (type)PY_SSIZE_T_MAX ||\
686  v == (type)PY_SSIZE_T_MAX) &&\
687  (!is_signed || likely(v > (type)PY_SSIZE_T_MIN ||\
688  v == (type)PY_SSIZE_T_MIN))) ||\
689  (sizeof(type) == sizeof(Py_ssize_t) &&\
690  (is_signed || likely(v < (type)PY_SSIZE_T_MAX ||\
691  v == (type)PY_SSIZE_T_MAX))) )
692 static CYTHON_INLINE int __Pyx_is_valid_index(Py_ssize_t i, Py_ssize_t limit) {
693  return (size_t) i < (size_t) limit;
694 }
695 #if defined (__cplusplus) && __cplusplus >= 201103L
696  #include <cstdlib>
697  #define __Pyx_sst_abs(value) std::abs(value)
698 #elif SIZEOF_INT >= SIZEOF_SIZE_T
699  #define __Pyx_sst_abs(value) abs(value)
700 #elif SIZEOF_LONG >= SIZEOF_SIZE_T
701  #define __Pyx_sst_abs(value) labs(value)
702 #elif defined (_MSC_VER)
703  #define __Pyx_sst_abs(value) ((Py_ssize_t)_abs64(value))
704 #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
705  #define __Pyx_sst_abs(value) llabs(value)
706 #elif defined (__GNUC__)
707  #define __Pyx_sst_abs(value) __builtin_llabs(value)
708 #else
709  #define __Pyx_sst_abs(value) ((value<0) ? -value : value)
710 #endif
711 static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject*);
712 static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject*, Py_ssize_t* length);
713 #define __Pyx_PyByteArray_FromString(s) PyByteArray_FromStringAndSize((const char*)s, strlen((const char*)s))
714 #define __Pyx_PyByteArray_FromStringAndSize(s, l) PyByteArray_FromStringAndSize((const char*)s, l)
715 #define __Pyx_PyBytes_FromString PyBytes_FromString
716 #define __Pyx_PyBytes_FromStringAndSize PyBytes_FromStringAndSize
717 static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char*);
718 #if PY_MAJOR_VERSION < 3
719  #define __Pyx_PyStr_FromString __Pyx_PyBytes_FromString
720  #define __Pyx_PyStr_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
721 #else
722  #define __Pyx_PyStr_FromString __Pyx_PyUnicode_FromString
723  #define __Pyx_PyStr_FromStringAndSize __Pyx_PyUnicode_FromStringAndSize
724 #endif
725 #define __Pyx_PyBytes_AsWritableString(s) ((char*) PyBytes_AS_STRING(s))
726 #define __Pyx_PyBytes_AsWritableSString(s) ((signed char*) PyBytes_AS_STRING(s))
727 #define __Pyx_PyBytes_AsWritableUString(s) ((unsigned char*) PyBytes_AS_STRING(s))
728 #define __Pyx_PyBytes_AsString(s) ((const char*) PyBytes_AS_STRING(s))
729 #define __Pyx_PyBytes_AsSString(s) ((const signed char*) PyBytes_AS_STRING(s))
730 #define __Pyx_PyBytes_AsUString(s) ((const unsigned char*) PyBytes_AS_STRING(s))
731 #define __Pyx_PyObject_AsWritableString(s) ((char*) __Pyx_PyObject_AsString(s))
732 #define __Pyx_PyObject_AsWritableSString(s) ((signed char*) __Pyx_PyObject_AsString(s))
733 #define __Pyx_PyObject_AsWritableUString(s) ((unsigned char*) __Pyx_PyObject_AsString(s))
734 #define __Pyx_PyObject_AsSString(s) ((const signed char*) __Pyx_PyObject_AsString(s))
735 #define __Pyx_PyObject_AsUString(s) ((const unsigned char*) __Pyx_PyObject_AsString(s))
736 #define __Pyx_PyObject_FromCString(s) __Pyx_PyObject_FromString((const char*)s)
737 #define __Pyx_PyBytes_FromCString(s) __Pyx_PyBytes_FromString((const char*)s)
738 #define __Pyx_PyByteArray_FromCString(s) __Pyx_PyByteArray_FromString((const char*)s)
739 #define __Pyx_PyStr_FromCString(s) __Pyx_PyStr_FromString((const char*)s)
740 #define __Pyx_PyUnicode_FromCString(s) __Pyx_PyUnicode_FromString((const char*)s)
741 static CYTHON_INLINE size_t __Pyx_Py_UNICODE_strlen(const Py_UNICODE *u) {
742  const Py_UNICODE *u_end = u;
743  while (*u_end++) ;
744  return (size_t)(u_end - u - 1);
745 }
746 #define __Pyx_PyUnicode_FromUnicode(u) PyUnicode_FromUnicode(u, __Pyx_Py_UNICODE_strlen(u))
747 #define __Pyx_PyUnicode_FromUnicodeAndLength PyUnicode_FromUnicode
748 #define __Pyx_PyUnicode_AsUnicode PyUnicode_AsUnicode
749 #define __Pyx_NewRef(obj) (Py_INCREF(obj), obj)
750 #define __Pyx_Owned_Py_None(b) __Pyx_NewRef(Py_None)
751 static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b);
752 static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*);
753 static CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject*);
754 static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x);
755 #define __Pyx_PySequence_Tuple(obj)\
756  (likely(PyTuple_CheckExact(obj)) ? __Pyx_NewRef(obj) : PySequence_Tuple(obj))
757 static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject*);
758 static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t);
759 #if CYTHON_ASSUME_SAFE_MACROS
760 #define __pyx_PyFloat_AsDouble(x) (PyFloat_CheckExact(x) ? PyFloat_AS_DOUBLE(x) : PyFloat_AsDouble(x))
761 #else
762 #define __pyx_PyFloat_AsDouble(x) PyFloat_AsDouble(x)
763 #endif
764 #define __pyx_PyFloat_AsFloat(x) ((float) __pyx_PyFloat_AsDouble(x))
765 #if PY_MAJOR_VERSION >= 3
766 #define __Pyx_PyNumber_Int(x) (PyLong_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Long(x))
767 #else
768 #define __Pyx_PyNumber_Int(x) (PyInt_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Int(x))
769 #endif
770 #define __Pyx_PyNumber_Float(x) (PyFloat_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Float(x))
771 #if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
772 static int __Pyx_sys_getdefaultencoding_not_ascii;
773 static int __Pyx_init_sys_getdefaultencoding_params(void) {
774  PyObject* sys;
775  PyObject* default_encoding = NULL;
776  PyObject* ascii_chars_u = NULL;
777  PyObject* ascii_chars_b = NULL;
778  const char* default_encoding_c;
779  sys = PyImport_ImportModule("sys");
780  if (!sys) goto bad;
781  default_encoding = PyObject_CallMethod(sys, (char*) "getdefaultencoding", NULL);
782  Py_DECREF(sys);
783  if (!default_encoding) goto bad;
784  default_encoding_c = PyBytes_AsString(default_encoding);
785  if (!default_encoding_c) goto bad;
786  if (strcmp(default_encoding_c, "ascii") == 0) {
787  __Pyx_sys_getdefaultencoding_not_ascii = 0;
788  } else {
789  char ascii_chars[128];
790  int c;
791  for (c = 0; c < 128; c++) {
792  ascii_chars[c] = c;
793  }
794  __Pyx_sys_getdefaultencoding_not_ascii = 1;
795  ascii_chars_u = PyUnicode_DecodeASCII(ascii_chars, 128, NULL);
796  if (!ascii_chars_u) goto bad;
797  ascii_chars_b = PyUnicode_AsEncodedString(ascii_chars_u, default_encoding_c, NULL);
798  if (!ascii_chars_b || !PyBytes_Check(ascii_chars_b) || memcmp(ascii_chars, PyBytes_AS_STRING(ascii_chars_b), 128) != 0) {
799  PyErr_Format(
800  PyExc_ValueError,
801  "This module compiled with c_string_encoding=ascii, but default encoding '%.200s' is not a superset of ascii.",
802  default_encoding_c);
803  goto bad;
804  }
805  Py_DECREF(ascii_chars_u);
806  Py_DECREF(ascii_chars_b);
807  }
808  Py_DECREF(default_encoding);
809  return 0;
810 bad:
811  Py_XDECREF(default_encoding);
812  Py_XDECREF(ascii_chars_u);
813  Py_XDECREF(ascii_chars_b);
814  return -1;
815 }
816 #endif
817 #if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT && PY_MAJOR_VERSION >= 3
818 #define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_DecodeUTF8(c_str, size, NULL)
819 #else
820 #define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_Decode(c_str, size, __PYX_DEFAULT_STRING_ENCODING, NULL)
821 #if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
822 static char* __PYX_DEFAULT_STRING_ENCODING;
823 static int __Pyx_init_sys_getdefaultencoding_params(void) {
824  PyObject* sys;
825  PyObject* default_encoding = NULL;
826  char* default_encoding_c;
827  sys = PyImport_ImportModule("sys");
828  if (!sys) goto bad;
829  default_encoding = PyObject_CallMethod(sys, (char*) (const char*) "getdefaultencoding", NULL);
830  Py_DECREF(sys);
831  if (!default_encoding) goto bad;
832  default_encoding_c = PyBytes_AsString(default_encoding);
833  if (!default_encoding_c) goto bad;
834  __PYX_DEFAULT_STRING_ENCODING = (char*) malloc(strlen(default_encoding_c) + 1);
835  if (!__PYX_DEFAULT_STRING_ENCODING) goto bad;
836  strcpy(__PYX_DEFAULT_STRING_ENCODING, default_encoding_c);
837  Py_DECREF(default_encoding);
838  return 0;
839 bad:
840  Py_XDECREF(default_encoding);
841  return -1;
842 }
843 #endif
844 #endif
845 
846 
847 /* Test for GCC > 2.95 */
848 #if defined(__GNUC__) && (__GNUC__ > 2 || (__GNUC__ == 2 && (__GNUC_MINOR__ > 95)))
849  #define likely(x) __builtin_expect(!!(x), 1)
850  #define unlikely(x) __builtin_expect(!!(x), 0)
851 #else /* !__GNUC__ or GCC < 2.95 */
852  #define likely(x) (x)
853  #define unlikely(x) (x)
854 #endif /* __GNUC__ */
855 static CYTHON_INLINE void __Pyx_pretend_to_initialize(void* ptr) { (void)ptr; }
856 
857 static PyObject *__pyx_m = NULL;
858 static PyObject *__pyx_d;
859 static PyObject *__pyx_b;
860 static PyObject *__pyx_cython_runtime = NULL;
861 static PyObject *__pyx_empty_tuple;
862 static PyObject *__pyx_empty_bytes;
863 static PyObject *__pyx_empty_unicode;
864 static int __pyx_lineno;
865 static int __pyx_clineno = 0;
866 static const char * __pyx_cfilenm= __FILE__;
867 static const char *__pyx_filename;
868 
869 
870 static const char *__pyx_f[] = {
871  "PyClical.pyx",
872  "stringsource",
873 };
874 
875 /*--- Type declarations ---*/
876 struct __pyx_obj_8PyClical_index_set;
877 struct __pyx_obj_8PyClical_clifford;
878 struct __pyx_obj_8PyClical___pyx_scope_struct____iter__;
879 struct __pyx_opt_args_8PyClical_sqrt;
880 struct __pyx_opt_args_8PyClical_log;
881 struct __pyx_opt_args_8PyClical_cos;
882 struct __pyx_opt_args_8PyClical_acos;
883 struct __pyx_opt_args_8PyClical_acosh;
884 struct __pyx_opt_args_8PyClical_sin;
885 struct __pyx_opt_args_8PyClical_asin;
886 struct __pyx_opt_args_8PyClical_asinh;
887 struct __pyx_opt_args_8PyClical_tan;
888 struct __pyx_opt_args_8PyClical_atan;
889 struct __pyx_opt_args_8PyClical_atanh;
890 struct __pyx_opt_args_8PyClical_random_clifford;
891 
892 /* "PyClical.pyx":1542
893  * return clifford().wrap( glucat.complexifier(toClifford(obj)) )
894  *
895  * cpdef inline sqrt(obj, i = None): # <<<<<<<<<<<<<<
896  * """
897  * Square root of multivector with optional complexifier.
898  */
899 struct __pyx_opt_args_8PyClical_sqrt {
900  int __pyx_n;
901  PyObject *i;
902 };
903 
904 /* "PyClical.pyx":1579
905  * return clifford().wrap( glucat.exp(toClifford(obj)) )
906  *
907  * cpdef inline log(obj,i = None): # <<<<<<<<<<<<<<
908  * """
909  * Natural logarithm of multivector with optional complexifier.
910  */
911 struct __pyx_opt_args_8PyClical_log {
912  int __pyx_n;
913  PyObject *i;
914 };
915 
916 /* "PyClical.pyx":1602
917  * return clifford().wrap( glucat.log(toClifford(obj)) )
918  *
919  * cpdef inline cos(obj,i = None): # <<<<<<<<<<<<<<
920  * """
921  * Cosine of multivector with optional complexifier.
922  */
923 struct __pyx_opt_args_8PyClical_cos {
924  int __pyx_n;
925  PyObject *i;
926 };
927 
928 /* "PyClical.pyx":1619
929  * return clifford().wrap( glucat.cos(toClifford(obj)) )
930  *
931  * cpdef inline acos(obj,i = None): # <<<<<<<<<<<<<<
932  * """
933  * Inverse cosine of multivector with optional complexifier.
934  */
935 struct __pyx_opt_args_8PyClical_acos {
936  int __pyx_n;
937  PyObject *i;
938 };
939 
940 /* "PyClical.pyx":1656
941  * return clifford().wrap( glucat.cosh(toClifford(obj)) )
942  *
943  * cpdef inline acosh(obj,i = None): # <<<<<<<<<<<<<<
944  * """
945  * Inverse hyperbolic cosine of multivector with optional complexifier.
946  */
947 struct __pyx_opt_args_8PyClical_acosh {
948  int __pyx_n;
949  PyObject *i;
950 };
951 
952 /* "PyClical.pyx":1679
953  * return clifford().wrap( glucat.acosh(toClifford(obj)) )
954  *
955  * cpdef inline sin(obj,i = None): # <<<<<<<<<<<<<<
956  * """
957  * Sine of multivector with optional complexifier.
958  */
959 struct __pyx_opt_args_8PyClical_sin {
960  int __pyx_n;
961  PyObject *i;
962 };
963 
964 /* "PyClical.pyx":1698
965  * return clifford().wrap( glucat.sin(toClifford(obj)) )
966  *
967  * cpdef inline asin(obj,i = None): # <<<<<<<<<<<<<<
968  * """
969  * Inverse sine of multivector with optional complexifier.
970  */
971 struct __pyx_opt_args_8PyClical_asin {
972  int __pyx_n;
973  PyObject *i;
974 };
975 
976 /* "PyClical.pyx":1733
977  * return clifford().wrap( glucat.sinh(toClifford(obj)) )
978  *
979  * cpdef inline asinh(obj,i = None): # <<<<<<<<<<<<<<
980  * """
981  * Inverse hyperbolic sine of multivector with optional complexifier.
982  */
983 struct __pyx_opt_args_8PyClical_asinh {
984  int __pyx_n;
985  PyObject *i;
986 };
987 
988 /* "PyClical.pyx":1752
989  * return clifford().wrap( glucat.asinh(toClifford(obj)) )
990  *
991  * cpdef inline tan(obj,i = None): # <<<<<<<<<<<<<<
992  * """
993  * Tangent of multivector with optional complexifier.
994  */
995 struct __pyx_opt_args_8PyClical_tan {
996  int __pyx_n;
997  PyObject *i;
998 };
999 
1000 /* "PyClical.pyx":1769
1001  * return clifford().wrap( glucat.tan(toClifford(obj)) )
1002  *
1003  * cpdef inline atan(obj,i = None): # <<<<<<<<<<<<<<
1004  * """
1005  * Inverse tangent of multivector with optional complexifier.
1006  */
1007 struct __pyx_opt_args_8PyClical_atan {
1008  int __pyx_n;
1009  PyObject *i;
1010 };
1011 
1012 /* "PyClical.pyx":1798
1013  * return clifford().wrap( glucat.tanh(toClifford(obj)) )
1014  *
1015  * cpdef inline atanh(obj,i = None): # <<<<<<<<<<<<<<
1016  * """
1017  * Inverse hyperbolic tangent of multivector with optional complexifier.
1018  */
1019 struct __pyx_opt_args_8PyClical_atanh {
1020  int __pyx_n;
1021  PyObject *i;
1022 };
1023 
1024 /* "PyClical.pyx":1815
1025  * return clifford().wrap( glucat.atanh(toClifford(obj)) )
1026  *
1027  * cpdef inline random_clifford(index_set ixt, fill = 1.0): # <<<<<<<<<<<<<<
1028  * """
1029  * Random multivector within a frame.
1030  */
1031 struct __pyx_opt_args_8PyClical_random_clifford {
1032  int __pyx_n;
1033  PyObject *fill;
1034 };
1035 
1036 /* "PyClical.pyx":37
1037  *
1038  * # Forward reference
1039  * cdef class index_set # <<<<<<<<<<<<<<
1040  *
1041  * cdef inline IndexSet toIndexSet(obj):
1042  */
1043 struct __pyx_obj_8PyClical_index_set {
1044  PyObject_HEAD
1045  struct __pyx_vtabstruct_8PyClical_index_set *__pyx_vtab;
1046  IndexSet *instance;
1047 };
1048 
1049 
1050 /* "PyClical.pyx":530
1051  *
1052  * # Forward reference.
1053  * cdef class clifford # <<<<<<<<<<<<<<
1054  *
1055  * cdef inline Clifford toClifford(obj):
1056  */
1057 struct __pyx_obj_8PyClical_clifford {
1058  PyObject_HEAD
1059  struct __pyx_vtabstruct_8PyClical_clifford *__pyx_vtab;
1060  Clifford *instance;
1061 };
1062 
1063 
1064 /* "PyClical.pyx":227
1065  * return self.instance.getitem(idx)
1066  *
1067  * def __iter__(self): # <<<<<<<<<<<<<<
1068  * """
1069  * Iterate over the indices of an index_set.
1070  */
1071 struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ {
1072  PyObject_HEAD
1073  PyObject *__pyx_v_idx;
1074  struct __pyx_obj_8PyClical_index_set *__pyx_v_self;
1075  PyObject *__pyx_t_0;
1076  Py_ssize_t __pyx_t_1;
1077  PyObject *(*__pyx_t_2)(PyObject *);
1078 };
1079 
1080 
1081 
1082 /* "PyClical.pyx":45
1083  * return index_set(obj).instance[0]
1084  *
1085  * cdef class index_set: # <<<<<<<<<<<<<<
1086  * """
1087  * Python class index_set wraps C++ class IndexSet.
1088  */
1089 
1090 struct __pyx_vtabstruct_8PyClical_index_set {
1091  PyObject *(*wrap)(struct __pyx_obj_8PyClical_index_set *, IndexSet);
1092  IndexSet (*unwrap)(struct __pyx_obj_8PyClical_index_set *);
1093  PyObject *(*copy)(struct __pyx_obj_8PyClical_index_set *, int __pyx_skip_dispatch);
1094 };
1095 static struct __pyx_vtabstruct_8PyClical_index_set *__pyx_vtabptr_8PyClical_index_set;
1096 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_9index_set_wrap(struct __pyx_obj_8PyClical_index_set *, IndexSet);
1097 static CYTHON_INLINE IndexSet __pyx_f_8PyClical_9index_set_unwrap(struct __pyx_obj_8PyClical_index_set *);
1098 
1099 
1100 /* "PyClical.pyx":535
1101  * return clifford(obj).instance[0]
1102  *
1103  * cdef class clifford: # <<<<<<<<<<<<<<
1104  * """
1105  * Python class clifford wraps C++ class Clifford.
1106  */
1107 
1108 struct __pyx_vtabstruct_8PyClical_clifford {
1109  PyObject *(*wrap)(struct __pyx_obj_8PyClical_clifford *, Clifford);
1110  Clifford (*unwrap)(struct __pyx_obj_8PyClical_clifford *);
1111  PyObject *(*copy)(struct __pyx_obj_8PyClical_clifford *, int __pyx_skip_dispatch);
1112 };
1113 static struct __pyx_vtabstruct_8PyClical_clifford *__pyx_vtabptr_8PyClical_clifford;
1114 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_8clifford_wrap(struct __pyx_obj_8PyClical_clifford *, Clifford);
1115 static CYTHON_INLINE Clifford __pyx_f_8PyClical_8clifford_unwrap(struct __pyx_obj_8PyClical_clifford *);
1116 
1117 /* --- Runtime support code (head) --- */
1118 /* Refnanny.proto */
1119 #ifndef CYTHON_REFNANNY
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1121 #endif
1122 #if CYTHON_REFNANNY
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1124  void (*INCREF)(void*, PyObject*, int);
1125  void (*DECREF)(void*, PyObject*, int);
1126  void (*GOTREF)(void*, PyObject*, int);
1127  void (*GIVEREF)(void*, PyObject*, int);
1128  void* (*SetupContext)(const char*, int, const char*);
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1139  PyGILState_Release(__pyx_gilstate_save);\
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1144  #define __Pyx_RefNannySetupContext(name, acquire_gil)\
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1149  #define __Pyx_INCREF(r) __Pyx_RefNanny->INCREF(__pyx_refnanny, (PyObject *)(r), __LINE__)
1150  #define __Pyx_DECREF(r) __Pyx_RefNanny->DECREF(__pyx_refnanny, (PyObject *)(r), __LINE__)
1151  #define __Pyx_GOTREF(r) __Pyx_RefNanny->GOTREF(__pyx_refnanny, (PyObject *)(r), __LINE__)
1152  #define __Pyx_GIVEREF(r) __Pyx_RefNanny->GIVEREF(__pyx_refnanny, (PyObject *)(r), __LINE__)
1153  #define __Pyx_XINCREF(r) do { if((r) != NULL) {__Pyx_INCREF(r); }} while(0)
1154  #define __Pyx_XDECREF(r) do { if((r) != NULL) {__Pyx_DECREF(r); }} while(0)
1155  #define __Pyx_XGOTREF(r) do { if((r) != NULL) {__Pyx_GOTREF(r); }} while(0)
1156  #define __Pyx_XGIVEREF(r) do { if((r) != NULL) {__Pyx_GIVEREF(r);}} while(0)
1157 #else
1158  #define __Pyx_RefNannyDeclarations
1159  #define __Pyx_RefNannySetupContext(name, acquire_gil)
1160  #define __Pyx_RefNannyFinishContext()
1161  #define __Pyx_INCREF(r) Py_INCREF(r)
1162  #define __Pyx_DECREF(r) Py_DECREF(r)
1163  #define __Pyx_GOTREF(r)
1164  #define __Pyx_GIVEREF(r)
1165  #define __Pyx_XINCREF(r) Py_XINCREF(r)
1166  #define __Pyx_XDECREF(r) Py_XDECREF(r)
1167  #define __Pyx_XGOTREF(r)
1168  #define __Pyx_XGIVEREF(r)
1169 #endif
1170 #define __Pyx_XDECREF_SET(r, v) do {\
1171  PyObject *tmp = (PyObject *) r;\
1172  r = v; __Pyx_XDECREF(tmp);\
1173  } while (0)
1174 #define __Pyx_DECREF_SET(r, v) do {\
1175  PyObject *tmp = (PyObject *) r;\
1176  r = v; __Pyx_DECREF(tmp);\
1177  } while (0)
1178 #define __Pyx_CLEAR(r) do { PyObject* tmp = ((PyObject*)(r)); r = NULL; __Pyx_DECREF(tmp);} while(0)
1179 #define __Pyx_XCLEAR(r) do { if((r) != NULL) {PyObject* tmp = ((PyObject*)(r)); r = NULL; __Pyx_DECREF(tmp);}} while(0)
1180 
1181 /* PyObjectGetAttrStr.proto */
1182 #if CYTHON_USE_TYPE_SLOTS
1183 static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStr(PyObject* obj, PyObject* attr_name);
1184 #else
1185 #define __Pyx_PyObject_GetAttrStr(o,n) PyObject_GetAttr(o,n)
1186 #endif
1187 
1188 /* GetBuiltinName.proto */
1189 static PyObject *__Pyx_GetBuiltinName(PyObject *name);
1190 
1191 /* PyCFunctionFastCall.proto */
1192 #if CYTHON_FAST_PYCCALL
1193 static CYTHON_INLINE PyObject *__Pyx_PyCFunction_FastCall(PyObject *func, PyObject **args, Py_ssize_t nargs);
1194 #else
1195 #define __Pyx_PyCFunction_FastCall(func, args, nargs) (assert(0), NULL)
1196 #endif
1197 
1198 /* PyFunctionFastCall.proto */
1199 #if CYTHON_FAST_PYCALL
1200 #define __Pyx_PyFunction_FastCall(func, args, nargs)\
1201  __Pyx_PyFunction_FastCallDict((func), (args), (nargs), NULL)
1202 #if 1 || PY_VERSION_HEX < 0x030600B1
1203 static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, int nargs, PyObject *kwargs);
1204 #else
1205 #define __Pyx_PyFunction_FastCallDict(func, args, nargs, kwargs) _PyFunction_FastCallDict(func, args, nargs, kwargs)
1206 #endif
1207 #define __Pyx_BUILD_ASSERT_EXPR(cond)\
1208  (sizeof(char [1 - 2*!(cond)]) - 1)
1209 #ifndef Py_MEMBER_SIZE
1210 #define Py_MEMBER_SIZE(type, member) sizeof(((type *)0)->member)
1211 #endif
1212  static size_t __pyx_pyframe_localsplus_offset = 0;
1213  #include "frameobject.h"
1214  #define __Pxy_PyFrame_Initialize_Offsets()\
1215  ((void)__Pyx_BUILD_ASSERT_EXPR(sizeof(PyFrameObject) == offsetof(PyFrameObject, f_localsplus) + Py_MEMBER_SIZE(PyFrameObject, f_localsplus)),\
1216  (void)(__pyx_pyframe_localsplus_offset = ((size_t)PyFrame_Type.tp_basicsize) - Py_MEMBER_SIZE(PyFrameObject, f_localsplus)))
1217  #define __Pyx_PyFrame_GetLocalsplus(frame)\
1218  (assert(__pyx_pyframe_localsplus_offset), (PyObject **)(((char *)(frame)) + __pyx_pyframe_localsplus_offset))
1219 #endif
1220 
1221 /* PyObjectCall.proto */
1222 #if CYTHON_COMPILING_IN_CPYTHON
1223 static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw);
1224 #else
1225 #define __Pyx_PyObject_Call(func, arg, kw) PyObject_Call(func, arg, kw)
1226 #endif
1227 
1228 /* PyObjectCallMethO.proto */
1229 #if CYTHON_COMPILING_IN_CPYTHON
1230 static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg);
1231 #endif
1232 
1233 /* PyObjectCallOneArg.proto */
1234 static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg);
1235 
1236 /* PyThreadStateGet.proto */
1237 #if CYTHON_FAST_THREAD_STATE
1238 #define __Pyx_PyThreadState_declare PyThreadState *__pyx_tstate;
1239 #define __Pyx_PyThreadState_assign __pyx_tstate = __Pyx_PyThreadState_Current;
1240 #define __Pyx_PyErr_Occurred() __pyx_tstate->curexc_type
1241 #else
1242 #define __Pyx_PyThreadState_declare
1243 #define __Pyx_PyThreadState_assign
1244 #define __Pyx_PyErr_Occurred() PyErr_Occurred()
1245 #endif
1246 
1247 /* PyErrFetchRestore.proto */
1248 #if CYTHON_FAST_THREAD_STATE
1249 #define __Pyx_PyErr_Clear() __Pyx_ErrRestore(NULL, NULL, NULL)
1250 #define __Pyx_ErrRestoreWithState(type, value, tb) __Pyx_ErrRestoreInState(PyThreadState_GET(), type, value, tb)
1251 #define __Pyx_ErrFetchWithState(type, value, tb) __Pyx_ErrFetchInState(PyThreadState_GET(), type, value, tb)
1252 #define __Pyx_ErrRestore(type, value, tb) __Pyx_ErrRestoreInState(__pyx_tstate, type, value, tb)
1253 #define __Pyx_ErrFetch(type, value, tb) __Pyx_ErrFetchInState(__pyx_tstate, type, value, tb)
1254 static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb);
1255 static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
1256 #if CYTHON_COMPILING_IN_CPYTHON
1257 #define __Pyx_PyErr_SetNone(exc) (Py_INCREF(exc), __Pyx_ErrRestore((exc), NULL, NULL))
1258 #else
1259 #define __Pyx_PyErr_SetNone(exc) PyErr_SetNone(exc)
1260 #endif
1261 #else
1262 #define __Pyx_PyErr_Clear() PyErr_Clear()
1263 #define __Pyx_PyErr_SetNone(exc) PyErr_SetNone(exc)
1264 #define __Pyx_ErrRestoreWithState(type, value, tb) PyErr_Restore(type, value, tb)
1265 #define __Pyx_ErrFetchWithState(type, value, tb) PyErr_Fetch(type, value, tb)
1266 #define __Pyx_ErrRestoreInState(tstate, type, value, tb) PyErr_Restore(type, value, tb)
1267 #define __Pyx_ErrFetchInState(tstate, type, value, tb) PyErr_Fetch(type, value, tb)
1268 #define __Pyx_ErrRestore(type, value, tb) PyErr_Restore(type, value, tb)
1269 #define __Pyx_ErrFetch(type, value, tb) PyErr_Fetch(type, value, tb)
1270 #endif
1271 
1272 /* WriteUnraisableException.proto */
1273 static void __Pyx_WriteUnraisable(const char *name, int clineno,
1274  int lineno, const char *filename,
1275  int full_traceback, int nogil);
1276 
1277 /* PyDictVersioning.proto */
1278 #if CYTHON_USE_DICT_VERSIONS && CYTHON_USE_TYPE_SLOTS
1279 #define __PYX_DICT_VERSION_INIT ((PY_UINT64_T) -1)
1280 #define __PYX_GET_DICT_VERSION(dict) (((PyDictObject*)(dict))->ma_version_tag)
1281 #define __PYX_UPDATE_DICT_CACHE(dict, value, cache_var, version_var)\
1282  (version_var) = __PYX_GET_DICT_VERSION(dict);\
1283  (cache_var) = (value);
1284 #define __PYX_PY_DICT_LOOKUP_IF_MODIFIED(VAR, DICT, LOOKUP) {\
1285  static PY_UINT64_T __pyx_dict_version = 0;\
1286  static PyObject *__pyx_dict_cached_value = NULL;\
1287  if (likely(__PYX_GET_DICT_VERSION(DICT) == __pyx_dict_version)) {\
1288  (VAR) = __pyx_dict_cached_value;\
1289  } else {\
1290  (VAR) = __pyx_dict_cached_value = (LOOKUP);\
1291  __pyx_dict_version = __PYX_GET_DICT_VERSION(DICT);\
1292  }\
1293 }
1294 static CYTHON_INLINE PY_UINT64_T __Pyx_get_tp_dict_version(PyObject *obj);
1295 static CYTHON_INLINE PY_UINT64_T __Pyx_get_object_dict_version(PyObject *obj);
1296 static CYTHON_INLINE int __Pyx_object_dict_version_matches(PyObject* obj, PY_UINT64_T tp_dict_version, PY_UINT64_T obj_dict_version);
1297 #else
1298 #define __PYX_GET_DICT_VERSION(dict) (0)
1299 #define __PYX_UPDATE_DICT_CACHE(dict, value, cache_var, version_var)
1300 #define __PYX_PY_DICT_LOOKUP_IF_MODIFIED(VAR, DICT, LOOKUP) (VAR) = (LOOKUP);
1301 #endif
1302 
1303 /* PyObjectCallNoArg.proto */
1304 #if CYTHON_COMPILING_IN_CPYTHON
1305 static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func);
1306 #else
1307 #define __Pyx_PyObject_CallNoArg(func) __Pyx_PyObject_Call(func, __pyx_empty_tuple, NULL)
1308 #endif
1309 
1310 /* RaiseDoubleKeywords.proto */
1311 static void __Pyx_RaiseDoubleKeywordsError(const char* func_name, PyObject* kw_name);
1312 
1313 /* ParseKeywords.proto */
1314 static int __Pyx_ParseOptionalKeywords(PyObject *kwds, PyObject **argnames[],\
1315  PyObject *kwds2, PyObject *values[], Py_ssize_t num_pos_args,\
1316  const char* function_name);
1317 
1318 /* RaiseArgTupleInvalid.proto */
1319 static void __Pyx_RaiseArgtupleInvalid(const char* func_name, int exact,
1320  Py_ssize_t num_min, Py_ssize_t num_max, Py_ssize_t num_found);
1321 
1322 /* GetModuleGlobalName.proto */
1323 #if CYTHON_USE_DICT_VERSIONS
1324 #define __Pyx_GetModuleGlobalName(var, name) {\
1325  static PY_UINT64_T __pyx_dict_version = 0;\
1326  static PyObject *__pyx_dict_cached_value = NULL;\
1327  (var) = (likely(__pyx_dict_version == __PYX_GET_DICT_VERSION(__pyx_d))) ?\
1328  (likely(__pyx_dict_cached_value) ? __Pyx_NewRef(__pyx_dict_cached_value) : __Pyx_GetBuiltinName(name)) :\
1329  __Pyx__GetModuleGlobalName(name, &__pyx_dict_version, &__pyx_dict_cached_value);\
1330 }
1331 #define __Pyx_GetModuleGlobalNameUncached(var, name) {\
1332  PY_UINT64_T __pyx_dict_version;\
1333  PyObject *__pyx_dict_cached_value;\
1334  (var) = __Pyx__GetModuleGlobalName(name, &__pyx_dict_version, &__pyx_dict_cached_value);\
1335 }
1336 static PyObject *__Pyx__GetModuleGlobalName(PyObject *name, PY_UINT64_T *dict_version, PyObject **dict_cached_value);
1337 #else
1338 #define __Pyx_GetModuleGlobalName(var, name) (var) = __Pyx__GetModuleGlobalName(name)
1339 #define __Pyx_GetModuleGlobalNameUncached(var, name) (var) = __Pyx__GetModuleGlobalName(name)
1340 static CYTHON_INLINE PyObject *__Pyx__GetModuleGlobalName(PyObject *name);
1341 #endif
1342 
1343 /* GetTopmostException.proto */
1344 #if CYTHON_USE_EXC_INFO_STACK
1345 static _PyErr_StackItem * __Pyx_PyErr_GetTopmostException(PyThreadState *tstate);
1346 #endif
1347 
1348 /* SaveResetException.proto */
1349 #if CYTHON_FAST_THREAD_STATE
1350 #define __Pyx_ExceptionSave(type, value, tb) __Pyx__ExceptionSave(__pyx_tstate, type, value, tb)
1351 static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
1352 #define __Pyx_ExceptionReset(type, value, tb) __Pyx__ExceptionReset(__pyx_tstate, type, value, tb)
1353 static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb);
1354 #else
1355 #define __Pyx_ExceptionSave(type, value, tb) PyErr_GetExcInfo(type, value, tb)
1356 #define __Pyx_ExceptionReset(type, value, tb) PyErr_SetExcInfo(type, value, tb)
1357 #endif
1358 
1359 /* PyErrExceptionMatches.proto */
1360 #if CYTHON_FAST_THREAD_STATE
1361 #define __Pyx_PyErr_ExceptionMatches(err) __Pyx_PyErr_ExceptionMatchesInState(__pyx_tstate, err)
1362 static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err);
1363 #else
1364 #define __Pyx_PyErr_ExceptionMatches(err) PyErr_ExceptionMatches(err)
1365 #endif
1366 
1367 /* GetException.proto */
1368 #if CYTHON_FAST_THREAD_STATE
1369 #define __Pyx_GetException(type, value, tb) __Pyx__GetException(__pyx_tstate, type, value, tb)
1370 static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
1371 #else
1372 static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb);
1373 #endif
1374 
1375 /* RaiseException.proto */
1376 static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause);
1377 
1378 /* PyIntBinop.proto */
1379 #if !CYTHON_COMPILING_IN_PYPY
1380 static PyObject* __Pyx_PyInt_AddObjC(PyObject *op1, PyObject *op2, long intval, int inplace, int zerodivision_check);
1381 #else
1382 #define __Pyx_PyInt_AddObjC(op1, op2, intval, inplace, zerodivision_check)\
1383  (inplace ? PyNumber_InPlaceAdd(op1, op2) : PyNumber_Add(op1, op2))
1384 #endif
1385 
1386 /* PySequenceContains.proto */
1387 static CYTHON_INLINE int __Pyx_PySequence_ContainsTF(PyObject* item, PyObject* seq, int eq) {
1388  int result = PySequence_Contains(seq, item);
1389  return unlikely(result < 0) ? result : (result == (eq == Py_EQ));
1390 }
1391 
1392 /* SetItemInt.proto */
1393 #define __Pyx_SetItemInt(o, i, v, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
1394  (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\
1395  __Pyx_SetItemInt_Fast(o, (Py_ssize_t)i, v, is_list, wraparound, boundscheck) :\
1396  (is_list ? (PyErr_SetString(PyExc_IndexError, "list assignment index out of range"), -1) :\
1397  __Pyx_SetItemInt_Generic(o, to_py_func(i), v)))
1398 static int __Pyx_SetItemInt_Generic(PyObject *o, PyObject *j, PyObject *v);
1399 static CYTHON_INLINE int __Pyx_SetItemInt_Fast(PyObject *o, Py_ssize_t i, PyObject *v,
1400  int is_list, int wraparound, int boundscheck);
1401 
1402 /* PyObjectCall2Args.proto */
1403 static CYTHON_UNUSED PyObject* __Pyx_PyObject_Call2Args(PyObject* function, PyObject* arg1, PyObject* arg2);
1404 
1405 /* ArgTypeTest.proto */
1406 #define __Pyx_ArgTypeTest(obj, type, none_allowed, name, exact)\
1407  ((likely((Py_TYPE(obj) == type) | (none_allowed && (obj == Py_None)))) ? 1 :\
1408  __Pyx__ArgTypeTest(obj, type, name, exact))
1409 static int __Pyx__ArgTypeTest(PyObject *obj, PyTypeObject *type, const char *name, int exact);
1410 
1411 /* Import.proto */
1412 static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level);
1413 
1414 /* IncludeStringH.proto */
1415 #include <string.h>
1416 
1417 /* PyObject_GenericGetAttrNoDict.proto */
1418 #if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000
1419 static CYTHON_INLINE PyObject* __Pyx_PyObject_GenericGetAttrNoDict(PyObject* obj, PyObject* attr_name);
1420 #else
1421 #define __Pyx_PyObject_GenericGetAttrNoDict PyObject_GenericGetAttr
1422 #endif
1423 
1424 /* PyObject_GenericGetAttr.proto */
1425 #if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000
1426 static PyObject* __Pyx_PyObject_GenericGetAttr(PyObject* obj, PyObject* attr_name);
1427 #else
1428 #define __Pyx_PyObject_GenericGetAttr PyObject_GenericGetAttr
1429 #endif
1430 
1431 /* SetVTable.proto */
1432 static int __Pyx_SetVtable(PyObject *dict, void *vtable);
1433 
1434 /* SetupReduce.proto */
1435 static int __Pyx_setup_reduce(PyObject* type_obj);
1436 
1437 /* PyFloatBinop.proto */
1438 #if !CYTHON_COMPILING_IN_PYPY
1439 static PyObject* __Pyx_PyFloat_DivideObjC(PyObject *op1, PyObject *op2, double floatval, int inplace, int zerodivision_check);
1440 #else
1441 #define __Pyx_PyFloat_DivideObjC(op1, op2, floatval, inplace, zerodivision_check)\
1442  ((inplace ? __Pyx_PyNumber_InPlaceDivide(op1, op2) : __Pyx_PyNumber_Divide(op1, op2)))
1443  #endif
1444 
1445 /* BytesEquals.proto */
1446 static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals);
1447 
1448 /* UnicodeEquals.proto */
1449 static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals);
1450 
1451 /* StrEquals.proto */
1452 #if PY_MAJOR_VERSION >= 3
1453 #define __Pyx_PyString_Equals __Pyx_PyUnicode_Equals
1454 #else
1455 #define __Pyx_PyString_Equals __Pyx_PyBytes_Equals
1456 #endif
1457 
1458 /* CLineInTraceback.proto */
1459 #ifdef CYTHON_CLINE_IN_TRACEBACK
1460 #define __Pyx_CLineForTraceback(tstate, c_line) (((CYTHON_CLINE_IN_TRACEBACK)) ? c_line : 0)
1461 #else
1462 static int __Pyx_CLineForTraceback(PyThreadState *tstate, int c_line);
1463 #endif
1464 
1465 /* CodeObjectCache.proto */
1466 typedef struct {
1467  PyCodeObject* code_object;
1468  int code_line;
1469 } __Pyx_CodeObjectCacheEntry;
1470 struct __Pyx_CodeObjectCache {
1471  int count;
1472  int max_count;
1473  __Pyx_CodeObjectCacheEntry* entries;
1474 };
1475 static struct __Pyx_CodeObjectCache __pyx_code_cache = {0,0,NULL};
1476 static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line);
1477 static PyCodeObject *__pyx_find_code_object(int code_line);
1478 static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object);
1479 
1480 /* AddTraceback.proto */
1481 static void __Pyx_AddTraceback(const char *funcname, int c_line,
1482  int py_line, const char *filename);
1483 
1484 /* CppExceptionConversion.proto */
1485 #ifndef __Pyx_CppExn2PyErr
1486 #include <new>
1487 #include <typeinfo>
1488 #include <stdexcept>
1489 #include <ios>
1490 static void __Pyx_CppExn2PyErr() {
1491  try {
1492  if (PyErr_Occurred())
1493  ; // let the latest Python exn pass through and ignore the current one
1494  else
1495  throw;
1496  } catch (const std::bad_alloc& exn) {
1497  PyErr_SetString(PyExc_MemoryError, exn.what());
1498  } catch (const std::bad_cast& exn) {
1499  PyErr_SetString(PyExc_TypeError, exn.what());
1500  } catch (const std::bad_typeid& exn) {
1501  PyErr_SetString(PyExc_TypeError, exn.what());
1502  } catch (const std::domain_error& exn) {
1503  PyErr_SetString(PyExc_ValueError, exn.what());
1504  } catch (const std::invalid_argument& exn) {
1505  PyErr_SetString(PyExc_ValueError, exn.what());
1506  } catch (const std::ios_base::failure& exn) {
1507  PyErr_SetString(PyExc_IOError, exn.what());
1508  } catch (const std::out_of_range& exn) {
1509  PyErr_SetString(PyExc_IndexError, exn.what());
1510  } catch (const std::overflow_error& exn) {
1511  PyErr_SetString(PyExc_OverflowError, exn.what());
1512  } catch (const std::range_error& exn) {
1513  PyErr_SetString(PyExc_ArithmeticError, exn.what());
1514  } catch (const std::underflow_error& exn) {
1515  PyErr_SetString(PyExc_ArithmeticError, exn.what());
1516  } catch (const std::exception& exn) {
1517  PyErr_SetString(PyExc_RuntimeError, exn.what());
1518  }
1519  catch (...)
1520  {
1521  PyErr_SetString(PyExc_RuntimeError, "Unknown exception");
1522  }
1523 }
1524 #endif
1525 
1526 /* CIntToPy.proto */
1527 static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value);
1528 
1529 /* CIntFromPy.proto */
1530 static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *);
1531 
1532 /* CIntToPy.proto */
1533 static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value);
1534 
1535 /* CIntFromPy.proto */
1536 static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *);
1537 
1538 /* FastTypeChecks.proto */
1539 #if CYTHON_COMPILING_IN_CPYTHON
1540 #define __Pyx_TypeCheck(obj, type) __Pyx_IsSubtype(Py_TYPE(obj), (PyTypeObject *)type)
1541 static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b);
1542 static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject *type);
1543 static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *type1, PyObject *type2);
1544 #else
1545 #define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type)
1546 #define __Pyx_PyErr_GivenExceptionMatches(err, type) PyErr_GivenExceptionMatches(err, type)
1547 #define __Pyx_PyErr_GivenExceptionMatches2(err, type1, type2) (PyErr_GivenExceptionMatches(err, type1) || PyErr_GivenExceptionMatches(err, type2))
1548 #endif
1549 #define __Pyx_PyException_Check(obj) __Pyx_TypeCheck(obj, PyExc_Exception)
1550 
1551 /* FetchCommonType.proto */
1552 static PyTypeObject* __Pyx_FetchCommonType(PyTypeObject* type);
1553 
1554 /* SwapException.proto */
1555 #if CYTHON_FAST_THREAD_STATE
1556 #define __Pyx_ExceptionSwap(type, value, tb) __Pyx__ExceptionSwap(__pyx_tstate, type, value, tb)
1557 static CYTHON_INLINE void __Pyx__ExceptionSwap(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
1558 #else
1559 static CYTHON_INLINE void __Pyx_ExceptionSwap(PyObject **type, PyObject **value, PyObject **tb);
1560 #endif
1561 
1562 /* PyObjectGetMethod.proto */
1563 static int __Pyx_PyObject_GetMethod(PyObject *obj, PyObject *name, PyObject **method);
1564 
1565 /* PyObjectCallMethod1.proto */
1566 static PyObject* __Pyx_PyObject_CallMethod1(PyObject* obj, PyObject* method_name, PyObject* arg);
1567 
1568 /* CoroutineBase.proto */
1569 typedef PyObject *(*__pyx_coroutine_body_t)(PyObject *, PyThreadState *, PyObject *);
1570 #if CYTHON_USE_EXC_INFO_STACK
1571 #define __Pyx_ExcInfoStruct _PyErr_StackItem
1572 #else
1573 typedef struct {
1574  PyObject *exc_type;
1575  PyObject *exc_value;
1576  PyObject *exc_traceback;
1577 } __Pyx_ExcInfoStruct;
1578 #endif
1579 typedef struct {
1580  PyObject_HEAD
1581  __pyx_coroutine_body_t body;
1582  PyObject *closure;
1583  __Pyx_ExcInfoStruct gi_exc_state;
1584  PyObject *gi_weakreflist;
1585  PyObject *classobj;
1586  PyObject *yieldfrom;
1587  PyObject *gi_name;
1588  PyObject *gi_qualname;
1589  PyObject *gi_modulename;
1590  PyObject *gi_code;
1591  int resume_label;
1592  char is_running;
1593 } __pyx_CoroutineObject;
1594 static __pyx_CoroutineObject *__Pyx__Coroutine_New(
1595  PyTypeObject *type, __pyx_coroutine_body_t body, PyObject *code, PyObject *closure,
1596  PyObject *name, PyObject *qualname, PyObject *module_name);
1597 static __pyx_CoroutineObject *__Pyx__Coroutine_NewInit(
1598  __pyx_CoroutineObject *gen, __pyx_coroutine_body_t body, PyObject *code, PyObject *closure,
1599  PyObject *name, PyObject *qualname, PyObject *module_name);
1600 static CYTHON_INLINE void __Pyx_Coroutine_ExceptionClear(__Pyx_ExcInfoStruct *self);
1601 static int __Pyx_Coroutine_clear(PyObject *self);
1602 static PyObject *__Pyx_Coroutine_Send(PyObject *self, PyObject *value);
1603 static PyObject *__Pyx_Coroutine_Close(PyObject *self);
1604 static PyObject *__Pyx_Coroutine_Throw(PyObject *gen, PyObject *args);
1605 #if CYTHON_USE_EXC_INFO_STACK
1606 #define __Pyx_Coroutine_SwapException(self)
1607 #define __Pyx_Coroutine_ResetAndClearException(self) __Pyx_Coroutine_ExceptionClear(&(self)->gi_exc_state)
1608 #else
1609 #define __Pyx_Coroutine_SwapException(self) {\
1610  __Pyx_ExceptionSwap(&(self)->gi_exc_state.exc_type, &(self)->gi_exc_state.exc_value, &(self)->gi_exc_state.exc_traceback);\
1611  __Pyx_Coroutine_ResetFrameBackpointer(&(self)->gi_exc_state);\
1612  }
1613 #define __Pyx_Coroutine_ResetAndClearException(self) {\
1614  __Pyx_ExceptionReset((self)->gi_exc_state.exc_type, (self)->gi_exc_state.exc_value, (self)->gi_exc_state.exc_traceback);\
1615  (self)->gi_exc_state.exc_type = (self)->gi_exc_state.exc_value = (self)->gi_exc_state.exc_traceback = NULL;\
1616  }
1617 #endif
1618 #if CYTHON_FAST_THREAD_STATE
1619 #define __Pyx_PyGen_FetchStopIterationValue(pvalue)\
1620  __Pyx_PyGen__FetchStopIterationValue(__pyx_tstate, pvalue)
1621 #else
1622 #define __Pyx_PyGen_FetchStopIterationValue(pvalue)\
1623  __Pyx_PyGen__FetchStopIterationValue(__Pyx_PyThreadState_Current, pvalue)
1624 #endif
1625 static int __Pyx_PyGen__FetchStopIterationValue(PyThreadState *tstate, PyObject **pvalue);
1626 static CYTHON_INLINE void __Pyx_Coroutine_ResetFrameBackpointer(__Pyx_ExcInfoStruct *exc_state);
1627 
1628 /* PatchModuleWithCoroutine.proto */
1629 static PyObject* __Pyx_Coroutine_patch_module(PyObject* module, const char* py_code);
1630 
1631 /* PatchGeneratorABC.proto */
1632 static int __Pyx_patch_abc(void);
1633 
1634 /* Generator.proto */
1635 #define __Pyx_Generator_USED
1636 static PyTypeObject *__pyx_GeneratorType = 0;
1637 #define __Pyx_Generator_CheckExact(obj) (Py_TYPE(obj) == __pyx_GeneratorType)
1638 #define __Pyx_Generator_New(body, code, closure, name, qualname, module_name)\
1639  __Pyx__Coroutine_New(__pyx_GeneratorType, body, code, closure, name, qualname, module_name)
1640 static PyObject *__Pyx_Generator_Next(PyObject *self);
1641 static int __pyx_Generator_init(void);
1642 
1643 /* CheckBinaryVersion.proto */
1644 static int __Pyx_check_binary_version(void);
1645 
1646 /* InitStrings.proto */
1647 static int __Pyx_InitStrings(__Pyx_StringTabEntry *t);
1648 
1649 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_9index_set_wrap(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, IndexSet __pyx_v_other); /* proto*/
1650 static CYTHON_INLINE IndexSet __pyx_f_8PyClical_9index_set_unwrap(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto*/
1651 static PyObject *__pyx_f_8PyClical_9index_set_copy(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, int __pyx_skip_dispatch); /* proto*/
1652 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_8clifford_wrap(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, Clifford __pyx_v_other); /* proto*/
1653 static CYTHON_INLINE Clifford __pyx_f_8PyClical_8clifford_unwrap(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto*/
1654 static PyObject *__pyx_f_8PyClical_8clifford_copy(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, int __pyx_skip_dispatch); /* proto*/
1655 
1656 /* Module declarations from 'libcpp.vector' */
1657 
1658 /* Module declarations from 'glucat' */
1659 
1660 /* Module declarations from 'PyClical' */
1661 static PyTypeObject *__pyx_ptype_8PyClical_index_set = 0;
1662 static PyTypeObject *__pyx_ptype_8PyClical_clifford = 0;
1663 static PyTypeObject *__pyx_ptype_8PyClical___pyx_scope_struct____iter__ = 0;
1664 static CYTHON_INLINE IndexSet __pyx_f_8PyClical_toIndexSet(PyObject *); /*proto*/
1665 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_compare(PyObject *, PyObject *, int __pyx_skip_dispatch); /*proto*/
1666 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_min_neg(PyObject *, int __pyx_skip_dispatch); /*proto*/
1667 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_max_pos(PyObject *, int __pyx_skip_dispatch); /*proto*/
1668 static CYTHON_INLINE std::vector<scalar_t> __pyx_f_8PyClical_list_to_vector(PyObject *); /*proto*/
1669 static CYTHON_INLINE Clifford __pyx_f_8PyClical_toClifford(PyObject *); /*proto*/
1670 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_inv(PyObject *, int __pyx_skip_dispatch); /*proto*/
1671 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_scalar(PyObject *, int __pyx_skip_dispatch); /*proto*/
1672 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_real(PyObject *, int __pyx_skip_dispatch); /*proto*/
1673 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_imag(PyObject *, int __pyx_skip_dispatch); /*proto*/
1674 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_pure(PyObject *, int __pyx_skip_dispatch); /*proto*/
1675 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_even(PyObject *, int __pyx_skip_dispatch); /*proto*/
1676 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_odd(PyObject *, int __pyx_skip_dispatch); /*proto*/
1677 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_involute(PyObject *, int __pyx_skip_dispatch); /*proto*/
1678 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_reverse(PyObject *, int __pyx_skip_dispatch); /*proto*/
1679 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_conj(PyObject *, int __pyx_skip_dispatch); /*proto*/
1680 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_quad(PyObject *, int __pyx_skip_dispatch); /*proto*/
1681 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_norm(PyObject *, int __pyx_skip_dispatch); /*proto*/
1682 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_abs(PyObject *, int __pyx_skip_dispatch); /*proto*/
1683 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_max_abs(PyObject *, int __pyx_skip_dispatch); /*proto*/
1684 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_pow(PyObject *, PyObject *, int __pyx_skip_dispatch); /*proto*/
1685 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_outer_pow(PyObject *, PyObject *, int __pyx_skip_dispatch); /*proto*/
1686 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_complexifier(PyObject *, int __pyx_skip_dispatch); /*proto*/
1687 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_sqrt(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_sqrt *__pyx_optional_args); /*proto*/
1688 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_exp(PyObject *, int __pyx_skip_dispatch); /*proto*/
1689 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_log(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_log *__pyx_optional_args); /*proto*/
1690 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_cos(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_cos *__pyx_optional_args); /*proto*/
1691 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_acos(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_acos *__pyx_optional_args); /*proto*/
1692 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_cosh(PyObject *, int __pyx_skip_dispatch); /*proto*/
1693 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_acosh(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_acosh *__pyx_optional_args); /*proto*/
1694 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_sin(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_sin *__pyx_optional_args); /*proto*/
1695 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_asin(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_asin *__pyx_optional_args); /*proto*/
1696 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_sinh(PyObject *, int __pyx_skip_dispatch); /*proto*/
1697 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_asinh(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_asinh *__pyx_optional_args); /*proto*/
1698 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_tan(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_tan *__pyx_optional_args); /*proto*/
1699 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_atan(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_atan *__pyx_optional_args); /*proto*/
1700 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_tanh(PyObject *, int __pyx_skip_dispatch); /*proto*/
1701 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_atanh(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_atanh *__pyx_optional_args); /*proto*/
1702 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*/
1703 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_cga3(PyObject *, int __pyx_skip_dispatch); /*proto*/
1704 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_cga3std(PyObject *, int __pyx_skip_dispatch); /*proto*/
1705 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_agc3(PyObject *, int __pyx_skip_dispatch); /*proto*/
1706 #define __Pyx_MODULE_NAME "PyClical"
1707 extern int __pyx_module_is_main_PyClical;
1708 int __pyx_module_is_main_PyClical = 0;
1709 
1710 /* Implementation of 'PyClical' */
1711 static PyObject *__pyx_builtin_IndexError;
1712 static PyObject *__pyx_builtin_RuntimeError;
1713 static PyObject *__pyx_builtin_TypeError;
1714 static PyObject *__pyx_builtin_ValueError;
1715 static PyObject *__pyx_builtin_NotImplemented;
1716 static PyObject *__pyx_builtin_range;
1717 static PyObject *__pyx_builtin_xrange;
1718 static const char __pyx_k_[] = ".";
1719 static const char __pyx_k_e[] = "e";
1720 static const char __pyx_k_i[] = "i";
1721 static const char __pyx_k_m[] = "m";
1722 static const char __pyx_k_p[] = "p";
1723 static const char __pyx_k_q[] = "q";
1724 static const char __pyx_k__2[] = " ";
1725 static const char __pyx_k__5[] = ":";
1726 static const char __pyx_k__6[] = "\n\t";
1727 static const char __pyx_k__7[] = " (";
1728 static const char __pyx_k__8[] = ", ";
1729 static const char __pyx_k__9[] = ").";
1730 static const char __pyx_k_cl[] = "cl";
1731 static const char __pyx_k_pi[] = "pi";
1732 static const char __pyx_k_cos[] = "cos";
1733 static const char __pyx_k_exp[] = "exp";
1734 static const char __pyx_k_frm[] = "frm";
1735 static const char __pyx_k_inv[] = "inv";
1736 static const char __pyx_k_ist[] = "ist";
1737 static const char __pyx_k_ixt[] = "ixt";
1738 static const char __pyx_k_lhs[] = "lhs";
1739 static const char __pyx_k_log[] = "log";
1740 static const char __pyx_k_max[] = "max";
1741 static const char __pyx_k_min[] = "min";
1742 static const char __pyx_k_obj[] = "obj";
1743 static const char __pyx_k_odd[] = "odd";
1744 static const char __pyx_k_pow[] = "pow";
1745 static const char __pyx_k_rhs[] = "rhs";
1746 static const char __pyx_k_sin[] = "sin";
1747 static const char __pyx_k_tan[] = "tan";
1748 static const char __pyx_k_tau[] = "tau";
1749 static const char __pyx_k_Real[] = "Real";
1750 static const char __pyx_k_acos[] = "acos";
1751 static const char __pyx_k_args[] = "args";
1752 static const char __pyx_k_asin[] = "asin";
1753 static const char __pyx_k_atan[] = "atan";
1754 static const char __pyx_k_conj[] = "conj";
1755 static const char __pyx_k_copy[] = "copy";
1756 static const char __pyx_k_cosh[] = "cosh";
1757 static const char __pyx_k_even[] = "even";
1758 static const char __pyx_k_fill[] = "fill";
1759 static const char __pyx_k_from[] = " from ";
1760 static const char __pyx_k_iter[] = "__iter__";
1761 static const char __pyx_k_main[] = "__main__";
1762 static const char __pyx_k_math[] = "math";
1763 static const char __pyx_k_name[] = "__name__";
1764 static const char __pyx_k_norm[] = "norm";
1765 static const char __pyx_k_pure[] = "pure";
1766 static const char __pyx_k_quad[] = "quad";
1767 static const char __pyx_k_send[] = "send";
1768 static const char __pyx_k_sinh[] = "sinh";
1769 static const char __pyx_k_sqrt[] = "sqrt";
1770 static const char __pyx_k_tanh[] = "tanh";
1771 static const char __pyx_k_test[] = "_test";
1772 static const char __pyx_k_0_8_2[] = "0.8.2";
1773 static const char __pyx_k_acosh[] = "acosh";
1774 static const char __pyx_k_asinh[] = "asinh";
1775 static const char __pyx_k_atanh[] = "atanh";
1776 static const char __pyx_k_close[] = "close";
1777 static const char __pyx_k_grade[] = "grade";
1778 static const char __pyx_k_istpq[] = "istpq";
1779 static const char __pyx_k_nbar3[] = "nbar3";
1780 static const char __pyx_k_ninf3[] = "ninf3";
1781 static const char __pyx_k_other[] = "other";
1782 static const char __pyx_k_range[] = "range";
1783 static const char __pyx_k_throw[] = "throw";
1784 static const char __pyx_k_using[] = " using (";
1785 static const char __pyx_k_value[] = " value ";
1786 static const char __pyx_k_import[] = "__import__";
1787 static const char __pyx_k_reduce[] = "__reduce__";
1788 static const char __pyx_k_scalar[] = "scalar";
1789 static const char __pyx_k_test_2[] = "__test__";
1790 static const char __pyx_k_xrange[] = "xrange";
1791 static const char __pyx_k_doctest[] = "doctest";
1792 static const char __pyx_k_invalid[] = " invalid ";
1793 static const char __pyx_k_numbers[] = "numbers";
1794 static const char __pyx_k_reverse[] = "reverse";
1795 static const char __pyx_k_testmod[] = "testmod";
1796 static const char __pyx_k_version[] = "__version__";
1797 static const char __pyx_k_Integral[] = "Integral";
1798 static const char __pyx_k_PyClical[] = "PyClical";
1799 static const char __pyx_k_Sequence[] = "Sequence";
1800 static const char __pyx_k_as_frame[] = " as frame:\n\t";
1801 static const char __pyx_k_clifford[] = "clifford";
1802 static const char __pyx_k_getstate[] = "__getstate__";
1803 static const char __pyx_k_involute[] = "involute";
1804 static const char __pyx_k_setstate[] = "__setstate__";
1805 static const char __pyx_k_to_frame[] = " to frame ";
1806 static const char __pyx_k_TypeError[] = "TypeError";
1807 static const char __pyx_k_index_set[] = "index_set";
1808 static const char __pyx_k_outer_pow[] = "outer_pow";
1809 static const char __pyx_k_reduce_ex[] = "__reduce_ex__";
1810 static const char __pyx_k_IndexError[] = "IndexError";
1811 static const char __pyx_k_ValueError[] = "ValueError";
1812 static const char __pyx_k_pyx_vtable[] = "__pyx_vtable__";
1813 static const char __pyx_k_collections[] = "collections";
1814 static const char __pyx_k_e_line_1887[] = "e (line 1887)";
1815 static const char __pyx_k_PyClical_pyx[] = "PyClical.pyx";
1816 static const char __pyx_k_RuntimeError[] = "RuntimeError";
1817 static const char __pyx_k_abs_line_1473[] = "abs (line 1473)";
1818 static const char __pyx_k_cos_line_1602[] = "cos (line 1602)";
1819 static const char __pyx_k_exp_line_1565[] = "exp (line 1565)";
1820 static const char __pyx_k_inv_line_1329[] = "inv (line 1329)";
1821 static const char __pyx_k_log_line_1579[] = "log (line 1579)";
1822 static const char __pyx_k_odd_line_1397[] = "odd (line 1397)";
1823 static const char __pyx_k_pow_line_1494[] = "pow (line 1494)";
1824 static const char __pyx_k_reduce_cython[] = "__reduce_cython__";
1825 static const char __pyx_k_sin_line_1679[] = "sin (line 1679)";
1826 static const char __pyx_k_tan_line_1752[] = "tan (line 1752)";
1827 static const char __pyx_k_using_invalid[] = " using invalid ";
1828 static const char __pyx_k_Cannot_reframe[] = "Cannot reframe";
1829 static const char __pyx_k_NotImplemented[] = "NotImplemented";
1830 static const char __pyx_k_Not_applicable[] = "Not applicable.";
1831 static const char __pyx_k_acos_line_1619[] = "acos (line 1619)";
1832 static const char __pyx_k_agc3_line_1844[] = "agc3 (line 1844)";
1833 static const char __pyx_k_asin_line_1698[] = "asin (line 1698)";
1834 static const char __pyx_k_atan_line_1769[] = "atan (line 1769)";
1835 static const char __pyx_k_cga3_line_1824[] = "cga3 (line 1824)";
1836 static const char __pyx_k_conj_line_1436[] = "conj (line 1436)";
1837 static const char __pyx_k_cosh_line_1640[] = "cosh (line 1640)";
1838 static const char __pyx_k_even_line_1388[] = "even (line 1388)";
1839 static const char __pyx_k_imag_line_1366[] = "imag (line 1366)";
1840 static const char __pyx_k_invalid_string[] = " invalid string ";
1841 static const char __pyx_k_norm_line_1462[] = "norm (line 1462)";
1842 static const char __pyx_k_pure_line_1377[] = "pure (line 1377)";
1843 static const char __pyx_k_quad_line_1451[] = "quad (line 1451)";
1844 static const char __pyx_k_real_line_1355[] = "real (line 1355)";
1845 static const char __pyx_k_sinh_line_1719[] = "sinh (line 1719)";
1846 static const char __pyx_k_sqrt_line_1542[] = "sqrt (line 1542)";
1847 static const char __pyx_k_tanh_line_1786[] = "tanh (line 1786)";
1848 static const char __pyx_k_acosh_line_1656[] = "acosh (line 1656)";
1849 static const char __pyx_k_asinh_line_1733[] = "asinh (line 1733)";
1850 static const char __pyx_k_atanh_line_1798[] = "atanh (line 1798)";
1851 static const char __pyx_k_istpq_line_1900[] = "istpq (line 1900)";
1852 static const char __pyx_k_setstate_cython[] = "__setstate_cython__";
1853 static const char __pyx_k_compare_line_490[] = "compare (line 490)";
1854 static const char __pyx_k_index_set___iter[] = "index_set.__iter__";
1855 static const char __pyx_k_max_pos_line_511[] = "max_pos (line 511)";
1856 static const char __pyx_k_min_neg_line_502[] = "min_neg (line 502)";
1857 static const char __pyx_k_scalar_line_1344[] = "scalar (line 1344)";
1858 static const char __pyx_k_cga3std_line_1833[] = "cga3std (line 1833)";
1859 static const char __pyx_k_max_abs_line_1482[] = "max_abs (line 1482)";
1860 static const char __pyx_k_reverse_line_1421[] = "reverse (line 1421)";
1861 static const char __pyx_k_cline_in_traceback[] = "cline_in_traceback";
1862 static const char __pyx_k_involute_line_1406[] = "involute (line 1406)";
1863 static const char __pyx_k_outer_pow_line_1518[] = "outer_pow (line 1518)";
1864 static const char __pyx_k_clifford_inv_line_925[] = "clifford.inv (line 925)";
1865 static const char __pyx_k_clifford_pow_line_979[] = "clifford.pow (line 979)";
1866 static const char __pyx_k_clifford_abs_line_1174[] = "clifford.abs (line 1174)";
1867 static const char __pyx_k_clifford_copy_line_554[] = "clifford.copy (line 554)";
1868 static const char __pyx_k_clifford_odd_line_1069[] = "clifford.odd (line 1069)";
1869 static const char __pyx_k_complexifier_line_1527[] = "complexifier (line 1527)";
1870 static const char __pyx_k_index_set_copy_line_64[] = "index_set.copy (line 64)";
1871 static const char __pyx_k_index_set_max_line_349[] = "index_set.max (line 349)";
1872 static const char __pyx_k_index_set_min_line_340[] = "index_set.min (line 340)";
1873 static const char __pyx_k_clifford_conj_line_1137[] = "clifford.conj (line 1137)";
1874 static const char __pyx_k_clifford_even_line_1060[] = "clifford.even (line 1060)";
1875 static const char __pyx_k_clifford_norm_line_1163[] = "clifford.norm (line 1163)";
1876 static const char __pyx_k_clifford_pure_line_1049[] = "clifford.pure (line 1049)";
1877 static const char __pyx_k_clifford_quad_line_1152[] = "clifford.quad (line 1152)";
1878 static const char __pyx_k_Unary_print_clifford_1_1[] = "\n Unary -.\n\n >>> print -clifford(\"{1}\")\n -{1}\n ";
1879 static const char __pyx_k_clifford___or___line_938[] = "clifford.__or__ (line 938)";
1880 static const char __pyx_k_clifford_frame_line_1214[] = "clifford.frame (line 1214)";
1881 static const char __pyx_k_clifford_hidden_doctests[] = "clifford_hidden_doctests";
1882 static const char __pyx_k_clifford_isnan_line_1205[] = "clifford.isnan (line 1205)";
1883 static const char __pyx_k_index_set_count_line_313[] = "index_set.count (line 313)";
1884 static const char __pyx_k_clifford___add___line_739[] = "clifford.__add__ (line 739)";
1885 static const char __pyx_k_clifford___and___line_835[] = "clifford.__and__ (line 835)";
1886 static const char __pyx_k_clifford___div___line_895[] = "clifford.__div__ (line 895)";
1887 static const char __pyx_k_clifford___ior___line_949[] = "clifford.__ior__ (line 949)";
1888 static const char __pyx_k_clifford___mod___line_805[] = "clifford.__mod__ (line 805)";
1889 static const char __pyx_k_clifford___mul___line_779[] = "clifford.__mul__ (line 779)";
1890 static const char __pyx_k_clifford___neg___line_721[] = "clifford.__neg__ (line 721)";
1891 static const char __pyx_k_clifford___pos___line_730[] = "clifford.__pos__ (line 730)";
1892 static const char __pyx_k_clifford___pow___line_960[] = "clifford.__pow__ (line 960)";
1893 static const char __pyx_k_clifford___sub___line_759[] = "clifford.__sub__ (line 759)";
1894 static const char __pyx_k_clifford___xor___line_865[] = "clifford.__xor__ (line 865)";
1895 static const char __pyx_k_clifford_reframe_line_648[] = "clifford.reframe (line 648)";
1896 static const char __pyx_k_clifford_scalar_line_1038[] = "clifford.scalar (line 1038)";
1897 static const char __pyx_k_index_set___or___line_291[] = "index_set.__or__ (line 291)";
1898 static const char __pyx_k_index_set_hidden_doctests[] = "index_set_hidden_doctests";
1899 static const char __pyx_k_random_clifford_line_1815[] = "random_clifford (line 1815)";
1900 static const char __pyx_k_Cannot_take_vector_part_of[] = "Cannot take vector part of ";
1901 static const char __pyx_k_Unary_print_clifford_1_1_2[] = "\n Unary +.\n\n >>> print +clifford(\"{1}\")\n {1}\n ";
1902 static const char __pyx_k_clifford___iadd___line_750[] = "clifford.__iadd__ (line 750)";
1903 static const char __pyx_k_clifford___iand___line_850[] = "clifford.__iand__ (line 850)";
1904 static const char __pyx_k_clifford___idiv___line_910[] = "clifford.__idiv__ (line 910)";
1905 static const char __pyx_k_clifford___imod___line_820[] = "clifford.__imod__ (line 820)";
1906 static const char __pyx_k_clifford___imul___line_792[] = "clifford.__imul__ (line 792)";
1907 static const char __pyx_k_clifford___isub___line_770[] = "clifford.__isub__ (line 770)";
1908 static const char __pyx_k_clifford___iter___line_637[] = "clifford.__iter__ (line 637)";
1909 static const char __pyx_k_clifford___ixor___line_880[] = "clifford.__ixor__ (line 880)";
1910 static const char __pyx_k_clifford___str___line_1234[] = "clifford.__str__ (line 1234)";
1911 static const char __pyx_k_clifford_max_abs_line_1183[] = "clifford.max_abs (line 1183)";
1912 static const char __pyx_k_clifford_reverse_line_1122[] = "clifford.reverse (line 1122)";
1913 static const char __pyx_k_index_set___and___line_269[] = "index_set.__and__ (line 269)";
1914 static const char __pyx_k_index_set___ior___line_302[] = "index_set.__ior__ (line 302)";
1915 static const char __pyx_k_index_set___str___line_393[] = "index_set.__str__ (line 393)";
1916 static const char __pyx_k_index_set___xor___line_247[] = "index_set.__xor__ (line 247)";
1917 static const char __pyx_k_clifford___call___line_1019[] = "clifford.__call__ (line 1019)";
1918 static const char __pyx_k_clifford___repr___line_1225[] = "clifford.__repr__ (line 1225)";
1919 static const char __pyx_k_clifford_involute_line_1106[] = "clifford.involute (line 1106)";
1920 static const char __pyx_k_index_set___iand___line_280[] = "index_set.__iand__ (line 280)";
1921 static const char __pyx_k_index_set___iter___line_227[] = "index_set.__iter__ (line 227)";
1922 static const char __pyx_k_index_set___ixor___line_258[] = "index_set.__ixor__ (line 258)";
1923 static const char __pyx_k_index_set___repr___line_382[] = "index_set.__repr__ (line 382)";
1924 static const char __pyx_k_clifford_outer_pow_line_1003[] = "clifford.outer_pow (line 1003)";
1925 static const char __pyx_k_clifford_truncated_line_1194[] = "clifford.truncated (line 1194)";
1926 static const char __pyx_k_index_set_count_neg_line_322[] = "index_set.count_neg (line 322)";
1927 static const char __pyx_k_index_set_count_pos_line_331[] = "index_set.count_pos (line 331)";
1928 static const char __pyx_k_clifford___getitem___line_706[] = "clifford.__getitem__ (line 706)";
1929 static const char __pyx_k_index_set___invert___line_238[] = "index_set.__invert__ (line 238)";
1930 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 ";
1931 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 ";
1932 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 ";
1933 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 ";
1934 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 ";
1935 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 ";
1936 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 ";
1937 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,\n -3 4 7\n ";
1938 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 ";
1939 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 ";
1940 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 ";
1941 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 ";
1942 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 ";
1943 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 ";
1944 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 ";
1945 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 ";
1946 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 ";
1947 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 ";
1948 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 ";
1949 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 ";
1950 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 ";
1951 static const char __pyx_k_clifford_vector_part_line_1078[] = "clifford.vector_part (line 1078)";
1952 static const char __pyx_k_index_set___getitem___line_189[] = "index_set.__getitem__ (line 189)";
1953 static const char __pyx_k_index_set___setitem___line_177[] = "index_set.__setitem__ (line 177)";
1954 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 ";
1955 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 ";
1956 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 ";
1957 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 ";
1958 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 ";
1959 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 ";
1960 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 ";
1961 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 ";
1962 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 ";
1963 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 ";
1964 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 ";
1965 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 ";
1966 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 ";
1967 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 ";
1968 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 ";
1969 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 ";
1970 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 ";
1971 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 ";
1972 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 ";
1973 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 ";
1974 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 ";
1975 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 ";
1976 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 ";
1977 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 ";
1978 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 ";
1979 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 ";
1980 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 ";
1981 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 ";
1982 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 ";
1983 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 ";
1984 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 ";
1985 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 ";
1986 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 ";
1987 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 ";
1988 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 ";
1989 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 ";
1990 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 ";
1991 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 ";
1992 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 ";
1993 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,\n Traceback (most recent call last):\n ...\n TypeError: Not applicable.\n ";
1994 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 ";
1995 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 ";
1996 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 ";
1997 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 ";
1998 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 ";
1999 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 ";
2000 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 ";
2001 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 ";
2002 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 ";
2003 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 ";
2004 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 ";
2005 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 ";
2006 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 ";
2007 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 ";
2008 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 ";
2009 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 ";
2010 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 ";
2011 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 ";
2012 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 ";
2013 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 ";
2014 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 ";
2015 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 ";
2016 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 ";
2017 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 <type 'PyClical.index_set'>\n ";
2018 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 ";
2019 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 ";
2020 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 ";
2021 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 set([1, 2, 100]).\n >>> print index_set([1,2])\n Traceback (most recent call last):\n ...\n TypeError: Cannot initialize index_set object from <type '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_se""t({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 ";
2022  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 ";
2023  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 ";
2024  static const char __pyx_k_This_comparison_operator_is_not[] = "This comparison operator is not implemented for ";
2025  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 ";
2026  static const char __pyx_k_index_set_sign_of_mult_line_364[] = "index_set.sign_of_mult (line 364)";
2027  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 ";
2028  static const char __pyx_k_Cannot_initialize_clifford_objec[] = "Cannot initialize clifford object from";
2029  static const char __pyx_k_Cannot_initialize_index_set_obje[] = "Cannot initialize index_set object from";
2030  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 ";
2031  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 ";
2032  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 ";
2033  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 ";
2034  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 ";
2035  static const char __pyx_k_clifford_hidden_doctests_line_12[] = "clifford_hidden_doctests (line 1243)";
2036  static const char __pyx_k_index_set_hidden_doctests_line_4[] = "index_set_hidden_doctests (line 404)";
2037  static const char __pyx_k_index_set_sign_of_square_line_37[] = "index_set.sign_of_square (line 373)";
2038  static const char __pyx_k_no_default___reduce___due_to_non[] = "no default __reduce__ due to non-trivial __cinit__";
2039  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 ";
2040  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 ";
2041  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 ";
2042  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 ";
2043  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(2L)\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 <type 'list'>.\n >>> print clifford(None)\n Traceback (most recent call last):\n ...\n TypeError: Cannot initialize clifford object from <type 'NoneType'>.\n >>> print clifford(None,[1,2])\n Traceback (most recent call last):\n ...\n TypeError: Cannot initialize clifford object from (<type 'NoneType'>, <type 'list'>).\n >>> print clifford([1,2],[1,2])\n Traceback (most recent call last):\n ...\n TypeError: Cannot initialize clifford object from (<type 'list'>, <type '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 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\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 ";
2044  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 ";
2045  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 ";
2046  static PyObject *__pyx_kp_s_;
2047  static PyObject *__pyx_kp_s_0_8_2;
2048  static PyObject *__pyx_kp_u_Abbreviation_for_clifford_index;
2049  static PyObject *__pyx_kp_u_Abbreviation_for_index_set_q_p;
2050  static PyObject *__pyx_kp_u_Absolute_value_of_multivector_m;
2051  static PyObject *__pyx_kp_u_Absolute_value_square_root_of_n;
2052  static PyObject *__pyx_kp_s_Cannot_initialize_clifford_objec;
2053  static PyObject *__pyx_kp_s_Cannot_initialize_index_set_obje;
2054  static PyObject *__pyx_kp_s_Cannot_reframe;
2055  static PyObject *__pyx_kp_s_Cannot_take_vector_part_of;
2056  static PyObject *__pyx_kp_u_Cardinality_Number_of_indices_i;
2057  static PyObject *__pyx_kp_u_Check_if_a_multivector_contains;
2058  static PyObject *__pyx_kp_u_Conjugation_reverse_o_involute;
2059  static PyObject *__pyx_kp_u_Conjugation_reverse_o_involute_2;
2060  static PyObject *__pyx_kp_u_Contraction_print_clifford_1_cl;
2061  static PyObject *__pyx_kp_u_Contraction_x_clifford_1_x_clif;
2062  static PyObject *__pyx_kp_u_Convert_CGA3_null_vector_to_Euc;
2063  static PyObject *__pyx_kp_u_Convert_CGA3_null_vector_to_sta;
2064  static PyObject *__pyx_kp_u_Convert_Euclidean_3D_multivecto;
2065  static PyObject *__pyx_kp_u_Copy_this_clifford_object_x_cli;
2066  static PyObject *__pyx_kp_u_Copy_this_index_set_object_s_in;
2067  static PyObject *__pyx_kp_u_Cosine_of_multivector_with_opti;
2068  static PyObject *__pyx_kp_u_Even_part_of_multivector_sum_of;
2069  static PyObject *__pyx_kp_u_Even_part_of_multivector_sum_of_2;
2070  static PyObject *__pyx_kp_u_Exponential_of_multivector_x_cl;
2071  static PyObject *__pyx_kp_u_Geometric_difference_print_clif;
2072  static PyObject *__pyx_kp_u_Geometric_difference_x_clifford;
2073  static PyObject *__pyx_kp_u_Geometric_multiplicative_invers;
2074  static PyObject *__pyx_kp_u_Geometric_multiplicative_invers_2;
2075  static PyObject *__pyx_kp_u_Geometric_product_print_cliffor;
2076  static PyObject *__pyx_kp_u_Geometric_product_x_clifford_2;
2077  static PyObject *__pyx_kp_u_Geometric_quotient_print_cliffo;
2078  static PyObject *__pyx_kp_u_Geometric_quotient_x_clifford_1;
2079  static PyObject *__pyx_kp_u_Geometric_sum_print_clifford_1;
2080  static PyObject *__pyx_kp_u_Geometric_sum_x_clifford_1_x_cl;
2081  static PyObject *__pyx_kp_u_Get_the_value_of_an_index_set_o;
2082  static PyObject *__pyx_kp_u_Hyperbolic_cosine_of_multivecto;
2083  static PyObject *__pyx_kp_u_Hyperbolic_sine_of_multivector;
2084  static PyObject *__pyx_kp_u_Hyperbolic_tangent_of_multivect;
2085  static PyObject *__pyx_kp_u_Imaginary_part_deprecated_alway;
2086  static PyObject *__pyx_n_s_IndexError;
2087  static PyObject *__pyx_kp_u_Inner_product_print_clifford_1;
2088  static PyObject *__pyx_kp_u_Inner_product_x_clifford_1_x_cl;
2089  static PyObject *__pyx_kp_u_Integer_power_of_multivector_ob;
2090  static PyObject *__pyx_n_s_Integral;
2091  static PyObject *__pyx_kp_u_Inverse_cosine_of_multivector_w;
2092  static PyObject *__pyx_kp_u_Inverse_hyperbolic_cosine_of_mu;
2093  static PyObject *__pyx_kp_u_Inverse_hyperbolic_sine_of_mult;
2094  static PyObject *__pyx_kp_u_Inverse_hyperbolic_tangent_of_m;
2095  static PyObject *__pyx_kp_u_Inverse_sine_of_multivector_wit;
2096  static PyObject *__pyx_kp_u_Inverse_tangent_of_multivector;
2097  static PyObject *__pyx_kp_u_Iterate_over_the_indices_of_an;
2098  static PyObject *__pyx_kp_u_Main_involution_each_i_is_repla;
2099  static PyObject *__pyx_kp_u_Main_involution_each_i_is_repla_2;
2100  static PyObject *__pyx_kp_u_Maximum_absolute_value_of_coord;
2101  static PyObject *__pyx_kp_u_Maximum_member_index_set_1_1_2;
2102  static PyObject *__pyx_kp_u_Maximum_of_absolute_values_of_c;
2103  static PyObject *__pyx_kp_u_Maximum_positive_index_or_0_if;
2104  static PyObject *__pyx_kp_u_Minimum_member_index_set_1_1_2;
2105  static PyObject *__pyx_kp_u_Minimum_negative_index_or_0_if;
2106  static PyObject *__pyx_kp_u_Natural_logarithm_of_multivecto;
2107  static PyObject *__pyx_kp_u_Norm_sum_of_squares_of_coordina;
2108  static PyObject *__pyx_n_s_NotImplemented;
2109  static PyObject *__pyx_kp_s_Not_applicable;
2110  static PyObject *__pyx_kp_u_Not_applicable_for_a_in_cliffor;
2111  static PyObject *__pyx_kp_u_Number_of_negative_indices_incl;
2112  static PyObject *__pyx_kp_u_Number_of_positive_indices_incl;
2113  static PyObject *__pyx_kp_u_Odd_part_of_multivector_sum_of;
2114  static PyObject *__pyx_kp_u_Odd_part_of_multivector_sum_of_2;
2115  static PyObject *__pyx_kp_u_Outer_product_power_of_multivec;
2116  static PyObject *__pyx_kp_u_Outer_product_power_x_clifford;
2117  static PyObject *__pyx_kp_u_Outer_product_print_clifford_1;
2118  static PyObject *__pyx_kp_u_Outer_product_x_clifford_1_x_cl;
2119  static PyObject *__pyx_kp_u_Power_self_to_the_m_x_clifford;
2120  static PyObject *__pyx_kp_u_Power_self_to_the_m_x_clifford_2;
2121  static PyObject *__pyx_kp_u_Pure_grade_vector_part_print_cl;
2122  static PyObject *__pyx_kp_u_Pure_part_print_clifford_1_1_1;
2123  static PyObject *__pyx_kp_u_Pure_part_print_pure_clifford_1;
2124  static PyObject *__pyx_kp_u_Put_self_into_a_larger_frame_co;
2125  static PyObject *__pyx_n_s_PyClical;
2126  static PyObject *__pyx_kp_s_PyClical_pyx;
2127  static PyObject *__pyx_kp_u_Quadratic_form_rev_x_x_0_print;
2128  static PyObject *__pyx_kp_u_Quadratic_form_rev_x_x_0_print_2;
2129  static PyObject *__pyx_kp_u_Random_multivector_within_a_fra;
2130  static PyObject *__pyx_n_s_Real;
2131  static PyObject *__pyx_kp_u_Real_part_synonym_for_scalar_pa;
2132  static PyObject *__pyx_kp_u_Remove_all_terms_of_self_with_r;
2133  static PyObject *__pyx_kp_u_Reversion_eg_1_2_2_1_print_reve;
2134  static PyObject *__pyx_kp_u_Reversion_eg_clifford_1_cliffor;
2135  static PyObject *__pyx_n_s_RuntimeError;
2136  static PyObject *__pyx_kp_u_Scalar_part_clifford_1_1_1_2_sc;
2137  static PyObject *__pyx_kp_u_Scalar_part_scalar_clifford_1_1;
2138  static PyObject *__pyx_n_s_Sequence;
2139  static PyObject *__pyx_kp_u_Set_complement_not_print_index;
2140  static PyObject *__pyx_kp_u_Set_intersection_and_print_inde;
2141  static PyObject *__pyx_kp_u_Set_intersection_and_x_index_se;
2142  static PyObject *__pyx_kp_u_Set_the_value_of_an_index_set_o;
2143  static PyObject *__pyx_kp_u_Set_union_or_print_index_set_1;
2144  static PyObject *__pyx_kp_u_Set_union_or_x_index_set_1_x_in;
2145  static PyObject *__pyx_kp_u_Sign_of_geometric_product_of_tw;
2146  static PyObject *__pyx_kp_u_Sign_of_geometric_square_of_a_C;
2147  static PyObject *__pyx_kp_u_Sine_of_multivector_with_option;
2148  static PyObject *__pyx_kp_u_Square_root_of_1_which_commutes;
2149  static PyObject *__pyx_kp_u_Square_root_of_multivector_with;
2150  static PyObject *__pyx_kp_u_Subalgebra_generated_by_all_gen;
2151  static PyObject *__pyx_kp_u_Subscripting_map_from_index_set;
2152  static PyObject *__pyx_kp_u_Symmetric_set_difference_exclus;
2153  static PyObject *__pyx_kp_u_Symmetric_set_difference_exclus_2;
2154  static PyObject *__pyx_kp_u_Tangent_of_multivector_with_opt;
2155  static PyObject *__pyx_kp_u_Tests_for_functions_that_Doctes;
2156  static PyObject *__pyx_kp_u_Tests_for_functions_that_Doctes_2;
2157  static PyObject *__pyx_kp_u_The_informal_string_representat;
2158  static PyObject *__pyx_kp_u_The_informal_string_representat_2;
2159  static PyObject *__pyx_kp_u_The_official_string_representat;
2160  static PyObject *__pyx_kp_u_The_official_string_representat_2;
2161  static PyObject *__pyx_kp_s_This_comparison_operator_is_not;
2162  static PyObject *__pyx_kp_u_Transform_left_hand_side_using;
2163  static PyObject *__pyx_kp_u_Transform_left_hand_side_using_2;
2164  static PyObject *__pyx_n_s_TypeError;
2165  static PyObject *__pyx_kp_u_Unary_print_clifford_1_1;
2166  static PyObject *__pyx_kp_u_Unary_print_clifford_1_1_2;
2167  static PyObject *__pyx_n_s_ValueError;
2168  static PyObject *__pyx_kp_u_Vector_part_of_multivector_as_a;
2169  static PyObject *__pyx_kp_s__2;
2170  static PyObject *__pyx_kp_s__5;
2171  static PyObject *__pyx_kp_s__6;
2172  static PyObject *__pyx_kp_s__7;
2173  static PyObject *__pyx_kp_s__8;
2174  static PyObject *__pyx_kp_s__9;
2175  static PyObject *__pyx_kp_u_abs_line_1473;
2176  static PyObject *__pyx_n_s_acos;
2177  static PyObject *__pyx_kp_u_acos_line_1619;
2178  static PyObject *__pyx_n_s_acosh;
2179  static PyObject *__pyx_kp_u_acosh_line_1656;
2180  static PyObject *__pyx_kp_u_agc3_line_1844;
2181  static PyObject *__pyx_n_s_args;
2182  static PyObject *__pyx_kp_s_as_frame;
2183  static PyObject *__pyx_n_s_asin;
2184  static PyObject *__pyx_kp_u_asin_line_1698;
2185  static PyObject *__pyx_n_s_asinh;
2186  static PyObject *__pyx_kp_u_asinh_line_1733;
2187  static PyObject *__pyx_n_s_atan;
2188  static PyObject *__pyx_kp_u_atan_line_1769;
2189  static PyObject *__pyx_n_s_atanh;
2190  static PyObject *__pyx_kp_u_atanh_line_1798;
2191  static PyObject *__pyx_kp_u_cga3_line_1824;
2192  static PyObject *__pyx_kp_u_cga3std_line_1833;
2193  static PyObject *__pyx_n_s_cl;
2194  static PyObject *__pyx_n_s_clifford;
2195  static PyObject *__pyx_kp_u_clifford___add___line_739;
2196  static PyObject *__pyx_kp_u_clifford___and___line_835;
2197  static PyObject *__pyx_kp_u_clifford___call___line_1019;
2198  static PyObject *__pyx_kp_u_clifford___div___line_895;
2199  static PyObject *__pyx_kp_u_clifford___getitem___line_706;
2200  static PyObject *__pyx_kp_u_clifford___iadd___line_750;
2201  static PyObject *__pyx_kp_u_clifford___iand___line_850;
2202  static PyObject *__pyx_kp_u_clifford___idiv___line_910;
2203  static PyObject *__pyx_kp_u_clifford___imod___line_820;
2204  static PyObject *__pyx_kp_u_clifford___imul___line_792;
2205  static PyObject *__pyx_kp_u_clifford___ior___line_949;
2206  static PyObject *__pyx_kp_u_clifford___isub___line_770;
2207  static PyObject *__pyx_kp_u_clifford___iter___line_637;
2208  static PyObject *__pyx_kp_u_clifford___ixor___line_880;
2209  static PyObject *__pyx_kp_u_clifford___mod___line_805;
2210  static PyObject *__pyx_kp_u_clifford___mul___line_779;
2211  static PyObject *__pyx_kp_u_clifford___neg___line_721;
2212  static PyObject *__pyx_kp_u_clifford___or___line_938;
2213  static PyObject *__pyx_kp_u_clifford___pos___line_730;
2214  static PyObject *__pyx_kp_u_clifford___pow___line_960;
2215  static PyObject *__pyx_kp_u_clifford___repr___line_1225;
2216  static PyObject *__pyx_kp_u_clifford___str___line_1234;
2217  static PyObject *__pyx_kp_u_clifford___sub___line_759;
2218  static PyObject *__pyx_kp_u_clifford___xor___line_865;
2219  static PyObject *__pyx_kp_u_clifford_abs_line_1174;
2220  static PyObject *__pyx_kp_u_clifford_conj_line_1137;
2221  static PyObject *__pyx_kp_u_clifford_copy_line_554;
2222  static PyObject *__pyx_kp_u_clifford_even_line_1060;
2223  static PyObject *__pyx_kp_u_clifford_frame_line_1214;
2224  static PyObject *__pyx_n_s_clifford_hidden_doctests;
2225  static PyObject *__pyx_kp_u_clifford_hidden_doctests_line_12;
2226  static PyObject *__pyx_kp_u_clifford_inv_line_925;
2227  static PyObject *__pyx_kp_u_clifford_involute_line_1106;
2228  static PyObject *__pyx_kp_u_clifford_isnan_line_1205;
2229  static PyObject *__pyx_kp_u_clifford_max_abs_line_1183;
2230  static PyObject *__pyx_kp_u_clifford_norm_line_1163;
2231  static PyObject *__pyx_kp_u_clifford_odd_line_1069;
2232  static PyObject *__pyx_kp_u_clifford_outer_pow_line_1003;
2233  static PyObject *__pyx_kp_u_clifford_pow_line_979;
2234  static PyObject *__pyx_kp_u_clifford_pure_line_1049;
2235  static PyObject *__pyx_kp_u_clifford_quad_line_1152;
2236  static PyObject *__pyx_kp_u_clifford_reframe_line_648;
2237  static PyObject *__pyx_kp_u_clifford_reverse_line_1122;
2238  static PyObject *__pyx_kp_u_clifford_scalar_line_1038;
2239  static PyObject *__pyx_kp_u_clifford_truncated_line_1194;
2240  static PyObject *__pyx_kp_u_clifford_vector_part_line_1078;
2241  static PyObject *__pyx_n_s_cline_in_traceback;
2242  static PyObject *__pyx_n_s_close;
2243  static PyObject *__pyx_n_s_collections;
2244  static PyObject *__pyx_kp_u_compare_line_490;
2245  static PyObject *__pyx_kp_u_complexifier_line_1527;
2246  static PyObject *__pyx_n_s_conj;
2247  static PyObject *__pyx_kp_u_conj_line_1436;
2248  static PyObject *__pyx_n_s_copy;
2249  static PyObject *__pyx_n_s_cos;
2250  static PyObject *__pyx_kp_u_cos_line_1602;
2251  static PyObject *__pyx_n_s_cosh;
2252  static PyObject *__pyx_kp_u_cosh_line_1640;
2253  static PyObject *__pyx_n_s_doctest;
2254  static PyObject *__pyx_n_s_e;
2255  static PyObject *__pyx_kp_u_e_line_1887;
2256  static PyObject *__pyx_n_s_even;
2257  static PyObject *__pyx_kp_u_even_line_1388;
2258  static PyObject *__pyx_n_s_exp;
2259  static PyObject *__pyx_kp_u_exp_line_1565;
2260  static PyObject *__pyx_n_s_fill;
2261  static PyObject *__pyx_n_s_frm;
2262  static PyObject *__pyx_kp_s_from;
2263  static PyObject *__pyx_n_s_getstate;
2264  static PyObject *__pyx_n_s_grade;
2265  static PyObject *__pyx_n_s_i;
2266  static PyObject *__pyx_kp_u_imag_line_1366;
2267  static PyObject *__pyx_n_s_import;
2268  static PyObject *__pyx_n_s_index_set;
2269  static PyObject *__pyx_kp_u_index_set___and___line_269;
2270  static PyObject *__pyx_kp_u_index_set___getitem___line_189;
2271  static PyObject *__pyx_kp_u_index_set___iand___line_280;
2272  static PyObject *__pyx_kp_u_index_set___invert___line_238;
2273  static PyObject *__pyx_kp_u_index_set___ior___line_302;
2274  static PyObject *__pyx_n_s_index_set___iter;
2275  static PyObject *__pyx_kp_u_index_set___iter___line_227;
2276  static PyObject *__pyx_kp_u_index_set___ixor___line_258;
2277  static PyObject *__pyx_kp_u_index_set___or___line_291;
2278  static PyObject *__pyx_kp_u_index_set___repr___line_382;
2279  static PyObject *__pyx_kp_u_index_set___setitem___line_177;
2280  static PyObject *__pyx_kp_u_index_set___str___line_393;
2281  static PyObject *__pyx_kp_u_index_set___xor___line_247;
2282  static PyObject *__pyx_kp_u_index_set_copy_line_64;
2283  static PyObject *__pyx_kp_u_index_set_count_line_313;
2284  static PyObject *__pyx_kp_u_index_set_count_neg_line_322;
2285  static PyObject *__pyx_kp_u_index_set_count_pos_line_331;
2286  static PyObject *__pyx_n_s_index_set_hidden_doctests;
2287  static PyObject *__pyx_kp_u_index_set_hidden_doctests_line_4;
2288  static PyObject *__pyx_kp_u_index_set_max_line_349;
2289  static PyObject *__pyx_kp_u_index_set_min_line_340;
2290  static PyObject *__pyx_kp_u_index_set_sign_of_mult_line_364;
2291  static PyObject *__pyx_kp_u_index_set_sign_of_square_line_37;
2292  static PyObject *__pyx_n_s_inv;
2293  static PyObject *__pyx_kp_u_inv_line_1329;
2294  static PyObject *__pyx_kp_s_invalid;
2295  static PyObject *__pyx_kp_s_invalid_string;
2296  static PyObject *__pyx_n_s_involute;
2297  static PyObject *__pyx_kp_u_involute_line_1406;
2298  static PyObject *__pyx_n_s_ist;
2299  static PyObject *__pyx_n_s_istpq;
2300  static PyObject *__pyx_kp_u_istpq_line_1900;
2301  static PyObject *__pyx_n_s_iter;
2302  static PyObject *__pyx_n_s_ixt;
2303  static PyObject *__pyx_kp_u_lexicographic_compare_eg_3_4_5;
2304  static PyObject *__pyx_n_s_lhs;
2305  static PyObject *__pyx_n_s_log;
2306  static PyObject *__pyx_kp_u_log_line_1579;
2307  static PyObject *__pyx_n_s_m;
2308  static PyObject *__pyx_n_s_main;
2309  static PyObject *__pyx_n_s_math;
2310  static PyObject *__pyx_n_s_max;
2311  static PyObject *__pyx_kp_u_max_abs_line_1482;
2312  static PyObject *__pyx_kp_u_max_pos_line_511;
2313  static PyObject *__pyx_n_s_min;
2314  static PyObject *__pyx_kp_u_min_neg_line_502;
2315  static PyObject *__pyx_n_s_name;
2316  static PyObject *__pyx_n_s_nbar3;
2317  static PyObject *__pyx_n_s_ninf3;
2318  static PyObject *__pyx_kp_s_no_default___reduce___due_to_non;
2319  static PyObject *__pyx_n_s_norm;
2320  static PyObject *__pyx_kp_u_norm_line_1462;
2321  static PyObject *__pyx_kp_u_norm_sum_of_squares_of_coordina;
2322  static PyObject *__pyx_n_s_numbers;
2323  static PyObject *__pyx_n_s_obj;
2324  static PyObject *__pyx_n_s_odd;
2325  static PyObject *__pyx_kp_u_odd_line_1397;
2326  static PyObject *__pyx_n_s_other;
2327  static PyObject *__pyx_n_s_outer_pow;
2328  static PyObject *__pyx_kp_u_outer_pow_line_1518;
2329  static PyObject *__pyx_n_s_p;
2330  static PyObject *__pyx_n_s_pi;
2331  static PyObject *__pyx_n_s_pow;
2332  static PyObject *__pyx_kp_u_pow_line_1494;
2333  static PyObject *__pyx_n_s_pure;
2334  static PyObject *__pyx_kp_u_pure_line_1377;
2335  static PyObject *__pyx_n_s_pyx_vtable;
2336  static PyObject *__pyx_n_s_q;
2337  static PyObject *__pyx_n_s_quad;
2338  static PyObject *__pyx_kp_u_quad_line_1451;
2339  static PyObject *__pyx_kp_u_random_clifford_line_1815;
2340  static PyObject *__pyx_n_s_range;
2341  static PyObject *__pyx_kp_u_real_line_1355;
2342  static PyObject *__pyx_n_s_reduce;
2343  static PyObject *__pyx_n_s_reduce_cython;
2344  static PyObject *__pyx_n_s_reduce_ex;
2345  static PyObject *__pyx_n_s_reverse;
2346  static PyObject *__pyx_kp_u_reverse_line_1421;
2347  static PyObject *__pyx_n_s_rhs;
2348  static PyObject *__pyx_n_s_scalar;
2349  static PyObject *__pyx_kp_u_scalar_line_1344;
2350  static PyObject *__pyx_n_s_send;
2351  static PyObject *__pyx_n_s_setstate;
2352  static PyObject *__pyx_n_s_setstate_cython;
2353  static PyObject *__pyx_n_s_sin;
2354  static PyObject *__pyx_kp_u_sin_line_1679;
2355  static PyObject *__pyx_n_s_sinh;
2356  static PyObject *__pyx_kp_u_sinh_line_1719;
2357  static PyObject *__pyx_n_s_sqrt;
2358  static PyObject *__pyx_kp_u_sqrt_line_1542;
2359  static PyObject *__pyx_n_s_tan;
2360  static PyObject *__pyx_kp_u_tan_line_1752;
2361  static PyObject *__pyx_n_s_tanh;
2362  static PyObject *__pyx_kp_u_tanh_line_1786;
2363  static PyObject *__pyx_n_s_tau;
2364  static PyObject *__pyx_n_s_test;
2365  static PyObject *__pyx_n_s_test_2;
2366  static PyObject *__pyx_n_s_testmod;
2367  static PyObject *__pyx_n_s_throw;
2368  static PyObject *__pyx_kp_s_to_frame;
2369  static PyObject *__pyx_kp_s_using;
2370  static PyObject *__pyx_kp_s_using_invalid;
2371  static PyObject *__pyx_kp_s_value;
2372  static PyObject *__pyx_n_s_version;
2373  static PyObject *__pyx_n_s_xrange;
2374 static PyObject *__pyx_pf_8PyClical_9index_set_copy(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2375 static int __pyx_pf_8PyClical_9index_set_2__cinit__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_other); /* proto */
2376 static void __pyx_pf_8PyClical_9index_set_4__dealloc__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2377 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 */
2378 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 */
2379 static PyObject *__pyx_pf_8PyClical_9index_set_10__getitem__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_idx); /* proto */
2380 static int __pyx_pf_8PyClical_9index_set_12__contains__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_idx); /* proto */
2381 static PyObject *__pyx_pf_8PyClical_9index_set_14__iter__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2382 static PyObject *__pyx_pf_8PyClical_9index_set_17__invert__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2383 static PyObject *__pyx_pf_8PyClical_9index_set_19__xor__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2384 static PyObject *__pyx_pf_8PyClical_9index_set_21__ixor__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2385 static PyObject *__pyx_pf_8PyClical_9index_set_23__and__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2386 static PyObject *__pyx_pf_8PyClical_9index_set_25__iand__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2387 static PyObject *__pyx_pf_8PyClical_9index_set_27__or__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2388 static PyObject *__pyx_pf_8PyClical_9index_set_29__ior__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2389 static PyObject *__pyx_pf_8PyClical_9index_set_31count(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2390 static PyObject *__pyx_pf_8PyClical_9index_set_33count_neg(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2391 static PyObject *__pyx_pf_8PyClical_9index_set_35count_pos(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2392 static PyObject *__pyx_pf_8PyClical_9index_set_37min(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2393 static PyObject *__pyx_pf_8PyClical_9index_set_39max(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2394 static PyObject *__pyx_pf_8PyClical_9index_set_41hash_fn(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2395 static PyObject *__pyx_pf_8PyClical_9index_set_43sign_of_mult(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2396 static PyObject *__pyx_pf_8PyClical_9index_set_45sign_of_square(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2397 static PyObject *__pyx_pf_8PyClical_9index_set_47__repr__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2398 static PyObject *__pyx_pf_8PyClical_9index_set_49__str__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2399 static PyObject *__pyx_pf_8PyClical_9index_set_51__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2400 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 */
2401 static PyObject *__pyx_pf_8PyClical_index_set_hidden_doctests(CYTHON_UNUSED PyObject *__pyx_self); /* proto */
2402 static PyObject *__pyx_pf_8PyClical_2compare(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2403 static PyObject *__pyx_pf_8PyClical_4min_neg(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2404 static PyObject *__pyx_pf_8PyClical_6max_pos(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2405 static PyObject *__pyx_pf_8PyClical_8clifford_copy(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2406 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 */
2407 static void __pyx_pf_8PyClical_8clifford_4__dealloc__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2408 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 */
2409 static PyObject *__pyx_pf_8PyClical_8clifford_8__iter__(CYTHON_UNUSED struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2410 static PyObject *__pyx_pf_8PyClical_8clifford_10reframe(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_ixt); /* proto */
2411 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 */
2412 static PyObject *__pyx_pf_8PyClical_8clifford_14__getitem__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_ixt); /* proto */
2413 static PyObject *__pyx_pf_8PyClical_8clifford_16__neg__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2414 static PyObject *__pyx_pf_8PyClical_8clifford_18__pos__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2415 static PyObject *__pyx_pf_8PyClical_8clifford_20__add__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2416 static PyObject *__pyx_pf_8PyClical_8clifford_22__iadd__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2417 static PyObject *__pyx_pf_8PyClical_8clifford_24__sub__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2418 static PyObject *__pyx_pf_8PyClical_8clifford_26__isub__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2419 static PyObject *__pyx_pf_8PyClical_8clifford_28__mul__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2420 static PyObject *__pyx_pf_8PyClical_8clifford_30__imul__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2421 static PyObject *__pyx_pf_8PyClical_8clifford_32__mod__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2422 static PyObject *__pyx_pf_8PyClical_8clifford_34__imod__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2423 static PyObject *__pyx_pf_8PyClical_8clifford_36__and__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2424 static PyObject *__pyx_pf_8PyClical_8clifford_38__iand__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2425 static PyObject *__pyx_pf_8PyClical_8clifford_40__xor__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2426 static PyObject *__pyx_pf_8PyClical_8clifford_42__ixor__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2427 #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
2428 static PyObject *__pyx_pf_8PyClical_8clifford_44__div__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2429 #endif
2430 #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
2431 static PyObject *__pyx_pf_8PyClical_8clifford_46__idiv__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2432 #endif
2433 static PyObject *__pyx_pf_8PyClical_8clifford_48inv(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2434 static PyObject *__pyx_pf_8PyClical_8clifford_50__or__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2435 static PyObject *__pyx_pf_8PyClical_8clifford_52__ior__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2436 static PyObject *__pyx_pf_8PyClical_8clifford_54__pow__(PyObject *__pyx_v_self, PyObject *__pyx_v_m, CYTHON_UNUSED PyObject *__pyx_v_dummy); /* proto */
2437 static PyObject *__pyx_pf_8PyClical_8clifford_56pow(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_m); /* proto */
2438 static PyObject *__pyx_pf_8PyClical_8clifford_58outer_pow(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_m); /* proto */
2439 static PyObject *__pyx_pf_8PyClical_8clifford_60__call__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_grade); /* proto */
2440 static PyObject *__pyx_pf_8PyClical_8clifford_62scalar(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2441 static PyObject *__pyx_pf_8PyClical_8clifford_64pure(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2442 static PyObject *__pyx_pf_8PyClical_8clifford_66even(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2443 static PyObject *__pyx_pf_8PyClical_8clifford_68odd(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2444 static PyObject *__pyx_pf_8PyClical_8clifford_70vector_part(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_frm); /* proto */
2445 static PyObject *__pyx_pf_8PyClical_8clifford_72involute(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2446 static PyObject *__pyx_pf_8PyClical_8clifford_74reverse(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2447 static PyObject *__pyx_pf_8PyClical_8clifford_76conj(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2448 static PyObject *__pyx_pf_8PyClical_8clifford_78quad(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2449 static PyObject *__pyx_pf_8PyClical_8clifford_80norm(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2450 static PyObject *__pyx_pf_8PyClical_8clifford_82abs(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2451 static PyObject *__pyx_pf_8PyClical_8clifford_84max_abs(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2452 static PyObject *__pyx_pf_8PyClical_8clifford_86truncated(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_limit); /* proto */
2453 static PyObject *__pyx_pf_8PyClical_8clifford_88isnan(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2454 static PyObject *__pyx_pf_8PyClical_8clifford_90frame(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2455 static PyObject *__pyx_pf_8PyClical_8clifford_92__repr__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2456 static PyObject *__pyx_pf_8PyClical_8clifford_94__str__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2457 static PyObject *__pyx_pf_8PyClical_8clifford_96__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2458 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 */
2459 static PyObject *__pyx_pf_8PyClical_8clifford_hidden_doctests(CYTHON_UNUSED PyObject *__pyx_self); /* proto */
2460 static PyObject *__pyx_pf_8PyClical_10inv(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2461 static PyObject *__pyx_pf_8PyClical_12scalar(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2462 static PyObject *__pyx_pf_8PyClical_14real(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2463 static PyObject *__pyx_pf_8PyClical_16imag(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2464 static PyObject *__pyx_pf_8PyClical_18pure(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2465 static PyObject *__pyx_pf_8PyClical_20even(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2466 static PyObject *__pyx_pf_8PyClical_22odd(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2467 static PyObject *__pyx_pf_8PyClical_24involute(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2468 static PyObject *__pyx_pf_8PyClical_26reverse(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2469 static PyObject *__pyx_pf_8PyClical_28conj(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2470 static PyObject *__pyx_pf_8PyClical_30quad(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2471 static PyObject *__pyx_pf_8PyClical_32norm(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2472 static PyObject *__pyx_pf_8PyClical_34abs(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2473 static PyObject *__pyx_pf_8PyClical_36max_abs(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2474 static PyObject *__pyx_pf_8PyClical_38pow(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_m); /* proto */
2475 static PyObject *__pyx_pf_8PyClical_40outer_pow(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_m); /* proto */
2476 static PyObject *__pyx_pf_8PyClical_42complexifier(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2477 static PyObject *__pyx_pf_8PyClical_44sqrt(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2478 static PyObject *__pyx_pf_8PyClical_46exp(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2479 static PyObject *__pyx_pf_8PyClical_48log(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2480 static PyObject *__pyx_pf_8PyClical_50cos(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2481 static PyObject *__pyx_pf_8PyClical_52acos(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2482 static PyObject *__pyx_pf_8PyClical_54cosh(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2483 static PyObject *__pyx_pf_8PyClical_56acosh(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2484 static PyObject *__pyx_pf_8PyClical_58sin(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2485 static PyObject *__pyx_pf_8PyClical_60asin(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2486 static PyObject *__pyx_pf_8PyClical_62sinh(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2487 static PyObject *__pyx_pf_8PyClical_64asinh(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2488 static PyObject *__pyx_pf_8PyClical_66tan(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2489 static PyObject *__pyx_pf_8PyClical_68atan(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2490 static PyObject *__pyx_pf_8PyClical_70tanh(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2491 static PyObject *__pyx_pf_8PyClical_72atanh(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2492 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 */
2493 static PyObject *__pyx_pf_8PyClical_76cga3(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2494 static PyObject *__pyx_pf_8PyClical_78cga3std(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2495 static PyObject *__pyx_pf_8PyClical_80agc3(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2496 static PyObject *__pyx_pf_8PyClical_82e(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2497 static PyObject *__pyx_pf_8PyClical_84istpq(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_p, PyObject *__pyx_v_q); /* proto */
2498 static PyObject *__pyx_pf_8PyClical_86_test(CYTHON_UNUSED PyObject *__pyx_self); /* proto */
2499 static PyObject *__pyx_tp_new_8PyClical_index_set(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
2500 static PyObject *__pyx_tp_new_8PyClical_clifford(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
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2503 static PyObject *__pyx_float_1_0;
2504 static PyObject *__pyx_float_2_0;
2505 static PyObject *__pyx_float_8_0;
2506 static PyObject *__pyx_int_0;
2507 static PyObject *__pyx_int_1;
2508 static PyObject *__pyx_int_4;
2509 static PyObject *__pyx_int_neg_1;
2510 static PyObject *__pyx_tuple__3;
2511 static PyObject *__pyx_tuple__4;
2512 static PyObject *__pyx_tuple__10;
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2514 static PyObject *__pyx_tuple__12;
2515 static PyObject *__pyx_tuple__15;
2516 static PyObject *__pyx_tuple__16;
2517 static PyObject *__pyx_tuple__18;
2518 static PyObject *__pyx_tuple__20;
2519 static PyObject *__pyx_tuple__21;
2520 static PyObject *__pyx_tuple__22;
2521 static PyObject *__pyx_codeobj__13;
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2555  /* "PyClical.pyx":39
2556  * cdef class index_set
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2558  * cdef inline IndexSet toIndexSet(obj): # <<<<<<<<<<<<<<
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2581 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_9index_set_wrap(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, IndexSet __pyx_v_other) {
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2667 static PyObject *__pyx_pw_8PyClical_9index_set_1copy(PyObject *__pyx_v_self, CYTHON_UNUSED PyObject *unused); /*proto*/
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3597  /* "PyClical.pyx":151
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3600  * return eq # <<<<<<<<<<<<<<
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3606  __pyx_r = __pyx_v_eq;
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3609  /* "PyClical.pyx":150
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3611  * return False
3612  * elif op == 1: # <= # <<<<<<<<<<<<<<
3613  * return eq
3614  * elif op == 4: # >
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3619  /* "PyClical.pyx":153
3620  * return eq
3621  * elif op == 4: # >
3622  * return False # <<<<<<<<<<<<<<
3623  * elif op == 5: # >=
3624  * return eq
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3626  __Pyx_XDECREF(__pyx_r);
3627  __Pyx_INCREF(Py_False);
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3631  /* "PyClical.pyx":152
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3633  * return eq
3634  * elif op == 4: # > # <<<<<<<<<<<<<<
3635  * return False
3636  * elif op == 5: # >=
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3639  case 5:
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3642  * return False
3643  * elif op == 5: # >=
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3649  __Pyx_INCREF(__pyx_v_eq);
3650  __pyx_r = __pyx_v_eq;
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3655  * return False
3656  * elif op == 5: # >= # <<<<<<<<<<<<<<
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3658  * else:
3659  */
3660  break;
3661  default:
3662 
3663  /* "PyClical.pyx":157
3664  * return eq
3665  * else:
3666  * return NotImplemented # <<<<<<<<<<<<<<
3667  * else:
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3670  __Pyx_XDECREF(__pyx_r);
3671  __Pyx_INCREF(__pyx_builtin_NotImplemented);
3672  __pyx_r = __pyx_builtin_NotImplemented;
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3674  break;
3675  }
3676  break;
3677  }
3678 
3679  /* "PyClical.pyx":141
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3682  * if (lhs is None) or (rhs is None): # <<<<<<<<<<<<<<
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3684  * if op == 2: # ==
3685  */
3686  }
3687 
3688  /* "PyClical.pyx":159
3689  * return NotImplemented
3690  * else:
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3692  * if op == 2: # ==
3693  * return eq
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3695  /*else*/ {
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3702  /* "PyClical.pyx":160
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3709  switch (__pyx_v_op) {
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3712  /* "PyClical.pyx":161
3713  * eq = bool( toIndexSet(lhs) == toIndexSet(rhs) )
3714  * if op == 2: # ==
3715  * return eq # <<<<<<<<<<<<<<
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3723 
3724  /* "PyClical.pyx":160
3725  * else:
3726  * eq = bool( toIndexSet(lhs) == toIndexSet(rhs) )
3727  * if op == 2: # == # <<<<<<<<<<<<<<
3728  * return eq
3729  * elif op == 3: # !=
3730  */
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3732  case 3:
3733 
3734  /* "PyClical.pyx":163
3735  * return eq
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3737  * return not eq # <<<<<<<<<<<<<<
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3741  __Pyx_XDECREF(__pyx_r);
3742  __pyx_t_1 = __Pyx_PyObject_IsTrue(__pyx_v_eq); if (unlikely(__pyx_t_1 < 0)) __PYX_ERR(0, 163, __pyx_L1_error)
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3746  __pyx_t_4 = 0;
3747  goto __pyx_L0;
3748 
3749  /* "PyClical.pyx":162
3750  * if op == 2: # ==
3751  * return eq
3752  * elif op == 3: # != # <<<<<<<<<<<<<<
3753  * return not eq
3754  * else:
3755  */
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3757  default:
3758 
3759  /* "PyClical.pyx":165
3760  * return not eq
3761  * else:
3762  * lt = bool( toIndexSet(lhs) < toIndexSet(rhs) ) # <<<<<<<<<<<<<<
3763  * if op == 0: # <
3764  * return lt
3765  */
3766  __pyx_t_1 = (__pyx_f_8PyClical_toIndexSet(((PyObject *)__pyx_v_lhs)) < __pyx_f_8PyClical_toIndexSet(__pyx_v_rhs));
3767  __pyx_t_4 = __Pyx_PyBool_FromLong((!(!__pyx_t_1))); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 165, __pyx_L1_error)
3768  __Pyx_GOTREF(__pyx_t_4);
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3770  __pyx_t_4 = 0;
3771 
3772  /* "PyClical.pyx":166
3773  * else:
3774  * lt = bool( toIndexSet(lhs) < toIndexSet(rhs) )
3775  * if op == 0: # < # <<<<<<<<<<<<<<
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3780  case 0:
3781 
3782  /* "PyClical.pyx":167
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3792  goto __pyx_L0;
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3794  /* "PyClical.pyx":166
3795  * else:
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3799  * elif op == 1: # <=
3800  */
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3802  case 1:
3803 
3804  /* "PyClical.pyx":169
3805  * return lt
3806  * elif op == 1: # <=
3807  * return lt or eq # <<<<<<<<<<<<<<
3808  * elif op == 4: # >
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3816  __pyx_t_4 = __pyx_v_lt;
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3821  __pyx_L6_bool_binop_done:;
3822  __pyx_r = __pyx_t_4;
3823  __pyx_t_4 = 0;
3824  goto __pyx_L0;
3825 
3826  /* "PyClical.pyx":168
3827  * if op == 0: # <
3828  * return lt
3829  * elif op == 1: # <= # <<<<<<<<<<<<<<
3830  * return lt or eq
3831  * elif op == 4: # >
3832  */
3833  break;
3834  case 4:
3835 
3836  /* "PyClical.pyx":171
3837  * return lt or eq
3838  * elif op == 4: # >
3839  * return not (lt or eq) # <<<<<<<<<<<<<<
3840  * elif op == 5: # >=
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3846  } else {
3847  __pyx_t_1 = __pyx_t_2;
3848  goto __pyx_L8_bool_binop_done;
3849  }
3850  __pyx_t_2 = __Pyx_PyObject_IsTrue(__pyx_v_eq); if (unlikely(__pyx_t_2 < 0)) __PYX_ERR(0, 171, __pyx_L1_error)
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3856  __pyx_t_4 = 0;
3857  goto __pyx_L0;
3858 
3859  /* "PyClical.pyx":170
3860  * elif op == 1: # <=
3861  * return lt or eq
3862  * elif op == 4: # > # <<<<<<<<<<<<<<
3863  * return not (lt or eq)
3864  * elif op == 5: # >=
3865  */
3866  break;
3867  case 5:
3868 
3869  /* "PyClical.pyx":173
3870  * return not (lt or eq)
3871  * elif op == 5: # >=
3872  * return not lt # <<<<<<<<<<<<<<
3873  * else:
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3881  __pyx_t_4 = 0;
3882  goto __pyx_L0;
3883 
3884  /* "PyClical.pyx":172
3885  * elif op == 4: # >
3886  * return not (lt or eq)
3887  * elif op == 5: # >= # <<<<<<<<<<<<<<
3888  * return not lt
3889  * else:
3890  */
3891  break;
3892  default:
3893 
3894  /* "PyClical.pyx":175
3895  * return not lt
3896  * else:
3897  * return NotImplemented # <<<<<<<<<<<<<<
3898  *
3899  * def __setitem__(self, idx, val):
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3904  goto __pyx_L0;
3905  break;
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3907  break;
3908  }
3909  }
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3912  * del self.instance
3913  *
3914  * def __richcmp__(lhs, rhs, int op): # <<<<<<<<<<<<<<
3915  * """
3916  * Compare two objects of class index_set.
3917  */
3918 
3919  /* function exit code */
3920  __pyx_L1_error:;
3921  __Pyx_XDECREF(__pyx_t_4);
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3935  * def __setitem__(self, idx, val): # <<<<<<<<<<<<<<
3936  * """
3937  * Set the value of an index_set object at index idx to value val.
3938  */
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3944 struct wrapperbase __pyx_wrapperbase_8PyClical_9index_set_8__setitem__;
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3968  * return
3969  *
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3988  goto __pyx_L0;
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3991  * return NotImplemented
3992  *
3993  * def __setitem__(self, idx, val): # <<<<<<<<<<<<<<
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4014 
4015 /* Python wrapper */
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4018 #if CYTHON_COMPILING_IN_CPYTHON
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4043  *
4044  * def __contains__(self, idx):
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4055  * return
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4057  * def __getitem__(self, idx): # <<<<<<<<<<<<<<
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6615  __Pyx_PyThreadState_assign
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6623  * elif isinstance(other, str):
6624  * try:
6625  * self.instance = new Clifford(<char *>other) # <<<<<<<<<<<<<<
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6627  * raise ValueError(error_msg_prefix + " invalid string " + repr(other) + ".")
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6639  * self.instance = new Clifford(<scalar_t>other)
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6650  __pyx_L11_error:;
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6652  __Pyx_XDECREF(__pyx_t_8); __pyx_t_8 = 0;
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6656  * self.instance = new Clifford(<char *>other)
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6695  __pyx_L13_except_error:;
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6698  * self.instance = new Clifford(<scalar_t>other)
6699  * elif isinstance(other, str):
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6706  __Pyx_XGIVEREF(__pyx_t_12);
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6709  __pyx_L16_try_end:;
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6759  __Pyx_XDECREF(__pyx_t_4); __pyx_t_4 = 0;
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6768  __Pyx_XDECREF(__pyx_t_8); __pyx_t_8 = 0;
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6801  __Pyx_DECREF(__pyx_t_17); __pyx_t_17 = 0;
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6838  __Pyx_DECREF(__pyx_t_16); __pyx_t_16 = 0;
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6855  __pyx_L6_except_error:;
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6861  * if isinstance(other, clifford):
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6865  __Pyx_XGIVEREF(__pyx_t_4);
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6877  * if isinstance(other, clifford):
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6929  * if isinstance(other, numbers.Real): # <<<<<<<<<<<<<<
6930  * self.instance = new Clifford((<index_set>ixt).unwrap(), <scalar_t>other)
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6933  goto __pyx_L21;
6934  }
6935 
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6938  * self.instance = new Clifford((<index_set>ixt).unwrap(), <scalar_t>other)
6939  * elif isinstance(other, collections.Sequence): # <<<<<<<<<<<<<<
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6955  * elif isinstance(other, collections.Sequence):
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6968  /* "PyClical.pyx":611
6969  * if isinstance(other, numbers.Real):
6970  * self.instance = new Clifford((<index_set>ixt).unwrap(), <scalar_t>other)
6971  * elif isinstance(other, collections.Sequence): # <<<<<<<<<<<<<<
6972  * self.instance = new Clifford(list_to_vector(other), (<index_set>ixt).unwrap())
6973  * else:
6974  */
6975  goto __pyx_L21;
6976  }
6977 
6978  /* "PyClical.pyx":614
6979  * self.instance = new Clifford(list_to_vector(other), (<index_set>ixt).unwrap())
6980  * else:
6981  * raise TypeError(error_msg_prefix + " (" + str(type(other)) # <<<<<<<<<<<<<<
6982  * + ", " + repr(ixt) + ").")
6983  * else:
6984  */
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6993  __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
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6995  /* "PyClical.pyx":615
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6997  * raise TypeError(error_msg_prefix + " (" + str(type(other))
6998  * + ", " + repr(ixt) + ").") # <<<<<<<<<<<<<<
6999  * else:
7000  * raise TypeError(error_msg_prefix + " (" + str(type(other))
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7011  __pyx_t_8 = PyNumber_Add(__pyx_t_15, __pyx_kp_s__9); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 615, __pyx_L1_error)
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7013  __Pyx_DECREF(__pyx_t_15); __pyx_t_15 = 0;
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7015  /* "PyClical.pyx":614
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7017  * else:
7018  * raise TypeError(error_msg_prefix + " (" + str(type(other)) # <<<<<<<<<<<<<<
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7020  * else:
7021  */
7022  __pyx_t_15 = __Pyx_PyObject_CallOneArg(__pyx_builtin_TypeError, __pyx_t_8); if (unlikely(!__pyx_t_15)) __PYX_ERR(0, 614, __pyx_L1_error)
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7024  __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
7025  __Pyx_Raise(__pyx_t_15, 0, 0, 0);
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7027  __PYX_ERR(0, 614, __pyx_L1_error)
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7029  __pyx_L21:;
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7034  * elif isinstance(ixt, index_set): # <<<<<<<<<<<<<<
7035  * if isinstance(other, numbers.Real):
7036  * self.instance = new Clifford((<index_set>ixt).unwrap(), <scalar_t>other)
7037  */
7038  goto __pyx_L3;
7039  }
7040 
7041  /* "PyClical.pyx":617
7042  * + ", " + repr(ixt) + ").")
7043  * else:
7044  * raise TypeError(error_msg_prefix + " (" + str(type(other)) # <<<<<<<<<<<<<<
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7047  */
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7056  __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
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7058  /* "PyClical.pyx":618
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7060  * raise TypeError(error_msg_prefix + " (" + str(type(other))
7061  * + ", " + str(type(ixt)) + ").") # <<<<<<<<<<<<<<
7062  *
7063  * def __dealloc__(self):
7064  */
7065  __pyx_t_8 = PyNumber_Add(__pyx_t_7, __pyx_kp_s__8); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 618, __pyx_L1_error)
7066  __Pyx_GOTREF(__pyx_t_8);
7067  __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
7068  __pyx_t_7 = __Pyx_PyObject_CallOneArg(((PyObject *)(&PyString_Type)), ((PyObject *)Py_TYPE(__pyx_v_ixt))); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 618, __pyx_L1_error)
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7073  __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
7074  __pyx_t_7 = PyNumber_Add(__pyx_t_15, __pyx_kp_s__9); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 618, __pyx_L1_error)
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7078  /* "PyClical.pyx":617
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7080  * else:
7081  * raise TypeError(error_msg_prefix + " (" + str(type(other)) # <<<<<<<<<<<<<<
7082  * + ", " + str(type(ixt)) + ").")
7083  *
7084  */
7085  __pyx_t_15 = __Pyx_PyObject_CallOneArg(__pyx_builtin_TypeError, __pyx_t_7); if (unlikely(!__pyx_t_15)) __PYX_ERR(0, 617, __pyx_L1_error)
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7092  __pyx_L3:;
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7096  *
7097  * def __cinit__(self, other = 0, ixt = None): # <<<<<<<<<<<<<<
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7102  /* function exit code */
7103  __pyx_r = 0;
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7105  __pyx_L1_error:;
7106  __Pyx_XDECREF(__pyx_t_7);
7107  __Pyx_XDECREF(__pyx_t_8);
7108  __Pyx_XDECREF(__pyx_t_15);
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7114  __pyx_L0:;
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7123  *
7124  * def __dealloc__(self): # <<<<<<<<<<<<<<
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7126  * Clean up by deallocating the instance of C++ class Clifford.
7127  */
7128 
7129  /* Python wrapper */
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7156  * def __dealloc__(self): # <<<<<<<<<<<<<<
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7168  * def __contains__(self, x): # <<<<<<<<<<<<<<
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7211  *
7212  * def __contains__(self, x): # <<<<<<<<<<<<<<
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7214  * Not applicable.
7215  */
7216 
7217  /* function exit code */
7218  __pyx_L1_error:;
7219  __Pyx_XDECREF(__pyx_t_1);
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7230  * """
7231  * Not applicable.
7232  */
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7246  /* function exit code */
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7260  * raise TypeError("Not applicable.") # <<<<<<<<<<<<<<
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7263  */
7264  __pyx_t_1 = __Pyx_PyObject_Call(__pyx_builtin_TypeError, __pyx_tuple__10, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 646, __pyx_L1_error)
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7276  */
7277 
7278  /* function exit code */
7279  __pyx_L1_error:;
7280  __Pyx_XDECREF(__pyx_t_1);
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7311  PyObject *__pyx_v_error_msg_prefix = NULL;
7312  struct __pyx_obj_8PyClical_clifford *__pyx_v_result = NULL;
7313  PyObject *__pyx_v_err = NULL;
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7318  PyObject *__pyx_t_3 = NULL;
7319  PyObject *__pyx_t_4 = NULL;
7320  PyObject *__pyx_t_5 = NULL;
7321  PyObject *__pyx_t_6 = NULL;
7322  Clifford *__pyx_t_7;
7323  int __pyx_t_8;
7324  PyObject *__pyx_t_9 = NULL;
7325  PyObject *__pyx_t_10 = NULL;
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7332  * True
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7341  /* "PyClical.pyx":659
7342  * """
7343  * error_msg_prefix = "Cannot reframe"
7344  * if isinstance(ixt, index_set): # <<<<<<<<<<<<<<
7345  * try:
7346  * result = clifford()
7347  */
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7352  /* "PyClical.pyx":660
7353  * error_msg_prefix = "Cannot reframe"
7354  * if isinstance(ixt, index_set):
7355  * try: # <<<<<<<<<<<<<<
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7371  * result = clifford() # <<<<<<<<<<<<<<
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7381  * try:
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7383  * result.instance = new Clifford(self.unwrap(), (<index_set>ixt).unwrap()) # <<<<<<<<<<<<<<
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7498  * error_msg_prefix = "Cannot reframe"
7499  * if isinstance(ixt, index_set):
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7670  * return bool(lhs is rhs)
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7672  */
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7678  * return bool( toClifford(lhs) == toClifford(rhs) ) # <<<<<<<<<<<<<<
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7758  * return bool( toClifford(lhs) != toClifford(rhs) ) # <<<<<<<<<<<<<<
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9938  * cdef int n
9939  * cdef int i
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9954  * cdef int i
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17898  Py_ssize_t kw_args;
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17901  case 2: values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
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17925  } else {
17926  values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
17927  values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
17928  }
17929  __pyx_v_p = values[0];
17930  __pyx_v_q = values[1];
17931  }
17932  goto __pyx_L4_argument_unpacking_done;
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17946 
17947  static PyObject *__pyx_pf_8PyClical_84istpq(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_p, PyObject *__pyx_v_q) {
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17956  * {-3,-2,-1,1,2}
17957  * """
17958  * return index_set(set(range(-q,p+1))) # <<<<<<<<<<<<<<
17959  *
17960  * ninf3 = e(4) + e(-1) # Null infinity point in 3D Conformal Geometric Algebra [DL].
17961  */
17962  __Pyx_XDECREF(__pyx_r);
17963  __pyx_t_1 = PyNumber_Negative(__pyx_v_q); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 1907, __pyx_L1_error)
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17968  __Pyx_GOTREF(__pyx_t_3);
17969  __Pyx_GIVEREF(__pyx_t_1);
17970  PyTuple_SET_ITEM(__pyx_t_3, 0, __pyx_t_1);
17971  __Pyx_GIVEREF(__pyx_t_2);
17972  PyTuple_SET_ITEM(__pyx_t_3, 1, __pyx_t_2);
17973  __pyx_t_1 = 0;
17974  __pyx_t_2 = 0;
17975  __pyx_t_2 = __Pyx_PyObject_Call(__pyx_builtin_range, __pyx_t_3, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 1907, __pyx_L1_error)
17976  __Pyx_GOTREF(__pyx_t_2);
17977  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
17978  __pyx_t_3 = PySet_New(__pyx_t_2); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 1907, __pyx_L1_error)
17979  __Pyx_GOTREF(__pyx_t_3);
17980  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
17981  __pyx_t_2 = __Pyx_PyObject_CallOneArg(((PyObject *)__pyx_ptype_8PyClical_index_set), __pyx_t_3); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 1907, __pyx_L1_error)
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17985  __pyx_t_2 = 0;
17986  goto __pyx_L0;
17987 
17988  /* "PyClical.pyx":1900
17989  * return clifford(index_set(obj))
17990  *
17991  * def istpq(p, q): # <<<<<<<<<<<<<<
17992  * """
17993  * Abbreviation for index_set({-q,...p}).
17994  */
17995 
17996  /* function exit code */
17997  __pyx_L1_error:;
17998  __Pyx_XDECREF(__pyx_t_1);
17999  __Pyx_XDECREF(__pyx_t_2);
18000  __Pyx_XDECREF(__pyx_t_3);
18001  __Pyx_AddTraceback("PyClical.istpq", __pyx_clineno, __pyx_lineno, __pyx_filename);
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18003  __pyx_L0:;
18004  __Pyx_XGIVEREF(__pyx_r);
18005  __Pyx_RefNannyFinishContext();
18006  return __pyx_r;
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18008 
18009  /* "PyClical.pyx":1913
18010  *
18011  * # Doctest interface.
18012  * def _test(): # <<<<<<<<<<<<<<
18013  * import PyClical, doctest
18014  * return doctest.testmod(PyClical)
18015  */
18016 
18017  /* Python wrapper */
18018  static PyObject *__pyx_pw_8PyClical_87_test(PyObject *__pyx_self, CYTHON_UNUSED PyObject *unused); /*proto*/
18019  static PyMethodDef __pyx_mdef_8PyClical_87_test = {"_test", (PyCFunction)__pyx_pw_8PyClical_87_test, METH_NOARGS, 0};
18020  static PyObject *__pyx_pw_8PyClical_87_test(PyObject *__pyx_self, CYTHON_UNUSED PyObject *unused) {
18021  PyObject *__pyx_r = 0;
18022  __Pyx_RefNannyDeclarations
18023  __Pyx_RefNannySetupContext("_test (wrapper)", 0);
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18025 
18026  /* function exit code */
18027  __Pyx_RefNannyFinishContext();
18028  return __pyx_r;
18029  }
18030 
18031  static PyObject *__pyx_pf_8PyClical_86_test(CYTHON_UNUSED PyObject *__pyx_self) {
18032  PyObject *__pyx_v_PyClical = NULL;
18033  PyObject *__pyx_v_doctest = NULL;
18034  PyObject *__pyx_r = NULL;
18035  __Pyx_RefNannyDeclarations
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18037  PyObject *__pyx_t_2 = NULL;
18038  PyObject *__pyx_t_3 = NULL;
18039  __Pyx_RefNannySetupContext("_test", 0);
18040 
18041  /* "PyClical.pyx":1914
18042  * # Doctest interface.
18043  * def _test():
18044  * import PyClical, doctest # <<<<<<<<<<<<<<
18045  * return doctest.testmod(PyClical)
18046  *
18047  */
18048  __pyx_t_1 = __Pyx_Import(__pyx_n_s_PyClical, 0, -1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 1914, __pyx_L1_error)
18049  __Pyx_GOTREF(__pyx_t_1);
18050  __pyx_v_PyClical = __pyx_t_1;
18051  __pyx_t_1 = 0;
18052  __pyx_t_1 = __Pyx_Import(__pyx_n_s_doctest, 0, -1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 1914, __pyx_L1_error)
18053  __Pyx_GOTREF(__pyx_t_1);
18054  __pyx_v_doctest = __pyx_t_1;
18055  __pyx_t_1 = 0;
18056 
18057  /* "PyClical.pyx":1915
18058  * def _test():
18059  * import PyClical, doctest
18060  * return doctest.testmod(PyClical) # <<<<<<<<<<<<<<
18061  *
18062  * if __name__ == "__main__":
18063  */
18064  __Pyx_XDECREF(__pyx_r);
18065  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_v_doctest, __pyx_n_s_testmod); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 1915, __pyx_L1_error)
18066  __Pyx_GOTREF(__pyx_t_2);
18067  __pyx_t_3 = NULL;
18068  if (CYTHON_UNPACK_METHODS && likely(PyMethod_Check(__pyx_t_2))) {
18069  __pyx_t_3 = PyMethod_GET_SELF(__pyx_t_2);
18070  if (likely(__pyx_t_3)) {
18071  PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_2);
18072  __Pyx_INCREF(__pyx_t_3);
18073  __Pyx_INCREF(function);
18074  __Pyx_DECREF_SET(__pyx_t_2, function);
18075  }
18076  }
18077  __pyx_t_1 = (__pyx_t_3) ? __Pyx_PyObject_Call2Args(__pyx_t_2, __pyx_t_3, __pyx_v_PyClical) : __Pyx_PyObject_CallOneArg(__pyx_t_2, __pyx_v_PyClical);
18078  __Pyx_XDECREF(__pyx_t_3); __pyx_t_3 = 0;
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18081  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
18082  __pyx_r = __pyx_t_1;
18083  __pyx_t_1 = 0;
18084  goto __pyx_L0;
18085 
18086  /* "PyClical.pyx":1913
18087  *
18088  * # Doctest interface.
18089  * def _test(): # <<<<<<<<<<<<<<
18090  * import PyClical, doctest
18091  * return doctest.testmod(PyClical)
18092  */
18093 
18094  /* function exit code */
18095  __pyx_L1_error:;
18096  __Pyx_XDECREF(__pyx_t_1);
18097  __Pyx_XDECREF(__pyx_t_2);
18098  __Pyx_XDECREF(__pyx_t_3);
18099  __Pyx_AddTraceback("PyClical._test", __pyx_clineno, __pyx_lineno, __pyx_filename);
18100  __pyx_r = NULL;
18101  __pyx_L0:;
18102  __Pyx_XDECREF(__pyx_v_PyClical);
18103  __Pyx_XDECREF(__pyx_v_doctest);
18104  __Pyx_XGIVEREF(__pyx_r);
18105  __Pyx_RefNannyFinishContext();
18106  return __pyx_r;
18107  }
18108  static struct __pyx_vtabstruct_8PyClical_index_set __pyx_vtable_8PyClical_index_set;
18109 
18110  static PyObject *__pyx_tp_new_8PyClical_index_set(PyTypeObject *t, PyObject *a, PyObject *k) {
18111  struct __pyx_obj_8PyClical_index_set *p;
18112  PyObject *o;
18113  if (likely((t->tp_flags & Py_TPFLAGS_IS_ABSTRACT) == 0)) {
18114  o = (*t->tp_alloc)(t, 0);
18115  } else {
18116  o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_empty_tuple, 0);
18117  }
18118  if (unlikely(!o)) return 0;
18119  p = ((struct __pyx_obj_8PyClical_index_set *)o);
18120  p->__pyx_vtab = __pyx_vtabptr_8PyClical_index_set;
18121  if (unlikely(__pyx_pw_8PyClical_9index_set_3__cinit__(o, a, k) < 0)) goto bad;
18122  return o;
18123  bad:
18124  Py_DECREF(o); o = 0;
18125  return NULL;
18126  }
18127 
18128  static void __pyx_tp_dealloc_8PyClical_index_set(PyObject *o) {
18129  #if CYTHON_USE_TP_FINALIZE
18130  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))) {
18131  if (PyObject_CallFinalizerFromDealloc(o)) return;
18132  }
18133  #endif
18134  {
18135  PyObject *etype, *eval, *etb;
18136  PyErr_Fetch(&etype, &eval, &etb);
18137  ++Py_REFCNT(o);
18138  __pyx_pw_8PyClical_9index_set_5__dealloc__(o);
18139  --Py_REFCNT(o);
18140  PyErr_Restore(etype, eval, etb);
18141  }
18142  (*Py_TYPE(o)->tp_free)(o);
18143  }
18144  static PyObject *__pyx_sq_item_8PyClical_index_set(PyObject *o, Py_ssize_t i) {
18145  PyObject *r;
18146  PyObject *x = PyInt_FromSsize_t(i); if(!x) return 0;
18147  r = Py_TYPE(o)->tp_as_mapping->mp_subscript(o, x);
18148  Py_DECREF(x);
18149  return r;
18150  }
18151 
18152  static int __pyx_mp_ass_subscript_8PyClical_index_set(PyObject *o, PyObject *i, PyObject *v) {
18153  if (v) {
18154  return __pyx_pw_8PyClical_9index_set_9__setitem__(o, i, v);
18155  }
18156  else {
18157  PyErr_Format(PyExc_NotImplementedError,
18158  "Subscript deletion not supported by %.200s", Py_TYPE(o)->tp_name);
18159  return -1;
18160  }
18161  }
18162 
18163  static PyMethodDef __pyx_methods_8PyClical_index_set[] = {
18164  {"copy", (PyCFunction)__pyx_pw_8PyClical_9index_set_1copy, METH_NOARGS, __pyx_doc_8PyClical_9index_set_copy},
18165  {"count", (PyCFunction)__pyx_pw_8PyClical_9index_set_32count, METH_NOARGS, __pyx_doc_8PyClical_9index_set_31count},
18166  {"count_neg", (PyCFunction)__pyx_pw_8PyClical_9index_set_34count_neg, METH_NOARGS, __pyx_doc_8PyClical_9index_set_33count_neg},
18167  {"count_pos", (PyCFunction)__pyx_pw_8PyClical_9index_set_36count_pos, METH_NOARGS, __pyx_doc_8PyClical_9index_set_35count_pos},
18168  {"min", (PyCFunction)__pyx_pw_8PyClical_9index_set_38min, METH_NOARGS, __pyx_doc_8PyClical_9index_set_37min},
18169  {"max", (PyCFunction)__pyx_pw_8PyClical_9index_set_40max, METH_NOARGS, __pyx_doc_8PyClical_9index_set_39max},
18170  {"hash_fn", (PyCFunction)__pyx_pw_8PyClical_9index_set_42hash_fn, METH_NOARGS, __pyx_doc_8PyClical_9index_set_41hash_fn},
18171  {"sign_of_mult", (PyCFunction)__pyx_pw_8PyClical_9index_set_44sign_of_mult, METH_O, __pyx_doc_8PyClical_9index_set_43sign_of_mult},
18172  {"sign_of_square", (PyCFunction)__pyx_pw_8PyClical_9index_set_46sign_of_square, METH_NOARGS, __pyx_doc_8PyClical_9index_set_45sign_of_square},
18173  {"__reduce_cython__", (PyCFunction)__pyx_pw_8PyClical_9index_set_52__reduce_cython__, METH_NOARGS, 0},
18174  {"__setstate_cython__", (PyCFunction)__pyx_pw_8PyClical_9index_set_54__setstate_cython__, METH_O, 0},
18175  {0, 0, 0, 0}
18176  };
18177 
18178  static PyNumberMethods __pyx_tp_as_number_index_set = {
18179  0, /*nb_add*/
18180  0, /*nb_subtract*/
18181  0, /*nb_multiply*/
18182  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18183  0, /*nb_divide*/
18184  #endif
18185  0, /*nb_remainder*/
18186  0, /*nb_divmod*/
18187  0, /*nb_power*/
18188  0, /*nb_negative*/
18189  0, /*nb_positive*/
18190  0, /*nb_absolute*/
18191  0, /*nb_nonzero*/
18192  __pyx_pw_8PyClical_9index_set_18__invert__, /*nb_invert*/
18193  0, /*nb_lshift*/
18194  0, /*nb_rshift*/
18195  __pyx_pw_8PyClical_9index_set_24__and__, /*nb_and*/
18196  __pyx_pw_8PyClical_9index_set_20__xor__, /*nb_xor*/
18197  __pyx_pw_8PyClical_9index_set_28__or__, /*nb_or*/
18198  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18199  0, /*nb_coerce*/
18200  #endif
18201  0, /*nb_int*/
18202  #if PY_MAJOR_VERSION < 3
18203  0, /*nb_long*/
18204  #else
18205  0, /*reserved*/
18206  #endif
18207  0, /*nb_float*/
18208  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18209  0, /*nb_oct*/
18210  #endif
18211  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18212  0, /*nb_hex*/
18213  #endif
18214  0, /*nb_inplace_add*/
18215  0, /*nb_inplace_subtract*/
18216  0, /*nb_inplace_multiply*/
18217  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18218  0, /*nb_inplace_divide*/
18219  #endif
18220  0, /*nb_inplace_remainder*/
18221  0, /*nb_inplace_power*/
18222  0, /*nb_inplace_lshift*/
18223  0, /*nb_inplace_rshift*/
18224  __pyx_pw_8PyClical_9index_set_26__iand__, /*nb_inplace_and*/
18225  __pyx_pw_8PyClical_9index_set_22__ixor__, /*nb_inplace_xor*/
18226  __pyx_pw_8PyClical_9index_set_30__ior__, /*nb_inplace_or*/
18227  0, /*nb_floor_divide*/
18228  0, /*nb_true_divide*/
18229  0, /*nb_inplace_floor_divide*/
18230  0, /*nb_inplace_true_divide*/
18231  0, /*nb_index*/
18232  #if PY_VERSION_HEX >= 0x03050000
18233  0, /*nb_matrix_multiply*/
18234  #endif
18235  #if PY_VERSION_HEX >= 0x03050000
18236  0, /*nb_inplace_matrix_multiply*/
18237  #endif
18238  };
18239 
18240  static PySequenceMethods __pyx_tp_as_sequence_index_set = {
18241  0, /*sq_length*/
18242  0, /*sq_concat*/
18243  0, /*sq_repeat*/
18244  __pyx_sq_item_8PyClical_index_set, /*sq_item*/
18245  0, /*sq_slice*/
18246  0, /*sq_ass_item*/
18247  0, /*sq_ass_slice*/
18248  __pyx_pw_8PyClical_9index_set_13__contains__, /*sq_contains*/
18249  0, /*sq_inplace_concat*/
18250  0, /*sq_inplace_repeat*/
18251  };
18252 
18253  static PyMappingMethods __pyx_tp_as_mapping_index_set = {
18254  0, /*mp_length*/
18255  __pyx_pw_8PyClical_9index_set_11__getitem__, /*mp_subscript*/
18256  __pyx_mp_ass_subscript_8PyClical_index_set, /*mp_ass_subscript*/
18257  };
18258 
18259  static PyTypeObject __pyx_type_8PyClical_index_set = {
18260  PyVarObject_HEAD_INIT(0, 0)
18261  "PyClical.index_set", /*tp_name*/
18262  sizeof(struct __pyx_obj_8PyClical_index_set), /*tp_basicsize*/
18263  0, /*tp_itemsize*/
18264  __pyx_tp_dealloc_8PyClical_index_set, /*tp_dealloc*/
18265  0, /*tp_print*/
18266  0, /*tp_getattr*/
18267  0, /*tp_setattr*/
18268  #if PY_MAJOR_VERSION < 3
18269  0, /*tp_compare*/
18270  #endif
18271  #if PY_MAJOR_VERSION >= 3
18272  0, /*tp_as_async*/
18273  #endif
18274  __pyx_pw_8PyClical_9index_set_48__repr__, /*tp_repr*/
18275  &__pyx_tp_as_number_index_set, /*tp_as_number*/
18276  &__pyx_tp_as_sequence_index_set, /*tp_as_sequence*/
18277  &__pyx_tp_as_mapping_index_set, /*tp_as_mapping*/
18278  0, /*tp_hash*/
18279  0, /*tp_call*/
18280  __pyx_pw_8PyClical_9index_set_50__str__, /*tp_str*/
18281  0, /*tp_getattro*/
18282  0, /*tp_setattro*/
18283  0, /*tp_as_buffer*/
18284  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE, /*tp_flags*/
18285  "\n Python class index_set wraps C++ class IndexSet.\n ", /*tp_doc*/
18286  0, /*tp_traverse*/
18287  0, /*tp_clear*/
18288  __pyx_pw_8PyClical_9index_set_7__richcmp__, /*tp_richcompare*/
18289  0, /*tp_weaklistoffset*/
18290  __pyx_pw_8PyClical_9index_set_15__iter__, /*tp_iter*/
18291  0, /*tp_iternext*/
18292  __pyx_methods_8PyClical_index_set, /*tp_methods*/
18293  0, /*tp_members*/
18294  0, /*tp_getset*/
18295  0, /*tp_base*/
18296  0, /*tp_dict*/
18297  0, /*tp_descr_get*/
18298  0, /*tp_descr_set*/
18299  0, /*tp_dictoffset*/
18300  0, /*tp_init*/
18301  0, /*tp_alloc*/
18302  __pyx_tp_new_8PyClical_index_set, /*tp_new*/
18303  0, /*tp_free*/
18304  0, /*tp_is_gc*/
18305  0, /*tp_bases*/
18306  0, /*tp_mro*/
18307  0, /*tp_cache*/
18308  0, /*tp_subclasses*/
18309  0, /*tp_weaklist*/
18310  0, /*tp_del*/
18311  0, /*tp_version_tag*/
18312  #if PY_VERSION_HEX >= 0x030400a1
18313  0, /*tp_finalize*/
18314  #endif
18315  };
18316  static struct __pyx_vtabstruct_8PyClical_clifford __pyx_vtable_8PyClical_clifford;
18317 
18318  static PyObject *__pyx_tp_new_8PyClical_clifford(PyTypeObject *t, PyObject *a, PyObject *k) {
18319  struct __pyx_obj_8PyClical_clifford *p;
18320  PyObject *o;
18321  if (likely((t->tp_flags & Py_TPFLAGS_IS_ABSTRACT) == 0)) {
18322  o = (*t->tp_alloc)(t, 0);
18323  } else {
18324  o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_empty_tuple, 0);
18325  }
18326  if (unlikely(!o)) return 0;
18327  p = ((struct __pyx_obj_8PyClical_clifford *)o);
18328  p->__pyx_vtab = __pyx_vtabptr_8PyClical_clifford;
18329  if (unlikely(__pyx_pw_8PyClical_8clifford_3__cinit__(o, a, k) < 0)) goto bad;
18330  return o;
18331  bad:
18332  Py_DECREF(o); o = 0;
18333  return NULL;
18334  }
18335 
18336  static void __pyx_tp_dealloc_8PyClical_clifford(PyObject *o) {
18337  #if CYTHON_USE_TP_FINALIZE
18338  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))) {
18339  if (PyObject_CallFinalizerFromDealloc(o)) return;
18340  }
18341  #endif
18342  {
18343  PyObject *etype, *eval, *etb;
18344  PyErr_Fetch(&etype, &eval, &etb);
18345  ++Py_REFCNT(o);
18346  __pyx_pw_8PyClical_8clifford_5__dealloc__(o);
18347  --Py_REFCNT(o);
18348  PyErr_Restore(etype, eval, etb);
18349  }
18350  (*Py_TYPE(o)->tp_free)(o);
18351  }
18352  static PyObject *__pyx_sq_item_8PyClical_clifford(PyObject *o, Py_ssize_t i) {
18353  PyObject *r;
18354  PyObject *x = PyInt_FromSsize_t(i); if(!x) return 0;
18355  r = Py_TYPE(o)->tp_as_mapping->mp_subscript(o, x);
18356  Py_DECREF(x);
18357  return r;
18358  }
18359 
18360  static PyMethodDef __pyx_methods_8PyClical_clifford[] = {
18361  {"copy", (PyCFunction)__pyx_pw_8PyClical_8clifford_1copy, METH_NOARGS, __pyx_doc_8PyClical_8clifford_copy},
18362  {"reframe", (PyCFunction)__pyx_pw_8PyClical_8clifford_11reframe, METH_O, __pyx_doc_8PyClical_8clifford_10reframe},
18363  {"inv", (PyCFunction)__pyx_pw_8PyClical_8clifford_49inv, METH_NOARGS, __pyx_doc_8PyClical_8clifford_48inv},
18364  {"pow", (PyCFunction)__pyx_pw_8PyClical_8clifford_57pow, METH_O, __pyx_doc_8PyClical_8clifford_56pow},
18365  {"outer_pow", (PyCFunction)__pyx_pw_8PyClical_8clifford_59outer_pow, METH_O, __pyx_doc_8PyClical_8clifford_58outer_pow},
18366  {"scalar", (PyCFunction)__pyx_pw_8PyClical_8clifford_63scalar, METH_NOARGS, __pyx_doc_8PyClical_8clifford_62scalar},
18367  {"pure", (PyCFunction)__pyx_pw_8PyClical_8clifford_65pure, METH_NOARGS, __pyx_doc_8PyClical_8clifford_64pure},
18368  {"even", (PyCFunction)__pyx_pw_8PyClical_8clifford_67even, METH_NOARGS, __pyx_doc_8PyClical_8clifford_66even},
18369  {"odd", (PyCFunction)__pyx_pw_8PyClical_8clifford_69odd, METH_NOARGS, __pyx_doc_8PyClical_8clifford_68odd},
18370  {"vector_part", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_8clifford_71vector_part, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_8clifford_70vector_part},
18371  {"involute", (PyCFunction)__pyx_pw_8PyClical_8clifford_73involute, METH_NOARGS, __pyx_doc_8PyClical_8clifford_72involute},
18372  {"reverse", (PyCFunction)__pyx_pw_8PyClical_8clifford_75reverse, METH_NOARGS, __pyx_doc_8PyClical_8clifford_74reverse},
18373  {"conj", (PyCFunction)__pyx_pw_8PyClical_8clifford_77conj, METH_NOARGS, __pyx_doc_8PyClical_8clifford_76conj},
18374  {"quad", (PyCFunction)__pyx_pw_8PyClical_8clifford_79quad, METH_NOARGS, __pyx_doc_8PyClical_8clifford_78quad},
18375  {"norm", (PyCFunction)__pyx_pw_8PyClical_8clifford_81norm, METH_NOARGS, __pyx_doc_8PyClical_8clifford_80norm},
18376  {"abs", (PyCFunction)__pyx_pw_8PyClical_8clifford_83abs, METH_NOARGS, __pyx_doc_8PyClical_8clifford_82abs},
18377  {"max_abs", (PyCFunction)__pyx_pw_8PyClical_8clifford_85max_abs, METH_NOARGS, __pyx_doc_8PyClical_8clifford_84max_abs},
18378  {"truncated", (PyCFunction)__pyx_pw_8PyClical_8clifford_87truncated, METH_O, __pyx_doc_8PyClical_8clifford_86truncated},
18379  {"isnan", (PyCFunction)__pyx_pw_8PyClical_8clifford_89isnan, METH_NOARGS, __pyx_doc_8PyClical_8clifford_88isnan},
18380  {"frame", (PyCFunction)__pyx_pw_8PyClical_8clifford_91frame, METH_NOARGS, __pyx_doc_8PyClical_8clifford_90frame},
18381  {"__reduce_cython__", (PyCFunction)__pyx_pw_8PyClical_8clifford_97__reduce_cython__, METH_NOARGS, 0},
18382  {"__setstate_cython__", (PyCFunction)__pyx_pw_8PyClical_8clifford_99__setstate_cython__, METH_O, 0},
18383  {0, 0, 0, 0}
18384  };
18385 
18386  static PyNumberMethods __pyx_tp_as_number_clifford = {
18387  __pyx_pw_8PyClical_8clifford_21__add__, /*nb_add*/
18388  __pyx_pw_8PyClical_8clifford_25__sub__, /*nb_subtract*/
18389  __pyx_pw_8PyClical_8clifford_29__mul__, /*nb_multiply*/
18390  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18391  __pyx_pw_8PyClical_8clifford_45__div__, /*nb_divide*/
18392  #endif
18393  __pyx_pw_8PyClical_8clifford_33__mod__, /*nb_remainder*/
18394  0, /*nb_divmod*/
18395  __pyx_pw_8PyClical_8clifford_55__pow__, /*nb_power*/
18396  __pyx_pw_8PyClical_8clifford_17__neg__, /*nb_negative*/
18397  __pyx_pw_8PyClical_8clifford_19__pos__, /*nb_positive*/
18398  0, /*nb_absolute*/
18399  0, /*nb_nonzero*/
18400  0, /*nb_invert*/
18401  0, /*nb_lshift*/
18402  0, /*nb_rshift*/
18403  __pyx_pw_8PyClical_8clifford_37__and__, /*nb_and*/
18404  __pyx_pw_8PyClical_8clifford_41__xor__, /*nb_xor*/
18405  __pyx_pw_8PyClical_8clifford_51__or__, /*nb_or*/
18406  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18407  0, /*nb_coerce*/
18408  #endif
18409  0, /*nb_int*/
18410  #if PY_MAJOR_VERSION < 3
18411  0, /*nb_long*/
18412  #else
18413  0, /*reserved*/
18414  #endif
18415  0, /*nb_float*/
18416  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18417  0, /*nb_oct*/
18418  #endif
18419  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18420  0, /*nb_hex*/
18421  #endif
18422  __pyx_pw_8PyClical_8clifford_23__iadd__, /*nb_inplace_add*/
18423  __pyx_pw_8PyClical_8clifford_27__isub__, /*nb_inplace_subtract*/
18424  __pyx_pw_8PyClical_8clifford_31__imul__, /*nb_inplace_multiply*/
18425  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18426  __pyx_pw_8PyClical_8clifford_47__idiv__, /*nb_inplace_divide*/
18427  #endif
18428  __pyx_pw_8PyClical_8clifford_35__imod__, /*nb_inplace_remainder*/
18429  0, /*nb_inplace_power*/
18430  0, /*nb_inplace_lshift*/
18431  0, /*nb_inplace_rshift*/
18432  __pyx_pw_8PyClical_8clifford_39__iand__, /*nb_inplace_and*/
18433  __pyx_pw_8PyClical_8clifford_43__ixor__, /*nb_inplace_xor*/
18434  __pyx_pw_8PyClical_8clifford_53__ior__, /*nb_inplace_or*/
18435  0, /*nb_floor_divide*/
18436  0, /*nb_true_divide*/
18437  0, /*nb_inplace_floor_divide*/
18438  0, /*nb_inplace_true_divide*/
18439  0, /*nb_index*/
18440  #if PY_VERSION_HEX >= 0x03050000
18441  0, /*nb_matrix_multiply*/
18442  #endif
18443  #if PY_VERSION_HEX >= 0x03050000
18444  0, /*nb_inplace_matrix_multiply*/
18445  #endif
18446  };
18447 
18448  static PySequenceMethods __pyx_tp_as_sequence_clifford = {
18449  0, /*sq_length*/
18450  0, /*sq_concat*/
18451  0, /*sq_repeat*/
18452  __pyx_sq_item_8PyClical_clifford, /*sq_item*/
18453  0, /*sq_slice*/
18454  0, /*sq_ass_item*/
18455  0, /*sq_ass_slice*/
18456  __pyx_pw_8PyClical_8clifford_7__contains__, /*sq_contains*/
18457  0, /*sq_inplace_concat*/
18458  0, /*sq_inplace_repeat*/
18459  };
18460 
18461  static PyMappingMethods __pyx_tp_as_mapping_clifford = {
18462  0, /*mp_length*/
18463  __pyx_pw_8PyClical_8clifford_15__getitem__, /*mp_subscript*/
18464  0, /*mp_ass_subscript*/
18465  };
18466 
18467  static PyTypeObject __pyx_type_8PyClical_clifford = {
18468  PyVarObject_HEAD_INIT(0, 0)
18469  "PyClical.clifford", /*tp_name*/
18470  sizeof(struct __pyx_obj_8PyClical_clifford), /*tp_basicsize*/
18471  0, /*tp_itemsize*/
18472  __pyx_tp_dealloc_8PyClical_clifford, /*tp_dealloc*/
18473  0, /*tp_print*/
18474  0, /*tp_getattr*/
18475  0, /*tp_setattr*/
18476  #if PY_MAJOR_VERSION < 3
18477  0, /*tp_compare*/
18478  #endif
18479  #if PY_MAJOR_VERSION >= 3
18480  0, /*tp_as_async*/
18481  #endif
18482  __pyx_pw_8PyClical_8clifford_93__repr__, /*tp_repr*/
18483  &__pyx_tp_as_number_clifford, /*tp_as_number*/
18484  &__pyx_tp_as_sequence_clifford, /*tp_as_sequence*/
18485  &__pyx_tp_as_mapping_clifford, /*tp_as_mapping*/
18486  0, /*tp_hash*/
18487  __pyx_pw_8PyClical_8clifford_61__call__, /*tp_call*/
18488  __pyx_pw_8PyClical_8clifford_95__str__, /*tp_str*/
18489  0, /*tp_getattro*/
18490  0, /*tp_setattro*/
18491  0, /*tp_as_buffer*/
18492  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE, /*tp_flags*/
18493  "\n Python class clifford wraps C++ class Clifford.\n ", /*tp_doc*/
18494  0, /*tp_traverse*/
18495  0, /*tp_clear*/
18496  __pyx_pw_8PyClical_8clifford_13__richcmp__, /*tp_richcompare*/
18497  0, /*tp_weaklistoffset*/
18498  __pyx_pw_8PyClical_8clifford_9__iter__, /*tp_iter*/
18499  0, /*tp_iternext*/
18500  __pyx_methods_8PyClical_clifford, /*tp_methods*/
18501  0, /*tp_members*/
18502  0, /*tp_getset*/
18503  0, /*tp_base*/
18504  0, /*tp_dict*/
18505  0, /*tp_descr_get*/
18506  0, /*tp_descr_set*/
18507  0, /*tp_dictoffset*/
18508  0, /*tp_init*/
18509  0, /*tp_alloc*/
18510  __pyx_tp_new_8PyClical_clifford, /*tp_new*/
18511  0, /*tp_free*/
18512  0, /*tp_is_gc*/
18513  0, /*tp_bases*/
18514  0, /*tp_mro*/
18515  0, /*tp_cache*/
18516  0, /*tp_subclasses*/
18517  0, /*tp_weaklist*/
18518  0, /*tp_del*/
18519  0, /*tp_version_tag*/
18520  #if PY_VERSION_HEX >= 0x030400a1
18521  0, /*tp_finalize*/
18522  #endif
18523  };
18524 
18525  static struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *__pyx_freelist_8PyClical___pyx_scope_struct____iter__[8];
18526  static int __pyx_freecount_8PyClical___pyx_scope_struct____iter__ = 0;
18527 
18528  static PyObject *__pyx_tp_new_8PyClical___pyx_scope_struct____iter__(PyTypeObject *t, CYTHON_UNUSED PyObject *a, CYTHON_UNUSED PyObject *k) {
18529  PyObject *o;
18530  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__)))) {
18531  o = (PyObject*)__pyx_freelist_8PyClical___pyx_scope_struct____iter__[--__pyx_freecount_8PyClical___pyx_scope_struct____iter__];
18532  memset(o, 0, sizeof(struct __pyx_obj_8PyClical___pyx_scope_struct____iter__));
18533  (void) PyObject_INIT(o, t);
18534  PyObject_GC_Track(o);
18535  } else {
18536  o = (*t->tp_alloc)(t, 0);
18537  if (unlikely(!o)) return 0;
18538  }
18539  return o;
18540  }
18541 
18542  static void __pyx_tp_dealloc_8PyClical___pyx_scope_struct____iter__(PyObject *o) {
18543  struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *p = (struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *)o;
18544  PyObject_GC_UnTrack(o);
18545  Py_CLEAR(p->__pyx_v_idx);
18546  Py_CLEAR(p->__pyx_v_self);
18547  Py_CLEAR(p->__pyx_t_0);
18548  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__)))) {
18549  __pyx_freelist_8PyClical___pyx_scope_struct____iter__[__pyx_freecount_8PyClical___pyx_scope_struct____iter__++] = ((struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *)o);
18550  } else {
18551  (*Py_TYPE(o)->tp_free)(o);
18552  }
18553  }
18554 
18555  static int __pyx_tp_traverse_8PyClical___pyx_scope_struct____iter__(PyObject *o, visitproc v, void *a) {
18556  int e;
18557  struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *p = (struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *)o;
18558  if (p->__pyx_v_idx) {
18559  e = (*v)(p->__pyx_v_idx, a); if (e) return e;
18560  }
18561  if (p->__pyx_v_self) {
18562  e = (*v)(((PyObject *)p->__pyx_v_self), a); if (e) return e;
18563  }
18564  if (p->__pyx_t_0) {
18565  e = (*v)(p->__pyx_t_0, a); if (e) return e;
18566  }
18567  return 0;
18568  }
18569 
18570  static PyTypeObject __pyx_type_8PyClical___pyx_scope_struct____iter__ = {
18571  PyVarObject_HEAD_INIT(0, 0)
18572  "PyClical.__pyx_scope_struct____iter__", /*tp_name*/
18573  sizeof(struct __pyx_obj_8PyClical___pyx_scope_struct____iter__), /*tp_basicsize*/
18574  0, /*tp_itemsize*/
18575  __pyx_tp_dealloc_8PyClical___pyx_scope_struct____iter__, /*tp_dealloc*/
18576  0, /*tp_print*/
18577  0, /*tp_getattr*/
18578  0, /*tp_setattr*/
18579  #if PY_MAJOR_VERSION < 3
18580  0, /*tp_compare*/
18581  #endif
18582  #if PY_MAJOR_VERSION >= 3
18583  0, /*tp_as_async*/
18584  #endif
18585  0, /*tp_repr*/
18586  0, /*tp_as_number*/
18587  0, /*tp_as_sequence*/
18588  0, /*tp_as_mapping*/
18589  0, /*tp_hash*/
18590  0, /*tp_call*/
18591  0, /*tp_str*/
18592  0, /*tp_getattro*/
18593  0, /*tp_setattro*/
18594  0, /*tp_as_buffer*/
18595  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_HAVE_GC, /*tp_flags*/
18596  0, /*tp_doc*/
18597  __pyx_tp_traverse_8PyClical___pyx_scope_struct____iter__, /*tp_traverse*/
18598  0, /*tp_clear*/
18599  0, /*tp_richcompare*/
18600  0, /*tp_weaklistoffset*/
18601  0, /*tp_iter*/
18602  0, /*tp_iternext*/
18603  0, /*tp_methods*/
18604  0, /*tp_members*/
18605  0, /*tp_getset*/
18606  0, /*tp_base*/
18607  0, /*tp_dict*/
18608  0, /*tp_descr_get*/
18609  0, /*tp_descr_set*/
18610  0, /*tp_dictoffset*/
18611  0, /*tp_init*/
18612  0, /*tp_alloc*/
18613  __pyx_tp_new_8PyClical___pyx_scope_struct____iter__, /*tp_new*/
18614  0, /*tp_free*/
18615  0, /*tp_is_gc*/
18616  0, /*tp_bases*/
18617  0, /*tp_mro*/
18618  0, /*tp_cache*/
18619  0, /*tp_subclasses*/
18620  0, /*tp_weaklist*/
18621  0, /*tp_del*/
18622  0, /*tp_version_tag*/
18623  #if PY_VERSION_HEX >= 0x030400a1
18624  0, /*tp_finalize*/
18625  #endif
18626  };
18627 
18628  static PyMethodDef __pyx_methods[] = {
18629  {"compare", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_3compare, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_2compare},
18630  {"min_neg", (PyCFunction)__pyx_pw_8PyClical_5min_neg, METH_O, __pyx_doc_8PyClical_4min_neg},
18631  {"max_pos", (PyCFunction)__pyx_pw_8PyClical_7max_pos, METH_O, __pyx_doc_8PyClical_6max_pos},
18632  {"inv", (PyCFunction)__pyx_pw_8PyClical_11inv, METH_O, __pyx_doc_8PyClical_10inv},
18633  {"scalar", (PyCFunction)__pyx_pw_8PyClical_13scalar, METH_O, __pyx_doc_8PyClical_12scalar},
18634  {"real", (PyCFunction)__pyx_pw_8PyClical_15real, METH_O, __pyx_doc_8PyClical_14real},
18635  {"imag", (PyCFunction)__pyx_pw_8PyClical_17imag, METH_O, __pyx_doc_8PyClical_16imag},
18636  {"pure", (PyCFunction)__pyx_pw_8PyClical_19pure, METH_O, __pyx_doc_8PyClical_18pure},
18637  {"even", (PyCFunction)__pyx_pw_8PyClical_21even, METH_O, __pyx_doc_8PyClical_20even},
18638  {"odd", (PyCFunction)__pyx_pw_8PyClical_23odd, METH_O, __pyx_doc_8PyClical_22odd},
18639  {"involute", (PyCFunction)__pyx_pw_8PyClical_25involute, METH_O, __pyx_doc_8PyClical_24involute},
18640  {"reverse", (PyCFunction)__pyx_pw_8PyClical_27reverse, METH_O, __pyx_doc_8PyClical_26reverse},
18641  {"conj", (PyCFunction)__pyx_pw_8PyClical_29conj, METH_O, __pyx_doc_8PyClical_28conj},
18642  {"quad", (PyCFunction)__pyx_pw_8PyClical_31quad, METH_O, __pyx_doc_8PyClical_30quad},
18643  {"norm", (PyCFunction)__pyx_pw_8PyClical_33norm, METH_O, __pyx_doc_8PyClical_32norm},
18644  {"abs", (PyCFunction)__pyx_pw_8PyClical_35abs, METH_O, __pyx_doc_8PyClical_34abs},
18645  {"max_abs", (PyCFunction)__pyx_pw_8PyClical_37max_abs, METH_O, __pyx_doc_8PyClical_36max_abs},
18646  {"pow", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_39pow, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_38pow},
18647  {"outer_pow", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_41outer_pow, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_40outer_pow},
18648  {"complexifier", (PyCFunction)__pyx_pw_8PyClical_43complexifier, METH_O, __pyx_doc_8PyClical_42complexifier},
18649  {"sqrt", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_45sqrt, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_44sqrt},
18650  {"exp", (PyCFunction)__pyx_pw_8PyClical_47exp, METH_O, __pyx_doc_8PyClical_46exp},
18651  {"log", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_49log, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_48log},
18652  {"cos", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_51cos, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_50cos},
18653  {"acos", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_53acos, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_52acos},
18654  {"cosh", (PyCFunction)__pyx_pw_8PyClical_55cosh, METH_O, __pyx_doc_8PyClical_54cosh},
18655  {"acosh", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_57acosh, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_56acosh},
18656  {"sin", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_59sin, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_58sin},
18657  {"asin", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_61asin, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_60asin},
18658  {"sinh", (PyCFunction)__pyx_pw_8PyClical_63sinh, METH_O, __pyx_doc_8PyClical_62sinh},
18659  {"asinh", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_65asinh, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_64asinh},
18660  {"tan", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_67tan, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_66tan},
18661  {"atan", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_69atan, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_68atan},
18662  {"tanh", (PyCFunction)__pyx_pw_8PyClical_71tanh, METH_O, __pyx_doc_8PyClical_70tanh},
18663  {"atanh", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_73atanh, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_72atanh},
18664  {"random_clifford", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_75random_clifford, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_74random_clifford},
18665  {"cga3", (PyCFunction)__pyx_pw_8PyClical_77cga3, METH_O, __pyx_doc_8PyClical_76cga3},
18666  {"cga3std", (PyCFunction)__pyx_pw_8PyClical_79cga3std, METH_O, __pyx_doc_8PyClical_78cga3std},
18667  {"agc3", (PyCFunction)__pyx_pw_8PyClical_81agc3, METH_O, __pyx_doc_8PyClical_80agc3},
18668  {0, 0, 0, 0}
18669  };
18670 
18671  #if PY_MAJOR_VERSION >= 3
18672  #if CYTHON_PEP489_MULTI_PHASE_INIT
18673  static PyObject* __pyx_pymod_create(PyObject *spec, PyModuleDef *def); /*proto*/
18674  static int __pyx_pymod_exec_PyClical(PyObject* module); /*proto*/
18675  static PyModuleDef_Slot __pyx_moduledef_slots[] = {
18676  {Py_mod_create, (void*)__pyx_pymod_create},
18677  {Py_mod_exec, (void*)__pyx_pymod_exec_PyClical},
18678  {0, NULL}
18679  };
18680  #endif
18681 
18682  static struct PyModuleDef __pyx_moduledef = {
18683  PyModuleDef_HEAD_INIT,
18684  "PyClical",
18685  0, /* m_doc */
18686  #if CYTHON_PEP489_MULTI_PHASE_INIT
18687  0, /* m_size */
18688  #else
18689  -1, /* m_size */
18690  #endif
18691  __pyx_methods /* m_methods */,
18692  #if CYTHON_PEP489_MULTI_PHASE_INIT
18693  __pyx_moduledef_slots, /* m_slots */
18694  #else
18695  NULL, /* m_reload */
18696  #endif
18697  NULL, /* m_traverse */
18698  NULL, /* m_clear */
18699  NULL /* m_free */
18700  };
18701  #endif
18702  #ifndef CYTHON_SMALL_CODE
18703 #if defined(__clang__)
18704  #define CYTHON_SMALL_CODE
18705 #elif defined(__GNUC__) && (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 3))
18706  #define CYTHON_SMALL_CODE __attribute__((cold))
18707 #else
18708  #define CYTHON_SMALL_CODE
18709 #endif
18710 #endif
18711 
18712 static __Pyx_StringTabEntry __pyx_string_tab[] = {
18713  {&__pyx_kp_s_, __pyx_k_, sizeof(__pyx_k_), 0, 0, 1, 0},
18714  {&__pyx_kp_s_0_8_2, __pyx_k_0_8_2, sizeof(__pyx_k_0_8_2), 0, 0, 1, 0},
18715  {&__pyx_kp_u_Abbreviation_for_clifford_index, __pyx_k_Abbreviation_for_clifford_index, sizeof(__pyx_k_Abbreviation_for_clifford_index), 0, 1, 0, 0},
18716  {&__pyx_kp_u_Abbreviation_for_index_set_q_p, __pyx_k_Abbreviation_for_index_set_q_p, sizeof(__pyx_k_Abbreviation_for_index_set_q_p), 0, 1, 0, 0},
18717  {&__pyx_kp_u_Absolute_value_of_multivector_m, __pyx_k_Absolute_value_of_multivector_m, sizeof(__pyx_k_Absolute_value_of_multivector_m), 0, 1, 0, 0},
18718  {&__pyx_kp_u_Absolute_value_square_root_of_n, __pyx_k_Absolute_value_square_root_of_n, sizeof(__pyx_k_Absolute_value_square_root_of_n), 0, 1, 0, 0},
18719  {&__pyx_kp_s_Cannot_initialize_clifford_objec, __pyx_k_Cannot_initialize_clifford_objec, sizeof(__pyx_k_Cannot_initialize_clifford_objec), 0, 0, 1, 0},
18720  {&__pyx_kp_s_Cannot_initialize_index_set_obje, __pyx_k_Cannot_initialize_index_set_obje, sizeof(__pyx_k_Cannot_initialize_index_set_obje), 0, 0, 1, 0},
18721  {&__pyx_kp_s_Cannot_reframe, __pyx_k_Cannot_reframe, sizeof(__pyx_k_Cannot_reframe), 0, 0, 1, 0},
18722  {&__pyx_kp_s_Cannot_take_vector_part_of, __pyx_k_Cannot_take_vector_part_of, sizeof(__pyx_k_Cannot_take_vector_part_of), 0, 0, 1, 0},
18723  {&__pyx_kp_u_Cardinality_Number_of_indices_i, __pyx_k_Cardinality_Number_of_indices_i, sizeof(__pyx_k_Cardinality_Number_of_indices_i), 0, 1, 0, 0},
18724  {&__pyx_kp_u_Check_if_a_multivector_contains, __pyx_k_Check_if_a_multivector_contains, sizeof(__pyx_k_Check_if_a_multivector_contains), 0, 1, 0, 0},
18725  {&__pyx_kp_u_Conjugation_reverse_o_involute, __pyx_k_Conjugation_reverse_o_involute, sizeof(__pyx_k_Conjugation_reverse_o_involute), 0, 1, 0, 0},
18726  {&__pyx_kp_u_Conjugation_reverse_o_involute_2, __pyx_k_Conjugation_reverse_o_involute_2, sizeof(__pyx_k_Conjugation_reverse_o_involute_2), 0, 1, 0, 0},
18727  {&__pyx_kp_u_Contraction_print_clifford_1_cl, __pyx_k_Contraction_print_clifford_1_cl, sizeof(__pyx_k_Contraction_print_clifford_1_cl), 0, 1, 0, 0},
18728  {&__pyx_kp_u_Contraction_x_clifford_1_x_clif, __pyx_k_Contraction_x_clifford_1_x_clif, sizeof(__pyx_k_Contraction_x_clifford_1_x_clif), 0, 1, 0, 0},
18729  {&__pyx_kp_u_Convert_CGA3_null_vector_to_Euc, __pyx_k_Convert_CGA3_null_vector_to_Euc, sizeof(__pyx_k_Convert_CGA3_null_vector_to_Euc), 0, 1, 0, 0},
18730  {&__pyx_kp_u_Convert_CGA3_null_vector_to_sta, __pyx_k_Convert_CGA3_null_vector_to_sta, sizeof(__pyx_k_Convert_CGA3_null_vector_to_sta), 0, 1, 0, 0},
18731  {&__pyx_kp_u_Convert_Euclidean_3D_multivecto, __pyx_k_Convert_Euclidean_3D_multivecto, sizeof(__pyx_k_Convert_Euclidean_3D_multivecto), 0, 1, 0, 0},
18732  {&__pyx_kp_u_Copy_this_clifford_object_x_cli, __pyx_k_Copy_this_clifford_object_x_cli, sizeof(__pyx_k_Copy_this_clifford_object_x_cli), 0, 1, 0, 0},
18733  {&__pyx_kp_u_Copy_this_index_set_object_s_in, __pyx_k_Copy_this_index_set_object_s_in, sizeof(__pyx_k_Copy_this_index_set_object_s_in), 0, 1, 0, 0},
18734  {&__pyx_kp_u_Cosine_of_multivector_with_opti, __pyx_k_Cosine_of_multivector_with_opti, sizeof(__pyx_k_Cosine_of_multivector_with_opti), 0, 1, 0, 0},
18735  {&__pyx_kp_u_Even_part_of_multivector_sum_of, __pyx_k_Even_part_of_multivector_sum_of, sizeof(__pyx_k_Even_part_of_multivector_sum_of), 0, 1, 0, 0},
18736  {&__pyx_kp_u_Even_part_of_multivector_sum_of_2, __pyx_k_Even_part_of_multivector_sum_of_2, sizeof(__pyx_k_Even_part_of_multivector_sum_of_2), 0, 1, 0, 0},
18737  {&__pyx_kp_u_Exponential_of_multivector_x_cl, __pyx_k_Exponential_of_multivector_x_cl, sizeof(__pyx_k_Exponential_of_multivector_x_cl), 0, 1, 0, 0},
18738  {&__pyx_kp_u_Geometric_difference_print_clif, __pyx_k_Geometric_difference_print_clif, sizeof(__pyx_k_Geometric_difference_print_clif), 0, 1, 0, 0},
18739  {&__pyx_kp_u_Geometric_difference_x_clifford, __pyx_k_Geometric_difference_x_clifford, sizeof(__pyx_k_Geometric_difference_x_clifford), 0, 1, 0, 0},
18740  {&__pyx_kp_u_Geometric_multiplicative_invers, __pyx_k_Geometric_multiplicative_invers, sizeof(__pyx_k_Geometric_multiplicative_invers), 0, 1, 0, 0},
18741  {&__pyx_kp_u_Geometric_multiplicative_invers_2, __pyx_k_Geometric_multiplicative_invers_2, sizeof(__pyx_k_Geometric_multiplicative_invers_2), 0, 1, 0, 0},
18742  {&__pyx_kp_u_Geometric_product_print_cliffor, __pyx_k_Geometric_product_print_cliffor, sizeof(__pyx_k_Geometric_product_print_cliffor), 0, 1, 0, 0},
18743  {&__pyx_kp_u_Geometric_product_x_clifford_2, __pyx_k_Geometric_product_x_clifford_2, sizeof(__pyx_k_Geometric_product_x_clifford_2), 0, 1, 0, 0},
18744  {&__pyx_kp_u_Geometric_quotient_print_cliffo, __pyx_k_Geometric_quotient_print_cliffo, sizeof(__pyx_k_Geometric_quotient_print_cliffo), 0, 1, 0, 0},
18745  {&__pyx_kp_u_Geometric_quotient_x_clifford_1, __pyx_k_Geometric_quotient_x_clifford_1, sizeof(__pyx_k_Geometric_quotient_x_clifford_1), 0, 1, 0, 0},
18746  {&__pyx_kp_u_Geometric_sum_print_clifford_1, __pyx_k_Geometric_sum_print_clifford_1, sizeof(__pyx_k_Geometric_sum_print_clifford_1), 0, 1, 0, 0},
18747  {&__pyx_kp_u_Geometric_sum_x_clifford_1_x_cl, __pyx_k_Geometric_sum_x_clifford_1_x_cl, sizeof(__pyx_k_Geometric_sum_x_clifford_1_x_cl), 0, 1, 0, 0},
18748  {&__pyx_kp_u_Get_the_value_of_an_index_set_o, __pyx_k_Get_the_value_of_an_index_set_o, sizeof(__pyx_k_Get_the_value_of_an_index_set_o), 0, 1, 0, 0},
18749  {&__pyx_kp_u_Hyperbolic_cosine_of_multivecto, __pyx_k_Hyperbolic_cosine_of_multivecto, sizeof(__pyx_k_Hyperbolic_cosine_of_multivecto), 0, 1, 0, 0},
18750  {&__pyx_kp_u_Hyperbolic_sine_of_multivector, __pyx_k_Hyperbolic_sine_of_multivector, sizeof(__pyx_k_Hyperbolic_sine_of_multivector), 0, 1, 0, 0},
18751  {&__pyx_kp_u_Hyperbolic_tangent_of_multivect, __pyx_k_Hyperbolic_tangent_of_multivect, sizeof(__pyx_k_Hyperbolic_tangent_of_multivect), 0, 1, 0, 0},
18752  {&__pyx_kp_u_Imaginary_part_deprecated_alway, __pyx_k_Imaginary_part_deprecated_alway, sizeof(__pyx_k_Imaginary_part_deprecated_alway), 0, 1, 0, 0},
18753  {&__pyx_n_s_IndexError, __pyx_k_IndexError, sizeof(__pyx_k_IndexError), 0, 0, 1, 1},
18754  {&__pyx_kp_u_Inner_product_print_clifford_1, __pyx_k_Inner_product_print_clifford_1, sizeof(__pyx_k_Inner_product_print_clifford_1), 0, 1, 0, 0},
18755  {&__pyx_kp_u_Inner_product_x_clifford_1_x_cl, __pyx_k_Inner_product_x_clifford_1_x_cl, sizeof(__pyx_k_Inner_product_x_clifford_1_x_cl), 0, 1, 0, 0},
18756  {&__pyx_kp_u_Integer_power_of_multivector_ob, __pyx_k_Integer_power_of_multivector_ob, sizeof(__pyx_k_Integer_power_of_multivector_ob), 0, 1, 0, 0},
18757  {&__pyx_n_s_Integral, __pyx_k_Integral, sizeof(__pyx_k_Integral), 0, 0, 1, 1},
18758  {&__pyx_kp_u_Inverse_cosine_of_multivector_w, __pyx_k_Inverse_cosine_of_multivector_w, sizeof(__pyx_k_Inverse_cosine_of_multivector_w), 0, 1, 0, 0},
18759  {&__pyx_kp_u_Inverse_hyperbolic_cosine_of_mu, __pyx_k_Inverse_hyperbolic_cosine_of_mu, sizeof(__pyx_k_Inverse_hyperbolic_cosine_of_mu), 0, 1, 0, 0},
18760  {&__pyx_kp_u_Inverse_hyperbolic_sine_of_mult, __pyx_k_Inverse_hyperbolic_sine_of_mult, sizeof(__pyx_k_Inverse_hyperbolic_sine_of_mult), 0, 1, 0, 0},
18761  {&__pyx_kp_u_Inverse_hyperbolic_tangent_of_m, __pyx_k_Inverse_hyperbolic_tangent_of_m, sizeof(__pyx_k_Inverse_hyperbolic_tangent_of_m), 0, 1, 0, 0},
18762  {&__pyx_kp_u_Inverse_sine_of_multivector_wit, __pyx_k_Inverse_sine_of_multivector_wit, sizeof(__pyx_k_Inverse_sine_of_multivector_wit), 0, 1, 0, 0},
18763  {&__pyx_kp_u_Inverse_tangent_of_multivector, __pyx_k_Inverse_tangent_of_multivector, sizeof(__pyx_k_Inverse_tangent_of_multivector), 0, 1, 0, 0},
18764  {&__pyx_kp_u_Iterate_over_the_indices_of_an, __pyx_k_Iterate_over_the_indices_of_an, sizeof(__pyx_k_Iterate_over_the_indices_of_an), 0, 1, 0, 0},
18765  {&__pyx_kp_u_Main_involution_each_i_is_repla, __pyx_k_Main_involution_each_i_is_repla, sizeof(__pyx_k_Main_involution_each_i_is_repla), 0, 1, 0, 0},
18766  {&__pyx_kp_u_Main_involution_each_i_is_repla_2, __pyx_k_Main_involution_each_i_is_repla_2, sizeof(__pyx_k_Main_involution_each_i_is_repla_2), 0, 1, 0, 0},
18767  {&__pyx_kp_u_Maximum_absolute_value_of_coord, __pyx_k_Maximum_absolute_value_of_coord, sizeof(__pyx_k_Maximum_absolute_value_of_coord), 0, 1, 0, 0},
18768  {&__pyx_kp_u_Maximum_member_index_set_1_1_2, __pyx_k_Maximum_member_index_set_1_1_2, sizeof(__pyx_k_Maximum_member_index_set_1_1_2), 0, 1, 0, 0},
18769  {&__pyx_kp_u_Maximum_of_absolute_values_of_c, __pyx_k_Maximum_of_absolute_values_of_c, sizeof(__pyx_k_Maximum_of_absolute_values_of_c), 0, 1, 0, 0},
18770  {&__pyx_kp_u_Maximum_positive_index_or_0_if, __pyx_k_Maximum_positive_index_or_0_if, sizeof(__pyx_k_Maximum_positive_index_or_0_if), 0, 1, 0, 0},
18771  {&__pyx_kp_u_Minimum_member_index_set_1_1_2, __pyx_k_Minimum_member_index_set_1_1_2, sizeof(__pyx_k_Minimum_member_index_set_1_1_2), 0, 1, 0, 0},
18772  {&__pyx_kp_u_Minimum_negative_index_or_0_if, __pyx_k_Minimum_negative_index_or_0_if, sizeof(__pyx_k_Minimum_negative_index_or_0_if), 0, 1, 0, 0},
18773  {&__pyx_kp_u_Natural_logarithm_of_multivecto, __pyx_k_Natural_logarithm_of_multivecto, sizeof(__pyx_k_Natural_logarithm_of_multivecto), 0, 1, 0, 0},
18774  {&__pyx_kp_u_Norm_sum_of_squares_of_coordina, __pyx_k_Norm_sum_of_squares_of_coordina, sizeof(__pyx_k_Norm_sum_of_squares_of_coordina), 0, 1, 0, 0},
18775  {&__pyx_n_s_NotImplemented, __pyx_k_NotImplemented, sizeof(__pyx_k_NotImplemented), 0, 0, 1, 1},
18776  {&__pyx_kp_s_Not_applicable, __pyx_k_Not_applicable, sizeof(__pyx_k_Not_applicable), 0, 0, 1, 0},
18777  {&__pyx_kp_u_Not_applicable_for_a_in_cliffor, __pyx_k_Not_applicable_for_a_in_cliffor, sizeof(__pyx_k_Not_applicable_for_a_in_cliffor), 0, 1, 0, 0},
18778  {&__pyx_kp_u_Number_of_negative_indices_incl, __pyx_k_Number_of_negative_indices_incl, sizeof(__pyx_k_Number_of_negative_indices_incl), 0, 1, 0, 0},
18779  {&__pyx_kp_u_Number_of_positive_indices_incl, __pyx_k_Number_of_positive_indices_incl, sizeof(__pyx_k_Number_of_positive_indices_incl), 0, 1, 0, 0},
18780  {&__pyx_kp_u_Odd_part_of_multivector_sum_of, __pyx_k_Odd_part_of_multivector_sum_of, sizeof(__pyx_k_Odd_part_of_multivector_sum_of), 0, 1, 0, 0},
18781  {&__pyx_kp_u_Odd_part_of_multivector_sum_of_2, __pyx_k_Odd_part_of_multivector_sum_of_2, sizeof(__pyx_k_Odd_part_of_multivector_sum_of_2), 0, 1, 0, 0},
18782  {&__pyx_kp_u_Outer_product_power_of_multivec, __pyx_k_Outer_product_power_of_multivec, sizeof(__pyx_k_Outer_product_power_of_multivec), 0, 1, 0, 0},
18783  {&__pyx_kp_u_Outer_product_power_x_clifford, __pyx_k_Outer_product_power_x_clifford, sizeof(__pyx_k_Outer_product_power_x_clifford), 0, 1, 0, 0},
18784  {&__pyx_kp_u_Outer_product_print_clifford_1, __pyx_k_Outer_product_print_clifford_1, sizeof(__pyx_k_Outer_product_print_clifford_1), 0, 1, 0, 0},
18785  {&__pyx_kp_u_Outer_product_x_clifford_1_x_cl, __pyx_k_Outer_product_x_clifford_1_x_cl, sizeof(__pyx_k_Outer_product_x_clifford_1_x_cl), 0, 1, 0, 0},
18786  {&__pyx_kp_u_Power_self_to_the_m_x_clifford, __pyx_k_Power_self_to_the_m_x_clifford, sizeof(__pyx_k_Power_self_to_the_m_x_clifford), 0, 1, 0, 0},
18787  {&__pyx_kp_u_Power_self_to_the_m_x_clifford_2, __pyx_k_Power_self_to_the_m_x_clifford_2, sizeof(__pyx_k_Power_self_to_the_m_x_clifford_2), 0, 1, 0, 0},
18788  {&__pyx_kp_u_Pure_grade_vector_part_print_cl, __pyx_k_Pure_grade_vector_part_print_cl, sizeof(__pyx_k_Pure_grade_vector_part_print_cl), 0, 1, 0, 0},
18789  {&__pyx_kp_u_Pure_part_print_clifford_1_1_1, __pyx_k_Pure_part_print_clifford_1_1_1, sizeof(__pyx_k_Pure_part_print_clifford_1_1_1), 0, 1, 0, 0},
18790  {&__pyx_kp_u_Pure_part_print_pure_clifford_1, __pyx_k_Pure_part_print_pure_clifford_1, sizeof(__pyx_k_Pure_part_print_pure_clifford_1), 0, 1, 0, 0},
18791  {&__pyx_kp_u_Put_self_into_a_larger_frame_co, __pyx_k_Put_self_into_a_larger_frame_co, sizeof(__pyx_k_Put_self_into_a_larger_frame_co), 0, 1, 0, 0},
18792  {&__pyx_n_s_PyClical, __pyx_k_PyClical, sizeof(__pyx_k_PyClical), 0, 0, 1, 1},
18793  {&__pyx_kp_s_PyClical_pyx, __pyx_k_PyClical_pyx, sizeof(__pyx_k_PyClical_pyx), 0, 0, 1, 0},
18794  {&__pyx_kp_u_Quadratic_form_rev_x_x_0_print, __pyx_k_Quadratic_form_rev_x_x_0_print, sizeof(__pyx_k_Quadratic_form_rev_x_x_0_print), 0, 1, 0, 0},
18795  {&__pyx_kp_u_Quadratic_form_rev_x_x_0_print_2, __pyx_k_Quadratic_form_rev_x_x_0_print_2, sizeof(__pyx_k_Quadratic_form_rev_x_x_0_print_2), 0, 1, 0, 0},
18796  {&__pyx_kp_u_Random_multivector_within_a_fra, __pyx_k_Random_multivector_within_a_fra, sizeof(__pyx_k_Random_multivector_within_a_fra), 0, 1, 0, 0},
18797  {&__pyx_n_s_Real, __pyx_k_Real, sizeof(__pyx_k_Real), 0, 0, 1, 1},
18798  {&__pyx_kp_u_Real_part_synonym_for_scalar_pa, __pyx_k_Real_part_synonym_for_scalar_pa, sizeof(__pyx_k_Real_part_synonym_for_scalar_pa), 0, 1, 0, 0},
18799  {&__pyx_kp_u_Remove_all_terms_of_self_with_r, __pyx_k_Remove_all_terms_of_self_with_r, sizeof(__pyx_k_Remove_all_terms_of_self_with_r), 0, 1, 0, 0},
18800  {&__pyx_kp_u_Reversion_eg_1_2_2_1_print_reve, __pyx_k_Reversion_eg_1_2_2_1_print_reve, sizeof(__pyx_k_Reversion_eg_1_2_2_1_print_reve), 0, 1, 0, 0},
18801  {&__pyx_kp_u_Reversion_eg_clifford_1_cliffor, __pyx_k_Reversion_eg_clifford_1_cliffor, sizeof(__pyx_k_Reversion_eg_clifford_1_cliffor), 0, 1, 0, 0},
18802  {&__pyx_n_s_RuntimeError, __pyx_k_RuntimeError, sizeof(__pyx_k_RuntimeError), 0, 0, 1, 1},
18803  {&__pyx_kp_u_Scalar_part_clifford_1_1_1_2_sc, __pyx_k_Scalar_part_clifford_1_1_1_2_sc, sizeof(__pyx_k_Scalar_part_clifford_1_1_1_2_sc), 0, 1, 0, 0},
18804  {&__pyx_kp_u_Scalar_part_scalar_clifford_1_1, __pyx_k_Scalar_part_scalar_clifford_1_1, sizeof(__pyx_k_Scalar_part_scalar_clifford_1_1), 0, 1, 0, 0},
18805  {&__pyx_n_s_Sequence, __pyx_k_Sequence, sizeof(__pyx_k_Sequence), 0, 0, 1, 1},
18806  {&__pyx_kp_u_Set_complement_not_print_index, __pyx_k_Set_complement_not_print_index, sizeof(__pyx_k_Set_complement_not_print_index), 0, 1, 0, 0},
18807  {&__pyx_kp_u_Set_intersection_and_print_inde, __pyx_k_Set_intersection_and_print_inde, sizeof(__pyx_k_Set_intersection_and_print_inde), 0, 1, 0, 0},
18808  {&__pyx_kp_u_Set_intersection_and_x_index_se, __pyx_k_Set_intersection_and_x_index_se, sizeof(__pyx_k_Set_intersection_and_x_index_se), 0, 1, 0, 0},
18809  {&__pyx_kp_u_Set_the_value_of_an_index_set_o, __pyx_k_Set_the_value_of_an_index_set_o, sizeof(__pyx_k_Set_the_value_of_an_index_set_o), 0, 1, 0, 0},
18810  {&__pyx_kp_u_Set_union_or_print_index_set_1, __pyx_k_Set_union_or_print_index_set_1, sizeof(__pyx_k_Set_union_or_print_index_set_1), 0, 1, 0, 0},
18811  {&__pyx_kp_u_Set_union_or_x_index_set_1_x_in, __pyx_k_Set_union_or_x_index_set_1_x_in, sizeof(__pyx_k_Set_union_or_x_index_set_1_x_in), 0, 1, 0, 0},
18812  {&__pyx_kp_u_Sign_of_geometric_product_of_tw, __pyx_k_Sign_of_geometric_product_of_tw, sizeof(__pyx_k_Sign_of_geometric_product_of_tw), 0, 1, 0, 0},
18813  {&__pyx_kp_u_Sign_of_geometric_square_of_a_C, __pyx_k_Sign_of_geometric_square_of_a_C, sizeof(__pyx_k_Sign_of_geometric_square_of_a_C), 0, 1, 0, 0},
18814  {&__pyx_kp_u_Sine_of_multivector_with_option, __pyx_k_Sine_of_multivector_with_option, sizeof(__pyx_k_Sine_of_multivector_with_option), 0, 1, 0, 0},
18815  {&__pyx_kp_u_Square_root_of_1_which_commutes, __pyx_k_Square_root_of_1_which_commutes, sizeof(__pyx_k_Square_root_of_1_which_commutes), 0, 1, 0, 0},
18816  {&__pyx_kp_u_Square_root_of_multivector_with, __pyx_k_Square_root_of_multivector_with, sizeof(__pyx_k_Square_root_of_multivector_with), 0, 1, 0, 0},
18817  {&__pyx_kp_u_Subalgebra_generated_by_all_gen, __pyx_k_Subalgebra_generated_by_all_gen, sizeof(__pyx_k_Subalgebra_generated_by_all_gen), 0, 1, 0, 0},
18818  {&__pyx_kp_u_Subscripting_map_from_index_set, __pyx_k_Subscripting_map_from_index_set, sizeof(__pyx_k_Subscripting_map_from_index_set), 0, 1, 0, 0},
18819  {&__pyx_kp_u_Symmetric_set_difference_exclus, __pyx_k_Symmetric_set_difference_exclus, sizeof(__pyx_k_Symmetric_set_difference_exclus), 0, 1, 0, 0},
18820  {&__pyx_kp_u_Symmetric_set_difference_exclus_2, __pyx_k_Symmetric_set_difference_exclus_2, sizeof(__pyx_k_Symmetric_set_difference_exclus_2), 0, 1, 0, 0},
18821  {&__pyx_kp_u_Tangent_of_multivector_with_opt, __pyx_k_Tangent_of_multivector_with_opt, sizeof(__pyx_k_Tangent_of_multivector_with_opt), 0, 1, 0, 0},
18822  {&__pyx_kp_u_Tests_for_functions_that_Doctes, __pyx_k_Tests_for_functions_that_Doctes, sizeof(__pyx_k_Tests_for_functions_that_Doctes), 0, 1, 0, 0},
18823  {&__pyx_kp_u_Tests_for_functions_that_Doctes_2, __pyx_k_Tests_for_functions_that_Doctes_2, sizeof(__pyx_k_Tests_for_functions_that_Doctes_2), 0, 1, 0, 0},
18824  {&__pyx_kp_u_The_informal_string_representat, __pyx_k_The_informal_string_representat, sizeof(__pyx_k_The_informal_string_representat), 0, 1, 0, 0},
18825  {&__pyx_kp_u_The_informal_string_representat_2, __pyx_k_The_informal_string_representat_2, sizeof(__pyx_k_The_informal_string_representat_2), 0, 1, 0, 0},
18826  {&__pyx_kp_u_The_official_string_representat, __pyx_k_The_official_string_representat, sizeof(__pyx_k_The_official_string_representat), 0, 1, 0, 0},
18827  {&__pyx_kp_u_The_official_string_representat_2, __pyx_k_The_official_string_representat_2, sizeof(__pyx_k_The_official_string_representat_2), 0, 1, 0, 0},
18828  {&__pyx_kp_s_This_comparison_operator_is_not, __pyx_k_This_comparison_operator_is_not, sizeof(__pyx_k_This_comparison_operator_is_not), 0, 0, 1, 0},
18829  {&__pyx_kp_u_Transform_left_hand_side_using, __pyx_k_Transform_left_hand_side_using, sizeof(__pyx_k_Transform_left_hand_side_using), 0, 1, 0, 0},
18830  {&__pyx_kp_u_Transform_left_hand_side_using_2, __pyx_k_Transform_left_hand_side_using_2, sizeof(__pyx_k_Transform_left_hand_side_using_2), 0, 1, 0, 0},
18831  {&__pyx_n_s_TypeError, __pyx_k_TypeError, sizeof(__pyx_k_TypeError), 0, 0, 1, 1},
18832  {&__pyx_kp_u_Unary_print_clifford_1_1, __pyx_k_Unary_print_clifford_1_1, sizeof(__pyx_k_Unary_print_clifford_1_1), 0, 1, 0, 0},
18833  {&__pyx_kp_u_Unary_print_clifford_1_1_2, __pyx_k_Unary_print_clifford_1_1_2, sizeof(__pyx_k_Unary_print_clifford_1_1_2), 0, 1, 0, 0},
18834  {&__pyx_n_s_ValueError, __pyx_k_ValueError, sizeof(__pyx_k_ValueError), 0, 0, 1, 1},
18835  {&__pyx_kp_u_Vector_part_of_multivector_as_a, __pyx_k_Vector_part_of_multivector_as_a, sizeof(__pyx_k_Vector_part_of_multivector_as_a), 0, 1, 0, 0},
18836  {&__pyx_kp_s__2, __pyx_k__2, sizeof(__pyx_k__2), 0, 0, 1, 0},
18837  {&__pyx_kp_s__5, __pyx_k__5, sizeof(__pyx_k__5), 0, 0, 1, 0},
18838  {&__pyx_kp_s__6, __pyx_k__6, sizeof(__pyx_k__6), 0, 0, 1, 0},
18839  {&__pyx_kp_s__7, __pyx_k__7, sizeof(__pyx_k__7), 0, 0, 1, 0},
18840  {&__pyx_kp_s__8, __pyx_k__8, sizeof(__pyx_k__8), 0, 0, 1, 0},
18841  {&__pyx_kp_s__9, __pyx_k__9, sizeof(__pyx_k__9), 0, 0, 1, 0},
18842  {&__pyx_kp_u_abs_line_1473, __pyx_k_abs_line_1473, sizeof(__pyx_k_abs_line_1473), 0, 1, 0, 0},
18843  {&__pyx_n_s_acos, __pyx_k_acos, sizeof(__pyx_k_acos), 0, 0, 1, 1},
18844  {&__pyx_kp_u_acos_line_1619, __pyx_k_acos_line_1619, sizeof(__pyx_k_acos_line_1619), 0, 1, 0, 0},
18845  {&__pyx_n_s_acosh, __pyx_k_acosh, sizeof(__pyx_k_acosh), 0, 0, 1, 1},
18846  {&__pyx_kp_u_acosh_line_1656, __pyx_k_acosh_line_1656, sizeof(__pyx_k_acosh_line_1656), 0, 1, 0, 0},
18847  {&__pyx_kp_u_agc3_line_1844, __pyx_k_agc3_line_1844, sizeof(__pyx_k_agc3_line_1844), 0, 1, 0, 0},
18848  {&__pyx_n_s_args, __pyx_k_args, sizeof(__pyx_k_args), 0, 0, 1, 1},
18849  {&__pyx_kp_s_as_frame, __pyx_k_as_frame, sizeof(__pyx_k_as_frame), 0, 0, 1, 0},
18850  {&__pyx_n_s_asin, __pyx_k_asin, sizeof(__pyx_k_asin), 0, 0, 1, 1},
18851  {&__pyx_kp_u_asin_line_1698, __pyx_k_asin_line_1698, sizeof(__pyx_k_asin_line_1698), 0, 1, 0, 0},
18852  {&__pyx_n_s_asinh, __pyx_k_asinh, sizeof(__pyx_k_asinh), 0, 0, 1, 1},
18853  {&__pyx_kp_u_asinh_line_1733, __pyx_k_asinh_line_1733, sizeof(__pyx_k_asinh_line_1733), 0, 1, 0, 0},
18854  {&__pyx_n_s_atan, __pyx_k_atan, sizeof(__pyx_k_atan), 0, 0, 1, 1},
18855  {&__pyx_kp_u_atan_line_1769, __pyx_k_atan_line_1769, sizeof(__pyx_k_atan_line_1769), 0, 1, 0, 0},
18856  {&__pyx_n_s_atanh, __pyx_k_atanh, sizeof(__pyx_k_atanh), 0, 0, 1, 1},
18857  {&__pyx_kp_u_atanh_line_1798, __pyx_k_atanh_line_1798, sizeof(__pyx_k_atanh_line_1798), 0, 1, 0, 0},
18858  {&__pyx_kp_u_cga3_line_1824, __pyx_k_cga3_line_1824, sizeof(__pyx_k_cga3_line_1824), 0, 1, 0, 0},
18859  {&__pyx_kp_u_cga3std_line_1833, __pyx_k_cga3std_line_1833, sizeof(__pyx_k_cga3std_line_1833), 0, 1, 0, 0},
18860  {&__pyx_n_s_cl, __pyx_k_cl, sizeof(__pyx_k_cl), 0, 0, 1, 1},
18861  {&__pyx_n_s_clifford, __pyx_k_clifford, sizeof(__pyx_k_clifford), 0, 0, 1, 1},
18862  {&__pyx_kp_u_clifford___add___line_739, __pyx_k_clifford___add___line_739, sizeof(__pyx_k_clifford___add___line_739), 0, 1, 0, 0},
18863  {&__pyx_kp_u_clifford___and___line_835, __pyx_k_clifford___and___line_835, sizeof(__pyx_k_clifford___and___line_835), 0, 1, 0, 0},
18864  {&__pyx_kp_u_clifford___call___line_1019, __pyx_k_clifford___call___line_1019, sizeof(__pyx_k_clifford___call___line_1019), 0, 1, 0, 0},
18865  {&__pyx_kp_u_clifford___div___line_895, __pyx_k_clifford___div___line_895, sizeof(__pyx_k_clifford___div___line_895), 0, 1, 0, 0},
18866  {&__pyx_kp_u_clifford___getitem___line_706, __pyx_k_clifford___getitem___line_706, sizeof(__pyx_k_clifford___getitem___line_706), 0, 1, 0, 0},
18867  {&__pyx_kp_u_clifford___iadd___line_750, __pyx_k_clifford___iadd___line_750, sizeof(__pyx_k_clifford___iadd___line_750), 0, 1, 0, 0},
18868  {&__pyx_kp_u_clifford___iand___line_850, __pyx_k_clifford___iand___line_850, sizeof(__pyx_k_clifford___iand___line_850), 0, 1, 0, 0},
18869  {&__pyx_kp_u_clifford___idiv___line_910, __pyx_k_clifford___idiv___line_910, sizeof(__pyx_k_clifford___idiv___line_910), 0, 1, 0, 0},
18870  {&__pyx_kp_u_clifford___imod___line_820, __pyx_k_clifford___imod___line_820, sizeof(__pyx_k_clifford___imod___line_820), 0, 1, 0, 0},
18871  {&__pyx_kp_u_clifford___imul___line_792, __pyx_k_clifford___imul___line_792, sizeof(__pyx_k_clifford___imul___line_792), 0, 1, 0, 0},
18872  {&__pyx_kp_u_clifford___ior___line_949, __pyx_k_clifford___ior___line_949, sizeof(__pyx_k_clifford___ior___line_949), 0, 1, 0, 0},
18873  {&__pyx_kp_u_clifford___isub___line_770, __pyx_k_clifford___isub___line_770, sizeof(__pyx_k_clifford___isub___line_770), 0, 1, 0, 0},
18874  {&__pyx_kp_u_clifford___iter___line_637, __pyx_k_clifford___iter___line_637, sizeof(__pyx_k_clifford___iter___line_637), 0, 1, 0, 0},
18875  {&__pyx_kp_u_clifford___ixor___line_880, __pyx_k_clifford___ixor___line_880, sizeof(__pyx_k_clifford___ixor___line_880), 0, 1, 0, 0},
18876  {&__pyx_kp_u_clifford___mod___line_805, __pyx_k_clifford___mod___line_805, sizeof(__pyx_k_clifford___mod___line_805), 0, 1, 0, 0},
18877  {&__pyx_kp_u_clifford___mul___line_779, __pyx_k_clifford___mul___line_779, sizeof(__pyx_k_clifford___mul___line_779), 0, 1, 0, 0},
18878  {&__pyx_kp_u_clifford___neg___line_721, __pyx_k_clifford___neg___line_721, sizeof(__pyx_k_clifford___neg___line_721), 0, 1, 0, 0},
18879  {&__pyx_kp_u_clifford___or___line_938, __pyx_k_clifford___or___line_938, sizeof(__pyx_k_clifford___or___line_938), 0, 1, 0, 0},
18880  {&__pyx_kp_u_clifford___pos___line_730, __pyx_k_clifford___pos___line_730, sizeof(__pyx_k_clifford___pos___line_730), 0, 1, 0, 0},
18881  {&__pyx_kp_u_clifford___pow___line_960, __pyx_k_clifford___pow___line_960, sizeof(__pyx_k_clifford___pow___line_960), 0, 1, 0, 0},
18882  {&__pyx_kp_u_clifford___repr___line_1225, __pyx_k_clifford___repr___line_1225, sizeof(__pyx_k_clifford___repr___line_1225), 0, 1, 0, 0},
18883  {&__pyx_kp_u_clifford___str___line_1234, __pyx_k_clifford___str___line_1234, sizeof(__pyx_k_clifford___str___line_1234), 0, 1, 0, 0},
18884  {&__pyx_kp_u_clifford___sub___line_759, __pyx_k_clifford___sub___line_759, sizeof(__pyx_k_clifford___sub___line_759), 0, 1, 0, 0},
18885  {&__pyx_kp_u_clifford___xor___line_865, __pyx_k_clifford___xor___line_865, sizeof(__pyx_k_clifford___xor___line_865), 0, 1, 0, 0},
18886  {&__pyx_kp_u_clifford_abs_line_1174, __pyx_k_clifford_abs_line_1174, sizeof(__pyx_k_clifford_abs_line_1174), 0, 1, 0, 0},
18887  {&__pyx_kp_u_clifford_conj_line_1137, __pyx_k_clifford_conj_line_1137, sizeof(__pyx_k_clifford_conj_line_1137), 0, 1, 0, 0},
18888  {&__pyx_kp_u_clifford_copy_line_554, __pyx_k_clifford_copy_line_554, sizeof(__pyx_k_clifford_copy_line_554), 0, 1, 0, 0},
18889  {&__pyx_kp_u_clifford_even_line_1060, __pyx_k_clifford_even_line_1060, sizeof(__pyx_k_clifford_even_line_1060), 0, 1, 0, 0},
18890  {&__pyx_kp_u_clifford_frame_line_1214, __pyx_k_clifford_frame_line_1214, sizeof(__pyx_k_clifford_frame_line_1214), 0, 1, 0, 0},
18891  {&__pyx_n_s_clifford_hidden_doctests, __pyx_k_clifford_hidden_doctests, sizeof(__pyx_k_clifford_hidden_doctests), 0, 0, 1, 1},
18892  {&__pyx_kp_u_clifford_hidden_doctests_line_12, __pyx_k_clifford_hidden_doctests_line_12, sizeof(__pyx_k_clifford_hidden_doctests_line_12), 0, 1, 0, 0},
18893  {&__pyx_kp_u_clifford_inv_line_925, __pyx_k_clifford_inv_line_925, sizeof(__pyx_k_clifford_inv_line_925), 0, 1, 0, 0},
18894  {&__pyx_kp_u_clifford_involute_line_1106, __pyx_k_clifford_involute_line_1106, sizeof(__pyx_k_clifford_involute_line_1106), 0, 1, 0, 0},
18895  {&__pyx_kp_u_clifford_isnan_line_1205, __pyx_k_clifford_isnan_line_1205, sizeof(__pyx_k_clifford_isnan_line_1205), 0, 1, 0, 0},
18896  {&__pyx_kp_u_clifford_max_abs_line_1183, __pyx_k_clifford_max_abs_line_1183, sizeof(__pyx_k_clifford_max_abs_line_1183), 0, 1, 0, 0},
18897  {&__pyx_kp_u_clifford_norm_line_1163, __pyx_k_clifford_norm_line_1163, sizeof(__pyx_k_clifford_norm_line_1163), 0, 1, 0, 0},
18898  {&__pyx_kp_u_clifford_odd_line_1069, __pyx_k_clifford_odd_line_1069, sizeof(__pyx_k_clifford_odd_line_1069), 0, 1, 0, 0},
18899  {&__pyx_kp_u_clifford_outer_pow_line_1003, __pyx_k_clifford_outer_pow_line_1003, sizeof(__pyx_k_clifford_outer_pow_line_1003), 0, 1, 0, 0},
18900  {&__pyx_kp_u_clifford_pow_line_979, __pyx_k_clifford_pow_line_979, sizeof(__pyx_k_clifford_pow_line_979), 0, 1, 0, 0},
18901  {&__pyx_kp_u_clifford_pure_line_1049, __pyx_k_clifford_pure_line_1049, sizeof(__pyx_k_clifford_pure_line_1049), 0, 1, 0, 0},
18902  {&__pyx_kp_u_clifford_quad_line_1152, __pyx_k_clifford_quad_line_1152, sizeof(__pyx_k_clifford_quad_line_1152), 0, 1, 0, 0},
18903  {&__pyx_kp_u_clifford_reframe_line_648, __pyx_k_clifford_reframe_line_648, sizeof(__pyx_k_clifford_reframe_line_648), 0, 1, 0, 0},
18904  {&__pyx_kp_u_clifford_reverse_line_1122, __pyx_k_clifford_reverse_line_1122, sizeof(__pyx_k_clifford_reverse_line_1122), 0, 1, 0, 0},
18905  {&__pyx_kp_u_clifford_scalar_line_1038, __pyx_k_clifford_scalar_line_1038, sizeof(__pyx_k_clifford_scalar_line_1038), 0, 1, 0, 0},
18906  {&__pyx_kp_u_clifford_truncated_line_1194, __pyx_k_clifford_truncated_line_1194, sizeof(__pyx_k_clifford_truncated_line_1194), 0, 1, 0, 0},
18907  {&__pyx_kp_u_clifford_vector_part_line_1078, __pyx_k_clifford_vector_part_line_1078, sizeof(__pyx_k_clifford_vector_part_line_1078), 0, 1, 0, 0},
18908  {&__pyx_n_s_cline_in_traceback, __pyx_k_cline_in_traceback, sizeof(__pyx_k_cline_in_traceback), 0, 0, 1, 1},
18909  {&__pyx_n_s_close, __pyx_k_close, sizeof(__pyx_k_close), 0, 0, 1, 1},
18910  {&__pyx_n_s_collections, __pyx_k_collections, sizeof(__pyx_k_collections), 0, 0, 1, 1},
18911  {&__pyx_kp_u_compare_line_490, __pyx_k_compare_line_490, sizeof(__pyx_k_compare_line_490), 0, 1, 0, 0},
18912  {&__pyx_kp_u_complexifier_line_1527, __pyx_k_complexifier_line_1527, sizeof(__pyx_k_complexifier_line_1527), 0, 1, 0, 0},
18913  {&__pyx_n_s_conj, __pyx_k_conj, sizeof(__pyx_k_conj), 0, 0, 1, 1},
18914  {&__pyx_kp_u_conj_line_1436, __pyx_k_conj_line_1436, sizeof(__pyx_k_conj_line_1436), 0, 1, 0, 0},
18915  {&__pyx_n_s_copy, __pyx_k_copy, sizeof(__pyx_k_copy), 0, 0, 1, 1},
18916  {&__pyx_n_s_cos, __pyx_k_cos, sizeof(__pyx_k_cos), 0, 0, 1, 1},
18917  {&__pyx_kp_u_cos_line_1602, __pyx_k_cos_line_1602, sizeof(__pyx_k_cos_line_1602), 0, 1, 0, 0},
18918  {&__pyx_n_s_cosh, __pyx_k_cosh, sizeof(__pyx_k_cosh), 0, 0, 1, 1},
18919  {&__pyx_kp_u_cosh_line_1640, __pyx_k_cosh_line_1640, sizeof(__pyx_k_cosh_line_1640), 0, 1, 0, 0},
18920  {&__pyx_n_s_doctest, __pyx_k_doctest, sizeof(__pyx_k_doctest), 0, 0, 1, 1},
18921  {&__pyx_n_s_e, __pyx_k_e, sizeof(__pyx_k_e), 0, 0, 1, 1},
18922  {&__pyx_kp_u_e_line_1887, __pyx_k_e_line_1887, sizeof(__pyx_k_e_line_1887), 0, 1, 0, 0},
18923  {&__pyx_n_s_even, __pyx_k_even, sizeof(__pyx_k_even), 0, 0, 1, 1},
18924  {&__pyx_kp_u_even_line_1388, __pyx_k_even_line_1388, sizeof(__pyx_k_even_line_1388), 0, 1, 0, 0},
18925  {&__pyx_n_s_exp, __pyx_k_exp, sizeof(__pyx_k_exp), 0, 0, 1, 1},
18926  {&__pyx_kp_u_exp_line_1565, __pyx_k_exp_line_1565, sizeof(__pyx_k_exp_line_1565), 0, 1, 0, 0},
18927  {&__pyx_n_s_fill, __pyx_k_fill, sizeof(__pyx_k_fill), 0, 0, 1, 1},
18928  {&__pyx_n_s_frm, __pyx_k_frm, sizeof(__pyx_k_frm), 0, 0, 1, 1},
18929  {&__pyx_kp_s_from, __pyx_k_from, sizeof(__pyx_k_from), 0, 0, 1, 0},
18930  {&__pyx_n_s_getstate, __pyx_k_getstate, sizeof(__pyx_k_getstate), 0, 0, 1, 1},
18931  {&__pyx_n_s_grade, __pyx_k_grade, sizeof(__pyx_k_grade), 0, 0, 1, 1},
18932  {&__pyx_n_s_i, __pyx_k_i, sizeof(__pyx_k_i), 0, 0, 1, 1},
18933  {&__pyx_kp_u_imag_line_1366, __pyx_k_imag_line_1366, sizeof(__pyx_k_imag_line_1366), 0, 1, 0, 0},
18934  {&__pyx_n_s_import, __pyx_k_import, sizeof(__pyx_k_import), 0, 0, 1, 1},
18935  {&__pyx_n_s_index_set, __pyx_k_index_set, sizeof(__pyx_k_index_set), 0, 0, 1, 1},
18936  {&__pyx_kp_u_index_set___and___line_269, __pyx_k_index_set___and___line_269, sizeof(__pyx_k_index_set___and___line_269), 0, 1, 0, 0},
18937  {&__pyx_kp_u_index_set___getitem___line_189, __pyx_k_index_set___getitem___line_189, sizeof(__pyx_k_index_set___getitem___line_189), 0, 1, 0, 0},
18938  {&__pyx_kp_u_index_set___iand___line_280, __pyx_k_index_set___iand___line_280, sizeof(__pyx_k_index_set___iand___line_280), 0, 1, 0, 0},
18939  {&__pyx_kp_u_index_set___invert___line_238, __pyx_k_index_set___invert___line_238, sizeof(__pyx_k_index_set___invert___line_238), 0, 1, 0, 0},
18940  {&__pyx_kp_u_index_set___ior___line_302, __pyx_k_index_set___ior___line_302, sizeof(__pyx_k_index_set___ior___line_302), 0, 1, 0, 0},
18941  {&__pyx_n_s_index_set___iter, __pyx_k_index_set___iter, sizeof(__pyx_k_index_set___iter), 0, 0, 1, 1},
18942  {&__pyx_kp_u_index_set___iter___line_227, __pyx_k_index_set___iter___line_227, sizeof(__pyx_k_index_set___iter___line_227), 0, 1, 0, 0},
18943  {&__pyx_kp_u_index_set___ixor___line_258, __pyx_k_index_set___ixor___line_258, sizeof(__pyx_k_index_set___ixor___line_258), 0, 1, 0, 0},
18944  {&__pyx_kp_u_index_set___or___line_291, __pyx_k_index_set___or___line_291, sizeof(__pyx_k_index_set___or___line_291), 0, 1, 0, 0},
18945  {&__pyx_kp_u_index_set___repr___line_382, __pyx_k_index_set___repr___line_382, sizeof(__pyx_k_index_set___repr___line_382), 0, 1, 0, 0},
18946  {&__pyx_kp_u_index_set___setitem___line_177, __pyx_k_index_set___setitem___line_177, sizeof(__pyx_k_index_set___setitem___line_177), 0, 1, 0, 0},
18947  {&__pyx_kp_u_index_set___str___line_393, __pyx_k_index_set___str___line_393, sizeof(__pyx_k_index_set___str___line_393), 0, 1, 0, 0},
18948  {&__pyx_kp_u_index_set___xor___line_247, __pyx_k_index_set___xor___line_247, sizeof(__pyx_k_index_set___xor___line_247), 0, 1, 0, 0},
18949  {&__pyx_kp_u_index_set_copy_line_64, __pyx_k_index_set_copy_line_64, sizeof(__pyx_k_index_set_copy_line_64), 0, 1, 0, 0},
18950  {&__pyx_kp_u_index_set_count_line_313, __pyx_k_index_set_count_line_313, sizeof(__pyx_k_index_set_count_line_313), 0, 1, 0, 0},
18951  {&__pyx_kp_u_index_set_count_neg_line_322, __pyx_k_index_set_count_neg_line_322, sizeof(__pyx_k_index_set_count_neg_line_322), 0, 1, 0, 0},
18952  {&__pyx_kp_u_index_set_count_pos_line_331, __pyx_k_index_set_count_pos_line_331, sizeof(__pyx_k_index_set_count_pos_line_331), 0, 1, 0, 0},
18953  {&__pyx_n_s_index_set_hidden_doctests, __pyx_k_index_set_hidden_doctests, sizeof(__pyx_k_index_set_hidden_doctests), 0, 0, 1, 1},
18954  {&__pyx_kp_u_index_set_hidden_doctests_line_4, __pyx_k_index_set_hidden_doctests_line_4, sizeof(__pyx_k_index_set_hidden_doctests_line_4), 0, 1, 0, 0},
18955  {&__pyx_kp_u_index_set_max_line_349, __pyx_k_index_set_max_line_349, sizeof(__pyx_k_index_set_max_line_349), 0, 1, 0, 0},
18956  {&__pyx_kp_u_index_set_min_line_340, __pyx_k_index_set_min_line_340, sizeof(__pyx_k_index_set_min_line_340), 0, 1, 0, 0},
18957  {&__pyx_kp_u_index_set_sign_of_mult_line_364, __pyx_k_index_set_sign_of_mult_line_364, sizeof(__pyx_k_index_set_sign_of_mult_line_364), 0, 1, 0, 0},
18958  {&__pyx_kp_u_index_set_sign_of_square_line_37, __pyx_k_index_set_sign_of_square_line_37, sizeof(__pyx_k_index_set_sign_of_square_line_37), 0, 1, 0, 0},
18959  {&__pyx_n_s_inv, __pyx_k_inv, sizeof(__pyx_k_inv), 0, 0, 1, 1},
18960  {&__pyx_kp_u_inv_line_1329, __pyx_k_inv_line_1329, sizeof(__pyx_k_inv_line_1329), 0, 1, 0, 0},
18961  {&__pyx_kp_s_invalid, __pyx_k_invalid, sizeof(__pyx_k_invalid), 0, 0, 1, 0},
18962  {&__pyx_kp_s_invalid_string, __pyx_k_invalid_string, sizeof(__pyx_k_invalid_string), 0, 0, 1, 0},
18963  {&__pyx_n_s_involute, __pyx_k_involute, sizeof(__pyx_k_involute), 0, 0, 1, 1},
18964  {&__pyx_kp_u_involute_line_1406, __pyx_k_involute_line_1406, sizeof(__pyx_k_involute_line_1406), 0, 1, 0, 0},
18965  {&__pyx_n_s_ist, __pyx_k_ist, sizeof(__pyx_k_ist), 0, 0, 1, 1},
18966  {&__pyx_n_s_istpq, __pyx_k_istpq, sizeof(__pyx_k_istpq), 0, 0, 1, 1},
18967  {&__pyx_kp_u_istpq_line_1900, __pyx_k_istpq_line_1900, sizeof(__pyx_k_istpq_line_1900), 0, 1, 0, 0},
18968  {&__pyx_n_s_iter, __pyx_k_iter, sizeof(__pyx_k_iter), 0, 0, 1, 1},
18969  {&__pyx_n_s_ixt, __pyx_k_ixt, sizeof(__pyx_k_ixt), 0, 0, 1, 1},
18970  {&__pyx_kp_u_lexicographic_compare_eg_3_4_5, __pyx_k_lexicographic_compare_eg_3_4_5, sizeof(__pyx_k_lexicographic_compare_eg_3_4_5), 0, 1, 0, 0},
18971  {&__pyx_n_s_lhs, __pyx_k_lhs, sizeof(__pyx_k_lhs), 0, 0, 1, 1},
18972  {&__pyx_n_s_log, __pyx_k_log, sizeof(__pyx_k_log), 0, 0, 1, 1},
18973  {&__pyx_kp_u_log_line_1579, __pyx_k_log_line_1579, sizeof(__pyx_k_log_line_1579), 0, 1, 0, 0},
18974  {&__pyx_n_s_m, __pyx_k_m, sizeof(__pyx_k_m), 0, 0, 1, 1},
18975  {&__pyx_n_s_main, __pyx_k_main, sizeof(__pyx_k_main), 0, 0, 1, 1},
18976  {&__pyx_n_s_math, __pyx_k_math, sizeof(__pyx_k_math), 0, 0, 1, 1},
18977  {&__pyx_n_s_max, __pyx_k_max, sizeof(__pyx_k_max), 0, 0, 1, 1},
18978  {&__pyx_kp_u_max_abs_line_1482, __pyx_k_max_abs_line_1482, sizeof(__pyx_k_max_abs_line_1482), 0, 1, 0, 0},
18979  {&__pyx_kp_u_max_pos_line_511, __pyx_k_max_pos_line_511, sizeof(__pyx_k_max_pos_line_511), 0, 1, 0, 0},
18980  {&__pyx_n_s_min, __pyx_k_min, sizeof(__pyx_k_min), 0, 0, 1, 1},
18981  {&__pyx_kp_u_min_neg_line_502, __pyx_k_min_neg_line_502, sizeof(__pyx_k_min_neg_line_502), 0, 1, 0, 0},
18982  {&__pyx_n_s_name, __pyx_k_name, sizeof(__pyx_k_name), 0, 0, 1, 1},
18983  {&__pyx_n_s_nbar3, __pyx_k_nbar3, sizeof(__pyx_k_nbar3), 0, 0, 1, 1},
18984  {&__pyx_n_s_ninf3, __pyx_k_ninf3, sizeof(__pyx_k_ninf3), 0, 0, 1, 1},
18985  {&__pyx_kp_s_no_default___reduce___due_to_non, __pyx_k_no_default___reduce___due_to_non, sizeof(__pyx_k_no_default___reduce___due_to_non), 0, 0, 1, 0},
18986  {&__pyx_n_s_norm, __pyx_k_norm, sizeof(__pyx_k_norm), 0, 0, 1, 1},
18987  {&__pyx_kp_u_norm_line_1462, __pyx_k_norm_line_1462, sizeof(__pyx_k_norm_line_1462), 0, 1, 0, 0},
18988  {&__pyx_kp_u_norm_sum_of_squares_of_coordina, __pyx_k_norm_sum_of_squares_of_coordina, sizeof(__pyx_k_norm_sum_of_squares_of_coordina), 0, 1, 0, 0},
18989  {&__pyx_n_s_numbers, __pyx_k_numbers, sizeof(__pyx_k_numbers), 0, 0, 1, 1},
18990  {&__pyx_n_s_obj, __pyx_k_obj, sizeof(__pyx_k_obj), 0, 0, 1, 1},
18991  {&__pyx_n_s_odd, __pyx_k_odd, sizeof(__pyx_k_odd), 0, 0, 1, 1},
18992  {&__pyx_kp_u_odd_line_1397, __pyx_k_odd_line_1397, sizeof(__pyx_k_odd_line_1397), 0, 1, 0, 0},
18993  {&__pyx_n_s_other, __pyx_k_other, sizeof(__pyx_k_other), 0, 0, 1, 1},
18994  {&__pyx_n_s_outer_pow, __pyx_k_outer_pow, sizeof(__pyx_k_outer_pow), 0, 0, 1, 1},
18995  {&__pyx_kp_u_outer_pow_line_1518, __pyx_k_outer_pow_line_1518, sizeof(__pyx_k_outer_pow_line_1518), 0, 1, 0, 0},
18996  {&__pyx_n_s_p, __pyx_k_p, sizeof(__pyx_k_p), 0, 0, 1, 1},
18997  {&__pyx_n_s_pi, __pyx_k_pi, sizeof(__pyx_k_pi), 0, 0, 1, 1},
18998  {&__pyx_n_s_pow, __pyx_k_pow, sizeof(__pyx_k_pow), 0, 0, 1, 1},
18999  {&__pyx_kp_u_pow_line_1494, __pyx_k_pow_line_1494, sizeof(__pyx_k_pow_line_1494), 0, 1, 0, 0},
19000  {&__pyx_n_s_pure, __pyx_k_pure, sizeof(__pyx_k_pure), 0, 0, 1, 1},
19001  {&__pyx_kp_u_pure_line_1377, __pyx_k_pure_line_1377, sizeof(__pyx_k_pure_line_1377), 0, 1, 0, 0},
19002  {&__pyx_n_s_pyx_vtable, __pyx_k_pyx_vtable, sizeof(__pyx_k_pyx_vtable), 0, 0, 1, 1},
19003  {&__pyx_n_s_q, __pyx_k_q, sizeof(__pyx_k_q), 0, 0, 1, 1},
19004  {&__pyx_n_s_quad, __pyx_k_quad, sizeof(__pyx_k_quad), 0, 0, 1, 1},
19005  {&__pyx_kp_u_quad_line_1451, __pyx_k_quad_line_1451, sizeof(__pyx_k_quad_line_1451), 0, 1, 0, 0},
19006  {&__pyx_kp_u_random_clifford_line_1815, __pyx_k_random_clifford_line_1815, sizeof(__pyx_k_random_clifford_line_1815), 0, 1, 0, 0},
19007  {&__pyx_n_s_range, __pyx_k_range, sizeof(__pyx_k_range), 0, 0, 1, 1},
19008  {&__pyx_kp_u_real_line_1355, __pyx_k_real_line_1355, sizeof(__pyx_k_real_line_1355), 0, 1, 0, 0},
19009  {&__pyx_n_s_reduce, __pyx_k_reduce, sizeof(__pyx_k_reduce), 0, 0, 1, 1},
19010  {&__pyx_n_s_reduce_cython, __pyx_k_reduce_cython, sizeof(__pyx_k_reduce_cython), 0, 0, 1, 1},
19011  {&__pyx_n_s_reduce_ex, __pyx_k_reduce_ex, sizeof(__pyx_k_reduce_ex), 0, 0, 1, 1},
19012  {&__pyx_n_s_reverse, __pyx_k_reverse, sizeof(__pyx_k_reverse), 0, 0, 1, 1},
19013  {&__pyx_kp_u_reverse_line_1421, __pyx_k_reverse_line_1421, sizeof(__pyx_k_reverse_line_1421), 0, 1, 0, 0},
19014  {&__pyx_n_s_rhs, __pyx_k_rhs, sizeof(__pyx_k_rhs), 0, 0, 1, 1},
19015  {&__pyx_n_s_scalar, __pyx_k_scalar, sizeof(__pyx_k_scalar), 0, 0, 1, 1},
19016  {&__pyx_kp_u_scalar_line_1344, __pyx_k_scalar_line_1344, sizeof(__pyx_k_scalar_line_1344), 0, 1, 0, 0},
19017  {&__pyx_n_s_send, __pyx_k_send, sizeof(__pyx_k_send), 0, 0, 1, 1},
19018  {&__pyx_n_s_setstate, __pyx_k_setstate, sizeof(__pyx_k_setstate), 0, 0, 1, 1},
19019  {&__pyx_n_s_setstate_cython, __pyx_k_setstate_cython, sizeof(__pyx_k_setstate_cython), 0, 0, 1, 1},
19020  {&__pyx_n_s_sin, __pyx_k_sin, sizeof(__pyx_k_sin), 0, 0, 1, 1},
19021  {&__pyx_kp_u_sin_line_1679, __pyx_k_sin_line_1679, sizeof(__pyx_k_sin_line_1679), 0, 1, 0, 0},
19022  {&__pyx_n_s_sinh, __pyx_k_sinh, sizeof(__pyx_k_sinh), 0, 0, 1, 1},
19023  {&__pyx_kp_u_sinh_line_1719, __pyx_k_sinh_line_1719, sizeof(__pyx_k_sinh_line_1719), 0, 1, 0, 0},
19024  {&__pyx_n_s_sqrt, __pyx_k_sqrt, sizeof(__pyx_k_sqrt), 0, 0, 1, 1},
19025  {&__pyx_kp_u_sqrt_line_1542, __pyx_k_sqrt_line_1542, sizeof(__pyx_k_sqrt_line_1542), 0, 1, 0, 0},
19026  {&__pyx_n_s_tan, __pyx_k_tan, sizeof(__pyx_k_tan), 0, 0, 1, 1},
19027  {&__pyx_kp_u_tan_line_1752, __pyx_k_tan_line_1752, sizeof(__pyx_k_tan_line_1752), 0, 1, 0, 0},
19028  {&__pyx_n_s_tanh, __pyx_k_tanh, sizeof(__pyx_k_tanh), 0, 0, 1, 1},
19029  {&__pyx_kp_u_tanh_line_1786, __pyx_k_tanh_line_1786, sizeof(__pyx_k_tanh_line_1786), 0, 1, 0, 0},
19030  {&__pyx_n_s_tau, __pyx_k_tau, sizeof(__pyx_k_tau), 0, 0, 1, 1},
19031  {&__pyx_n_s_test, __pyx_k_test, sizeof(__pyx_k_test), 0, 0, 1, 1},
19032  {&__pyx_n_s_test_2, __pyx_k_test_2, sizeof(__pyx_k_test_2), 0, 0, 1, 1},
19033  {&__pyx_n_s_testmod, __pyx_k_testmod, sizeof(__pyx_k_testmod), 0, 0, 1, 1},
19034  {&__pyx_n_s_throw, __pyx_k_throw, sizeof(__pyx_k_throw), 0, 0, 1, 1},
19035  {&__pyx_kp_s_to_frame, __pyx_k_to_frame, sizeof(__pyx_k_to_frame), 0, 0, 1, 0},
19036  {&__pyx_kp_s_using, __pyx_k_using, sizeof(__pyx_k_using), 0, 0, 1, 0},
19037  {&__pyx_kp_s_using_invalid, __pyx_k_using_invalid, sizeof(__pyx_k_using_invalid), 0, 0, 1, 0},
19038  {&__pyx_kp_s_value, __pyx_k_value, sizeof(__pyx_k_value), 0, 0, 1, 0},
19039  {&__pyx_n_s_version, __pyx_k_version, sizeof(__pyx_k_version), 0, 0, 1, 1},
19040  {&__pyx_n_s_xrange, __pyx_k_xrange, sizeof(__pyx_k_xrange), 0, 0, 1, 1},
19041  {0, 0, 0, 0, 0, 0, 0}
19042 };
19043 static CYTHON_SMALL_CODE int __Pyx_InitCachedBuiltins(void) {
19044  __pyx_builtin_IndexError = __Pyx_GetBuiltinName(__pyx_n_s_IndexError); if (!__pyx_builtin_IndexError) __PYX_ERR(0, 102, __pyx_L1_error)
19045  __pyx_builtin_RuntimeError = __Pyx_GetBuiltinName(__pyx_n_s_RuntimeError); if (!__pyx_builtin_RuntimeError) __PYX_ERR(0, 104, __pyx_L1_error)
19046  __pyx_builtin_TypeError = __Pyx_GetBuiltinName(__pyx_n_s_TypeError); if (!__pyx_builtin_TypeError) __PYX_ERR(0, 104, __pyx_L1_error)
19047  __pyx_builtin_ValueError = __Pyx_GetBuiltinName(__pyx_n_s_ValueError); if (!__pyx_builtin_ValueError) __PYX_ERR(0, 105, __pyx_L1_error)
19048  __pyx_builtin_NotImplemented = __Pyx_GetBuiltinName(__pyx_n_s_NotImplemented); if (!__pyx_builtin_NotImplemented) __PYX_ERR(0, 157, __pyx_L1_error)
19049  __pyx_builtin_range = __Pyx_GetBuiltinName(__pyx_n_s_range); if (!__pyx_builtin_range) __PYX_ERR(0, 234, __pyx_L1_error)
19050  #if PY_MAJOR_VERSION >= 3
19051  __pyx_builtin_xrange = __Pyx_GetBuiltinName(__pyx_n_s_range); if (!__pyx_builtin_xrange) __PYX_ERR(0, 1098, __pyx_L1_error)
19052  #else
19053  __pyx_builtin_xrange = __Pyx_GetBuiltinName(__pyx_n_s_xrange); if (!__pyx_builtin_xrange) __PYX_ERR(0, 1098, __pyx_L1_error)
19054  #endif
19055  return 0;
19056  __pyx_L1_error:;
19057  return -1;
19058 }
19059 
19060 static CYTHON_SMALL_CODE int __Pyx_InitCachedConstants(void) {
19061  __Pyx_RefNannyDeclarations
19062  __Pyx_RefNannySetupContext("__Pyx_InitCachedConstants", 0);
19063 
19064  /* "(tree fragment)":2
19065  * def __reduce_cython__(self):
19066  * raise TypeError("no default __reduce__ due to non-trivial __cinit__") # <<<<<<<<<<<<<<
19067  * def __setstate_cython__(self, __pyx_state):
19068  * raise TypeError("no default __reduce__ due to non-trivial __cinit__")
19069  */
19070  __pyx_tuple__3 = PyTuple_Pack(1, __pyx_kp_s_no_default___reduce___due_to_non); if (unlikely(!__pyx_tuple__3)) __PYX_ERR(1, 2, __pyx_L1_error)
19071  __Pyx_GOTREF(__pyx_tuple__3);
19072  __Pyx_GIVEREF(__pyx_tuple__3);
19073 
19074  /* "(tree fragment)":4
19075  * raise TypeError("no default __reduce__ due to non-trivial __cinit__")
19076  * def __setstate_cython__(self, __pyx_state):
19077  * raise TypeError("no default __reduce__ due to non-trivial __cinit__") # <<<<<<<<<<<<<<
19078  */
19079  __pyx_tuple__4 = PyTuple_Pack(1, __pyx_kp_s_no_default___reduce___due_to_non); if (unlikely(!__pyx_tuple__4)) __PYX_ERR(1, 4, __pyx_L1_error)
19080  __Pyx_GOTREF(__pyx_tuple__4);
19081  __Pyx_GIVEREF(__pyx_tuple__4);
19082 
19083  /* "PyClical.pyx":635
19084  * TypeError: Not applicable.
19085  * """
19086  * raise TypeError("Not applicable.") # <<<<<<<<<<<<<<
19087  *
19088  * def __iter__(self):
19089  */
19090  __pyx_tuple__10 = PyTuple_Pack(1, __pyx_kp_s_Not_applicable); if (unlikely(!__pyx_tuple__10)) __PYX_ERR(0, 635, __pyx_L1_error)
19091  __Pyx_GOTREF(__pyx_tuple__10);
19092  __Pyx_GIVEREF(__pyx_tuple__10);
19093 
19094  /* "(tree fragment)":2
19095  * def __reduce_cython__(self):
19096  * raise TypeError("no default __reduce__ due to non-trivial __cinit__") # <<<<<<<<<<<<<<
19097  * def __setstate_cython__(self, __pyx_state):
19098  * raise TypeError("no default __reduce__ due to non-trivial __cinit__")
19099  */
19100  __pyx_tuple__11 = PyTuple_Pack(1, __pyx_kp_s_no_default___reduce___due_to_non); if (unlikely(!__pyx_tuple__11)) __PYX_ERR(1, 2, __pyx_L1_error)
19101  __Pyx_GOTREF(__pyx_tuple__11);
19102  __Pyx_GIVEREF(__pyx_tuple__11);
19103 
19104  /* "(tree fragment)":4
19105  * raise TypeError("no default __reduce__ due to non-trivial __cinit__")
19106  * def __setstate_cython__(self, __pyx_state):
19107  * raise TypeError("no default __reduce__ due to non-trivial __cinit__") # <<<<<<<<<<<<<<
19108  */
19109  __pyx_tuple__12 = PyTuple_Pack(1, __pyx_kp_s_no_default___reduce___due_to_non); if (unlikely(!__pyx_tuple__12)) __PYX_ERR(1, 4, __pyx_L1_error)
19110  __Pyx_GOTREF(__pyx_tuple__12);
19111  __Pyx_GIVEREF(__pyx_tuple__12);
19112 
19113  /* "PyClical.pyx":404
19114  * return index_set_to_str( self.unwrap() ).c_str()
19115  *
19116  * def index_set_hidden_doctests(): # <<<<<<<<<<<<<<
19117  * """
19118  * Tests for functions that Doctest cannot see.
19119  */
19120  __pyx_codeobj__13 = (PyObject*)__Pyx_PyCode_New(0, 0, 0, 0, CO_OPTIMIZED|CO_NEWLOCALS, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_PyClical_pyx, __pyx_n_s_index_set_hidden_doctests, 404, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__13)) __PYX_ERR(0, 404, __pyx_L1_error)
19121 
19122  /* "PyClical.pyx":1243
19123  * return clifford_to_str( self.unwrap() ).c_str()
19124  *
19125  * def clifford_hidden_doctests(): # <<<<<<<<<<<<<<
19126  * """
19127  * Tests for functions that Doctest cannot see.
19128  */
19129  __pyx_codeobj__14 = (PyObject*)__Pyx_PyCode_New(0, 0, 0, 0, CO_OPTIMIZED|CO_NEWLOCALS, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_PyClical_pyx, __pyx_n_s_clifford_hidden_doctests, 1243, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__14)) __PYX_ERR(0, 1243, __pyx_L1_error)
19130 
19131  /* "PyClical.pyx":1856
19132  *
19133  * # Some abbreviations.
19134  * tau = atan(clifford(1.0)) * 8.0 # <<<<<<<<<<<<<<
19135  * pi = tau / 2.0
19136  *
19137  */
19138  __pyx_tuple__15 = PyTuple_Pack(1, __pyx_float_1_0); if (unlikely(!__pyx_tuple__15)) __PYX_ERR(0, 1856, __pyx_L1_error)
19139  __Pyx_GOTREF(__pyx_tuple__15);
19140  __Pyx_GIVEREF(__pyx_tuple__15);
19141 
19142  /* "PyClical.pyx":1887
19143  * """
19144  *
19145  * def e(obj): # <<<<<<<<<<<<<<
19146  * """
19147  * Abbreviation for clifford(index_set(obj)).
19148  */
19149  __pyx_tuple__16 = PyTuple_Pack(1, __pyx_n_s_obj); if (unlikely(!__pyx_tuple__16)) __PYX_ERR(0, 1887, __pyx_L1_error)
19150  __Pyx_GOTREF(__pyx_tuple__16);
19151  __Pyx_GIVEREF(__pyx_tuple__16);
19152  __pyx_codeobj__17 = (PyObject*)__Pyx_PyCode_New(1, 0, 1, 0, CO_OPTIMIZED|CO_NEWLOCALS, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__16, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_PyClical_pyx, __pyx_n_s_e, 1887, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__17)) __PYX_ERR(0, 1887, __pyx_L1_error)
19153 
19154  /* "PyClical.pyx":1900
19155  * return clifford(index_set(obj))
19156  *
19157  * def istpq(p, q): # <<<<<<<<<<<<<<
19158  * """
19159  * Abbreviation for index_set({-q,...p}).
19160  */
19161  __pyx_tuple__18 = PyTuple_Pack(2, __pyx_n_s_p, __pyx_n_s_q); if (unlikely(!__pyx_tuple__18)) __PYX_ERR(0, 1900, __pyx_L1_error)
19162  __Pyx_GOTREF(__pyx_tuple__18);
19163  __Pyx_GIVEREF(__pyx_tuple__18);
19164  __pyx_codeobj__19 = (PyObject*)__Pyx_PyCode_New(2, 0, 2, 0, CO_OPTIMIZED|CO_NEWLOCALS, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__18, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_PyClical_pyx, __pyx_n_s_istpq, 1900, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__19)) __PYX_ERR(0, 1900, __pyx_L1_error)
19165 
19166  /* "PyClical.pyx":1909
19167  * return index_set(set(range(-q,p+1)))
19168  *
19169  * ninf3 = e(4) + e(-1) # Null infinity point in 3D Conformal Geometric Algebra [DL]. # <<<<<<<<<<<<<<
19170  * nbar3 = e(4) - e(-1) # Null bar point in 3D Conformal Geometric Algebra [DL].
19171  *
19172  */
19173  __pyx_tuple__20 = PyTuple_Pack(1, __pyx_int_4); if (unlikely(!__pyx_tuple__20)) __PYX_ERR(0, 1909, __pyx_L1_error)
19174  __Pyx_GOTREF(__pyx_tuple__20);
19175  __Pyx_GIVEREF(__pyx_tuple__20);
19176  __pyx_tuple__21 = PyTuple_Pack(1, __pyx_int_neg_1); if (unlikely(!__pyx_tuple__21)) __PYX_ERR(0, 1909, __pyx_L1_error)
19177  __Pyx_GOTREF(__pyx_tuple__21);
19178  __Pyx_GIVEREF(__pyx_tuple__21);
19179 
19180  /* "PyClical.pyx":1913
19181  *
19182  * # Doctest interface.
19183  * def _test(): # <<<<<<<<<<<<<<
19184  * import PyClical, doctest
19185  * return doctest.testmod(PyClical)
19186  */
19187  __pyx_tuple__22 = PyTuple_Pack(2, __pyx_n_s_PyClical, __pyx_n_s_doctest); if (unlikely(!__pyx_tuple__22)) __PYX_ERR(0, 1913, __pyx_L1_error)
19188  __Pyx_GOTREF(__pyx_tuple__22);
19189  __Pyx_GIVEREF(__pyx_tuple__22);
19190  __pyx_codeobj__23 = (PyObject*)__Pyx_PyCode_New(0, 0, 2, 0, CO_OPTIMIZED|CO_NEWLOCALS, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__22, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_PyClical_pyx, __pyx_n_s_test, 1913, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__23)) __PYX_ERR(0, 1913, __pyx_L1_error)
19191  __Pyx_RefNannyFinishContext();
19192  return 0;
19193  __pyx_L1_error:;
19194  __Pyx_RefNannyFinishContext();
19195  return -1;
19196 }
19197 
19198 static CYTHON_SMALL_CODE int __Pyx_InitGlobals(void) {
19199  if (__Pyx_InitStrings(__pyx_string_tab) < 0) __PYX_ERR(0, 1, __pyx_L1_error);
19200  __pyx_float_0_0 = PyFloat_FromDouble(0.0); if (unlikely(!__pyx_float_0_0)) __PYX_ERR(0, 1, __pyx_L1_error)
19201  __pyx_float_1_0 = PyFloat_FromDouble(1.0); if (unlikely(!__pyx_float_1_0)) __PYX_ERR(0, 1, __pyx_L1_error)
19202  __pyx_float_2_0 = PyFloat_FromDouble(2.0); if (unlikely(!__pyx_float_2_0)) __PYX_ERR(0, 1, __pyx_L1_error)
19203  __pyx_float_8_0 = PyFloat_FromDouble(8.0); if (unlikely(!__pyx_float_8_0)) __PYX_ERR(0, 1, __pyx_L1_error)
19204  __pyx_int_0 = PyInt_FromLong(0); if (unlikely(!__pyx_int_0)) __PYX_ERR(0, 1, __pyx_L1_error)
19205  __pyx_int_1 = PyInt_FromLong(1); if (unlikely(!__pyx_int_1)) __PYX_ERR(0, 1, __pyx_L1_error)
19206  __pyx_int_4 = PyInt_FromLong(4); if (unlikely(!__pyx_int_4)) __PYX_ERR(0, 1, __pyx_L1_error)
19207  __pyx_int_neg_1 = PyInt_FromLong(-1); if (unlikely(!__pyx_int_neg_1)) __PYX_ERR(0, 1, __pyx_L1_error)
19208  return 0;
19209  __pyx_L1_error:;
19210  return -1;
19211 }
19212 
19213 static CYTHON_SMALL_CODE int __Pyx_modinit_global_init_code(void); /*proto*/
19214 static CYTHON_SMALL_CODE int __Pyx_modinit_variable_export_code(void); /*proto*/
19215 static CYTHON_SMALL_CODE int __Pyx_modinit_function_export_code(void); /*proto*/
19216 static CYTHON_SMALL_CODE int __Pyx_modinit_type_init_code(void); /*proto*/
19217 static CYTHON_SMALL_CODE int __Pyx_modinit_type_import_code(void); /*proto*/
19218 static CYTHON_SMALL_CODE int __Pyx_modinit_variable_import_code(void); /*proto*/
19219 static CYTHON_SMALL_CODE int __Pyx_modinit_function_import_code(void); /*proto*/
19220 
19221 static int __Pyx_modinit_global_init_code(void) {
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19223  __Pyx_RefNannySetupContext("__Pyx_modinit_global_init_code", 0);
19224  /*--- Global init code ---*/
19225  __Pyx_RefNannyFinishContext();
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19229 static int __Pyx_modinit_variable_export_code(void) {
19230  __Pyx_RefNannyDeclarations
19231  __Pyx_RefNannySetupContext("__Pyx_modinit_variable_export_code", 0);
19232  /*--- Variable export code ---*/
19233  __Pyx_RefNannyFinishContext();
19234  return 0;
19235 }
19236 
19237 static int __Pyx_modinit_function_export_code(void) {
19238  __Pyx_RefNannyDeclarations
19239  __Pyx_RefNannySetupContext("__Pyx_modinit_function_export_code", 0);
19240  /*--- Function export code ---*/
19241  __Pyx_RefNannyFinishContext();
19242  return 0;
19243 }
19244 
19245 static int __Pyx_modinit_type_init_code(void) {
19246  __Pyx_RefNannyDeclarations
19247  __Pyx_RefNannySetupContext("__Pyx_modinit_type_init_code", 0);
19248  /*--- Type init code ---*/
19249  __pyx_vtabptr_8PyClical_index_set = &__pyx_vtable_8PyClical_index_set;
19250  __pyx_vtable_8PyClical_index_set.wrap = (PyObject *(*)(struct __pyx_obj_8PyClical_index_set *, IndexSet))__pyx_f_8PyClical_9index_set_wrap;
19251  __pyx_vtable_8PyClical_index_set.unwrap = (IndexSet (*)(struct __pyx_obj_8PyClical_index_set *))__pyx_f_8PyClical_9index_set_unwrap;
19252  __pyx_vtable_8PyClical_index_set.copy = (PyObject *(*)(struct __pyx_obj_8PyClical_index_set *, int __pyx_skip_dispatch))__pyx_f_8PyClical_9index_set_copy;
19253  if (PyType_Ready(&__pyx_type_8PyClical_index_set) < 0) __PYX_ERR(0, 45, __pyx_L1_error)
19254  __pyx_type_8PyClical_index_set.tp_print = 0;
19255  if ((CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP) && likely(!__pyx_type_8PyClical_index_set.tp_dictoffset && __pyx_type_8PyClical_index_set.tp_getattro == PyObject_GenericGetAttr)) {
19256  __pyx_type_8PyClical_index_set.tp_getattro = __Pyx_PyObject_GenericGetAttr;
19257  }
19258  #if CYTHON_COMPILING_IN_CPYTHON
19259  {
19260  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__setitem__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19261  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19262  __pyx_wrapperbase_8PyClical_9index_set_8__setitem__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19263  __pyx_wrapperbase_8PyClical_9index_set_8__setitem__.doc = __pyx_doc_8PyClical_9index_set_8__setitem__;
19264  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_8__setitem__;
19265  }
19266  }
19267  #endif
19268  #if CYTHON_COMPILING_IN_CPYTHON
19269  {
19270  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__getitem__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19271  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19272  __pyx_wrapperbase_8PyClical_9index_set_10__getitem__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19273  __pyx_wrapperbase_8PyClical_9index_set_10__getitem__.doc = __pyx_doc_8PyClical_9index_set_10__getitem__;
19274  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_10__getitem__;
19275  }
19276  }
19277  #endif
19278  #if CYTHON_COMPILING_IN_CPYTHON
19279  {
19280  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__contains__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19281  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19282  __pyx_wrapperbase_8PyClical_9index_set_12__contains__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19283  __pyx_wrapperbase_8PyClical_9index_set_12__contains__.doc = __pyx_doc_8PyClical_9index_set_12__contains__;
19284  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_12__contains__;
19285  }
19286  }
19287  #endif
19288  #if CYTHON_COMPILING_IN_CPYTHON
19289  {
19290  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__iter__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19291  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19292  __pyx_wrapperbase_8PyClical_9index_set_14__iter__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19293  __pyx_wrapperbase_8PyClical_9index_set_14__iter__.doc = __pyx_doc_8PyClical_9index_set_14__iter__;
19294  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_14__iter__;
19295  }
19296  }
19297  #endif
19298  #if CYTHON_COMPILING_IN_CPYTHON
19299  {
19300  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__invert__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19301  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19302  __pyx_wrapperbase_8PyClical_9index_set_17__invert__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19303  __pyx_wrapperbase_8PyClical_9index_set_17__invert__.doc = __pyx_doc_8PyClical_9index_set_17__invert__;
19304  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_17__invert__;
19305  }
19306  }
19307  #endif
19308  #if CYTHON_COMPILING_IN_CPYTHON
19309  {
19310  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__xor__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19311  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19312  __pyx_wrapperbase_8PyClical_9index_set_19__xor__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19313  __pyx_wrapperbase_8PyClical_9index_set_19__xor__.doc = __pyx_doc_8PyClical_9index_set_19__xor__;
19314  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_19__xor__;
19315  }
19316  }
19317  #endif
19318  #if CYTHON_COMPILING_IN_CPYTHON
19319  {
19320  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__ixor__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19321  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19322  __pyx_wrapperbase_8PyClical_9index_set_21__ixor__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19323  __pyx_wrapperbase_8PyClical_9index_set_21__ixor__.doc = __pyx_doc_8PyClical_9index_set_21__ixor__;
19324  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_21__ixor__;
19325  }
19326  }
19327  #endif
19328  #if CYTHON_COMPILING_IN_CPYTHON
19329  {
19330  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__and__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19331  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19332  __pyx_wrapperbase_8PyClical_9index_set_23__and__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19333  __pyx_wrapperbase_8PyClical_9index_set_23__and__.doc = __pyx_doc_8PyClical_9index_set_23__and__;
19334  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_23__and__;
19335  }
19336  }
19337  #endif
19338  #if CYTHON_COMPILING_IN_CPYTHON
19339  {
19340  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__iand__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19341  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19342  __pyx_wrapperbase_8PyClical_9index_set_25__iand__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19343  __pyx_wrapperbase_8PyClical_9index_set_25__iand__.doc = __pyx_doc_8PyClical_9index_set_25__iand__;
19344  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_25__iand__;
19345  }
19346  }
19347  #endif
19348  #if CYTHON_COMPILING_IN_CPYTHON
19349  {
19350  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__or__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19351  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19352  __pyx_wrapperbase_8PyClical_9index_set_27__or__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19353  __pyx_wrapperbase_8PyClical_9index_set_27__or__.doc = __pyx_doc_8PyClical_9index_set_27__or__;
19354  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_27__or__;
19355  }
19356  }
19357  #endif
19358  #if CYTHON_COMPILING_IN_CPYTHON
19359  {
19360  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__ior__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19361  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19362  __pyx_wrapperbase_8PyClical_9index_set_29__ior__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19363  __pyx_wrapperbase_8PyClical_9index_set_29__ior__.doc = __pyx_doc_8PyClical_9index_set_29__ior__;
19364  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_29__ior__;
19365  }
19366  }
19367  #endif
19368  #if CYTHON_COMPILING_IN_CPYTHON
19369  {
19370  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__repr__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19371  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19372  __pyx_wrapperbase_8PyClical_9index_set_47__repr__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19373  __pyx_wrapperbase_8PyClical_9index_set_47__repr__.doc = __pyx_doc_8PyClical_9index_set_47__repr__;
19374  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_47__repr__;
19375  }
19376  }
19377  #endif
19378  #if CYTHON_COMPILING_IN_CPYTHON
19379  {
19380  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__str__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19381  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19382  __pyx_wrapperbase_8PyClical_9index_set_49__str__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19383  __pyx_wrapperbase_8PyClical_9index_set_49__str__.doc = __pyx_doc_8PyClical_9index_set_49__str__;
19384  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_49__str__;
19385  }
19386  }
19387  #endif
19388  if (__Pyx_SetVtable(__pyx_type_8PyClical_index_set.tp_dict, __pyx_vtabptr_8PyClical_index_set) < 0) __PYX_ERR(0, 45, __pyx_L1_error)
19389  if (PyObject_SetAttr(__pyx_m, __pyx_n_s_index_set, (PyObject *)&__pyx_type_8PyClical_index_set) < 0) __PYX_ERR(0, 45, __pyx_L1_error)
19390  if (__Pyx_setup_reduce((PyObject*)&__pyx_type_8PyClical_index_set) < 0) __PYX_ERR(0, 45, __pyx_L1_error)
19391  __pyx_ptype_8PyClical_index_set = &__pyx_type_8PyClical_index_set;
19392  __pyx_vtabptr_8PyClical_clifford = &__pyx_vtable_8PyClical_clifford;
19393  __pyx_vtable_8PyClical_clifford.wrap = (PyObject *(*)(struct __pyx_obj_8PyClical_clifford *, Clifford))__pyx_f_8PyClical_8clifford_wrap;
19394  __pyx_vtable_8PyClical_clifford.unwrap = (Clifford (*)(struct __pyx_obj_8PyClical_clifford *))__pyx_f_8PyClical_8clifford_unwrap;
19395  __pyx_vtable_8PyClical_clifford.copy = (PyObject *(*)(struct __pyx_obj_8PyClical_clifford *, int __pyx_skip_dispatch))__pyx_f_8PyClical_8clifford_copy;
19396  if (PyType_Ready(&__pyx_type_8PyClical_clifford) < 0) __PYX_ERR(0, 535, __pyx_L1_error)
19397  __pyx_type_8PyClical_clifford.tp_print = 0;
19398  if ((CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP) && likely(!__pyx_type_8PyClical_clifford.tp_dictoffset && __pyx_type_8PyClical_clifford.tp_getattro == PyObject_GenericGetAttr)) {
19399  __pyx_type_8PyClical_clifford.tp_getattro = __Pyx_PyObject_GenericGetAttr;
19400  }
19401  #if CYTHON_COMPILING_IN_CPYTHON
19402  {
19403  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__contains__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19404  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19405  __pyx_wrapperbase_8PyClical_8clifford_6__contains__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19406  __pyx_wrapperbase_8PyClical_8clifford_6__contains__.doc = __pyx_doc_8PyClical_8clifford_6__contains__;
19407  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_6__contains__;
19408  }
19409  }
19410  #endif
19411  #if CYTHON_COMPILING_IN_CPYTHON
19412  {
19413  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__iter__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19414  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19415  __pyx_wrapperbase_8PyClical_8clifford_8__iter__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19416  __pyx_wrapperbase_8PyClical_8clifford_8__iter__.doc = __pyx_doc_8PyClical_8clifford_8__iter__;
19417  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_8__iter__;
19418  }
19419  }
19420  #endif
19421  #if CYTHON_COMPILING_IN_CPYTHON
19422  {
19423  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__getitem__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19424  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19425  __pyx_wrapperbase_8PyClical_8clifford_14__getitem__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19426  __pyx_wrapperbase_8PyClical_8clifford_14__getitem__.doc = __pyx_doc_8PyClical_8clifford_14__getitem__;
19427  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_14__getitem__;
19428  }
19429  }
19430  #endif
19431  #if CYTHON_COMPILING_IN_CPYTHON
19432  {
19433  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__neg__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19434  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19435  __pyx_wrapperbase_8PyClical_8clifford_16__neg__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19436  __pyx_wrapperbase_8PyClical_8clifford_16__neg__.doc = __pyx_doc_8PyClical_8clifford_16__neg__;
19437  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_16__neg__;
19438  }
19439  }
19440  #endif
19441  #if CYTHON_COMPILING_IN_CPYTHON
19442  {
19443  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__pos__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19444  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19445  __pyx_wrapperbase_8PyClical_8clifford_18__pos__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19446  __pyx_wrapperbase_8PyClical_8clifford_18__pos__.doc = __pyx_doc_8PyClical_8clifford_18__pos__;
19447  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_18__pos__;
19448  }
19449  }
19450  #endif
19451  #if CYTHON_COMPILING_IN_CPYTHON
19452  {
19453  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__add__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19454  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19455  __pyx_wrapperbase_8PyClical_8clifford_20__add__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19456  __pyx_wrapperbase_8PyClical_8clifford_20__add__.doc = __pyx_doc_8PyClical_8clifford_20__add__;
19457  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_20__add__;
19458  }
19459  }
19460  #endif
19461  #if CYTHON_COMPILING_IN_CPYTHON
19462  {
19463  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__iadd__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19464  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19465  __pyx_wrapperbase_8PyClical_8clifford_22__iadd__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19466  __pyx_wrapperbase_8PyClical_8clifford_22__iadd__.doc = __pyx_doc_8PyClical_8clifford_22__iadd__;
19467  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_22__iadd__;
19468  }
19469  }
19470  #endif
19471  #if CYTHON_COMPILING_IN_CPYTHON
19472  {
19473  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__sub__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19474  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19475  __pyx_wrapperbase_8PyClical_8clifford_24__sub__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19476  __pyx_wrapperbase_8PyClical_8clifford_24__sub__.doc = __pyx_doc_8PyClical_8clifford_24__sub__;
19477  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_24__sub__;
19478  }
19479  }
19480  #endif
19481  #if CYTHON_COMPILING_IN_CPYTHON
19482  {
19483  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__isub__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19484  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19485  __pyx_wrapperbase_8PyClical_8clifford_26__isub__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19486  __pyx_wrapperbase_8PyClical_8clifford_26__isub__.doc = __pyx_doc_8PyClical_8clifford_26__isub__;
19487  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_26__isub__;
19488  }
19489  }
19490  #endif
19491  #if CYTHON_COMPILING_IN_CPYTHON
19492  {
19493  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__mul__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19494  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19495  __pyx_wrapperbase_8PyClical_8clifford_28__mul__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19496  __pyx_wrapperbase_8PyClical_8clifford_28__mul__.doc = __pyx_doc_8PyClical_8clifford_28__mul__;
19497  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_28__mul__;
19498  }
19499  }
19500  #endif
19501  #if CYTHON_COMPILING_IN_CPYTHON
19502  {
19503  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__imul__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19504  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19505  __pyx_wrapperbase_8PyClical_8clifford_30__imul__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19506  __pyx_wrapperbase_8PyClical_8clifford_30__imul__.doc = __pyx_doc_8PyClical_8clifford_30__imul__;
19507  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_30__imul__;
19508  }
19509  }
19510  #endif
19511  #if CYTHON_COMPILING_IN_CPYTHON
19512  {
19513  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__mod__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19514  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19515  __pyx_wrapperbase_8PyClical_8clifford_32__mod__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19516  __pyx_wrapperbase_8PyClical_8clifford_32__mod__.doc = __pyx_doc_8PyClical_8clifford_32__mod__;
19517  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_32__mod__;
19518  }
19519  }
19520  #endif
19521  #if CYTHON_COMPILING_IN_CPYTHON
19522  {
19523  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__imod__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19524  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19525  __pyx_wrapperbase_8PyClical_8clifford_34__imod__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19526  __pyx_wrapperbase_8PyClical_8clifford_34__imod__.doc = __pyx_doc_8PyClical_8clifford_34__imod__;
19527  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_34__imod__;
19528  }
19529  }
19530  #endif
19531  #if CYTHON_COMPILING_IN_CPYTHON
19532  {
19533  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__and__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19534  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19535  __pyx_wrapperbase_8PyClical_8clifford_36__and__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19536  __pyx_wrapperbase_8PyClical_8clifford_36__and__.doc = __pyx_doc_8PyClical_8clifford_36__and__;
19537  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_36__and__;
19538  }
19539  }
19540  #endif
19541  #if CYTHON_COMPILING_IN_CPYTHON
19542  {
19543  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__iand__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19544  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19545  __pyx_wrapperbase_8PyClical_8clifford_38__iand__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19546  __pyx_wrapperbase_8PyClical_8clifford_38__iand__.doc = __pyx_doc_8PyClical_8clifford_38__iand__;
19547  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_38__iand__;
19548  }
19549  }
19550  #endif
19551  #if CYTHON_COMPILING_IN_CPYTHON
19552  {
19553  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__xor__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19554  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19555  __pyx_wrapperbase_8PyClical_8clifford_40__xor__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19556  __pyx_wrapperbase_8PyClical_8clifford_40__xor__.doc = __pyx_doc_8PyClical_8clifford_40__xor__;
19557  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_40__xor__;
19558  }
19559  }
19560  #endif
19561  #if CYTHON_COMPILING_IN_CPYTHON
19562  {
19563  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__ixor__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19564  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19565  __pyx_wrapperbase_8PyClical_8clifford_42__ixor__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19566  __pyx_wrapperbase_8PyClical_8clifford_42__ixor__.doc = __pyx_doc_8PyClical_8clifford_42__ixor__;
19567  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_42__ixor__;
19568  }
19569  }
19570  #endif
19571  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
19572  #if CYTHON_COMPILING_IN_CPYTHON
19573  {
19574  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__div__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19575  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19576  __pyx_wrapperbase_8PyClical_8clifford_44__div__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19577  __pyx_wrapperbase_8PyClical_8clifford_44__div__.doc = __pyx_doc_8PyClical_8clifford_44__div__;
19578  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_44__div__;
19579  }
19580  }
19581  #endif
19582  #endif
19583  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
19584  #if CYTHON_COMPILING_IN_CPYTHON
19585  {
19586  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__idiv__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19587  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19588  __pyx_wrapperbase_8PyClical_8clifford_46__idiv__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19589  __pyx_wrapperbase_8PyClical_8clifford_46__idiv__.doc = __pyx_doc_8PyClical_8clifford_46__idiv__;
19590  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_46__idiv__;
19591  }
19592  }
19593  #endif
19594  #endif
19595  #if CYTHON_COMPILING_IN_CPYTHON
19596  {
19597  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__or__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19598  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19599  __pyx_wrapperbase_8PyClical_8clifford_50__or__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19600  __pyx_wrapperbase_8PyClical_8clifford_50__or__.doc = __pyx_doc_8PyClical_8clifford_50__or__;
19601  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_50__or__;
19602  }
19603  }
19604  #endif
19605  #if CYTHON_COMPILING_IN_CPYTHON
19606  {
19607  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__ior__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19608  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19609  __pyx_wrapperbase_8PyClical_8clifford_52__ior__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19610  __pyx_wrapperbase_8PyClical_8clifford_52__ior__.doc = __pyx_doc_8PyClical_8clifford_52__ior__;
19611  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_52__ior__;
19612  }
19613  }
19614  #endif
19615  #if CYTHON_COMPILING_IN_CPYTHON
19616  {
19617  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__pow__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19618  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19619  __pyx_wrapperbase_8PyClical_8clifford_54__pow__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19620  __pyx_wrapperbase_8PyClical_8clifford_54__pow__.doc = __pyx_doc_8PyClical_8clifford_54__pow__;
19621  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_54__pow__;
19622  }
19623  }
19624  #endif
19625  #if CYTHON_COMPILING_IN_CPYTHON
19626  {
19627  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__call__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19628  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19629  __pyx_wrapperbase_8PyClical_8clifford_60__call__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19630  __pyx_wrapperbase_8PyClical_8clifford_60__call__.doc = __pyx_doc_8PyClical_8clifford_60__call__;
19631  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_60__call__;
19632  }
19633  }
19634  #endif
19635  #if CYTHON_COMPILING_IN_CPYTHON
19636  {
19637  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__repr__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19638  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19639  __pyx_wrapperbase_8PyClical_8clifford_92__repr__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19640  __pyx_wrapperbase_8PyClical_8clifford_92__repr__.doc = __pyx_doc_8PyClical_8clifford_92__repr__;
19641  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_92__repr__;
19642  }
19643  }
19644  #endif
19645  #if CYTHON_COMPILING_IN_CPYTHON
19646  {
19647  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__str__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19648  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19649  __pyx_wrapperbase_8PyClical_8clifford_94__str__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19650  __pyx_wrapperbase_8PyClical_8clifford_94__str__.doc = __pyx_doc_8PyClical_8clifford_94__str__;
19651  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_94__str__;
19652  }
19653  }
19654  #endif
19655  if (__Pyx_SetVtable(__pyx_type_8PyClical_clifford.tp_dict, __pyx_vtabptr_8PyClical_clifford) < 0) __PYX_ERR(0, 535, __pyx_L1_error)
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19658  __pyx_ptype_8PyClical_clifford = &__pyx_type_8PyClical_clifford;
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19660  __pyx_type_8PyClical___pyx_scope_struct____iter__.tp_print = 0;
19661  if ((CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP) && likely(!__pyx_type_8PyClical___pyx_scope_struct____iter__.tp_dictoffset && __pyx_type_8PyClical___pyx_scope_struct____iter__.tp_getattro == PyObject_GenericGetAttr)) {
19662  __pyx_type_8PyClical___pyx_scope_struct____iter__.tp_getattro = __Pyx_PyObject_GenericGetAttrNoDict;
19663  }
19664  __pyx_ptype_8PyClical___pyx_scope_struct____iter__ = &__pyx_type_8PyClical___pyx_scope_struct____iter__;
19665  __Pyx_RefNannyFinishContext();
19666  return 0;
19667  __pyx_L1_error:;
19668  __Pyx_RefNannyFinishContext();
19669  return -1;
19670 }
19671 
19672 static int __Pyx_modinit_type_import_code(void) {
19673  __Pyx_RefNannyDeclarations
19674  __Pyx_RefNannySetupContext("__Pyx_modinit_type_import_code", 0);
19675  /*--- Type import code ---*/
19676  __Pyx_RefNannyFinishContext();
19677  return 0;
19678 }
19679 
19680 static int __Pyx_modinit_variable_import_code(void) {
19681  __Pyx_RefNannyDeclarations
19682  __Pyx_RefNannySetupContext("__Pyx_modinit_variable_import_code", 0);
19683  /*--- Variable import code ---*/
19684  __Pyx_RefNannyFinishContext();
19685  return 0;
19686 }
19687 
19688 static int __Pyx_modinit_function_import_code(void) {
19689  __Pyx_RefNannyDeclarations
19690  __Pyx_RefNannySetupContext("__Pyx_modinit_function_import_code", 0);
19691  /*--- Function import code ---*/
19692  __Pyx_RefNannyFinishContext();
19693  return 0;
19694 }
19695 
19696 
19697 #if PY_MAJOR_VERSION < 3
19698 #ifdef CYTHON_NO_PYINIT_EXPORT
19699 #define __Pyx_PyMODINIT_FUNC void
19700 #else
19701 #define __Pyx_PyMODINIT_FUNC PyMODINIT_FUNC
19702 #endif
19703 #else
19704 #ifdef CYTHON_NO_PYINIT_EXPORT
19705 #define __Pyx_PyMODINIT_FUNC PyObject *
19706 #else
19707 #define __Pyx_PyMODINIT_FUNC PyMODINIT_FUNC
19708 #endif
19709 #endif
19710 
19711 
19712 #if PY_MAJOR_VERSION < 3
19713 __Pyx_PyMODINIT_FUNC initPyClical(void) CYTHON_SMALL_CODE; /*proto*/
19714 __Pyx_PyMODINIT_FUNC initPyClical(void)
19715 #else
19716 __Pyx_PyMODINIT_FUNC PyInit_PyClical(void) CYTHON_SMALL_CODE; /*proto*/
19717 __Pyx_PyMODINIT_FUNC PyInit_PyClical(void)
19718 #if CYTHON_PEP489_MULTI_PHASE_INIT
19719 {
19720  return PyModuleDef_Init(&__pyx_moduledef);
19721 }
19722 static CYTHON_SMALL_CODE int __Pyx_check_single_interpreter(void) {
19723  #if PY_VERSION_HEX >= 0x030700A1
19724  static PY_INT64_T main_interpreter_id = -1;
19725  PY_INT64_T current_id = PyInterpreterState_GetID(PyThreadState_Get()->interp);
19726  if (main_interpreter_id == -1) {
19727  main_interpreter_id = current_id;
19728  return (unlikely(current_id == -1)) ? -1 : 0;
19729  } else if (unlikely(main_interpreter_id != current_id))
19730  #else
19731  static PyInterpreterState *main_interpreter = NULL;
19732  PyInterpreterState *current_interpreter = PyThreadState_Get()->interp;
19733  if (!main_interpreter) {
19734  main_interpreter = current_interpreter;
19735  } else if (unlikely(main_interpreter != current_interpreter))
19736  #endif
19737  {
19738  PyErr_SetString(
19739  PyExc_ImportError,
19740  "Interpreter change detected - this module can only be loaded into one interpreter per process.");
19741  return -1;
19742  }
19743  return 0;
19744 }
19745 static CYTHON_SMALL_CODE int __Pyx_copy_spec_to_module(PyObject *spec, PyObject *moddict, const char* from_name, const char* to_name, int allow_none) {
19746  PyObject *value = PyObject_GetAttrString(spec, from_name);
19747  int result = 0;
19748  if (likely(value)) {
19749  if (allow_none || value != Py_None) {
19750  result = PyDict_SetItemString(moddict, to_name, value);
19751  }
19752  Py_DECREF(value);
19753  } else if (PyErr_ExceptionMatches(PyExc_AttributeError)) {
19754  PyErr_Clear();
19755  } else {
19756  result = -1;
19757  }
19758  return result;
19759 }
19760 static CYTHON_SMALL_CODE PyObject* __pyx_pymod_create(PyObject *spec, CYTHON_UNUSED PyModuleDef *def) {
19761  PyObject *module = NULL, *moddict, *modname;
19762  if (__Pyx_check_single_interpreter())
19763  return NULL;
19764  if (__pyx_m)
19765  return __Pyx_NewRef(__pyx_m);
19766  modname = PyObject_GetAttrString(spec, "name");
19767  if (unlikely(!modname)) goto bad;
19768  module = PyModule_NewObject(modname);
19769  Py_DECREF(modname);
19770  if (unlikely(!module)) goto bad;
19771  moddict = PyModule_GetDict(module);
19772  if (unlikely(!moddict)) goto bad;
19773  if (unlikely(__Pyx_copy_spec_to_module(spec, moddict, "loader", "__loader__", 1) < 0)) goto bad;
19774  if (unlikely(__Pyx_copy_spec_to_module(spec, moddict, "origin", "__file__", 1) < 0)) goto bad;
19775  if (unlikely(__Pyx_copy_spec_to_module(spec, moddict, "parent", "__package__", 1) < 0)) goto bad;
19776  if (unlikely(__Pyx_copy_spec_to_module(spec, moddict, "submodule_search_locations", "__path__", 0) < 0)) goto bad;
19777  return module;
19778 bad:
19779  Py_XDECREF(module);
19780  return NULL;
19781 }
19782 
19783 
19784 static CYTHON_SMALL_CODE int __pyx_pymod_exec_PyClical(PyObject *__pyx_pyinit_module)
19785 #endif
19786 #endif
19787 {
19788  PyObject *__pyx_t_1 = NULL;
19789  PyObject *__pyx_t_2 = NULL;
19790  PyObject *__pyx_t_3 = NULL;
19791  int __pyx_t_4;
19792  __Pyx_RefNannyDeclarations
19793  #if CYTHON_PEP489_MULTI_PHASE_INIT
19794  if (__pyx_m) {
19795  if (__pyx_m == __pyx_pyinit_module) return 0;
19796  PyErr_SetString(PyExc_RuntimeError, "Module 'PyClical' has already been imported. Re-initialisation is not supported.");
19797  return -1;
19798  }
19799  #elif PY_MAJOR_VERSION >= 3
19800  if (__pyx_m) return __Pyx_NewRef(__pyx_m);
19801  #endif
19802  #if CYTHON_REFNANNY
19803 __Pyx_RefNanny = __Pyx_RefNannyImportAPI("refnanny");
19804 if (!__Pyx_RefNanny) {
19805  PyErr_Clear();
19806  __Pyx_RefNanny = __Pyx_RefNannyImportAPI("Cython.Runtime.refnanny");
19807  if (!__Pyx_RefNanny)
19808  Py_FatalError("failed to import 'refnanny' module");
19809 }
19810 #endif
19811  __Pyx_RefNannySetupContext("__Pyx_PyMODINIT_FUNC PyInit_PyClical(void)", 0);
19812  if (__Pyx_check_binary_version() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
19813  #ifdef __Pxy_PyFrame_Initialize_Offsets
19814  __Pxy_PyFrame_Initialize_Offsets();
19815  #endif
19816  __pyx_empty_tuple = PyTuple_New(0); if (unlikely(!__pyx_empty_tuple)) __PYX_ERR(0, 1, __pyx_L1_error)
19817  __pyx_empty_bytes = PyBytes_FromStringAndSize("", 0); if (unlikely(!__pyx_empty_bytes)) __PYX_ERR(0, 1, __pyx_L1_error)
19818  __pyx_empty_unicode = PyUnicode_FromStringAndSize("", 0); if (unlikely(!__pyx_empty_unicode)) __PYX_ERR(0, 1, __pyx_L1_error)
19819  #ifdef __Pyx_CyFunction_USED
19820  if (__pyx_CyFunction_init() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
19821  #endif
19822  #ifdef __Pyx_FusedFunction_USED
19823  if (__pyx_FusedFunction_init() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
19824  #endif
19825  #ifdef __Pyx_Coroutine_USED
19826  if (__pyx_Coroutine_init() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
19827  #endif
19828  #ifdef __Pyx_Generator_USED
19829  if (__pyx_Generator_init() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
19830  #endif
19831  #ifdef __Pyx_AsyncGen_USED
19832  if (__pyx_AsyncGen_init() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
19833  #endif
19834  #ifdef __Pyx_StopAsyncIteration_USED
19835  if (__pyx_StopAsyncIteration_init() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
19836  #endif
19837  /*--- Library function declarations ---*/
19838  /*--- Threads initialization code ---*/
19839  #if defined(__PYX_FORCE_INIT_THREADS) && __PYX_FORCE_INIT_THREADS
19840  #ifdef WITH_THREAD /* Python build with threading support? */
19841  PyEval_InitThreads();
19842  #endif
19843  #endif
19844  /*--- Module creation code ---*/
19845  #if CYTHON_PEP489_MULTI_PHASE_INIT
19846  __pyx_m = __pyx_pyinit_module;
19847  Py_INCREF(__pyx_m);
19848  #else
19849  #if PY_MAJOR_VERSION < 3
19850  __pyx_m = Py_InitModule4("PyClical", __pyx_methods, 0, 0, PYTHON_API_VERSION); Py_XINCREF(__pyx_m);
19851  #else
19852  __pyx_m = PyModule_Create(&__pyx_moduledef);
19853  #endif
19854  if (unlikely(!__pyx_m)) __PYX_ERR(0, 1, __pyx_L1_error)
19855  #endif
19856  __pyx_d = PyModule_GetDict(__pyx_m); if (unlikely(!__pyx_d)) __PYX_ERR(0, 1, __pyx_L1_error)
19857  Py_INCREF(__pyx_d);
19858  __pyx_b = PyImport_AddModule(__Pyx_BUILTIN_MODULE_NAME); if (unlikely(!__pyx_b)) __PYX_ERR(0, 1, __pyx_L1_error)
19859  __pyx_cython_runtime = PyImport_AddModule((char *) "cython_runtime"); if (unlikely(!__pyx_cython_runtime)) __PYX_ERR(0, 1, __pyx_L1_error)
19860  #if CYTHON_COMPILING_IN_PYPY
19861  Py_INCREF(__pyx_b);
19862  #endif
19863  if (PyObject_SetAttrString(__pyx_m, "__builtins__", __pyx_b) < 0) __PYX_ERR(0, 1, __pyx_L1_error);
19864  /*--- Initialize various global constants etc. ---*/
19865  if (__Pyx_InitGlobals() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
19866  #if PY_MAJOR_VERSION < 3 && (__PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT)
19867  if (__Pyx_init_sys_getdefaultencoding_params() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
19868  #endif
19869  if (__pyx_module_is_main_PyClical) {
19870  if (PyObject_SetAttr(__pyx_m, __pyx_n_s_name, __pyx_n_s_main) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
19871  }
19872  #if PY_MAJOR_VERSION >= 3
19873  {
19874  PyObject *modules = PyImport_GetModuleDict(); if (unlikely(!modules)) __PYX_ERR(0, 1, __pyx_L1_error)
19875  if (!PyDict_GetItemString(modules, "PyClical")) {
19876  if (unlikely(PyDict_SetItemString(modules, "PyClical", __pyx_m) < 0)) __PYX_ERR(0, 1, __pyx_L1_error)
19877  }
19878  }
19879  #endif
19880  /*--- Builtin init code ---*/
19881  if (__Pyx_InitCachedBuiltins() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
19882  /*--- Constants init code ---*/
19883  if (__Pyx_InitCachedConstants() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
19884  /*--- Global type/function init code ---*/
19885  (void)__Pyx_modinit_global_init_code();
19886  (void)__Pyx_modinit_variable_export_code();
19887  (void)__Pyx_modinit_function_export_code();
19888  if (unlikely(__Pyx_modinit_type_init_code() != 0)) goto __pyx_L1_error;
19889  (void)__Pyx_modinit_type_import_code();
19890  (void)__Pyx_modinit_variable_import_code();
19891  (void)__Pyx_modinit_function_import_code();
19892  /*--- Execution code ---*/
19893  #if defined(__Pyx_Generator_USED) || defined(__Pyx_Coroutine_USED)
19894  if (__Pyx_patch_abc() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
19895  #endif
19896 
19897  /* "PyClical.pyx":28
19898  * # C. Doran and A. Lasenby, "Geometric algebra for physicists", Cambridge, 2003.
19899  *
19900  * import math # <<<<<<<<<<<<<<
19901  * import numbers
19902  * import collections
19903  */
19904  __pyx_t_1 = __Pyx_Import(__pyx_n_s_math, 0, -1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 28, __pyx_L1_error)
19905  __Pyx_GOTREF(__pyx_t_1);
19906  if (PyDict_SetItem(__pyx_d, __pyx_n_s_math, __pyx_t_1) < 0) __PYX_ERR(0, 28, __pyx_L1_error)
19907  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
19908 
19909  /* "PyClical.pyx":29
19910  *
19911  * import math
19912  * import numbers # <<<<<<<<<<<<<<
19913  * import collections
19914  *
19915  */
19916  __pyx_t_1 = __Pyx_Import(__pyx_n_s_numbers, 0, -1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 29, __pyx_L1_error)
19917  __Pyx_GOTREF(__pyx_t_1);
19918  if (PyDict_SetItem(__pyx_d, __pyx_n_s_numbers, __pyx_t_1) < 0) __PYX_ERR(0, 29, __pyx_L1_error)
19919  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
19920 
19921  /* "PyClical.pyx":30
19922  * import math
19923  * import numbers
19924  * import collections # <<<<<<<<<<<<<<
19925  *
19926  * __version__ = "0.8.2"
19927  */
19928  __pyx_t_1 = __Pyx_Import(__pyx_n_s_collections, 0, -1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 30, __pyx_L1_error)
19929  __Pyx_GOTREF(__pyx_t_1);
19930  if (PyDict_SetItem(__pyx_d, __pyx_n_s_collections, __pyx_t_1) < 0) __PYX_ERR(0, 30, __pyx_L1_error)
19931  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
19932 
19933  /* "PyClical.pyx":32
19934  * import collections
19935  *
19936  * __version__ = "0.8.2" # <<<<<<<<<<<<<<
19937  *
19938  * from PyClical cimport *
19939  */
19940  if (PyDict_SetItem(__pyx_d, __pyx_n_s_version, __pyx_kp_s_0_8_2) < 0) __PYX_ERR(0, 32, __pyx_L1_error)
19941 
19942  /* "PyClical.pyx":404
19943  * return index_set_to_str( self.unwrap() ).c_str()
19944  *
19945  * def index_set_hidden_doctests(): # <<<<<<<<<<<<<<
19946  * """
19947  * Tests for functions that Doctest cannot see.
19948  */
19949  __pyx_t_1 = PyCFunction_NewEx(&__pyx_mdef_8PyClical_1index_set_hidden_doctests, NULL, __pyx_n_s_PyClical); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 404, __pyx_L1_error)
19950  __Pyx_GOTREF(__pyx_t_1);
19951  if (PyDict_SetItem(__pyx_d, __pyx_n_s_index_set_hidden_doctests, __pyx_t_1) < 0) __PYX_ERR(0, 404, __pyx_L1_error)
19952  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
19953 
19954  /* "PyClical.pyx":1243
19955  * return clifford_to_str( self.unwrap() ).c_str()
19956  *
19957  * def clifford_hidden_doctests(): # <<<<<<<<<<<<<<
19958  * """
19959  * Tests for functions that Doctest cannot see.
19960  */
19961  __pyx_t_1 = PyCFunction_NewEx(&__pyx_mdef_8PyClical_9clifford_hidden_doctests, NULL, __pyx_n_s_PyClical); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 1243, __pyx_L1_error)
19962  __Pyx_GOTREF(__pyx_t_1);
19963  if (PyDict_SetItem(__pyx_d, __pyx_n_s_clifford_hidden_doctests, __pyx_t_1) < 0) __PYX_ERR(0, 1243, __pyx_L1_error)
19964  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
19965 
19966  /* "PyClical.pyx":1856
19967  *
19968  * # Some abbreviations.
19969  * tau = atan(clifford(1.0)) * 8.0 # <<<<<<<<<<<<<<
19970  * pi = tau / 2.0
19971  *
19972  */
19973  __pyx_t_1 = __Pyx_PyObject_Call(((PyObject *)__pyx_ptype_8PyClical_clifford), __pyx_tuple__15, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 1856, __pyx_L1_error)
19974  __Pyx_GOTREF(__pyx_t_1);
19975  __pyx_t_2 = __pyx_f_8PyClical_atan(__pyx_t_1, 0, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 1856, __pyx_L1_error)
19976  __Pyx_GOTREF(__pyx_t_2);
19977  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
19978  __pyx_t_1 = PyNumber_Multiply(__pyx_t_2, __pyx_float_8_0); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 1856, __pyx_L1_error)
19979  __Pyx_GOTREF(__pyx_t_1);
19980  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
19981  if (PyDict_SetItem(__pyx_d, __pyx_n_s_tau, __pyx_t_1) < 0) __PYX_ERR(0, 1856, __pyx_L1_error)
19982  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
19983 
19984  /* "PyClical.pyx":1857
19985  * # Some abbreviations.
19986  * tau = atan(clifford(1.0)) * 8.0
19987  * pi = tau / 2.0 # <<<<<<<<<<<<<<
19988  *
19989  * cl = clifford
19990  */
19991  __Pyx_GetModuleGlobalName(__pyx_t_1, __pyx_n_s_tau); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 1857, __pyx_L1_error)
19992  __Pyx_GOTREF(__pyx_t_1);
19993  __pyx_t_2 = __Pyx_PyFloat_DivideObjC(__pyx_t_1, __pyx_float_2_0, 2.0, 0, 0); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 1857, __pyx_L1_error)
19994  __Pyx_GOTREF(__pyx_t_2);
19995  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
19996  if (PyDict_SetItem(__pyx_d, __pyx_n_s_pi, __pyx_t_2) < 0) __PYX_ERR(0, 1857, __pyx_L1_error)
19997  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
19998 
19999  /* "PyClical.pyx":1859
20000  * pi = tau / 2.0
20001  *
20002  * cl = clifford # <<<<<<<<<<<<<<
20003  * """
20004  * Abbreviation for clifford.
20005  */
20006  if (PyDict_SetItem(__pyx_d, __pyx_n_s_cl, ((PyObject *)__pyx_ptype_8PyClical_clifford)) < 0) __PYX_ERR(0, 1859, __pyx_L1_error)
20007 
20008  /* "PyClical.pyx":1879
20009  * """
20010  *
20011  * ist = index_set # <<<<<<<<<<<<<<
20012  * """
20013  * Abbreviation for index_set.
20014  */
20015  if (PyDict_SetItem(__pyx_d, __pyx_n_s_ist, ((PyObject *)__pyx_ptype_8PyClical_index_set)) < 0) __PYX_ERR(0, 1879, __pyx_L1_error)
20016 
20017  /* "PyClical.pyx":1887
20018  * """
20019  *
20020  * def e(obj): # <<<<<<<<<<<<<<
20021  * """
20022  * Abbreviation for clifford(index_set(obj)).
20023  */
20024  __pyx_t_2 = PyCFunction_NewEx(&__pyx_mdef_8PyClical_83e, NULL, __pyx_n_s_PyClical); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 1887, __pyx_L1_error)
20025  __Pyx_GOTREF(__pyx_t_2);
20026  if (PyDict_SetItem(__pyx_d, __pyx_n_s_e, __pyx_t_2) < 0) __PYX_ERR(0, 1887, __pyx_L1_error)
20027  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
20028 
20029  /* "PyClical.pyx":1900
20030  * return clifford(index_set(obj))
20031  *
20032  * def istpq(p, q): # <<<<<<<<<<<<<<
20033  * """
20034  * Abbreviation for index_set({-q,...p}).
20035  */
20036  __pyx_t_2 = PyCFunction_NewEx(&__pyx_mdef_8PyClical_85istpq, NULL, __pyx_n_s_PyClical); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 1900, __pyx_L1_error)
20037  __Pyx_GOTREF(__pyx_t_2);
20038  if (PyDict_SetItem(__pyx_d, __pyx_n_s_istpq, __pyx_t_2) < 0) __PYX_ERR(0, 1900, __pyx_L1_error)
20039  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
20040 
20041  /* "PyClical.pyx":1909
20042  * return index_set(set(range(-q,p+1)))
20043  *
20044  * ninf3 = e(4) + e(-1) # Null infinity point in 3D Conformal Geometric Algebra [DL]. # <<<<<<<<<<<<<<
20045  * nbar3 = e(4) - e(-1) # Null bar point in 3D Conformal Geometric Algebra [DL].
20046  *
20047  */
20048  __Pyx_GetModuleGlobalName(__pyx_t_2, __pyx_n_s_e); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 1909, __pyx_L1_error)
20049  __Pyx_GOTREF(__pyx_t_2);
20050  __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_2, __pyx_tuple__20, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 1909, __pyx_L1_error)
20051  __Pyx_GOTREF(__pyx_t_1);
20052  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
20053  __Pyx_GetModuleGlobalName(__pyx_t_2, __pyx_n_s_e); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 1909, __pyx_L1_error)
20054  __Pyx_GOTREF(__pyx_t_2);
20055  __pyx_t_3 = __Pyx_PyObject_Call(__pyx_t_2, __pyx_tuple__21, NULL); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 1909, __pyx_L1_error)
20056  __Pyx_GOTREF(__pyx_t_3);
20057  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
20058  __pyx_t_2 = PyNumber_Add(__pyx_t_1, __pyx_t_3); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 1909, __pyx_L1_error)
20059  __Pyx_GOTREF(__pyx_t_2);
20060  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
20061  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
20062  if (PyDict_SetItem(__pyx_d, __pyx_n_s_ninf3, __pyx_t_2) < 0) __PYX_ERR(0, 1909, __pyx_L1_error)
20063  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
20064 
20065  /* "PyClical.pyx":1910
20066  *
20067  * ninf3 = e(4) + e(-1) # Null infinity point in 3D Conformal Geometric Algebra [DL].
20068  * nbar3 = e(4) - e(-1) # Null bar point in 3D Conformal Geometric Algebra [DL]. # <<<<<<<<<<<<<<
20069  *
20070  * # Doctest interface.
20071  */
20072  __Pyx_GetModuleGlobalName(__pyx_t_2, __pyx_n_s_e); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 1910, __pyx_L1_error)
20073  __Pyx_GOTREF(__pyx_t_2);
20074  __pyx_t_3 = __Pyx_PyObject_Call(__pyx_t_2, __pyx_tuple__20, NULL); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 1910, __pyx_L1_error)
20075  __Pyx_GOTREF(__pyx_t_3);
20076  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
20077  __Pyx_GetModuleGlobalName(__pyx_t_2, __pyx_n_s_e); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 1910, __pyx_L1_error)
20078  __Pyx_GOTREF(__pyx_t_2);
20079  __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_2, __pyx_tuple__21, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 1910, __pyx_L1_error)
20080  __Pyx_GOTREF(__pyx_t_1);
20081  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
20082  __pyx_t_2 = PyNumber_Subtract(__pyx_t_3, __pyx_t_1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 1910, __pyx_L1_error)
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20090  *
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20224  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_outer_pow_line_1518, __pyx_kp_u_Outer_product_power_of_multivec) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20225  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_complexifier_line_1527, __pyx_kp_u_Square_root_of_1_which_commutes) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20226  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_sqrt_line_1542, __pyx_kp_u_Square_root_of_multivector_with) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20227  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_exp_line_1565, __pyx_kp_u_Exponential_of_multivector_x_cl) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20228  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_log_line_1579, __pyx_kp_u_Natural_logarithm_of_multivecto) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20229  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_cos_line_1602, __pyx_kp_u_Cosine_of_multivector_with_opti) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20230  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_acos_line_1619, __pyx_kp_u_Inverse_cosine_of_multivector_w) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20231  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_cosh_line_1640, __pyx_kp_u_Hyperbolic_cosine_of_multivecto) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20232  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_acosh_line_1656, __pyx_kp_u_Inverse_hyperbolic_cosine_of_mu) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20233  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_sin_line_1679, __pyx_kp_u_Sine_of_multivector_with_option) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20234  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_asin_line_1698, __pyx_kp_u_Inverse_sine_of_multivector_wit) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20235  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_sinh_line_1719, __pyx_kp_u_Hyperbolic_sine_of_multivector) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20236  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_asinh_line_1733, __pyx_kp_u_Inverse_hyperbolic_sine_of_mult) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20237  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_tan_line_1752, __pyx_kp_u_Tangent_of_multivector_with_opt) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20238  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_atan_line_1769, __pyx_kp_u_Inverse_tangent_of_multivector) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20239  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_tanh_line_1786, __pyx_kp_u_Hyperbolic_tangent_of_multivect) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20240  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_atanh_line_1798, __pyx_kp_u_Inverse_hyperbolic_tangent_of_m) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20241  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_random_clifford_line_1815, __pyx_kp_u_Random_multivector_within_a_fra) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20242  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_cga3_line_1824, __pyx_kp_u_Convert_Euclidean_3D_multivecto) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20243  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_cga3std_line_1833, __pyx_kp_u_Convert_CGA3_null_vector_to_sta) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20244  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_agc3_line_1844, __pyx_kp_u_Convert_CGA3_null_vector_to_Euc) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20245  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_e_line_1887, __pyx_kp_u_Abbreviation_for_clifford_index) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20246  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_istpq_line_1900, __pyx_kp_u_Abbreviation_for_index_set_q_p) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20247  if (PyDict_SetItem(__pyx_d, __pyx_n_s_test_2, __pyx_t_1) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20248  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
20249 
20250  /*--- Wrapped vars code ---*/
20251 
20252  goto __pyx_L0;
20253  __pyx_L1_error:;
20254  __Pyx_XDECREF(__pyx_t_1);
20255  __Pyx_XDECREF(__pyx_t_2);
20256  __Pyx_XDECREF(__pyx_t_3);
20257  if (__pyx_m) {
20258  if (__pyx_d) {
20259  __Pyx_AddTraceback("init PyClical", __pyx_clineno, __pyx_lineno, __pyx_filename);
20260  }
20261  Py_CLEAR(__pyx_m);
20262  } else if (!PyErr_Occurred()) {
20263  PyErr_SetString(PyExc_ImportError, "init PyClical");
20264  }
20265  __pyx_L0:;
20266  __Pyx_RefNannyFinishContext();
20267  #if CYTHON_PEP489_MULTI_PHASE_INIT
20268  return (__pyx_m != NULL) ? 0 : -1;
20269  #elif PY_MAJOR_VERSION >= 3
20270  return __pyx_m;
20271  #else
20272  return;
20273  #endif
20274 }
20275 
20276 /* --- Runtime support code --- */
20277 /* Refnanny */
20278 #if CYTHON_REFNANNY
20279 static __Pyx_RefNannyAPIStruct *__Pyx_RefNannyImportAPI(const char *modname) {
20280  PyObject *m = NULL, *p = NULL;
20281  void *r = NULL;
20282  m = PyImport_ImportModule(modname);
20283  if (!m) goto end;
20284  p = PyObject_GetAttrString(m, "RefNannyAPI");
20285  if (!p) goto end;
20286  r = PyLong_AsVoidPtr(p);
20287 end:
20288  Py_XDECREF(p);
20289  Py_XDECREF(m);
20290  return (__Pyx_RefNannyAPIStruct *)r;
20291 }
20292 #endif
20293 
20294 /* PyObjectGetAttrStr */
20295 #if CYTHON_USE_TYPE_SLOTS
20296 static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStr(PyObject* obj, PyObject* attr_name) {
20297  PyTypeObject* tp = Py_TYPE(obj);
20298  if (likely(tp->tp_getattro))
20299  return tp->tp_getattro(obj, attr_name);
20300 #if PY_MAJOR_VERSION < 3
20301  if (likely(tp->tp_getattr))
20302  return tp->tp_getattr(obj, PyString_AS_STRING(attr_name));
20303 #endif
20304  return PyObject_GetAttr(obj, attr_name);
20305 }
20306 #endif
20307 
20308 /* GetBuiltinName */
20309 static PyObject *__Pyx_GetBuiltinName(PyObject *name) {
20310  PyObject* result = __Pyx_PyObject_GetAttrStr(__pyx_b, name);
20311  if (unlikely(!result)) {
20312  PyErr_Format(PyExc_NameError,
20313 #if PY_MAJOR_VERSION >= 3
20314  "name '%U' is not defined", name);
20315 #else
20316  "name '%.200s' is not defined", PyString_AS_STRING(name));
20317 #endif
20318  }
20319  return result;
20320 }
20321 
20322 /* PyCFunctionFastCall */
20323 #if CYTHON_FAST_PYCCALL
20324 static CYTHON_INLINE PyObject * __Pyx_PyCFunction_FastCall(PyObject *func_obj, PyObject **args, Py_ssize_t nargs) {
20325  PyCFunctionObject *func = (PyCFunctionObject*)func_obj;
20326  PyCFunction meth = PyCFunction_GET_FUNCTION(func);
20327  PyObject *self = PyCFunction_GET_SELF(func);
20328  int flags = PyCFunction_GET_FLAGS(func);
20329  assert(PyCFunction_Check(func));
20330  assert(METH_FASTCALL == (flags & ~(METH_CLASS | METH_STATIC | METH_COEXIST | METH_KEYWORDS | METH_STACKLESS)));
20331  assert(nargs >= 0);
20332  assert(nargs == 0 || args != NULL);
20333  /* _PyCFunction_FastCallDict() must not be called with an exception set,
20334  because it may clear it (directly or indirectly) and so the
20335  caller loses its exception */
20336  assert(!PyErr_Occurred());
20337  if ((PY_VERSION_HEX < 0x030700A0) || unlikely(flags & METH_KEYWORDS)) {
20338  return (*((__Pyx_PyCFunctionFastWithKeywords)(void*)meth)) (self, args, nargs, NULL);
20339  } else {
20340  return (*((__Pyx_PyCFunctionFast)(void*)meth)) (self, args, nargs);
20341  }
20342 }
20343 #endif
20344 
20345 /* PyFunctionFastCall */
20346 #if CYTHON_FAST_PYCALL
20347 static PyObject* __Pyx_PyFunction_FastCallNoKw(PyCodeObject *co, PyObject **args, Py_ssize_t na,
20348  PyObject *globals) {
20349  PyFrameObject *f;
20350  PyThreadState *tstate = __Pyx_PyThreadState_Current;
20351  PyObject **fastlocals;
20352  Py_ssize_t i;
20353  PyObject *result;
20354  assert(globals != NULL);
20355  /* XXX Perhaps we should create a specialized
20356  PyFrame_New() that doesn't take locals, but does
20357  take builtins without sanity checking them.
20358  */
20359  assert(tstate != NULL);
20360  f = PyFrame_New(tstate, co, globals, NULL);
20361  if (f == NULL) {
20362  return NULL;
20363  }
20364  fastlocals = __Pyx_PyFrame_GetLocalsplus(f);
20365  for (i = 0; i < na; i++) {
20366  Py_INCREF(*args);
20367  fastlocals[i] = *args++;
20368  }
20369  result = PyEval_EvalFrameEx(f,0);
20370  ++tstate->recursion_depth;
20371  Py_DECREF(f);
20372  --tstate->recursion_depth;
20373  return result;
20374 }
20375 #if 1 || PY_VERSION_HEX < 0x030600B1
20376 static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, int nargs, PyObject *kwargs) {
20377  PyCodeObject *co = (PyCodeObject *)PyFunction_GET_CODE(func);
20378  PyObject *globals = PyFunction_GET_GLOBALS(func);
20379  PyObject *argdefs = PyFunction_GET_DEFAULTS(func);
20380  PyObject *closure;
20381 #if PY_MAJOR_VERSION >= 3
20382  PyObject *kwdefs;
20383 #endif
20384  PyObject *kwtuple, **k;
20385  PyObject **d;
20386  Py_ssize_t nd;
20387  Py_ssize_t nk;
20388  PyObject *result;
20389  assert(kwargs == NULL || PyDict_Check(kwargs));
20390  nk = kwargs ? PyDict_Size(kwargs) : 0;
20391  if (Py_EnterRecursiveCall((char*)" while calling a Python object")) {
20392  return NULL;
20393  }
20394  if (
20395 #if PY_MAJOR_VERSION >= 3
20396  co->co_kwonlyargcount == 0 &&
20397 #endif
20398  likely(kwargs == NULL || nk == 0) &&
20399  co->co_flags == (CO_OPTIMIZED | CO_NEWLOCALS | CO_NOFREE)) {
20400  if (argdefs == NULL && co->co_argcount == nargs) {
20401  result = __Pyx_PyFunction_FastCallNoKw(co, args, nargs, globals);
20402  goto done;
20403  }
20404  else if (nargs == 0 && argdefs != NULL
20405  && co->co_argcount == Py_SIZE(argdefs)) {
20406  /* function called with no arguments, but all parameters have
20407  a default value: use default values as arguments .*/
20408  args = &PyTuple_GET_ITEM(argdefs, 0);
20409  result =__Pyx_PyFunction_FastCallNoKw(co, args, Py_SIZE(argdefs), globals);
20410  goto done;
20411  }
20412  }
20413  if (kwargs != NULL) {
20414  Py_ssize_t pos, i;
20415  kwtuple = PyTuple_New(2 * nk);
20416  if (kwtuple == NULL) {
20417  result = NULL;
20418  goto done;
20419  }
20420  k = &PyTuple_GET_ITEM(kwtuple, 0);
20421  pos = i = 0;
20422  while (PyDict_Next(kwargs, &pos, &k[i], &k[i+1])) {
20423  Py_INCREF(k[i]);
20424  Py_INCREF(k[i+1]);
20425  i += 2;
20426  }
20427  nk = i / 2;
20428  }
20429  else {
20430  kwtuple = NULL;
20431  k = NULL;
20432  }
20433  closure = PyFunction_GET_CLOSURE(func);
20434 #if PY_MAJOR_VERSION >= 3
20435  kwdefs = PyFunction_GET_KW_DEFAULTS(func);
20436 #endif
20437  if (argdefs != NULL) {
20438  d = &PyTuple_GET_ITEM(argdefs, 0);
20439  nd = Py_SIZE(argdefs);
20440  }
20441  else {
20442  d = NULL;
20443  nd = 0;
20444  }
20445 #if PY_MAJOR_VERSION >= 3
20446  result = PyEval_EvalCodeEx((PyObject*)co, globals, (PyObject *)NULL,
20447  args, nargs,
20448  k, (int)nk,
20449  d, (int)nd, kwdefs, closure);
20450 #else
20451  result = PyEval_EvalCodeEx(co, globals, (PyObject *)NULL,
20452  args, nargs,
20453  k, (int)nk,
20454  d, (int)nd, closure);
20455 #endif
20456  Py_XDECREF(kwtuple);
20457 done:
20458  Py_LeaveRecursiveCall();
20459  return result;
20460 }
20461 #endif
20462 #endif
20463 
20464 /* PyObjectCall */
20465 #if CYTHON_COMPILING_IN_CPYTHON
20466 static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw) {
20467  PyObject *result;
20468  ternaryfunc call = func->ob_type->tp_call;
20469  if (unlikely(!call))
20470  return PyObject_Call(func, arg, kw);
20471  if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
20472  return NULL;
20473  result = (*call)(func, arg, kw);
20474  Py_LeaveRecursiveCall();
20475  if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
20476  PyErr_SetString(
20477  PyExc_SystemError,
20478  "NULL result without error in PyObject_Call");
20479  }
20480  return result;
20481 }
20482 #endif
20483 
20484 /* PyObjectCallMethO */
20485 #if CYTHON_COMPILING_IN_CPYTHON
20486 static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg) {
20487  PyObject *self, *result;
20488  PyCFunction cfunc;
20489  cfunc = PyCFunction_GET_FUNCTION(func);
20490  self = PyCFunction_GET_SELF(func);
20491  if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
20492  return NULL;
20493  result = cfunc(self, arg);
20494  Py_LeaveRecursiveCall();
20495  if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
20496  PyErr_SetString(
20497  PyExc_SystemError,
20498  "NULL result without error in PyObject_Call");
20499  }
20500  return result;
20501 }
20502 #endif
20503 
20504 /* PyObjectCallOneArg */
20505 #if CYTHON_COMPILING_IN_CPYTHON
20506 static PyObject* __Pyx__PyObject_CallOneArg(PyObject *func, PyObject *arg) {
20507  PyObject *result;
20508  PyObject *args = PyTuple_New(1);
20509  if (unlikely(!args)) return NULL;
20510  Py_INCREF(arg);
20511  PyTuple_SET_ITEM(args, 0, arg);
20512  result = __Pyx_PyObject_Call(func, args, NULL);
20513  Py_DECREF(args);
20514  return result;
20515 }
20516 static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
20517 #if CYTHON_FAST_PYCALL
20518  if (PyFunction_Check(func)) {
20519  return __Pyx_PyFunction_FastCall(func, &arg, 1);
20520  }
20521 #endif
20522  if (likely(PyCFunction_Check(func))) {
20523  if (likely(PyCFunction_GET_FLAGS(func) & METH_O)) {
20524  return __Pyx_PyObject_CallMethO(func, arg);
20525 #if CYTHON_FAST_PYCCALL
20526  } else if (PyCFunction_GET_FLAGS(func) & METH_FASTCALL) {
20527  return __Pyx_PyCFunction_FastCall(func, &arg, 1);
20528 #endif
20529  }
20530  }
20531  return __Pyx__PyObject_CallOneArg(func, arg);
20532 }
20533 #else
20534 static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
20535  PyObject *result;
20536  PyObject *args = PyTuple_Pack(1, arg);
20537  if (unlikely(!args)) return NULL;
20538  result = __Pyx_PyObject_Call(func, args, NULL);
20539  Py_DECREF(args);
20540  return result;
20541 }
20542 #endif
20543 
20544 /* PyErrFetchRestore */
20545 #if CYTHON_FAST_THREAD_STATE
20546 static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {
20547  PyObject *tmp_type, *tmp_value, *tmp_tb;
20548  tmp_type = tstate->curexc_type;
20549  tmp_value = tstate->curexc_value;
20550  tmp_tb = tstate->curexc_traceback;
20551  tstate->curexc_type = type;
20552  tstate->curexc_value = value;
20553  tstate->curexc_traceback = tb;
20554  Py_XDECREF(tmp_type);
20555  Py_XDECREF(tmp_value);
20556  Py_XDECREF(tmp_tb);
20557 }
20558 static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
20559  *type = tstate->curexc_type;
20560  *value = tstate->curexc_value;
20561  *tb = tstate->curexc_traceback;
20562  tstate->curexc_type = 0;
20563  tstate->curexc_value = 0;
20564  tstate->curexc_traceback = 0;
20565 }
20566 #endif
20567 
20568 /* WriteUnraisableException */
20569 static void __Pyx_WriteUnraisable(const char *name, CYTHON_UNUSED int clineno,
20570  CYTHON_UNUSED int lineno, CYTHON_UNUSED const char *filename,
20571  int full_traceback, CYTHON_UNUSED int nogil) {
20572  PyObject *old_exc, *old_val, *old_tb;
20573  PyObject *ctx;
20574  __Pyx_PyThreadState_declare
20575 #ifdef WITH_THREAD
20576  PyGILState_STATE state;
20577  if (nogil)
20578  state = PyGILState_Ensure();
20579 #ifdef _MSC_VER
20580  else state = (PyGILState_STATE)-1;
20581 #endif
20582 #endif
20583  __Pyx_PyThreadState_assign
20584  __Pyx_ErrFetch(&old_exc, &old_val, &old_tb);
20585  if (full_traceback) {
20586  Py_XINCREF(old_exc);
20587  Py_XINCREF(old_val);
20588  Py_XINCREF(old_tb);
20589  __Pyx_ErrRestore(old_exc, old_val, old_tb);
20590  PyErr_PrintEx(1);
20591  }
20592  #if PY_MAJOR_VERSION < 3
20593  ctx = PyString_FromString(name);
20594  #else
20595  ctx = PyUnicode_FromString(name);
20596  #endif
20597  __Pyx_ErrRestore(old_exc, old_val, old_tb);
20598  if (!ctx) {
20599  PyErr_WriteUnraisable(Py_None);
20600  } else {
20601  PyErr_WriteUnraisable(ctx);
20602  Py_DECREF(ctx);
20603  }
20604 #ifdef WITH_THREAD
20605  if (nogil)
20606  PyGILState_Release(state);
20607 #endif
20608 }
20609 
20610 /* PyDictVersioning */
20611 #if CYTHON_USE_DICT_VERSIONS && CYTHON_USE_TYPE_SLOTS
20612 static CYTHON_INLINE PY_UINT64_T __Pyx_get_tp_dict_version(PyObject *obj) {
20613  PyObject *dict = Py_TYPE(obj)->tp_dict;
20614  return likely(dict) ? __PYX_GET_DICT_VERSION(dict) : 0;
20615 }
20616 static CYTHON_INLINE PY_UINT64_T __Pyx_get_object_dict_version(PyObject *obj) {
20617  PyObject **dictptr = NULL;
20618  Py_ssize_t offset = Py_TYPE(obj)->tp_dictoffset;
20619  if (offset) {
20620 #if CYTHON_COMPILING_IN_CPYTHON
20621  dictptr = (likely(offset > 0)) ? (PyObject **) ((char *)obj + offset) : _PyObject_GetDictPtr(obj);
20622 #else
20623  dictptr = _PyObject_GetDictPtr(obj);
20624 #endif
20625  }
20626  return (dictptr && *dictptr) ? __PYX_GET_DICT_VERSION(*dictptr) : 0;
20627 }
20628 static CYTHON_INLINE int __Pyx_object_dict_version_matches(PyObject* obj, PY_UINT64_T tp_dict_version, PY_UINT64_T obj_dict_version) {
20629  PyObject *dict = Py_TYPE(obj)->tp_dict;
20630  if (unlikely(!dict) || unlikely(tp_dict_version != __PYX_GET_DICT_VERSION(dict)))
20631  return 0;
20632  return obj_dict_version == __Pyx_get_object_dict_version(obj);
20633 }
20634 #endif
20635 
20636 /* PyObjectCallNoArg */
20637 #if CYTHON_COMPILING_IN_CPYTHON
20638 static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func) {
20639 #if CYTHON_FAST_PYCALL
20640  if (PyFunction_Check(func)) {
20641  return __Pyx_PyFunction_FastCall(func, NULL, 0);
20642  }
20643 #endif
20644 #ifdef __Pyx_CyFunction_USED
20645  if (likely(PyCFunction_Check(func) || __Pyx_CyFunction_Check(func)))
20646 #else
20647  if (likely(PyCFunction_Check(func)))
20648 #endif
20649  {
20650  if (likely(PyCFunction_GET_FLAGS(func) & METH_NOARGS)) {
20651  return __Pyx_PyObject_CallMethO(func, NULL);
20652  }
20653  }
20654  return __Pyx_PyObject_Call(func, __pyx_empty_tuple, NULL);
20655 }
20656 #endif
20657 
20658 /* RaiseDoubleKeywords */
20659 static void __Pyx_RaiseDoubleKeywordsError(
20660  const char* func_name,
20661  PyObject* kw_name)
20662 {
20663  PyErr_Format(PyExc_TypeError,
20664  #if PY_MAJOR_VERSION >= 3
20665  "%s() got multiple values for keyword argument '%U'", func_name, kw_name);
20666  #else
20667  "%s() got multiple values for keyword argument '%s'", func_name,
20668  PyString_AsString(kw_name));
20669  #endif
20670 }
20671 
20672 /* ParseKeywords */
20673 static int __Pyx_ParseOptionalKeywords(
20674  PyObject *kwds,
20675  PyObject **argnames[],
20676  PyObject *kwds2,
20677  PyObject *values[],
20678  Py_ssize_t num_pos_args,
20679  const char* function_name)
20680 {
20681  PyObject *key = 0, *value = 0;
20682  Py_ssize_t pos = 0;
20683  PyObject*** name;
20684  PyObject*** first_kw_arg = argnames + num_pos_args;
20685  while (PyDict_Next(kwds, &pos, &key, &value)) {
20686  name = first_kw_arg;
20687  while (*name && (**name != key)) name++;
20688  if (*name) {
20689  values[name-argnames] = value;
20690  continue;
20691  }
20692  name = first_kw_arg;
20693  #if PY_MAJOR_VERSION < 3
20694  if (likely(PyString_CheckExact(key)) || likely(PyString_Check(key))) {
20695  while (*name) {
20696  if ((CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**name) == PyString_GET_SIZE(key))
20697  && _PyString_Eq(**name, key)) {
20698  values[name-argnames] = value;
20699  break;
20700  }
20701  name++;
20702  }
20703  if (*name) continue;
20704  else {
20705  PyObject*** argname = argnames;
20706  while (argname != first_kw_arg) {
20707  if ((**argname == key) || (
20708  (CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**argname) == PyString_GET_SIZE(key))
20709  && _PyString_Eq(**argname, key))) {
20710  goto arg_passed_twice;
20711  }
20712  argname++;
20713  }
20714  }
20715  } else
20716  #endif
20717  if (likely(PyUnicode_Check(key))) {
20718  while (*name) {
20719  int cmp = (**name == key) ? 0 :
20720  #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
20721  (PyUnicode_GET_SIZE(**name) != PyUnicode_GET_SIZE(key)) ? 1 :
20722  #endif
20723  PyUnicode_Compare(**name, key);
20724  if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
20725  if (cmp == 0) {
20726  values[name-argnames] = value;
20727  break;
20728  }
20729  name++;
20730  }
20731  if (*name) continue;
20732  else {
20733  PyObject*** argname = argnames;
20734  while (argname != first_kw_arg) {
20735  int cmp = (**argname == key) ? 0 :
20736  #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
20737  (PyUnicode_GET_SIZE(**argname) != PyUnicode_GET_SIZE(key)) ? 1 :
20738  #endif
20739  PyUnicode_Compare(**argname, key);
20740  if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
20741  if (cmp == 0) goto arg_passed_twice;
20742  argname++;
20743  }
20744  }
20745  } else
20746  goto invalid_keyword_type;
20747  if (kwds2) {
20748  if (unlikely(PyDict_SetItem(kwds2, key, value))) goto bad;
20749  } else {
20750  goto invalid_keyword;
20751  }
20752  }
20753  return 0;
20754 arg_passed_twice:
20755  __Pyx_RaiseDoubleKeywordsError(function_name, key);
20756  goto bad;
20757 invalid_keyword_type:
20758  PyErr_Format(PyExc_TypeError,
20759  "%.200s() keywords must be strings", function_name);
20760  goto bad;
20761 invalid_keyword:
20762  PyErr_Format(PyExc_TypeError,
20763  #if PY_MAJOR_VERSION < 3
20764  "%.200s() got an unexpected keyword argument '%.200s'",
20765  function_name, PyString_AsString(key));
20766  #else
20767  "%s() got an unexpected keyword argument '%U'",
20768  function_name, key);
20769  #endif
20770 bad:
20771  return -1;
20772 }
20773 
20774 /* RaiseArgTupleInvalid */
20775 static void __Pyx_RaiseArgtupleInvalid(
20776  const char* func_name,
20777  int exact,
20778  Py_ssize_t num_min,
20779  Py_ssize_t num_max,
20780  Py_ssize_t num_found)
20781 {
20782  Py_ssize_t num_expected;
20783  const char *more_or_less;
20784  if (num_found < num_min) {
20785  num_expected = num_min;
20786  more_or_less = "at least";
20787  } else {
20788  num_expected = num_max;
20789  more_or_less = "at most";
20790  }
20791  if (exact) {
20792  more_or_less = "exactly";
20793  }
20794  PyErr_Format(PyExc_TypeError,
20795  "%.200s() takes %.8s %" CYTHON_FORMAT_SSIZE_T "d positional argument%.1s (%" CYTHON_FORMAT_SSIZE_T "d given)",
20796  func_name, more_or_less, num_expected,
20797  (num_expected == 1) ? "" : "s", num_found);
20798 }
20799 
20800 /* GetModuleGlobalName */
20801 #if CYTHON_USE_DICT_VERSIONS
20802 static PyObject *__Pyx__GetModuleGlobalName(PyObject *name, PY_UINT64_T *dict_version, PyObject **dict_cached_value)
20803 #else
20804 static CYTHON_INLINE PyObject *__Pyx__GetModuleGlobalName(PyObject *name)
20805 #endif
20806 {
20807  PyObject *result;
20808 #if !CYTHON_AVOID_BORROWED_REFS
20809 #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030500A1
20810  result = _PyDict_GetItem_KnownHash(__pyx_d, name, ((PyASCIIObject *) name)->hash);
20811  __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version)
20812  if (likely(result)) {
20813  return __Pyx_NewRef(result);
20814  } else if (unlikely(PyErr_Occurred())) {
20815  return NULL;
20816  }
20817 #else
20818  result = PyDict_GetItem(__pyx_d, name);
20819  __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version)
20820  if (likely(result)) {
20821  return __Pyx_NewRef(result);
20822  }
20823 #endif
20824 #else
20825  result = PyObject_GetItem(__pyx_d, name);
20826  __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version)
20827  if (likely(result)) {
20828  return __Pyx_NewRef(result);
20829  }
20830  PyErr_Clear();
20831 #endif
20832  return __Pyx_GetBuiltinName(name);
20833 }
20834 
20835 /* GetTopmostException */
20836 #if CYTHON_USE_EXC_INFO_STACK
20837 static _PyErr_StackItem *
20838 __Pyx_PyErr_GetTopmostException(PyThreadState *tstate)
20839 {
20840  _PyErr_StackItem *exc_info = tstate->exc_info;
20841  while ((exc_info->exc_type == NULL || exc_info->exc_type == Py_None) &&
20842  exc_info->previous_item != NULL)
20843  {
20844  exc_info = exc_info->previous_item;
20845  }
20846  return exc_info;
20847 }
20848 #endif
20849 
20850 /* SaveResetException */
20851 #if CYTHON_FAST_THREAD_STATE
20852 static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
20853  #if CYTHON_USE_EXC_INFO_STACK
20854  _PyErr_StackItem *exc_info = __Pyx_PyErr_GetTopmostException(tstate);
20855  *type = exc_info->exc_type;
20856  *value = exc_info->exc_value;
20857  *tb = exc_info->exc_traceback;
20858  #else
20859  *type = tstate->exc_type;
20860  *value = tstate->exc_value;
20861  *tb = tstate->exc_traceback;
20862  #endif
20863  Py_XINCREF(*type);
20864  Py_XINCREF(*value);
20865  Py_XINCREF(*tb);
20866 }
20867 static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {
20868  PyObject *tmp_type, *tmp_value, *tmp_tb;
20869  #if CYTHON_USE_EXC_INFO_STACK
20870  _PyErr_StackItem *exc_info = tstate->exc_info;
20871  tmp_type = exc_info->exc_type;
20872  tmp_value = exc_info->exc_value;
20873  tmp_tb = exc_info->exc_traceback;
20874  exc_info->exc_type = type;
20875  exc_info->exc_value = value;
20876  exc_info->exc_traceback = tb;
20877  #else
20878  tmp_type = tstate->exc_type;
20879  tmp_value = tstate->exc_value;
20880  tmp_tb = tstate->exc_traceback;
20881  tstate->exc_type = type;
20882  tstate->exc_value = value;
20883  tstate->exc_traceback = tb;
20884  #endif
20885  Py_XDECREF(tmp_type);
20886  Py_XDECREF(tmp_value);
20887  Py_XDECREF(tmp_tb);
20888 }
20889 #endif
20890 
20891 /* PyErrExceptionMatches */
20892 #if CYTHON_FAST_THREAD_STATE
20893 static int __Pyx_PyErr_ExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) {
20894  Py_ssize_t i, n;
20895  n = PyTuple_GET_SIZE(tuple);
20896 #if PY_MAJOR_VERSION >= 3
20897  for (i=0; i<n; i++) {
20898  if (exc_type == PyTuple_GET_ITEM(tuple, i)) return 1;
20899  }
20900 #endif
20901  for (i=0; i<n; i++) {
20902  if (__Pyx_PyErr_GivenExceptionMatches(exc_type, PyTuple_GET_ITEM(tuple, i))) return 1;
20903  }
20904  return 0;
20905 }
20906 static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err) {
20907  PyObject *exc_type = tstate->curexc_type;
20908  if (exc_type == err) return 1;
20909  if (unlikely(!exc_type)) return 0;
20910  if (unlikely(PyTuple_Check(err)))
20911  return __Pyx_PyErr_ExceptionMatchesTuple(exc_type, err);
20912  return __Pyx_PyErr_GivenExceptionMatches(exc_type, err);
20913 }
20914 #endif
20915 
20916 /* GetException */
20917 #if CYTHON_FAST_THREAD_STATE
20918 static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb)
20919 #else
20920 static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb)
20921 #endif
20922 {
20923  PyObject *local_type, *local_value, *local_tb;
20924 #if CYTHON_FAST_THREAD_STATE
20925  PyObject *tmp_type, *tmp_value, *tmp_tb;
20926  local_type = tstate->curexc_type;
20927  local_value = tstate->curexc_value;
20928  local_tb = tstate->curexc_traceback;
20929  tstate->curexc_type = 0;
20930  tstate->curexc_value = 0;
20931  tstate->curexc_traceback = 0;
20932 #else
20933  PyErr_Fetch(&local_type, &local_value, &local_tb);
20934 #endif
20935  PyErr_NormalizeException(&local_type, &local_value, &local_tb);
20936 #if CYTHON_FAST_THREAD_STATE
20937  if (unlikely(tstate->curexc_type))
20938 #else
20939  if (unlikely(PyErr_Occurred()))
20940 #endif
20941  goto bad;
20942  #if PY_MAJOR_VERSION >= 3
20943  if (local_tb) {
20944  if (unlikely(PyException_SetTraceback(local_value, local_tb) < 0))
20945  goto bad;
20946  }
20947  #endif
20948  Py_XINCREF(local_tb);
20949  Py_XINCREF(local_type);
20950  Py_XINCREF(local_value);
20951  *type = local_type;
20952  *value = local_value;
20953  *tb = local_tb;
20954 #if CYTHON_FAST_THREAD_STATE
20955  #if CYTHON_USE_EXC_INFO_STACK
20956  {
20957  _PyErr_StackItem *exc_info = tstate->exc_info;
20958  tmp_type = exc_info->exc_type;
20959  tmp_value = exc_info->exc_value;
20960  tmp_tb = exc_info->exc_traceback;
20961  exc_info->exc_type = local_type;
20962  exc_info->exc_value = local_value;
20963  exc_info->exc_traceback = local_tb;
20964  }
20965  #else
20966  tmp_type = tstate->exc_type;
20967  tmp_value = tstate->exc_value;
20968  tmp_tb = tstate->exc_traceback;
20969  tstate->exc_type = local_type;
20970  tstate->exc_value = local_value;
20971  tstate->exc_traceback = local_tb;
20972  #endif
20973  Py_XDECREF(tmp_type);
20974  Py_XDECREF(tmp_value);
20975  Py_XDECREF(tmp_tb);
20976 #else
20977  PyErr_SetExcInfo(local_type, local_value, local_tb);
20978 #endif
20979  return 0;
20980 bad:
20981  *type = 0;
20982  *value = 0;
20983  *tb = 0;
20984  Py_XDECREF(local_type);
20985  Py_XDECREF(local_value);
20986  Py_XDECREF(local_tb);
20987  return -1;
20988 }
20989 
20990 /* RaiseException */
20991 #if PY_MAJOR_VERSION < 3
20992 static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb,
20993  CYTHON_UNUSED PyObject *cause) {
20994  __Pyx_PyThreadState_declare
20995  Py_XINCREF(type);
20996  if (!value || value == Py_None)
20997  value = NULL;
20998  else
20999  Py_INCREF(value);
21000  if (!tb || tb == Py_None)
21001  tb = NULL;
21002  else {
21003  Py_INCREF(tb);
21004  if (!PyTraceBack_Check(tb)) {
21005  PyErr_SetString(PyExc_TypeError,
21006  "raise: arg 3 must be a traceback or None");
21007  goto raise_error;
21008  }
21009  }
21010  if (PyType_Check(type)) {
21011 #if CYTHON_COMPILING_IN_PYPY
21012  if (!value) {
21013  Py_INCREF(Py_None);
21014  value = Py_None;
21015  }
21016 #endif
21017  PyErr_NormalizeException(&type, &value, &tb);
21018  } else {
21019  if (value) {
21020  PyErr_SetString(PyExc_TypeError,
21021  "instance exception may not have a separate value");
21022  goto raise_error;
21023  }
21024  value = type;
21025  type = (PyObject*) Py_TYPE(type);
21026  Py_INCREF(type);
21027  if (!PyType_IsSubtype((PyTypeObject *)type, (PyTypeObject *)PyExc_BaseException)) {
21028  PyErr_SetString(PyExc_TypeError,
21029  "raise: exception class must be a subclass of BaseException");
21030  goto raise_error;
21031  }
21032  }
21033  __Pyx_PyThreadState_assign
21034  __Pyx_ErrRestore(type, value, tb);
21035  return;
21036 raise_error:
21037  Py_XDECREF(value);
21038  Py_XDECREF(type);
21039  Py_XDECREF(tb);
21040  return;
21041 }
21042 #else
21043 static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause) {
21044  PyObject* owned_instance = NULL;
21045  if (tb == Py_None) {
21046  tb = 0;
21047  } else if (tb && !PyTraceBack_Check(tb)) {
21048  PyErr_SetString(PyExc_TypeError,
21049  "raise: arg 3 must be a traceback or None");
21050  goto bad;
21051  }
21052  if (value == Py_None)
21053  value = 0;
21054  if (PyExceptionInstance_Check(type)) {
21055  if (value) {
21056  PyErr_SetString(PyExc_TypeError,
21057  "instance exception may not have a separate value");
21058  goto bad;
21059  }
21060  value = type;
21061  type = (PyObject*) Py_TYPE(value);
21062  } else if (PyExceptionClass_Check(type)) {
21063  PyObject *instance_class = NULL;
21064  if (value && PyExceptionInstance_Check(value)) {
21065  instance_class = (PyObject*) Py_TYPE(value);
21066  if (instance_class != type) {
21067  int is_subclass = PyObject_IsSubclass(instance_class, type);
21068  if (!is_subclass) {
21069  instance_class = NULL;
21070  } else if (unlikely(is_subclass == -1)) {
21071  goto bad;
21072  } else {
21073  type = instance_class;
21074  }
21075  }
21076  }
21077  if (!instance_class) {
21078  PyObject *args;
21079  if (!value)
21080  args = PyTuple_New(0);
21081  else if (PyTuple_Check(value)) {
21082  Py_INCREF(value);
21083  args = value;
21084  } else
21085  args = PyTuple_Pack(1, value);
21086  if (!args)
21087  goto bad;
21088  owned_instance = PyObject_Call(type, args, NULL);
21089  Py_DECREF(args);
21090  if (!owned_instance)
21091  goto bad;
21092  value = owned_instance;
21093  if (!PyExceptionInstance_Check(value)) {
21094  PyErr_Format(PyExc_TypeError,
21095  "calling %R should have returned an instance of "
21096  "BaseException, not %R",
21097  type, Py_TYPE(value));
21098  goto bad;
21099  }
21100  }
21101  } else {
21102  PyErr_SetString(PyExc_TypeError,
21103  "raise: exception class must be a subclass of BaseException");
21104  goto bad;
21105  }
21106  if (cause) {
21107  PyObject *fixed_cause;
21108  if (cause == Py_None) {
21109  fixed_cause = NULL;
21110  } else if (PyExceptionClass_Check(cause)) {
21111  fixed_cause = PyObject_CallObject(cause, NULL);
21112  if (fixed_cause == NULL)
21113  goto bad;
21114  } else if (PyExceptionInstance_Check(cause)) {
21115  fixed_cause = cause;
21116  Py_INCREF(fixed_cause);
21117  } else {
21118  PyErr_SetString(PyExc_TypeError,
21119  "exception causes must derive from "
21120  "BaseException");
21121  goto bad;
21122  }
21123  PyException_SetCause(value, fixed_cause);
21124  }
21125  PyErr_SetObject(type, value);
21126  if (tb) {
21127 #if CYTHON_COMPILING_IN_PYPY
21128  PyObject *tmp_type, *tmp_value, *tmp_tb;
21129  PyErr_Fetch(&tmp_type, &tmp_value, &tmp_tb);
21130  Py_INCREF(tb);
21131  PyErr_Restore(tmp_type, tmp_value, tb);
21132  Py_XDECREF(tmp_tb);
21133 #else
21134  PyThreadState *tstate = __Pyx_PyThreadState_Current;
21135  PyObject* tmp_tb = tstate->curexc_traceback;
21136  if (tb != tmp_tb) {
21137  Py_INCREF(tb);
21138  tstate->curexc_traceback = tb;
21139  Py_XDECREF(tmp_tb);
21140  }
21141 #endif
21142  }
21143 bad:
21144  Py_XDECREF(owned_instance);
21145  return;
21146 }
21147 #endif
21148 
21149 /* PyIntBinop */
21150 #if !CYTHON_COMPILING_IN_PYPY
21151 static PyObject* __Pyx_PyInt_AddObjC(PyObject *op1, PyObject *op2, CYTHON_UNUSED long intval, int inplace, int zerodivision_check) {
21152  (void)inplace;
21153  (void)zerodivision_check;
21154  #if PY_MAJOR_VERSION < 3
21155  if (likely(PyInt_CheckExact(op1))) {
21156  const long b = intval;
21157  long x;
21158  long a = PyInt_AS_LONG(op1);
21159  x = (long)((unsigned long)a + b);
21160  if (likely((x^a) >= 0 || (x^b) >= 0))
21161  return PyInt_FromLong(x);
21162  return PyLong_Type.tp_as_number->nb_add(op1, op2);
21163  }
21164  #endif
21165  #if CYTHON_USE_PYLONG_INTERNALS
21166  if (likely(PyLong_CheckExact(op1))) {
21167  const long b = intval;
21168  long a, x;
21169 #ifdef HAVE_LONG_LONG
21170  const PY_LONG_LONG llb = intval;
21171  PY_LONG_LONG lla, llx;
21172 #endif
21173  const digit* digits = ((PyLongObject*)op1)->ob_digit;
21174  const Py_ssize_t size = Py_SIZE(op1);
21175  if (likely(__Pyx_sst_abs(size) <= 1)) {
21176  a = likely(size) ? digits[0] : 0;
21177  if (size == -1) a = -a;
21178  } else {
21179  switch (size) {
21180  case -2:
21181  if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
21182  a = -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
21183  break;
21184 #ifdef HAVE_LONG_LONG
21185  } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
21186  lla = -(PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
21187  goto long_long;
21188 #endif
21189  }
21190  CYTHON_FALLTHROUGH;
21191  case 2:
21192  if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
21193  a = (long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
21194  break;
21195 #ifdef HAVE_LONG_LONG
21196  } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
21197  lla = (PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
21198  goto long_long;
21199 #endif
21200  }
21201  CYTHON_FALLTHROUGH;
21202  case -3:
21203  if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
21204  a = -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
21205  break;
21206 #ifdef HAVE_LONG_LONG
21207  } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
21208  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]));
21209  goto long_long;
21210 #endif
21211  }
21212  CYTHON_FALLTHROUGH;
21213  case 3:
21214  if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
21215  a = (long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
21216  break;
21217 #ifdef HAVE_LONG_LONG
21218  } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
21219  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]));
21220  goto long_long;
21221 #endif
21222  }
21223  CYTHON_FALLTHROUGH;
21224  case -4:
21225  if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
21226  a = -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
21227  break;
21228 #ifdef HAVE_LONG_LONG
21229  } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
21230  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]));
21231  goto long_long;
21232 #endif
21233  }
21234  CYTHON_FALLTHROUGH;
21235  case 4:
21236  if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
21237  a = (long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
21238  break;
21239 #ifdef HAVE_LONG_LONG
21240  } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
21241  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]));
21242  goto long_long;
21243 #endif
21244  }
21245  CYTHON_FALLTHROUGH;
21246  default: return PyLong_Type.tp_as_number->nb_add(op1, op2);
21247  }
21248  }
21249  x = a + b;
21250  return PyLong_FromLong(x);
21251 #ifdef HAVE_LONG_LONG
21252  long_long:
21253  llx = lla + llb;
21254  return PyLong_FromLongLong(llx);
21255 #endif
21256 
21257 
21258  }
21259  #endif
21260  if (PyFloat_CheckExact(op1)) {
21261  const long b = intval;
21262  double a = PyFloat_AS_DOUBLE(op1);
21263  double result;
21264  PyFPE_START_PROTECT("add", return NULL)
21265  result = ((double)a) + (double)b;
21266  PyFPE_END_PROTECT(result)
21267  return PyFloat_FromDouble(result);
21268  }
21269  return (inplace ? PyNumber_InPlaceAdd : PyNumber_Add)(op1, op2);
21270 }
21271 #endif
21272 
21273 /* SetItemInt */
21274 static int __Pyx_SetItemInt_Generic(PyObject *o, PyObject *j, PyObject *v) {
21275  int r;
21276  if (!j) return -1;
21277  r = PyObject_SetItem(o, j, v);
21278  Py_DECREF(j);
21279  return r;
21280 }
21281 static CYTHON_INLINE int __Pyx_SetItemInt_Fast(PyObject *o, Py_ssize_t i, PyObject *v, int is_list,
21282  CYTHON_NCP_UNUSED int wraparound, CYTHON_NCP_UNUSED int boundscheck) {
21283 #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS && CYTHON_USE_TYPE_SLOTS
21284  if (is_list || PyList_CheckExact(o)) {
21285  Py_ssize_t n = (!wraparound) ? i : ((likely(i >= 0)) ? i : i + PyList_GET_SIZE(o));
21286  if ((!boundscheck) || likely(__Pyx_is_valid_index(n, PyList_GET_SIZE(o)))) {
21287  PyObject* old = PyList_GET_ITEM(o, n);
21288  Py_INCREF(v);
21289  PyList_SET_ITEM(o, n, v);
21290  Py_DECREF(old);
21291  return 1;
21292  }
21293  } else {
21294  PySequenceMethods *m = Py_TYPE(o)->tp_as_sequence;
21295  if (likely(m && m->sq_ass_item)) {
21296  if (wraparound && unlikely(i < 0) && likely(m->sq_length)) {
21297  Py_ssize_t l = m->sq_length(o);
21298  if (likely(l >= 0)) {
21299  i += l;
21300  } else {
21301  if (!PyErr_ExceptionMatches(PyExc_OverflowError))
21302  return -1;
21303  PyErr_Clear();
21304  }
21305  }
21306  return m->sq_ass_item(o, i, v);
21307  }
21308  }
21309 #else
21310 #if CYTHON_COMPILING_IN_PYPY
21311  if (is_list || (PySequence_Check(o) && !PyDict_Check(o)))
21312 #else
21313  if (is_list || PySequence_Check(o))
21314 #endif
21315  {
21316  return PySequence_SetItem(o, i, v);
21317  }
21318 #endif
21319  return __Pyx_SetItemInt_Generic(o, PyInt_FromSsize_t(i), v);
21320 }
21321 
21322 /* PyObjectCall2Args */
21323 static CYTHON_UNUSED PyObject* __Pyx_PyObject_Call2Args(PyObject* function, PyObject* arg1, PyObject* arg2) {
21324  PyObject *args, *result = NULL;
21325  #if CYTHON_FAST_PYCALL
21326  if (PyFunction_Check(function)) {
21327  PyObject *args[2] = {arg1, arg2};
21328  return __Pyx_PyFunction_FastCall(function, args, 2);
21329  }
21330  #endif
21331  #if CYTHON_FAST_PYCCALL
21332  if (__Pyx_PyFastCFunction_Check(function)) {
21333  PyObject *args[2] = {arg1, arg2};
21334  return __Pyx_PyCFunction_FastCall(function, args, 2);
21335  }
21336  #endif
21337  args = PyTuple_New(2);
21338  if (unlikely(!args)) goto done;
21339  Py_INCREF(arg1);
21340  PyTuple_SET_ITEM(args, 0, arg1);
21341  Py_INCREF(arg2);
21342  PyTuple_SET_ITEM(args, 1, arg2);
21343  Py_INCREF(function);
21344  result = __Pyx_PyObject_Call(function, args, NULL);
21345  Py_DECREF(args);
21346  Py_DECREF(function);
21347 done:
21348  return result;
21349 }
21350 
21351 /* ArgTypeTest */
21352 static int __Pyx__ArgTypeTest(PyObject *obj, PyTypeObject *type, const char *name, int exact)
21353 {
21354  if (unlikely(!type)) {
21355  PyErr_SetString(PyExc_SystemError, "Missing type object");
21356  return 0;
21357  }
21358  else if (exact) {
21359  #if PY_MAJOR_VERSION == 2
21360  if ((type == &PyBaseString_Type) && likely(__Pyx_PyBaseString_CheckExact(obj))) return 1;
21361  #endif
21362  }
21363  else {
21364  if (likely(__Pyx_TypeCheck(obj, type))) return 1;
21365  }
21366  PyErr_Format(PyExc_TypeError,
21367  "Argument '%.200s' has incorrect type (expected %.200s, got %.200s)",
21368  name, type->tp_name, Py_TYPE(obj)->tp_name);
21369  return 0;
21370 }
21371 
21372 /* Import */
21373 static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level) {
21374  PyObject *empty_list = 0;
21375  PyObject *module = 0;
21376  PyObject *global_dict = 0;
21377  PyObject *empty_dict = 0;
21378  PyObject *list;
21379  #if PY_MAJOR_VERSION < 3
21380  PyObject *py_import;
21381  py_import = __Pyx_PyObject_GetAttrStr(__pyx_b, __pyx_n_s_import);
21382  if (!py_import)
21383  goto bad;
21384  #endif
21385  if (from_list)
21386  list = from_list;
21387  else {
21388  empty_list = PyList_New(0);
21389  if (!empty_list)
21390  goto bad;
21391  list = empty_list;
21392  }
21393  global_dict = PyModule_GetDict(__pyx_m);
21394  if (!global_dict)
21395  goto bad;
21396  empty_dict = PyDict_New();
21397  if (!empty_dict)
21398  goto bad;
21399  {
21400  #if PY_MAJOR_VERSION >= 3
21401  if (level == -1) {
21402  if (strchr(__Pyx_MODULE_NAME, '.')) {
21403  module = PyImport_ImportModuleLevelObject(
21404  name, global_dict, empty_dict, list, 1);
21405  if (!module) {
21406  if (!PyErr_ExceptionMatches(PyExc_ImportError))
21407  goto bad;
21408  PyErr_Clear();
21409  }
21410  }
21411  level = 0;
21412  }
21413  #endif
21414  if (!module) {
21415  #if PY_MAJOR_VERSION < 3
21416  PyObject *py_level = PyInt_FromLong(level);
21417  if (!py_level)
21418  goto bad;
21419  module = PyObject_CallFunctionObjArgs(py_import,
21420  name, global_dict, empty_dict, list, py_level, (PyObject *)NULL);
21421  Py_DECREF(py_level);
21422  #else
21423  module = PyImport_ImportModuleLevelObject(
21424  name, global_dict, empty_dict, list, level);
21425  #endif
21426  }
21427  }
21428 bad:
21429  #if PY_MAJOR_VERSION < 3
21430  Py_XDECREF(py_import);
21431  #endif
21432  Py_XDECREF(empty_list);
21433  Py_XDECREF(empty_dict);
21434  return module;
21435 }
21436 
21437 /* PyObject_GenericGetAttrNoDict */
21438 #if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000
21439 static PyObject *__Pyx_RaiseGenericGetAttributeError(PyTypeObject *tp, PyObject *attr_name) {
21440  PyErr_Format(PyExc_AttributeError,
21441 #if PY_MAJOR_VERSION >= 3
21442  "'%.50s' object has no attribute '%U'",
21443  tp->tp_name, attr_name);
21444 #else
21445  "'%.50s' object has no attribute '%.400s'",
21446  tp->tp_name, PyString_AS_STRING(attr_name));
21447 #endif
21448  return NULL;
21449 }
21450 static CYTHON_INLINE PyObject* __Pyx_PyObject_GenericGetAttrNoDict(PyObject* obj, PyObject* attr_name) {
21451  PyObject *descr;
21452  PyTypeObject *tp = Py_TYPE(obj);
21453  if (unlikely(!PyString_Check(attr_name))) {
21454  return PyObject_GenericGetAttr(obj, attr_name);
21455  }
21456  assert(!tp->tp_dictoffset);
21457  descr = _PyType_Lookup(tp, attr_name);
21458  if (unlikely(!descr)) {
21459  return __Pyx_RaiseGenericGetAttributeError(tp, attr_name);
21460  }
21461  Py_INCREF(descr);
21462  #if PY_MAJOR_VERSION < 3
21463  if (likely(PyType_HasFeature(Py_TYPE(descr), Py_TPFLAGS_HAVE_CLASS)))
21464  #endif
21465  {
21466  descrgetfunc f = Py_TYPE(descr)->tp_descr_get;
21467  if (unlikely(f)) {
21468  PyObject *res = f(descr, obj, (PyObject *)tp);
21469  Py_DECREF(descr);
21470  return res;
21471  }
21472  }
21473  return descr;
21474 }
21475 #endif
21476 
21477 /* PyObject_GenericGetAttr */
21478 #if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000
21479 static PyObject* __Pyx_PyObject_GenericGetAttr(PyObject* obj, PyObject* attr_name) {
21480  if (unlikely(Py_TYPE(obj)->tp_dictoffset)) {
21481  return PyObject_GenericGetAttr(obj, attr_name);
21482  }
21483  return __Pyx_PyObject_GenericGetAttrNoDict(obj, attr_name);
21484 }
21485 #endif
21486 
21487 /* SetVTable */
21488 static int __Pyx_SetVtable(PyObject *dict, void *vtable) {
21489 #if PY_VERSION_HEX >= 0x02070000
21490  PyObject *ob = PyCapsule_New(vtable, 0, 0);
21491 #else
21492  PyObject *ob = PyCObject_FromVoidPtr(vtable, 0);
21493 #endif
21494  if (!ob)
21495  goto bad;
21496  if (PyDict_SetItem(dict, __pyx_n_s_pyx_vtable, ob) < 0)
21497  goto bad;
21498  Py_DECREF(ob);
21499  return 0;
21500 bad:
21501  Py_XDECREF(ob);
21502  return -1;
21503 }
21504 
21505 /* SetupReduce */
21506 static int __Pyx_setup_reduce_is_named(PyObject* meth, PyObject* name) {
21507  int ret;
21508  PyObject *name_attr;
21509  name_attr = __Pyx_PyObject_GetAttrStr(meth, __pyx_n_s_name);
21510  if (likely(name_attr)) {
21511  ret = PyObject_RichCompareBool(name_attr, name, Py_EQ);
21512  } else {
21513  ret = -1;
21514  }
21515  if (unlikely(ret < 0)) {
21516  PyErr_Clear();
21517  ret = 0;
21518  }
21519  Py_XDECREF(name_attr);
21520  return ret;
21521 }
21522 static int __Pyx_setup_reduce(PyObject* type_obj) {
21523  int ret = 0;
21524  PyObject *object_reduce = NULL;
21525  PyObject *object_reduce_ex = NULL;
21526  PyObject *reduce = NULL;
21527  PyObject *reduce_ex = NULL;
21528  PyObject *reduce_cython = NULL;
21529  PyObject *setstate = NULL;
21530  PyObject *setstate_cython = NULL;
21531 #if CYTHON_USE_PYTYPE_LOOKUP
21532  if (_PyType_Lookup((PyTypeObject*)type_obj, __pyx_n_s_getstate)) goto GOOD;
21533 #else
21534  if (PyObject_HasAttr(type_obj, __pyx_n_s_getstate)) goto GOOD;
21535 #endif
21536 #if CYTHON_USE_PYTYPE_LOOKUP
21537  object_reduce_ex = _PyType_Lookup(&PyBaseObject_Type, __pyx_n_s_reduce_ex); if (!object_reduce_ex) goto BAD;
21538 #else
21539  object_reduce_ex = __Pyx_PyObject_GetAttrStr((PyObject*)&PyBaseObject_Type, __pyx_n_s_reduce_ex); if (!object_reduce_ex) goto BAD;
21540 #endif
21541  reduce_ex = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_n_s_reduce_ex); if (unlikely(!reduce_ex)) goto BAD;
21542  if (reduce_ex == object_reduce_ex) {
21543 #if CYTHON_USE_PYTYPE_LOOKUP
21544  object_reduce = _PyType_Lookup(&PyBaseObject_Type, __pyx_n_s_reduce); if (!object_reduce) goto BAD;
21545 #else
21546  object_reduce = __Pyx_PyObject_GetAttrStr((PyObject*)&PyBaseObject_Type, __pyx_n_s_reduce); if (!object_reduce) goto BAD;
21547 #endif
21548  reduce = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_n_s_reduce); if (unlikely(!reduce)) goto BAD;
21549  if (reduce == object_reduce || __Pyx_setup_reduce_is_named(reduce, __pyx_n_s_reduce_cython)) {
21550  reduce_cython = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_n_s_reduce_cython); if (unlikely(!reduce_cython)) goto BAD;
21551  ret = PyDict_SetItem(((PyTypeObject*)type_obj)->tp_dict, __pyx_n_s_reduce, reduce_cython); if (unlikely(ret < 0)) goto BAD;
21552  ret = PyDict_DelItem(((PyTypeObject*)type_obj)->tp_dict, __pyx_n_s_reduce_cython); if (unlikely(ret < 0)) goto BAD;
21553  setstate = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_n_s_setstate);
21554  if (!setstate) PyErr_Clear();
21555  if (!setstate || __Pyx_setup_reduce_is_named(setstate, __pyx_n_s_setstate_cython)) {
21556  setstate_cython = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_n_s_setstate_cython); if (unlikely(!setstate_cython)) goto BAD;
21557  ret = PyDict_SetItem(((PyTypeObject*)type_obj)->tp_dict, __pyx_n_s_setstate, setstate_cython); if (unlikely(ret < 0)) goto BAD;
21558  ret = PyDict_DelItem(((PyTypeObject*)type_obj)->tp_dict, __pyx_n_s_setstate_cython); if (unlikely(ret < 0)) goto BAD;
21559  }
21560  PyType_Modified((PyTypeObject*)type_obj);
21561  }
21562  }
21563  goto GOOD;
21564 BAD:
21565  if (!PyErr_Occurred())
21566  PyErr_Format(PyExc_RuntimeError, "Unable to initialize pickling for %s", ((PyTypeObject*)type_obj)->tp_name);
21567  ret = -1;
21568 GOOD:
21569 #if !CYTHON_USE_PYTYPE_LOOKUP
21570  Py_XDECREF(object_reduce);
21571  Py_XDECREF(object_reduce_ex);
21572 #endif
21573  Py_XDECREF(reduce);
21574  Py_XDECREF(reduce_ex);
21575  Py_XDECREF(reduce_cython);
21576  Py_XDECREF(setstate);
21577  Py_XDECREF(setstate_cython);
21578  return ret;
21579 }
21580 
21581 /* PyFloatBinop */
21582 #if !CYTHON_COMPILING_IN_PYPY
21583 static PyObject* __Pyx_PyFloat_DivideObjC(PyObject *op1, PyObject *op2, double floatval, int inplace, int zerodivision_check) {
21584  const double b = floatval;
21585  double a, result;
21586  (void)inplace;
21587  (void)zerodivision_check;
21588  if (likely(PyFloat_CheckExact(op1))) {
21589  a = PyFloat_AS_DOUBLE(op1);
21590 
21591  } else
21592  #if PY_MAJOR_VERSION < 3
21593  if (likely(PyInt_CheckExact(op1))) {
21594  a = (double) PyInt_AS_LONG(op1);
21595 
21596  } else
21597  #endif
21598  if (likely(PyLong_CheckExact(op1))) {
21599  #if CYTHON_USE_PYLONG_INTERNALS
21600  const digit* digits = ((PyLongObject*)op1)->ob_digit;
21601  const Py_ssize_t size = Py_SIZE(op1);
21602  switch (size) {
21603  case 0: a = 0.0; break;
21604  case -1: a = -(double) digits[0]; break;
21605  case 1: a = (double) digits[0]; break;
21606  case -2:
21607  case 2:
21608  if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (1 * PyLong_SHIFT < 53))) {
21609  a = (double) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
21610  if ((8 * sizeof(unsigned long) < 53) || (2 * PyLong_SHIFT < 53) || (a < (double) ((PY_LONG_LONG)1 << 53))) {
21611  if (size == -2)
21612  a = -a;
21613  break;
21614  }
21615  }
21616  CYTHON_FALLTHROUGH;
21617  case -3:
21618  case 3:
21619  if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (2 * PyLong_SHIFT < 53))) {
21620  a = (double) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
21621  if ((8 * sizeof(unsigned long) < 53) || (3 * PyLong_SHIFT < 53) || (a < (double) ((PY_LONG_LONG)1 << 53))) {
21622  if (size == -3)
21623  a = -a;
21624  break;
21625  }
21626  }
21627  CYTHON_FALLTHROUGH;
21628  case -4:
21629  case 4:
21630  if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (3 * PyLong_SHIFT < 53))) {
21631  a = (double) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
21632  if ((8 * sizeof(unsigned long) < 53) || (4 * PyLong_SHIFT < 53) || (a < (double) ((PY_LONG_LONG)1 << 53))) {
21633  if (size == -4)
21634  a = -a;
21635  break;
21636  }
21637  }
21638  CYTHON_FALLTHROUGH;
21639  default:
21640  #else
21641  {
21642  #endif
21643  a = PyLong_AsDouble(op1);
21644  if (unlikely(a == -1.0 && PyErr_Occurred())) return NULL;
21645 
21646  }
21647  } else {
21648  return (inplace ? __Pyx_PyNumber_InPlaceDivide(op1, op2) : __Pyx_PyNumber_Divide(op1, op2));
21649  }
21650 
21651  PyFPE_START_PROTECT("divide", return NULL)
21652  result = a / b;
21653  PyFPE_END_PROTECT(result)
21654  return PyFloat_FromDouble(result);
21655 }
21656 #endif
21657 
21658 /* BytesEquals */
21659  static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals) {
21660 #if CYTHON_COMPILING_IN_PYPY
21661  return PyObject_RichCompareBool(s1, s2, equals);
21662 #else
21663  if (s1 == s2) {
21664  return (equals == Py_EQ);
21665  } else if (PyBytes_CheckExact(s1) & PyBytes_CheckExact(s2)) {
21666  const char *ps1, *ps2;
21667  Py_ssize_t length = PyBytes_GET_SIZE(s1);
21668  if (length != PyBytes_GET_SIZE(s2))
21669  return (equals == Py_NE);
21670  ps1 = PyBytes_AS_STRING(s1);
21671  ps2 = PyBytes_AS_STRING(s2);
21672  if (ps1[0] != ps2[0]) {
21673  return (equals == Py_NE);
21674  } else if (length == 1) {
21675  return (equals == Py_EQ);
21676  } else {
21677  int result;
21678 #if CYTHON_USE_UNICODE_INTERNALS
21679  Py_hash_t hash1, hash2;
21680  hash1 = ((PyBytesObject*)s1)->ob_shash;
21681  hash2 = ((PyBytesObject*)s2)->ob_shash;
21682  if (hash1 != hash2 && hash1 != -1 && hash2 != -1) {
21683  return (equals == Py_NE);
21684  }
21685 #endif
21686  result = memcmp(ps1, ps2, (size_t)length);
21687  return (equals == Py_EQ) ? (result == 0) : (result != 0);
21688  }
21689  } else if ((s1 == Py_None) & PyBytes_CheckExact(s2)) {
21690  return (equals == Py_NE);
21691  } else if ((s2 == Py_None) & PyBytes_CheckExact(s1)) {
21692  return (equals == Py_NE);
21693  } else {
21694  int result;
21695  PyObject* py_result = PyObject_RichCompare(s1, s2, equals);
21696  if (!py_result)
21697  return -1;
21698  result = __Pyx_PyObject_IsTrue(py_result);
21699  Py_DECREF(py_result);
21700  return result;
21701  }
21702 #endif
21703 }
21704 
21705 /* UnicodeEquals */
21706  static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals) {
21707 #if CYTHON_COMPILING_IN_PYPY
21708  return PyObject_RichCompareBool(s1, s2, equals);
21709 #else
21710 #if PY_MAJOR_VERSION < 3
21711  PyObject* owned_ref = NULL;
21712 #endif
21713  int s1_is_unicode, s2_is_unicode;
21714  if (s1 == s2) {
21715  goto return_eq;
21716  }
21717  s1_is_unicode = PyUnicode_CheckExact(s1);
21718  s2_is_unicode = PyUnicode_CheckExact(s2);
21719 #if PY_MAJOR_VERSION < 3
21720  if ((s1_is_unicode & (!s2_is_unicode)) && PyString_CheckExact(s2)) {
21721  owned_ref = PyUnicode_FromObject(s2);
21722  if (unlikely(!owned_ref))
21723  return -1;
21724  s2 = owned_ref;
21725  s2_is_unicode = 1;
21726  } else if ((s2_is_unicode & (!s1_is_unicode)) && PyString_CheckExact(s1)) {
21727  owned_ref = PyUnicode_FromObject(s1);
21728  if (unlikely(!owned_ref))
21729  return -1;
21730  s1 = owned_ref;
21731  s1_is_unicode = 1;
21732  } else if (((!s2_is_unicode) & (!s1_is_unicode))) {
21733  return __Pyx_PyBytes_Equals(s1, s2, equals);
21734  }
21735 #endif
21736  if (s1_is_unicode & s2_is_unicode) {
21737  Py_ssize_t length;
21738  int kind;
21739  void *data1, *data2;
21740  if (unlikely(__Pyx_PyUnicode_READY(s1) < 0) || unlikely(__Pyx_PyUnicode_READY(s2) < 0))
21741  return -1;
21742  length = __Pyx_PyUnicode_GET_LENGTH(s1);
21743  if (length != __Pyx_PyUnicode_GET_LENGTH(s2)) {
21744  goto return_ne;
21745  }
21746 #if CYTHON_USE_UNICODE_INTERNALS
21747  {
21748  Py_hash_t hash1, hash2;
21749  #if CYTHON_PEP393_ENABLED
21750  hash1 = ((PyASCIIObject*)s1)->hash;
21751  hash2 = ((PyASCIIObject*)s2)->hash;
21752  #else
21753  hash1 = ((PyUnicodeObject*)s1)->hash;
21754  hash2 = ((PyUnicodeObject*)s2)->hash;
21755  #endif
21756  if (hash1 != hash2 && hash1 != -1 && hash2 != -1) {
21757  goto return_ne;
21758  }
21759  }
21760 #endif
21761  kind = __Pyx_PyUnicode_KIND(s1);
21762  if (kind != __Pyx_PyUnicode_KIND(s2)) {
21763  goto return_ne;
21764  }
21765  data1 = __Pyx_PyUnicode_DATA(s1);
21766  data2 = __Pyx_PyUnicode_DATA(s2);
21767  if (__Pyx_PyUnicode_READ(kind, data1, 0) != __Pyx_PyUnicode_READ(kind, data2, 0)) {
21768  goto return_ne;
21769  } else if (length == 1) {
21770  goto return_eq;
21771  } else {
21772  int result = memcmp(data1, data2, (size_t)(length * kind));
21773  #if PY_MAJOR_VERSION < 3
21774  Py_XDECREF(owned_ref);
21775  #endif
21776  return (equals == Py_EQ) ? (result == 0) : (result != 0);
21777  }
21778  } else if ((s1 == Py_None) & s2_is_unicode) {
21779  goto return_ne;
21780  } else if ((s2 == Py_None) & s1_is_unicode) {
21781  goto return_ne;
21782  } else {
21783  int result;
21784  PyObject* py_result = PyObject_RichCompare(s1, s2, equals);
21785  #if PY_MAJOR_VERSION < 3
21786  Py_XDECREF(owned_ref);
21787  #endif
21788  if (!py_result)
21789  return -1;
21790  result = __Pyx_PyObject_IsTrue(py_result);
21791  Py_DECREF(py_result);
21792  return result;
21793  }
21794 return_eq:
21795  #if PY_MAJOR_VERSION < 3
21796  Py_XDECREF(owned_ref);
21797  #endif
21798  return (equals == Py_EQ);
21799 return_ne:
21800  #if PY_MAJOR_VERSION < 3
21801  Py_XDECREF(owned_ref);
21802  #endif
21803  return (equals == Py_NE);
21804 #endif
21805 }
21806 
21807 /* CLineInTraceback */
21808  #ifndef CYTHON_CLINE_IN_TRACEBACK
21809 static int __Pyx_CLineForTraceback(PyThreadState *tstate, int c_line) {
21810  PyObject *use_cline;
21811  PyObject *ptype, *pvalue, *ptraceback;
21812 #if CYTHON_COMPILING_IN_CPYTHON
21813  PyObject **cython_runtime_dict;
21814 #endif
21815  if (unlikely(!__pyx_cython_runtime)) {
21816  return c_line;
21817  }
21818  __Pyx_ErrFetchInState(tstate, &ptype, &pvalue, &ptraceback);
21819 #if CYTHON_COMPILING_IN_CPYTHON
21820  cython_runtime_dict = _PyObject_GetDictPtr(__pyx_cython_runtime);
21821  if (likely(cython_runtime_dict)) {
21822  __PYX_PY_DICT_LOOKUP_IF_MODIFIED(
21823  use_cline, *cython_runtime_dict,
21824  __Pyx_PyDict_GetItemStr(*cython_runtime_dict, __pyx_n_s_cline_in_traceback))
21825  } else
21826 #endif
21827  {
21828  PyObject *use_cline_obj = __Pyx_PyObject_GetAttrStr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback);
21829  if (use_cline_obj) {
21830  use_cline = PyObject_Not(use_cline_obj) ? Py_False : Py_True;
21831  Py_DECREF(use_cline_obj);
21832  } else {
21833  PyErr_Clear();
21834  use_cline = NULL;
21835  }
21836  }
21837  if (!use_cline) {
21838  c_line = 0;
21839  PyObject_SetAttr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback, Py_False);
21840  }
21841  else if (use_cline == Py_False || (use_cline != Py_True && PyObject_Not(use_cline) != 0)) {
21842  c_line = 0;
21843  }
21844  __Pyx_ErrRestoreInState(tstate, ptype, pvalue, ptraceback);
21845  return c_line;
21846 }
21847 #endif
21848 
21849 /* CodeObjectCache */
21850  static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line) {
21851  int start = 0, mid = 0, end = count - 1;
21852  if (end >= 0 && code_line > entries[end].code_line) {
21853  return count;
21854  }
21855  while (start < end) {
21856  mid = start + (end - start) / 2;
21857  if (code_line < entries[mid].code_line) {
21858  end = mid;
21859  } else if (code_line > entries[mid].code_line) {
21860  start = mid + 1;
21861  } else {
21862  return mid;
21863  }
21864  }
21865  if (code_line <= entries[mid].code_line) {
21866  return mid;
21867  } else {
21868  return mid + 1;
21869  }
21870 }
21871 static PyCodeObject *__pyx_find_code_object(int code_line) {
21872  PyCodeObject* code_object;
21873  int pos;
21874  if (unlikely(!code_line) || unlikely(!__pyx_code_cache.entries)) {
21875  return NULL;
21876  }
21877  pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
21878  if (unlikely(pos >= __pyx_code_cache.count) || unlikely(__pyx_code_cache.entries[pos].code_line != code_line)) {
21879  return NULL;
21880  }
21881  code_object = __pyx_code_cache.entries[pos].code_object;
21882  Py_INCREF(code_object);
21883  return code_object;
21884 }
21885 static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object) {
21886  int pos, i;
21887  __Pyx_CodeObjectCacheEntry* entries = __pyx_code_cache.entries;
21888  if (unlikely(!code_line)) {
21889  return;
21890  }
21891  if (unlikely(!entries)) {
21892  entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Malloc(64*sizeof(__Pyx_CodeObjectCacheEntry));
21893  if (likely(entries)) {
21894  __pyx_code_cache.entries = entries;
21895  __pyx_code_cache.max_count = 64;
21896  __pyx_code_cache.count = 1;
21897  entries[0].code_line = code_line;
21898  entries[0].code_object = code_object;
21899  Py_INCREF(code_object);
21900  }
21901  return;
21902  }
21903  pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
21904  if ((pos < __pyx_code_cache.count) && unlikely(__pyx_code_cache.entries[pos].code_line == code_line)) {
21905  PyCodeObject* tmp = entries[pos].code_object;
21906  entries[pos].code_object = code_object;
21907  Py_DECREF(tmp);
21908  return;
21909  }
21910  if (__pyx_code_cache.count == __pyx_code_cache.max_count) {
21911  int new_max = __pyx_code_cache.max_count + 64;
21912  entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Realloc(
21913  __pyx_code_cache.entries, (size_t)new_max*sizeof(__Pyx_CodeObjectCacheEntry));
21914  if (unlikely(!entries)) {
21915  return;
21916  }
21917  __pyx_code_cache.entries = entries;
21918  __pyx_code_cache.max_count = new_max;
21919  }
21920  for (i=__pyx_code_cache.count; i>pos; i--) {
21921  entries[i] = entries[i-1];
21922  }
21923  entries[pos].code_line = code_line;
21924  entries[pos].code_object = code_object;
21925  __pyx_code_cache.count++;
21926  Py_INCREF(code_object);
21927 }
21928 
21929 /* AddTraceback */
21930  #include "compile.h"
21931 #include "frameobject.h"
21932 #include "traceback.h"
21933 static PyCodeObject* __Pyx_CreateCodeObjectForTraceback(
21934  const char *funcname, int c_line,
21935  int py_line, const char *filename) {
21936  PyCodeObject *py_code = 0;
21937  PyObject *py_srcfile = 0;
21938  PyObject *py_funcname = 0;
21939  #if PY_MAJOR_VERSION < 3
21940  py_srcfile = PyString_FromString(filename);
21941  #else
21942  py_srcfile = PyUnicode_FromString(filename);
21943  #endif
21944  if (!py_srcfile) goto bad;
21945  if (c_line) {
21946  #if PY_MAJOR_VERSION < 3
21947  py_funcname = PyString_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
21948  #else
21949  py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
21950  #endif
21951  }
21952  else {
21953  #if PY_MAJOR_VERSION < 3
21954  py_funcname = PyString_FromString(funcname);
21955  #else
21956  py_funcname = PyUnicode_FromString(funcname);
21957  #endif
21958  }
21959  if (!py_funcname) goto bad;
21960  py_code = __Pyx_PyCode_New(
21961  0,
21962  0,
21963  0,
21964  0,
21965  0,
21966  __pyx_empty_bytes, /*PyObject *code,*/
21967  __pyx_empty_tuple, /*PyObject *consts,*/
21968  __pyx_empty_tuple, /*PyObject *names,*/
21969  __pyx_empty_tuple, /*PyObject *varnames,*/
21970  __pyx_empty_tuple, /*PyObject *freevars,*/
21971  __pyx_empty_tuple, /*PyObject *cellvars,*/
21972  py_srcfile, /*PyObject *filename,*/
21973  py_funcname, /*PyObject *name,*/
21974  py_line,
21975  __pyx_empty_bytes /*PyObject *lnotab*/
21976  );
21977  Py_DECREF(py_srcfile);
21978  Py_DECREF(py_funcname);
21979  return py_code;
21980 bad:
21981  Py_XDECREF(py_srcfile);
21982  Py_XDECREF(py_funcname);
21983  return NULL;
21984 }
21985 static void __Pyx_AddTraceback(const char *funcname, int c_line,
21986  int py_line, const char *filename) {
21987  PyCodeObject *py_code = 0;
21988  PyFrameObject *py_frame = 0;
21989  PyThreadState *tstate = __Pyx_PyThreadState_Current;
21990  if (c_line) {
21991  c_line = __Pyx_CLineForTraceback(tstate, c_line);
21992  }
21993  py_code = __pyx_find_code_object(c_line ? -c_line : py_line);
21994  if (!py_code) {
21995  py_code = __Pyx_CreateCodeObjectForTraceback(
21996  funcname, c_line, py_line, filename);
21997  if (!py_code) goto bad;
21998  __pyx_insert_code_object(c_line ? -c_line : py_line, py_code);
21999  }
22000  py_frame = PyFrame_New(
22001  tstate, /*PyThreadState *tstate,*/
22002  py_code, /*PyCodeObject *code,*/
22003  __pyx_d, /*PyObject *globals,*/
22004  0 /*PyObject *locals*/
22005  );
22006  if (!py_frame) goto bad;
22007  __Pyx_PyFrame_SetLineNumber(py_frame, py_line);
22008  PyTraceBack_Here(py_frame);
22009 bad:
22010  Py_XDECREF(py_code);
22011  Py_XDECREF(py_frame);
22012 }
22013 
22014 /* CIntFromPyVerify */
22015  #define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)\
22016  __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 0)
22017 #define __PYX_VERIFY_RETURN_INT_EXC(target_type, func_type, func_value)\
22018  __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 1)
22019 #define __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, exc)\
22020  {\
22021  func_type value = func_value;\
22022  if (sizeof(target_type) < sizeof(func_type)) {\
22023  if (unlikely(value != (func_type) (target_type) value)) {\
22024  func_type zero = 0;\
22025  if (exc && unlikely(value == (func_type)-1 && PyErr_Occurred()))\
22026  return (target_type) -1;\
22027  if (is_unsigned && unlikely(value < zero))\
22028  goto raise_neg_overflow;\
22029  else\
22030  goto raise_overflow;\
22031  }\
22032  }\
22033  return (target_type) value;\
22034  }
22035 
22036 /* CIntToPy */
22037  static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value) {
22038  const int neg_one = (int) ((int) 0 - (int) 1), const_zero = (int) 0;
22039  const int is_unsigned = neg_one > const_zero;
22040  if (is_unsigned) {
22041  if (sizeof(int) < sizeof(long)) {
22042  return PyInt_FromLong((long) value);
22043  } else if (sizeof(int) <= sizeof(unsigned long)) {
22044  return PyLong_FromUnsignedLong((unsigned long) value);
22045 #ifdef HAVE_LONG_LONG
22046  } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {
22047  return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
22048 #endif
22049  }
22050  } else {
22051  if (sizeof(int) <= sizeof(long)) {
22052  return PyInt_FromLong((long) value);
22053 #ifdef HAVE_LONG_LONG
22054  } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
22055  return PyLong_FromLongLong((PY_LONG_LONG) value);
22056 #endif
22057  }
22058  }
22059  {
22060  int one = 1; int little = (int)*(unsigned char *)&one;
22061  unsigned char *bytes = (unsigned char *)&value;
22062  return _PyLong_FromByteArray(bytes, sizeof(int),
22063  little, !is_unsigned);
22064  }
22065 }
22066 
22067 /* CIntFromPy */
22068  static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) {
22069  const int neg_one = (int) ((int) 0 - (int) 1), const_zero = (int) 0;
22070  const int is_unsigned = neg_one > const_zero;
22071 #if PY_MAJOR_VERSION < 3
22072  if (likely(PyInt_Check(x))) {
22073  if (sizeof(int) < sizeof(long)) {
22074  __PYX_VERIFY_RETURN_INT(int, long, PyInt_AS_LONG(x))
22075  } else {
22076  long val = PyInt_AS_LONG(x);
22077  if (is_unsigned && unlikely(val < 0)) {
22078  goto raise_neg_overflow;
22079  }
22080  return (int) val;
22081  }
22082  } else
22083 #endif
22084  if (likely(PyLong_Check(x))) {
22085  if (is_unsigned) {
22086 #if CYTHON_USE_PYLONG_INTERNALS
22087  const digit* digits = ((PyLongObject*)x)->ob_digit;
22088  switch (Py_SIZE(x)) {
22089  case 0: return (int) 0;
22090  case 1: __PYX_VERIFY_RETURN_INT(int, digit, digits[0])
22091  case 2:
22092  if (8 * sizeof(int) > 1 * PyLong_SHIFT) {
22093  if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
22094  __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22095  } else if (8 * sizeof(int) >= 2 * PyLong_SHIFT) {
22096  return (int) (((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
22097  }
22098  }
22099  break;
22100  case 3:
22101  if (8 * sizeof(int) > 2 * PyLong_SHIFT) {
22102  if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
22103  __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22104  } else if (8 * sizeof(int) >= 3 * PyLong_SHIFT) {
22105  return (int) (((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
22106  }
22107  }
22108  break;
22109  case 4:
22110  if (8 * sizeof(int) > 3 * PyLong_SHIFT) {
22111  if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
22112  __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])))
22113  } else if (8 * sizeof(int) >= 4 * PyLong_SHIFT) {
22114  return (int) (((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
22115  }
22116  }
22117  break;
22118  }
22119 #endif
22120 #if CYTHON_COMPILING_IN_CPYTHON
22121  if (unlikely(Py_SIZE(x) < 0)) {
22122  goto raise_neg_overflow;
22123  }
22124 #else
22125  {
22126  int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
22127  if (unlikely(result < 0))
22128  return (int) -1;
22129  if (unlikely(result == 1))
22130  goto raise_neg_overflow;
22131  }
22132 #endif
22133  if (sizeof(int) <= sizeof(unsigned long)) {
22134  __PYX_VERIFY_RETURN_INT_EXC(int, unsigned long, PyLong_AsUnsignedLong(x))
22135 #ifdef HAVE_LONG_LONG
22136  } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {
22137  __PYX_VERIFY_RETURN_INT_EXC(int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
22138 #endif
22139  }
22140  } else {
22141 #if CYTHON_USE_PYLONG_INTERNALS
22142  const digit* digits = ((PyLongObject*)x)->ob_digit;
22143  switch (Py_SIZE(x)) {
22144  case 0: return (int) 0;
22145  case -1: __PYX_VERIFY_RETURN_INT(int, sdigit, (sdigit) (-(sdigit)digits[0]))
22146  case 1: __PYX_VERIFY_RETURN_INT(int, digit, +digits[0])
22147  case -2:
22148  if (8 * sizeof(int) - 1 > 1 * PyLong_SHIFT) {
22149  if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
22150  __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22151  } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
22152  return (int) (((int)-1)*(((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
22153  }
22154  }
22155  break;
22156  case 2:
22157  if (8 * sizeof(int) > 1 * PyLong_SHIFT) {
22158  if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
22159  __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22160  } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
22161  return (int) ((((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
22162  }
22163  }
22164  break;
22165  case -3:
22166  if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
22167  if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
22168  __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22169  } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
22170  return (int) (((int)-1)*(((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
22171  }
22172  }
22173  break;
22174  case 3:
22175  if (8 * sizeof(int) > 2 * PyLong_SHIFT) {
22176  if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
22177  __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22178  } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
22179  return (int) ((((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
22180  }
22181  }
22182  break;
22183  case -4:
22184  if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
22185  if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
22186  __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])))
22187  } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) {
22188  return (int) (((int)-1)*(((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
22189  }
22190  }
22191  break;
22192  case 4:
22193  if (8 * sizeof(int) > 3 * PyLong_SHIFT) {
22194  if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
22195  __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])))
22196  } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) {
22197  return (int) ((((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
22198  }
22199  }
22200  break;
22201  }
22202 #endif
22203  if (sizeof(int) <= sizeof(long)) {
22204  __PYX_VERIFY_RETURN_INT_EXC(int, long, PyLong_AsLong(x))
22205 #ifdef HAVE_LONG_LONG
22206  } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
22207  __PYX_VERIFY_RETURN_INT_EXC(int, PY_LONG_LONG, PyLong_AsLongLong(x))
22208 #endif
22209  }
22210  }
22211  {
22212 #if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
22213  PyErr_SetString(PyExc_RuntimeError,
22214  "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
22215 #else
22216  int val;
22217  PyObject *v = __Pyx_PyNumber_IntOrLong(x);
22218  #if PY_MAJOR_VERSION < 3
22219  if (likely(v) && !PyLong_Check(v)) {
22220  PyObject *tmp = v;
22221  v = PyNumber_Long(tmp);
22222  Py_DECREF(tmp);
22223  }
22224  #endif
22225  if (likely(v)) {
22226  int one = 1; int is_little = (int)*(unsigned char *)&one;
22227  unsigned char *bytes = (unsigned char *)&val;
22228  int ret = _PyLong_AsByteArray((PyLongObject *)v,
22229  bytes, sizeof(val),
22230  is_little, !is_unsigned);
22231  Py_DECREF(v);
22232  if (likely(!ret))
22233  return val;
22234  }
22235 #endif
22236  return (int) -1;
22237  }
22238  } else {
22239  int val;
22240  PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
22241  if (!tmp) return (int) -1;
22242  val = __Pyx_PyInt_As_int(tmp);
22243  Py_DECREF(tmp);
22244  return val;
22245  }
22246 raise_overflow:
22247  PyErr_SetString(PyExc_OverflowError,
22248  "value too large to convert to int");
22249  return (int) -1;
22250 raise_neg_overflow:
22251  PyErr_SetString(PyExc_OverflowError,
22252  "can't convert negative value to int");
22253  return (int) -1;
22254 }
22255 
22256 /* CIntToPy */
22257  static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) {
22258  const long neg_one = (long) ((long) 0 - (long) 1), const_zero = (long) 0;
22259  const int is_unsigned = neg_one > const_zero;
22260  if (is_unsigned) {
22261  if (sizeof(long) < sizeof(long)) {
22262  return PyInt_FromLong((long) value);
22263  } else if (sizeof(long) <= sizeof(unsigned long)) {
22264  return PyLong_FromUnsignedLong((unsigned long) value);
22265 #ifdef HAVE_LONG_LONG
22266  } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
22267  return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
22268 #endif
22269  }
22270  } else {
22271  if (sizeof(long) <= sizeof(long)) {
22272  return PyInt_FromLong((long) value);
22273 #ifdef HAVE_LONG_LONG
22274  } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
22275  return PyLong_FromLongLong((PY_LONG_LONG) value);
22276 #endif
22277  }
22278  }
22279  {
22280  int one = 1; int little = (int)*(unsigned char *)&one;
22281  unsigned char *bytes = (unsigned char *)&value;
22282  return _PyLong_FromByteArray(bytes, sizeof(long),
22283  little, !is_unsigned);
22284  }
22285 }
22286 
22287 /* CIntFromPy */
22288  static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *x) {
22289  const long neg_one = (long) ((long) 0 - (long) 1), const_zero = (long) 0;
22290  const int is_unsigned = neg_one > const_zero;
22291 #if PY_MAJOR_VERSION < 3
22292  if (likely(PyInt_Check(x))) {
22293  if (sizeof(long) < sizeof(long)) {
22294  __PYX_VERIFY_RETURN_INT(long, long, PyInt_AS_LONG(x))
22295  } else {
22296  long val = PyInt_AS_LONG(x);
22297  if (is_unsigned && unlikely(val < 0)) {
22298  goto raise_neg_overflow;
22299  }
22300  return (long) val;
22301  }
22302  } else
22303 #endif
22304  if (likely(PyLong_Check(x))) {
22305  if (is_unsigned) {
22306 #if CYTHON_USE_PYLONG_INTERNALS
22307  const digit* digits = ((PyLongObject*)x)->ob_digit;
22308  switch (Py_SIZE(x)) {
22309  case 0: return (long) 0;
22310  case 1: __PYX_VERIFY_RETURN_INT(long, digit, digits[0])
22311  case 2:
22312  if (8 * sizeof(long) > 1 * PyLong_SHIFT) {
22313  if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
22314  __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22315  } else if (8 * sizeof(long) >= 2 * PyLong_SHIFT) {
22316  return (long) (((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
22317  }
22318  }
22319  break;
22320  case 3:
22321  if (8 * sizeof(long) > 2 * PyLong_SHIFT) {
22322  if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
22323  __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22324  } else if (8 * sizeof(long) >= 3 * PyLong_SHIFT) {
22325  return (long) (((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
22326  }
22327  }
22328  break;
22329  case 4:
22330  if (8 * sizeof(long) > 3 * PyLong_SHIFT) {
22331  if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
22332  __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])))
22333  } else if (8 * sizeof(long) >= 4 * PyLong_SHIFT) {
22334  return (long) (((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
22335  }
22336  }
22337  break;
22338  }
22339 #endif
22340 #if CYTHON_COMPILING_IN_CPYTHON
22341  if (unlikely(Py_SIZE(x) < 0)) {
22342  goto raise_neg_overflow;
22343  }
22344 #else
22345  {
22346  int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
22347  if (unlikely(result < 0))
22348  return (long) -1;
22349  if (unlikely(result == 1))
22350  goto raise_neg_overflow;
22351  }
22352 #endif
22353  if (sizeof(long) <= sizeof(unsigned long)) {
22354  __PYX_VERIFY_RETURN_INT_EXC(long, unsigned long, PyLong_AsUnsignedLong(x))
22355 #ifdef HAVE_LONG_LONG
22356  } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
22357  __PYX_VERIFY_RETURN_INT_EXC(long, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
22358 #endif
22359  }
22360  } else {
22361 #if CYTHON_USE_PYLONG_INTERNALS
22362  const digit* digits = ((PyLongObject*)x)->ob_digit;
22363  switch (Py_SIZE(x)) {
22364  case 0: return (long) 0;
22365  case -1: __PYX_VERIFY_RETURN_INT(long, sdigit, (sdigit) (-(sdigit)digits[0]))
22366  case 1: __PYX_VERIFY_RETURN_INT(long, digit, +digits[0])
22367  case -2:
22368  if (8 * sizeof(long) - 1 > 1 * PyLong_SHIFT) {
22369  if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
22370  __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22371  } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
22372  return (long) (((long)-1)*(((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
22373  }
22374  }
22375  break;
22376  case 2:
22377  if (8 * sizeof(long) > 1 * PyLong_SHIFT) {
22378  if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
22379  __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22380  } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
22381  return (long) ((((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
22382  }
22383  }
22384  break;
22385  case -3:
22386  if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
22387  if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
22388  __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22389  } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
22390  return (long) (((long)-1)*(((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
22391  }
22392  }
22393  break;
22394  case 3:
22395  if (8 * sizeof(long) > 2 * PyLong_SHIFT) {
22396  if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
22397  __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22398  } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
22399  return (long) ((((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
22400  }
22401  }
22402  break;
22403  case -4:
22404  if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
22405  if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
22406  __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])))
22407  } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
22408  return (long) (((long)-1)*(((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
22409  }
22410  }
22411  break;
22412  case 4:
22413  if (8 * sizeof(long) > 3 * PyLong_SHIFT) {
22414  if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
22415  __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])))
22416  } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
22417  return (long) ((((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
22418  }
22419  }
22420  break;
22421  }
22422 #endif
22423  if (sizeof(long) <= sizeof(long)) {
22424  __PYX_VERIFY_RETURN_INT_EXC(long, long, PyLong_AsLong(x))
22425 #ifdef HAVE_LONG_LONG
22426  } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
22427  __PYX_VERIFY_RETURN_INT_EXC(long, PY_LONG_LONG, PyLong_AsLongLong(x))
22428 #endif
22429  }
22430  }
22431  {
22432 #if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
22433  PyErr_SetString(PyExc_RuntimeError,
22434  "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
22435 #else
22436  long val;
22437  PyObject *v = __Pyx_PyNumber_IntOrLong(x);
22438  #if PY_MAJOR_VERSION < 3
22439  if (likely(v) && !PyLong_Check(v)) {
22440  PyObject *tmp = v;
22441  v = PyNumber_Long(tmp);
22442  Py_DECREF(tmp);
22443  }
22444  #endif
22445  if (likely(v)) {
22446  int one = 1; int is_little = (int)*(unsigned char *)&one;
22447  unsigned char *bytes = (unsigned char *)&val;
22448  int ret = _PyLong_AsByteArray((PyLongObject *)v,
22449  bytes, sizeof(val),
22450  is_little, !is_unsigned);
22451  Py_DECREF(v);
22452  if (likely(!ret))
22453  return val;
22454  }
22455 #endif
22456  return (long) -1;
22457  }
22458  } else {
22459  long val;
22460  PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
22461  if (!tmp) return (long) -1;
22462  val = __Pyx_PyInt_As_long(tmp);
22463  Py_DECREF(tmp);
22464  return val;
22465  }
22466 raise_overflow:
22467  PyErr_SetString(PyExc_OverflowError,
22468  "value too large to convert to long");
22469  return (long) -1;
22470 raise_neg_overflow:
22471  PyErr_SetString(PyExc_OverflowError,
22472  "can't convert negative value to long");
22473  return (long) -1;
22474 }
22475 
22476 /* FastTypeChecks */
22477  #if CYTHON_COMPILING_IN_CPYTHON
22478 static int __Pyx_InBases(PyTypeObject *a, PyTypeObject *b) {
22479  while (a) {
22480  a = a->tp_base;
22481  if (a == b)
22482  return 1;
22483  }
22484  return b == &PyBaseObject_Type;
22485 }
22486 static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b) {
22487  PyObject *mro;
22488  if (a == b) return 1;
22489  mro = a->tp_mro;
22490  if (likely(mro)) {
22491  Py_ssize_t i, n;
22492  n = PyTuple_GET_SIZE(mro);
22493  for (i = 0; i < n; i++) {
22494  if (PyTuple_GET_ITEM(mro, i) == (PyObject *)b)
22495  return 1;
22496  }
22497  return 0;
22498  }
22499  return __Pyx_InBases(a, b);
22500 }
22501 #if PY_MAJOR_VERSION == 2
22502 static int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject* exc_type2) {
22503  PyObject *exception, *value, *tb;
22504  int res;
22505  __Pyx_PyThreadState_declare
22506  __Pyx_PyThreadState_assign
22507  __Pyx_ErrFetch(&exception, &value, &tb);
22508  res = exc_type1 ? PyObject_IsSubclass(err, exc_type1) : 0;
22509  if (unlikely(res == -1)) {
22510  PyErr_WriteUnraisable(err);
22511  res = 0;
22512  }
22513  if (!res) {
22514  res = PyObject_IsSubclass(err, exc_type2);
22515  if (unlikely(res == -1)) {
22516  PyErr_WriteUnraisable(err);
22517  res = 0;
22518  }
22519  }
22520  __Pyx_ErrRestore(exception, value, tb);
22521  return res;
22522 }
22523 #else
22524 static CYTHON_INLINE int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject *exc_type2) {
22525  int res = exc_type1 ? __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type1) : 0;
22526  if (!res) {
22527  res = __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type2);
22528  }
22529  return res;
22530 }
22531 #endif
22532 static int __Pyx_PyErr_GivenExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) {
22533  Py_ssize_t i, n;
22534  assert(PyExceptionClass_Check(exc_type));
22535  n = PyTuple_GET_SIZE(tuple);
22536 #if PY_MAJOR_VERSION >= 3
22537  for (i=0; i<n; i++) {
22538  if (exc_type == PyTuple_GET_ITEM(tuple, i)) return 1;
22539  }
22540 #endif
22541  for (i=0; i<n; i++) {
22542  PyObject *t = PyTuple_GET_ITEM(tuple, i);
22543  #if PY_MAJOR_VERSION < 3
22544  if (likely(exc_type == t)) return 1;
22545  #endif
22546  if (likely(PyExceptionClass_Check(t))) {
22547  if (__Pyx_inner_PyErr_GivenExceptionMatches2(exc_type, NULL, t)) return 1;
22548  } else {
22549  }
22550  }
22551  return 0;
22552 }
22553 static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject* exc_type) {
22554  if (likely(err == exc_type)) return 1;
22555  if (likely(PyExceptionClass_Check(err))) {
22556  if (likely(PyExceptionClass_Check(exc_type))) {
22557  return __Pyx_inner_PyErr_GivenExceptionMatches2(err, NULL, exc_type);
22558  } else if (likely(PyTuple_Check(exc_type))) {
22559  return __Pyx_PyErr_GivenExceptionMatchesTuple(err, exc_type);
22560  } else {
22561  }
22562  }
22563  return PyErr_GivenExceptionMatches(err, exc_type);
22564 }
22565 static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *exc_type1, PyObject *exc_type2) {
22566  assert(PyExceptionClass_Check(exc_type1));
22567  assert(PyExceptionClass_Check(exc_type2));
22568  if (likely(err == exc_type1 || err == exc_type2)) return 1;
22569  if (likely(PyExceptionClass_Check(err))) {
22570  return __Pyx_inner_PyErr_GivenExceptionMatches2(err, exc_type1, exc_type2);
22571  }
22572  return (PyErr_GivenExceptionMatches(err, exc_type1) || PyErr_GivenExceptionMatches(err, exc_type2));
22573 }
22574 #endif
22575 
22576 /* FetchCommonType */
22577  static PyTypeObject* __Pyx_FetchCommonType(PyTypeObject* type) {
22578  PyObject* fake_module;
22579  PyTypeObject* cached_type = NULL;
22580  fake_module = PyImport_AddModule((char*) "_cython_" CYTHON_ABI);
22581  if (!fake_module) return NULL;
22582  Py_INCREF(fake_module);
22583  cached_type = (PyTypeObject*) PyObject_GetAttrString(fake_module, type->tp_name);
22584  if (cached_type) {
22585  if (!PyType_Check((PyObject*)cached_type)) {
22586  PyErr_Format(PyExc_TypeError,
22587  "Shared Cython type %.200s is not a type object",
22588  type->tp_name);
22589  goto bad;
22590  }
22591  if (cached_type->tp_basicsize != type->tp_basicsize) {
22592  PyErr_Format(PyExc_TypeError,
22593  "Shared Cython type %.200s has the wrong size, try recompiling",
22594  type->tp_name);
22595  goto bad;
22596  }
22597  } else {
22598  if (!PyErr_ExceptionMatches(PyExc_AttributeError)) goto bad;
22599  PyErr_Clear();
22600  if (PyType_Ready(type) < 0) goto bad;
22601  if (PyObject_SetAttrString(fake_module, type->tp_name, (PyObject*) type) < 0)
22602  goto bad;
22603  Py_INCREF(type);
22604  cached_type = type;
22605  }
22606 done:
22607  Py_DECREF(fake_module);
22608  return cached_type;
22609 bad:
22610  Py_XDECREF(cached_type);
22611  cached_type = NULL;
22612  goto done;
22613 }
22614 
22615 /* SwapException */
22616  #if CYTHON_FAST_THREAD_STATE
22617 static CYTHON_INLINE void __Pyx__ExceptionSwap(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
22618  PyObject *tmp_type, *tmp_value, *tmp_tb;
22619  #if CYTHON_USE_EXC_INFO_STACK
22620  _PyErr_StackItem *exc_info = tstate->exc_info;
22621  tmp_type = exc_info->exc_type;
22622  tmp_value = exc_info->exc_value;
22623  tmp_tb = exc_info->exc_traceback;
22624  exc_info->exc_type = *type;
22625  exc_info->exc_value = *value;
22626  exc_info->exc_traceback = *tb;
22627  #else
22628  tmp_type = tstate->exc_type;
22629  tmp_value = tstate->exc_value;
22630  tmp_tb = tstate->exc_traceback;
22631  tstate->exc_type = *type;
22632  tstate->exc_value = *value;
22633  tstate->exc_traceback = *tb;
22634  #endif
22635  *type = tmp_type;
22636  *value = tmp_value;
22637  *tb = tmp_tb;
22638 }
22639 #else
22640 static CYTHON_INLINE void __Pyx_ExceptionSwap(PyObject **type, PyObject **value, PyObject **tb) {
22641  PyObject *tmp_type, *tmp_value, *tmp_tb;
22642  PyErr_GetExcInfo(&tmp_type, &tmp_value, &tmp_tb);
22643  PyErr_SetExcInfo(*type, *value, *tb);
22644  *type = tmp_type;
22645  *value = tmp_value;
22646  *tb = tmp_tb;
22647 }
22648 #endif
22649 
22650 /* PyObjectGetMethod */
22651  static int __Pyx_PyObject_GetMethod(PyObject *obj, PyObject *name, PyObject **method) {
22652  PyObject *attr;
22653 #if CYTHON_UNPACK_METHODS && CYTHON_COMPILING_IN_CPYTHON && CYTHON_USE_PYTYPE_LOOKUP
22654  PyTypeObject *tp = Py_TYPE(obj);
22655  PyObject *descr;
22656  descrgetfunc f = NULL;
22657  PyObject **dictptr, *dict;
22658  int meth_found = 0;
22659  assert (*method == NULL);
22660  if (unlikely(tp->tp_getattro != PyObject_GenericGetAttr)) {
22661  attr = __Pyx_PyObject_GetAttrStr(obj, name);
22662  goto try_unpack;
22663  }
22664  if (unlikely(tp->tp_dict == NULL) && unlikely(PyType_Ready(tp) < 0)) {
22665  return 0;
22666  }
22667  descr = _PyType_Lookup(tp, name);
22668  if (likely(descr != NULL)) {
22669  Py_INCREF(descr);
22670 #if PY_MAJOR_VERSION >= 3
22671  #ifdef __Pyx_CyFunction_USED
22672  if (likely(PyFunction_Check(descr) || (Py_TYPE(descr) == &PyMethodDescr_Type) || __Pyx_CyFunction_Check(descr)))
22673  #else
22674  if (likely(PyFunction_Check(descr) || (Py_TYPE(descr) == &PyMethodDescr_Type)))
22675  #endif
22676 #else
22677  #ifdef __Pyx_CyFunction_USED
22678  if (likely(PyFunction_Check(descr) || __Pyx_CyFunction_Check(descr)))
22679  #else
22680  if (likely(PyFunction_Check(descr)))
22681  #endif
22682 #endif
22683  {
22684  meth_found = 1;
22685  } else {
22686  f = Py_TYPE(descr)->tp_descr_get;
22687  if (f != NULL && PyDescr_IsData(descr)) {
22688  attr = f(descr, obj, (PyObject *)Py_TYPE(obj));
22689  Py_DECREF(descr);
22690  goto try_unpack;
22691  }
22692  }
22693  }
22694  dictptr = _PyObject_GetDictPtr(obj);
22695  if (dictptr != NULL && (dict = *dictptr) != NULL) {
22696  Py_INCREF(dict);
22697  attr = __Pyx_PyDict_GetItemStr(dict, name);
22698  if (attr != NULL) {
22699  Py_INCREF(attr);
22700  Py_DECREF(dict);
22701  Py_XDECREF(descr);
22702  goto try_unpack;
22703  }
22704  Py_DECREF(dict);
22705  }
22706  if (meth_found) {
22707  *method = descr;
22708  return 1;
22709  }
22710  if (f != NULL) {
22711  attr = f(descr, obj, (PyObject *)Py_TYPE(obj));
22712  Py_DECREF(descr);
22713  goto try_unpack;
22714  }
22715  if (descr != NULL) {
22716  *method = descr;
22717  return 0;
22718  }
22719  PyErr_Format(PyExc_AttributeError,
22720 #if PY_MAJOR_VERSION >= 3
22721  "'%.50s' object has no attribute '%U'",
22722  tp->tp_name, name);
22723 #else
22724  "'%.50s' object has no attribute '%.400s'",
22725  tp->tp_name, PyString_AS_STRING(name));
22726 #endif
22727  return 0;
22728 #else
22729  attr = __Pyx_PyObject_GetAttrStr(obj, name);
22730  goto try_unpack;
22731 #endif
22732 try_unpack:
22733 #if CYTHON_UNPACK_METHODS
22734  if (likely(attr) && PyMethod_Check(attr) && likely(PyMethod_GET_SELF(attr) == obj)) {
22735  PyObject *function = PyMethod_GET_FUNCTION(attr);
22736  Py_INCREF(function);
22737  Py_DECREF(attr);
22738  *method = function;
22739  return 1;
22740  }
22741 #endif
22742  *method = attr;
22743  return 0;
22744 }
22745 
22746 /* PyObjectCallMethod1 */
22747  static PyObject* __Pyx__PyObject_CallMethod1(PyObject* method, PyObject* arg) {
22748  PyObject *result = __Pyx_PyObject_CallOneArg(method, arg);
22749  Py_DECREF(method);
22750  return result;
22751 }
22752 static PyObject* __Pyx_PyObject_CallMethod1(PyObject* obj, PyObject* method_name, PyObject* arg) {
22753  PyObject *method = NULL, *result;
22754  int is_method = __Pyx_PyObject_GetMethod(obj, method_name, &method);
22755  if (likely(is_method)) {
22756  result = __Pyx_PyObject_Call2Args(method, obj, arg);
22757  Py_DECREF(method);
22758  return result;
22759  }
22760  if (unlikely(!method)) return NULL;
22761  return __Pyx__PyObject_CallMethod1(method, arg);
22762 }
22763 
22764 /* CoroutineBase */
22765  #include <structmember.h>
22766 #include <frameobject.h>
22767 #define __Pyx_Coroutine_Undelegate(gen) Py_CLEAR((gen)->yieldfrom)
22768 static int __Pyx_PyGen__FetchStopIterationValue(CYTHON_UNUSED PyThreadState *__pyx_tstate, PyObject **pvalue) {
22769  PyObject *et, *ev, *tb;
22770  PyObject *value = NULL;
22771  __Pyx_ErrFetch(&et, &ev, &tb);
22772  if (!et) {
22773  Py_XDECREF(tb);
22774  Py_XDECREF(ev);
22775  Py_INCREF(Py_None);
22776  *pvalue = Py_None;
22777  return 0;
22778  }
22779  if (likely(et == PyExc_StopIteration)) {
22780  if (!ev) {
22781  Py_INCREF(Py_None);
22782  value = Py_None;
22783  }
22784 #if PY_VERSION_HEX >= 0x030300A0
22785  else if (Py_TYPE(ev) == (PyTypeObject*)PyExc_StopIteration) {
22786  value = ((PyStopIterationObject *)ev)->value;
22787  Py_INCREF(value);
22788  Py_DECREF(ev);
22789  }
22790 #endif
22791  else if (unlikely(PyTuple_Check(ev))) {
22792  if (PyTuple_GET_SIZE(ev) >= 1) {
22793 #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
22794  value = PyTuple_GET_ITEM(ev, 0);
22795  Py_INCREF(value);
22796 #else
22797  value = PySequence_ITEM(ev, 0);
22798 #endif
22799  } else {
22800  Py_INCREF(Py_None);
22801  value = Py_None;
22802  }
22803  Py_DECREF(ev);
22804  }
22805  else if (!__Pyx_TypeCheck(ev, (PyTypeObject*)PyExc_StopIteration)) {
22806  value = ev;
22807  }
22808  if (likely(value)) {
22809  Py_XDECREF(tb);
22810  Py_DECREF(et);
22811  *pvalue = value;
22812  return 0;
22813  }
22814  } else if (!__Pyx_PyErr_GivenExceptionMatches(et, PyExc_StopIteration)) {
22815  __Pyx_ErrRestore(et, ev, tb);
22816  return -1;
22817  }
22818  PyErr_NormalizeException(&et, &ev, &tb);
22819  if (unlikely(!PyObject_TypeCheck(ev, (PyTypeObject*)PyExc_StopIteration))) {
22820  __Pyx_ErrRestore(et, ev, tb);
22821  return -1;
22822  }
22823  Py_XDECREF(tb);
22824  Py_DECREF(et);
22825 #if PY_VERSION_HEX >= 0x030300A0
22826  value = ((PyStopIterationObject *)ev)->value;
22827  Py_INCREF(value);
22828  Py_DECREF(ev);
22829 #else
22830  {
22831  PyObject* args = __Pyx_PyObject_GetAttrStr(ev, __pyx_n_s_args);
22832  Py_DECREF(ev);
22833  if (likely(args)) {
22834  value = PySequence_GetItem(args, 0);
22835  Py_DECREF(args);
22836  }
22837  if (unlikely(!value)) {
22838  __Pyx_ErrRestore(NULL, NULL, NULL);
22839  Py_INCREF(Py_None);
22840  value = Py_None;
22841  }
22842  }
22843 #endif
22844  *pvalue = value;
22845  return 0;
22846 }
22847 static CYTHON_INLINE
22848 void __Pyx_Coroutine_ExceptionClear(__Pyx_ExcInfoStruct *exc_state) {
22849  PyObject *t, *v, *tb;
22850  t = exc_state->exc_type;
22851  v = exc_state->exc_value;
22852  tb = exc_state->exc_traceback;
22853  exc_state->exc_type = NULL;
22854  exc_state->exc_value = NULL;
22855  exc_state->exc_traceback = NULL;
22856  Py_XDECREF(t);
22857  Py_XDECREF(v);
22858  Py_XDECREF(tb);
22859 }
22860 #define __Pyx_Coroutine_AlreadyRunningError(gen) (__Pyx__Coroutine_AlreadyRunningError(gen), (PyObject*)NULL)
22861 static void __Pyx__Coroutine_AlreadyRunningError(CYTHON_UNUSED __pyx_CoroutineObject *gen) {
22862  const char *msg;
22863  if ((0)) {
22864  #ifdef __Pyx_Coroutine_USED
22865  } else if (__Pyx_Coroutine_Check((PyObject*)gen)) {
22866  msg = "coroutine already executing";
22867  #endif
22868  #ifdef __Pyx_AsyncGen_USED
22869  } else if (__Pyx_AsyncGen_CheckExact((PyObject*)gen)) {
22870  msg = "async generator already executing";
22871  #endif
22872  } else {
22873  msg = "generator already executing";
22874  }
22875  PyErr_SetString(PyExc_ValueError, msg);
22876 }
22877 #define __Pyx_Coroutine_NotStartedError(gen) (__Pyx__Coroutine_NotStartedError(gen), (PyObject*)NULL)
22878 static void __Pyx__Coroutine_NotStartedError(CYTHON_UNUSED PyObject *gen) {
22879  const char *msg;
22880  if ((0)) {
22881  #ifdef __Pyx_Coroutine_USED
22882  } else if (__Pyx_Coroutine_Check(gen)) {
22883  msg = "can't send non-None value to a just-started coroutine";
22884  #endif
22885  #ifdef __Pyx_AsyncGen_USED
22886  } else if (__Pyx_AsyncGen_CheckExact(gen)) {
22887  msg = "can't send non-None value to a just-started async generator";
22888  #endif
22889  } else {
22890  msg = "can't send non-None value to a just-started generator";
22891  }
22892  PyErr_SetString(PyExc_TypeError, msg);
22893 }
22894 #define __Pyx_Coroutine_AlreadyTerminatedError(gen, value, closing) (__Pyx__Coroutine_AlreadyTerminatedError(gen, value, closing), (PyObject*)NULL)
22895 static void __Pyx__Coroutine_AlreadyTerminatedError(CYTHON_UNUSED PyObject *gen, PyObject *value, CYTHON_UNUSED int closing) {
22896  #ifdef __Pyx_Coroutine_USED
22897  if (!closing && __Pyx_Coroutine_Check(gen)) {
22898  PyErr_SetString(PyExc_RuntimeError, "cannot reuse already awaited coroutine");
22899  } else
22900  #endif
22901  if (value) {
22902  #ifdef __Pyx_AsyncGen_USED
22903  if (__Pyx_AsyncGen_CheckExact(gen))
22904  PyErr_SetNone(__Pyx_PyExc_StopAsyncIteration);
22905  else
22906  #endif
22907  PyErr_SetNone(PyExc_StopIteration);
22908  }
22909 }
22910 static
22911 PyObject *__Pyx_Coroutine_SendEx(__pyx_CoroutineObject *self, PyObject *value, int closing) {
22912  __Pyx_PyThreadState_declare
22913  PyThreadState *tstate;
22914  __Pyx_ExcInfoStruct *exc_state;
22915  PyObject *retval;
22916  assert(!self->is_running);
22917  if (unlikely(self->resume_label == 0)) {
22918  if (unlikely(value && value != Py_None)) {
22919  return __Pyx_Coroutine_NotStartedError((PyObject*)self);
22920  }
22921  }
22922  if (unlikely(self->resume_label == -1)) {
22923  return __Pyx_Coroutine_AlreadyTerminatedError((PyObject*)self, value, closing);
22924  }
22925 #if CYTHON_FAST_THREAD_STATE
22926  __Pyx_PyThreadState_assign
22927  tstate = __pyx_tstate;
22928 #else
22929  tstate = __Pyx_PyThreadState_Current;
22930 #endif
22931  exc_state = &self->gi_exc_state;
22932  if (exc_state->exc_type) {
22933  #if CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_PYSTON
22934  #else
22935  if (exc_state->exc_traceback) {
22936  PyTracebackObject *tb = (PyTracebackObject *) exc_state->exc_traceback;
22937  PyFrameObject *f = tb->tb_frame;
22938  Py_XINCREF(tstate->frame);
22939  assert(f->f_back == NULL);
22940  f->f_back = tstate->frame;
22941  }
22942  #endif
22943  }
22944 #if CYTHON_USE_EXC_INFO_STACK
22945  exc_state->previous_item = tstate->exc_info;
22946  tstate->exc_info = exc_state;
22947 #else
22948  if (exc_state->exc_type) {
22949  __Pyx_ExceptionSwap(&exc_state->exc_type, &exc_state->exc_value, &exc_state->exc_traceback);
22950  } else {
22951  __Pyx_Coroutine_ExceptionClear(exc_state);
22952  __Pyx_ExceptionSave(&exc_state->exc_type, &exc_state->exc_value, &exc_state->exc_traceback);
22953  }
22954 #endif
22955  self->is_running = 1;
22956  retval = self->body((PyObject *) self, tstate, value);
22957  self->is_running = 0;
22958 #if CYTHON_USE_EXC_INFO_STACK
22959  exc_state = &self->gi_exc_state;
22960  tstate->exc_info = exc_state->previous_item;
22961  exc_state->previous_item = NULL;
22962  __Pyx_Coroutine_ResetFrameBackpointer(exc_state);
22963 #endif
22964  return retval;
22965 }
22966 static CYTHON_INLINE void __Pyx_Coroutine_ResetFrameBackpointer(__Pyx_ExcInfoStruct *exc_state) {
22967  PyObject *exc_tb = exc_state->exc_traceback;
22968  if (likely(exc_tb)) {
22969 #if CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_PYSTON
22970 #else
22971  PyTracebackObject *tb = (PyTracebackObject *) exc_tb;
22972  PyFrameObject *f = tb->tb_frame;
22973  Py_CLEAR(f->f_back);
22974 #endif
22975  }
22976 }
22977 static CYTHON_INLINE
22978 PyObject *__Pyx_Coroutine_MethodReturn(CYTHON_UNUSED PyObject* gen, PyObject *retval) {
22979  if (unlikely(!retval)) {
22980  __Pyx_PyThreadState_declare
22981  __Pyx_PyThreadState_assign
22982  if (!__Pyx_PyErr_Occurred()) {
22983  PyObject *exc = PyExc_StopIteration;
22984  #ifdef __Pyx_AsyncGen_USED
22985  if (__Pyx_AsyncGen_CheckExact(gen))
22986  exc = __Pyx_PyExc_StopAsyncIteration;
22987  #endif
22988  __Pyx_PyErr_SetNone(exc);
22989  }
22990  }
22991  return retval;
22992 }
22993 static CYTHON_INLINE
22994 PyObject *__Pyx_Coroutine_FinishDelegation(__pyx_CoroutineObject *gen) {
22995  PyObject *ret;
22996  PyObject *val = NULL;
22997  __Pyx_Coroutine_Undelegate(gen);
22998  __Pyx_PyGen__FetchStopIterationValue(__Pyx_PyThreadState_Current, &val);
22999  ret = __Pyx_Coroutine_SendEx(gen, val, 0);
23000  Py_XDECREF(val);
23001  return ret;
23002 }
23003 static PyObject *__Pyx_Coroutine_Send(PyObject *self, PyObject *value) {
23004  PyObject *retval;
23005  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject*) self;
23006  PyObject *yf = gen->yieldfrom;
23007  if (unlikely(gen->is_running))
23008  return __Pyx_Coroutine_AlreadyRunningError(gen);
23009  if (yf) {
23010  PyObject *ret;
23011  gen->is_running = 1;
23012  #ifdef __Pyx_Generator_USED
23013  if (__Pyx_Generator_CheckExact(yf)) {
23014  ret = __Pyx_Coroutine_Send(yf, value);
23015  } else
23016  #endif
23017  #ifdef __Pyx_Coroutine_USED
23018  if (__Pyx_Coroutine_Check(yf)) {
23019  ret = __Pyx_Coroutine_Send(yf, value);
23020  } else
23021  #endif
23022  #ifdef __Pyx_AsyncGen_USED
23023  if (__pyx_PyAsyncGenASend_CheckExact(yf)) {
23024  ret = __Pyx_async_gen_asend_send(yf, value);
23025  } else
23026  #endif
23027  #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x03030000 && (defined(__linux__) || PY_VERSION_HEX >= 0x030600B3)
23028  if (PyGen_CheckExact(yf)) {
23029  ret = _PyGen_Send((PyGenObject*)yf, value == Py_None ? NULL : value);
23030  } else
23031  #endif
23032  #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x03050000 && defined(PyCoro_CheckExact) && (defined(__linux__) || PY_VERSION_HEX >= 0x030600B3)
23033  if (PyCoro_CheckExact(yf)) {
23034  ret = _PyGen_Send((PyGenObject*)yf, value == Py_None ? NULL : value);
23035  } else
23036  #endif
23037  {
23038  if (value == Py_None)
23039  ret = Py_TYPE(yf)->tp_iternext(yf);
23040  else
23041  ret = __Pyx_PyObject_CallMethod1(yf, __pyx_n_s_send, value);
23042  }
23043  gen->is_running = 0;
23044  if (likely(ret)) {
23045  return ret;
23046  }
23047  retval = __Pyx_Coroutine_FinishDelegation(gen);
23048  } else {
23049  retval = __Pyx_Coroutine_SendEx(gen, value, 0);
23050  }
23051  return __Pyx_Coroutine_MethodReturn(self, retval);
23052 }
23053 static int __Pyx_Coroutine_CloseIter(__pyx_CoroutineObject *gen, PyObject *yf) {
23054  PyObject *retval = NULL;
23055  int err = 0;
23056  #ifdef __Pyx_Generator_USED
23057  if (__Pyx_Generator_CheckExact(yf)) {
23058  retval = __Pyx_Coroutine_Close(yf);
23059  if (!retval)
23060  return -1;
23061  } else
23062  #endif
23063  #ifdef __Pyx_Coroutine_USED
23064  if (__Pyx_Coroutine_Check(yf)) {
23065  retval = __Pyx_Coroutine_Close(yf);
23066  if (!retval)
23067  return -1;
23068  } else
23069  if (__Pyx_CoroutineAwait_CheckExact(yf)) {
23070  retval = __Pyx_CoroutineAwait_Close((__pyx_CoroutineAwaitObject*)yf, NULL);
23071  if (!retval)
23072  return -1;
23073  } else
23074  #endif
23075  #ifdef __Pyx_AsyncGen_USED
23076  if (__pyx_PyAsyncGenASend_CheckExact(yf)) {
23077  retval = __Pyx_async_gen_asend_close(yf, NULL);
23078  } else
23079  if (__pyx_PyAsyncGenAThrow_CheckExact(yf)) {
23080  retval = __Pyx_async_gen_athrow_close(yf, NULL);
23081  } else
23082  #endif
23083  {
23084  PyObject *meth;
23085  gen->is_running = 1;
23086  meth = __Pyx_PyObject_GetAttrStr(yf, __pyx_n_s_close);
23087  if (unlikely(!meth)) {
23088  if (!PyErr_ExceptionMatches(PyExc_AttributeError)) {
23089  PyErr_WriteUnraisable(yf);
23090  }
23091  PyErr_Clear();
23092  } else {
23093  retval = PyObject_CallFunction(meth, NULL);
23094  Py_DECREF(meth);
23095  if (!retval)
23096  err = -1;
23097  }
23098  gen->is_running = 0;
23099  }
23100  Py_XDECREF(retval);
23101  return err;
23102 }
23103 static PyObject *__Pyx_Generator_Next(PyObject *self) {
23104  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject*) self;
23105  PyObject *yf = gen->yieldfrom;
23106  if (unlikely(gen->is_running))
23107  return __Pyx_Coroutine_AlreadyRunningError(gen);
23108  if (yf) {
23109  PyObject *ret;
23110  gen->is_running = 1;
23111  #ifdef __Pyx_Generator_USED
23112  if (__Pyx_Generator_CheckExact(yf)) {
23113  ret = __Pyx_Generator_Next(yf);
23114  } else
23115  #endif
23116  #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x03030000 && (defined(__linux__) || PY_VERSION_HEX >= 0x030600B3)
23117  if (PyGen_CheckExact(yf)) {
23118  ret = _PyGen_Send((PyGenObject*)yf, NULL);
23119  } else
23120  #endif
23121  #ifdef __Pyx_Coroutine_USED
23122  if (__Pyx_Coroutine_Check(yf)) {
23123  ret = __Pyx_Coroutine_Send(yf, Py_None);
23124  } else
23125  #endif
23126  ret = Py_TYPE(yf)->tp_iternext(yf);
23127  gen->is_running = 0;
23128  if (likely(ret)) {
23129  return ret;
23130  }
23131  return __Pyx_Coroutine_FinishDelegation(gen);
23132  }
23133  return __Pyx_Coroutine_SendEx(gen, Py_None, 0);
23134 }
23135 static PyObject *__Pyx_Coroutine_Close_Method(PyObject *self, CYTHON_UNUSED PyObject *arg) {
23136  return __Pyx_Coroutine_Close(self);
23137 }
23138 static PyObject *__Pyx_Coroutine_Close(PyObject *self) {
23139  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
23140  PyObject *retval, *raised_exception;
23141  PyObject *yf = gen->yieldfrom;
23142  int err = 0;
23143  if (unlikely(gen->is_running))
23144  return __Pyx_Coroutine_AlreadyRunningError(gen);
23145  if (yf) {
23146  Py_INCREF(yf);
23147  err = __Pyx_Coroutine_CloseIter(gen, yf);
23148  __Pyx_Coroutine_Undelegate(gen);
23149  Py_DECREF(yf);
23150  }
23151  if (err == 0)
23152  PyErr_SetNone(PyExc_GeneratorExit);
23153  retval = __Pyx_Coroutine_SendEx(gen, NULL, 1);
23154  if (unlikely(retval)) {
23155  const char *msg;
23156  Py_DECREF(retval);
23157  if ((0)) {
23158  #ifdef __Pyx_Coroutine_USED
23159  } else if (__Pyx_Coroutine_Check(self)) {
23160  msg = "coroutine ignored GeneratorExit";
23161  #endif
23162  #ifdef __Pyx_AsyncGen_USED
23163  } else if (__Pyx_AsyncGen_CheckExact(self)) {
23164 #if PY_VERSION_HEX < 0x03060000
23165  msg = "async generator ignored GeneratorExit - might require Python 3.6+ finalisation (PEP 525)";
23166 #else
23167  msg = "async generator ignored GeneratorExit";
23168 #endif
23169  #endif
23170  } else {
23171  msg = "generator ignored GeneratorExit";
23172  }
23173  PyErr_SetString(PyExc_RuntimeError, msg);
23174  return NULL;
23175  }
23176  raised_exception = PyErr_Occurred();
23177  if (likely(!raised_exception || __Pyx_PyErr_GivenExceptionMatches2(raised_exception, PyExc_GeneratorExit, PyExc_StopIteration))) {
23178  if (raised_exception) PyErr_Clear();
23179  Py_INCREF(Py_None);
23180  return Py_None;
23181  }
23182  return NULL;
23183 }
23184 static PyObject *__Pyx__Coroutine_Throw(PyObject *self, PyObject *typ, PyObject *val, PyObject *tb,
23185  PyObject *args, int close_on_genexit) {
23186  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
23187  PyObject *yf = gen->yieldfrom;
23188  if (unlikely(gen->is_running))
23189  return __Pyx_Coroutine_AlreadyRunningError(gen);
23190  if (yf) {
23191  PyObject *ret;
23192  Py_INCREF(yf);
23193  if (__Pyx_PyErr_GivenExceptionMatches(typ, PyExc_GeneratorExit) && close_on_genexit) {
23194  int err = __Pyx_Coroutine_CloseIter(gen, yf);
23195  Py_DECREF(yf);
23196  __Pyx_Coroutine_Undelegate(gen);
23197  if (err < 0)
23198  return __Pyx_Coroutine_MethodReturn(self, __Pyx_Coroutine_SendEx(gen, NULL, 0));
23199  goto throw_here;
23200  }
23201  gen->is_running = 1;
23202  if (0
23203  #ifdef __Pyx_Generator_USED
23204  || __Pyx_Generator_CheckExact(yf)
23205  #endif
23206  #ifdef __Pyx_Coroutine_USED
23207  || __Pyx_Coroutine_Check(yf)
23208  #endif
23209  ) {
23210  ret = __Pyx__Coroutine_Throw(yf, typ, val, tb, args, close_on_genexit);
23211  #ifdef __Pyx_Coroutine_USED
23212  } else if (__Pyx_CoroutineAwait_CheckExact(yf)) {
23213  ret = __Pyx__Coroutine_Throw(((__pyx_CoroutineAwaitObject*)yf)->coroutine, typ, val, tb, args, close_on_genexit);
23214  #endif
23215  } else {
23216  PyObject *meth = __Pyx_PyObject_GetAttrStr(yf, __pyx_n_s_throw);
23217  if (unlikely(!meth)) {
23218  Py_DECREF(yf);
23219  if (!PyErr_ExceptionMatches(PyExc_AttributeError)) {
23220  gen->is_running = 0;
23221  return NULL;
23222  }
23223  PyErr_Clear();
23224  __Pyx_Coroutine_Undelegate(gen);
23225  gen->is_running = 0;
23226  goto throw_here;
23227  }
23228  if (likely(args)) {
23229  ret = PyObject_CallObject(meth, args);
23230  } else {
23231  ret = PyObject_CallFunctionObjArgs(meth, typ, val, tb, NULL);
23232  }
23233  Py_DECREF(meth);
23234  }
23235  gen->is_running = 0;
23236  Py_DECREF(yf);
23237  if (!ret) {
23238  ret = __Pyx_Coroutine_FinishDelegation(gen);
23239  }
23240  return __Pyx_Coroutine_MethodReturn(self, ret);
23241  }
23242 throw_here:
23243  __Pyx_Raise(typ, val, tb, NULL);
23244  return __Pyx_Coroutine_MethodReturn(self, __Pyx_Coroutine_SendEx(gen, NULL, 0));
23245 }
23246 static PyObject *__Pyx_Coroutine_Throw(PyObject *self, PyObject *args) {
23247  PyObject *typ;
23248  PyObject *val = NULL;
23249  PyObject *tb = NULL;
23250  if (!PyArg_UnpackTuple(args, (char *)"throw", 1, 3, &typ, &val, &tb))
23251  return NULL;
23252  return __Pyx__Coroutine_Throw(self, typ, val, tb, args, 1);
23253 }
23254 static CYTHON_INLINE int __Pyx_Coroutine_traverse_excstate(__Pyx_ExcInfoStruct *exc_state, visitproc visit, void *arg) {
23255  Py_VISIT(exc_state->exc_type);
23256  Py_VISIT(exc_state->exc_value);
23257  Py_VISIT(exc_state->exc_traceback);
23258  return 0;
23259 }
23260 static int __Pyx_Coroutine_traverse(__pyx_CoroutineObject *gen, visitproc visit, void *arg) {
23261  Py_VISIT(gen->closure);
23262  Py_VISIT(gen->classobj);
23263  Py_VISIT(gen->yieldfrom);
23264  return __Pyx_Coroutine_traverse_excstate(&gen->gi_exc_state, visit, arg);
23265 }
23266 static int __Pyx_Coroutine_clear(PyObject *self) {
23267  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
23268  Py_CLEAR(gen->closure);
23269  Py_CLEAR(gen->classobj);
23270  Py_CLEAR(gen->yieldfrom);
23271  __Pyx_Coroutine_ExceptionClear(&gen->gi_exc_state);
23272 #ifdef __Pyx_AsyncGen_USED
23273  if (__Pyx_AsyncGen_CheckExact(self)) {
23274  Py_CLEAR(((__pyx_PyAsyncGenObject*)gen)->ag_finalizer);
23275  }
23276 #endif
23277  Py_CLEAR(gen->gi_code);
23278  Py_CLEAR(gen->gi_name);
23279  Py_CLEAR(gen->gi_qualname);
23280  Py_CLEAR(gen->gi_modulename);
23281  return 0;
23282 }
23283 static void __Pyx_Coroutine_dealloc(PyObject *self) {
23284  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
23285  PyObject_GC_UnTrack(gen);
23286  if (gen->gi_weakreflist != NULL)
23287  PyObject_ClearWeakRefs(self);
23288  if (gen->resume_label >= 0) {
23289  PyObject_GC_Track(self);
23290 #if PY_VERSION_HEX >= 0x030400a1 && CYTHON_USE_TP_FINALIZE
23291  if (PyObject_CallFinalizerFromDealloc(self))
23292 #else
23293  Py_TYPE(gen)->tp_del(self);
23294  if (self->ob_refcnt > 0)
23295 #endif
23296  {
23297  return;
23298  }
23299  PyObject_GC_UnTrack(self);
23300  }
23301 #ifdef __Pyx_AsyncGen_USED
23302  if (__Pyx_AsyncGen_CheckExact(self)) {
23303  /* We have to handle this case for asynchronous generators
23304  right here, because this code has to be between UNTRACK
23305  and GC_Del. */
23306  Py_CLEAR(((__pyx_PyAsyncGenObject*)self)->ag_finalizer);
23307  }
23308 #endif
23309  __Pyx_Coroutine_clear(self);
23310  PyObject_GC_Del(gen);
23311 }
23312 static void __Pyx_Coroutine_del(PyObject *self) {
23313  PyObject *error_type, *error_value, *error_traceback;
23314  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
23315  __Pyx_PyThreadState_declare
23316  if (gen->resume_label < 0) {
23317  return;
23318  }
23319 #if !CYTHON_USE_TP_FINALIZE
23320  assert(self->ob_refcnt == 0);
23321  self->ob_refcnt = 1;
23322 #endif
23323  __Pyx_PyThreadState_assign
23324  __Pyx_ErrFetch(&error_type, &error_value, &error_traceback);
23325 #ifdef __Pyx_AsyncGen_USED
23326  if (__Pyx_AsyncGen_CheckExact(self)) {
23327  __pyx_PyAsyncGenObject *agen = (__pyx_PyAsyncGenObject*)self;
23328  PyObject *finalizer = agen->ag_finalizer;
23329  if (finalizer && !agen->ag_closed) {
23330  PyObject *res = __Pyx_PyObject_CallOneArg(finalizer, self);
23331  if (unlikely(!res)) {
23332  PyErr_WriteUnraisable(self);
23333  } else {
23334  Py_DECREF(res);
23335  }
23336  __Pyx_ErrRestore(error_type, error_value, error_traceback);
23337  return;
23338  }
23339  }
23340 #endif
23341  if (unlikely(gen->resume_label == 0 && !error_value)) {
23342 #ifdef __Pyx_Coroutine_USED
23343 #ifdef __Pyx_Generator_USED
23344  if (!__Pyx_Generator_CheckExact(self))
23345 #endif
23346  {
23347  PyObject_GC_UnTrack(self);
23348 #if PY_MAJOR_VERSION >= 3 || defined(PyErr_WarnFormat)
23349  if (unlikely(PyErr_WarnFormat(PyExc_RuntimeWarning, 1, "coroutine '%.50S' was never awaited", gen->gi_qualname) < 0))
23350  PyErr_WriteUnraisable(self);
23351 #else
23352  {PyObject *msg;
23353  char *cmsg;
23354  #if CYTHON_COMPILING_IN_PYPY
23355  msg = NULL;
23356  cmsg = (char*) "coroutine was never awaited";
23357  #else
23358  char *cname;
23359  PyObject *qualname;
23360  qualname = gen->gi_qualname;
23361  cname = PyString_AS_STRING(qualname);
23362  msg = PyString_FromFormat("coroutine '%.50s' was never awaited", cname);
23363  if (unlikely(!msg)) {
23364  PyErr_Clear();
23365  cmsg = (char*) "coroutine was never awaited";
23366  } else {
23367  cmsg = PyString_AS_STRING(msg);
23368  }
23369  #endif
23370  if (unlikely(PyErr_WarnEx(PyExc_RuntimeWarning, cmsg, 1) < 0))
23371  PyErr_WriteUnraisable(self);
23372  Py_XDECREF(msg);}
23373 #endif
23374  PyObject_GC_Track(self);
23375  }
23376 #endif
23377  } else {
23378  PyObject *res = __Pyx_Coroutine_Close(self);
23379  if (unlikely(!res)) {
23380  if (PyErr_Occurred())
23381  PyErr_WriteUnraisable(self);
23382  } else {
23383  Py_DECREF(res);
23384  }
23385  }
23386  __Pyx_ErrRestore(error_type, error_value, error_traceback);
23387 #if !CYTHON_USE_TP_FINALIZE
23388  assert(self->ob_refcnt > 0);
23389  if (--self->ob_refcnt == 0) {
23390  return;
23391  }
23392  {
23393  Py_ssize_t refcnt = self->ob_refcnt;
23394  _Py_NewReference(self);
23395  self->ob_refcnt = refcnt;
23396  }
23397 #if CYTHON_COMPILING_IN_CPYTHON
23398  assert(PyType_IS_GC(self->ob_type) &&
23399  _Py_AS_GC(self)->gc.gc_refs != _PyGC_REFS_UNTRACKED);
23400  _Py_DEC_REFTOTAL;
23401 #endif
23402 #ifdef COUNT_ALLOCS
23403  --Py_TYPE(self)->tp_frees;
23404  --Py_TYPE(self)->tp_allocs;
23405 #endif
23406 #endif
23407 }
23408 static PyObject *
23409 __Pyx_Coroutine_get_name(__pyx_CoroutineObject *self, CYTHON_UNUSED void *context)
23410 {
23411  PyObject *name = self->gi_name;
23412  if (unlikely(!name)) name = Py_None;
23413  Py_INCREF(name);
23414  return name;
23415 }
23416 static int
23417 __Pyx_Coroutine_set_name(__pyx_CoroutineObject *self, PyObject *value, CYTHON_UNUSED void *context)
23418 {
23419  PyObject *tmp;
23420 #if PY_MAJOR_VERSION >= 3
23421  if (unlikely(value == NULL || !PyUnicode_Check(value)))
23422 #else
23423  if (unlikely(value == NULL || !PyString_Check(value)))
23424 #endif
23425  {
23426  PyErr_SetString(PyExc_TypeError,
23427  "__name__ must be set to a string object");
23428  return -1;
23429  }
23430  tmp = self->gi_name;
23431  Py_INCREF(value);
23432  self->gi_name = value;
23433  Py_XDECREF(tmp);
23434  return 0;
23435 }
23436 static PyObject *
23437 __Pyx_Coroutine_get_qualname(__pyx_CoroutineObject *self, CYTHON_UNUSED void *context)
23438 {
23439  PyObject *name = self->gi_qualname;
23440  if (unlikely(!name)) name = Py_None;
23441  Py_INCREF(name);
23442  return name;
23443 }
23444 static int
23445 __Pyx_Coroutine_set_qualname(__pyx_CoroutineObject *self, PyObject *value, CYTHON_UNUSED void *context)
23446 {
23447  PyObject *tmp;
23448 #if PY_MAJOR_VERSION >= 3
23449  if (unlikely(value == NULL || !PyUnicode_Check(value)))
23450 #else
23451  if (unlikely(value == NULL || !PyString_Check(value)))
23452 #endif
23453  {
23454  PyErr_SetString(PyExc_TypeError,
23455  "__qualname__ must be set to a string object");
23456  return -1;
23457  }
23458  tmp = self->gi_qualname;
23459  Py_INCREF(value);
23460  self->gi_qualname = value;
23461  Py_XDECREF(tmp);
23462  return 0;
23463 }
23464 static __pyx_CoroutineObject *__Pyx__Coroutine_New(
23465  PyTypeObject* type, __pyx_coroutine_body_t body, PyObject *code, PyObject *closure,
23466  PyObject *name, PyObject *qualname, PyObject *module_name) {
23467  __pyx_CoroutineObject *gen = PyObject_GC_New(__pyx_CoroutineObject, type);
23468  if (unlikely(!gen))
23469  return NULL;
23470  return __Pyx__Coroutine_NewInit(gen, body, code, closure, name, qualname, module_name);
23471 }
23472 static __pyx_CoroutineObject *__Pyx__Coroutine_NewInit(
23473  __pyx_CoroutineObject *gen, __pyx_coroutine_body_t body, PyObject *code, PyObject *closure,
23474  PyObject *name, PyObject *qualname, PyObject *module_name) {
23475  gen->body = body;
23476  gen->closure = closure;
23477  Py_XINCREF(closure);
23478  gen->is_running = 0;
23479  gen->resume_label = 0;
23480  gen->classobj = NULL;
23481  gen->yieldfrom = NULL;
23482  gen->gi_exc_state.exc_type = NULL;
23483  gen->gi_exc_state.exc_value = NULL;
23484  gen->gi_exc_state.exc_traceback = NULL;
23485 #if CYTHON_USE_EXC_INFO_STACK
23486  gen->gi_exc_state.previous_item = NULL;
23487 #endif
23488  gen->gi_weakreflist = NULL;
23489  Py_XINCREF(qualname);
23490  gen->gi_qualname = qualname;
23491  Py_XINCREF(name);
23492  gen->gi_name = name;
23493  Py_XINCREF(module_name);
23494  gen->gi_modulename = module_name;
23495  Py_XINCREF(code);
23496  gen->gi_code = code;
23497  PyObject_GC_Track(gen);
23498  return gen;
23499 }
23500 
23501 /* PatchModuleWithCoroutine */
23502  static PyObject* __Pyx_Coroutine_patch_module(PyObject* module, const char* py_code) {
23503 #if defined(__Pyx_Generator_USED) || defined(__Pyx_Coroutine_USED)
23504  int result;
23505  PyObject *globals, *result_obj;
23506  globals = PyDict_New(); if (unlikely(!globals)) goto ignore;
23507  result = PyDict_SetItemString(globals, "_cython_coroutine_type",
23508  #ifdef __Pyx_Coroutine_USED
23509  (PyObject*)__pyx_CoroutineType);
23510  #else
23511  Py_None);
23512  #endif
23513  if (unlikely(result < 0)) goto ignore;
23514  result = PyDict_SetItemString(globals, "_cython_generator_type",
23515  #ifdef __Pyx_Generator_USED
23516  (PyObject*)__pyx_GeneratorType);
23517  #else
23518  Py_None);
23519  #endif
23520  if (unlikely(result < 0)) goto ignore;
23521  if (unlikely(PyDict_SetItemString(globals, "_module", module) < 0)) goto ignore;
23522  if (unlikely(PyDict_SetItemString(globals, "__builtins__", __pyx_b) < 0)) goto ignore;
23523  result_obj = PyRun_String(py_code, Py_file_input, globals, globals);
23524  if (unlikely(!result_obj)) goto ignore;
23525  Py_DECREF(result_obj);
23526  Py_DECREF(globals);
23527  return module;
23528 ignore:
23529  Py_XDECREF(globals);
23530  PyErr_WriteUnraisable(module);
23531  if (unlikely(PyErr_WarnEx(PyExc_RuntimeWarning, "Cython module failed to patch module with custom type", 1) < 0)) {
23532  Py_DECREF(module);
23533  module = NULL;
23534  }
23535 #else
23536  py_code++;
23537 #endif
23538  return module;
23539 }
23540 
23541 /* PatchGeneratorABC */
23542  #ifndef CYTHON_REGISTER_ABCS
23543 #define CYTHON_REGISTER_ABCS 1
23544 #endif
23545 #if defined(__Pyx_Generator_USED) || defined(__Pyx_Coroutine_USED)
23546 static PyObject* __Pyx_patch_abc_module(PyObject *module);
23547 static PyObject* __Pyx_patch_abc_module(PyObject *module) {
23548  module = __Pyx_Coroutine_patch_module(
23549  module, ""
23550 "if _cython_generator_type is not None:\n"
23551 " try: Generator = _module.Generator\n"
23552 " except AttributeError: pass\n"
23553 " else: Generator.register(_cython_generator_type)\n"
23554 "if _cython_coroutine_type is not None:\n"
23555 " try: Coroutine = _module.Coroutine\n"
23556 " except AttributeError: pass\n"
23557 " else: Coroutine.register(_cython_coroutine_type)\n"
23558  );
23559  return module;
23560 }
23561 #endif
23562 static int __Pyx_patch_abc(void) {
23563 #if defined(__Pyx_Generator_USED) || defined(__Pyx_Coroutine_USED)
23564  static int abc_patched = 0;
23565  if (CYTHON_REGISTER_ABCS && !abc_patched) {
23566  PyObject *module;
23567  module = PyImport_ImportModule((PY_MAJOR_VERSION >= 3) ? "collections.abc" : "collections");
23568  if (!module) {
23569  PyErr_WriteUnraisable(NULL);
23570  if (unlikely(PyErr_WarnEx(PyExc_RuntimeWarning,
23571  ((PY_MAJOR_VERSION >= 3) ?
23572  "Cython module failed to register with collections.abc module" :
23573  "Cython module failed to register with collections module"), 1) < 0)) {
23574  return -1;
23575  }
23576  } else {
23577  module = __Pyx_patch_abc_module(module);
23578  abc_patched = 1;
23579  if (unlikely(!module))
23580  return -1;
23581  Py_DECREF(module);
23582  }
23583  module = PyImport_ImportModule("backports_abc");
23584  if (module) {
23585  module = __Pyx_patch_abc_module(module);
23586  Py_XDECREF(module);
23587  }
23588  if (!module) {
23589  PyErr_Clear();
23590  }
23591  }
23592 #else
23593  if ((0)) __Pyx_Coroutine_patch_module(NULL, NULL);
23594 #endif
23595  return 0;
23596 }
23597 
23598 /* Generator */
23599  static PyMethodDef __pyx_Generator_methods[] = {
23600  {"send", (PyCFunction) __Pyx_Coroutine_Send, METH_O,
23601  (char*) PyDoc_STR("send(arg) -> send 'arg' into generator,\nreturn next yielded value or raise StopIteration.")},
23602  {"throw", (PyCFunction) __Pyx_Coroutine_Throw, METH_VARARGS,
23603  (char*) PyDoc_STR("throw(typ[,val[,tb]]) -> raise exception in generator,\nreturn next yielded value or raise StopIteration.")},
23604  {"close", (PyCFunction) __Pyx_Coroutine_Close_Method, METH_NOARGS,
23605  (char*) PyDoc_STR("close() -> raise GeneratorExit inside generator.")},
23606  {0, 0, 0, 0}
23607 };
23608 static PyMemberDef __pyx_Generator_memberlist[] = {
23609  {(char *) "gi_running", T_BOOL, offsetof(__pyx_CoroutineObject, is_running), READONLY, NULL},
23610  {(char*) "gi_yieldfrom", T_OBJECT, offsetof(__pyx_CoroutineObject, yieldfrom), READONLY,
23611  (char*) PyDoc_STR("object being iterated by 'yield from', or None")},
23612  {(char*) "gi_code", T_OBJECT, offsetof(__pyx_CoroutineObject, gi_code), READONLY, NULL},
23613  {0, 0, 0, 0, 0}
23614 };
23615 static PyGetSetDef __pyx_Generator_getsets[] = {
23616  {(char *) "__name__", (getter)__Pyx_Coroutine_get_name, (setter)__Pyx_Coroutine_set_name,
23617  (char*) PyDoc_STR("name of the generator"), 0},
23618  {(char *) "__qualname__", (getter)__Pyx_Coroutine_get_qualname, (setter)__Pyx_Coroutine_set_qualname,
23619  (char*) PyDoc_STR("qualified name of the generator"), 0},
23620  {0, 0, 0, 0, 0}
23621 };
23622 static PyTypeObject __pyx_GeneratorType_type = {
23623  PyVarObject_HEAD_INIT(0, 0)
23624  "generator",
23625  sizeof(__pyx_CoroutineObject),
23626  0,
23627  (destructor) __Pyx_Coroutine_dealloc,
23628  0,
23629  0,
23630  0,
23631  0,
23632  0,
23633  0,
23634  0,
23635  0,
23636  0,
23637  0,
23638  0,
23639  0,
23640  0,
23641  0,
23642  Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC | Py_TPFLAGS_HAVE_FINALIZE,
23643  0,
23644  (traverseproc) __Pyx_Coroutine_traverse,
23645  0,
23646  0,
23647  offsetof(__pyx_CoroutineObject, gi_weakreflist),
23648  0,
23649  (iternextfunc) __Pyx_Generator_Next,
23650  __pyx_Generator_methods,
23651  __pyx_Generator_memberlist,
23652  __pyx_Generator_getsets,
23653  0,
23654  0,
23655  0,
23656  0,
23657  0,
23658  0,
23659  0,
23660  0,
23661  0,
23662  0,
23663  0,
23664  0,
23665  0,
23666  0,
23667  0,
23668 #if CYTHON_USE_TP_FINALIZE
23669  0,
23670 #else
23671  __Pyx_Coroutine_del,
23672 #endif
23673  0,
23674 #if CYTHON_USE_TP_FINALIZE
23675  __Pyx_Coroutine_del,
23676 #elif PY_VERSION_HEX >= 0x030400a1
23677  0,
23678 #endif
23679 };
23680 static int __pyx_Generator_init(void) {
23681  __pyx_GeneratorType_type.tp_getattro = __Pyx_PyObject_GenericGetAttrNoDict;
23682  __pyx_GeneratorType_type.tp_iter = PyObject_SelfIter;
23683  __pyx_GeneratorType = __Pyx_FetchCommonType(&__pyx_GeneratorType_type);
23684  if (unlikely(!__pyx_GeneratorType)) {
23685  return -1;
23686  }
23687  return 0;
23688 }
23689 
23690 /* CheckBinaryVersion */
23691  static int __Pyx_check_binary_version(void) {
23692  char ctversion[4], rtversion[4];
23693  PyOS_snprintf(ctversion, 4, "%d.%d", PY_MAJOR_VERSION, PY_MINOR_VERSION);
23694  PyOS_snprintf(rtversion, 4, "%s", Py_GetVersion());
23695  if (ctversion[0] != rtversion[0] || ctversion[2] != rtversion[2]) {
23696  char message[200];
23697  PyOS_snprintf(message, sizeof(message),
23698  "compiletime version %s of module '%.100s' "
23699  "does not match runtime version %s",
23700  ctversion, __Pyx_MODULE_NAME, rtversion);
23701  return PyErr_WarnEx(NULL, message, 1);
23702  }
23703  return 0;
23704 }
23705 
23706 /* InitStrings */
23707  static int __Pyx_InitStrings(__Pyx_StringTabEntry *t) {
23708  while (t->p) {
23709  #if PY_MAJOR_VERSION < 3
23710  if (t->is_unicode) {
23711  *t->p = PyUnicode_DecodeUTF8(t->s, t->n - 1, NULL);
23712  } else if (t->intern) {
23713  *t->p = PyString_InternFromString(t->s);
23714  } else {
23715  *t->p = PyString_FromStringAndSize(t->s, t->n - 1);
23716  }
23717  #else
23718  if (t->is_unicode | t->is_str) {
23719  if (t->intern) {
23720  *t->p = PyUnicode_InternFromString(t->s);
23721  } else if (t->encoding) {
23722  *t->p = PyUnicode_Decode(t->s, t->n - 1, t->encoding, NULL);
23723  } else {
23724  *t->p = PyUnicode_FromStringAndSize(t->s, t->n - 1);
23725  }
23726  } else {
23727  *t->p = PyBytes_FromStringAndSize(t->s, t->n - 1);
23728  }
23729  #endif
23730  if (!*t->p)
23731  return -1;
23732  if (PyObject_Hash(*t->p) == -1)
23733  return -1;
23734  ++t;
23735  }
23736  return 0;
23737 }
23738 
23739 static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char* c_str) {
23740  return __Pyx_PyUnicode_FromStringAndSize(c_str, (Py_ssize_t)strlen(c_str));
23741 }
23742 static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject* o) {
23743  Py_ssize_t ignore;
23744  return __Pyx_PyObject_AsStringAndSize(o, &ignore);
23745 }
23746 #if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
23747 #if !CYTHON_PEP393_ENABLED
23748 static const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
23749  char* defenc_c;
23750  PyObject* defenc = _PyUnicode_AsDefaultEncodedString(o, NULL);
23751  if (!defenc) return NULL;
23752  defenc_c = PyBytes_AS_STRING(defenc);
23753 #if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
23754  {
23755  char* end = defenc_c + PyBytes_GET_SIZE(defenc);
23756  char* c;
23757  for (c = defenc_c; c < end; c++) {
23758  if ((unsigned char) (*c) >= 128) {
23759  PyUnicode_AsASCIIString(o);
23760  return NULL;
23761  }
23762  }
23763  }
23764 #endif
23765  *length = PyBytes_GET_SIZE(defenc);
23766  return defenc_c;
23767 }
23768 #else
23769 static CYTHON_INLINE const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
23770  if (unlikely(__Pyx_PyUnicode_READY(o) == -1)) return NULL;
23771 #if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
23772  if (likely(PyUnicode_IS_ASCII(o))) {
23773  *length = PyUnicode_GET_LENGTH(o);
23774  return PyUnicode_AsUTF8(o);
23775  } else {
23776  PyUnicode_AsASCIIString(o);
23777  return NULL;
23778  }
23779 #else
23780  return PyUnicode_AsUTF8AndSize(o, length);
23781 #endif
23782 }
23783 #endif
23784 #endif
23785 static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
23786 #if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
23787  if (
23788 #if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
23789  __Pyx_sys_getdefaultencoding_not_ascii &&
23790 #endif
23791  PyUnicode_Check(o)) {
23792  return __Pyx_PyUnicode_AsStringAndSize(o, length);
23793  } else
23794 #endif
23795 #if (!CYTHON_COMPILING_IN_PYPY) || (defined(PyByteArray_AS_STRING) && defined(PyByteArray_GET_SIZE))
23796  if (PyByteArray_Check(o)) {
23797  *length = PyByteArray_GET_SIZE(o);
23798  return PyByteArray_AS_STRING(o);
23799  } else
23800 #endif
23801  {
23802  char* result;
23803  int r = PyBytes_AsStringAndSize(o, &result, length);
23804  if (unlikely(r < 0)) {
23805  return NULL;
23806  } else {
23807  return result;
23808  }
23809  }
23810 }
23811 static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) {
23812  int is_true = x == Py_True;
23813  if (is_true | (x == Py_False) | (x == Py_None)) return is_true;
23814  else return PyObject_IsTrue(x);
23815 }
23816 static CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject* x) {
23817  int retval;
23818  if (unlikely(!x)) return -1;
23819  retval = __Pyx_PyObject_IsTrue(x);
23820  Py_DECREF(x);
23821  return retval;
23822 }
23823 static PyObject* __Pyx_PyNumber_IntOrLongWrongResultType(PyObject* result, const char* type_name) {
23824 #if PY_MAJOR_VERSION >= 3
23825  if (PyLong_Check(result)) {
23826  if (PyErr_WarnFormat(PyExc_DeprecationWarning, 1,
23827  "__int__ returned non-int (type %.200s). "
23828  "The ability to return an instance of a strict subclass of int "
23829  "is deprecated, and may be removed in a future version of Python.",
23830  Py_TYPE(result)->tp_name)) {
23831  Py_DECREF(result);
23832  return NULL;
23833  }
23834  return result;
23835  }
23836 #endif
23837  PyErr_Format(PyExc_TypeError,
23838  "__%.4s__ returned non-%.4s (type %.200s)",
23839  type_name, type_name, Py_TYPE(result)->tp_name);
23840  Py_DECREF(result);
23841  return NULL;
23842 }
23843 static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x) {
23844 #if CYTHON_USE_TYPE_SLOTS
23845  PyNumberMethods *m;
23846 #endif
23847  const char *name = NULL;
23848  PyObject *res = NULL;
23849 #if PY_MAJOR_VERSION < 3
23850  if (likely(PyInt_Check(x) || PyLong_Check(x)))
23851 #else
23852  if (likely(PyLong_Check(x)))
23853 #endif
23854  return __Pyx_NewRef(x);
23855 #if CYTHON_USE_TYPE_SLOTS
23856  m = Py_TYPE(x)->tp_as_number;
23857  #if PY_MAJOR_VERSION < 3
23858  if (m && m->nb_int) {
23859  name = "int";
23860  res = m->nb_int(x);
23861  }
23862  else if (m && m->nb_long) {
23863  name = "long";
23864  res = m->nb_long(x);
23865  }
23866  #else
23867  if (likely(m && m->nb_int)) {
23868  name = "int";
23869  res = m->nb_int(x);
23870  }
23871  #endif
23872 #else
23873  if (!PyBytes_CheckExact(x) && !PyUnicode_CheckExact(x)) {
23874  res = PyNumber_Int(x);
23875  }
23876 #endif
23877  if (likely(res)) {
23878 #if PY_MAJOR_VERSION < 3
23879  if (unlikely(!PyInt_Check(res) && !PyLong_Check(res))) {
23880 #else
23881  if (unlikely(!PyLong_CheckExact(res))) {
23882 #endif
23883  return __Pyx_PyNumber_IntOrLongWrongResultType(res, name);
23884  }
23885  }
23886  else if (!PyErr_Occurred()) {
23887  PyErr_SetString(PyExc_TypeError,
23888  "an integer is required");
23889  }
23890  return res;
23891 }
23892 static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject* b) {
23893  Py_ssize_t ival;
23894  PyObject *x;
23895 #if PY_MAJOR_VERSION < 3
23896  if (likely(PyInt_CheckExact(b))) {
23897  if (sizeof(Py_ssize_t) >= sizeof(long))
23898  return PyInt_AS_LONG(b);
23899  else
23900  return PyInt_AsSsize_t(b);
23901  }
23902 #endif
23903  if (likely(PyLong_CheckExact(b))) {
23904  #if CYTHON_USE_PYLONG_INTERNALS
23905  const digit* digits = ((PyLongObject*)b)->ob_digit;
23906  const Py_ssize_t size = Py_SIZE(b);
23907  if (likely(__Pyx_sst_abs(size) <= 1)) {
23908  ival = likely(size) ? digits[0] : 0;
23909  if (size == -1) ival = -ival;
23910  return ival;
23911  } else {
23912  switch (size) {
23913  case 2:
23914  if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
23915  return (Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
23916  }
23917  break;
23918  case -2:
23919  if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
23920  return -(Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
23921  }
23922  break;
23923  case 3:
23924  if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
23925  return (Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
23926  }
23927  break;
23928  case -3:
23929  if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
23930  return -(Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
23931  }
23932  break;
23933  case 4:
23934  if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
23935  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]));
23936  }
23937  break;
23938  case -4:
23939  if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
23940  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]));
23941  }
23942  break;
23943  }
23944  }
23945  #endif
23946  return PyLong_AsSsize_t(b);
23947  }
23948  x = PyNumber_Index(b);
23949  if (!x) return -1;
23950  ival = PyInt_AsSsize_t(x);
23951  Py_DECREF(x);
23952  return ival;
23953 }
23954 static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b) {
23955  return b ? __Pyx_NewRef(Py_True) : __Pyx_NewRef(Py_False);
23956 }
23957 static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) {
23958  return PyInt_FromSize_t(ival);
23959 }
23960 
23961 
23962 #endif /* Py_PYTHON_H */
glucat::compare
int compare(const index_set< LO, HI > &a, const index_set< LO, HI > &b)
"lexicographic compare" eg. {3,4,5} is less than {3,7,8}
Definition: index_set_imp.h:573
glucat::sqrt
const Multivector< Scalar_T, LO, HI > sqrt(const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false)
Square root of multivector with specified complexifier.
Definition: clifford_algebra_imp.h:589
clifford_to_str
String clifford_to_str(const Multivector_T &mv)
The "informal" string representation of Multivector_T mv.
Definition: PyClical.h:98
glucat::acosh
const Multivector< Scalar_T, LO, HI > acosh(const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false)
Inverse hyperbolic cosine of multivector with specified complexifier.
Definition: clifford_algebra_imp.h:738
index_set_to_repr
String index_set_to_repr(const Index_Set_T &ist)
The “official” string representation of Index_Set_T ist.
Definition: PyClical.h:69
glucat::sinh
const Multivector< Scalar_T, LO, HI > sinh(const Multivector< Scalar_T, LO, HI > &val)
Hyperbolic sine of multivector.
Definition: clifford_algebra_imp.h:826
IndexSet
index_set< lo_ndx, hi_ndx > IndexSet
Definition: PyClical.h:157
glucat::abs
Scalar_T abs(const Multivector< Scalar_T, LO, HI > &val)
Absolute value == sqrt(norm)
Definition: clifford_algebra_imp.h:491
glucat::log
const Multivector< Scalar_T, LO, HI > log(const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false)
Natural logarithm of multivector with specified complexifier.
Definition: clifford_algebra_imp.h:704
clifford_to_repr
String clifford_to_repr(const Multivector_T &mv)
The “official” string representation of Multivector_T mv.
Definition: PyClical.h:87
cga3::cga3
Multivector_T cga3(const Multivector_T &x)
Convert Euclidean 3D vector to Conformal Geometric Algebra null vector [DL (10.50)].
Definition: PyClical.h:115
glucat::sin
const Multivector< Scalar_T, LO, HI > sin(const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false)
Sine of multivector with specified complexifier.
Definition: clifford_algebra_imp.h:872
glucat::atanh
const Multivector< Scalar_T, LO, HI > atanh(const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false)
Inverse hyperbolic tangent of multivector with specified complexifier.
Definition: clifford_algebra_imp.h:952
glucat::exp
const framed_multi< Scalar_T, LO, HI > exp(const framed_multi< Scalar_T, LO, HI > &val)
Exponential of multivector.
Definition: framed_multi_imp.h:1947
glucat::cos
const Multivector< Scalar_T, LO, HI > cos(const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false)
Cosine of multivector with specified complexifier.
Definition: clifford_algebra_imp.h:765
glucat::tanh
const Multivector< Scalar_T, LO, HI > tanh(const Multivector< Scalar_T, LO, HI > &val)
Hyperbolic tangent of multivector.
Definition: clifford_algebra_imp.h:933
glucat::min_neg
index_t min_neg(const index_set< LO, HI > &ist)
Minimum negative index, or 0 if none.
Definition: index_set_imp.h:967
glucat::asin
const Multivector< Scalar_T, LO, HI > asin(const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false)
Inverse sine of multivector with specified complexifier.
Definition: clifford_algebra_imp.h:905
glucat::operator &
const Multivector< Scalar_T, LO, HI > operator &(const Multivector< Scalar_T, LO, HI > &lhs, const RHS< Scalar_T, LO, HI > &rhs)
Inner product.
Definition: clifford_algebra_imp.h:228
Clifford
matrix_multi< scalar_t > Clifford
Definition: PyClical.h:160
glucat::complexifier
const Multivector< Scalar_T, LO, HI > complexifier(const Multivector< Scalar_T, LO, HI > &val)
Square root of -1 which commutes with all members of the frame of the given multivector.
Definition: clifford_algebra_imp.h:506
PyFloat_FromDouble
PyObject * PyFloat_FromDouble(Scalar_T v)
Definition: PyClical.h:59
glucat::atan
const Multivector< Scalar_T, LO, HI > atan(const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false)
Inverse tangent of multivector with specified complexifier.
Definition: clifford_algebra_imp.h:1005
scalar_t
double scalar_t
Definition: PyClical.h:159
glucat::tan
const Multivector< Scalar_T, LO, HI > tan(const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false)
Tangent of multivector with specified complexifier.
Definition: clifford_algebra_imp.h:977
glucat::acos
const Multivector< Scalar_T, LO, HI > acos(const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false)
Inverse cosine of multivector with specified complexifier.
Definition: clifford_algebra_imp.h:798
index_set_to_str
String index_set_to_str(const Index_Set_T &ist)
The "informal" string representation of Index_Set_T ist.
Definition: PyClical.h:78
glucat::max_pos
index_t max_pos(const index_set< LO, HI > &ist)
Maximum positive index, or 0 if none.
Definition: index_set_imp.h:974
glucat::asinh
const Multivector< Scalar_T, LO, HI > asinh(const Multivector< Scalar_T, LO, HI > &val, const Multivector< Scalar_T, LO, HI > &i, const bool prechecked=false)
Inverse hyperbolic sine of multivector with specified complexifier.
Definition: clifford_algebra_imp.h:845
glucat::max_abs
Scalar_T max_abs(const Multivector< Scalar_T, LO, HI > &val)
Maximum of absolute values of components of multivector: multivector infinity norm.
Definition: clifford_algebra_imp.h:499
PyClical.e
def e(obj)
Definition: PyClical.pyx:1887
glucat::cosh
const Multivector< Scalar_T, LO, HI > cosh(const Multivector< Scalar_T, LO, HI > &val)
Hyperbolic cosine of multivector.
Definition: clifford_algebra_imp.h:720
cga3::cga3std
Multivector_T cga3std(const Multivector_T &X)
Convert CGA3 null vector to standard Conformal Geometric Algebra null vector [DL (10....
Definition: PyClical.h:126
cga3::agc3
Multivector_T agc3(const Multivector_T &X)
Convert CGA3 null vector to Euclidean 3D vector [DL (10.50)].
Definition: PyClical.h:138
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