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  "-fmessage-length=0",
19  "-grecord-gcc-switches",
20  "-O2",
21  "-Wall",
22  "-D_FORTIFY_SOURCE=2",
23  "-fstack-protector-strong",
24  "-funwind-tables",
25  "-fasynchronous-unwind-tables",
26  "-fstack-clash-protection",
27  "-g",
28  "-finline-limit=4000",
29  "--param",
30  "inline-unit-growth=200",
31  "-funroll-loops",
32  "-fvariable-expansion-in-unroller",
33  "-DNDEBUG",
34  "-DHAVE_BITS_WORDSIZE_H",
35  "-D_GLUCAT_USE_STD_UNORDERED_MAP",
36  "-D_GLUCAT_USE_DENSE_MATRICES",
37  "-D_GLUCAT_CHECK_ISNAN",
38  "-Wno-unused-local-typedefs",
39  "-Wno-misleading-indentation",
40  "-fno-check-new",
41  "-fexceptions"
42  ],
43  "include_dirs": [
44  ".",
45  ".."
46  ],
47  "language": "c++",
48  "name": "PyClical",
49  "sources": [
50  "PyClical.pyx"
51  ]
52  },
53  "module_name": "PyClical"
54 }
55 END: Cython Metadata */
56 
57 #define PY_SSIZE_T_CLEAN
58 #include "Python.h"
59 #ifndef Py_PYTHON_H
60  #error Python headers needed to compile C extensions, please install development version of Python.
61 #elif PY_VERSION_HEX < 0x02060000 || (0x03000000 <= PY_VERSION_HEX && PY_VERSION_HEX < 0x03030000)
62  #error Cython requires Python 2.6+ or Python 3.3+.
63 #else
64 #define CYTHON_ABI "0_29_6"
65 #define CYTHON_HEX_VERSION 0x001D06F0
66 #define CYTHON_FUTURE_DIVISION 0
67 #include <stddef.h>
68 #ifndef offsetof
69  #define offsetof(type, member) ( (size_t) & ((type*)0) -> member )
70 #endif
71 #if !defined(WIN32) && !defined(MS_WINDOWS)
72  #ifndef __stdcall
73  #define __stdcall
74  #endif
75  #ifndef __cdecl
76  #define __cdecl
77  #endif
78  #ifndef __fastcall
79  #define __fastcall
80  #endif
81 #endif
82 #ifndef DL_IMPORT
83  #define DL_IMPORT(t) t
84 #endif
85 #ifndef DL_EXPORT
86  #define DL_EXPORT(t) t
87 #endif
88 #define __PYX_COMMA ,
89 #ifndef HAVE_LONG_LONG
90  #if PY_VERSION_HEX >= 0x02070000
91  #define HAVE_LONG_LONG
92  #endif
93 #endif
94 #ifndef PY_LONG_LONG
95  #define PY_LONG_LONG LONG_LONG
96 #endif
97 #ifndef Py_HUGE_VAL
98  #define Py_HUGE_VAL HUGE_VAL
99 #endif
100 #ifdef PYPY_VERSION
101  #define CYTHON_COMPILING_IN_PYPY 1
102  #define CYTHON_COMPILING_IN_PYSTON 0
103  #define CYTHON_COMPILING_IN_CPYTHON 0
104  #undef CYTHON_USE_TYPE_SLOTS
105  #define CYTHON_USE_TYPE_SLOTS 0
106  #undef CYTHON_USE_PYTYPE_LOOKUP
107  #define CYTHON_USE_PYTYPE_LOOKUP 0
108  #if PY_VERSION_HEX < 0x03050000
109  #undef CYTHON_USE_ASYNC_SLOTS
110  #define CYTHON_USE_ASYNC_SLOTS 0
111  #elif !defined(CYTHON_USE_ASYNC_SLOTS)
112  #define CYTHON_USE_ASYNC_SLOTS 1
113  #endif
114  #undef CYTHON_USE_PYLIST_INTERNALS
115  #define CYTHON_USE_PYLIST_INTERNALS 0
116  #undef CYTHON_USE_UNICODE_INTERNALS
117  #define CYTHON_USE_UNICODE_INTERNALS 0
118  #undef CYTHON_USE_UNICODE_WRITER
119  #define CYTHON_USE_UNICODE_WRITER 0
120  #undef CYTHON_USE_PYLONG_INTERNALS
121  #define CYTHON_USE_PYLONG_INTERNALS 0
122  #undef CYTHON_AVOID_BORROWED_REFS
123  #define CYTHON_AVOID_BORROWED_REFS 1
124  #undef CYTHON_ASSUME_SAFE_MACROS
125  #define CYTHON_ASSUME_SAFE_MACROS 0
126  #undef CYTHON_UNPACK_METHODS
127  #define CYTHON_UNPACK_METHODS 0
128  #undef CYTHON_FAST_THREAD_STATE
129  #define CYTHON_FAST_THREAD_STATE 0
130  #undef CYTHON_FAST_PYCALL
131  #define CYTHON_FAST_PYCALL 0
132  #undef CYTHON_PEP489_MULTI_PHASE_INIT
133  #define CYTHON_PEP489_MULTI_PHASE_INIT 0
134  #undef CYTHON_USE_TP_FINALIZE
135  #define CYTHON_USE_TP_FINALIZE 0
136  #undef CYTHON_USE_DICT_VERSIONS
137  #define CYTHON_USE_DICT_VERSIONS 0
138  #undef CYTHON_USE_EXC_INFO_STACK
139  #define CYTHON_USE_EXC_INFO_STACK 0
140 #elif defined(PYSTON_VERSION)
141  #define CYTHON_COMPILING_IN_PYPY 0
142  #define CYTHON_COMPILING_IN_PYSTON 1
143  #define CYTHON_COMPILING_IN_CPYTHON 0
144  #ifndef CYTHON_USE_TYPE_SLOTS
145  #define CYTHON_USE_TYPE_SLOTS 1
146  #endif
147  #undef CYTHON_USE_PYTYPE_LOOKUP
148  #define CYTHON_USE_PYTYPE_LOOKUP 0
149  #undef CYTHON_USE_ASYNC_SLOTS
150  #define CYTHON_USE_ASYNC_SLOTS 0
151  #undef CYTHON_USE_PYLIST_INTERNALS
152  #define CYTHON_USE_PYLIST_INTERNALS 0
153  #ifndef CYTHON_USE_UNICODE_INTERNALS
154  #define CYTHON_USE_UNICODE_INTERNALS 1
155  #endif
156  #undef CYTHON_USE_UNICODE_WRITER
157  #define CYTHON_USE_UNICODE_WRITER 0
158  #undef CYTHON_USE_PYLONG_INTERNALS
159  #define CYTHON_USE_PYLONG_INTERNALS 0
160  #ifndef CYTHON_AVOID_BORROWED_REFS
161  #define CYTHON_AVOID_BORROWED_REFS 0
162  #endif
163  #ifndef CYTHON_ASSUME_SAFE_MACROS
164  #define CYTHON_ASSUME_SAFE_MACROS 1
165  #endif
166  #ifndef CYTHON_UNPACK_METHODS
167  #define CYTHON_UNPACK_METHODS 1
168  #endif
169  #undef CYTHON_FAST_THREAD_STATE
170  #define CYTHON_FAST_THREAD_STATE 0
171  #undef CYTHON_FAST_PYCALL
172  #define CYTHON_FAST_PYCALL 0
173  #undef CYTHON_PEP489_MULTI_PHASE_INIT
174  #define CYTHON_PEP489_MULTI_PHASE_INIT 0
175  #undef CYTHON_USE_TP_FINALIZE
176  #define CYTHON_USE_TP_FINALIZE 0
177  #undef CYTHON_USE_DICT_VERSIONS
178  #define CYTHON_USE_DICT_VERSIONS 0
179  #undef CYTHON_USE_EXC_INFO_STACK
180  #define CYTHON_USE_EXC_INFO_STACK 0
181 #else
182  #define CYTHON_COMPILING_IN_PYPY 0
183  #define CYTHON_COMPILING_IN_PYSTON 0
184  #define CYTHON_COMPILING_IN_CPYTHON 1
185  #ifndef CYTHON_USE_TYPE_SLOTS
186  #define CYTHON_USE_TYPE_SLOTS 1
187  #endif
188  #if PY_VERSION_HEX < 0x02070000
189  #undef CYTHON_USE_PYTYPE_LOOKUP
190  #define CYTHON_USE_PYTYPE_LOOKUP 0
191  #elif !defined(CYTHON_USE_PYTYPE_LOOKUP)
192  #define CYTHON_USE_PYTYPE_LOOKUP 1
193  #endif
194  #if PY_MAJOR_VERSION < 3
195  #undef CYTHON_USE_ASYNC_SLOTS
196  #define CYTHON_USE_ASYNC_SLOTS 0
197  #elif !defined(CYTHON_USE_ASYNC_SLOTS)
198  #define CYTHON_USE_ASYNC_SLOTS 1
199  #endif
200  #if PY_VERSION_HEX < 0x02070000
201  #undef CYTHON_USE_PYLONG_INTERNALS
202  #define CYTHON_USE_PYLONG_INTERNALS 0
203  #elif !defined(CYTHON_USE_PYLONG_INTERNALS)
204  #define CYTHON_USE_PYLONG_INTERNALS 1
205  #endif
206  #ifndef CYTHON_USE_PYLIST_INTERNALS
207  #define CYTHON_USE_PYLIST_INTERNALS 1
208  #endif
209  #ifndef CYTHON_USE_UNICODE_INTERNALS
210  #define CYTHON_USE_UNICODE_INTERNALS 1
211  #endif
212  #if PY_VERSION_HEX < 0x030300F0
213  #undef CYTHON_USE_UNICODE_WRITER
214  #define CYTHON_USE_UNICODE_WRITER 0
215  #elif !defined(CYTHON_USE_UNICODE_WRITER)
216  #define CYTHON_USE_UNICODE_WRITER 1
217  #endif
218  #ifndef CYTHON_AVOID_BORROWED_REFS
219  #define CYTHON_AVOID_BORROWED_REFS 0
220  #endif
221  #ifndef CYTHON_ASSUME_SAFE_MACROS
222  #define CYTHON_ASSUME_SAFE_MACROS 1
223  #endif
224  #ifndef CYTHON_UNPACK_METHODS
225  #define CYTHON_UNPACK_METHODS 1
226  #endif
227  #ifndef CYTHON_FAST_THREAD_STATE
228  #define CYTHON_FAST_THREAD_STATE 1
229  #endif
230  #ifndef CYTHON_FAST_PYCALL
231  #define CYTHON_FAST_PYCALL 1
232  #endif
233  #ifndef CYTHON_PEP489_MULTI_PHASE_INIT
234  #define CYTHON_PEP489_MULTI_PHASE_INIT (PY_VERSION_HEX >= 0x03050000)
235  #endif
236  #ifndef CYTHON_USE_TP_FINALIZE
237  #define CYTHON_USE_TP_FINALIZE (PY_VERSION_HEX >= 0x030400a1)
238  #endif
239  #ifndef CYTHON_USE_DICT_VERSIONS
240  #define CYTHON_USE_DICT_VERSIONS (PY_VERSION_HEX >= 0x030600B1)
241  #endif
242  #ifndef CYTHON_USE_EXC_INFO_STACK
243  #define CYTHON_USE_EXC_INFO_STACK (PY_VERSION_HEX >= 0x030700A3)
244  #endif
245 #endif
246 #if !defined(CYTHON_FAST_PYCCALL)
247 #define CYTHON_FAST_PYCCALL (CYTHON_FAST_PYCALL && PY_VERSION_HEX >= 0x030600B1)
248 #endif
249 #if CYTHON_USE_PYLONG_INTERNALS
250  #include "longintrepr.h"
251  #undef SHIFT
252  #undef BASE
253  #undef MASK
254  #ifdef SIZEOF_VOID_P
255  enum { __pyx_check_sizeof_voidp = 1 / (int)(SIZEOF_VOID_P == sizeof(void*)) };
256  #endif
257 #endif
258 #ifndef __has_attribute
259  #define __has_attribute(x) 0
260 #endif
261 #ifndef __has_cpp_attribute
262  #define __has_cpp_attribute(x) 0
263 #endif
264 #ifndef CYTHON_RESTRICT
265  #if defined(__GNUC__)
266  #define CYTHON_RESTRICT __restrict__
267  #elif defined(_MSC_VER) && _MSC_VER >= 1400
268  #define CYTHON_RESTRICT __restrict
269  #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
270  #define CYTHON_RESTRICT restrict
271  #else
272  #define CYTHON_RESTRICT
273  #endif
274 #endif
275 #ifndef CYTHON_UNUSED
276 # if defined(__GNUC__)
277 # if !(defined(__cplusplus)) || (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 4))
278 # define CYTHON_UNUSED __attribute__ ((__unused__))
279 # else
280 # define CYTHON_UNUSED
281 # endif
282 # elif defined(__ICC) || (defined(__INTEL_COMPILER) && !defined(_MSC_VER))
283 # define CYTHON_UNUSED __attribute__ ((__unused__))
284 # else
285 # define CYTHON_UNUSED
286 # endif
287 #endif
288 #ifndef CYTHON_MAYBE_UNUSED_VAR
289 # if defined(__cplusplus)
290  template<class T> void CYTHON_MAYBE_UNUSED_VAR( const T& ) { }
291 # else
292 # define CYTHON_MAYBE_UNUSED_VAR(x) (void)(x)
293 # endif
294 #endif
295 #ifndef CYTHON_NCP_UNUSED
296 # if CYTHON_COMPILING_IN_CPYTHON
297 # define CYTHON_NCP_UNUSED
298 # else
299 # define CYTHON_NCP_UNUSED CYTHON_UNUSED
300 # endif
301 #endif
302 #define __Pyx_void_to_None(void_result) ((void)(void_result), Py_INCREF(Py_None), Py_None)
303 #ifdef _MSC_VER
304  #ifndef _MSC_STDINT_H_
305  #if _MSC_VER < 1300
306  typedef unsigned char uint8_t;
307  typedef unsigned int uint32_t;
308  #else
309  typedef unsigned __int8 uint8_t;
310  typedef unsigned __int32 uint32_t;
311  #endif
312  #endif
313 #else
314  #include <stdint.h>
315 #endif
316 #ifndef CYTHON_FALLTHROUGH
317  #if defined(__cplusplus) && __cplusplus >= 201103L
318  #if __has_cpp_attribute(fallthrough)
319  #define CYTHON_FALLTHROUGH [[fallthrough]]
320  #elif __has_cpp_attribute(clang::fallthrough)
321  #define CYTHON_FALLTHROUGH [[clang::fallthrough]]
322  #elif __has_cpp_attribute(gnu::fallthrough)
323  #define CYTHON_FALLTHROUGH [[gnu::fallthrough]]
324  #endif
325  #endif
326  #ifndef CYTHON_FALLTHROUGH
327  #if __has_attribute(fallthrough)
328  #define CYTHON_FALLTHROUGH __attribute__((fallthrough))
329  #else
330  #define CYTHON_FALLTHROUGH
331  #endif
332  #endif
333  #if defined(__clang__ ) && defined(__apple_build_version__)
334  #if __apple_build_version__ < 7000000
335  #undef CYTHON_FALLTHROUGH
336  #define CYTHON_FALLTHROUGH
337  #endif
338  #endif
339 #endif
340 
341 #ifndef __cplusplus
342  #error "Cython files generated with the C++ option must be compiled with a C++ compiler."
343 #endif
344 #ifndef CYTHON_INLINE
345  #if defined(__clang__)
346  #define CYTHON_INLINE __inline__ __attribute__ ((__unused__))
347  #else
348  #define CYTHON_INLINE inline
349  #endif
350 #endif
351 template<typename T>
352 void __Pyx_call_destructor(T& x) {
353  x.~T();
354 }
355 template<typename T>
356 class __Pyx_FakeReference {
357  public:
358  __Pyx_FakeReference() : ptr(NULL) { }
359  __Pyx_FakeReference(const T& ref) : ptr(const_cast<T*>(&ref)) { }
360  T *operator->() { return ptr; }
361  T *operator&() { return ptr; }
362  operator T&() { return *ptr; }
363  template<typename U> bool operator ==(U other) { return *ptr == other; }
364  template<typename U> bool operator !=(U other) { return *ptr != other; }
365  private:
366  T *ptr;
367 };
368 
369 #if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x02070600 && !defined(Py_OptimizeFlag)
370  #define Py_OptimizeFlag 0
371 #endif
372 #define __PYX_BUILD_PY_SSIZE_T "n"
373 #define CYTHON_FORMAT_SSIZE_T "z"
374 #if PY_MAJOR_VERSION < 3
375  #define __Pyx_BUILTIN_MODULE_NAME "__builtin__"
376  #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
377  PyCode_New(a+k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)
378  #define __Pyx_DefaultClassType PyClass_Type
379 #else
380  #define __Pyx_BUILTIN_MODULE_NAME "builtins"
381  #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
382  PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)
383  #define __Pyx_DefaultClassType PyType_Type
384 #endif
385 #ifndef Py_TPFLAGS_CHECKTYPES
386  #define Py_TPFLAGS_CHECKTYPES 0
387 #endif
388 #ifndef Py_TPFLAGS_HAVE_INDEX
389  #define Py_TPFLAGS_HAVE_INDEX 0
390 #endif
391 #ifndef Py_TPFLAGS_HAVE_NEWBUFFER
392  #define Py_TPFLAGS_HAVE_NEWBUFFER 0
393 #endif
394 #ifndef Py_TPFLAGS_HAVE_FINALIZE
395  #define Py_TPFLAGS_HAVE_FINALIZE 0
396 #endif
397 #ifndef METH_STACKLESS
398  #define METH_STACKLESS 0
399 #endif
400 #if PY_VERSION_HEX <= 0x030700A3 || !defined(METH_FASTCALL)
401  #ifndef METH_FASTCALL
402  #define METH_FASTCALL 0x80
403  #endif
404  typedef PyObject *(*__Pyx_PyCFunctionFast) (PyObject *self, PyObject *const *args, Py_ssize_t nargs);
405  typedef PyObject *(*__Pyx_PyCFunctionFastWithKeywords) (PyObject *self, PyObject *const *args,
406  Py_ssize_t nargs, PyObject *kwnames);
407 #else
408  #define __Pyx_PyCFunctionFast _PyCFunctionFast
409  #define __Pyx_PyCFunctionFastWithKeywords _PyCFunctionFastWithKeywords
410 #endif
411 #if CYTHON_FAST_PYCCALL
412 #define __Pyx_PyFastCFunction_Check(func)\
413  ((PyCFunction_Check(func) && (METH_FASTCALL == (PyCFunction_GET_FLAGS(func) & ~(METH_CLASS | METH_STATIC | METH_COEXIST | METH_KEYWORDS | METH_STACKLESS)))))
414 #else
415 #define __Pyx_PyFastCFunction_Check(func) 0
416 #endif
417 #if CYTHON_COMPILING_IN_PYPY && !defined(PyObject_Malloc)
418  #define PyObject_Malloc(s) PyMem_Malloc(s)
419  #define PyObject_Free(p) PyMem_Free(p)
420  #define PyObject_Realloc(p) PyMem_Realloc(p)
421 #endif
422 #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX < 0x030400A1
423  #define PyMem_RawMalloc(n) PyMem_Malloc(n)
424  #define PyMem_RawRealloc(p, n) PyMem_Realloc(p, n)
425  #define PyMem_RawFree(p) PyMem_Free(p)
426 #endif
427 #if CYTHON_COMPILING_IN_PYSTON
428  #define __Pyx_PyCode_HasFreeVars(co) PyCode_HasFreeVars(co)
429  #define __Pyx_PyFrame_SetLineNumber(frame, lineno) PyFrame_SetLineNumber(frame, lineno)
430 #else
431  #define __Pyx_PyCode_HasFreeVars(co) (PyCode_GetNumFree(co) > 0)
432  #define __Pyx_PyFrame_SetLineNumber(frame, lineno) (frame)->f_lineno = (lineno)
433 #endif
434 #if !CYTHON_FAST_THREAD_STATE || PY_VERSION_HEX < 0x02070000
435  #define __Pyx_PyThreadState_Current PyThreadState_GET()
436 #elif PY_VERSION_HEX >= 0x03060000
437  #define __Pyx_PyThreadState_Current _PyThreadState_UncheckedGet()
438 #elif PY_VERSION_HEX >= 0x03000000
439  #define __Pyx_PyThreadState_Current PyThreadState_GET()
440 #else
441  #define __Pyx_PyThreadState_Current _PyThreadState_Current
442 #endif
443 #if PY_VERSION_HEX < 0x030700A2 && !defined(PyThread_tss_create) && !defined(Py_tss_NEEDS_INIT)
444 #include "pythread.h"
445 #define Py_tss_NEEDS_INIT 0
446 typedef int Py_tss_t;
447 static CYTHON_INLINE int PyThread_tss_create(Py_tss_t *key) {
448  *key = PyThread_create_key();
449  return 0;
450 }
451 static CYTHON_INLINE Py_tss_t * PyThread_tss_alloc(void) {
452  Py_tss_t *key = (Py_tss_t *)PyObject_Malloc(sizeof(Py_tss_t));
453  *key = Py_tss_NEEDS_INIT;
454  return key;
455 }
456 static CYTHON_INLINE void PyThread_tss_free(Py_tss_t *key) {
457  PyObject_Free(key);
458 }
459 static CYTHON_INLINE int PyThread_tss_is_created(Py_tss_t *key) {
460  return *key != Py_tss_NEEDS_INIT;
461 }
462 static CYTHON_INLINE void PyThread_tss_delete(Py_tss_t *key) {
463  PyThread_delete_key(*key);
464  *key = Py_tss_NEEDS_INIT;
465 }
466 static CYTHON_INLINE int PyThread_tss_set(Py_tss_t *key, void *value) {
467  return PyThread_set_key_value(*key, value);
468 }
469 static CYTHON_INLINE void * PyThread_tss_get(Py_tss_t *key) {
470  return PyThread_get_key_value(*key);
471 }
472 #endif
473 #if CYTHON_COMPILING_IN_CPYTHON || defined(_PyDict_NewPresized)
474 #define __Pyx_PyDict_NewPresized(n) ((n <= 8) ? PyDict_New() : _PyDict_NewPresized(n))
475 #else
476 #define __Pyx_PyDict_NewPresized(n) PyDict_New()
477 #endif
478 #if PY_MAJOR_VERSION >= 3 || CYTHON_FUTURE_DIVISION
479  #define __Pyx_PyNumber_Divide(x,y) PyNumber_TrueDivide(x,y)
480  #define __Pyx_PyNumber_InPlaceDivide(x,y) PyNumber_InPlaceTrueDivide(x,y)
481 #else
482  #define __Pyx_PyNumber_Divide(x,y) PyNumber_Divide(x,y)
483  #define __Pyx_PyNumber_InPlaceDivide(x,y) PyNumber_InPlaceDivide(x,y)
484 #endif
485 #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030500A1 && CYTHON_USE_UNICODE_INTERNALS
486 #define __Pyx_PyDict_GetItemStr(dict, name) _PyDict_GetItem_KnownHash(dict, name, ((PyASCIIObject *) name)->hash)
487 #else
488 #define __Pyx_PyDict_GetItemStr(dict, name) PyDict_GetItem(dict, name)
489 #endif
490 #if PY_VERSION_HEX > 0x03030000 && defined(PyUnicode_KIND)
491  #define CYTHON_PEP393_ENABLED 1
492  #define __Pyx_PyUnicode_READY(op) (likely(PyUnicode_IS_READY(op)) ?\
493  0 : _PyUnicode_Ready((PyObject *)(op)))
494  #define __Pyx_PyUnicode_GET_LENGTH(u) PyUnicode_GET_LENGTH(u)
495  #define __Pyx_PyUnicode_READ_CHAR(u, i) PyUnicode_READ_CHAR(u, i)
496  #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u) PyUnicode_MAX_CHAR_VALUE(u)
497  #define __Pyx_PyUnicode_KIND(u) PyUnicode_KIND(u)
498  #define __Pyx_PyUnicode_DATA(u) PyUnicode_DATA(u)
499  #define __Pyx_PyUnicode_READ(k, d, i) PyUnicode_READ(k, d, i)
500  #define __Pyx_PyUnicode_WRITE(k, d, i, ch) PyUnicode_WRITE(k, d, i, ch)
501  #define __Pyx_PyUnicode_IS_TRUE(u) (0 != (likely(PyUnicode_IS_READY(u)) ? PyUnicode_GET_LENGTH(u) : PyUnicode_GET_SIZE(u)))
502 #else
503  #define CYTHON_PEP393_ENABLED 0
504  #define PyUnicode_1BYTE_KIND 1
505  #define PyUnicode_2BYTE_KIND 2
506  #define PyUnicode_4BYTE_KIND 4
507  #define __Pyx_PyUnicode_READY(op) (0)
508  #define __Pyx_PyUnicode_GET_LENGTH(u) PyUnicode_GET_SIZE(u)
509  #define __Pyx_PyUnicode_READ_CHAR(u, i) ((Py_UCS4)(PyUnicode_AS_UNICODE(u)[i]))
510  #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u) ((sizeof(Py_UNICODE) == 2) ? 65535 : 1114111)
511  #define __Pyx_PyUnicode_KIND(u) (sizeof(Py_UNICODE))
512  #define __Pyx_PyUnicode_DATA(u) ((void*)PyUnicode_AS_UNICODE(u))
513  #define __Pyx_PyUnicode_READ(k, d, i) ((void)(k), (Py_UCS4)(((Py_UNICODE*)d)[i]))
514  #define __Pyx_PyUnicode_WRITE(k, d, i, ch) (((void)(k)), ((Py_UNICODE*)d)[i] = ch)
515  #define __Pyx_PyUnicode_IS_TRUE(u) (0 != PyUnicode_GET_SIZE(u))
516 #endif
517 #if CYTHON_COMPILING_IN_PYPY
518  #define __Pyx_PyUnicode_Concat(a, b) PyNumber_Add(a, b)
519  #define __Pyx_PyUnicode_ConcatSafe(a, b) PyNumber_Add(a, b)
520 #else
521  #define __Pyx_PyUnicode_Concat(a, b) PyUnicode_Concat(a, b)
522  #define __Pyx_PyUnicode_ConcatSafe(a, b) ((unlikely((a) == Py_None) || unlikely((b) == Py_None)) ?\
523  PyNumber_Add(a, b) : __Pyx_PyUnicode_Concat(a, b))
524 #endif
525 #if CYTHON_COMPILING_IN_PYPY && !defined(PyUnicode_Contains)
526  #define PyUnicode_Contains(u, s) PySequence_Contains(u, s)
527 #endif
528 #if CYTHON_COMPILING_IN_PYPY && !defined(PyByteArray_Check)
529  #define PyByteArray_Check(obj) PyObject_TypeCheck(obj, &PyByteArray_Type)
530 #endif
531 #if CYTHON_COMPILING_IN_PYPY && !defined(PyObject_Format)
532  #define PyObject_Format(obj, fmt) PyObject_CallMethod(obj, "__format__", "O", fmt)
533 #endif
534 #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))
535 #define __Pyx_PyUnicode_FormatSafe(a, b) ((unlikely((a) == Py_None || (PyUnicode_Check(b) && !PyUnicode_CheckExact(b)))) ? PyNumber_Remainder(a, b) : PyUnicode_Format(a, b))
536 #if PY_MAJOR_VERSION >= 3
537  #define __Pyx_PyString_Format(a, b) PyUnicode_Format(a, b)
538 #else
539  #define __Pyx_PyString_Format(a, b) PyString_Format(a, b)
540 #endif
541 #if PY_MAJOR_VERSION < 3 && !defined(PyObject_ASCII)
542  #define PyObject_ASCII(o) PyObject_Repr(o)
543 #endif
544 #if PY_MAJOR_VERSION >= 3
545  #define PyBaseString_Type PyUnicode_Type
546  #define PyStringObject PyUnicodeObject
547  #define PyString_Type PyUnicode_Type
548  #define PyString_Check PyUnicode_Check
549  #define PyString_CheckExact PyUnicode_CheckExact
550  #define PyObject_Unicode PyObject_Str
551 #endif
552 #if PY_MAJOR_VERSION >= 3
553  #define __Pyx_PyBaseString_Check(obj) PyUnicode_Check(obj)
554  #define __Pyx_PyBaseString_CheckExact(obj) PyUnicode_CheckExact(obj)
555 #else
556  #define __Pyx_PyBaseString_Check(obj) (PyString_Check(obj) || PyUnicode_Check(obj))
557  #define __Pyx_PyBaseString_CheckExact(obj) (PyString_CheckExact(obj) || PyUnicode_CheckExact(obj))
558 #endif
559 #ifndef PySet_CheckExact
560  #define PySet_CheckExact(obj) (Py_TYPE(obj) == &PySet_Type)
561 #endif
562 #if CYTHON_ASSUME_SAFE_MACROS
563  #define __Pyx_PySequence_SIZE(seq) Py_SIZE(seq)
564 #else
565  #define __Pyx_PySequence_SIZE(seq) PySequence_Size(seq)
566 #endif
567 #if PY_MAJOR_VERSION >= 3
568  #define PyIntObject PyLongObject
569  #define PyInt_Type PyLong_Type
570  #define PyInt_Check(op) PyLong_Check(op)
571  #define PyInt_CheckExact(op) PyLong_CheckExact(op)
572  #define PyInt_FromString PyLong_FromString
573  #define PyInt_FromUnicode PyLong_FromUnicode
574  #define PyInt_FromLong PyLong_FromLong
575  #define PyInt_FromSize_t PyLong_FromSize_t
576  #define PyInt_FromSsize_t PyLong_FromSsize_t
577  #define PyInt_AsLong PyLong_AsLong
578  #define PyInt_AS_LONG PyLong_AS_LONG
579  #define PyInt_AsSsize_t PyLong_AsSsize_t
580  #define PyInt_AsUnsignedLongMask PyLong_AsUnsignedLongMask
581  #define PyInt_AsUnsignedLongLongMask PyLong_AsUnsignedLongLongMask
582  #define PyNumber_Int PyNumber_Long
583 #endif
584 #if PY_MAJOR_VERSION >= 3
585  #define PyBoolObject PyLongObject
586 #endif
587 #if PY_MAJOR_VERSION >= 3 && CYTHON_COMPILING_IN_PYPY
588  #ifndef PyUnicode_InternFromString
589  #define PyUnicode_InternFromString(s) PyUnicode_FromString(s)
590  #endif
591 #endif
592 #if PY_VERSION_HEX < 0x030200A4
593  typedef long Py_hash_t;
594  #define __Pyx_PyInt_FromHash_t PyInt_FromLong
595  #define __Pyx_PyInt_AsHash_t PyInt_AsLong
596 #else
597  #define __Pyx_PyInt_FromHash_t PyInt_FromSsize_t
598  #define __Pyx_PyInt_AsHash_t PyInt_AsSsize_t
599 #endif
600 #if PY_MAJOR_VERSION >= 3
601  #define __Pyx_PyMethod_New(func, self, klass) ((self) ? PyMethod_New(func, self) : (Py_INCREF(func), func))
602 #else
603  #define __Pyx_PyMethod_New(func, self, klass) PyMethod_New(func, self, klass)
604 #endif
605 #if CYTHON_USE_ASYNC_SLOTS
606  #if PY_VERSION_HEX >= 0x030500B1
607  #define __Pyx_PyAsyncMethodsStruct PyAsyncMethods
608  #define __Pyx_PyType_AsAsync(obj) (Py_TYPE(obj)->tp_as_async)
609  #else
610  #define __Pyx_PyType_AsAsync(obj) ((__Pyx_PyAsyncMethodsStruct*) (Py_TYPE(obj)->tp_reserved))
611  #endif
612 #else
613  #define __Pyx_PyType_AsAsync(obj) NULL
614 #endif
615 #ifndef __Pyx_PyAsyncMethodsStruct
616  typedef struct {
617  unaryfunc am_await;
618  unaryfunc am_aiter;
619  unaryfunc am_anext;
620  } __Pyx_PyAsyncMethodsStruct;
621 #endif
622 
623 #if defined(WIN32) || defined(MS_WINDOWS)
624  #define _USE_MATH_DEFINES
625 #endif
626 #include <math.h>
627 #ifdef NAN
628 #define __PYX_NAN() ((float) NAN)
629 #else
630 static CYTHON_INLINE float __PYX_NAN() {
631  float value;
632  memset(&value, 0xFF, sizeof(value));
633  return value;
634 }
635 #endif
636 #if defined(__CYGWIN__) && defined(_LDBL_EQ_DBL)
637 #define __Pyx_truncl trunc
638 #else
639 #define __Pyx_truncl truncl
640 #endif
641 
642 
643 #define __PYX_ERR(f_index, lineno, Ln_error) \
644 { \
645  __pyx_filename = __pyx_f[f_index]; __pyx_lineno = lineno; __pyx_clineno = __LINE__; goto Ln_error; \
646 }
647 
648 #ifndef __PYX_EXTERN_C
649  #ifdef __cplusplus
650  #define __PYX_EXTERN_C extern "C"
651  #else
652  #define __PYX_EXTERN_C extern
653  #endif
654 #endif
655 
656 #define __PYX_HAVE__PyClical
657 #define __PYX_HAVE_API__PyClical
658 /* Early includes */
659 #include "ios"
660 #include "new"
661 #include "stdexcept"
662 #include "typeinfo"
663 #include <vector>
664 #include "PyClical.h"
665 #ifdef _OPENMP
666 #include <omp.h>
667 #endif /* _OPENMP */
668 
669 #if defined(PYREX_WITHOUT_ASSERTIONS) && !defined(CYTHON_WITHOUT_ASSERTIONS)
670 #define CYTHON_WITHOUT_ASSERTIONS
671 #endif
672 
673 typedef struct {PyObject **p; const char *s; const Py_ssize_t n; const char* encoding;
674  const char is_unicode; const char is_str; const char intern; } __Pyx_StringTabEntry;
675 
676 #define __PYX_DEFAULT_STRING_ENCODING_IS_ASCII 0
677 #define __PYX_DEFAULT_STRING_ENCODING_IS_UTF8 0
678 #define __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT (PY_MAJOR_VERSION >= 3 && __PYX_DEFAULT_STRING_ENCODING_IS_UTF8)
679 #define __PYX_DEFAULT_STRING_ENCODING ""
680 #define __Pyx_PyObject_FromString __Pyx_PyBytes_FromString
681 #define __Pyx_PyObject_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
682 #define __Pyx_uchar_cast(c) ((unsigned char)c)
683 #define __Pyx_long_cast(x) ((long)x)
684 #define __Pyx_fits_Py_ssize_t(v, type, is_signed) (\
685  (sizeof(type) < sizeof(Py_ssize_t)) ||\
686  (sizeof(type) > sizeof(Py_ssize_t) &&\
687  likely(v < (type)PY_SSIZE_T_MAX ||\
688  v == (type)PY_SSIZE_T_MAX) &&\
689  (!is_signed || likely(v > (type)PY_SSIZE_T_MIN ||\
690  v == (type)PY_SSIZE_T_MIN))) ||\
691  (sizeof(type) == sizeof(Py_ssize_t) &&\
692  (is_signed || likely(v < (type)PY_SSIZE_T_MAX ||\
693  v == (type)PY_SSIZE_T_MAX))) )
694 static CYTHON_INLINE int __Pyx_is_valid_index(Py_ssize_t i, Py_ssize_t limit) {
695  return (size_t) i < (size_t) limit;
696 }
697 #if defined (__cplusplus) && __cplusplus >= 201103L
698  #include <cstdlib>
699  #define __Pyx_sst_abs(value) std::abs(value)
700 #elif SIZEOF_INT >= SIZEOF_SIZE_T
701  #define __Pyx_sst_abs(value) abs(value)
702 #elif SIZEOF_LONG >= SIZEOF_SIZE_T
703  #define __Pyx_sst_abs(value) labs(value)
704 #elif defined (_MSC_VER)
705  #define __Pyx_sst_abs(value) ((Py_ssize_t)_abs64(value))
706 #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
707  #define __Pyx_sst_abs(value) llabs(value)
708 #elif defined (__GNUC__)
709  #define __Pyx_sst_abs(value) __builtin_llabs(value)
710 #else
711  #define __Pyx_sst_abs(value) ((value<0) ? -value : value)
712 #endif
713 static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject*);
714 static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject*, Py_ssize_t* length);
715 #define __Pyx_PyByteArray_FromString(s) PyByteArray_FromStringAndSize((const char*)s, strlen((const char*)s))
716 #define __Pyx_PyByteArray_FromStringAndSize(s, l) PyByteArray_FromStringAndSize((const char*)s, l)
717 #define __Pyx_PyBytes_FromString PyBytes_FromString
718 #define __Pyx_PyBytes_FromStringAndSize PyBytes_FromStringAndSize
719 static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char*);
720 #if PY_MAJOR_VERSION < 3
721  #define __Pyx_PyStr_FromString __Pyx_PyBytes_FromString
722  #define __Pyx_PyStr_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
723 #else
724  #define __Pyx_PyStr_FromString __Pyx_PyUnicode_FromString
725  #define __Pyx_PyStr_FromStringAndSize __Pyx_PyUnicode_FromStringAndSize
726 #endif
727 #define __Pyx_PyBytes_AsWritableString(s) ((char*) PyBytes_AS_STRING(s))
728 #define __Pyx_PyBytes_AsWritableSString(s) ((signed char*) PyBytes_AS_STRING(s))
729 #define __Pyx_PyBytes_AsWritableUString(s) ((unsigned char*) PyBytes_AS_STRING(s))
730 #define __Pyx_PyBytes_AsString(s) ((const char*) PyBytes_AS_STRING(s))
731 #define __Pyx_PyBytes_AsSString(s) ((const signed char*) PyBytes_AS_STRING(s))
732 #define __Pyx_PyBytes_AsUString(s) ((const unsigned char*) PyBytes_AS_STRING(s))
733 #define __Pyx_PyObject_AsWritableString(s) ((char*) __Pyx_PyObject_AsString(s))
734 #define __Pyx_PyObject_AsWritableSString(s) ((signed char*) __Pyx_PyObject_AsString(s))
735 #define __Pyx_PyObject_AsWritableUString(s) ((unsigned char*) __Pyx_PyObject_AsString(s))
736 #define __Pyx_PyObject_AsSString(s) ((const signed char*) __Pyx_PyObject_AsString(s))
737 #define __Pyx_PyObject_AsUString(s) ((const unsigned char*) __Pyx_PyObject_AsString(s))
738 #define __Pyx_PyObject_FromCString(s) __Pyx_PyObject_FromString((const char*)s)
739 #define __Pyx_PyBytes_FromCString(s) __Pyx_PyBytes_FromString((const char*)s)
740 #define __Pyx_PyByteArray_FromCString(s) __Pyx_PyByteArray_FromString((const char*)s)
741 #define __Pyx_PyStr_FromCString(s) __Pyx_PyStr_FromString((const char*)s)
742 #define __Pyx_PyUnicode_FromCString(s) __Pyx_PyUnicode_FromString((const char*)s)
743 static CYTHON_INLINE size_t __Pyx_Py_UNICODE_strlen(const Py_UNICODE *u) {
744  const Py_UNICODE *u_end = u;
745  while (*u_end++) ;
746  return (size_t)(u_end - u - 1);
747 }
748 #define __Pyx_PyUnicode_FromUnicode(u) PyUnicode_FromUnicode(u, __Pyx_Py_UNICODE_strlen(u))
749 #define __Pyx_PyUnicode_FromUnicodeAndLength PyUnicode_FromUnicode
750 #define __Pyx_PyUnicode_AsUnicode PyUnicode_AsUnicode
751 #define __Pyx_NewRef(obj) (Py_INCREF(obj), obj)
752 #define __Pyx_Owned_Py_None(b) __Pyx_NewRef(Py_None)
753 static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b);
754 static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*);
755 static CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject*);
756 static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x);
757 #define __Pyx_PySequence_Tuple(obj)\
758  (likely(PyTuple_CheckExact(obj)) ? __Pyx_NewRef(obj) : PySequence_Tuple(obj))
759 static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject*);
760 static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t);
761 #if CYTHON_ASSUME_SAFE_MACROS
762 #define __pyx_PyFloat_AsDouble(x) (PyFloat_CheckExact(x) ? PyFloat_AS_DOUBLE(x) : PyFloat_AsDouble(x))
763 #else
764 #define __pyx_PyFloat_AsDouble(x) PyFloat_AsDouble(x)
765 #endif
766 #define __pyx_PyFloat_AsFloat(x) ((float) __pyx_PyFloat_AsDouble(x))
767 #if PY_MAJOR_VERSION >= 3
768 #define __Pyx_PyNumber_Int(x) (PyLong_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Long(x))
769 #else
770 #define __Pyx_PyNumber_Int(x) (PyInt_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Int(x))
771 #endif
772 #define __Pyx_PyNumber_Float(x) (PyFloat_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Float(x))
773 #if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
774 static int __Pyx_sys_getdefaultencoding_not_ascii;
775 static int __Pyx_init_sys_getdefaultencoding_params(void) {
776  PyObject* sys;
777  PyObject* default_encoding = NULL;
778  PyObject* ascii_chars_u = NULL;
779  PyObject* ascii_chars_b = NULL;
780  const char* default_encoding_c;
781  sys = PyImport_ImportModule("sys");
782  if (!sys) goto bad;
783  default_encoding = PyObject_CallMethod(sys, (char*) "getdefaultencoding", NULL);
784  Py_DECREF(sys);
785  if (!default_encoding) goto bad;
786  default_encoding_c = PyBytes_AsString(default_encoding);
787  if (!default_encoding_c) goto bad;
788  if (strcmp(default_encoding_c, "ascii") == 0) {
789  __Pyx_sys_getdefaultencoding_not_ascii = 0;
790  } else {
791  char ascii_chars[128];
792  int c;
793  for (c = 0; c < 128; c++) {
794  ascii_chars[c] = c;
795  }
796  __Pyx_sys_getdefaultencoding_not_ascii = 1;
797  ascii_chars_u = PyUnicode_DecodeASCII(ascii_chars, 128, NULL);
798  if (!ascii_chars_u) goto bad;
799  ascii_chars_b = PyUnicode_AsEncodedString(ascii_chars_u, default_encoding_c, NULL);
800  if (!ascii_chars_b || !PyBytes_Check(ascii_chars_b) || memcmp(ascii_chars, PyBytes_AS_STRING(ascii_chars_b), 128) != 0) {
801  PyErr_Format(
802  PyExc_ValueError,
803  "This module compiled with c_string_encoding=ascii, but default encoding '%.200s' is not a superset of ascii.",
804  default_encoding_c);
805  goto bad;
806  }
807  Py_DECREF(ascii_chars_u);
808  Py_DECREF(ascii_chars_b);
809  }
810  Py_DECREF(default_encoding);
811  return 0;
812 bad:
813  Py_XDECREF(default_encoding);
814  Py_XDECREF(ascii_chars_u);
815  Py_XDECREF(ascii_chars_b);
816  return -1;
817 }
818 #endif
819 #if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT && PY_MAJOR_VERSION >= 3
820 #define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_DecodeUTF8(c_str, size, NULL)
821 #else
822 #define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_Decode(c_str, size, __PYX_DEFAULT_STRING_ENCODING, NULL)
823 #if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
824 static char* __PYX_DEFAULT_STRING_ENCODING;
825 static int __Pyx_init_sys_getdefaultencoding_params(void) {
826  PyObject* sys;
827  PyObject* default_encoding = NULL;
828  char* default_encoding_c;
829  sys = PyImport_ImportModule("sys");
830  if (!sys) goto bad;
831  default_encoding = PyObject_CallMethod(sys, (char*) (const char*) "getdefaultencoding", NULL);
832  Py_DECREF(sys);
833  if (!default_encoding) goto bad;
834  default_encoding_c = PyBytes_AsString(default_encoding);
835  if (!default_encoding_c) goto bad;
836  __PYX_DEFAULT_STRING_ENCODING = (char*) malloc(strlen(default_encoding_c) + 1);
837  if (!__PYX_DEFAULT_STRING_ENCODING) goto bad;
838  strcpy(__PYX_DEFAULT_STRING_ENCODING, default_encoding_c);
839  Py_DECREF(default_encoding);
840  return 0;
841 bad:
842  Py_XDECREF(default_encoding);
843  return -1;
844 }
845 #endif
846 #endif
847 
848 
849 /* Test for GCC > 2.95 */
850 #if defined(__GNUC__) && (__GNUC__ > 2 || (__GNUC__ == 2 && (__GNUC_MINOR__ > 95)))
851  #define likely(x) __builtin_expect(!!(x), 1)
852  #define unlikely(x) __builtin_expect(!!(x), 0)
853 #else /* !__GNUC__ or GCC < 2.95 */
854  #define likely(x) (x)
855  #define unlikely(x) (x)
856 #endif /* __GNUC__ */
857 static CYTHON_INLINE void __Pyx_pretend_to_initialize(void* ptr) { (void)ptr; }
858 
859 static PyObject *__pyx_m = NULL;
860 static PyObject *__pyx_d;
861 static PyObject *__pyx_b;
862 static PyObject *__pyx_cython_runtime = NULL;
863 static PyObject *__pyx_empty_tuple;
864 static PyObject *__pyx_empty_bytes;
865 static PyObject *__pyx_empty_unicode;
866 static int __pyx_lineno;
867 static int __pyx_clineno = 0;
868 static const char * __pyx_cfilenm= __FILE__;
869 static const char *__pyx_filename;
870 
871 
872 static const char *__pyx_f[] = {
873  "PyClical.pyx",
874  "stringsource",
875 };
876 
877 /*--- Type declarations ---*/
878 struct __pyx_obj_8PyClical_index_set;
879 struct __pyx_obj_8PyClical_clifford;
880 struct __pyx_obj_8PyClical___pyx_scope_struct____iter__;
881 struct __pyx_opt_args_8PyClical_sqrt;
882 struct __pyx_opt_args_8PyClical_log;
883 struct __pyx_opt_args_8PyClical_cos;
884 struct __pyx_opt_args_8PyClical_acos;
885 struct __pyx_opt_args_8PyClical_acosh;
886 struct __pyx_opt_args_8PyClical_sin;
887 struct __pyx_opt_args_8PyClical_asin;
888 struct __pyx_opt_args_8PyClical_asinh;
889 struct __pyx_opt_args_8PyClical_tan;
890 struct __pyx_opt_args_8PyClical_atan;
891 struct __pyx_opt_args_8PyClical_atanh;
892 struct __pyx_opt_args_8PyClical_random_clifford;
893 
894 /* "PyClical.pyx":1542
895  * return clifford().wrap( glucat.complexifier(toClifford(obj)) )
896  *
897  * cpdef inline sqrt(obj, i = None): # <<<<<<<<<<<<<<
898  * """
899  * Square root of multivector with optional complexifier.
900  */
901 struct __pyx_opt_args_8PyClical_sqrt {
902  int __pyx_n;
903  PyObject *i;
904 };
905 
906 /* "PyClical.pyx":1579
907  * return clifford().wrap( glucat.exp(toClifford(obj)) )
908  *
909  * cpdef inline log(obj,i = None): # <<<<<<<<<<<<<<
910  * """
911  * Natural logarithm of multivector with optional complexifier.
912  */
913 struct __pyx_opt_args_8PyClical_log {
914  int __pyx_n;
915  PyObject *i;
916 };
917 
918 /* "PyClical.pyx":1602
919  * return clifford().wrap( glucat.log(toClifford(obj)) )
920  *
921  * cpdef inline cos(obj,i = None): # <<<<<<<<<<<<<<
922  * """
923  * Cosine of multivector with optional complexifier.
924  */
925 struct __pyx_opt_args_8PyClical_cos {
926  int __pyx_n;
927  PyObject *i;
928 };
929 
930 /* "PyClical.pyx":1619
931  * return clifford().wrap( glucat.cos(toClifford(obj)) )
932  *
933  * cpdef inline acos(obj,i = None): # <<<<<<<<<<<<<<
934  * """
935  * Inverse cosine of multivector with optional complexifier.
936  */
937 struct __pyx_opt_args_8PyClical_acos {
938  int __pyx_n;
939  PyObject *i;
940 };
941 
942 /* "PyClical.pyx":1656
943  * return clifford().wrap( glucat.cosh(toClifford(obj)) )
944  *
945  * cpdef inline acosh(obj,i = None): # <<<<<<<<<<<<<<
946  * """
947  * Inverse hyperbolic cosine of multivector with optional complexifier.
948  */
949 struct __pyx_opt_args_8PyClical_acosh {
950  int __pyx_n;
951  PyObject *i;
952 };
953 
954 /* "PyClical.pyx":1679
955  * return clifford().wrap( glucat.acosh(toClifford(obj)) )
956  *
957  * cpdef inline sin(obj,i = None): # <<<<<<<<<<<<<<
958  * """
959  * Sine of multivector with optional complexifier.
960  */
961 struct __pyx_opt_args_8PyClical_sin {
962  int __pyx_n;
963  PyObject *i;
964 };
965 
966 /* "PyClical.pyx":1698
967  * return clifford().wrap( glucat.sin(toClifford(obj)) )
968  *
969  * cpdef inline asin(obj,i = None): # <<<<<<<<<<<<<<
970  * """
971  * Inverse sine of multivector with optional complexifier.
972  */
973 struct __pyx_opt_args_8PyClical_asin {
974  int __pyx_n;
975  PyObject *i;
976 };
977 
978 /* "PyClical.pyx":1733
979  * return clifford().wrap( glucat.sinh(toClifford(obj)) )
980  *
981  * cpdef inline asinh(obj,i = None): # <<<<<<<<<<<<<<
982  * """
983  * Inverse hyperbolic sine of multivector with optional complexifier.
984  */
985 struct __pyx_opt_args_8PyClical_asinh {
986  int __pyx_n;
987  PyObject *i;
988 };
989 
990 /* "PyClical.pyx":1752
991  * return clifford().wrap( glucat.asinh(toClifford(obj)) )
992  *
993  * cpdef inline tan(obj,i = None): # <<<<<<<<<<<<<<
994  * """
995  * Tangent of multivector with optional complexifier.
996  */
997 struct __pyx_opt_args_8PyClical_tan {
998  int __pyx_n;
999  PyObject *i;
1000 };
1001 
1002 /* "PyClical.pyx":1769
1003  * return clifford().wrap( glucat.tan(toClifford(obj)) )
1004  *
1005  * cpdef inline atan(obj,i = None): # <<<<<<<<<<<<<<
1006  * """
1007  * Inverse tangent of multivector with optional complexifier.
1008  */
1009 struct __pyx_opt_args_8PyClical_atan {
1010  int __pyx_n;
1011  PyObject *i;
1012 };
1013 
1014 /* "PyClical.pyx":1798
1015  * return clifford().wrap( glucat.tanh(toClifford(obj)) )
1016  *
1017  * cpdef inline atanh(obj,i = None): # <<<<<<<<<<<<<<
1018  * """
1019  * Inverse hyperbolic tangent of multivector with optional complexifier.
1020  */
1021 struct __pyx_opt_args_8PyClical_atanh {
1022  int __pyx_n;
1023  PyObject *i;
1024 };
1025 
1026 /* "PyClical.pyx":1815
1027  * return clifford().wrap( glucat.atanh(toClifford(obj)) )
1028  *
1029  * cpdef inline random_clifford(index_set ixt, fill = 1.0): # <<<<<<<<<<<<<<
1030  * """
1031  * Random multivector within a frame.
1032  */
1033 struct __pyx_opt_args_8PyClical_random_clifford {
1034  int __pyx_n;
1035  PyObject *fill;
1036 };
1037 
1038 /* "PyClical.pyx":37
1039  *
1040  * # Forward reference
1041  * cdef class index_set # <<<<<<<<<<<<<<
1042  *
1043  * cdef inline IndexSet toIndexSet(obj):
1044  */
1045 struct __pyx_obj_8PyClical_index_set {
1046  PyObject_HEAD
1047  struct __pyx_vtabstruct_8PyClical_index_set *__pyx_vtab;
1048  IndexSet *instance;
1049 };
1050 
1051 
1052 /* "PyClical.pyx":530
1053  *
1054  * # Forward reference.
1055  * cdef class clifford # <<<<<<<<<<<<<<
1056  *
1057  * cdef inline Clifford toClifford(obj):
1058  */
1059 struct __pyx_obj_8PyClical_clifford {
1060  PyObject_HEAD
1061  struct __pyx_vtabstruct_8PyClical_clifford *__pyx_vtab;
1062  Clifford *instance;
1063 };
1064 
1065 
1066 /* "PyClical.pyx":227
1067  * return self.instance.getitem(idx)
1068  *
1069  * def __iter__(self): # <<<<<<<<<<<<<<
1070  * """
1071  * Iterate over the indices of an index_set.
1072  */
1073 struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ {
1074  PyObject_HEAD
1075  PyObject *__pyx_v_idx;
1076  struct __pyx_obj_8PyClical_index_set *__pyx_v_self;
1077  PyObject *__pyx_t_0;
1078  Py_ssize_t __pyx_t_1;
1079  PyObject *(*__pyx_t_2)(PyObject *);
1080 };
1081 
1082 
1083 
1084 /* "PyClical.pyx":45
1085  * return index_set(obj).instance[0]
1086  *
1087  * cdef class index_set: # <<<<<<<<<<<<<<
1088  * """
1089  * Python class index_set wraps C++ class IndexSet.
1090  */
1091 
1092 struct __pyx_vtabstruct_8PyClical_index_set {
1093  PyObject *(*wrap)(struct __pyx_obj_8PyClical_index_set *, IndexSet);
1094  IndexSet (*unwrap)(struct __pyx_obj_8PyClical_index_set *);
1095  PyObject *(*copy)(struct __pyx_obj_8PyClical_index_set *, int __pyx_skip_dispatch);
1096 };
1097 static struct __pyx_vtabstruct_8PyClical_index_set *__pyx_vtabptr_8PyClical_index_set;
1098 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_9index_set_wrap(struct __pyx_obj_8PyClical_index_set *, IndexSet);
1099 static CYTHON_INLINE IndexSet __pyx_f_8PyClical_9index_set_unwrap(struct __pyx_obj_8PyClical_index_set *);
1100 
1101 
1102 /* "PyClical.pyx":535
1103  * return clifford(obj).instance[0]
1104  *
1105  * cdef class clifford: # <<<<<<<<<<<<<<
1106  * """
1107  * Python class clifford wraps C++ class Clifford.
1108  */
1109 
1110 struct __pyx_vtabstruct_8PyClical_clifford {
1111  PyObject *(*wrap)(struct __pyx_obj_8PyClical_clifford *, Clifford);
1112  Clifford (*unwrap)(struct __pyx_obj_8PyClical_clifford *);
1113  PyObject *(*copy)(struct __pyx_obj_8PyClical_clifford *, int __pyx_skip_dispatch);
1114 };
1115 static struct __pyx_vtabstruct_8PyClical_clifford *__pyx_vtabptr_8PyClical_clifford;
1116 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_8clifford_wrap(struct __pyx_obj_8PyClical_clifford *, Clifford);
1117 static CYTHON_INLINE Clifford __pyx_f_8PyClical_8clifford_unwrap(struct __pyx_obj_8PyClical_clifford *);
1118 
1119 /* --- Runtime support code (head) --- */
1120 /* Refnanny.proto */
1121 #ifndef CYTHON_REFNANNY
1122  #define CYTHON_REFNANNY 0
1123 #endif
1124 #if CYTHON_REFNANNY
1125  typedef struct {
1126  void (*INCREF)(void*, PyObject*, int);
1127  void (*DECREF)(void*, PyObject*, int);
1128  void (*GOTREF)(void*, PyObject*, int);
1129  void (*GIVEREF)(void*, PyObject*, int);
1130  void* (*SetupContext)(const char*, int, const char*);
1131  void (*FinishContext)(void**);
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1134  static __Pyx_RefNannyAPIStruct *__Pyx_RefNannyImportAPI(const char *modname);
1135  #define __Pyx_RefNannyDeclarations void *__pyx_refnanny = NULL;
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1139  PyGILState_STATE __pyx_gilstate_save = PyGILState_Ensure();\
1140  __pyx_refnanny = __Pyx_RefNanny->SetupContext((name), __LINE__, __FILE__);\
1141  PyGILState_Release(__pyx_gilstate_save);\
1142  } else {\
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1145 #else
1146  #define __Pyx_RefNannySetupContext(name, acquire_gil)\
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1148 #endif
1149  #define __Pyx_RefNannyFinishContext()\
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1151  #define __Pyx_INCREF(r) __Pyx_RefNanny->INCREF(__pyx_refnanny, (PyObject *)(r), __LINE__)
1152  #define __Pyx_DECREF(r) __Pyx_RefNanny->DECREF(__pyx_refnanny, (PyObject *)(r), __LINE__)
1153  #define __Pyx_GOTREF(r) __Pyx_RefNanny->GOTREF(__pyx_refnanny, (PyObject *)(r), __LINE__)
1154  #define __Pyx_GIVEREF(r) __Pyx_RefNanny->GIVEREF(__pyx_refnanny, (PyObject *)(r), __LINE__)
1155  #define __Pyx_XINCREF(r) do { if((r) != NULL) {__Pyx_INCREF(r); }} while(0)
1156  #define __Pyx_XDECREF(r) do { if((r) != NULL) {__Pyx_DECREF(r); }} while(0)
1157  #define __Pyx_XGOTREF(r) do { if((r) != NULL) {__Pyx_GOTREF(r); }} while(0)
1158  #define __Pyx_XGIVEREF(r) do { if((r) != NULL) {__Pyx_GIVEREF(r);}} while(0)
1159 #else
1160  #define __Pyx_RefNannyDeclarations
1161  #define __Pyx_RefNannySetupContext(name, acquire_gil)
1162  #define __Pyx_RefNannyFinishContext()
1163  #define __Pyx_INCREF(r) Py_INCREF(r)
1164  #define __Pyx_DECREF(r) Py_DECREF(r)
1165  #define __Pyx_GOTREF(r)
1166  #define __Pyx_GIVEREF(r)
1167  #define __Pyx_XINCREF(r) Py_XINCREF(r)
1168  #define __Pyx_XDECREF(r) Py_XDECREF(r)
1169  #define __Pyx_XGOTREF(r)
1170  #define __Pyx_XGIVEREF(r)
1171 #endif
1172 #define __Pyx_XDECREF_SET(r, v) do {\
1173  PyObject *tmp = (PyObject *) r;\
1174  r = v; __Pyx_XDECREF(tmp);\
1175  } while (0)
1176 #define __Pyx_DECREF_SET(r, v) do {\
1177  PyObject *tmp = (PyObject *) r;\
1178  r = v; __Pyx_DECREF(tmp);\
1179  } while (0)
1180 #define __Pyx_CLEAR(r) do { PyObject* tmp = ((PyObject*)(r)); r = NULL; __Pyx_DECREF(tmp);} while(0)
1181 #define __Pyx_XCLEAR(r) do { if((r) != NULL) {PyObject* tmp = ((PyObject*)(r)); r = NULL; __Pyx_DECREF(tmp);}} while(0)
1182 
1183 /* PyObjectGetAttrStr.proto */
1184 #if CYTHON_USE_TYPE_SLOTS
1185 static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStr(PyObject* obj, PyObject* attr_name);
1186 #else
1187 #define __Pyx_PyObject_GetAttrStr(o,n) PyObject_GetAttr(o,n)
1188 #endif
1189 
1190 /* GetBuiltinName.proto */
1191 static PyObject *__Pyx_GetBuiltinName(PyObject *name);
1192 
1193 /* PyCFunctionFastCall.proto */
1194 #if CYTHON_FAST_PYCCALL
1195 static CYTHON_INLINE PyObject *__Pyx_PyCFunction_FastCall(PyObject *func, PyObject **args, Py_ssize_t nargs);
1196 #else
1197 #define __Pyx_PyCFunction_FastCall(func, args, nargs) (assert(0), NULL)
1198 #endif
1199 
1200 /* PyFunctionFastCall.proto */
1201 #if CYTHON_FAST_PYCALL
1202 #define __Pyx_PyFunction_FastCall(func, args, nargs)\
1203  __Pyx_PyFunction_FastCallDict((func), (args), (nargs), NULL)
1204 #if 1 || PY_VERSION_HEX < 0x030600B1
1205 static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, int nargs, PyObject *kwargs);
1206 #else
1207 #define __Pyx_PyFunction_FastCallDict(func, args, nargs, kwargs) _PyFunction_FastCallDict(func, args, nargs, kwargs)
1208 #endif
1209 #define __Pyx_BUILD_ASSERT_EXPR(cond)\
1210  (sizeof(char [1 - 2*!(cond)]) - 1)
1211 #ifndef Py_MEMBER_SIZE
1212 #define Py_MEMBER_SIZE(type, member) sizeof(((type *)0)->member)
1213 #endif
1214  static size_t __pyx_pyframe_localsplus_offset = 0;
1215  #include "frameobject.h"
1216  #define __Pxy_PyFrame_Initialize_Offsets()\
1217  ((void)__Pyx_BUILD_ASSERT_EXPR(sizeof(PyFrameObject) == offsetof(PyFrameObject, f_localsplus) + Py_MEMBER_SIZE(PyFrameObject, f_localsplus)),\
1218  (void)(__pyx_pyframe_localsplus_offset = ((size_t)PyFrame_Type.tp_basicsize) - Py_MEMBER_SIZE(PyFrameObject, f_localsplus)))
1219  #define __Pyx_PyFrame_GetLocalsplus(frame)\
1220  (assert(__pyx_pyframe_localsplus_offset), (PyObject **)(((char *)(frame)) + __pyx_pyframe_localsplus_offset))
1221 #endif
1222 
1223 /* PyObjectCall.proto */
1224 #if CYTHON_COMPILING_IN_CPYTHON
1225 static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw);
1226 #else
1227 #define __Pyx_PyObject_Call(func, arg, kw) PyObject_Call(func, arg, kw)
1228 #endif
1229 
1230 /* PyObjectCallMethO.proto */
1231 #if CYTHON_COMPILING_IN_CPYTHON
1232 static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg);
1233 #endif
1234 
1235 /* PyObjectCallOneArg.proto */
1236 static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg);
1237 
1238 /* PyThreadStateGet.proto */
1239 #if CYTHON_FAST_THREAD_STATE
1240 #define __Pyx_PyThreadState_declare PyThreadState *__pyx_tstate;
1241 #define __Pyx_PyThreadState_assign __pyx_tstate = __Pyx_PyThreadState_Current;
1242 #define __Pyx_PyErr_Occurred() __pyx_tstate->curexc_type
1243 #else
1244 #define __Pyx_PyThreadState_declare
1245 #define __Pyx_PyThreadState_assign
1246 #define __Pyx_PyErr_Occurred() PyErr_Occurred()
1247 #endif
1248 
1249 /* PyErrFetchRestore.proto */
1250 #if CYTHON_FAST_THREAD_STATE
1251 #define __Pyx_PyErr_Clear() __Pyx_ErrRestore(NULL, NULL, NULL)
1252 #define __Pyx_ErrRestoreWithState(type, value, tb) __Pyx_ErrRestoreInState(PyThreadState_GET(), type, value, tb)
1253 #define __Pyx_ErrFetchWithState(type, value, tb) __Pyx_ErrFetchInState(PyThreadState_GET(), type, value, tb)
1254 #define __Pyx_ErrRestore(type, value, tb) __Pyx_ErrRestoreInState(__pyx_tstate, type, value, tb)
1255 #define __Pyx_ErrFetch(type, value, tb) __Pyx_ErrFetchInState(__pyx_tstate, type, value, tb)
1256 static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb);
1257 static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
1258 #if CYTHON_COMPILING_IN_CPYTHON
1259 #define __Pyx_PyErr_SetNone(exc) (Py_INCREF(exc), __Pyx_ErrRestore((exc), NULL, NULL))
1260 #else
1261 #define __Pyx_PyErr_SetNone(exc) PyErr_SetNone(exc)
1262 #endif
1263 #else
1264 #define __Pyx_PyErr_Clear() PyErr_Clear()
1265 #define __Pyx_PyErr_SetNone(exc) PyErr_SetNone(exc)
1266 #define __Pyx_ErrRestoreWithState(type, value, tb) PyErr_Restore(type, value, tb)
1267 #define __Pyx_ErrFetchWithState(type, value, tb) PyErr_Fetch(type, value, tb)
1268 #define __Pyx_ErrRestoreInState(tstate, type, value, tb) PyErr_Restore(type, value, tb)
1269 #define __Pyx_ErrFetchInState(tstate, type, value, tb) PyErr_Fetch(type, value, tb)
1270 #define __Pyx_ErrRestore(type, value, tb) PyErr_Restore(type, value, tb)
1271 #define __Pyx_ErrFetch(type, value, tb) PyErr_Fetch(type, value, tb)
1272 #endif
1273 
1274 /* WriteUnraisableException.proto */
1275 static void __Pyx_WriteUnraisable(const char *name, int clineno,
1276  int lineno, const char *filename,
1277  int full_traceback, int nogil);
1278 
1279 /* PyDictVersioning.proto */
1280 #if CYTHON_USE_DICT_VERSIONS && CYTHON_USE_TYPE_SLOTS
1281 #define __PYX_DICT_VERSION_INIT ((PY_UINT64_T) -1)
1282 #define __PYX_GET_DICT_VERSION(dict) (((PyDictObject*)(dict))->ma_version_tag)
1283 #define __PYX_UPDATE_DICT_CACHE(dict, value, cache_var, version_var)\
1284  (version_var) = __PYX_GET_DICT_VERSION(dict);\
1285  (cache_var) = (value);
1286 #define __PYX_PY_DICT_LOOKUP_IF_MODIFIED(VAR, DICT, LOOKUP) {\
1287  static PY_UINT64_T __pyx_dict_version = 0;\
1288  static PyObject *__pyx_dict_cached_value = NULL;\
1289  if (likely(__PYX_GET_DICT_VERSION(DICT) == __pyx_dict_version)) {\
1290  (VAR) = __pyx_dict_cached_value;\
1291  } else {\
1292  (VAR) = __pyx_dict_cached_value = (LOOKUP);\
1293  __pyx_dict_version = __PYX_GET_DICT_VERSION(DICT);\
1294  }\
1295 }
1296 static CYTHON_INLINE PY_UINT64_T __Pyx_get_tp_dict_version(PyObject *obj);
1297 static CYTHON_INLINE PY_UINT64_T __Pyx_get_object_dict_version(PyObject *obj);
1298 static CYTHON_INLINE int __Pyx_object_dict_version_matches(PyObject* obj, PY_UINT64_T tp_dict_version, PY_UINT64_T obj_dict_version);
1299 #else
1300 #define __PYX_GET_DICT_VERSION(dict) (0)
1301 #define __PYX_UPDATE_DICT_CACHE(dict, value, cache_var, version_var)
1302 #define __PYX_PY_DICT_LOOKUP_IF_MODIFIED(VAR, DICT, LOOKUP) (VAR) = (LOOKUP);
1303 #endif
1304 
1305 /* PyObjectCallNoArg.proto */
1306 #if CYTHON_COMPILING_IN_CPYTHON
1307 static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func);
1308 #else
1309 #define __Pyx_PyObject_CallNoArg(func) __Pyx_PyObject_Call(func, __pyx_empty_tuple, NULL)
1310 #endif
1311 
1312 /* RaiseDoubleKeywords.proto */
1313 static void __Pyx_RaiseDoubleKeywordsError(const char* func_name, PyObject* kw_name);
1314 
1315 /* ParseKeywords.proto */
1316 static int __Pyx_ParseOptionalKeywords(PyObject *kwds, PyObject **argnames[],\
1317  PyObject *kwds2, PyObject *values[], Py_ssize_t num_pos_args,\
1318  const char* function_name);
1319 
1320 /* RaiseArgTupleInvalid.proto */
1321 static void __Pyx_RaiseArgtupleInvalid(const char* func_name, int exact,
1322  Py_ssize_t num_min, Py_ssize_t num_max, Py_ssize_t num_found);
1323 
1324 /* GetModuleGlobalName.proto */
1325 #if CYTHON_USE_DICT_VERSIONS
1326 #define __Pyx_GetModuleGlobalName(var, name) {\
1327  static PY_UINT64_T __pyx_dict_version = 0;\
1328  static PyObject *__pyx_dict_cached_value = NULL;\
1329  (var) = (likely(__pyx_dict_version == __PYX_GET_DICT_VERSION(__pyx_d))) ?\
1330  (likely(__pyx_dict_cached_value) ? __Pyx_NewRef(__pyx_dict_cached_value) : __Pyx_GetBuiltinName(name)) :\
1331  __Pyx__GetModuleGlobalName(name, &__pyx_dict_version, &__pyx_dict_cached_value);\
1332 }
1333 #define __Pyx_GetModuleGlobalNameUncached(var, name) {\
1334  PY_UINT64_T __pyx_dict_version;\
1335  PyObject *__pyx_dict_cached_value;\
1336  (var) = __Pyx__GetModuleGlobalName(name, &__pyx_dict_version, &__pyx_dict_cached_value);\
1337 }
1338 static PyObject *__Pyx__GetModuleGlobalName(PyObject *name, PY_UINT64_T *dict_version, PyObject **dict_cached_value);
1339 #else
1340 #define __Pyx_GetModuleGlobalName(var, name) (var) = __Pyx__GetModuleGlobalName(name)
1341 #define __Pyx_GetModuleGlobalNameUncached(var, name) (var) = __Pyx__GetModuleGlobalName(name)
1342 static CYTHON_INLINE PyObject *__Pyx__GetModuleGlobalName(PyObject *name);
1343 #endif
1344 
1345 /* GetTopmostException.proto */
1346 #if CYTHON_USE_EXC_INFO_STACK
1347 static _PyErr_StackItem * __Pyx_PyErr_GetTopmostException(PyThreadState *tstate);
1348 #endif
1349 
1350 /* SaveResetException.proto */
1351 #if CYTHON_FAST_THREAD_STATE
1352 #define __Pyx_ExceptionSave(type, value, tb) __Pyx__ExceptionSave(__pyx_tstate, type, value, tb)
1353 static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
1354 #define __Pyx_ExceptionReset(type, value, tb) __Pyx__ExceptionReset(__pyx_tstate, type, value, tb)
1355 static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb);
1356 #else
1357 #define __Pyx_ExceptionSave(type, value, tb) PyErr_GetExcInfo(type, value, tb)
1358 #define __Pyx_ExceptionReset(type, value, tb) PyErr_SetExcInfo(type, value, tb)
1359 #endif
1360 
1361 /* PyErrExceptionMatches.proto */
1362 #if CYTHON_FAST_THREAD_STATE
1363 #define __Pyx_PyErr_ExceptionMatches(err) __Pyx_PyErr_ExceptionMatchesInState(__pyx_tstate, err)
1364 static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err);
1365 #else
1366 #define __Pyx_PyErr_ExceptionMatches(err) PyErr_ExceptionMatches(err)
1367 #endif
1368 
1369 /* GetException.proto */
1370 #if CYTHON_FAST_THREAD_STATE
1371 #define __Pyx_GetException(type, value, tb) __Pyx__GetException(__pyx_tstate, type, value, tb)
1372 static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
1373 #else
1374 static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb);
1375 #endif
1376 
1377 /* RaiseException.proto */
1378 static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause);
1379 
1380 /* PyIntBinop.proto */
1381 #if !CYTHON_COMPILING_IN_PYPY
1382 static PyObject* __Pyx_PyInt_AddObjC(PyObject *op1, PyObject *op2, long intval, int inplace, int zerodivision_check);
1383 #else
1384 #define __Pyx_PyInt_AddObjC(op1, op2, intval, inplace, zerodivision_check)\
1385  (inplace ? PyNumber_InPlaceAdd(op1, op2) : PyNumber_Add(op1, op2))
1386 #endif
1387 
1388 /* PySequenceContains.proto */
1389 static CYTHON_INLINE int __Pyx_PySequence_ContainsTF(PyObject* item, PyObject* seq, int eq) {
1390  int result = PySequence_Contains(seq, item);
1391  return unlikely(result < 0) ? result : (result == (eq == Py_EQ));
1392 }
1393 
1394 /* SetItemInt.proto */
1395 #define __Pyx_SetItemInt(o, i, v, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
1396  (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\
1397  __Pyx_SetItemInt_Fast(o, (Py_ssize_t)i, v, is_list, wraparound, boundscheck) :\
1398  (is_list ? (PyErr_SetString(PyExc_IndexError, "list assignment index out of range"), -1) :\
1399  __Pyx_SetItemInt_Generic(o, to_py_func(i), v)))
1400 static int __Pyx_SetItemInt_Generic(PyObject *o, PyObject *j, PyObject *v);
1401 static CYTHON_INLINE int __Pyx_SetItemInt_Fast(PyObject *o, Py_ssize_t i, PyObject *v,
1402  int is_list, int wraparound, int boundscheck);
1403 
1404 /* PyObjectCall2Args.proto */
1405 static CYTHON_UNUSED PyObject* __Pyx_PyObject_Call2Args(PyObject* function, PyObject* arg1, PyObject* arg2);
1406 
1407 /* ArgTypeTest.proto */
1408 #define __Pyx_ArgTypeTest(obj, type, none_allowed, name, exact)\
1409  ((likely((Py_TYPE(obj) == type) | (none_allowed && (obj == Py_None)))) ? 1 :\
1410  __Pyx__ArgTypeTest(obj, type, name, exact))
1411 static int __Pyx__ArgTypeTest(PyObject *obj, PyTypeObject *type, const char *name, int exact);
1412 
1413 /* Import.proto */
1414 static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level);
1415 
1416 /* IncludeStringH.proto */
1417 #include <string.h>
1418 
1419 /* PyObject_GenericGetAttrNoDict.proto */
1420 #if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000
1421 static CYTHON_INLINE PyObject* __Pyx_PyObject_GenericGetAttrNoDict(PyObject* obj, PyObject* attr_name);
1422 #else
1423 #define __Pyx_PyObject_GenericGetAttrNoDict PyObject_GenericGetAttr
1424 #endif
1425 
1426 /* PyObject_GenericGetAttr.proto */
1427 #if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000
1428 static PyObject* __Pyx_PyObject_GenericGetAttr(PyObject* obj, PyObject* attr_name);
1429 #else
1430 #define __Pyx_PyObject_GenericGetAttr PyObject_GenericGetAttr
1431 #endif
1432 
1433 /* SetVTable.proto */
1434 static int __Pyx_SetVtable(PyObject *dict, void *vtable);
1435 
1436 /* SetupReduce.proto */
1437 static int __Pyx_setup_reduce(PyObject* type_obj);
1438 
1439 /* PyFloatBinop.proto */
1440 #if !CYTHON_COMPILING_IN_PYPY
1441 static PyObject* __Pyx_PyFloat_DivideObjC(PyObject *op1, PyObject *op2, double floatval, int inplace, int zerodivision_check);
1442 #else
1443 #define __Pyx_PyFloat_DivideObjC(op1, op2, floatval, inplace, zerodivision_check)\
1444  ((inplace ? __Pyx_PyNumber_InPlaceDivide(op1, op2) : __Pyx_PyNumber_Divide(op1, op2)))
1445  #endif
1446 
1447 /* BytesEquals.proto */
1448 static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals);
1449 
1450 /* UnicodeEquals.proto */
1451 static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals);
1452 
1453 /* StrEquals.proto */
1454 #if PY_MAJOR_VERSION >= 3
1455 #define __Pyx_PyString_Equals __Pyx_PyUnicode_Equals
1456 #else
1457 #define __Pyx_PyString_Equals __Pyx_PyBytes_Equals
1458 #endif
1459 
1460 /* CLineInTraceback.proto */
1461 #ifdef CYTHON_CLINE_IN_TRACEBACK
1462 #define __Pyx_CLineForTraceback(tstate, c_line) (((CYTHON_CLINE_IN_TRACEBACK)) ? c_line : 0)
1463 #else
1464 static int __Pyx_CLineForTraceback(PyThreadState *tstate, int c_line);
1465 #endif
1466 
1467 /* CodeObjectCache.proto */
1468 typedef struct {
1469  PyCodeObject* code_object;
1470  int code_line;
1471 } __Pyx_CodeObjectCacheEntry;
1472 struct __Pyx_CodeObjectCache {
1473  int count;
1474  int max_count;
1475  __Pyx_CodeObjectCacheEntry* entries;
1476 };
1477 static struct __Pyx_CodeObjectCache __pyx_code_cache = {0,0,NULL};
1478 static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line);
1479 static PyCodeObject *__pyx_find_code_object(int code_line);
1480 static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object);
1481 
1482 /* AddTraceback.proto */
1483 static void __Pyx_AddTraceback(const char *funcname, int c_line,
1484  int py_line, const char *filename);
1485 
1486 /* CppExceptionConversion.proto */
1487 #ifndef __Pyx_CppExn2PyErr
1488 #include <new>
1489 #include <typeinfo>
1490 #include <stdexcept>
1491 #include <ios>
1492 static void __Pyx_CppExn2PyErr() {
1493  try {
1494  if (PyErr_Occurred())
1495  ; // let the latest Python exn pass through and ignore the current one
1496  else
1497  throw;
1498  } catch (const std::bad_alloc& exn) {
1499  PyErr_SetString(PyExc_MemoryError, exn.what());
1500  } catch (const std::bad_cast& exn) {
1501  PyErr_SetString(PyExc_TypeError, exn.what());
1502  } catch (const std::bad_typeid& exn) {
1503  PyErr_SetString(PyExc_TypeError, exn.what());
1504  } catch (const std::domain_error& exn) {
1505  PyErr_SetString(PyExc_ValueError, exn.what());
1506  } catch (const std::invalid_argument& exn) {
1507  PyErr_SetString(PyExc_ValueError, exn.what());
1508  } catch (const std::ios_base::failure& exn) {
1509  PyErr_SetString(PyExc_IOError, exn.what());
1510  } catch (const std::out_of_range& exn) {
1511  PyErr_SetString(PyExc_IndexError, exn.what());
1512  } catch (const std::overflow_error& exn) {
1513  PyErr_SetString(PyExc_OverflowError, exn.what());
1514  } catch (const std::range_error& exn) {
1515  PyErr_SetString(PyExc_ArithmeticError, exn.what());
1516  } catch (const std::underflow_error& exn) {
1517  PyErr_SetString(PyExc_ArithmeticError, exn.what());
1518  } catch (const std::exception& exn) {
1519  PyErr_SetString(PyExc_RuntimeError, exn.what());
1520  }
1521  catch (...)
1522  {
1523  PyErr_SetString(PyExc_RuntimeError, "Unknown exception");
1524  }
1525 }
1526 #endif
1527 
1528 /* CIntToPy.proto */
1529 static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value);
1530 
1531 /* CIntFromPy.proto */
1532 static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *);
1533 
1534 /* CIntToPy.proto */
1535 static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value);
1536 
1537 /* CIntFromPy.proto */
1538 static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *);
1539 
1540 /* FastTypeChecks.proto */
1541 #if CYTHON_COMPILING_IN_CPYTHON
1542 #define __Pyx_TypeCheck(obj, type) __Pyx_IsSubtype(Py_TYPE(obj), (PyTypeObject *)type)
1543 static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b);
1544 static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject *type);
1545 static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *type1, PyObject *type2);
1546 #else
1547 #define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type)
1548 #define __Pyx_PyErr_GivenExceptionMatches(err, type) PyErr_GivenExceptionMatches(err, type)
1549 #define __Pyx_PyErr_GivenExceptionMatches2(err, type1, type2) (PyErr_GivenExceptionMatches(err, type1) || PyErr_GivenExceptionMatches(err, type2))
1550 #endif
1551 #define __Pyx_PyException_Check(obj) __Pyx_TypeCheck(obj, PyExc_Exception)
1552 
1553 /* FetchCommonType.proto */
1554 static PyTypeObject* __Pyx_FetchCommonType(PyTypeObject* type);
1555 
1556 /* SwapException.proto */
1557 #if CYTHON_FAST_THREAD_STATE
1558 #define __Pyx_ExceptionSwap(type, value, tb) __Pyx__ExceptionSwap(__pyx_tstate, type, value, tb)
1559 static CYTHON_INLINE void __Pyx__ExceptionSwap(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
1560 #else
1561 static CYTHON_INLINE void __Pyx_ExceptionSwap(PyObject **type, PyObject **value, PyObject **tb);
1562 #endif
1563 
1564 /* PyObjectGetMethod.proto */
1565 static int __Pyx_PyObject_GetMethod(PyObject *obj, PyObject *name, PyObject **method);
1566 
1567 /* PyObjectCallMethod1.proto */
1568 static PyObject* __Pyx_PyObject_CallMethod1(PyObject* obj, PyObject* method_name, PyObject* arg);
1569 
1570 /* CoroutineBase.proto */
1571 typedef PyObject *(*__pyx_coroutine_body_t)(PyObject *, PyThreadState *, PyObject *);
1572 #if CYTHON_USE_EXC_INFO_STACK
1573 #define __Pyx_ExcInfoStruct _PyErr_StackItem
1574 #else
1575 typedef struct {
1576  PyObject *exc_type;
1577  PyObject *exc_value;
1578  PyObject *exc_traceback;
1579 } __Pyx_ExcInfoStruct;
1580 #endif
1581 typedef struct {
1582  PyObject_HEAD
1583  __pyx_coroutine_body_t body;
1584  PyObject *closure;
1585  __Pyx_ExcInfoStruct gi_exc_state;
1586  PyObject *gi_weakreflist;
1587  PyObject *classobj;
1588  PyObject *yieldfrom;
1589  PyObject *gi_name;
1590  PyObject *gi_qualname;
1591  PyObject *gi_modulename;
1592  PyObject *gi_code;
1593  int resume_label;
1594  char is_running;
1595 } __pyx_CoroutineObject;
1596 static __pyx_CoroutineObject *__Pyx__Coroutine_New(
1597  PyTypeObject *type, __pyx_coroutine_body_t body, PyObject *code, PyObject *closure,
1598  PyObject *name, PyObject *qualname, PyObject *module_name);
1599 static __pyx_CoroutineObject *__Pyx__Coroutine_NewInit(
1600  __pyx_CoroutineObject *gen, __pyx_coroutine_body_t body, PyObject *code, PyObject *closure,
1601  PyObject *name, PyObject *qualname, PyObject *module_name);
1602 static CYTHON_INLINE void __Pyx_Coroutine_ExceptionClear(__Pyx_ExcInfoStruct *self);
1603 static int __Pyx_Coroutine_clear(PyObject *self);
1604 static PyObject *__Pyx_Coroutine_Send(PyObject *self, PyObject *value);
1605 static PyObject *__Pyx_Coroutine_Close(PyObject *self);
1606 static PyObject *__Pyx_Coroutine_Throw(PyObject *gen, PyObject *args);
1607 #if CYTHON_USE_EXC_INFO_STACK
1608 #define __Pyx_Coroutine_SwapException(self)
1609 #define __Pyx_Coroutine_ResetAndClearException(self) __Pyx_Coroutine_ExceptionClear(&(self)->gi_exc_state)
1610 #else
1611 #define __Pyx_Coroutine_SwapException(self) {\
1612  __Pyx_ExceptionSwap(&(self)->gi_exc_state.exc_type, &(self)->gi_exc_state.exc_value, &(self)->gi_exc_state.exc_traceback);\
1613  __Pyx_Coroutine_ResetFrameBackpointer(&(self)->gi_exc_state);\
1614  }
1615 #define __Pyx_Coroutine_ResetAndClearException(self) {\
1616  __Pyx_ExceptionReset((self)->gi_exc_state.exc_type, (self)->gi_exc_state.exc_value, (self)->gi_exc_state.exc_traceback);\
1617  (self)->gi_exc_state.exc_type = (self)->gi_exc_state.exc_value = (self)->gi_exc_state.exc_traceback = NULL;\
1618  }
1619 #endif
1620 #if CYTHON_FAST_THREAD_STATE
1621 #define __Pyx_PyGen_FetchStopIterationValue(pvalue)\
1622  __Pyx_PyGen__FetchStopIterationValue(__pyx_tstate, pvalue)
1623 #else
1624 #define __Pyx_PyGen_FetchStopIterationValue(pvalue)\
1625  __Pyx_PyGen__FetchStopIterationValue(__Pyx_PyThreadState_Current, pvalue)
1626 #endif
1627 static int __Pyx_PyGen__FetchStopIterationValue(PyThreadState *tstate, PyObject **pvalue);
1628 static CYTHON_INLINE void __Pyx_Coroutine_ResetFrameBackpointer(__Pyx_ExcInfoStruct *exc_state);
1629 
1630 /* PatchModuleWithCoroutine.proto */
1631 static PyObject* __Pyx_Coroutine_patch_module(PyObject* module, const char* py_code);
1632 
1633 /* PatchGeneratorABC.proto */
1634 static int __Pyx_patch_abc(void);
1635 
1636 /* Generator.proto */
1637 #define __Pyx_Generator_USED
1638 static PyTypeObject *__pyx_GeneratorType = 0;
1639 #define __Pyx_Generator_CheckExact(obj) (Py_TYPE(obj) == __pyx_GeneratorType)
1640 #define __Pyx_Generator_New(body, code, closure, name, qualname, module_name)\
1641  __Pyx__Coroutine_New(__pyx_GeneratorType, body, code, closure, name, qualname, module_name)
1642 static PyObject *__Pyx_Generator_Next(PyObject *self);
1643 static int __pyx_Generator_init(void);
1644 
1645 /* CheckBinaryVersion.proto */
1646 static int __Pyx_check_binary_version(void);
1647 
1648 /* InitStrings.proto */
1649 static int __Pyx_InitStrings(__Pyx_StringTabEntry *t);
1650 
1651 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_9index_set_wrap(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, IndexSet __pyx_v_other); /* proto*/
1652 static CYTHON_INLINE IndexSet __pyx_f_8PyClical_9index_set_unwrap(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto*/
1653 static PyObject *__pyx_f_8PyClical_9index_set_copy(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, int __pyx_skip_dispatch); /* proto*/
1654 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_8clifford_wrap(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, Clifford __pyx_v_other); /* proto*/
1655 static CYTHON_INLINE Clifford __pyx_f_8PyClical_8clifford_unwrap(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto*/
1656 static PyObject *__pyx_f_8PyClical_8clifford_copy(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, int __pyx_skip_dispatch); /* proto*/
1657 
1658 /* Module declarations from 'libcpp.vector' */
1659 
1660 /* Module declarations from 'glucat' */
1661 
1662 /* Module declarations from 'PyClical' */
1663 static PyTypeObject *__pyx_ptype_8PyClical_index_set = 0;
1664 static PyTypeObject *__pyx_ptype_8PyClical_clifford = 0;
1665 static PyTypeObject *__pyx_ptype_8PyClical___pyx_scope_struct____iter__ = 0;
1666 static CYTHON_INLINE IndexSet __pyx_f_8PyClical_toIndexSet(PyObject *); /*proto*/
1667 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_compare(PyObject *, PyObject *, int __pyx_skip_dispatch); /*proto*/
1668 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_min_neg(PyObject *, int __pyx_skip_dispatch); /*proto*/
1669 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_max_pos(PyObject *, int __pyx_skip_dispatch); /*proto*/
1670 static CYTHON_INLINE std::vector<scalar_t> __pyx_f_8PyClical_list_to_vector(PyObject *); /*proto*/
1671 static CYTHON_INLINE Clifford __pyx_f_8PyClical_toClifford(PyObject *); /*proto*/
1672 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_inv(PyObject *, int __pyx_skip_dispatch); /*proto*/
1673 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_scalar(PyObject *, int __pyx_skip_dispatch); /*proto*/
1674 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_real(PyObject *, int __pyx_skip_dispatch); /*proto*/
1675 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_imag(PyObject *, int __pyx_skip_dispatch); /*proto*/
1676 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_pure(PyObject *, int __pyx_skip_dispatch); /*proto*/
1677 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_even(PyObject *, int __pyx_skip_dispatch); /*proto*/
1678 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_odd(PyObject *, int __pyx_skip_dispatch); /*proto*/
1679 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_involute(PyObject *, int __pyx_skip_dispatch); /*proto*/
1680 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_reverse(PyObject *, int __pyx_skip_dispatch); /*proto*/
1681 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_conj(PyObject *, int __pyx_skip_dispatch); /*proto*/
1682 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_quad(PyObject *, int __pyx_skip_dispatch); /*proto*/
1683 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_norm(PyObject *, int __pyx_skip_dispatch); /*proto*/
1684 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_abs(PyObject *, int __pyx_skip_dispatch); /*proto*/
1685 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_max_abs(PyObject *, int __pyx_skip_dispatch); /*proto*/
1686 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_pow(PyObject *, PyObject *, int __pyx_skip_dispatch); /*proto*/
1687 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_outer_pow(PyObject *, PyObject *, int __pyx_skip_dispatch); /*proto*/
1688 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_complexifier(PyObject *, int __pyx_skip_dispatch); /*proto*/
1689 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_sqrt(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_sqrt *__pyx_optional_args); /*proto*/
1690 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_exp(PyObject *, int __pyx_skip_dispatch); /*proto*/
1691 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_log(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_log *__pyx_optional_args); /*proto*/
1692 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_cos(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_cos *__pyx_optional_args); /*proto*/
1693 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_acos(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_acos *__pyx_optional_args); /*proto*/
1694 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_cosh(PyObject *, int __pyx_skip_dispatch); /*proto*/
1695 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_acosh(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_acosh *__pyx_optional_args); /*proto*/
1696 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_sin(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_sin *__pyx_optional_args); /*proto*/
1697 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_asin(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_asin *__pyx_optional_args); /*proto*/
1698 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_sinh(PyObject *, int __pyx_skip_dispatch); /*proto*/
1699 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_asinh(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_asinh *__pyx_optional_args); /*proto*/
1700 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_tan(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_tan *__pyx_optional_args); /*proto*/
1701 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_atan(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_atan *__pyx_optional_args); /*proto*/
1702 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_tanh(PyObject *, int __pyx_skip_dispatch); /*proto*/
1703 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_atanh(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_atanh *__pyx_optional_args); /*proto*/
1704 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*/
1705 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_cga3(PyObject *, int __pyx_skip_dispatch); /*proto*/
1706 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_cga3std(PyObject *, int __pyx_skip_dispatch); /*proto*/
1707 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_agc3(PyObject *, int __pyx_skip_dispatch); /*proto*/
1708 #define __Pyx_MODULE_NAME "PyClical"
1709 extern int __pyx_module_is_main_PyClical;
1710 int __pyx_module_is_main_PyClical = 0;
1711 
1712 /* Implementation of 'PyClical' */
1713 static PyObject *__pyx_builtin_IndexError;
1714 static PyObject *__pyx_builtin_RuntimeError;
1715 static PyObject *__pyx_builtin_TypeError;
1716 static PyObject *__pyx_builtin_ValueError;
1717 static PyObject *__pyx_builtin_NotImplemented;
1718 static PyObject *__pyx_builtin_range;
1719 static PyObject *__pyx_builtin_xrange;
1720 static const char __pyx_k_[] = ".";
1721 static const char __pyx_k_e[] = "e";
1722 static const char __pyx_k_i[] = "i";
1723 static const char __pyx_k_m[] = "m";
1724 static const char __pyx_k_p[] = "p";
1725 static const char __pyx_k_q[] = "q";
1726 static const char __pyx_k__2[] = " ";
1727 static const char __pyx_k__5[] = ":";
1728 static const char __pyx_k__6[] = "\n\t";
1729 static const char __pyx_k__7[] = " (";
1730 static const char __pyx_k__8[] = ", ";
1731 static const char __pyx_k__9[] = ").";
1732 static const char __pyx_k_cl[] = "cl";
1733 static const char __pyx_k_pi[] = "pi";
1734 static const char __pyx_k_cos[] = "cos";
1735 static const char __pyx_k_exp[] = "exp";
1736 static const char __pyx_k_frm[] = "frm";
1737 static const char __pyx_k_inv[] = "inv";
1738 static const char __pyx_k_ist[] = "ist";
1739 static const char __pyx_k_ixt[] = "ixt";
1740 static const char __pyx_k_lhs[] = "lhs";
1741 static const char __pyx_k_log[] = "log";
1742 static const char __pyx_k_max[] = "max";
1743 static const char __pyx_k_min[] = "min";
1744 static const char __pyx_k_obj[] = "obj";
1745 static const char __pyx_k_odd[] = "odd";
1746 static const char __pyx_k_pow[] = "pow";
1747 static const char __pyx_k_rhs[] = "rhs";
1748 static const char __pyx_k_sin[] = "sin";
1749 static const char __pyx_k_tan[] = "tan";
1750 static const char __pyx_k_tau[] = "tau";
1751 static const char __pyx_k_Real[] = "Real";
1752 static const char __pyx_k_acos[] = "acos";
1753 static const char __pyx_k_args[] = "args";
1754 static const char __pyx_k_asin[] = "asin";
1755 static const char __pyx_k_atan[] = "atan";
1756 static const char __pyx_k_conj[] = "conj";
1757 static const char __pyx_k_copy[] = "copy";
1758 static const char __pyx_k_cosh[] = "cosh";
1759 static const char __pyx_k_even[] = "even";
1760 static const char __pyx_k_fill[] = "fill";
1761 static const char __pyx_k_from[] = " from ";
1762 static const char __pyx_k_iter[] = "__iter__";
1763 static const char __pyx_k_main[] = "__main__";
1764 static const char __pyx_k_math[] = "math";
1765 static const char __pyx_k_name[] = "__name__";
1766 static const char __pyx_k_norm[] = "norm";
1767 static const char __pyx_k_pure[] = "pure";
1768 static const char __pyx_k_quad[] = "quad";
1769 static const char __pyx_k_send[] = "send";
1770 static const char __pyx_k_sinh[] = "sinh";
1771 static const char __pyx_k_sqrt[] = "sqrt";
1772 static const char __pyx_k_tanh[] = "tanh";
1773 static const char __pyx_k_test[] = "_test";
1774 static const char __pyx_k_0_8_2[] = "0.8.2";
1775 static const char __pyx_k_acosh[] = "acosh";
1776 static const char __pyx_k_asinh[] = "asinh";
1777 static const char __pyx_k_atanh[] = "atanh";
1778 static const char __pyx_k_close[] = "close";
1779 static const char __pyx_k_grade[] = "grade";
1780 static const char __pyx_k_istpq[] = "istpq";
1781 static const char __pyx_k_nbar3[] = "nbar3";
1782 static const char __pyx_k_ninf3[] = "ninf3";
1783 static const char __pyx_k_other[] = "other";
1784 static const char __pyx_k_range[] = "range";
1785 static const char __pyx_k_throw[] = "throw";
1786 static const char __pyx_k_using[] = " using (";
1787 static const char __pyx_k_value[] = " value ";
1788 static const char __pyx_k_import[] = "__import__";
1789 static const char __pyx_k_reduce[] = "__reduce__";
1790 static const char __pyx_k_scalar[] = "scalar";
1791 static const char __pyx_k_test_2[] = "__test__";
1792 static const char __pyx_k_xrange[] = "xrange";
1793 static const char __pyx_k_doctest[] = "doctest";
1794 static const char __pyx_k_invalid[] = " invalid ";
1795 static const char __pyx_k_numbers[] = "numbers";
1796 static const char __pyx_k_reverse[] = "reverse";
1797 static const char __pyx_k_testmod[] = "testmod";
1798 static const char __pyx_k_version[] = "__version__";
1799 static const char __pyx_k_Integral[] = "Integral";
1800 static const char __pyx_k_PyClical[] = "PyClical";
1801 static const char __pyx_k_Sequence[] = "Sequence";
1802 static const char __pyx_k_as_frame[] = " as frame:\n\t";
1803 static const char __pyx_k_clifford[] = "clifford";
1804 static const char __pyx_k_getstate[] = "__getstate__";
1805 static const char __pyx_k_involute[] = "involute";
1806 static const char __pyx_k_setstate[] = "__setstate__";
1807 static const char __pyx_k_to_frame[] = " to frame ";
1808 static const char __pyx_k_TypeError[] = "TypeError";
1809 static const char __pyx_k_index_set[] = "index_set";
1810 static const char __pyx_k_outer_pow[] = "outer_pow";
1811 static const char __pyx_k_reduce_ex[] = "__reduce_ex__";
1812 static const char __pyx_k_IndexError[] = "IndexError";
1813 static const char __pyx_k_ValueError[] = "ValueError";
1814 static const char __pyx_k_pyx_vtable[] = "__pyx_vtable__";
1815 static const char __pyx_k_collections[] = "collections";
1816 static const char __pyx_k_e_line_1887[] = "e (line 1887)";
1817 static const char __pyx_k_PyClical_pyx[] = "PyClical.pyx";
1818 static const char __pyx_k_RuntimeError[] = "RuntimeError";
1819 static const char __pyx_k_abs_line_1473[] = "abs (line 1473)";
1820 static const char __pyx_k_cos_line_1602[] = "cos (line 1602)";
1821 static const char __pyx_k_exp_line_1565[] = "exp (line 1565)";
1822 static const char __pyx_k_inv_line_1329[] = "inv (line 1329)";
1823 static const char __pyx_k_log_line_1579[] = "log (line 1579)";
1824 static const char __pyx_k_odd_line_1397[] = "odd (line 1397)";
1825 static const char __pyx_k_pow_line_1494[] = "pow (line 1494)";
1826 static const char __pyx_k_reduce_cython[] = "__reduce_cython__";
1827 static const char __pyx_k_sin_line_1679[] = "sin (line 1679)";
1828 static const char __pyx_k_tan_line_1752[] = "tan (line 1752)";
1829 static const char __pyx_k_using_invalid[] = " using invalid ";
1830 static const char __pyx_k_Cannot_reframe[] = "Cannot reframe";
1831 static const char __pyx_k_NotImplemented[] = "NotImplemented";
1832 static const char __pyx_k_Not_applicable[] = "Not applicable.";
1833 static const char __pyx_k_acos_line_1619[] = "acos (line 1619)";
1834 static const char __pyx_k_agc3_line_1844[] = "agc3 (line 1844)";
1835 static const char __pyx_k_asin_line_1698[] = "asin (line 1698)";
1836 static const char __pyx_k_atan_line_1769[] = "atan (line 1769)";
1837 static const char __pyx_k_cga3_line_1824[] = "cga3 (line 1824)";
1838 static const char __pyx_k_conj_line_1436[] = "conj (line 1436)";
1839 static const char __pyx_k_cosh_line_1640[] = "cosh (line 1640)";
1840 static const char __pyx_k_even_line_1388[] = "even (line 1388)";
1841 static const char __pyx_k_imag_line_1366[] = "imag (line 1366)";
1842 static const char __pyx_k_invalid_string[] = " invalid string ";
1843 static const char __pyx_k_norm_line_1462[] = "norm (line 1462)";
1844 static const char __pyx_k_pure_line_1377[] = "pure (line 1377)";
1845 static const char __pyx_k_quad_line_1451[] = "quad (line 1451)";
1846 static const char __pyx_k_real_line_1355[] = "real (line 1355)";
1847 static const char __pyx_k_sinh_line_1719[] = "sinh (line 1719)";
1848 static const char __pyx_k_sqrt_line_1542[] = "sqrt (line 1542)";
1849 static const char __pyx_k_tanh_line_1786[] = "tanh (line 1786)";
1850 static const char __pyx_k_acosh_line_1656[] = "acosh (line 1656)";
1851 static const char __pyx_k_asinh_line_1733[] = "asinh (line 1733)";
1852 static const char __pyx_k_atanh_line_1798[] = "atanh (line 1798)";
1853 static const char __pyx_k_istpq_line_1900[] = "istpq (line 1900)";
1854 static const char __pyx_k_setstate_cython[] = "__setstate_cython__";
1855 static const char __pyx_k_compare_line_490[] = "compare (line 490)";
1856 static const char __pyx_k_index_set___iter[] = "index_set.__iter__";
1857 static const char __pyx_k_max_pos_line_511[] = "max_pos (line 511)";
1858 static const char __pyx_k_min_neg_line_502[] = "min_neg (line 502)";
1859 static const char __pyx_k_scalar_line_1344[] = "scalar (line 1344)";
1860 static const char __pyx_k_cga3std_line_1833[] = "cga3std (line 1833)";
1861 static const char __pyx_k_max_abs_line_1482[] = "max_abs (line 1482)";
1862 static const char __pyx_k_reverse_line_1421[] = "reverse (line 1421)";
1863 static const char __pyx_k_cline_in_traceback[] = "cline_in_traceback";
1864 static const char __pyx_k_involute_line_1406[] = "involute (line 1406)";
1865 static const char __pyx_k_outer_pow_line_1518[] = "outer_pow (line 1518)";
1866 static const char __pyx_k_clifford_inv_line_925[] = "clifford.inv (line 925)";
1867 static const char __pyx_k_clifford_pow_line_979[] = "clifford.pow (line 979)";
1868 static const char __pyx_k_clifford_abs_line_1174[] = "clifford.abs (line 1174)";
1869 static const char __pyx_k_clifford_copy_line_554[] = "clifford.copy (line 554)";
1870 static const char __pyx_k_clifford_odd_line_1069[] = "clifford.odd (line 1069)";
1871 static const char __pyx_k_complexifier_line_1527[] = "complexifier (line 1527)";
1872 static const char __pyx_k_index_set_copy_line_64[] = "index_set.copy (line 64)";
1873 static const char __pyx_k_index_set_max_line_349[] = "index_set.max (line 349)";
1874 static const char __pyx_k_index_set_min_line_340[] = "index_set.min (line 340)";
1875 static const char __pyx_k_clifford_conj_line_1137[] = "clifford.conj (line 1137)";
1876 static const char __pyx_k_clifford_even_line_1060[] = "clifford.even (line 1060)";
1877 static const char __pyx_k_clifford_norm_line_1163[] = "clifford.norm (line 1163)";
1878 static const char __pyx_k_clifford_pure_line_1049[] = "clifford.pure (line 1049)";
1879 static const char __pyx_k_clifford_quad_line_1152[] = "clifford.quad (line 1152)";
1880 static const char __pyx_k_Unary_print_clifford_1_1[] = "\n Unary -.\n\n >>> print -clifford(\"{1}\")\n -{1}\n ";
1881 static const char __pyx_k_clifford___or___line_938[] = "clifford.__or__ (line 938)";
1882 static const char __pyx_k_clifford_frame_line_1214[] = "clifford.frame (line 1214)";
1883 static const char __pyx_k_clifford_hidden_doctests[] = "clifford_hidden_doctests";
1884 static const char __pyx_k_clifford_isnan_line_1205[] = "clifford.isnan (line 1205)";
1885 static const char __pyx_k_index_set_count_line_313[] = "index_set.count (line 313)";
1886 static const char __pyx_k_clifford___add___line_739[] = "clifford.__add__ (line 739)";
1887 static const char __pyx_k_clifford___and___line_835[] = "clifford.__and__ (line 835)";
1888 static const char __pyx_k_clifford___div___line_895[] = "clifford.__div__ (line 895)";
1889 static const char __pyx_k_clifford___ior___line_949[] = "clifford.__ior__ (line 949)";
1890 static const char __pyx_k_clifford___mod___line_805[] = "clifford.__mod__ (line 805)";
1891 static const char __pyx_k_clifford___mul___line_779[] = "clifford.__mul__ (line 779)";
1892 static const char __pyx_k_clifford___neg___line_721[] = "clifford.__neg__ (line 721)";
1893 static const char __pyx_k_clifford___pos___line_730[] = "clifford.__pos__ (line 730)";
1894 static const char __pyx_k_clifford___pow___line_960[] = "clifford.__pow__ (line 960)";
1895 static const char __pyx_k_clifford___sub___line_759[] = "clifford.__sub__ (line 759)";
1896 static const char __pyx_k_clifford___xor___line_865[] = "clifford.__xor__ (line 865)";
1897 static const char __pyx_k_clifford_reframe_line_648[] = "clifford.reframe (line 648)";
1898 static const char __pyx_k_clifford_scalar_line_1038[] = "clifford.scalar (line 1038)";
1899 static const char __pyx_k_index_set___or___line_291[] = "index_set.__or__ (line 291)";
1900 static const char __pyx_k_index_set_hidden_doctests[] = "index_set_hidden_doctests";
1901 static const char __pyx_k_random_clifford_line_1815[] = "random_clifford (line 1815)";
1902 static const char __pyx_k_Cannot_take_vector_part_of[] = "Cannot take vector part of ";
1903 static const char __pyx_k_Unary_print_clifford_1_1_2[] = "\n Unary +.\n\n >>> print +clifford(\"{1}\")\n {1}\n ";
1904 static const char __pyx_k_clifford___iadd___line_750[] = "clifford.__iadd__ (line 750)";
1905 static const char __pyx_k_clifford___iand___line_850[] = "clifford.__iand__ (line 850)";
1906 static const char __pyx_k_clifford___idiv___line_910[] = "clifford.__idiv__ (line 910)";
1907 static const char __pyx_k_clifford___imod___line_820[] = "clifford.__imod__ (line 820)";
1908 static const char __pyx_k_clifford___imul___line_792[] = "clifford.__imul__ (line 792)";
1909 static const char __pyx_k_clifford___isub___line_770[] = "clifford.__isub__ (line 770)";
1910 static const char __pyx_k_clifford___iter___line_637[] = "clifford.__iter__ (line 637)";
1911 static const char __pyx_k_clifford___ixor___line_880[] = "clifford.__ixor__ (line 880)";
1912 static const char __pyx_k_clifford___str___line_1234[] = "clifford.__str__ (line 1234)";
1913 static const char __pyx_k_clifford_max_abs_line_1183[] = "clifford.max_abs (line 1183)";
1914 static const char __pyx_k_clifford_reverse_line_1122[] = "clifford.reverse (line 1122)";
1915 static const char __pyx_k_index_set___and___line_269[] = "index_set.__and__ (line 269)";
1916 static const char __pyx_k_index_set___ior___line_302[] = "index_set.__ior__ (line 302)";
1917 static const char __pyx_k_index_set___str___line_393[] = "index_set.__str__ (line 393)";
1918 static const char __pyx_k_index_set___xor___line_247[] = "index_set.__xor__ (line 247)";
1919 static const char __pyx_k_clifford___call___line_1019[] = "clifford.__call__ (line 1019)";
1920 static const char __pyx_k_clifford___repr___line_1225[] = "clifford.__repr__ (line 1225)";
1921 static const char __pyx_k_clifford_involute_line_1106[] = "clifford.involute (line 1106)";
1922 static const char __pyx_k_index_set___iand___line_280[] = "index_set.__iand__ (line 280)";
1923 static const char __pyx_k_index_set___iter___line_227[] = "index_set.__iter__ (line 227)";
1924 static const char __pyx_k_index_set___ixor___line_258[] = "index_set.__ixor__ (line 258)";
1925 static const char __pyx_k_index_set___repr___line_382[] = "index_set.__repr__ (line 382)";
1926 static const char __pyx_k_clifford_outer_pow_line_1003[] = "clifford.outer_pow (line 1003)";
1927 static const char __pyx_k_clifford_truncated_line_1194[] = "clifford.truncated (line 1194)";
1928 static const char __pyx_k_index_set_count_neg_line_322[] = "index_set.count_neg (line 322)";
1929 static const char __pyx_k_index_set_count_pos_line_331[] = "index_set.count_pos (line 331)";
1930 static const char __pyx_k_clifford___getitem___line_706[] = "clifford.__getitem__ (line 706)";
1931 static const char __pyx_k_index_set___invert___line_238[] = "index_set.__invert__ (line 238)";
1932 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 ";
1933 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 ";
1934 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 ";
1935 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 ";
1936 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 ";
1937 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 ";
1938 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 ";
1939 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 ";
1940 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 ";
1941 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 ";
1942 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 ";
1943 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 ";
1944 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 ";
1945 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 ";
1946 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 ";
1947 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 ";
1948 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 ";
1949 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 ";
1950 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 ";
1951 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 ";
1952 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 ";
1953 static const char __pyx_k_clifford_vector_part_line_1078[] = "clifford.vector_part (line 1078)";
1954 static const char __pyx_k_index_set___getitem___line_189[] = "index_set.__getitem__ (line 189)";
1955 static const char __pyx_k_index_set___setitem___line_177[] = "index_set.__setitem__ (line 177)";
1956 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 ";
1957 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 ";
1958 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 ";
1959 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 ";
1960 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 ";
1961 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 ";
1962 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 ";
1963 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 ";
1964 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 ";
1965 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 ";
1966 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 ";
1967 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 ";
1968 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 ";
1969 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 ";
1970 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 ";
1971 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 ";
1972 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 ";
1973 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 ";
1974 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 ";
1975 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 ";
1976 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 ";
1977 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 ";
1978 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 ";
1979 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 ";
1980 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 ";
1981 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 ";
1982 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 ";
1983 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 ";
1984 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 ";
1985 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 ";
1986 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 ";
1987 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 ";
1988 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 ";
1989 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 ";
1990 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 ";
1991 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 ";
1992 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 ";
1993 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 ";
1994 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 ";
1995 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 ";
1996 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 ";
1997 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 ";
1998 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 ";
1999 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 ";
2000 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 ";
2001 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 ";
2002 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 ";
2003 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 ";
2004 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 ";
2005 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 ";
2006 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 ";
2007 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 ";
2008 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 ";
2009 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 ";
2010 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 ";
2011 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 ";
2012 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 ";
2013 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 ";
2014 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 ";
2015 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 ";
2016 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 ";
2017 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 ";
2018 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 ";
2019 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 ";
2020 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 ";
2021 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 ";
2022 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 ";
2023 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 ";
2024  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 ";
2025  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 ";
2026  static const char __pyx_k_This_comparison_operator_is_not[] = "This comparison operator is not implemented for ";
2027  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 ";
2028  static const char __pyx_k_index_set_sign_of_mult_line_364[] = "index_set.sign_of_mult (line 364)";
2029  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 ";
2030  static const char __pyx_k_Cannot_initialize_clifford_objec[] = "Cannot initialize clifford object from";
2031  static const char __pyx_k_Cannot_initialize_index_set_obje[] = "Cannot initialize index_set object from";
2032  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 ";
2033  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 ";
2034  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 ";
2035  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 ";
2036  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 ";
2037  static const char __pyx_k_clifford_hidden_doctests_line_12[] = "clifford_hidden_doctests (line 1243)";
2038  static const char __pyx_k_index_set_hidden_doctests_line_4[] = "index_set_hidden_doctests (line 404)";
2039  static const char __pyx_k_index_set_sign_of_square_line_37[] = "index_set.sign_of_square (line 373)";
2040  static const char __pyx_k_no_default___reduce___due_to_non[] = "no default __reduce__ due to non-trivial __cinit__";
2041  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 ";
2042  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 ";
2043  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 ";
2044  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 ";
2045  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 ";
2046  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 ";
2047  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 ";
2048  static PyObject *__pyx_kp_s_;
2049  static PyObject *__pyx_kp_s_0_8_2;
2050  static PyObject *__pyx_kp_u_Abbreviation_for_clifford_index;
2051  static PyObject *__pyx_kp_u_Abbreviation_for_index_set_q_p;
2052  static PyObject *__pyx_kp_u_Absolute_value_of_multivector_m;
2053  static PyObject *__pyx_kp_u_Absolute_value_square_root_of_n;
2054  static PyObject *__pyx_kp_s_Cannot_initialize_clifford_objec;
2055  static PyObject *__pyx_kp_s_Cannot_initialize_index_set_obje;
2056  static PyObject *__pyx_kp_s_Cannot_reframe;
2057  static PyObject *__pyx_kp_s_Cannot_take_vector_part_of;
2058  static PyObject *__pyx_kp_u_Cardinality_Number_of_indices_i;
2059  static PyObject *__pyx_kp_u_Check_if_a_multivector_contains;
2060  static PyObject *__pyx_kp_u_Conjugation_reverse_o_involute;
2061  static PyObject *__pyx_kp_u_Conjugation_reverse_o_involute_2;
2062  static PyObject *__pyx_kp_u_Contraction_print_clifford_1_cl;
2063  static PyObject *__pyx_kp_u_Contraction_x_clifford_1_x_clif;
2064  static PyObject *__pyx_kp_u_Convert_CGA3_null_vector_to_Euc;
2065  static PyObject *__pyx_kp_u_Convert_CGA3_null_vector_to_sta;
2066  static PyObject *__pyx_kp_u_Convert_Euclidean_3D_multivecto;
2067  static PyObject *__pyx_kp_u_Copy_this_clifford_object_x_cli;
2068  static PyObject *__pyx_kp_u_Copy_this_index_set_object_s_in;
2069  static PyObject *__pyx_kp_u_Cosine_of_multivector_with_opti;
2070  static PyObject *__pyx_kp_u_Even_part_of_multivector_sum_of;
2071  static PyObject *__pyx_kp_u_Even_part_of_multivector_sum_of_2;
2072  static PyObject *__pyx_kp_u_Exponential_of_multivector_x_cl;
2073  static PyObject *__pyx_kp_u_Geometric_difference_print_clif;
2074  static PyObject *__pyx_kp_u_Geometric_difference_x_clifford;
2075  static PyObject *__pyx_kp_u_Geometric_multiplicative_invers;
2076  static PyObject *__pyx_kp_u_Geometric_multiplicative_invers_2;
2077  static PyObject *__pyx_kp_u_Geometric_product_print_cliffor;
2078  static PyObject *__pyx_kp_u_Geometric_product_x_clifford_2;
2079  static PyObject *__pyx_kp_u_Geometric_quotient_print_cliffo;
2080  static PyObject *__pyx_kp_u_Geometric_quotient_x_clifford_1;
2081  static PyObject *__pyx_kp_u_Geometric_sum_print_clifford_1;
2082  static PyObject *__pyx_kp_u_Geometric_sum_x_clifford_1_x_cl;
2083  static PyObject *__pyx_kp_u_Get_the_value_of_an_index_set_o;
2084  static PyObject *__pyx_kp_u_Hyperbolic_cosine_of_multivecto;
2085  static PyObject *__pyx_kp_u_Hyperbolic_sine_of_multivector;
2086  static PyObject *__pyx_kp_u_Hyperbolic_tangent_of_multivect;
2087  static PyObject *__pyx_kp_u_Imaginary_part_deprecated_alway;
2088  static PyObject *__pyx_n_s_IndexError;
2089  static PyObject *__pyx_kp_u_Inner_product_print_clifford_1;
2090  static PyObject *__pyx_kp_u_Inner_product_x_clifford_1_x_cl;
2091  static PyObject *__pyx_kp_u_Integer_power_of_multivector_ob;
2092  static PyObject *__pyx_n_s_Integral;
2093  static PyObject *__pyx_kp_u_Inverse_cosine_of_multivector_w;
2094  static PyObject *__pyx_kp_u_Inverse_hyperbolic_cosine_of_mu;
2095  static PyObject *__pyx_kp_u_Inverse_hyperbolic_sine_of_mult;
2096  static PyObject *__pyx_kp_u_Inverse_hyperbolic_tangent_of_m;
2097  static PyObject *__pyx_kp_u_Inverse_sine_of_multivector_wit;
2098  static PyObject *__pyx_kp_u_Inverse_tangent_of_multivector;
2099  static PyObject *__pyx_kp_u_Iterate_over_the_indices_of_an;
2100  static PyObject *__pyx_kp_u_Main_involution_each_i_is_repla;
2101  static PyObject *__pyx_kp_u_Main_involution_each_i_is_repla_2;
2102  static PyObject *__pyx_kp_u_Maximum_absolute_value_of_coord;
2103  static PyObject *__pyx_kp_u_Maximum_member_index_set_1_1_2;
2104  static PyObject *__pyx_kp_u_Maximum_of_absolute_values_of_c;
2105  static PyObject *__pyx_kp_u_Maximum_positive_index_or_0_if;
2106  static PyObject *__pyx_kp_u_Minimum_member_index_set_1_1_2;
2107  static PyObject *__pyx_kp_u_Minimum_negative_index_or_0_if;
2108  static PyObject *__pyx_kp_u_Natural_logarithm_of_multivecto;
2109  static PyObject *__pyx_kp_u_Norm_sum_of_squares_of_coordina;
2110  static PyObject *__pyx_n_s_NotImplemented;
2111  static PyObject *__pyx_kp_s_Not_applicable;
2112  static PyObject *__pyx_kp_u_Not_applicable_for_a_in_cliffor;
2113  static PyObject *__pyx_kp_u_Number_of_negative_indices_incl;
2114  static PyObject *__pyx_kp_u_Number_of_positive_indices_incl;
2115  static PyObject *__pyx_kp_u_Odd_part_of_multivector_sum_of;
2116  static PyObject *__pyx_kp_u_Odd_part_of_multivector_sum_of_2;
2117  static PyObject *__pyx_kp_u_Outer_product_power_of_multivec;
2118  static PyObject *__pyx_kp_u_Outer_product_power_x_clifford;
2119  static PyObject *__pyx_kp_u_Outer_product_print_clifford_1;
2120  static PyObject *__pyx_kp_u_Outer_product_x_clifford_1_x_cl;
2121  static PyObject *__pyx_kp_u_Power_self_to_the_m_x_clifford;
2122  static PyObject *__pyx_kp_u_Power_self_to_the_m_x_clifford_2;
2123  static PyObject *__pyx_kp_u_Pure_grade_vector_part_print_cl;
2124  static PyObject *__pyx_kp_u_Pure_part_print_clifford_1_1_1;
2125  static PyObject *__pyx_kp_u_Pure_part_print_pure_clifford_1;
2126  static PyObject *__pyx_kp_u_Put_self_into_a_larger_frame_co;
2127  static PyObject *__pyx_n_s_PyClical;
2128  static PyObject *__pyx_kp_s_PyClical_pyx;
2129  static PyObject *__pyx_kp_u_Quadratic_form_rev_x_x_0_print;
2130  static PyObject *__pyx_kp_u_Quadratic_form_rev_x_x_0_print_2;
2131  static PyObject *__pyx_kp_u_Random_multivector_within_a_fra;
2132  static PyObject *__pyx_n_s_Real;
2133  static PyObject *__pyx_kp_u_Real_part_synonym_for_scalar_pa;
2134  static PyObject *__pyx_kp_u_Remove_all_terms_of_self_with_r;
2135  static PyObject *__pyx_kp_u_Reversion_eg_1_2_2_1_print_reve;
2136  static PyObject *__pyx_kp_u_Reversion_eg_clifford_1_cliffor;
2137  static PyObject *__pyx_n_s_RuntimeError;
2138  static PyObject *__pyx_kp_u_Scalar_part_clifford_1_1_1_2_sc;
2139  static PyObject *__pyx_kp_u_Scalar_part_scalar_clifford_1_1;
2140  static PyObject *__pyx_n_s_Sequence;
2141  static PyObject *__pyx_kp_u_Set_complement_not_print_index;
2142  static PyObject *__pyx_kp_u_Set_intersection_and_print_inde;
2143  static PyObject *__pyx_kp_u_Set_intersection_and_x_index_se;
2144  static PyObject *__pyx_kp_u_Set_the_value_of_an_index_set_o;
2145  static PyObject *__pyx_kp_u_Set_union_or_print_index_set_1;
2146  static PyObject *__pyx_kp_u_Set_union_or_x_index_set_1_x_in;
2147  static PyObject *__pyx_kp_u_Sign_of_geometric_product_of_tw;
2148  static PyObject *__pyx_kp_u_Sign_of_geometric_square_of_a_C;
2149  static PyObject *__pyx_kp_u_Sine_of_multivector_with_option;
2150  static PyObject *__pyx_kp_u_Square_root_of_1_which_commutes;
2151  static PyObject *__pyx_kp_u_Square_root_of_multivector_with;
2152  static PyObject *__pyx_kp_u_Subalgebra_generated_by_all_gen;
2153  static PyObject *__pyx_kp_u_Subscripting_map_from_index_set;
2154  static PyObject *__pyx_kp_u_Symmetric_set_difference_exclus;
2155  static PyObject *__pyx_kp_u_Symmetric_set_difference_exclus_2;
2156  static PyObject *__pyx_kp_u_Tangent_of_multivector_with_opt;
2157  static PyObject *__pyx_kp_u_Tests_for_functions_that_Doctes;
2158  static PyObject *__pyx_kp_u_Tests_for_functions_that_Doctes_2;
2159  static PyObject *__pyx_kp_u_The_informal_string_representat;
2160  static PyObject *__pyx_kp_u_The_informal_string_representat_2;
2161  static PyObject *__pyx_kp_u_The_official_string_representat;
2162  static PyObject *__pyx_kp_u_The_official_string_representat_2;
2163  static PyObject *__pyx_kp_s_This_comparison_operator_is_not;
2164  static PyObject *__pyx_kp_u_Transform_left_hand_side_using;
2165  static PyObject *__pyx_kp_u_Transform_left_hand_side_using_2;
2166  static PyObject *__pyx_n_s_TypeError;
2167  static PyObject *__pyx_kp_u_Unary_print_clifford_1_1;
2168  static PyObject *__pyx_kp_u_Unary_print_clifford_1_1_2;
2169  static PyObject *__pyx_n_s_ValueError;
2170  static PyObject *__pyx_kp_u_Vector_part_of_multivector_as_a;
2171  static PyObject *__pyx_kp_s__2;
2172  static PyObject *__pyx_kp_s__5;
2173  static PyObject *__pyx_kp_s__6;
2174  static PyObject *__pyx_kp_s__7;
2175  static PyObject *__pyx_kp_s__8;
2176  static PyObject *__pyx_kp_s__9;
2177  static PyObject *__pyx_kp_u_abs_line_1473;
2178  static PyObject *__pyx_n_s_acos;
2179  static PyObject *__pyx_kp_u_acos_line_1619;
2180  static PyObject *__pyx_n_s_acosh;
2181  static PyObject *__pyx_kp_u_acosh_line_1656;
2182  static PyObject *__pyx_kp_u_agc3_line_1844;
2183  static PyObject *__pyx_n_s_args;
2184  static PyObject *__pyx_kp_s_as_frame;
2185  static PyObject *__pyx_n_s_asin;
2186  static PyObject *__pyx_kp_u_asin_line_1698;
2187  static PyObject *__pyx_n_s_asinh;
2188  static PyObject *__pyx_kp_u_asinh_line_1733;
2189  static PyObject *__pyx_n_s_atan;
2190  static PyObject *__pyx_kp_u_atan_line_1769;
2191  static PyObject *__pyx_n_s_atanh;
2192  static PyObject *__pyx_kp_u_atanh_line_1798;
2193  static PyObject *__pyx_kp_u_cga3_line_1824;
2194  static PyObject *__pyx_kp_u_cga3std_line_1833;
2195  static PyObject *__pyx_n_s_cl;
2196  static PyObject *__pyx_n_s_clifford;
2197  static PyObject *__pyx_kp_u_clifford___add___line_739;
2198  static PyObject *__pyx_kp_u_clifford___and___line_835;
2199  static PyObject *__pyx_kp_u_clifford___call___line_1019;
2200  static PyObject *__pyx_kp_u_clifford___div___line_895;
2201  static PyObject *__pyx_kp_u_clifford___getitem___line_706;
2202  static PyObject *__pyx_kp_u_clifford___iadd___line_750;
2203  static PyObject *__pyx_kp_u_clifford___iand___line_850;
2204  static PyObject *__pyx_kp_u_clifford___idiv___line_910;
2205  static PyObject *__pyx_kp_u_clifford___imod___line_820;
2206  static PyObject *__pyx_kp_u_clifford___imul___line_792;
2207  static PyObject *__pyx_kp_u_clifford___ior___line_949;
2208  static PyObject *__pyx_kp_u_clifford___isub___line_770;
2209  static PyObject *__pyx_kp_u_clifford___iter___line_637;
2210  static PyObject *__pyx_kp_u_clifford___ixor___line_880;
2211  static PyObject *__pyx_kp_u_clifford___mod___line_805;
2212  static PyObject *__pyx_kp_u_clifford___mul___line_779;
2213  static PyObject *__pyx_kp_u_clifford___neg___line_721;
2214  static PyObject *__pyx_kp_u_clifford___or___line_938;
2215  static PyObject *__pyx_kp_u_clifford___pos___line_730;
2216  static PyObject *__pyx_kp_u_clifford___pow___line_960;
2217  static PyObject *__pyx_kp_u_clifford___repr___line_1225;
2218  static PyObject *__pyx_kp_u_clifford___str___line_1234;
2219  static PyObject *__pyx_kp_u_clifford___sub___line_759;
2220  static PyObject *__pyx_kp_u_clifford___xor___line_865;
2221  static PyObject *__pyx_kp_u_clifford_abs_line_1174;
2222  static PyObject *__pyx_kp_u_clifford_conj_line_1137;
2223  static PyObject *__pyx_kp_u_clifford_copy_line_554;
2224  static PyObject *__pyx_kp_u_clifford_even_line_1060;
2225  static PyObject *__pyx_kp_u_clifford_frame_line_1214;
2226  static PyObject *__pyx_n_s_clifford_hidden_doctests;
2227  static PyObject *__pyx_kp_u_clifford_hidden_doctests_line_12;
2228  static PyObject *__pyx_kp_u_clifford_inv_line_925;
2229  static PyObject *__pyx_kp_u_clifford_involute_line_1106;
2230  static PyObject *__pyx_kp_u_clifford_isnan_line_1205;
2231  static PyObject *__pyx_kp_u_clifford_max_abs_line_1183;
2232  static PyObject *__pyx_kp_u_clifford_norm_line_1163;
2233  static PyObject *__pyx_kp_u_clifford_odd_line_1069;
2234  static PyObject *__pyx_kp_u_clifford_outer_pow_line_1003;
2235  static PyObject *__pyx_kp_u_clifford_pow_line_979;
2236  static PyObject *__pyx_kp_u_clifford_pure_line_1049;
2237  static PyObject *__pyx_kp_u_clifford_quad_line_1152;
2238  static PyObject *__pyx_kp_u_clifford_reframe_line_648;
2239  static PyObject *__pyx_kp_u_clifford_reverse_line_1122;
2240  static PyObject *__pyx_kp_u_clifford_scalar_line_1038;
2241  static PyObject *__pyx_kp_u_clifford_truncated_line_1194;
2242  static PyObject *__pyx_kp_u_clifford_vector_part_line_1078;
2243  static PyObject *__pyx_n_s_cline_in_traceback;
2244  static PyObject *__pyx_n_s_close;
2245  static PyObject *__pyx_n_s_collections;
2246  static PyObject *__pyx_kp_u_compare_line_490;
2247  static PyObject *__pyx_kp_u_complexifier_line_1527;
2248  static PyObject *__pyx_n_s_conj;
2249  static PyObject *__pyx_kp_u_conj_line_1436;
2250  static PyObject *__pyx_n_s_copy;
2251  static PyObject *__pyx_n_s_cos;
2252  static PyObject *__pyx_kp_u_cos_line_1602;
2253  static PyObject *__pyx_n_s_cosh;
2254  static PyObject *__pyx_kp_u_cosh_line_1640;
2255  static PyObject *__pyx_n_s_doctest;
2256  static PyObject *__pyx_n_s_e;
2257  static PyObject *__pyx_kp_u_e_line_1887;
2258  static PyObject *__pyx_n_s_even;
2259  static PyObject *__pyx_kp_u_even_line_1388;
2260  static PyObject *__pyx_n_s_exp;
2261  static PyObject *__pyx_kp_u_exp_line_1565;
2262  static PyObject *__pyx_n_s_fill;
2263  static PyObject *__pyx_n_s_frm;
2264  static PyObject *__pyx_kp_s_from;
2265  static PyObject *__pyx_n_s_getstate;
2266  static PyObject *__pyx_n_s_grade;
2267  static PyObject *__pyx_n_s_i;
2268  static PyObject *__pyx_kp_u_imag_line_1366;
2269  static PyObject *__pyx_n_s_import;
2270  static PyObject *__pyx_n_s_index_set;
2271  static PyObject *__pyx_kp_u_index_set___and___line_269;
2272  static PyObject *__pyx_kp_u_index_set___getitem___line_189;
2273  static PyObject *__pyx_kp_u_index_set___iand___line_280;
2274  static PyObject *__pyx_kp_u_index_set___invert___line_238;
2275  static PyObject *__pyx_kp_u_index_set___ior___line_302;
2276  static PyObject *__pyx_n_s_index_set___iter;
2277  static PyObject *__pyx_kp_u_index_set___iter___line_227;
2278  static PyObject *__pyx_kp_u_index_set___ixor___line_258;
2279  static PyObject *__pyx_kp_u_index_set___or___line_291;
2280  static PyObject *__pyx_kp_u_index_set___repr___line_382;
2281  static PyObject *__pyx_kp_u_index_set___setitem___line_177;
2282  static PyObject *__pyx_kp_u_index_set___str___line_393;
2283  static PyObject *__pyx_kp_u_index_set___xor___line_247;
2284  static PyObject *__pyx_kp_u_index_set_copy_line_64;
2285  static PyObject *__pyx_kp_u_index_set_count_line_313;
2286  static PyObject *__pyx_kp_u_index_set_count_neg_line_322;
2287  static PyObject *__pyx_kp_u_index_set_count_pos_line_331;
2288  static PyObject *__pyx_n_s_index_set_hidden_doctests;
2289  static PyObject *__pyx_kp_u_index_set_hidden_doctests_line_4;
2290  static PyObject *__pyx_kp_u_index_set_max_line_349;
2291  static PyObject *__pyx_kp_u_index_set_min_line_340;
2292  static PyObject *__pyx_kp_u_index_set_sign_of_mult_line_364;
2293  static PyObject *__pyx_kp_u_index_set_sign_of_square_line_37;
2294  static PyObject *__pyx_n_s_inv;
2295  static PyObject *__pyx_kp_u_inv_line_1329;
2296  static PyObject *__pyx_kp_s_invalid;
2297  static PyObject *__pyx_kp_s_invalid_string;
2298  static PyObject *__pyx_n_s_involute;
2299  static PyObject *__pyx_kp_u_involute_line_1406;
2300  static PyObject *__pyx_n_s_ist;
2301  static PyObject *__pyx_n_s_istpq;
2302  static PyObject *__pyx_kp_u_istpq_line_1900;
2303  static PyObject *__pyx_n_s_iter;
2304  static PyObject *__pyx_n_s_ixt;
2305  static PyObject *__pyx_kp_u_lexicographic_compare_eg_3_4_5;
2306  static PyObject *__pyx_n_s_lhs;
2307  static PyObject *__pyx_n_s_log;
2308  static PyObject *__pyx_kp_u_log_line_1579;
2309  static PyObject *__pyx_n_s_m;
2310  static PyObject *__pyx_n_s_main;
2311  static PyObject *__pyx_n_s_math;
2312  static PyObject *__pyx_n_s_max;
2313  static PyObject *__pyx_kp_u_max_abs_line_1482;
2314  static PyObject *__pyx_kp_u_max_pos_line_511;
2315  static PyObject *__pyx_n_s_min;
2316  static PyObject *__pyx_kp_u_min_neg_line_502;
2317  static PyObject *__pyx_n_s_name;
2318  static PyObject *__pyx_n_s_nbar3;
2319  static PyObject *__pyx_n_s_ninf3;
2320  static PyObject *__pyx_kp_s_no_default___reduce___due_to_non;
2321  static PyObject *__pyx_n_s_norm;
2322  static PyObject *__pyx_kp_u_norm_line_1462;
2323  static PyObject *__pyx_kp_u_norm_sum_of_squares_of_coordina;
2324  static PyObject *__pyx_n_s_numbers;
2325  static PyObject *__pyx_n_s_obj;
2326  static PyObject *__pyx_n_s_odd;
2327  static PyObject *__pyx_kp_u_odd_line_1397;
2328  static PyObject *__pyx_n_s_other;
2329  static PyObject *__pyx_n_s_outer_pow;
2330  static PyObject *__pyx_kp_u_outer_pow_line_1518;
2331  static PyObject *__pyx_n_s_p;
2332  static PyObject *__pyx_n_s_pi;
2333  static PyObject *__pyx_n_s_pow;
2334  static PyObject *__pyx_kp_u_pow_line_1494;
2335  static PyObject *__pyx_n_s_pure;
2336  static PyObject *__pyx_kp_u_pure_line_1377;
2337  static PyObject *__pyx_n_s_pyx_vtable;
2338  static PyObject *__pyx_n_s_q;
2339  static PyObject *__pyx_n_s_quad;
2340  static PyObject *__pyx_kp_u_quad_line_1451;
2341  static PyObject *__pyx_kp_u_random_clifford_line_1815;
2342  static PyObject *__pyx_n_s_range;
2343  static PyObject *__pyx_kp_u_real_line_1355;
2344  static PyObject *__pyx_n_s_reduce;
2345  static PyObject *__pyx_n_s_reduce_cython;
2346  static PyObject *__pyx_n_s_reduce_ex;
2347  static PyObject *__pyx_n_s_reverse;
2348  static PyObject *__pyx_kp_u_reverse_line_1421;
2349  static PyObject *__pyx_n_s_rhs;
2350  static PyObject *__pyx_n_s_scalar;
2351  static PyObject *__pyx_kp_u_scalar_line_1344;
2352  static PyObject *__pyx_n_s_send;
2353  static PyObject *__pyx_n_s_setstate;
2354  static PyObject *__pyx_n_s_setstate_cython;
2355  static PyObject *__pyx_n_s_sin;
2356  static PyObject *__pyx_kp_u_sin_line_1679;
2357  static PyObject *__pyx_n_s_sinh;
2358  static PyObject *__pyx_kp_u_sinh_line_1719;
2359  static PyObject *__pyx_n_s_sqrt;
2360  static PyObject *__pyx_kp_u_sqrt_line_1542;
2361  static PyObject *__pyx_n_s_tan;
2362  static PyObject *__pyx_kp_u_tan_line_1752;
2363  static PyObject *__pyx_n_s_tanh;
2364  static PyObject *__pyx_kp_u_tanh_line_1786;
2365  static PyObject *__pyx_n_s_tau;
2366  static PyObject *__pyx_n_s_test;
2367  static PyObject *__pyx_n_s_test_2;
2368  static PyObject *__pyx_n_s_testmod;
2369  static PyObject *__pyx_n_s_throw;
2370  static PyObject *__pyx_kp_s_to_frame;
2371  static PyObject *__pyx_kp_s_using;
2372  static PyObject *__pyx_kp_s_using_invalid;
2373  static PyObject *__pyx_kp_s_value;
2374  static PyObject *__pyx_n_s_version;
2375  static PyObject *__pyx_n_s_xrange;
2376 static PyObject *__pyx_pf_8PyClical_9index_set_copy(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2377 static int __pyx_pf_8PyClical_9index_set_2__cinit__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_other); /* proto */
2378 static void __pyx_pf_8PyClical_9index_set_4__dealloc__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2379 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 */
2380 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 */
2381 static PyObject *__pyx_pf_8PyClical_9index_set_10__getitem__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_idx); /* proto */
2382 static int __pyx_pf_8PyClical_9index_set_12__contains__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_idx); /* proto */
2383 static PyObject *__pyx_pf_8PyClical_9index_set_14__iter__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2384 static PyObject *__pyx_pf_8PyClical_9index_set_17__invert__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2385 static PyObject *__pyx_pf_8PyClical_9index_set_19__xor__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2386 static PyObject *__pyx_pf_8PyClical_9index_set_21__ixor__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2387 static PyObject *__pyx_pf_8PyClical_9index_set_23__and__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2388 static PyObject *__pyx_pf_8PyClical_9index_set_25__iand__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2389 static PyObject *__pyx_pf_8PyClical_9index_set_27__or__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2390 static PyObject *__pyx_pf_8PyClical_9index_set_29__ior__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2391 static PyObject *__pyx_pf_8PyClical_9index_set_31count(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2392 static PyObject *__pyx_pf_8PyClical_9index_set_33count_neg(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2393 static PyObject *__pyx_pf_8PyClical_9index_set_35count_pos(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2394 static PyObject *__pyx_pf_8PyClical_9index_set_37min(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2395 static PyObject *__pyx_pf_8PyClical_9index_set_39max(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2396 static PyObject *__pyx_pf_8PyClical_9index_set_41hash_fn(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2397 static PyObject *__pyx_pf_8PyClical_9index_set_43sign_of_mult(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2398 static PyObject *__pyx_pf_8PyClical_9index_set_45sign_of_square(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2399 static PyObject *__pyx_pf_8PyClical_9index_set_47__repr__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2400 static PyObject *__pyx_pf_8PyClical_9index_set_49__str__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2401 static PyObject *__pyx_pf_8PyClical_9index_set_51__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2402 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 */
2403 static PyObject *__pyx_pf_8PyClical_index_set_hidden_doctests(CYTHON_UNUSED PyObject *__pyx_self); /* proto */
2404 static PyObject *__pyx_pf_8PyClical_2compare(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2405 static PyObject *__pyx_pf_8PyClical_4min_neg(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2406 static PyObject *__pyx_pf_8PyClical_6max_pos(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2407 static PyObject *__pyx_pf_8PyClical_8clifford_copy(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2408 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 */
2409 static void __pyx_pf_8PyClical_8clifford_4__dealloc__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2410 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 */
2411 static PyObject *__pyx_pf_8PyClical_8clifford_8__iter__(CYTHON_UNUSED struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2412 static PyObject *__pyx_pf_8PyClical_8clifford_10reframe(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_ixt); /* proto */
2413 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 */
2414 static PyObject *__pyx_pf_8PyClical_8clifford_14__getitem__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_ixt); /* proto */
2415 static PyObject *__pyx_pf_8PyClical_8clifford_16__neg__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2416 static PyObject *__pyx_pf_8PyClical_8clifford_18__pos__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2417 static PyObject *__pyx_pf_8PyClical_8clifford_20__add__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2418 static PyObject *__pyx_pf_8PyClical_8clifford_22__iadd__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2419 static PyObject *__pyx_pf_8PyClical_8clifford_24__sub__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2420 static PyObject *__pyx_pf_8PyClical_8clifford_26__isub__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2421 static PyObject *__pyx_pf_8PyClical_8clifford_28__mul__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2422 static PyObject *__pyx_pf_8PyClical_8clifford_30__imul__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2423 static PyObject *__pyx_pf_8PyClical_8clifford_32__mod__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2424 static PyObject *__pyx_pf_8PyClical_8clifford_34__imod__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2425 static PyObject *__pyx_pf_8PyClical_8clifford_36__and__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2426 static PyObject *__pyx_pf_8PyClical_8clifford_38__iand__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2427 static PyObject *__pyx_pf_8PyClical_8clifford_40__xor__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2428 static PyObject *__pyx_pf_8PyClical_8clifford_42__ixor__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2429 #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
2430 static PyObject *__pyx_pf_8PyClical_8clifford_44__div__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2431 #endif
2432 #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
2433 static PyObject *__pyx_pf_8PyClical_8clifford_46__idiv__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2434 #endif
2435 static PyObject *__pyx_pf_8PyClical_8clifford_48inv(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2436 static PyObject *__pyx_pf_8PyClical_8clifford_50__or__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2437 static PyObject *__pyx_pf_8PyClical_8clifford_52__ior__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2438 static PyObject *__pyx_pf_8PyClical_8clifford_54__pow__(PyObject *__pyx_v_self, PyObject *__pyx_v_m, CYTHON_UNUSED PyObject *__pyx_v_dummy); /* proto */
2439 static PyObject *__pyx_pf_8PyClical_8clifford_56pow(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_m); /* proto */
2440 static PyObject *__pyx_pf_8PyClical_8clifford_58outer_pow(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_m); /* proto */
2441 static PyObject *__pyx_pf_8PyClical_8clifford_60__call__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_grade); /* proto */
2442 static PyObject *__pyx_pf_8PyClical_8clifford_62scalar(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2443 static PyObject *__pyx_pf_8PyClical_8clifford_64pure(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2444 static PyObject *__pyx_pf_8PyClical_8clifford_66even(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2445 static PyObject *__pyx_pf_8PyClical_8clifford_68odd(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2446 static PyObject *__pyx_pf_8PyClical_8clifford_70vector_part(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_frm); /* proto */
2447 static PyObject *__pyx_pf_8PyClical_8clifford_72involute(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2448 static PyObject *__pyx_pf_8PyClical_8clifford_74reverse(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2449 static PyObject *__pyx_pf_8PyClical_8clifford_76conj(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2450 static PyObject *__pyx_pf_8PyClical_8clifford_78quad(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2451 static PyObject *__pyx_pf_8PyClical_8clifford_80norm(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2452 static PyObject *__pyx_pf_8PyClical_8clifford_82abs(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2453 static PyObject *__pyx_pf_8PyClical_8clifford_84max_abs(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2454 static PyObject *__pyx_pf_8PyClical_8clifford_86truncated(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_limit); /* proto */
2455 static PyObject *__pyx_pf_8PyClical_8clifford_88isnan(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2456 static PyObject *__pyx_pf_8PyClical_8clifford_90frame(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2457 static PyObject *__pyx_pf_8PyClical_8clifford_92__repr__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2458 static PyObject *__pyx_pf_8PyClical_8clifford_94__str__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2459 static PyObject *__pyx_pf_8PyClical_8clifford_96__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2460 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 */
2461 static PyObject *__pyx_pf_8PyClical_8clifford_hidden_doctests(CYTHON_UNUSED PyObject *__pyx_self); /* proto */
2462 static PyObject *__pyx_pf_8PyClical_10inv(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2463 static PyObject *__pyx_pf_8PyClical_12scalar(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2464 static PyObject *__pyx_pf_8PyClical_14real(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2465 static PyObject *__pyx_pf_8PyClical_16imag(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2466 static PyObject *__pyx_pf_8PyClical_18pure(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2467 static PyObject *__pyx_pf_8PyClical_20even(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2468 static PyObject *__pyx_pf_8PyClical_22odd(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2469 static PyObject *__pyx_pf_8PyClical_24involute(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2470 static PyObject *__pyx_pf_8PyClical_26reverse(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2471 static PyObject *__pyx_pf_8PyClical_28conj(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2472 static PyObject *__pyx_pf_8PyClical_30quad(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2473 static PyObject *__pyx_pf_8PyClical_32norm(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2474 static PyObject *__pyx_pf_8PyClical_34abs(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2475 static PyObject *__pyx_pf_8PyClical_36max_abs(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2476 static PyObject *__pyx_pf_8PyClical_38pow(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_m); /* proto */
2477 static PyObject *__pyx_pf_8PyClical_40outer_pow(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_m); /* proto */
2478 static PyObject *__pyx_pf_8PyClical_42complexifier(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2479 static PyObject *__pyx_pf_8PyClical_44sqrt(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2480 static PyObject *__pyx_pf_8PyClical_46exp(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2481 static PyObject *__pyx_pf_8PyClical_48log(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2482 static PyObject *__pyx_pf_8PyClical_50cos(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2483 static PyObject *__pyx_pf_8PyClical_52acos(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2484 static PyObject *__pyx_pf_8PyClical_54cosh(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2485 static PyObject *__pyx_pf_8PyClical_56acosh(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2486 static PyObject *__pyx_pf_8PyClical_58sin(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2487 static PyObject *__pyx_pf_8PyClical_60asin(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2488 static PyObject *__pyx_pf_8PyClical_62sinh(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2489 static PyObject *__pyx_pf_8PyClical_64asinh(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2490 static PyObject *__pyx_pf_8PyClical_66tan(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2491 static PyObject *__pyx_pf_8PyClical_68atan(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2492 static PyObject *__pyx_pf_8PyClical_70tanh(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2493 static PyObject *__pyx_pf_8PyClical_72atanh(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2494 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 */
2495 static PyObject *__pyx_pf_8PyClical_76cga3(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2496 static PyObject *__pyx_pf_8PyClical_78cga3std(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2497 static PyObject *__pyx_pf_8PyClical_80agc3(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2498 static PyObject *__pyx_pf_8PyClical_82e(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2499 static PyObject *__pyx_pf_8PyClical_84istpq(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_p, PyObject *__pyx_v_q); /* proto */
2500 static PyObject *__pyx_pf_8PyClical_86_test(CYTHON_UNUSED PyObject *__pyx_self); /* proto */
2501 static PyObject *__pyx_tp_new_8PyClical_index_set(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
2502 static PyObject *__pyx_tp_new_8PyClical_clifford(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
2503 static PyObject *__pyx_tp_new_8PyClical___pyx_scope_struct____iter__(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
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2505 static PyObject *__pyx_float_1_0;
2506 static PyObject *__pyx_float_2_0;
2507 static PyObject *__pyx_float_8_0;
2508 static PyObject *__pyx_int_0;
2509 static PyObject *__pyx_int_1;
2510 static PyObject *__pyx_int_4;
2511 static PyObject *__pyx_int_neg_1;
2512 static PyObject *__pyx_tuple__3;
2513 static PyObject *__pyx_tuple__4;
2514 static PyObject *__pyx_tuple__10;
2515 static PyObject *__pyx_tuple__11;
2516 static PyObject *__pyx_tuple__12;
2517 static PyObject *__pyx_tuple__15;
2518 static PyObject *__pyx_tuple__16;
2519 static PyObject *__pyx_tuple__18;
2520 static PyObject *__pyx_tuple__20;
2521 static PyObject *__pyx_tuple__21;
2522 static PyObject *__pyx_tuple__22;
2523 static PyObject *__pyx_codeobj__13;
2524 static PyObject *__pyx_codeobj__14;
2525 static PyObject *__pyx_codeobj__17;
2526 static PyObject *__pyx_codeobj__19;
2527 static PyObject *__pyx_codeobj__23;
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2530 /* "PyClical.pyx":39
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2557  /* "PyClical.pyx":39
2558  * cdef class index_set
2559  *
2560  * cdef inline IndexSet toIndexSet(obj): # <<<<<<<<<<<<<<
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2583 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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2669 static PyObject *__pyx_pw_8PyClical_9index_set_1copy(PyObject *__pyx_v_self, CYTHON_UNUSED PyObject *unused); /*proto*/
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3599  /* "PyClical.pyx":151
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3602  * return eq # <<<<<<<<<<<<<<
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3607  __Pyx_INCREF(__pyx_v_eq);
3608  __pyx_r = __pyx_v_eq;
3609  goto __pyx_L0;
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3611  /* "PyClical.pyx":150
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3613  * return False
3614  * elif op == 1: # <= # <<<<<<<<<<<<<<
3615  * return eq
3616  * elif op == 4: # >
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3619  case 4:
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3621  /* "PyClical.pyx":153
3622  * return eq
3623  * elif op == 4: # >
3624  * return False # <<<<<<<<<<<<<<
3625  * elif op == 5: # >=
3626  * return eq
3627  */
3628  __Pyx_XDECREF(__pyx_r);
3629  __Pyx_INCREF(Py_False);
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3633  /* "PyClical.pyx":152
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3635  * return eq
3636  * elif op == 4: # > # <<<<<<<<<<<<<<
3637  * return False
3638  * elif op == 5: # >=
3639  */
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3641  case 5:
3642 
3643  /* "PyClical.pyx":155
3644  * return False
3645  * elif op == 5: # >=
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3651  __Pyx_INCREF(__pyx_v_eq);
3652  __pyx_r = __pyx_v_eq;
3653  goto __pyx_L0;
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3655  /* "PyClical.pyx":154
3656  * elif op == 4: # >
3657  * return False
3658  * elif op == 5: # >= # <<<<<<<<<<<<<<
3659  * return eq
3660  * else:
3661  */
3662  break;
3663  default:
3664 
3665  /* "PyClical.pyx":157
3666  * return eq
3667  * else:
3668  * return NotImplemented # <<<<<<<<<<<<<<
3669  * else:
3670  * eq = bool( toIndexSet(lhs) == toIndexSet(rhs) )
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3672  __Pyx_XDECREF(__pyx_r);
3673  __Pyx_INCREF(__pyx_builtin_NotImplemented);
3674  __pyx_r = __pyx_builtin_NotImplemented;
3675  goto __pyx_L0;
3676  break;
3677  }
3678  break;
3679  }
3680 
3681  /* "PyClical.pyx":141
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3684  * if (lhs is None) or (rhs is None): # <<<<<<<<<<<<<<
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3686  * if op == 2: # ==
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3688  }
3689 
3690  /* "PyClical.pyx":159
3691  * return NotImplemented
3692  * else:
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3694  * if op == 2: # ==
3695  * return eq
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3699  __pyx_t_4 = __Pyx_PyBool_FromLong((!(!__pyx_t_1))); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 159, __pyx_L1_error)
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3704  /* "PyClical.pyx":160
3705  * else:
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3708  * return eq
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3711  switch (__pyx_v_op) {
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3714  /* "PyClical.pyx":161
3715  * eq = bool( toIndexSet(lhs) == toIndexSet(rhs) )
3716  * if op == 2: # ==
3717  * return eq # <<<<<<<<<<<<<<
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3722  __Pyx_INCREF(__pyx_v_eq);
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3725 
3726  /* "PyClical.pyx":160
3727  * else:
3728  * eq = bool( toIndexSet(lhs) == toIndexSet(rhs) )
3729  * if op == 2: # == # <<<<<<<<<<<<<<
3730  * return eq
3731  * elif op == 3: # !=
3732  */
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3734  case 3:
3735 
3736  /* "PyClical.pyx":163
3737  * return eq
3738  * elif op == 3: # !=
3739  * return not eq # <<<<<<<<<<<<<<
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3743  __Pyx_XDECREF(__pyx_r);
3744  __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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3748  __pyx_t_4 = 0;
3749  goto __pyx_L0;
3750 
3751  /* "PyClical.pyx":162
3752  * if op == 2: # ==
3753  * return eq
3754  * elif op == 3: # != # <<<<<<<<<<<<<<
3755  * return not eq
3756  * else:
3757  */
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3759  default:
3760 
3761  /* "PyClical.pyx":165
3762  * return not eq
3763  * else:
3764  * lt = bool( toIndexSet(lhs) < toIndexSet(rhs) ) # <<<<<<<<<<<<<<
3765  * if op == 0: # <
3766  * return lt
3767  */
3768  __pyx_t_1 = (__pyx_f_8PyClical_toIndexSet(((PyObject *)__pyx_v_lhs)) < __pyx_f_8PyClical_toIndexSet(__pyx_v_rhs));
3769  __pyx_t_4 = __Pyx_PyBool_FromLong((!(!__pyx_t_1))); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 165, __pyx_L1_error)
3770  __Pyx_GOTREF(__pyx_t_4);
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3772  __pyx_t_4 = 0;
3773 
3774  /* "PyClical.pyx":166
3775  * else:
3776  * lt = bool( toIndexSet(lhs) < toIndexSet(rhs) )
3777  * if op == 0: # < # <<<<<<<<<<<<<<
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3781  switch (__pyx_v_op) {
3782  case 0:
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3784  /* "PyClical.pyx":167
3785  * lt = bool( toIndexSet(lhs) < toIndexSet(rhs) )
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3787  * return lt # <<<<<<<<<<<<<<
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3793  __pyx_r = __pyx_v_lt;
3794  goto __pyx_L0;
3795 
3796  /* "PyClical.pyx":166
3797  * else:
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3800  * return lt
3801  * elif op == 1: # <=
3802  */
3803  break;
3804  case 1:
3805 
3806  /* "PyClical.pyx":169
3807  * return lt
3808  * elif op == 1: # <=
3809  * return lt or eq # <<<<<<<<<<<<<<
3810  * elif op == 4: # >
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3818  __pyx_t_4 = __pyx_v_lt;
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3823  __pyx_L6_bool_binop_done:;
3824  __pyx_r = __pyx_t_4;
3825  __pyx_t_4 = 0;
3826  goto __pyx_L0;
3827 
3828  /* "PyClical.pyx":168
3829  * if op == 0: # <
3830  * return lt
3831  * elif op == 1: # <= # <<<<<<<<<<<<<<
3832  * return lt or eq
3833  * elif op == 4: # >
3834  */
3835  break;
3836  case 4:
3837 
3838  /* "PyClical.pyx":171
3839  * return lt or eq
3840  * elif op == 4: # >
3841  * return not (lt or eq) # <<<<<<<<<<<<<<
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3846  __pyx_t_2 = __Pyx_PyObject_IsTrue(__pyx_v_lt); if (unlikely(__pyx_t_2 < 0)) __PYX_ERR(0, 171, __pyx_L1_error)
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3848  } else {
3849  __pyx_t_1 = __pyx_t_2;
3850  goto __pyx_L8_bool_binop_done;
3851  }
3852  __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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3857  __pyx_r = __pyx_t_4;
3858  __pyx_t_4 = 0;
3859  goto __pyx_L0;
3860 
3861  /* "PyClical.pyx":170
3862  * elif op == 1: # <=
3863  * return lt or eq
3864  * elif op == 4: # > # <<<<<<<<<<<<<<
3865  * return not (lt or eq)
3866  * elif op == 5: # >=
3867  */
3868  break;
3869  case 5:
3870 
3871  /* "PyClical.pyx":173
3872  * return not (lt or eq)
3873  * elif op == 5: # >=
3874  * return not lt # <<<<<<<<<<<<<<
3875  * else:
3876  * return NotImplemented
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3879  __pyx_t_1 = __Pyx_PyObject_IsTrue(__pyx_v_lt); if (unlikely(__pyx_t_1 < 0)) __PYX_ERR(0, 173, __pyx_L1_error)
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3883  __pyx_t_4 = 0;
3884  goto __pyx_L0;
3885 
3886  /* "PyClical.pyx":172
3887  * elif op == 4: # >
3888  * return not (lt or eq)
3889  * elif op == 5: # >= # <<<<<<<<<<<<<<
3890  * return not lt
3891  * else:
3892  */
3893  break;
3894  default:
3895 
3896  /* "PyClical.pyx":175
3897  * return not lt
3898  * else:
3899  * return NotImplemented # <<<<<<<<<<<<<<
3900  *
3901  * def __setitem__(self, idx, val):
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3905  __pyx_r = __pyx_builtin_NotImplemented;
3906  goto __pyx_L0;
3907  break;
3908  }
3909  break;
3910  }
3911  }
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3914  * del self.instance
3915  *
3916  * def __richcmp__(lhs, rhs, int op): # <<<<<<<<<<<<<<
3917  * """
3918  * Compare two objects of class index_set.
3919  */
3920 
3921  /* function exit code */
3922  __pyx_L1_error:;
3923  __Pyx_XDECREF(__pyx_t_4);
3924  __Pyx_AddTraceback("PyClical.index_set.__richcmp__", __pyx_clineno, __pyx_lineno, __pyx_filename);
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3935  * return NotImplemented
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3937  * def __setitem__(self, idx, val): # <<<<<<<<<<<<<<
3938  * """
3939  * Set the value of an index_set object at index idx to value val.
3940  */
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3946 struct wrapperbase __pyx_wrapperbase_8PyClical_9index_set_8__setitem__;
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3967  * {2}
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3970  * return
3971  *
3972  */
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3985  * return # <<<<<<<<<<<<<<
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3989  __pyx_r = 0;
3990  goto __pyx_L0;
3991 
3992  /* "PyClical.pyx":177
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3994  *
3995  * def __setitem__(self, idx, val): # <<<<<<<<<<<<<<
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4015  */
4016 
4017 /* Python wrapper */
4018 static PyObject *__pyx_pw_8PyClical_9index_set_11__getitem__(PyObject *__pyx_v_self, PyObject *__pyx_v_idx); /*proto*/
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4020 #if CYTHON_COMPILING_IN_CPYTHON
4021 struct wrapperbase __pyx_wrapperbase_8PyClical_9index_set_10__getitem__;
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4043  * """
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4045  *
4046  * def __contains__(self, idx):
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4057  * return
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4059  * def __getitem__(self, idx): # <<<<<<<<<<<<<<
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6617  __Pyx_PyThreadState_assign
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6624  /* "PyClical.pyx":599
6625  * elif isinstance(other, str):
6626  * try:
6627  * self.instance = new Clifford(<char *>other) # <<<<<<<<<<<<<<
6628  * except RuntimeError:
6629  * raise ValueError(error_msg_prefix + " invalid string " + repr(other) + ".")
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6641  * self.instance = new Clifford(<scalar_t>other)
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6658  * self.instance = new Clifford(<char *>other)
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6666  if (__Pyx_GetException(&__pyx_t_8, &__pyx_t_7, &__pyx_t_15) < 0) __PYX_ERR(0, 600, __pyx_L13_except_error)
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6697  __pyx_L13_except_error:;
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6700  * self.instance = new Clifford(<scalar_t>other)
6701  * elif isinstance(other, str):
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6708  __Pyx_XGIVEREF(__pyx_t_12);
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6761  __Pyx_XDECREF(__pyx_t_4); __pyx_t_4 = 0;
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6764  __pyx_L4_error:;
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6770  __Pyx_XDECREF(__pyx_t_8); __pyx_t_8 = 0;
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6803  __Pyx_DECREF(__pyx_t_17); __pyx_t_17 = 0;
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6830  * if isinstance(other, numbers.Real):
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6840  __Pyx_DECREF(__pyx_t_16); __pyx_t_16 = 0;
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6843  * raise TypeError(error_msg_prefix + " " + str(type(other)) + ".")
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6857  __pyx_L6_except_error:;
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6867  __Pyx_XGIVEREF(__pyx_t_4);
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6877  * if ixt is None: # <<<<<<<<<<<<<<
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6879  * if isinstance(other, clifford):
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6913  * elif isinstance(ixt, index_set):
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6931  * if isinstance(other, numbers.Real): # <<<<<<<<<<<<<<
6932  * self.instance = new Clifford((<index_set>ixt).unwrap(), <scalar_t>other)
6933  * elif isinstance(other, collections.Sequence):
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6935  goto __pyx_L21;
6936  }
6937 
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6940  * self.instance = new Clifford((<index_set>ixt).unwrap(), <scalar_t>other)
6941  * elif isinstance(other, collections.Sequence): # <<<<<<<<<<<<<<
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6957  * elif isinstance(other, collections.Sequence):
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6968  __pyx_v_self->instance = __pyx_t_6;
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6970  /* "PyClical.pyx":611
6971  * if isinstance(other, numbers.Real):
6972  * self.instance = new Clifford((<index_set>ixt).unwrap(), <scalar_t>other)
6973  * elif isinstance(other, collections.Sequence): # <<<<<<<<<<<<<<
6974  * self.instance = new Clifford(list_to_vector(other), (<index_set>ixt).unwrap())
6975  * else:
6976  */
6977  goto __pyx_L21;
6978  }
6979 
6980  /* "PyClical.pyx":614
6981  * self.instance = new Clifford(list_to_vector(other), (<index_set>ixt).unwrap())
6982  * else:
6983  * raise TypeError(error_msg_prefix + " (" + str(type(other)) # <<<<<<<<<<<<<<
6984  * + ", " + repr(ixt) + ").")
6985  * else:
6986  */
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6995  __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
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6997  /* "PyClical.pyx":615
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6999  * raise TypeError(error_msg_prefix + " (" + str(type(other))
7000  * + ", " + repr(ixt) + ").") # <<<<<<<<<<<<<<
7001  * else:
7002  * raise TypeError(error_msg_prefix + " (" + str(type(other))
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7012  __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
7013  __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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7015  __Pyx_DECREF(__pyx_t_15); __pyx_t_15 = 0;
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7017  /* "PyClical.pyx":614
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7019  * else:
7020  * raise TypeError(error_msg_prefix + " (" + str(type(other)) # <<<<<<<<<<<<<<
7021  * + ", " + repr(ixt) + ").")
7022  * else:
7023  */
7024  __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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7027  __Pyx_Raise(__pyx_t_15, 0, 0, 0);
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7029  __PYX_ERR(0, 614, __pyx_L1_error)
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7031  __pyx_L21:;
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7036  * elif isinstance(ixt, index_set): # <<<<<<<<<<<<<<
7037  * if isinstance(other, numbers.Real):
7038  * self.instance = new Clifford((<index_set>ixt).unwrap(), <scalar_t>other)
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7040  goto __pyx_L3;
7041  }
7042 
7043  /* "PyClical.pyx":617
7044  * + ", " + repr(ixt) + ").")
7045  * else:
7046  * raise TypeError(error_msg_prefix + " (" + str(type(other)) # <<<<<<<<<<<<<<
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7048  *
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7058  __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
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7060  /* "PyClical.pyx":618
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7062  * raise TypeError(error_msg_prefix + " (" + str(type(other))
7063  * + ", " + str(type(ixt)) + ").") # <<<<<<<<<<<<<<
7064  *
7065  * def __dealloc__(self):
7066  */
7067  __pyx_t_8 = PyNumber_Add(__pyx_t_7, __pyx_kp_s__8); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 618, __pyx_L1_error)
7068  __Pyx_GOTREF(__pyx_t_8);
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7070  __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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7074  __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
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7080  /* "PyClical.pyx":617
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7082  * else:
7083  * raise TypeError(error_msg_prefix + " (" + str(type(other)) # <<<<<<<<<<<<<<
7084  * + ", " + str(type(ixt)) + ").")
7085  *
7086  */
7087  __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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7094  __pyx_L3:;
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7098  *
7099  * def __cinit__(self, other = 0, ixt = None): # <<<<<<<<<<<<<<
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7101  * Construct an object of type clifford.
7102  */
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7104  /* function exit code */
7105  __pyx_r = 0;
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7107  __pyx_L1_error:;
7108  __Pyx_XDECREF(__pyx_t_7);
7109  __Pyx_XDECREF(__pyx_t_8);
7110  __Pyx_XDECREF(__pyx_t_15);
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7116  __pyx_L0:;
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7125  *
7126  * def __dealloc__(self): # <<<<<<<<<<<<<<
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7129  */
7130 
7131  /* Python wrapper */
7132  static void __pyx_pw_8PyClical_8clifford_5__dealloc__(PyObject *__pyx_v_self); /*proto*/
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7158  * def __dealloc__(self): # <<<<<<<<<<<<<<
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7170  * def __contains__(self, x): # <<<<<<<<<<<<<<
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7213  *
7214  * def __contains__(self, x): # <<<<<<<<<<<<<<
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7216  * Not applicable.
7217  */
7218 
7219  /* function exit code */
7220  __pyx_L1_error:;
7221  __Pyx_XDECREF(__pyx_t_1);
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7232  * """
7233  * Not applicable.
7234  */
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7239  #if CYTHON_COMPILING_IN_CPYTHON
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7248  /* function exit code */
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7278  */
7279 
7280  /* function exit code */
7281  __pyx_L1_error:;
7282  __Pyx_XDECREF(__pyx_t_1);
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7315  PyObject *__pyx_v_err = NULL;
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7320  PyObject *__pyx_t_3 = NULL;
7321  PyObject *__pyx_t_4 = NULL;
7322  PyObject *__pyx_t_5 = NULL;
7323  PyObject *__pyx_t_6 = NULL;
7324  Clifford *__pyx_t_7;
7325  int __pyx_t_8;
7326  PyObject *__pyx_t_9 = NULL;
7327  PyObject *__pyx_t_10 = NULL;
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7344  * """
7345  * error_msg_prefix = "Cannot reframe"
7346  * if isinstance(ixt, index_set): # <<<<<<<<<<<<<<
7347  * try:
7348  * result = clifford()
7349  */
7350  __pyx_t_1 = __Pyx_TypeCheck(__pyx_v_ixt, __pyx_ptype_8PyClical_index_set);
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7356  * if isinstance(ixt, index_set):
7357  * try: # <<<<<<<<<<<<<<
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7373  * result = clifford() # <<<<<<<<<<<<<<
7374  * result.instance = new Clifford(self.unwrap(), (<index_set>ixt).unwrap())
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7383  * try:
7384  * result = clifford()
7385  * result.instance = new Clifford(self.unwrap(), (<index_set>ixt).unwrap()) # <<<<<<<<<<<<<<
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7399  * if isinstance(ixt, index_set):
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7500  * error_msg_prefix = "Cannot reframe"
7501  * if isinstance(ixt, index_set):
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7503  * result = clifford()
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7508  __Pyx_XGIVEREF(__pyx_t_5);
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7628  * return bool(lhs is rhs)
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7672  * return bool(lhs is rhs)
7673  * else:
7674  */
7675  }
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7680  * return bool( toClifford(lhs) == toClifford(rhs) ) # <<<<<<<<<<<<<<
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7760  * return bool( toClifford(lhs) != toClifford(rhs) ) # <<<<<<<<<<<<<<
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17927  } else {
17928  values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
17929  values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
17930  }
17931  __pyx_v_p = values[0];
17932  __pyx_v_q = values[1];
17933  }
17934  goto __pyx_L4_argument_unpacking_done;
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17948 
17949  static PyObject *__pyx_pf_8PyClical_84istpq(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_p, PyObject *__pyx_v_q) {
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17958  * {-3,-2,-1,1,2}
17959  * """
17960  * return index_set(set(range(-q,p+1))) # <<<<<<<<<<<<<<
17961  *
17962  * ninf3 = e(4) + e(-1) # Null infinity point in 3D Conformal Geometric Algebra [DL].
17963  */
17964  __Pyx_XDECREF(__pyx_r);
17965  __pyx_t_1 = PyNumber_Negative(__pyx_v_q); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 1907, __pyx_L1_error)
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17971  __Pyx_GIVEREF(__pyx_t_1);
17972  PyTuple_SET_ITEM(__pyx_t_3, 0, __pyx_t_1);
17973  __Pyx_GIVEREF(__pyx_t_2);
17974  PyTuple_SET_ITEM(__pyx_t_3, 1, __pyx_t_2);
17975  __pyx_t_1 = 0;
17976  __pyx_t_2 = 0;
17977  __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)
17978  __Pyx_GOTREF(__pyx_t_2);
17979  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
17980  __pyx_t_3 = PySet_New(__pyx_t_2); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 1907, __pyx_L1_error)
17981  __Pyx_GOTREF(__pyx_t_3);
17982  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
17983  __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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17987  __pyx_t_2 = 0;
17988  goto __pyx_L0;
17989 
17990  /* "PyClical.pyx":1900
17991  * return clifford(index_set(obj))
17992  *
17993  * def istpq(p, q): # <<<<<<<<<<<<<<
17994  * """
17995  * Abbreviation for index_set({-q,...p}).
17996  */
17997 
17998  /* function exit code */
17999  __pyx_L1_error:;
18000  __Pyx_XDECREF(__pyx_t_1);
18001  __Pyx_XDECREF(__pyx_t_2);
18002  __Pyx_XDECREF(__pyx_t_3);
18003  __Pyx_AddTraceback("PyClical.istpq", __pyx_clineno, __pyx_lineno, __pyx_filename);
18004  __pyx_r = NULL;
18005  __pyx_L0:;
18006  __Pyx_XGIVEREF(__pyx_r);
18007  __Pyx_RefNannyFinishContext();
18008  return __pyx_r;
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18010 
18011  /* "PyClical.pyx":1913
18012  *
18013  * # Doctest interface.
18014  * def _test(): # <<<<<<<<<<<<<<
18015  * import PyClical, doctest
18016  * return doctest.testmod(PyClical)
18017  */
18018 
18019  /* Python wrapper */
18020  static PyObject *__pyx_pw_8PyClical_87_test(PyObject *__pyx_self, CYTHON_UNUSED PyObject *unused); /*proto*/
18021  static PyMethodDef __pyx_mdef_8PyClical_87_test = {"_test", (PyCFunction)__pyx_pw_8PyClical_87_test, METH_NOARGS, 0};
18022  static PyObject *__pyx_pw_8PyClical_87_test(PyObject *__pyx_self, CYTHON_UNUSED PyObject *unused) {
18023  PyObject *__pyx_r = 0;
18024  __Pyx_RefNannyDeclarations
18025  __Pyx_RefNannySetupContext("_test (wrapper)", 0);
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18027 
18028  /* function exit code */
18029  __Pyx_RefNannyFinishContext();
18030  return __pyx_r;
18031  }
18032 
18033  static PyObject *__pyx_pf_8PyClical_86_test(CYTHON_UNUSED PyObject *__pyx_self) {
18034  PyObject *__pyx_v_PyClical = NULL;
18035  PyObject *__pyx_v_doctest = NULL;
18036  PyObject *__pyx_r = NULL;
18037  __Pyx_RefNannyDeclarations
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18039  PyObject *__pyx_t_2 = NULL;
18040  PyObject *__pyx_t_3 = NULL;
18041  __Pyx_RefNannySetupContext("_test", 0);
18042 
18043  /* "PyClical.pyx":1914
18044  * # Doctest interface.
18045  * def _test():
18046  * import PyClical, doctest # <<<<<<<<<<<<<<
18047  * return doctest.testmod(PyClical)
18048  *
18049  */
18050  __pyx_t_1 = __Pyx_Import(__pyx_n_s_PyClical, 0, -1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 1914, __pyx_L1_error)
18051  __Pyx_GOTREF(__pyx_t_1);
18052  __pyx_v_PyClical = __pyx_t_1;
18053  __pyx_t_1 = 0;
18054  __pyx_t_1 = __Pyx_Import(__pyx_n_s_doctest, 0, -1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 1914, __pyx_L1_error)
18055  __Pyx_GOTREF(__pyx_t_1);
18056  __pyx_v_doctest = __pyx_t_1;
18057  __pyx_t_1 = 0;
18058 
18059  /* "PyClical.pyx":1915
18060  * def _test():
18061  * import PyClical, doctest
18062  * return doctest.testmod(PyClical) # <<<<<<<<<<<<<<
18063  *
18064  * if __name__ == "__main__":
18065  */
18066  __Pyx_XDECREF(__pyx_r);
18067  __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)
18068  __Pyx_GOTREF(__pyx_t_2);
18069  __pyx_t_3 = NULL;
18070  if (CYTHON_UNPACK_METHODS && likely(PyMethod_Check(__pyx_t_2))) {
18071  __pyx_t_3 = PyMethod_GET_SELF(__pyx_t_2);
18072  if (likely(__pyx_t_3)) {
18073  PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_2);
18074  __Pyx_INCREF(__pyx_t_3);
18075  __Pyx_INCREF(function);
18076  __Pyx_DECREF_SET(__pyx_t_2, function);
18077  }
18078  }
18079  __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);
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18083  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
18084  __pyx_r = __pyx_t_1;
18085  __pyx_t_1 = 0;
18086  goto __pyx_L0;
18087 
18088  /* "PyClical.pyx":1913
18089  *
18090  * # Doctest interface.
18091  * def _test(): # <<<<<<<<<<<<<<
18092  * import PyClical, doctest
18093  * return doctest.testmod(PyClical)
18094  */
18095 
18096  /* function exit code */
18097  __pyx_L1_error:;
18098  __Pyx_XDECREF(__pyx_t_1);
18099  __Pyx_XDECREF(__pyx_t_2);
18100  __Pyx_XDECREF(__pyx_t_3);
18101  __Pyx_AddTraceback("PyClical._test", __pyx_clineno, __pyx_lineno, __pyx_filename);
18102  __pyx_r = NULL;
18103  __pyx_L0:;
18104  __Pyx_XDECREF(__pyx_v_PyClical);
18105  __Pyx_XDECREF(__pyx_v_doctest);
18106  __Pyx_XGIVEREF(__pyx_r);
18107  __Pyx_RefNannyFinishContext();
18108  return __pyx_r;
18109  }
18110  static struct __pyx_vtabstruct_8PyClical_index_set __pyx_vtable_8PyClical_index_set;
18111 
18112  static PyObject *__pyx_tp_new_8PyClical_index_set(PyTypeObject *t, PyObject *a, PyObject *k) {
18113  struct __pyx_obj_8PyClical_index_set *p;
18114  PyObject *o;
18115  if (likely((t->tp_flags & Py_TPFLAGS_IS_ABSTRACT) == 0)) {
18116  o = (*t->tp_alloc)(t, 0);
18117  } else {
18118  o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_empty_tuple, 0);
18119  }
18120  if (unlikely(!o)) return 0;
18121  p = ((struct __pyx_obj_8PyClical_index_set *)o);
18122  p->__pyx_vtab = __pyx_vtabptr_8PyClical_index_set;
18123  if (unlikely(__pyx_pw_8PyClical_9index_set_3__cinit__(o, a, k) < 0)) goto bad;
18124  return o;
18125  bad:
18126  Py_DECREF(o); o = 0;
18127  return NULL;
18128  }
18129 
18130  static void __pyx_tp_dealloc_8PyClical_index_set(PyObject *o) {
18131  #if CYTHON_USE_TP_FINALIZE
18132  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))) {
18133  if (PyObject_CallFinalizerFromDealloc(o)) return;
18134  }
18135  #endif
18136  {
18137  PyObject *etype, *eval, *etb;
18138  PyErr_Fetch(&etype, &eval, &etb);
18139  ++Py_REFCNT(o);
18140  __pyx_pw_8PyClical_9index_set_5__dealloc__(o);
18141  --Py_REFCNT(o);
18142  PyErr_Restore(etype, eval, etb);
18143  }
18144  (*Py_TYPE(o)->tp_free)(o);
18145  }
18146  static PyObject *__pyx_sq_item_8PyClical_index_set(PyObject *o, Py_ssize_t i) {
18147  PyObject *r;
18148  PyObject *x = PyInt_FromSsize_t(i); if(!x) return 0;
18149  r = Py_TYPE(o)->tp_as_mapping->mp_subscript(o, x);
18150  Py_DECREF(x);
18151  return r;
18152  }
18153 
18154  static int __pyx_mp_ass_subscript_8PyClical_index_set(PyObject *o, PyObject *i, PyObject *v) {
18155  if (v) {
18156  return __pyx_pw_8PyClical_9index_set_9__setitem__(o, i, v);
18157  }
18158  else {
18159  PyErr_Format(PyExc_NotImplementedError,
18160  "Subscript deletion not supported by %.200s", Py_TYPE(o)->tp_name);
18161  return -1;
18162  }
18163  }
18164 
18165  static PyMethodDef __pyx_methods_8PyClical_index_set[] = {
18166  {"copy", (PyCFunction)__pyx_pw_8PyClical_9index_set_1copy, METH_NOARGS, __pyx_doc_8PyClical_9index_set_copy},
18167  {"count", (PyCFunction)__pyx_pw_8PyClical_9index_set_32count, METH_NOARGS, __pyx_doc_8PyClical_9index_set_31count},
18168  {"count_neg", (PyCFunction)__pyx_pw_8PyClical_9index_set_34count_neg, METH_NOARGS, __pyx_doc_8PyClical_9index_set_33count_neg},
18169  {"count_pos", (PyCFunction)__pyx_pw_8PyClical_9index_set_36count_pos, METH_NOARGS, __pyx_doc_8PyClical_9index_set_35count_pos},
18170  {"min", (PyCFunction)__pyx_pw_8PyClical_9index_set_38min, METH_NOARGS, __pyx_doc_8PyClical_9index_set_37min},
18171  {"max", (PyCFunction)__pyx_pw_8PyClical_9index_set_40max, METH_NOARGS, __pyx_doc_8PyClical_9index_set_39max},
18172  {"hash_fn", (PyCFunction)__pyx_pw_8PyClical_9index_set_42hash_fn, METH_NOARGS, __pyx_doc_8PyClical_9index_set_41hash_fn},
18173  {"sign_of_mult", (PyCFunction)__pyx_pw_8PyClical_9index_set_44sign_of_mult, METH_O, __pyx_doc_8PyClical_9index_set_43sign_of_mult},
18174  {"sign_of_square", (PyCFunction)__pyx_pw_8PyClical_9index_set_46sign_of_square, METH_NOARGS, __pyx_doc_8PyClical_9index_set_45sign_of_square},
18175  {"__reduce_cython__", (PyCFunction)__pyx_pw_8PyClical_9index_set_52__reduce_cython__, METH_NOARGS, 0},
18176  {"__setstate_cython__", (PyCFunction)__pyx_pw_8PyClical_9index_set_54__setstate_cython__, METH_O, 0},
18177  {0, 0, 0, 0}
18178  };
18179 
18180  static PyNumberMethods __pyx_tp_as_number_index_set = {
18181  0, /*nb_add*/
18182  0, /*nb_subtract*/
18183  0, /*nb_multiply*/
18184  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18185  0, /*nb_divide*/
18186  #endif
18187  0, /*nb_remainder*/
18188  0, /*nb_divmod*/
18189  0, /*nb_power*/
18190  0, /*nb_negative*/
18191  0, /*nb_positive*/
18192  0, /*nb_absolute*/
18193  0, /*nb_nonzero*/
18194  __pyx_pw_8PyClical_9index_set_18__invert__, /*nb_invert*/
18195  0, /*nb_lshift*/
18196  0, /*nb_rshift*/
18197  __pyx_pw_8PyClical_9index_set_24__and__, /*nb_and*/
18198  __pyx_pw_8PyClical_9index_set_20__xor__, /*nb_xor*/
18199  __pyx_pw_8PyClical_9index_set_28__or__, /*nb_or*/
18200  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18201  0, /*nb_coerce*/
18202  #endif
18203  0, /*nb_int*/
18204  #if PY_MAJOR_VERSION < 3
18205  0, /*nb_long*/
18206  #else
18207  0, /*reserved*/
18208  #endif
18209  0, /*nb_float*/
18210  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18211  0, /*nb_oct*/
18212  #endif
18213  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18214  0, /*nb_hex*/
18215  #endif
18216  0, /*nb_inplace_add*/
18217  0, /*nb_inplace_subtract*/
18218  0, /*nb_inplace_multiply*/
18219  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18220  0, /*nb_inplace_divide*/
18221  #endif
18222  0, /*nb_inplace_remainder*/
18223  0, /*nb_inplace_power*/
18224  0, /*nb_inplace_lshift*/
18225  0, /*nb_inplace_rshift*/
18226  __pyx_pw_8PyClical_9index_set_26__iand__, /*nb_inplace_and*/
18227  __pyx_pw_8PyClical_9index_set_22__ixor__, /*nb_inplace_xor*/
18228  __pyx_pw_8PyClical_9index_set_30__ior__, /*nb_inplace_or*/
18229  0, /*nb_floor_divide*/
18230  0, /*nb_true_divide*/
18231  0, /*nb_inplace_floor_divide*/
18232  0, /*nb_inplace_true_divide*/
18233  0, /*nb_index*/
18234  #if PY_VERSION_HEX >= 0x03050000
18235  0, /*nb_matrix_multiply*/
18236  #endif
18237  #if PY_VERSION_HEX >= 0x03050000
18238  0, /*nb_inplace_matrix_multiply*/
18239  #endif
18240  };
18241 
18242  static PySequenceMethods __pyx_tp_as_sequence_index_set = {
18243  0, /*sq_length*/
18244  0, /*sq_concat*/
18245  0, /*sq_repeat*/
18246  __pyx_sq_item_8PyClical_index_set, /*sq_item*/
18247  0, /*sq_slice*/
18248  0, /*sq_ass_item*/
18249  0, /*sq_ass_slice*/
18250  __pyx_pw_8PyClical_9index_set_13__contains__, /*sq_contains*/
18251  0, /*sq_inplace_concat*/
18252  0, /*sq_inplace_repeat*/
18253  };
18254 
18255  static PyMappingMethods __pyx_tp_as_mapping_index_set = {
18256  0, /*mp_length*/
18257  __pyx_pw_8PyClical_9index_set_11__getitem__, /*mp_subscript*/
18258  __pyx_mp_ass_subscript_8PyClical_index_set, /*mp_ass_subscript*/
18259  };
18260 
18261  static PyTypeObject __pyx_type_8PyClical_index_set = {
18262  PyVarObject_HEAD_INIT(0, 0)
18263  "PyClical.index_set", /*tp_name*/
18264  sizeof(struct __pyx_obj_8PyClical_index_set), /*tp_basicsize*/
18265  0, /*tp_itemsize*/
18266  __pyx_tp_dealloc_8PyClical_index_set, /*tp_dealloc*/
18267  0, /*tp_print*/
18268  0, /*tp_getattr*/
18269  0, /*tp_setattr*/
18270  #if PY_MAJOR_VERSION < 3
18271  0, /*tp_compare*/
18272  #endif
18273  #if PY_MAJOR_VERSION >= 3
18274  0, /*tp_as_async*/
18275  #endif
18276  __pyx_pw_8PyClical_9index_set_48__repr__, /*tp_repr*/
18277  &__pyx_tp_as_number_index_set, /*tp_as_number*/
18278  &__pyx_tp_as_sequence_index_set, /*tp_as_sequence*/
18279  &__pyx_tp_as_mapping_index_set, /*tp_as_mapping*/
18280  0, /*tp_hash*/
18281  0, /*tp_call*/
18282  __pyx_pw_8PyClical_9index_set_50__str__, /*tp_str*/
18283  0, /*tp_getattro*/
18284  0, /*tp_setattro*/
18285  0, /*tp_as_buffer*/
18286  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE, /*tp_flags*/
18287  "\n Python class index_set wraps C++ class IndexSet.\n ", /*tp_doc*/
18288  0, /*tp_traverse*/
18289  0, /*tp_clear*/
18290  __pyx_pw_8PyClical_9index_set_7__richcmp__, /*tp_richcompare*/
18291  0, /*tp_weaklistoffset*/
18292  __pyx_pw_8PyClical_9index_set_15__iter__, /*tp_iter*/
18293  0, /*tp_iternext*/
18294  __pyx_methods_8PyClical_index_set, /*tp_methods*/
18295  0, /*tp_members*/
18296  0, /*tp_getset*/
18297  0, /*tp_base*/
18298  0, /*tp_dict*/
18299  0, /*tp_descr_get*/
18300  0, /*tp_descr_set*/
18301  0, /*tp_dictoffset*/
18302  0, /*tp_init*/
18303  0, /*tp_alloc*/
18304  __pyx_tp_new_8PyClical_index_set, /*tp_new*/
18305  0, /*tp_free*/
18306  0, /*tp_is_gc*/
18307  0, /*tp_bases*/
18308  0, /*tp_mro*/
18309  0, /*tp_cache*/
18310  0, /*tp_subclasses*/
18311  0, /*tp_weaklist*/
18312  0, /*tp_del*/
18313  0, /*tp_version_tag*/
18314  #if PY_VERSION_HEX >= 0x030400a1
18315  0, /*tp_finalize*/
18316  #endif
18317  };
18318  static struct __pyx_vtabstruct_8PyClical_clifford __pyx_vtable_8PyClical_clifford;
18319 
18320  static PyObject *__pyx_tp_new_8PyClical_clifford(PyTypeObject *t, PyObject *a, PyObject *k) {
18321  struct __pyx_obj_8PyClical_clifford *p;
18322  PyObject *o;
18323  if (likely((t->tp_flags & Py_TPFLAGS_IS_ABSTRACT) == 0)) {
18324  o = (*t->tp_alloc)(t, 0);
18325  } else {
18326  o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_empty_tuple, 0);
18327  }
18328  if (unlikely(!o)) return 0;
18329  p = ((struct __pyx_obj_8PyClical_clifford *)o);
18330  p->__pyx_vtab = __pyx_vtabptr_8PyClical_clifford;
18331  if (unlikely(__pyx_pw_8PyClical_8clifford_3__cinit__(o, a, k) < 0)) goto bad;
18332  return o;
18333  bad:
18334  Py_DECREF(o); o = 0;
18335  return NULL;
18336  }
18337 
18338  static void __pyx_tp_dealloc_8PyClical_clifford(PyObject *o) {
18339  #if CYTHON_USE_TP_FINALIZE
18340  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))) {
18341  if (PyObject_CallFinalizerFromDealloc(o)) return;
18342  }
18343  #endif
18344  {
18345  PyObject *etype, *eval, *etb;
18346  PyErr_Fetch(&etype, &eval, &etb);
18347  ++Py_REFCNT(o);
18348  __pyx_pw_8PyClical_8clifford_5__dealloc__(o);
18349  --Py_REFCNT(o);
18350  PyErr_Restore(etype, eval, etb);
18351  }
18352  (*Py_TYPE(o)->tp_free)(o);
18353  }
18354  static PyObject *__pyx_sq_item_8PyClical_clifford(PyObject *o, Py_ssize_t i) {
18355  PyObject *r;
18356  PyObject *x = PyInt_FromSsize_t(i); if(!x) return 0;
18357  r = Py_TYPE(o)->tp_as_mapping->mp_subscript(o, x);
18358  Py_DECREF(x);
18359  return r;
18360  }
18361 
18362  static PyMethodDef __pyx_methods_8PyClical_clifford[] = {
18363  {"copy", (PyCFunction)__pyx_pw_8PyClical_8clifford_1copy, METH_NOARGS, __pyx_doc_8PyClical_8clifford_copy},
18364  {"reframe", (PyCFunction)__pyx_pw_8PyClical_8clifford_11reframe, METH_O, __pyx_doc_8PyClical_8clifford_10reframe},
18365  {"inv", (PyCFunction)__pyx_pw_8PyClical_8clifford_49inv, METH_NOARGS, __pyx_doc_8PyClical_8clifford_48inv},
18366  {"pow", (PyCFunction)__pyx_pw_8PyClical_8clifford_57pow, METH_O, __pyx_doc_8PyClical_8clifford_56pow},
18367  {"outer_pow", (PyCFunction)__pyx_pw_8PyClical_8clifford_59outer_pow, METH_O, __pyx_doc_8PyClical_8clifford_58outer_pow},
18368  {"scalar", (PyCFunction)__pyx_pw_8PyClical_8clifford_63scalar, METH_NOARGS, __pyx_doc_8PyClical_8clifford_62scalar},
18369  {"pure", (PyCFunction)__pyx_pw_8PyClical_8clifford_65pure, METH_NOARGS, __pyx_doc_8PyClical_8clifford_64pure},
18370  {"even", (PyCFunction)__pyx_pw_8PyClical_8clifford_67even, METH_NOARGS, __pyx_doc_8PyClical_8clifford_66even},
18371  {"odd", (PyCFunction)__pyx_pw_8PyClical_8clifford_69odd, METH_NOARGS, __pyx_doc_8PyClical_8clifford_68odd},
18372  {"vector_part", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_8clifford_71vector_part, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_8clifford_70vector_part},
18373  {"involute", (PyCFunction)__pyx_pw_8PyClical_8clifford_73involute, METH_NOARGS, __pyx_doc_8PyClical_8clifford_72involute},
18374  {"reverse", (PyCFunction)__pyx_pw_8PyClical_8clifford_75reverse, METH_NOARGS, __pyx_doc_8PyClical_8clifford_74reverse},
18375  {"conj", (PyCFunction)__pyx_pw_8PyClical_8clifford_77conj, METH_NOARGS, __pyx_doc_8PyClical_8clifford_76conj},
18376  {"quad", (PyCFunction)__pyx_pw_8PyClical_8clifford_79quad, METH_NOARGS, __pyx_doc_8PyClical_8clifford_78quad},
18377  {"norm", (PyCFunction)__pyx_pw_8PyClical_8clifford_81norm, METH_NOARGS, __pyx_doc_8PyClical_8clifford_80norm},
18378  {"abs", (PyCFunction)__pyx_pw_8PyClical_8clifford_83abs, METH_NOARGS, __pyx_doc_8PyClical_8clifford_82abs},
18379  {"max_abs", (PyCFunction)__pyx_pw_8PyClical_8clifford_85max_abs, METH_NOARGS, __pyx_doc_8PyClical_8clifford_84max_abs},
18380  {"truncated", (PyCFunction)__pyx_pw_8PyClical_8clifford_87truncated, METH_O, __pyx_doc_8PyClical_8clifford_86truncated},
18381  {"isnan", (PyCFunction)__pyx_pw_8PyClical_8clifford_89isnan, METH_NOARGS, __pyx_doc_8PyClical_8clifford_88isnan},
18382  {"frame", (PyCFunction)__pyx_pw_8PyClical_8clifford_91frame, METH_NOARGS, __pyx_doc_8PyClical_8clifford_90frame},
18383  {"__reduce_cython__", (PyCFunction)__pyx_pw_8PyClical_8clifford_97__reduce_cython__, METH_NOARGS, 0},
18384  {"__setstate_cython__", (PyCFunction)__pyx_pw_8PyClical_8clifford_99__setstate_cython__, METH_O, 0},
18385  {0, 0, 0, 0}
18386  };
18387 
18388  static PyNumberMethods __pyx_tp_as_number_clifford = {
18389  __pyx_pw_8PyClical_8clifford_21__add__, /*nb_add*/
18390  __pyx_pw_8PyClical_8clifford_25__sub__, /*nb_subtract*/
18391  __pyx_pw_8PyClical_8clifford_29__mul__, /*nb_multiply*/
18392  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18393  __pyx_pw_8PyClical_8clifford_45__div__, /*nb_divide*/
18394  #endif
18395  __pyx_pw_8PyClical_8clifford_33__mod__, /*nb_remainder*/
18396  0, /*nb_divmod*/
18397  __pyx_pw_8PyClical_8clifford_55__pow__, /*nb_power*/
18398  __pyx_pw_8PyClical_8clifford_17__neg__, /*nb_negative*/
18399  __pyx_pw_8PyClical_8clifford_19__pos__, /*nb_positive*/
18400  0, /*nb_absolute*/
18401  0, /*nb_nonzero*/
18402  0, /*nb_invert*/
18403  0, /*nb_lshift*/
18404  0, /*nb_rshift*/
18405  __pyx_pw_8PyClical_8clifford_37__and__, /*nb_and*/
18406  __pyx_pw_8PyClical_8clifford_41__xor__, /*nb_xor*/
18407  __pyx_pw_8PyClical_8clifford_51__or__, /*nb_or*/
18408  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18409  0, /*nb_coerce*/
18410  #endif
18411  0, /*nb_int*/
18412  #if PY_MAJOR_VERSION < 3
18413  0, /*nb_long*/
18414  #else
18415  0, /*reserved*/
18416  #endif
18417  0, /*nb_float*/
18418  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18419  0, /*nb_oct*/
18420  #endif
18421  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18422  0, /*nb_hex*/
18423  #endif
18424  __pyx_pw_8PyClical_8clifford_23__iadd__, /*nb_inplace_add*/
18425  __pyx_pw_8PyClical_8clifford_27__isub__, /*nb_inplace_subtract*/
18426  __pyx_pw_8PyClical_8clifford_31__imul__, /*nb_inplace_multiply*/
18427  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18428  __pyx_pw_8PyClical_8clifford_47__idiv__, /*nb_inplace_divide*/
18429  #endif
18430  __pyx_pw_8PyClical_8clifford_35__imod__, /*nb_inplace_remainder*/
18431  0, /*nb_inplace_power*/
18432  0, /*nb_inplace_lshift*/
18433  0, /*nb_inplace_rshift*/
18434  __pyx_pw_8PyClical_8clifford_39__iand__, /*nb_inplace_and*/
18435  __pyx_pw_8PyClical_8clifford_43__ixor__, /*nb_inplace_xor*/
18436  __pyx_pw_8PyClical_8clifford_53__ior__, /*nb_inplace_or*/
18437  0, /*nb_floor_divide*/
18438  0, /*nb_true_divide*/
18439  0, /*nb_inplace_floor_divide*/
18440  0, /*nb_inplace_true_divide*/
18441  0, /*nb_index*/
18442  #if PY_VERSION_HEX >= 0x03050000
18443  0, /*nb_matrix_multiply*/
18444  #endif
18445  #if PY_VERSION_HEX >= 0x03050000
18446  0, /*nb_inplace_matrix_multiply*/
18447  #endif
18448  };
18449 
18450  static PySequenceMethods __pyx_tp_as_sequence_clifford = {
18451  0, /*sq_length*/
18452  0, /*sq_concat*/
18453  0, /*sq_repeat*/
18454  __pyx_sq_item_8PyClical_clifford, /*sq_item*/
18455  0, /*sq_slice*/
18456  0, /*sq_ass_item*/
18457  0, /*sq_ass_slice*/
18458  __pyx_pw_8PyClical_8clifford_7__contains__, /*sq_contains*/
18459  0, /*sq_inplace_concat*/
18460  0, /*sq_inplace_repeat*/
18461  };
18462 
18463  static PyMappingMethods __pyx_tp_as_mapping_clifford = {
18464  0, /*mp_length*/
18465  __pyx_pw_8PyClical_8clifford_15__getitem__, /*mp_subscript*/
18466  0, /*mp_ass_subscript*/
18467  };
18468 
18469  static PyTypeObject __pyx_type_8PyClical_clifford = {
18470  PyVarObject_HEAD_INIT(0, 0)
18471  "PyClical.clifford", /*tp_name*/
18472  sizeof(struct __pyx_obj_8PyClical_clifford), /*tp_basicsize*/
18473  0, /*tp_itemsize*/
18474  __pyx_tp_dealloc_8PyClical_clifford, /*tp_dealloc*/
18475  0, /*tp_print*/
18476  0, /*tp_getattr*/
18477  0, /*tp_setattr*/
18478  #if PY_MAJOR_VERSION < 3
18479  0, /*tp_compare*/
18480  #endif
18481  #if PY_MAJOR_VERSION >= 3
18482  0, /*tp_as_async*/
18483  #endif
18484  __pyx_pw_8PyClical_8clifford_93__repr__, /*tp_repr*/
18485  &__pyx_tp_as_number_clifford, /*tp_as_number*/
18486  &__pyx_tp_as_sequence_clifford, /*tp_as_sequence*/
18487  &__pyx_tp_as_mapping_clifford, /*tp_as_mapping*/
18488  0, /*tp_hash*/
18489  __pyx_pw_8PyClical_8clifford_61__call__, /*tp_call*/
18490  __pyx_pw_8PyClical_8clifford_95__str__, /*tp_str*/
18491  0, /*tp_getattro*/
18492  0, /*tp_setattro*/
18493  0, /*tp_as_buffer*/
18494  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE, /*tp_flags*/
18495  "\n Python class clifford wraps C++ class Clifford.\n ", /*tp_doc*/
18496  0, /*tp_traverse*/
18497  0, /*tp_clear*/
18498  __pyx_pw_8PyClical_8clifford_13__richcmp__, /*tp_richcompare*/
18499  0, /*tp_weaklistoffset*/
18500  __pyx_pw_8PyClical_8clifford_9__iter__, /*tp_iter*/
18501  0, /*tp_iternext*/
18502  __pyx_methods_8PyClical_clifford, /*tp_methods*/
18503  0, /*tp_members*/
18504  0, /*tp_getset*/
18505  0, /*tp_base*/
18506  0, /*tp_dict*/
18507  0, /*tp_descr_get*/
18508  0, /*tp_descr_set*/
18509  0, /*tp_dictoffset*/
18510  0, /*tp_init*/
18511  0, /*tp_alloc*/
18512  __pyx_tp_new_8PyClical_clifford, /*tp_new*/
18513  0, /*tp_free*/
18514  0, /*tp_is_gc*/
18515  0, /*tp_bases*/
18516  0, /*tp_mro*/
18517  0, /*tp_cache*/
18518  0, /*tp_subclasses*/
18519  0, /*tp_weaklist*/
18520  0, /*tp_del*/
18521  0, /*tp_version_tag*/
18522  #if PY_VERSION_HEX >= 0x030400a1
18523  0, /*tp_finalize*/
18524  #endif
18525  };
18526 
18527  static struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *__pyx_freelist_8PyClical___pyx_scope_struct____iter__[8];
18528  static int __pyx_freecount_8PyClical___pyx_scope_struct____iter__ = 0;
18529 
18530  static PyObject *__pyx_tp_new_8PyClical___pyx_scope_struct____iter__(PyTypeObject *t, CYTHON_UNUSED PyObject *a, CYTHON_UNUSED PyObject *k) {
18531  PyObject *o;
18532  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__)))) {
18533  o = (PyObject*)__pyx_freelist_8PyClical___pyx_scope_struct____iter__[--__pyx_freecount_8PyClical___pyx_scope_struct____iter__];
18534  memset(o, 0, sizeof(struct __pyx_obj_8PyClical___pyx_scope_struct____iter__));
18535  (void) PyObject_INIT(o, t);
18536  PyObject_GC_Track(o);
18537  } else {
18538  o = (*t->tp_alloc)(t, 0);
18539  if (unlikely(!o)) return 0;
18540  }
18541  return o;
18542  }
18543 
18544  static void __pyx_tp_dealloc_8PyClical___pyx_scope_struct____iter__(PyObject *o) {
18545  struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *p = (struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *)o;
18546  PyObject_GC_UnTrack(o);
18547  Py_CLEAR(p->__pyx_v_idx);
18548  Py_CLEAR(p->__pyx_v_self);
18549  Py_CLEAR(p->__pyx_t_0);
18550  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__)))) {
18551  __pyx_freelist_8PyClical___pyx_scope_struct____iter__[__pyx_freecount_8PyClical___pyx_scope_struct____iter__++] = ((struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *)o);
18552  } else {
18553  (*Py_TYPE(o)->tp_free)(o);
18554  }
18555  }
18556 
18557  static int __pyx_tp_traverse_8PyClical___pyx_scope_struct____iter__(PyObject *o, visitproc v, void *a) {
18558  int e;
18559  struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *p = (struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *)o;
18560  if (p->__pyx_v_idx) {
18561  e = (*v)(p->__pyx_v_idx, a); if (e) return e;
18562  }
18563  if (p->__pyx_v_self) {
18564  e = (*v)(((PyObject *)p->__pyx_v_self), a); if (e) return e;
18565  }
18566  if (p->__pyx_t_0) {
18567  e = (*v)(p->__pyx_t_0, a); if (e) return e;
18568  }
18569  return 0;
18570  }
18571 
18572  static PyTypeObject __pyx_type_8PyClical___pyx_scope_struct____iter__ = {
18573  PyVarObject_HEAD_INIT(0, 0)
18574  "PyClical.__pyx_scope_struct____iter__", /*tp_name*/
18575  sizeof(struct __pyx_obj_8PyClical___pyx_scope_struct____iter__), /*tp_basicsize*/
18576  0, /*tp_itemsize*/
18577  __pyx_tp_dealloc_8PyClical___pyx_scope_struct____iter__, /*tp_dealloc*/
18578  0, /*tp_print*/
18579  0, /*tp_getattr*/
18580  0, /*tp_setattr*/
18581  #if PY_MAJOR_VERSION < 3
18582  0, /*tp_compare*/
18583  #endif
18584  #if PY_MAJOR_VERSION >= 3
18585  0, /*tp_as_async*/
18586  #endif
18587  0, /*tp_repr*/
18588  0, /*tp_as_number*/
18589  0, /*tp_as_sequence*/
18590  0, /*tp_as_mapping*/
18591  0, /*tp_hash*/
18592  0, /*tp_call*/
18593  0, /*tp_str*/
18594  0, /*tp_getattro*/
18595  0, /*tp_setattro*/
18596  0, /*tp_as_buffer*/
18597  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_HAVE_GC, /*tp_flags*/
18598  0, /*tp_doc*/
18599  __pyx_tp_traverse_8PyClical___pyx_scope_struct____iter__, /*tp_traverse*/
18600  0, /*tp_clear*/
18601  0, /*tp_richcompare*/
18602  0, /*tp_weaklistoffset*/
18603  0, /*tp_iter*/
18604  0, /*tp_iternext*/
18605  0, /*tp_methods*/
18606  0, /*tp_members*/
18607  0, /*tp_getset*/
18608  0, /*tp_base*/
18609  0, /*tp_dict*/
18610  0, /*tp_descr_get*/
18611  0, /*tp_descr_set*/
18612  0, /*tp_dictoffset*/
18613  0, /*tp_init*/
18614  0, /*tp_alloc*/
18615  __pyx_tp_new_8PyClical___pyx_scope_struct____iter__, /*tp_new*/
18616  0, /*tp_free*/
18617  0, /*tp_is_gc*/
18618  0, /*tp_bases*/
18619  0, /*tp_mro*/
18620  0, /*tp_cache*/
18621  0, /*tp_subclasses*/
18622  0, /*tp_weaklist*/
18623  0, /*tp_del*/
18624  0, /*tp_version_tag*/
18625  #if PY_VERSION_HEX >= 0x030400a1
18626  0, /*tp_finalize*/
18627  #endif
18628  };
18629 
18630  static PyMethodDef __pyx_methods[] = {
18631  {"compare", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_3compare, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_2compare},
18632  {"min_neg", (PyCFunction)__pyx_pw_8PyClical_5min_neg, METH_O, __pyx_doc_8PyClical_4min_neg},
18633  {"max_pos", (PyCFunction)__pyx_pw_8PyClical_7max_pos, METH_O, __pyx_doc_8PyClical_6max_pos},
18634  {"inv", (PyCFunction)__pyx_pw_8PyClical_11inv, METH_O, __pyx_doc_8PyClical_10inv},
18635  {"scalar", (PyCFunction)__pyx_pw_8PyClical_13scalar, METH_O, __pyx_doc_8PyClical_12scalar},
18636  {"real", (PyCFunction)__pyx_pw_8PyClical_15real, METH_O, __pyx_doc_8PyClical_14real},
18637  {"imag", (PyCFunction)__pyx_pw_8PyClical_17imag, METH_O, __pyx_doc_8PyClical_16imag},
18638  {"pure", (PyCFunction)__pyx_pw_8PyClical_19pure, METH_O, __pyx_doc_8PyClical_18pure},
18639  {"even", (PyCFunction)__pyx_pw_8PyClical_21even, METH_O, __pyx_doc_8PyClical_20even},
18640  {"odd", (PyCFunction)__pyx_pw_8PyClical_23odd, METH_O, __pyx_doc_8PyClical_22odd},
18641  {"involute", (PyCFunction)__pyx_pw_8PyClical_25involute, METH_O, __pyx_doc_8PyClical_24involute},
18642  {"reverse", (PyCFunction)__pyx_pw_8PyClical_27reverse, METH_O, __pyx_doc_8PyClical_26reverse},
18643  {"conj", (PyCFunction)__pyx_pw_8PyClical_29conj, METH_O, __pyx_doc_8PyClical_28conj},
18644  {"quad", (PyCFunction)__pyx_pw_8PyClical_31quad, METH_O, __pyx_doc_8PyClical_30quad},
18645  {"norm", (PyCFunction)__pyx_pw_8PyClical_33norm, METH_O, __pyx_doc_8PyClical_32norm},
18646  {"abs", (PyCFunction)__pyx_pw_8PyClical_35abs, METH_O, __pyx_doc_8PyClical_34abs},
18647  {"max_abs", (PyCFunction)__pyx_pw_8PyClical_37max_abs, METH_O, __pyx_doc_8PyClical_36max_abs},
18648  {"pow", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_39pow, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_38pow},
18649  {"outer_pow", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_41outer_pow, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_40outer_pow},
18650  {"complexifier", (PyCFunction)__pyx_pw_8PyClical_43complexifier, METH_O, __pyx_doc_8PyClical_42complexifier},
18651  {"sqrt", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_45sqrt, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_44sqrt},
18652  {"exp", (PyCFunction)__pyx_pw_8PyClical_47exp, METH_O, __pyx_doc_8PyClical_46exp},
18653  {"log", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_49log, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_48log},
18654  {"cos", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_51cos, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_50cos},
18655  {"acos", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_53acos, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_52acos},
18656  {"cosh", (PyCFunction)__pyx_pw_8PyClical_55cosh, METH_O, __pyx_doc_8PyClical_54cosh},
18657  {"acosh", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_57acosh, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_56acosh},
18658  {"sin", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_59sin, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_58sin},
18659  {"asin", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_61asin, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_60asin},
18660  {"sinh", (PyCFunction)__pyx_pw_8PyClical_63sinh, METH_O, __pyx_doc_8PyClical_62sinh},
18661  {"asinh", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_65asinh, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_64asinh},
18662  {"tan", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_67tan, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_66tan},
18663  {"atan", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_69atan, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_68atan},
18664  {"tanh", (PyCFunction)__pyx_pw_8PyClical_71tanh, METH_O, __pyx_doc_8PyClical_70tanh},
18665  {"atanh", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_73atanh, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_72atanh},
18666  {"random_clifford", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_8PyClical_75random_clifford, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_74random_clifford},
18667  {"cga3", (PyCFunction)__pyx_pw_8PyClical_77cga3, METH_O, __pyx_doc_8PyClical_76cga3},
18668  {"cga3std", (PyCFunction)__pyx_pw_8PyClical_79cga3std, METH_O, __pyx_doc_8PyClical_78cga3std},
18669  {"agc3", (PyCFunction)__pyx_pw_8PyClical_81agc3, METH_O, __pyx_doc_8PyClical_80agc3},
18670  {0, 0, 0, 0}
18671  };
18672 
18673  #if PY_MAJOR_VERSION >= 3
18674  #if CYTHON_PEP489_MULTI_PHASE_INIT
18675  static PyObject* __pyx_pymod_create(PyObject *spec, PyModuleDef *def); /*proto*/
18676  static int __pyx_pymod_exec_PyClical(PyObject* module); /*proto*/
18677  static PyModuleDef_Slot __pyx_moduledef_slots[] = {
18678  {Py_mod_create, (void*)__pyx_pymod_create},
18679  {Py_mod_exec, (void*)__pyx_pymod_exec_PyClical},
18680  {0, NULL}
18681  };
18682  #endif
18683 
18684  static struct PyModuleDef __pyx_moduledef = {
18685  PyModuleDef_HEAD_INIT,
18686  "PyClical",
18687  0, /* m_doc */
18688  #if CYTHON_PEP489_MULTI_PHASE_INIT
18689  0, /* m_size */
18690  #else
18691  -1, /* m_size */
18692  #endif
18693  __pyx_methods /* m_methods */,
18694  #if CYTHON_PEP489_MULTI_PHASE_INIT
18695  __pyx_moduledef_slots, /* m_slots */
18696  #else
18697  NULL, /* m_reload */
18698  #endif
18699  NULL, /* m_traverse */
18700  NULL, /* m_clear */
18701  NULL /* m_free */
18702  };
18703  #endif
18704  #ifndef CYTHON_SMALL_CODE
18705 #if defined(__clang__)
18706  #define CYTHON_SMALL_CODE
18707 #elif defined(__GNUC__) && (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 3))
18708  #define CYTHON_SMALL_CODE __attribute__((cold))
18709 #else
18710  #define CYTHON_SMALL_CODE
18711 #endif
18712 #endif
18713 
18714 static __Pyx_StringTabEntry __pyx_string_tab[] = {
18715  {&__pyx_kp_s_, __pyx_k_, sizeof(__pyx_k_), 0, 0, 1, 0},
18716  {&__pyx_kp_s_0_8_2, __pyx_k_0_8_2, sizeof(__pyx_k_0_8_2), 0, 0, 1, 0},
18717  {&__pyx_kp_u_Abbreviation_for_clifford_index, __pyx_k_Abbreviation_for_clifford_index, sizeof(__pyx_k_Abbreviation_for_clifford_index), 0, 1, 0, 0},
18718  {&__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},
18719  {&__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},
18720  {&__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},
18721  {&__pyx_kp_s_Cannot_initialize_clifford_objec, __pyx_k_Cannot_initialize_clifford_objec, sizeof(__pyx_k_Cannot_initialize_clifford_objec), 0, 0, 1, 0},
18722  {&__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},
18723  {&__pyx_kp_s_Cannot_reframe, __pyx_k_Cannot_reframe, sizeof(__pyx_k_Cannot_reframe), 0, 0, 1, 0},
18724  {&__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},
18725  {&__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},
18726  {&__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},
18727  {&__pyx_kp_u_Conjugation_reverse_o_involute, __pyx_k_Conjugation_reverse_o_involute, sizeof(__pyx_k_Conjugation_reverse_o_involute), 0, 1, 0, 0},
18728  {&__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},
18729  {&__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},
18730  {&__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},
18731  {&__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},
18732  {&__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},
18733  {&__pyx_kp_u_Convert_Euclidean_3D_multivecto, __pyx_k_Convert_Euclidean_3D_multivecto, sizeof(__pyx_k_Convert_Euclidean_3D_multivecto), 0, 1, 0, 0},
18734  {&__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},
18735  {&__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},
18736  {&__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},
18737  {&__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},
18738  {&__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},
18739  {&__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},
18740  {&__pyx_kp_u_Geometric_difference_print_clif, __pyx_k_Geometric_difference_print_clif, sizeof(__pyx_k_Geometric_difference_print_clif), 0, 1, 0, 0},
18741  {&__pyx_kp_u_Geometric_difference_x_clifford, __pyx_k_Geometric_difference_x_clifford, sizeof(__pyx_k_Geometric_difference_x_clifford), 0, 1, 0, 0},
18742  {&__pyx_kp_u_Geometric_multiplicative_invers, __pyx_k_Geometric_multiplicative_invers, sizeof(__pyx_k_Geometric_multiplicative_invers), 0, 1, 0, 0},
18743  {&__pyx_kp_u_Geometric_multiplicative_invers_2, __pyx_k_Geometric_multiplicative_invers_2, sizeof(__pyx_k_Geometric_multiplicative_invers_2), 0, 1, 0, 0},
18744  {&__pyx_kp_u_Geometric_product_print_cliffor, __pyx_k_Geometric_product_print_cliffor, sizeof(__pyx_k_Geometric_product_print_cliffor), 0, 1, 0, 0},
18745  {&__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},
18746  {&__pyx_kp_u_Geometric_quotient_print_cliffo, __pyx_k_Geometric_quotient_print_cliffo, sizeof(__pyx_k_Geometric_quotient_print_cliffo), 0, 1, 0, 0},
18747  {&__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},
18748  {&__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},
18749  {&__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},
18750  {&__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},
18751  {&__pyx_kp_u_Hyperbolic_cosine_of_multivecto, __pyx_k_Hyperbolic_cosine_of_multivecto, sizeof(__pyx_k_Hyperbolic_cosine_of_multivecto), 0, 1, 0, 0},
18752  {&__pyx_kp_u_Hyperbolic_sine_of_multivector, __pyx_k_Hyperbolic_sine_of_multivector, sizeof(__pyx_k_Hyperbolic_sine_of_multivector), 0, 1, 0, 0},
18753  {&__pyx_kp_u_Hyperbolic_tangent_of_multivect, __pyx_k_Hyperbolic_tangent_of_multivect, sizeof(__pyx_k_Hyperbolic_tangent_of_multivect), 0, 1, 0, 0},
18754  {&__pyx_kp_u_Imaginary_part_deprecated_alway, __pyx_k_Imaginary_part_deprecated_alway, sizeof(__pyx_k_Imaginary_part_deprecated_alway), 0, 1, 0, 0},
18755  {&__pyx_n_s_IndexError, __pyx_k_IndexError, sizeof(__pyx_k_IndexError), 0, 0, 1, 1},
18756  {&__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},
18757  {&__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},
18758  {&__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},
18759  {&__pyx_n_s_Integral, __pyx_k_Integral, sizeof(__pyx_k_Integral), 0, 0, 1, 1},
18760  {&__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},
18761  {&__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},
18762  {&__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},
18763  {&__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},
18764  {&__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},
18765  {&__pyx_kp_u_Inverse_tangent_of_multivector, __pyx_k_Inverse_tangent_of_multivector, sizeof(__pyx_k_Inverse_tangent_of_multivector), 0, 1, 0, 0},
18766  {&__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},
18767  {&__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},
18768  {&__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},
18769  {&__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},
18770  {&__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},
18771  {&__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},
18772  {&__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},
18773  {&__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},
18774  {&__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},
18775  {&__pyx_kp_u_Natural_logarithm_of_multivecto, __pyx_k_Natural_logarithm_of_multivecto, sizeof(__pyx_k_Natural_logarithm_of_multivecto), 0, 1, 0, 0},
18776  {&__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},
18777  {&__pyx_n_s_NotImplemented, __pyx_k_NotImplemented, sizeof(__pyx_k_NotImplemented), 0, 0, 1, 1},
18778  {&__pyx_kp_s_Not_applicable, __pyx_k_Not_applicable, sizeof(__pyx_k_Not_applicable), 0, 0, 1, 0},
18779  {&__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},
18780  {&__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},
18781  {&__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},
18782  {&__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},
18783  {&__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},
18784  {&__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},
18785  {&__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},
18786  {&__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},
18787  {&__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},
18788  {&__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},
18789  {&__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},
18790  {&__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},
18791  {&__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},
18792  {&__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},
18793  {&__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},
18794  {&__pyx_n_s_PyClical, __pyx_k_PyClical, sizeof(__pyx_k_PyClical), 0, 0, 1, 1},
18795  {&__pyx_kp_s_PyClical_pyx, __pyx_k_PyClical_pyx, sizeof(__pyx_k_PyClical_pyx), 0, 0, 1, 0},
18796  {&__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},
18797  {&__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},
18798  {&__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},
18799  {&__pyx_n_s_Real, __pyx_k_Real, sizeof(__pyx_k_Real), 0, 0, 1, 1},
18800  {&__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},
18801  {&__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},
18802  {&__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},
18803  {&__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},
18804  {&__pyx_n_s_RuntimeError, __pyx_k_RuntimeError, sizeof(__pyx_k_RuntimeError), 0, 0, 1, 1},
18805  {&__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},
18806  {&__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},
18807  {&__pyx_n_s_Sequence, __pyx_k_Sequence, sizeof(__pyx_k_Sequence), 0, 0, 1, 1},
18808  {&__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},
18809  {&__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},
18810  {&__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},
18811  {&__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},
18812  {&__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},
18813  {&__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},
18814  {&__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},
18815  {&__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},
18816  {&__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},
18817  {&__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},
18818  {&__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},
18819  {&__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},
18820  {&__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},
18821  {&__pyx_kp_u_Symmetric_set_difference_exclus, __pyx_k_Symmetric_set_difference_exclus, sizeof(__pyx_k_Symmetric_set_difference_exclus), 0, 1, 0, 0},
18822  {&__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},
18823  {&__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},
18824  {&__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},
18825  {&__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},
18826  {&__pyx_kp_u_The_informal_string_representat, __pyx_k_The_informal_string_representat, sizeof(__pyx_k_The_informal_string_representat), 0, 1, 0, 0},
18827  {&__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},
18828  {&__pyx_kp_u_The_official_string_representat, __pyx_k_The_official_string_representat, sizeof(__pyx_k_The_official_string_representat), 0, 1, 0, 0},
18829  {&__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},
18830  {&__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},
18831  {&__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},
18832  {&__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},
18833  {&__pyx_n_s_TypeError, __pyx_k_TypeError, sizeof(__pyx_k_TypeError), 0, 0, 1, 1},
18834  {&__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},
18835  {&__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},
18836  {&__pyx_n_s_ValueError, __pyx_k_ValueError, sizeof(__pyx_k_ValueError), 0, 0, 1, 1},
18837  {&__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},
18838  {&__pyx_kp_s__2, __pyx_k__2, sizeof(__pyx_k__2), 0, 0, 1, 0},
18839  {&__pyx_kp_s__5, __pyx_k__5, sizeof(__pyx_k__5), 0, 0, 1, 0},
18840  {&__pyx_kp_s__6, __pyx_k__6, sizeof(__pyx_k__6), 0, 0, 1, 0},
18841  {&__pyx_kp_s__7, __pyx_k__7, sizeof(__pyx_k__7), 0, 0, 1, 0},
18842  {&__pyx_kp_s__8, __pyx_k__8, sizeof(__pyx_k__8), 0, 0, 1, 0},
18843  {&__pyx_kp_s__9, __pyx_k__9, sizeof(__pyx_k__9), 0, 0, 1, 0},
18844  {&__pyx_kp_u_abs_line_1473, __pyx_k_abs_line_1473, sizeof(__pyx_k_abs_line_1473), 0, 1, 0, 0},
18845  {&__pyx_n_s_acos, __pyx_k_acos, sizeof(__pyx_k_acos), 0, 0, 1, 1},
18846  {&__pyx_kp_u_acos_line_1619, __pyx_k_acos_line_1619, sizeof(__pyx_k_acos_line_1619), 0, 1, 0, 0},
18847  {&__pyx_n_s_acosh, __pyx_k_acosh, sizeof(__pyx_k_acosh), 0, 0, 1, 1},
18848  {&__pyx_kp_u_acosh_line_1656, __pyx_k_acosh_line_1656, sizeof(__pyx_k_acosh_line_1656), 0, 1, 0, 0},
18849  {&__pyx_kp_u_agc3_line_1844, __pyx_k_agc3_line_1844, sizeof(__pyx_k_agc3_line_1844), 0, 1, 0, 0},
18850  {&__pyx_n_s_args, __pyx_k_args, sizeof(__pyx_k_args), 0, 0, 1, 1},
18851  {&__pyx_kp_s_as_frame, __pyx_k_as_frame, sizeof(__pyx_k_as_frame), 0, 0, 1, 0},
18852  {&__pyx_n_s_asin, __pyx_k_asin, sizeof(__pyx_k_asin), 0, 0, 1, 1},
18853  {&__pyx_kp_u_asin_line_1698, __pyx_k_asin_line_1698, sizeof(__pyx_k_asin_line_1698), 0, 1, 0, 0},
18854  {&__pyx_n_s_asinh, __pyx_k_asinh, sizeof(__pyx_k_asinh), 0, 0, 1, 1},
18855  {&__pyx_kp_u_asinh_line_1733, __pyx_k_asinh_line_1733, sizeof(__pyx_k_asinh_line_1733), 0, 1, 0, 0},
18856  {&__pyx_n_s_atan, __pyx_k_atan, sizeof(__pyx_k_atan), 0, 0, 1, 1},
18857  {&__pyx_kp_u_atan_line_1769, __pyx_k_atan_line_1769, sizeof(__pyx_k_atan_line_1769), 0, 1, 0, 0},
18858  {&__pyx_n_s_atanh, __pyx_k_atanh, sizeof(__pyx_k_atanh), 0, 0, 1, 1},
18859  {&__pyx_kp_u_atanh_line_1798, __pyx_k_atanh_line_1798, sizeof(__pyx_k_atanh_line_1798), 0, 1, 0, 0},
18860  {&__pyx_kp_u_cga3_line_1824, __pyx_k_cga3_line_1824, sizeof(__pyx_k_cga3_line_1824), 0, 1, 0, 0},
18861  {&__pyx_kp_u_cga3std_line_1833, __pyx_k_cga3std_line_1833, sizeof(__pyx_k_cga3std_line_1833), 0, 1, 0, 0},
18862  {&__pyx_n_s_cl, __pyx_k_cl, sizeof(__pyx_k_cl), 0, 0, 1, 1},
18863  {&__pyx_n_s_clifford, __pyx_k_clifford, sizeof(__pyx_k_clifford), 0, 0, 1, 1},
18864  {&__pyx_kp_u_clifford___add___line_739, __pyx_k_clifford___add___line_739, sizeof(__pyx_k_clifford___add___line_739), 0, 1, 0, 0},
18865  {&__pyx_kp_u_clifford___and___line_835, __pyx_k_clifford___and___line_835, sizeof(__pyx_k_clifford___and___line_835), 0, 1, 0, 0},
18866  {&__pyx_kp_u_clifford___call___line_1019, __pyx_k_clifford___call___line_1019, sizeof(__pyx_k_clifford___call___line_1019), 0, 1, 0, 0},
18867  {&__pyx_kp_u_clifford___div___line_895, __pyx_k_clifford___div___line_895, sizeof(__pyx_k_clifford___div___line_895), 0, 1, 0, 0},
18868  {&__pyx_kp_u_clifford___getitem___line_706, __pyx_k_clifford___getitem___line_706, sizeof(__pyx_k_clifford___getitem___line_706), 0, 1, 0, 0},
18869  {&__pyx_kp_u_clifford___iadd___line_750, __pyx_k_clifford___iadd___line_750, sizeof(__pyx_k_clifford___iadd___line_750), 0, 1, 0, 0},
18870  {&__pyx_kp_u_clifford___iand___line_850, __pyx_k_clifford___iand___line_850, sizeof(__pyx_k_clifford___iand___line_850), 0, 1, 0, 0},
18871  {&__pyx_kp_u_clifford___idiv___line_910, __pyx_k_clifford___idiv___line_910, sizeof(__pyx_k_clifford___idiv___line_910), 0, 1, 0, 0},
18872  {&__pyx_kp_u_clifford___imod___line_820, __pyx_k_clifford___imod___line_820, sizeof(__pyx_k_clifford___imod___line_820), 0, 1, 0, 0},
18873  {&__pyx_kp_u_clifford___imul___line_792, __pyx_k_clifford___imul___line_792, sizeof(__pyx_k_clifford___imul___line_792), 0, 1, 0, 0},
18874  {&__pyx_kp_u_clifford___ior___line_949, __pyx_k_clifford___ior___line_949, sizeof(__pyx_k_clifford___ior___line_949), 0, 1, 0, 0},
18875  {&__pyx_kp_u_clifford___isub___line_770, __pyx_k_clifford___isub___line_770, sizeof(__pyx_k_clifford___isub___line_770), 0, 1, 0, 0},
18876  {&__pyx_kp_u_clifford___iter___line_637, __pyx_k_clifford___iter___line_637, sizeof(__pyx_k_clifford___iter___line_637), 0, 1, 0, 0},
18877  {&__pyx_kp_u_clifford___ixor___line_880, __pyx_k_clifford___ixor___line_880, sizeof(__pyx_k_clifford___ixor___line_880), 0, 1, 0, 0},
18878  {&__pyx_kp_u_clifford___mod___line_805, __pyx_k_clifford___mod___line_805, sizeof(__pyx_k_clifford___mod___line_805), 0, 1, 0, 0},
18879  {&__pyx_kp_u_clifford___mul___line_779, __pyx_k_clifford___mul___line_779, sizeof(__pyx_k_clifford___mul___line_779), 0, 1, 0, 0},
18880  {&__pyx_kp_u_clifford___neg___line_721, __pyx_k_clifford___neg___line_721, sizeof(__pyx_k_clifford___neg___line_721), 0, 1, 0, 0},
18881  {&__pyx_kp_u_clifford___or___line_938, __pyx_k_clifford___or___line_938, sizeof(__pyx_k_clifford___or___line_938), 0, 1, 0, 0},
18882  {&__pyx_kp_u_clifford___pos___line_730, __pyx_k_clifford___pos___line_730, sizeof(__pyx_k_clifford___pos___line_730), 0, 1, 0, 0},
18883  {&__pyx_kp_u_clifford___pow___line_960, __pyx_k_clifford___pow___line_960, sizeof(__pyx_k_clifford___pow___line_960), 0, 1, 0, 0},
18884  {&__pyx_kp_u_clifford___repr___line_1225, __pyx_k_clifford___repr___line_1225, sizeof(__pyx_k_clifford___repr___line_1225), 0, 1, 0, 0},
18885  {&__pyx_kp_u_clifford___str___line_1234, __pyx_k_clifford___str___line_1234, sizeof(__pyx_k_clifford___str___line_1234), 0, 1, 0, 0},
18886  {&__pyx_kp_u_clifford___sub___line_759, __pyx_k_clifford___sub___line_759, sizeof(__pyx_k_clifford___sub___line_759), 0, 1, 0, 0},
18887  {&__pyx_kp_u_clifford___xor___line_865, __pyx_k_clifford___xor___line_865, sizeof(__pyx_k_clifford___xor___line_865), 0, 1, 0, 0},
18888  {&__pyx_kp_u_clifford_abs_line_1174, __pyx_k_clifford_abs_line_1174, sizeof(__pyx_k_clifford_abs_line_1174), 0, 1, 0, 0},
18889  {&__pyx_kp_u_clifford_conj_line_1137, __pyx_k_clifford_conj_line_1137, sizeof(__pyx_k_clifford_conj_line_1137), 0, 1, 0, 0},
18890  {&__pyx_kp_u_clifford_copy_line_554, __pyx_k_clifford_copy_line_554, sizeof(__pyx_k_clifford_copy_line_554), 0, 1, 0, 0},
18891  {&__pyx_kp_u_clifford_even_line_1060, __pyx_k_clifford_even_line_1060, sizeof(__pyx_k_clifford_even_line_1060), 0, 1, 0, 0},
18892  {&__pyx_kp_u_clifford_frame_line_1214, __pyx_k_clifford_frame_line_1214, sizeof(__pyx_k_clifford_frame_line_1214), 0, 1, 0, 0},
18893  {&__pyx_n_s_clifford_hidden_doctests, __pyx_k_clifford_hidden_doctests, sizeof(__pyx_k_clifford_hidden_doctests), 0, 0, 1, 1},
18894  {&__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},
18895  {&__pyx_kp_u_clifford_inv_line_925, __pyx_k_clifford_inv_line_925, sizeof(__pyx_k_clifford_inv_line_925), 0, 1, 0, 0},
18896  {&__pyx_kp_u_clifford_involute_line_1106, __pyx_k_clifford_involute_line_1106, sizeof(__pyx_k_clifford_involute_line_1106), 0, 1, 0, 0},
18897  {&__pyx_kp_u_clifford_isnan_line_1205, __pyx_k_clifford_isnan_line_1205, sizeof(__pyx_k_clifford_isnan_line_1205), 0, 1, 0, 0},
18898  {&__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},
18899  {&__pyx_kp_u_clifford_norm_line_1163, __pyx_k_clifford_norm_line_1163, sizeof(__pyx_k_clifford_norm_line_1163), 0, 1, 0, 0},
18900  {&__pyx_kp_u_clifford_odd_line_1069, __pyx_k_clifford_odd_line_1069, sizeof(__pyx_k_clifford_odd_line_1069), 0, 1, 0, 0},
18901  {&__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},
18902  {&__pyx_kp_u_clifford_pow_line_979, __pyx_k_clifford_pow_line_979, sizeof(__pyx_k_clifford_pow_line_979), 0, 1, 0, 0},
18903  {&__pyx_kp_u_clifford_pure_line_1049, __pyx_k_clifford_pure_line_1049, sizeof(__pyx_k_clifford_pure_line_1049), 0, 1, 0, 0},
18904  {&__pyx_kp_u_clifford_quad_line_1152, __pyx_k_clifford_quad_line_1152, sizeof(__pyx_k_clifford_quad_line_1152), 0, 1, 0, 0},
18905  {&__pyx_kp_u_clifford_reframe_line_648, __pyx_k_clifford_reframe_line_648, sizeof(__pyx_k_clifford_reframe_line_648), 0, 1, 0, 0},
18906  {&__pyx_kp_u_clifford_reverse_line_1122, __pyx_k_clifford_reverse_line_1122, sizeof(__pyx_k_clifford_reverse_line_1122), 0, 1, 0, 0},
18907  {&__pyx_kp_u_clifford_scalar_line_1038, __pyx_k_clifford_scalar_line_1038, sizeof(__pyx_k_clifford_scalar_line_1038), 0, 1, 0, 0},
18908  {&__pyx_kp_u_clifford_truncated_line_1194, __pyx_k_clifford_truncated_line_1194, sizeof(__pyx_k_clifford_truncated_line_1194), 0, 1, 0, 0},
18909  {&__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},
18910  {&__pyx_n_s_cline_in_traceback, __pyx_k_cline_in_traceback, sizeof(__pyx_k_cline_in_traceback), 0, 0, 1, 1},
18911  {&__pyx_n_s_close, __pyx_k_close, sizeof(__pyx_k_close), 0, 0, 1, 1},
18912  {&__pyx_n_s_collections, __pyx_k_collections, sizeof(__pyx_k_collections), 0, 0, 1, 1},
18913  {&__pyx_kp_u_compare_line_490, __pyx_k_compare_line_490, sizeof(__pyx_k_compare_line_490), 0, 1, 0, 0},
18914  {&__pyx_kp_u_complexifier_line_1527, __pyx_k_complexifier_line_1527, sizeof(__pyx_k_complexifier_line_1527), 0, 1, 0, 0},
18915  {&__pyx_n_s_conj, __pyx_k_conj, sizeof(__pyx_k_conj), 0, 0, 1, 1},
18916  {&__pyx_kp_u_conj_line_1436, __pyx_k_conj_line_1436, sizeof(__pyx_k_conj_line_1436), 0, 1, 0, 0},
18917  {&__pyx_n_s_copy, __pyx_k_copy, sizeof(__pyx_k_copy), 0, 0, 1, 1},
18918  {&__pyx_n_s_cos, __pyx_k_cos, sizeof(__pyx_k_cos), 0, 0, 1, 1},
18919  {&__pyx_kp_u_cos_line_1602, __pyx_k_cos_line_1602, sizeof(__pyx_k_cos_line_1602), 0, 1, 0, 0},
18920  {&__pyx_n_s_cosh, __pyx_k_cosh, sizeof(__pyx_k_cosh), 0, 0, 1, 1},
18921  {&__pyx_kp_u_cosh_line_1640, __pyx_k_cosh_line_1640, sizeof(__pyx_k_cosh_line_1640), 0, 1, 0, 0},
18922  {&__pyx_n_s_doctest, __pyx_k_doctest, sizeof(__pyx_k_doctest), 0, 0, 1, 1},
18923  {&__pyx_n_s_e, __pyx_k_e, sizeof(__pyx_k_e), 0, 0, 1, 1},
18924  {&__pyx_kp_u_e_line_1887, __pyx_k_e_line_1887, sizeof(__pyx_k_e_line_1887), 0, 1, 0, 0},
18925  {&__pyx_n_s_even, __pyx_k_even, sizeof(__pyx_k_even), 0, 0, 1, 1},
18926  {&__pyx_kp_u_even_line_1388, __pyx_k_even_line_1388, sizeof(__pyx_k_even_line_1388), 0, 1, 0, 0},
18927  {&__pyx_n_s_exp, __pyx_k_exp, sizeof(__pyx_k_exp), 0, 0, 1, 1},
18928  {&__pyx_kp_u_exp_line_1565, __pyx_k_exp_line_1565, sizeof(__pyx_k_exp_line_1565), 0, 1, 0, 0},
18929  {&__pyx_n_s_fill, __pyx_k_fill, sizeof(__pyx_k_fill), 0, 0, 1, 1},
18930  {&__pyx_n_s_frm, __pyx_k_frm, sizeof(__pyx_k_frm), 0, 0, 1, 1},
18931  {&__pyx_kp_s_from, __pyx_k_from, sizeof(__pyx_k_from), 0, 0, 1, 0},
18932  {&__pyx_n_s_getstate, __pyx_k_getstate, sizeof(__pyx_k_getstate), 0, 0, 1, 1},
18933  {&__pyx_n_s_grade, __pyx_k_grade, sizeof(__pyx_k_grade), 0, 0, 1, 1},
18934  {&__pyx_n_s_i, __pyx_k_i, sizeof(__pyx_k_i), 0, 0, 1, 1},
18935  {&__pyx_kp_u_imag_line_1366, __pyx_k_imag_line_1366, sizeof(__pyx_k_imag_line_1366), 0, 1, 0, 0},
18936  {&__pyx_n_s_import, __pyx_k_import, sizeof(__pyx_k_import), 0, 0, 1, 1},
18937  {&__pyx_n_s_index_set, __pyx_k_index_set, sizeof(__pyx_k_index_set), 0, 0, 1, 1},
18938  {&__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},
18939  {&__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},
18940  {&__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},
18941  {&__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},
18942  {&__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},
18943  {&__pyx_n_s_index_set___iter, __pyx_k_index_set___iter, sizeof(__pyx_k_index_set___iter), 0, 0, 1, 1},
18944  {&__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},
18945  {&__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},
18946  {&__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},
18947  {&__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},
18948  {&__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},
18949  {&__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},
18950  {&__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},
18951  {&__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},
18952  {&__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},
18953  {&__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},
18954  {&__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},
18955  {&__pyx_n_s_index_set_hidden_doctests, __pyx_k_index_set_hidden_doctests, sizeof(__pyx_k_index_set_hidden_doctests), 0, 0, 1, 1},
18956  {&__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},
18957  {&__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},
18958  {&__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},
18959  {&__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},
18960  {&__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},
18961  {&__pyx_n_s_inv, __pyx_k_inv, sizeof(__pyx_k_inv), 0, 0, 1, 1},
18962  {&__pyx_kp_u_inv_line_1329, __pyx_k_inv_line_1329, sizeof(__pyx_k_inv_line_1329), 0, 1, 0, 0},
18963  {&__pyx_kp_s_invalid, __pyx_k_invalid, sizeof(__pyx_k_invalid), 0, 0, 1, 0},
18964  {&__pyx_kp_s_invalid_string, __pyx_k_invalid_string, sizeof(__pyx_k_invalid_string), 0, 0, 1, 0},
18965  {&__pyx_n_s_involute, __pyx_k_involute, sizeof(__pyx_k_involute), 0, 0, 1, 1},
18966  {&__pyx_kp_u_involute_line_1406, __pyx_k_involute_line_1406, sizeof(__pyx_k_involute_line_1406), 0, 1, 0, 0},
18967  {&__pyx_n_s_ist, __pyx_k_ist, sizeof(__pyx_k_ist), 0, 0, 1, 1},
18968  {&__pyx_n_s_istpq, __pyx_k_istpq, sizeof(__pyx_k_istpq), 0, 0, 1, 1},
18969  {&__pyx_kp_u_istpq_line_1900, __pyx_k_istpq_line_1900, sizeof(__pyx_k_istpq_line_1900), 0, 1, 0, 0},
18970  {&__pyx_n_s_iter, __pyx_k_iter, sizeof(__pyx_k_iter), 0, 0, 1, 1},
18971  {&__pyx_n_s_ixt, __pyx_k_ixt, sizeof(__pyx_k_ixt), 0, 0, 1, 1},
18972  {&__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},
18973  {&__pyx_n_s_lhs, __pyx_k_lhs, sizeof(__pyx_k_lhs), 0, 0, 1, 1},
18974  {&__pyx_n_s_log, __pyx_k_log, sizeof(__pyx_k_log), 0, 0, 1, 1},
18975  {&__pyx_kp_u_log_line_1579, __pyx_k_log_line_1579, sizeof(__pyx_k_log_line_1579), 0, 1, 0, 0},
18976  {&__pyx_n_s_m, __pyx_k_m, sizeof(__pyx_k_m), 0, 0, 1, 1},
18977  {&__pyx_n_s_main, __pyx_k_main, sizeof(__pyx_k_main), 0, 0, 1, 1},
18978  {&__pyx_n_s_math, __pyx_k_math, sizeof(__pyx_k_math), 0, 0, 1, 1},
18979  {&__pyx_n_s_max, __pyx_k_max, sizeof(__pyx_k_max), 0, 0, 1, 1},
18980  {&__pyx_kp_u_max_abs_line_1482, __pyx_k_max_abs_line_1482, sizeof(__pyx_k_max_abs_line_1482), 0, 1, 0, 0},
18981  {&__pyx_kp_u_max_pos_line_511, __pyx_k_max_pos_line_511, sizeof(__pyx_k_max_pos_line_511), 0, 1, 0, 0},
18982  {&__pyx_n_s_min, __pyx_k_min, sizeof(__pyx_k_min), 0, 0, 1, 1},
18983  {&__pyx_kp_u_min_neg_line_502, __pyx_k_min_neg_line_502, sizeof(__pyx_k_min_neg_line_502), 0, 1, 0, 0},
18984  {&__pyx_n_s_name, __pyx_k_name, sizeof(__pyx_k_name), 0, 0, 1, 1},
18985  {&__pyx_n_s_nbar3, __pyx_k_nbar3, sizeof(__pyx_k_nbar3), 0, 0, 1, 1},
18986  {&__pyx_n_s_ninf3, __pyx_k_ninf3, sizeof(__pyx_k_ninf3), 0, 0, 1, 1},
18987  {&__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},
18988  {&__pyx_n_s_norm, __pyx_k_norm, sizeof(__pyx_k_norm), 0, 0, 1, 1},
18989  {&__pyx_kp_u_norm_line_1462, __pyx_k_norm_line_1462, sizeof(__pyx_k_norm_line_1462), 0, 1, 0, 0},
18990  {&__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},
18991  {&__pyx_n_s_numbers, __pyx_k_numbers, sizeof(__pyx_k_numbers), 0, 0, 1, 1},
18992  {&__pyx_n_s_obj, __pyx_k_obj, sizeof(__pyx_k_obj), 0, 0, 1, 1},
18993  {&__pyx_n_s_odd, __pyx_k_odd, sizeof(__pyx_k_odd), 0, 0, 1, 1},
18994  {&__pyx_kp_u_odd_line_1397, __pyx_k_odd_line_1397, sizeof(__pyx_k_odd_line_1397), 0, 1, 0, 0},
18995  {&__pyx_n_s_other, __pyx_k_other, sizeof(__pyx_k_other), 0, 0, 1, 1},
18996  {&__pyx_n_s_outer_pow, __pyx_k_outer_pow, sizeof(__pyx_k_outer_pow), 0, 0, 1, 1},
18997  {&__pyx_kp_u_outer_pow_line_1518, __pyx_k_outer_pow_line_1518, sizeof(__pyx_k_outer_pow_line_1518), 0, 1, 0, 0},
18998  {&__pyx_n_s_p, __pyx_k_p, sizeof(__pyx_k_p), 0, 0, 1, 1},
18999  {&__pyx_n_s_pi, __pyx_k_pi, sizeof(__pyx_k_pi), 0, 0, 1, 1},
19000  {&__pyx_n_s_pow, __pyx_k_pow, sizeof(__pyx_k_pow), 0, 0, 1, 1},
19001  {&__pyx_kp_u_pow_line_1494, __pyx_k_pow_line_1494, sizeof(__pyx_k_pow_line_1494), 0, 1, 0, 0},
19002  {&__pyx_n_s_pure, __pyx_k_pure, sizeof(__pyx_k_pure), 0, 0, 1, 1},
19003  {&__pyx_kp_u_pure_line_1377, __pyx_k_pure_line_1377, sizeof(__pyx_k_pure_line_1377), 0, 1, 0, 0},
19004  {&__pyx_n_s_pyx_vtable, __pyx_k_pyx_vtable, sizeof(__pyx_k_pyx_vtable), 0, 0, 1, 1},
19005  {&__pyx_n_s_q, __pyx_k_q, sizeof(__pyx_k_q), 0, 0, 1, 1},
19006  {&__pyx_n_s_quad, __pyx_k_quad, sizeof(__pyx_k_quad), 0, 0, 1, 1},
19007  {&__pyx_kp_u_quad_line_1451, __pyx_k_quad_line_1451, sizeof(__pyx_k_quad_line_1451), 0, 1, 0, 0},
19008  {&__pyx_kp_u_random_clifford_line_1815, __pyx_k_random_clifford_line_1815, sizeof(__pyx_k_random_clifford_line_1815), 0, 1, 0, 0},
19009  {&__pyx_n_s_range, __pyx_k_range, sizeof(__pyx_k_range), 0, 0, 1, 1},
19010  {&__pyx_kp_u_real_line_1355, __pyx_k_real_line_1355, sizeof(__pyx_k_real_line_1355), 0, 1, 0, 0},
19011  {&__pyx_n_s_reduce, __pyx_k_reduce, sizeof(__pyx_k_reduce), 0, 0, 1, 1},
19012  {&__pyx_n_s_reduce_cython, __pyx_k_reduce_cython, sizeof(__pyx_k_reduce_cython), 0, 0, 1, 1},
19013  {&__pyx_n_s_reduce_ex, __pyx_k_reduce_ex, sizeof(__pyx_k_reduce_ex), 0, 0, 1, 1},
19014  {&__pyx_n_s_reverse, __pyx_k_reverse, sizeof(__pyx_k_reverse), 0, 0, 1, 1},
19015  {&__pyx_kp_u_reverse_line_1421, __pyx_k_reverse_line_1421, sizeof(__pyx_k_reverse_line_1421), 0, 1, 0, 0},
19016  {&__pyx_n_s_rhs, __pyx_k_rhs, sizeof(__pyx_k_rhs), 0, 0, 1, 1},
19017  {&__pyx_n_s_scalar, __pyx_k_scalar, sizeof(__pyx_k_scalar), 0, 0, 1, 1},
19018  {&__pyx_kp_u_scalar_line_1344, __pyx_k_scalar_line_1344, sizeof(__pyx_k_scalar_line_1344), 0, 1, 0, 0},
19019  {&__pyx_n_s_send, __pyx_k_send, sizeof(__pyx_k_send), 0, 0, 1, 1},
19020  {&__pyx_n_s_setstate, __pyx_k_setstate, sizeof(__pyx_k_setstate), 0, 0, 1, 1},
19021  {&__pyx_n_s_setstate_cython, __pyx_k_setstate_cython, sizeof(__pyx_k_setstate_cython), 0, 0, 1, 1},
19022  {&__pyx_n_s_sin, __pyx_k_sin, sizeof(__pyx_k_sin), 0, 0, 1, 1},
19023  {&__pyx_kp_u_sin_line_1679, __pyx_k_sin_line_1679, sizeof(__pyx_k_sin_line_1679), 0, 1, 0, 0},
19024  {&__pyx_n_s_sinh, __pyx_k_sinh, sizeof(__pyx_k_sinh), 0, 0, 1, 1},
19025  {&__pyx_kp_u_sinh_line_1719, __pyx_k_sinh_line_1719, sizeof(__pyx_k_sinh_line_1719), 0, 1, 0, 0},
19026  {&__pyx_n_s_sqrt, __pyx_k_sqrt, sizeof(__pyx_k_sqrt), 0, 0, 1, 1},
19027  {&__pyx_kp_u_sqrt_line_1542, __pyx_k_sqrt_line_1542, sizeof(__pyx_k_sqrt_line_1542), 0, 1, 0, 0},
19028  {&__pyx_n_s_tan, __pyx_k_tan, sizeof(__pyx_k_tan), 0, 0, 1, 1},
19029  {&__pyx_kp_u_tan_line_1752, __pyx_k_tan_line_1752, sizeof(__pyx_k_tan_line_1752), 0, 1, 0, 0},
19030  {&__pyx_n_s_tanh, __pyx_k_tanh, sizeof(__pyx_k_tanh), 0, 0, 1, 1},
19031  {&__pyx_kp_u_tanh_line_1786, __pyx_k_tanh_line_1786, sizeof(__pyx_k_tanh_line_1786), 0, 1, 0, 0},
19032  {&__pyx_n_s_tau, __pyx_k_tau, sizeof(__pyx_k_tau), 0, 0, 1, 1},
19033  {&__pyx_n_s_test, __pyx_k_test, sizeof(__pyx_k_test), 0, 0, 1, 1},
19034  {&__pyx_n_s_test_2, __pyx_k_test_2, sizeof(__pyx_k_test_2), 0, 0, 1, 1},
19035  {&__pyx_n_s_testmod, __pyx_k_testmod, sizeof(__pyx_k_testmod), 0, 0, 1, 1},
19036  {&__pyx_n_s_throw, __pyx_k_throw, sizeof(__pyx_k_throw), 0, 0, 1, 1},
19037  {&__pyx_kp_s_to_frame, __pyx_k_to_frame, sizeof(__pyx_k_to_frame), 0, 0, 1, 0},
19038  {&__pyx_kp_s_using, __pyx_k_using, sizeof(__pyx_k_using), 0, 0, 1, 0},
19039  {&__pyx_kp_s_using_invalid, __pyx_k_using_invalid, sizeof(__pyx_k_using_invalid), 0, 0, 1, 0},
19040  {&__pyx_kp_s_value, __pyx_k_value, sizeof(__pyx_k_value), 0, 0, 1, 0},
19041  {&__pyx_n_s_version, __pyx_k_version, sizeof(__pyx_k_version), 0, 0, 1, 1},
19042  {&__pyx_n_s_xrange, __pyx_k_xrange, sizeof(__pyx_k_xrange), 0, 0, 1, 1},
19043  {0, 0, 0, 0, 0, 0, 0}
19044 };
19045 static CYTHON_SMALL_CODE int __Pyx_InitCachedBuiltins(void) {
19046  __pyx_builtin_IndexError = __Pyx_GetBuiltinName(__pyx_n_s_IndexError); if (!__pyx_builtin_IndexError) __PYX_ERR(0, 102, __pyx_L1_error)
19047  __pyx_builtin_RuntimeError = __Pyx_GetBuiltinName(__pyx_n_s_RuntimeError); if (!__pyx_builtin_RuntimeError) __PYX_ERR(0, 104, __pyx_L1_error)
19048  __pyx_builtin_TypeError = __Pyx_GetBuiltinName(__pyx_n_s_TypeError); if (!__pyx_builtin_TypeError) __PYX_ERR(0, 104, __pyx_L1_error)
19049  __pyx_builtin_ValueError = __Pyx_GetBuiltinName(__pyx_n_s_ValueError); if (!__pyx_builtin_ValueError) __PYX_ERR(0, 105, __pyx_L1_error)
19050  __pyx_builtin_NotImplemented = __Pyx_GetBuiltinName(__pyx_n_s_NotImplemented); if (!__pyx_builtin_NotImplemented) __PYX_ERR(0, 157, __pyx_L1_error)
19051  __pyx_builtin_range = __Pyx_GetBuiltinName(__pyx_n_s_range); if (!__pyx_builtin_range) __PYX_ERR(0, 234, __pyx_L1_error)
19052  #if PY_MAJOR_VERSION >= 3
19053  __pyx_builtin_xrange = __Pyx_GetBuiltinName(__pyx_n_s_range); if (!__pyx_builtin_xrange) __PYX_ERR(0, 1098, __pyx_L1_error)
19054  #else
19055  __pyx_builtin_xrange = __Pyx_GetBuiltinName(__pyx_n_s_xrange); if (!__pyx_builtin_xrange) __PYX_ERR(0, 1098, __pyx_L1_error)
19056  #endif
19057  return 0;
19058  __pyx_L1_error:;
19059  return -1;
19060 }
19061 
19062 static CYTHON_SMALL_CODE int __Pyx_InitCachedConstants(void) {
19063  __Pyx_RefNannyDeclarations
19064  __Pyx_RefNannySetupContext("__Pyx_InitCachedConstants", 0);
19065 
19066  /* "(tree fragment)":2
19067  * def __reduce_cython__(self):
19068  * raise TypeError("no default __reduce__ due to non-trivial __cinit__") # <<<<<<<<<<<<<<
19069  * def __setstate_cython__(self, __pyx_state):
19070  * raise TypeError("no default __reduce__ due to non-trivial __cinit__")
19071  */
19072  __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)
19073  __Pyx_GOTREF(__pyx_tuple__3);
19074  __Pyx_GIVEREF(__pyx_tuple__3);
19075 
19076  /* "(tree fragment)":4
19077  * raise TypeError("no default __reduce__ due to non-trivial __cinit__")
19078  * def __setstate_cython__(self, __pyx_state):
19079  * raise TypeError("no default __reduce__ due to non-trivial __cinit__") # <<<<<<<<<<<<<<
19080  */
19081  __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)
19082  __Pyx_GOTREF(__pyx_tuple__4);
19083  __Pyx_GIVEREF(__pyx_tuple__4);
19084 
19085  /* "PyClical.pyx":635
19086  * TypeError: Not applicable.
19087  * """
19088  * raise TypeError("Not applicable.") # <<<<<<<<<<<<<<
19089  *
19090  * def __iter__(self):
19091  */
19092  __pyx_tuple__10 = PyTuple_Pack(1, __pyx_kp_s_Not_applicable); if (unlikely(!__pyx_tuple__10)) __PYX_ERR(0, 635, __pyx_L1_error)
19093  __Pyx_GOTREF(__pyx_tuple__10);
19094  __Pyx_GIVEREF(__pyx_tuple__10);
19095 
19096  /* "(tree fragment)":2
19097  * def __reduce_cython__(self):
19098  * raise TypeError("no default __reduce__ due to non-trivial __cinit__") # <<<<<<<<<<<<<<
19099  * def __setstate_cython__(self, __pyx_state):
19100  * raise TypeError("no default __reduce__ due to non-trivial __cinit__")
19101  */
19102  __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)
19103  __Pyx_GOTREF(__pyx_tuple__11);
19104  __Pyx_GIVEREF(__pyx_tuple__11);
19105 
19106  /* "(tree fragment)":4
19107  * raise TypeError("no default __reduce__ due to non-trivial __cinit__")
19108  * def __setstate_cython__(self, __pyx_state):
19109  * raise TypeError("no default __reduce__ due to non-trivial __cinit__") # <<<<<<<<<<<<<<
19110  */
19111  __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)
19112  __Pyx_GOTREF(__pyx_tuple__12);
19113  __Pyx_GIVEREF(__pyx_tuple__12);
19114 
19115  /* "PyClical.pyx":404
19116  * return index_set_to_str( self.unwrap() ).c_str()
19117  *
19118  * def index_set_hidden_doctests(): # <<<<<<<<<<<<<<
19119  * """
19120  * Tests for functions that Doctest cannot see.
19121  */
19122  __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)
19123 
19124  /* "PyClical.pyx":1243
19125  * return clifford_to_str( self.unwrap() ).c_str()
19126  *
19127  * def clifford_hidden_doctests(): # <<<<<<<<<<<<<<
19128  * """
19129  * Tests for functions that Doctest cannot see.
19130  */
19131  __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)
19132 
19133  /* "PyClical.pyx":1856
19134  *
19135  * # Some abbreviations.
19136  * tau = atan(clifford(1.0)) * 8.0 # <<<<<<<<<<<<<<
19137  * pi = tau / 2.0
19138  *
19139  */
19140  __pyx_tuple__15 = PyTuple_Pack(1, __pyx_float_1_0); if (unlikely(!__pyx_tuple__15)) __PYX_ERR(0, 1856, __pyx_L1_error)
19141  __Pyx_GOTREF(__pyx_tuple__15);
19142  __Pyx_GIVEREF(__pyx_tuple__15);
19143 
19144  /* "PyClical.pyx":1887
19145  * """
19146  *
19147  * def e(obj): # <<<<<<<<<<<<<<
19148  * """
19149  * Abbreviation for clifford(index_set(obj)).
19150  */
19151  __pyx_tuple__16 = PyTuple_Pack(1, __pyx_n_s_obj); if (unlikely(!__pyx_tuple__16)) __PYX_ERR(0, 1887, __pyx_L1_error)
19152  __Pyx_GOTREF(__pyx_tuple__16);
19153  __Pyx_GIVEREF(__pyx_tuple__16);
19154  __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)
19155 
19156  /* "PyClical.pyx":1900
19157  * return clifford(index_set(obj))
19158  *
19159  * def istpq(p, q): # <<<<<<<<<<<<<<
19160  * """
19161  * Abbreviation for index_set({-q,...p}).
19162  */
19163  __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)
19164  __Pyx_GOTREF(__pyx_tuple__18);
19165  __Pyx_GIVEREF(__pyx_tuple__18);
19166  __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)
19167 
19168  /* "PyClical.pyx":1909
19169  * return index_set(set(range(-q,p+1)))
19170  *
19171  * ninf3 = e(4) + e(-1) # Null infinity point in 3D Conformal Geometric Algebra [DL]. # <<<<<<<<<<<<<<
19172  * nbar3 = e(4) - e(-1) # Null bar point in 3D Conformal Geometric Algebra [DL].
19173  *
19174  */
19175  __pyx_tuple__20 = PyTuple_Pack(1, __pyx_int_4); if (unlikely(!__pyx_tuple__20)) __PYX_ERR(0, 1909, __pyx_L1_error)
19176  __Pyx_GOTREF(__pyx_tuple__20);
19177  __Pyx_GIVEREF(__pyx_tuple__20);
19178  __pyx_tuple__21 = PyTuple_Pack(1, __pyx_int_neg_1); if (unlikely(!__pyx_tuple__21)) __PYX_ERR(0, 1909, __pyx_L1_error)
19179  __Pyx_GOTREF(__pyx_tuple__21);
19180  __Pyx_GIVEREF(__pyx_tuple__21);
19181 
19182  /* "PyClical.pyx":1913
19183  *
19184  * # Doctest interface.
19185  * def _test(): # <<<<<<<<<<<<<<
19186  * import PyClical, doctest
19187  * return doctest.testmod(PyClical)
19188  */
19189  __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)
19190  __Pyx_GOTREF(__pyx_tuple__22);
19191  __Pyx_GIVEREF(__pyx_tuple__22);
19192  __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)
19193  __Pyx_RefNannyFinishContext();
19194  return 0;
19195  __pyx_L1_error:;
19196  __Pyx_RefNannyFinishContext();
19197  return -1;
19198 }
19199 
19200 static CYTHON_SMALL_CODE int __Pyx_InitGlobals(void) {
19201  if (__Pyx_InitStrings(__pyx_string_tab) < 0) __PYX_ERR(0, 1, __pyx_L1_error);
19202  __pyx_float_0_0 = PyFloat_FromDouble(0.0); if (unlikely(!__pyx_float_0_0)) __PYX_ERR(0, 1, __pyx_L1_error)
19203  __pyx_float_1_0 = PyFloat_FromDouble(1.0); if (unlikely(!__pyx_float_1_0)) __PYX_ERR(0, 1, __pyx_L1_error)
19204  __pyx_float_2_0 = PyFloat_FromDouble(2.0); if (unlikely(!__pyx_float_2_0)) __PYX_ERR(0, 1, __pyx_L1_error)
19205  __pyx_float_8_0 = PyFloat_FromDouble(8.0); if (unlikely(!__pyx_float_8_0)) __PYX_ERR(0, 1, __pyx_L1_error)
19206  __pyx_int_0 = PyInt_FromLong(0); if (unlikely(!__pyx_int_0)) __PYX_ERR(0, 1, __pyx_L1_error)
19207  __pyx_int_1 = PyInt_FromLong(1); if (unlikely(!__pyx_int_1)) __PYX_ERR(0, 1, __pyx_L1_error)
19208  __pyx_int_4 = PyInt_FromLong(4); if (unlikely(!__pyx_int_4)) __PYX_ERR(0, 1, __pyx_L1_error)
19209  __pyx_int_neg_1 = PyInt_FromLong(-1); if (unlikely(!__pyx_int_neg_1)) __PYX_ERR(0, 1, __pyx_L1_error)
19210  return 0;
19211  __pyx_L1_error:;
19212  return -1;
19213 }
19214 
19215 static CYTHON_SMALL_CODE int __Pyx_modinit_global_init_code(void); /*proto*/
19216 static CYTHON_SMALL_CODE int __Pyx_modinit_variable_export_code(void); /*proto*/
19217 static CYTHON_SMALL_CODE int __Pyx_modinit_function_export_code(void); /*proto*/
19218 static CYTHON_SMALL_CODE int __Pyx_modinit_type_init_code(void); /*proto*/
19219 static CYTHON_SMALL_CODE int __Pyx_modinit_type_import_code(void); /*proto*/
19220 static CYTHON_SMALL_CODE int __Pyx_modinit_variable_import_code(void); /*proto*/
19221 static CYTHON_SMALL_CODE int __Pyx_modinit_function_import_code(void); /*proto*/
19222 
19223 static int __Pyx_modinit_global_init_code(void) {
19224  __Pyx_RefNannyDeclarations
19225  __Pyx_RefNannySetupContext("__Pyx_modinit_global_init_code", 0);
19226  /*--- Global init code ---*/
19227  __Pyx_RefNannyFinishContext();
19228  return 0;
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19230 
19231 static int __Pyx_modinit_variable_export_code(void) {
19232  __Pyx_RefNannyDeclarations
19233  __Pyx_RefNannySetupContext("__Pyx_modinit_variable_export_code", 0);
19234  /*--- Variable export code ---*/
19235  __Pyx_RefNannyFinishContext();
19236  return 0;
19237 }
19238 
19239 static int __Pyx_modinit_function_export_code(void) {
19240  __Pyx_RefNannyDeclarations
19241  __Pyx_RefNannySetupContext("__Pyx_modinit_function_export_code", 0);
19242  /*--- Function export code ---*/
19243  __Pyx_RefNannyFinishContext();
19244  return 0;
19245 }
19246 
19247 static int __Pyx_modinit_type_init_code(void) {
19248  __Pyx_RefNannyDeclarations
19249  __Pyx_RefNannySetupContext("__Pyx_modinit_type_init_code", 0);
19250  /*--- Type init code ---*/
19251  __pyx_vtabptr_8PyClical_index_set = &__pyx_vtable_8PyClical_index_set;
19252  __pyx_vtable_8PyClical_index_set.wrap = (PyObject *(*)(struct __pyx_obj_8PyClical_index_set *, IndexSet))__pyx_f_8PyClical_9index_set_wrap;
19253  __pyx_vtable_8PyClical_index_set.unwrap = (IndexSet (*)(struct __pyx_obj_8PyClical_index_set *))__pyx_f_8PyClical_9index_set_unwrap;
19254  __pyx_vtable_8PyClical_index_set.copy = (PyObject *(*)(struct __pyx_obj_8PyClical_index_set *, int __pyx_skip_dispatch))__pyx_f_8PyClical_9index_set_copy;
19255  if (PyType_Ready(&__pyx_type_8PyClical_index_set) < 0) __PYX_ERR(0, 45, __pyx_L1_error)
19256  __pyx_type_8PyClical_index_set.tp_print = 0;
19257  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)) {
19258  __pyx_type_8PyClical_index_set.tp_getattro = __Pyx_PyObject_GenericGetAttr;
19259  }
19260  #if CYTHON_COMPILING_IN_CPYTHON
19261  {
19262  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__setitem__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19263  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19264  __pyx_wrapperbase_8PyClical_9index_set_8__setitem__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19265  __pyx_wrapperbase_8PyClical_9index_set_8__setitem__.doc = __pyx_doc_8PyClical_9index_set_8__setitem__;
19266  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_8__setitem__;
19267  }
19268  }
19269  #endif
19270  #if CYTHON_COMPILING_IN_CPYTHON
19271  {
19272  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__getitem__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19273  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19274  __pyx_wrapperbase_8PyClical_9index_set_10__getitem__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19275  __pyx_wrapperbase_8PyClical_9index_set_10__getitem__.doc = __pyx_doc_8PyClical_9index_set_10__getitem__;
19276  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_10__getitem__;
19277  }
19278  }
19279  #endif
19280  #if CYTHON_COMPILING_IN_CPYTHON
19281  {
19282  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__contains__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19283  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19284  __pyx_wrapperbase_8PyClical_9index_set_12__contains__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19285  __pyx_wrapperbase_8PyClical_9index_set_12__contains__.doc = __pyx_doc_8PyClical_9index_set_12__contains__;
19286  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_12__contains__;
19287  }
19288  }
19289  #endif
19290  #if CYTHON_COMPILING_IN_CPYTHON
19291  {
19292  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__iter__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19293  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19294  __pyx_wrapperbase_8PyClical_9index_set_14__iter__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19295  __pyx_wrapperbase_8PyClical_9index_set_14__iter__.doc = __pyx_doc_8PyClical_9index_set_14__iter__;
19296  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_14__iter__;
19297  }
19298  }
19299  #endif
19300  #if CYTHON_COMPILING_IN_CPYTHON
19301  {
19302  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__invert__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19303  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19304  __pyx_wrapperbase_8PyClical_9index_set_17__invert__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19305  __pyx_wrapperbase_8PyClical_9index_set_17__invert__.doc = __pyx_doc_8PyClical_9index_set_17__invert__;
19306  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_17__invert__;
19307  }
19308  }
19309  #endif
19310  #if CYTHON_COMPILING_IN_CPYTHON
19311  {
19312  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__xor__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19313  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19314  __pyx_wrapperbase_8PyClical_9index_set_19__xor__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19315  __pyx_wrapperbase_8PyClical_9index_set_19__xor__.doc = __pyx_doc_8PyClical_9index_set_19__xor__;
19316  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_19__xor__;
19317  }
19318  }
19319  #endif
19320  #if CYTHON_COMPILING_IN_CPYTHON
19321  {
19322  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__ixor__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19323  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19324  __pyx_wrapperbase_8PyClical_9index_set_21__ixor__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19325  __pyx_wrapperbase_8PyClical_9index_set_21__ixor__.doc = __pyx_doc_8PyClical_9index_set_21__ixor__;
19326  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_21__ixor__;
19327  }
19328  }
19329  #endif
19330  #if CYTHON_COMPILING_IN_CPYTHON
19331  {
19332  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__and__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19333  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19334  __pyx_wrapperbase_8PyClical_9index_set_23__and__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19335  __pyx_wrapperbase_8PyClical_9index_set_23__and__.doc = __pyx_doc_8PyClical_9index_set_23__and__;
19336  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_23__and__;
19337  }
19338  }
19339  #endif
19340  #if CYTHON_COMPILING_IN_CPYTHON
19341  {
19342  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__iand__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19343  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19344  __pyx_wrapperbase_8PyClical_9index_set_25__iand__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19345  __pyx_wrapperbase_8PyClical_9index_set_25__iand__.doc = __pyx_doc_8PyClical_9index_set_25__iand__;
19346  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_25__iand__;
19347  }
19348  }
19349  #endif
19350  #if CYTHON_COMPILING_IN_CPYTHON
19351  {
19352  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__or__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19353  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19354  __pyx_wrapperbase_8PyClical_9index_set_27__or__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19355  __pyx_wrapperbase_8PyClical_9index_set_27__or__.doc = __pyx_doc_8PyClical_9index_set_27__or__;
19356  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_27__or__;
19357  }
19358  }
19359  #endif
19360  #if CYTHON_COMPILING_IN_CPYTHON
19361  {
19362  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__ior__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19363  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19364  __pyx_wrapperbase_8PyClical_9index_set_29__ior__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19365  __pyx_wrapperbase_8PyClical_9index_set_29__ior__.doc = __pyx_doc_8PyClical_9index_set_29__ior__;
19366  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_29__ior__;
19367  }
19368  }
19369  #endif
19370  #if CYTHON_COMPILING_IN_CPYTHON
19371  {
19372  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__repr__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19373  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19374  __pyx_wrapperbase_8PyClical_9index_set_47__repr__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19375  __pyx_wrapperbase_8PyClical_9index_set_47__repr__.doc = __pyx_doc_8PyClical_9index_set_47__repr__;
19376  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_47__repr__;
19377  }
19378  }
19379  #endif
19380  #if CYTHON_COMPILING_IN_CPYTHON
19381  {
19382  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__str__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19383  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19384  __pyx_wrapperbase_8PyClical_9index_set_49__str__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19385  __pyx_wrapperbase_8PyClical_9index_set_49__str__.doc = __pyx_doc_8PyClical_9index_set_49__str__;
19386  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_49__str__;
19387  }
19388  }
19389  #endif
19390  if (__Pyx_SetVtable(__pyx_type_8PyClical_index_set.tp_dict, __pyx_vtabptr_8PyClical_index_set) < 0) __PYX_ERR(0, 45, __pyx_L1_error)
19391  if (PyObject_SetAttr(__pyx_m, __pyx_n_s_index_set, (PyObject *)&__pyx_type_8PyClical_index_set) < 0) __PYX_ERR(0, 45, __pyx_L1_error)
19392  if (__Pyx_setup_reduce((PyObject*)&__pyx_type_8PyClical_index_set) < 0) __PYX_ERR(0, 45, __pyx_L1_error)
19393  __pyx_ptype_8PyClical_index_set = &__pyx_type_8PyClical_index_set;
19394  __pyx_vtabptr_8PyClical_clifford = &__pyx_vtable_8PyClical_clifford;
19395  __pyx_vtable_8PyClical_clifford.wrap = (PyObject *(*)(struct __pyx_obj_8PyClical_clifford *, Clifford))__pyx_f_8PyClical_8clifford_wrap;
19396  __pyx_vtable_8PyClical_clifford.unwrap = (Clifford (*)(struct __pyx_obj_8PyClical_clifford *))__pyx_f_8PyClical_8clifford_unwrap;
19397  __pyx_vtable_8PyClical_clifford.copy = (PyObject *(*)(struct __pyx_obj_8PyClical_clifford *, int __pyx_skip_dispatch))__pyx_f_8PyClical_8clifford_copy;
19398  if (PyType_Ready(&__pyx_type_8PyClical_clifford) < 0) __PYX_ERR(0, 535, __pyx_L1_error)
19399  __pyx_type_8PyClical_clifford.tp_print = 0;
19400  if ((CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP) && likely(!__pyx_type_8PyClical_clifford.tp_dictoffset && __pyx_type_8PyClical_clifford.tp_getattro == PyObject_GenericGetAttr)) {
19401  __pyx_type_8PyClical_clifford.tp_getattro = __Pyx_PyObject_GenericGetAttr;
19402  }
19403  #if CYTHON_COMPILING_IN_CPYTHON
19404  {
19405  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__contains__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19406  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19407  __pyx_wrapperbase_8PyClical_8clifford_6__contains__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19408  __pyx_wrapperbase_8PyClical_8clifford_6__contains__.doc = __pyx_doc_8PyClical_8clifford_6__contains__;
19409  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_6__contains__;
19410  }
19411  }
19412  #endif
19413  #if CYTHON_COMPILING_IN_CPYTHON
19414  {
19415  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__iter__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19416  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19417  __pyx_wrapperbase_8PyClical_8clifford_8__iter__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19418  __pyx_wrapperbase_8PyClical_8clifford_8__iter__.doc = __pyx_doc_8PyClical_8clifford_8__iter__;
19419  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_8__iter__;
19420  }
19421  }
19422  #endif
19423  #if CYTHON_COMPILING_IN_CPYTHON
19424  {
19425  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__getitem__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19426  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19427  __pyx_wrapperbase_8PyClical_8clifford_14__getitem__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19428  __pyx_wrapperbase_8PyClical_8clifford_14__getitem__.doc = __pyx_doc_8PyClical_8clifford_14__getitem__;
19429  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_14__getitem__;
19430  }
19431  }
19432  #endif
19433  #if CYTHON_COMPILING_IN_CPYTHON
19434  {
19435  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__neg__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19436  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19437  __pyx_wrapperbase_8PyClical_8clifford_16__neg__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19438  __pyx_wrapperbase_8PyClical_8clifford_16__neg__.doc = __pyx_doc_8PyClical_8clifford_16__neg__;
19439  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_16__neg__;
19440  }
19441  }
19442  #endif
19443  #if CYTHON_COMPILING_IN_CPYTHON
19444  {
19445  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__pos__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19446  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19447  __pyx_wrapperbase_8PyClical_8clifford_18__pos__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19448  __pyx_wrapperbase_8PyClical_8clifford_18__pos__.doc = __pyx_doc_8PyClical_8clifford_18__pos__;
19449  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_18__pos__;
19450  }
19451  }
19452  #endif
19453  #if CYTHON_COMPILING_IN_CPYTHON
19454  {
19455  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__add__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19456  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19457  __pyx_wrapperbase_8PyClical_8clifford_20__add__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19458  __pyx_wrapperbase_8PyClical_8clifford_20__add__.doc = __pyx_doc_8PyClical_8clifford_20__add__;
19459  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_20__add__;
19460  }
19461  }
19462  #endif
19463  #if CYTHON_COMPILING_IN_CPYTHON
19464  {
19465  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__iadd__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19466  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19467  __pyx_wrapperbase_8PyClical_8clifford_22__iadd__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19468  __pyx_wrapperbase_8PyClical_8clifford_22__iadd__.doc = __pyx_doc_8PyClical_8clifford_22__iadd__;
19469  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_22__iadd__;
19470  }
19471  }
19472  #endif
19473  #if CYTHON_COMPILING_IN_CPYTHON
19474  {
19475  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__sub__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19476  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19477  __pyx_wrapperbase_8PyClical_8clifford_24__sub__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19478  __pyx_wrapperbase_8PyClical_8clifford_24__sub__.doc = __pyx_doc_8PyClical_8clifford_24__sub__;
19479  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_24__sub__;
19480  }
19481  }
19482  #endif
19483  #if CYTHON_COMPILING_IN_CPYTHON
19484  {
19485  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__isub__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19486  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19487  __pyx_wrapperbase_8PyClical_8clifford_26__isub__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19488  __pyx_wrapperbase_8PyClical_8clifford_26__isub__.doc = __pyx_doc_8PyClical_8clifford_26__isub__;
19489  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_26__isub__;
19490  }
19491  }
19492  #endif
19493  #if CYTHON_COMPILING_IN_CPYTHON
19494  {
19495  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__mul__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19496  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19497  __pyx_wrapperbase_8PyClical_8clifford_28__mul__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19498  __pyx_wrapperbase_8PyClical_8clifford_28__mul__.doc = __pyx_doc_8PyClical_8clifford_28__mul__;
19499  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_28__mul__;
19500  }
19501  }
19502  #endif
19503  #if CYTHON_COMPILING_IN_CPYTHON
19504  {
19505  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__imul__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19506  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19507  __pyx_wrapperbase_8PyClical_8clifford_30__imul__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19508  __pyx_wrapperbase_8PyClical_8clifford_30__imul__.doc = __pyx_doc_8PyClical_8clifford_30__imul__;
19509  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_30__imul__;
19510  }
19511  }
19512  #endif
19513  #if CYTHON_COMPILING_IN_CPYTHON
19514  {
19515  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__mod__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19516  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19517  __pyx_wrapperbase_8PyClical_8clifford_32__mod__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19518  __pyx_wrapperbase_8PyClical_8clifford_32__mod__.doc = __pyx_doc_8PyClical_8clifford_32__mod__;
19519  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_32__mod__;
19520  }
19521  }
19522  #endif
19523  #if CYTHON_COMPILING_IN_CPYTHON
19524  {
19525  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__imod__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19526  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19527  __pyx_wrapperbase_8PyClical_8clifford_34__imod__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19528  __pyx_wrapperbase_8PyClical_8clifford_34__imod__.doc = __pyx_doc_8PyClical_8clifford_34__imod__;
19529  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_34__imod__;
19530  }
19531  }
19532  #endif
19533  #if CYTHON_COMPILING_IN_CPYTHON
19534  {
19535  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__and__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19536  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19537  __pyx_wrapperbase_8PyClical_8clifford_36__and__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19538  __pyx_wrapperbase_8PyClical_8clifford_36__and__.doc = __pyx_doc_8PyClical_8clifford_36__and__;
19539  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_36__and__;
19540  }
19541  }
19542  #endif
19543  #if CYTHON_COMPILING_IN_CPYTHON
19544  {
19545  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__iand__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19546  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19547  __pyx_wrapperbase_8PyClical_8clifford_38__iand__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19548  __pyx_wrapperbase_8PyClical_8clifford_38__iand__.doc = __pyx_doc_8PyClical_8clifford_38__iand__;
19549  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_38__iand__;
19550  }
19551  }
19552  #endif
19553  #if CYTHON_COMPILING_IN_CPYTHON
19554  {
19555  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__xor__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19556  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19557  __pyx_wrapperbase_8PyClical_8clifford_40__xor__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19558  __pyx_wrapperbase_8PyClical_8clifford_40__xor__.doc = __pyx_doc_8PyClical_8clifford_40__xor__;
19559  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_40__xor__;
19560  }
19561  }
19562  #endif
19563  #if CYTHON_COMPILING_IN_CPYTHON
19564  {
19565  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__ixor__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19566  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19567  __pyx_wrapperbase_8PyClical_8clifford_42__ixor__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19568  __pyx_wrapperbase_8PyClical_8clifford_42__ixor__.doc = __pyx_doc_8PyClical_8clifford_42__ixor__;
19569  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_42__ixor__;
19570  }
19571  }
19572  #endif
19573  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
19574  #if CYTHON_COMPILING_IN_CPYTHON
19575  {
19576  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__div__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19577  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19578  __pyx_wrapperbase_8PyClical_8clifford_44__div__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19579  __pyx_wrapperbase_8PyClical_8clifford_44__div__.doc = __pyx_doc_8PyClical_8clifford_44__div__;
19580  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_44__div__;
19581  }
19582  }
19583  #endif
19584  #endif
19585  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
19586  #if CYTHON_COMPILING_IN_CPYTHON
19587  {
19588  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__idiv__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19589  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19590  __pyx_wrapperbase_8PyClical_8clifford_46__idiv__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19591  __pyx_wrapperbase_8PyClical_8clifford_46__idiv__.doc = __pyx_doc_8PyClical_8clifford_46__idiv__;
19592  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_46__idiv__;
19593  }
19594  }
19595  #endif
19596  #endif
19597  #if CYTHON_COMPILING_IN_CPYTHON
19598  {
19599  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__or__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19600  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19601  __pyx_wrapperbase_8PyClical_8clifford_50__or__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19602  __pyx_wrapperbase_8PyClical_8clifford_50__or__.doc = __pyx_doc_8PyClical_8clifford_50__or__;
19603  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_50__or__;
19604  }
19605  }
19606  #endif
19607  #if CYTHON_COMPILING_IN_CPYTHON
19608  {
19609  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__ior__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19610  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19611  __pyx_wrapperbase_8PyClical_8clifford_52__ior__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19612  __pyx_wrapperbase_8PyClical_8clifford_52__ior__.doc = __pyx_doc_8PyClical_8clifford_52__ior__;
19613  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_52__ior__;
19614  }
19615  }
19616  #endif
19617  #if CYTHON_COMPILING_IN_CPYTHON
19618  {
19619  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__pow__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19620  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19621  __pyx_wrapperbase_8PyClical_8clifford_54__pow__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19622  __pyx_wrapperbase_8PyClical_8clifford_54__pow__.doc = __pyx_doc_8PyClical_8clifford_54__pow__;
19623  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_54__pow__;
19624  }
19625  }
19626  #endif
19627  #if CYTHON_COMPILING_IN_CPYTHON
19628  {
19629  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__call__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19630  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19631  __pyx_wrapperbase_8PyClical_8clifford_60__call__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19632  __pyx_wrapperbase_8PyClical_8clifford_60__call__.doc = __pyx_doc_8PyClical_8clifford_60__call__;
19633  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_60__call__;
19634  }
19635  }
19636  #endif
19637  #if CYTHON_COMPILING_IN_CPYTHON
19638  {
19639  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__repr__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19640  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19641  __pyx_wrapperbase_8PyClical_8clifford_92__repr__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19642  __pyx_wrapperbase_8PyClical_8clifford_92__repr__.doc = __pyx_doc_8PyClical_8clifford_92__repr__;
19643  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_92__repr__;
19644  }
19645  }
19646  #endif
19647  #if CYTHON_COMPILING_IN_CPYTHON
19648  {
19649  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__str__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19650  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19651  __pyx_wrapperbase_8PyClical_8clifford_94__str__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19652  __pyx_wrapperbase_8PyClical_8clifford_94__str__.doc = __pyx_doc_8PyClical_8clifford_94__str__;
19653  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_94__str__;
19654  }
19655  }
19656  #endif
19657  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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19660  __pyx_ptype_8PyClical_clifford = &__pyx_type_8PyClical_clifford;
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19662  __pyx_type_8PyClical___pyx_scope_struct____iter__.tp_print = 0;
19663  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)) {
19664  __pyx_type_8PyClical___pyx_scope_struct____iter__.tp_getattro = __Pyx_PyObject_GenericGetAttrNoDict;
19665  }
19666  __pyx_ptype_8PyClical___pyx_scope_struct____iter__ = &__pyx_type_8PyClical___pyx_scope_struct____iter__;
19667  __Pyx_RefNannyFinishContext();
19668  return 0;
19669  __pyx_L1_error:;
19670  __Pyx_RefNannyFinishContext();
19671  return -1;
19672 }
19673 
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19675  __Pyx_RefNannyDeclarations
19676  __Pyx_RefNannySetupContext("__Pyx_modinit_type_import_code", 0);
19677  /*--- Type import code ---*/
19678  __Pyx_RefNannyFinishContext();
19679  return 0;
19680 }
19681 
19682 static int __Pyx_modinit_variable_import_code(void) {
19683  __Pyx_RefNannyDeclarations
19684  __Pyx_RefNannySetupContext("__Pyx_modinit_variable_import_code", 0);
19685  /*--- Variable import code ---*/
19686  __Pyx_RefNannyFinishContext();
19687  return 0;
19688 }
19689 
19690 static int __Pyx_modinit_function_import_code(void) {
19691  __Pyx_RefNannyDeclarations
19692  __Pyx_RefNannySetupContext("__Pyx_modinit_function_import_code", 0);
19693  /*--- Function import code ---*/
19694  __Pyx_RefNannyFinishContext();
19695  return 0;
19696 }
19697 
19698 
19699 #if PY_MAJOR_VERSION < 3
19700 #ifdef CYTHON_NO_PYINIT_EXPORT
19701 #define __Pyx_PyMODINIT_FUNC void
19702 #else
19703 #define __Pyx_PyMODINIT_FUNC PyMODINIT_FUNC
19704 #endif
19705 #else
19706 #ifdef CYTHON_NO_PYINIT_EXPORT
19707 #define __Pyx_PyMODINIT_FUNC PyObject *
19708 #else
19709 #define __Pyx_PyMODINIT_FUNC PyMODINIT_FUNC
19710 #endif
19711 #endif
19712 
19713 
19714 #if PY_MAJOR_VERSION < 3
19715 __Pyx_PyMODINIT_FUNC initPyClical(void) CYTHON_SMALL_CODE; /*proto*/
19716 __Pyx_PyMODINIT_FUNC initPyClical(void)
19717 #else
19718 __Pyx_PyMODINIT_FUNC PyInit_PyClical(void) CYTHON_SMALL_CODE; /*proto*/
19719 __Pyx_PyMODINIT_FUNC PyInit_PyClical(void)
19720 #if CYTHON_PEP489_MULTI_PHASE_INIT
19721 {
19722  return PyModuleDef_Init(&__pyx_moduledef);
19723 }
19724 static CYTHON_SMALL_CODE int __Pyx_check_single_interpreter(void) {
19725  #if PY_VERSION_HEX >= 0x030700A1
19726  static PY_INT64_T main_interpreter_id = -1;
19727  PY_INT64_T current_id = PyInterpreterState_GetID(PyThreadState_Get()->interp);
19728  if (main_interpreter_id == -1) {
19729  main_interpreter_id = current_id;
19730  return (unlikely(current_id == -1)) ? -1 : 0;
19731  } else if (unlikely(main_interpreter_id != current_id))
19732  #else
19733  static PyInterpreterState *main_interpreter = NULL;
19734  PyInterpreterState *current_interpreter = PyThreadState_Get()->interp;
19735  if (!main_interpreter) {
19736  main_interpreter = current_interpreter;
19737  } else if (unlikely(main_interpreter != current_interpreter))
19738  #endif
19739  {
19740  PyErr_SetString(
19741  PyExc_ImportError,
19742  "Interpreter change detected - this module can only be loaded into one interpreter per process.");
19743  return -1;
19744  }
19745  return 0;
19746 }
19747 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) {
19748  PyObject *value = PyObject_GetAttrString(spec, from_name);
19749  int result = 0;
19750  if (likely(value)) {
19751  if (allow_none || value != Py_None) {
19752  result = PyDict_SetItemString(moddict, to_name, value);
19753  }
19754  Py_DECREF(value);
19755  } else if (PyErr_ExceptionMatches(PyExc_AttributeError)) {
19756  PyErr_Clear();
19757  } else {
19758  result = -1;
19759  }
19760  return result;
19761 }
19762 static CYTHON_SMALL_CODE PyObject* __pyx_pymod_create(PyObject *spec, CYTHON_UNUSED PyModuleDef *def) {
19763  PyObject *module = NULL, *moddict, *modname;
19764  if (__Pyx_check_single_interpreter())
19765  return NULL;
19766  if (__pyx_m)
19767  return __Pyx_NewRef(__pyx_m);
19768  modname = PyObject_GetAttrString(spec, "name");
19769  if (unlikely(!modname)) goto bad;
19770  module = PyModule_NewObject(modname);
19771  Py_DECREF(modname);
19772  if (unlikely(!module)) goto bad;
19773  moddict = PyModule_GetDict(module);
19774  if (unlikely(!moddict)) goto bad;
19775  if (unlikely(__Pyx_copy_spec_to_module(spec, moddict, "loader", "__loader__", 1) < 0)) goto bad;
19776  if (unlikely(__Pyx_copy_spec_to_module(spec, moddict, "origin", "__file__", 1) < 0)) goto bad;
19777  if (unlikely(__Pyx_copy_spec_to_module(spec, moddict, "parent", "__package__", 1) < 0)) goto bad;
19778  if (unlikely(__Pyx_copy_spec_to_module(spec, moddict, "submodule_search_locations", "__path__", 0) < 0)) goto bad;
19779  return module;
19780 bad:
19781  Py_XDECREF(module);
19782  return NULL;
19783 }
19784 
19785 
19786 static CYTHON_SMALL_CODE int __pyx_pymod_exec_PyClical(PyObject *__pyx_pyinit_module)
19787 #endif
19788 #endif
19789 {
19790  PyObject *__pyx_t_1 = NULL;
19791  PyObject *__pyx_t_2 = NULL;
19792  PyObject *__pyx_t_3 = NULL;
19793  int __pyx_t_4;
19794  __Pyx_RefNannyDeclarations
19795  #if CYTHON_PEP489_MULTI_PHASE_INIT
19796  if (__pyx_m) {
19797  if (__pyx_m == __pyx_pyinit_module) return 0;
19798  PyErr_SetString(PyExc_RuntimeError, "Module 'PyClical' has already been imported. Re-initialisation is not supported.");
19799  return -1;
19800  }
19801  #elif PY_MAJOR_VERSION >= 3
19802  if (__pyx_m) return __Pyx_NewRef(__pyx_m);
19803  #endif
19804  #if CYTHON_REFNANNY
19805 __Pyx_RefNanny = __Pyx_RefNannyImportAPI("refnanny");
19806 if (!__Pyx_RefNanny) {
19807  PyErr_Clear();
19808  __Pyx_RefNanny = __Pyx_RefNannyImportAPI("Cython.Runtime.refnanny");
19809  if (!__Pyx_RefNanny)
19810  Py_FatalError("failed to import 'refnanny' module");
19811 }
19812 #endif
19813  __Pyx_RefNannySetupContext("__Pyx_PyMODINIT_FUNC PyInit_PyClical(void)", 0);
19814  if (__Pyx_check_binary_version() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
19815  #ifdef __Pxy_PyFrame_Initialize_Offsets
19816  __Pxy_PyFrame_Initialize_Offsets();
19817  #endif
19818  __pyx_empty_tuple = PyTuple_New(0); if (unlikely(!__pyx_empty_tuple)) __PYX_ERR(0, 1, __pyx_L1_error)
19819  __pyx_empty_bytes = PyBytes_FromStringAndSize("", 0); if (unlikely(!__pyx_empty_bytes)) __PYX_ERR(0, 1, __pyx_L1_error)
19820  __pyx_empty_unicode = PyUnicode_FromStringAndSize("", 0); if (unlikely(!__pyx_empty_unicode)) __PYX_ERR(0, 1, __pyx_L1_error)
19821  #ifdef __Pyx_CyFunction_USED
19822  if (__pyx_CyFunction_init() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
19823  #endif
19824  #ifdef __Pyx_FusedFunction_USED
19825  if (__pyx_FusedFunction_init() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
19826  #endif
19827  #ifdef __Pyx_Coroutine_USED
19828  if (__pyx_Coroutine_init() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
19829  #endif
19830  #ifdef __Pyx_Generator_USED
19831  if (__pyx_Generator_init() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
19832  #endif
19833  #ifdef __Pyx_AsyncGen_USED
19834  if (__pyx_AsyncGen_init() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
19835  #endif
19836  #ifdef __Pyx_StopAsyncIteration_USED
19837  if (__pyx_StopAsyncIteration_init() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
19838  #endif
19839  /*--- Library function declarations ---*/
19840  /*--- Threads initialization code ---*/
19841  #if defined(__PYX_FORCE_INIT_THREADS) && __PYX_FORCE_INIT_THREADS
19842  #ifdef WITH_THREAD /* Python build with threading support? */
19843  PyEval_InitThreads();
19844  #endif
19845  #endif
19846  /*--- Module creation code ---*/
19847  #if CYTHON_PEP489_MULTI_PHASE_INIT
19848  __pyx_m = __pyx_pyinit_module;
19849  Py_INCREF(__pyx_m);
19850  #else
19851  #if PY_MAJOR_VERSION < 3
19852  __pyx_m = Py_InitModule4("PyClical", __pyx_methods, 0, 0, PYTHON_API_VERSION); Py_XINCREF(__pyx_m);
19853  #else
19854  __pyx_m = PyModule_Create(&__pyx_moduledef);
19855  #endif
19856  if (unlikely(!__pyx_m)) __PYX_ERR(0, 1, __pyx_L1_error)
19857  #endif
19858  __pyx_d = PyModule_GetDict(__pyx_m); if (unlikely(!__pyx_d)) __PYX_ERR(0, 1, __pyx_L1_error)
19859  Py_INCREF(__pyx_d);
19860  __pyx_b = PyImport_AddModule(__Pyx_BUILTIN_MODULE_NAME); if (unlikely(!__pyx_b)) __PYX_ERR(0, 1, __pyx_L1_error)
19861  __pyx_cython_runtime = PyImport_AddModule((char *) "cython_runtime"); if (unlikely(!__pyx_cython_runtime)) __PYX_ERR(0, 1, __pyx_L1_error)
19862  #if CYTHON_COMPILING_IN_PYPY
19863  Py_INCREF(__pyx_b);
19864  #endif
19865  if (PyObject_SetAttrString(__pyx_m, "__builtins__", __pyx_b) < 0) __PYX_ERR(0, 1, __pyx_L1_error);
19866  /*--- Initialize various global constants etc. ---*/
19867  if (__Pyx_InitGlobals() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
19868  #if PY_MAJOR_VERSION < 3 && (__PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT)
19869  if (__Pyx_init_sys_getdefaultencoding_params() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
19870  #endif
19871  if (__pyx_module_is_main_PyClical) {
19872  if (PyObject_SetAttr(__pyx_m, __pyx_n_s_name, __pyx_n_s_main) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
19873  }
19874  #if PY_MAJOR_VERSION >= 3
19875  {
19876  PyObject *modules = PyImport_GetModuleDict(); if (unlikely(!modules)) __PYX_ERR(0, 1, __pyx_L1_error)
19877  if (!PyDict_GetItemString(modules, "PyClical")) {
19878  if (unlikely(PyDict_SetItemString(modules, "PyClical", __pyx_m) < 0)) __PYX_ERR(0, 1, __pyx_L1_error)
19879  }
19880  }
19881  #endif
19882  /*--- Builtin init code ---*/
19883  if (__Pyx_InitCachedBuiltins() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
19884  /*--- Constants init code ---*/
19885  if (__Pyx_InitCachedConstants() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
19886  /*--- Global type/function init code ---*/
19887  (void)__Pyx_modinit_global_init_code();
19888  (void)__Pyx_modinit_variable_export_code();
19889  (void)__Pyx_modinit_function_export_code();
19890  if (unlikely(__Pyx_modinit_type_init_code() != 0)) goto __pyx_L1_error;
19891  (void)__Pyx_modinit_type_import_code();
19892  (void)__Pyx_modinit_variable_import_code();
19893  (void)__Pyx_modinit_function_import_code();
19894  /*--- Execution code ---*/
19895  #if defined(__Pyx_Generator_USED) || defined(__Pyx_Coroutine_USED)
19896  if (__Pyx_patch_abc() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
19897  #endif
19898 
19899  /* "PyClical.pyx":28
19900  * # C. Doran and A. Lasenby, "Geometric algebra for physicists", Cambridge, 2003.
19901  *
19902  * import math # <<<<<<<<<<<<<<
19903  * import numbers
19904  * import collections
19905  */
19906  __pyx_t_1 = __Pyx_Import(__pyx_n_s_math, 0, -1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 28, __pyx_L1_error)
19907  __Pyx_GOTREF(__pyx_t_1);
19908  if (PyDict_SetItem(__pyx_d, __pyx_n_s_math, __pyx_t_1) < 0) __PYX_ERR(0, 28, __pyx_L1_error)
19909  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
19910 
19911  /* "PyClical.pyx":29
19912  *
19913  * import math
19914  * import numbers # <<<<<<<<<<<<<<
19915  * import collections
19916  *
19917  */
19918  __pyx_t_1 = __Pyx_Import(__pyx_n_s_numbers, 0, -1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 29, __pyx_L1_error)
19919  __Pyx_GOTREF(__pyx_t_1);
19920  if (PyDict_SetItem(__pyx_d, __pyx_n_s_numbers, __pyx_t_1) < 0) __PYX_ERR(0, 29, __pyx_L1_error)
19921  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
19922 
19923  /* "PyClical.pyx":30
19924  * import math
19925  * import numbers
19926  * import collections # <<<<<<<<<<<<<<
19927  *
19928  * __version__ = "0.8.2"
19929  */
19930  __pyx_t_1 = __Pyx_Import(__pyx_n_s_collections, 0, -1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 30, __pyx_L1_error)
19931  __Pyx_GOTREF(__pyx_t_1);
19932  if (PyDict_SetItem(__pyx_d, __pyx_n_s_collections, __pyx_t_1) < 0) __PYX_ERR(0, 30, __pyx_L1_error)
19933  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
19934 
19935  /* "PyClical.pyx":32
19936  * import collections
19937  *
19938  * __version__ = "0.8.2" # <<<<<<<<<<<<<<
19939  *
19940  * from PyClical cimport *
19941  */
19942  if (PyDict_SetItem(__pyx_d, __pyx_n_s_version, __pyx_kp_s_0_8_2) < 0) __PYX_ERR(0, 32, __pyx_L1_error)
19943 
19944  /* "PyClical.pyx":404
19945  * return index_set_to_str( self.unwrap() ).c_str()
19946  *
19947  * def index_set_hidden_doctests(): # <<<<<<<<<<<<<<
19948  * """
19949  * Tests for functions that Doctest cannot see.
19950  */
19951  __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)
19952  __Pyx_GOTREF(__pyx_t_1);
19953  if (PyDict_SetItem(__pyx_d, __pyx_n_s_index_set_hidden_doctests, __pyx_t_1) < 0) __PYX_ERR(0, 404, __pyx_L1_error)
19954  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
19955 
19956  /* "PyClical.pyx":1243
19957  * return clifford_to_str( self.unwrap() ).c_str()
19958  *
19959  * def clifford_hidden_doctests(): # <<<<<<<<<<<<<<
19960  * """
19961  * Tests for functions that Doctest cannot see.
19962  */
19963  __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)
19964  __Pyx_GOTREF(__pyx_t_1);
19965  if (PyDict_SetItem(__pyx_d, __pyx_n_s_clifford_hidden_doctests, __pyx_t_1) < 0) __PYX_ERR(0, 1243, __pyx_L1_error)
19966  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
19967 
19968  /* "PyClical.pyx":1856
19969  *
19970  * # Some abbreviations.
19971  * tau = atan(clifford(1.0)) * 8.0 # <<<<<<<<<<<<<<
19972  * pi = tau / 2.0
19973  *
19974  */
19975  __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)
19976  __Pyx_GOTREF(__pyx_t_1);
19977  __pyx_t_2 = __pyx_f_8PyClical_atan(__pyx_t_1, 0, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 1856, __pyx_L1_error)
19978  __Pyx_GOTREF(__pyx_t_2);
19979  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
19980  __pyx_t_1 = PyNumber_Multiply(__pyx_t_2, __pyx_float_8_0); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 1856, __pyx_L1_error)
19981  __Pyx_GOTREF(__pyx_t_1);
19982  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
19983  if (PyDict_SetItem(__pyx_d, __pyx_n_s_tau, __pyx_t_1) < 0) __PYX_ERR(0, 1856, __pyx_L1_error)
19984  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
19985 
19986  /* "PyClical.pyx":1857
19987  * # Some abbreviations.
19988  * tau = atan(clifford(1.0)) * 8.0
19989  * pi = tau / 2.0 # <<<<<<<<<<<<<<
19990  *
19991  * cl = clifford
19992  */
19993  __Pyx_GetModuleGlobalName(__pyx_t_1, __pyx_n_s_tau); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 1857, __pyx_L1_error)
19994  __Pyx_GOTREF(__pyx_t_1);
19995  __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)
19996  __Pyx_GOTREF(__pyx_t_2);
19997  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
19998  if (PyDict_SetItem(__pyx_d, __pyx_n_s_pi, __pyx_t_2) < 0) __PYX_ERR(0, 1857, __pyx_L1_error)
19999  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
20000 
20001  /* "PyClical.pyx":1859
20002  * pi = tau / 2.0
20003  *
20004  * cl = clifford # <<<<<<<<<<<<<<
20005  * """
20006  * Abbreviation for clifford.
20007  */
20008  if (PyDict_SetItem(__pyx_d, __pyx_n_s_cl, ((PyObject *)__pyx_ptype_8PyClical_clifford)) < 0) __PYX_ERR(0, 1859, __pyx_L1_error)
20009 
20010  /* "PyClical.pyx":1879
20011  * """
20012  *
20013  * ist = index_set # <<<<<<<<<<<<<<
20014  * """
20015  * Abbreviation for index_set.
20016  */
20017  if (PyDict_SetItem(__pyx_d, __pyx_n_s_ist, ((PyObject *)__pyx_ptype_8PyClical_index_set)) < 0) __PYX_ERR(0, 1879, __pyx_L1_error)
20018 
20019  /* "PyClical.pyx":1887
20020  * """
20021  *
20022  * def e(obj): # <<<<<<<<<<<<<<
20023  * """
20024  * Abbreviation for clifford(index_set(obj)).
20025  */
20026  __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)
20027  __Pyx_GOTREF(__pyx_t_2);
20028  if (PyDict_SetItem(__pyx_d, __pyx_n_s_e, __pyx_t_2) < 0) __PYX_ERR(0, 1887, __pyx_L1_error)
20029  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
20030 
20031  /* "PyClical.pyx":1900
20032  * return clifford(index_set(obj))
20033  *
20034  * def istpq(p, q): # <<<<<<<<<<<<<<
20035  * """
20036  * Abbreviation for index_set({-q,...p}).
20037  */
20038  __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)
20039  __Pyx_GOTREF(__pyx_t_2);
20040  if (PyDict_SetItem(__pyx_d, __pyx_n_s_istpq, __pyx_t_2) < 0) __PYX_ERR(0, 1900, __pyx_L1_error)
20041  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
20042 
20043  /* "PyClical.pyx":1909
20044  * return index_set(set(range(-q,p+1)))
20045  *
20046  * ninf3 = e(4) + e(-1) # Null infinity point in 3D Conformal Geometric Algebra [DL]. # <<<<<<<<<<<<<<
20047  * nbar3 = e(4) - e(-1) # Null bar point in 3D Conformal Geometric Algebra [DL].
20048  *
20049  */
20050  __Pyx_GetModuleGlobalName(__pyx_t_2, __pyx_n_s_e); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 1909, __pyx_L1_error)
20051  __Pyx_GOTREF(__pyx_t_2);
20052  __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)
20053  __Pyx_GOTREF(__pyx_t_1);
20054  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
20055  __Pyx_GetModuleGlobalName(__pyx_t_2, __pyx_n_s_e); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 1909, __pyx_L1_error)
20056  __Pyx_GOTREF(__pyx_t_2);
20057  __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)
20058  __Pyx_GOTREF(__pyx_t_3);
20059  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
20060  __pyx_t_2 = PyNumber_Add(__pyx_t_1, __pyx_t_3); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 1909, __pyx_L1_error)
20061  __Pyx_GOTREF(__pyx_t_2);
20062  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
20063  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
20064  if (PyDict_SetItem(__pyx_d, __pyx_n_s_ninf3, __pyx_t_2) < 0) __PYX_ERR(0, 1909, __pyx_L1_error)
20065  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
20066 
20067  /* "PyClical.pyx":1910
20068  *
20069  * ninf3 = e(4) + e(-1) # Null infinity point in 3D Conformal Geometric Algebra [DL].
20070  * nbar3 = e(4) - e(-1) # Null bar point in 3D Conformal Geometric Algebra [DL]. # <<<<<<<<<<<<<<
20071  *
20072  * # Doctest interface.
20073  */
20074  __Pyx_GetModuleGlobalName(__pyx_t_2, __pyx_n_s_e); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 1910, __pyx_L1_error)
20075  __Pyx_GOTREF(__pyx_t_2);
20076  __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)
20077  __Pyx_GOTREF(__pyx_t_3);
20078  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
20079  __Pyx_GetModuleGlobalName(__pyx_t_2, __pyx_n_s_e); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 1910, __pyx_L1_error)
20080  __Pyx_GOTREF(__pyx_t_2);
20081  __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)
20082  __Pyx_GOTREF(__pyx_t_1);
20083  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
20084  __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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20092  *
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20226  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)
20227  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)
20228  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)
20229  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)
20230  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)
20231  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)
20232  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)
20233  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)
20234  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)
20235  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)
20236  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)
20237  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)
20238  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)
20239  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)
20240  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)
20241  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)
20242  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)
20243  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)
20244  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)
20245  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)
20246  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)
20247  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)
20248  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)
20249  if (PyDict_SetItem(__pyx_d, __pyx_n_s_test_2, __pyx_t_1) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20250  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
20251 
20252  /*--- Wrapped vars code ---*/
20253 
20254  goto __pyx_L0;
20255  __pyx_L1_error:;
20256  __Pyx_XDECREF(__pyx_t_1);
20257  __Pyx_XDECREF(__pyx_t_2);
20258  __Pyx_XDECREF(__pyx_t_3);
20259  if (__pyx_m) {
20260  if (__pyx_d) {
20261  __Pyx_AddTraceback("init PyClical", __pyx_clineno, __pyx_lineno, __pyx_filename);
20262  }
20263  Py_CLEAR(__pyx_m);
20264  } else if (!PyErr_Occurred()) {
20265  PyErr_SetString(PyExc_ImportError, "init PyClical");
20266  }
20267  __pyx_L0:;
20268  __Pyx_RefNannyFinishContext();
20269  #if CYTHON_PEP489_MULTI_PHASE_INIT
20270  return (__pyx_m != NULL) ? 0 : -1;
20271  #elif PY_MAJOR_VERSION >= 3
20272  return __pyx_m;
20273  #else
20274  return;
20275  #endif
20276 }
20277 
20278 /* --- Runtime support code --- */
20279 /* Refnanny */
20280 #if CYTHON_REFNANNY
20281 static __Pyx_RefNannyAPIStruct *__Pyx_RefNannyImportAPI(const char *modname) {
20282  PyObject *m = NULL, *p = NULL;
20283  void *r = NULL;
20284  m = PyImport_ImportModule(modname);
20285  if (!m) goto end;
20286  p = PyObject_GetAttrString(m, "RefNannyAPI");
20287  if (!p) goto end;
20288  r = PyLong_AsVoidPtr(p);
20289 end:
20290  Py_XDECREF(p);
20291  Py_XDECREF(m);
20292  return (__Pyx_RefNannyAPIStruct *)r;
20293 }
20294 #endif
20295 
20296 /* PyObjectGetAttrStr */
20297 #if CYTHON_USE_TYPE_SLOTS
20298 static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStr(PyObject* obj, PyObject* attr_name) {
20299  PyTypeObject* tp = Py_TYPE(obj);
20300  if (likely(tp->tp_getattro))
20301  return tp->tp_getattro(obj, attr_name);
20302 #if PY_MAJOR_VERSION < 3
20303  if (likely(tp->tp_getattr))
20304  return tp->tp_getattr(obj, PyString_AS_STRING(attr_name));
20305 #endif
20306  return PyObject_GetAttr(obj, attr_name);
20307 }
20308 #endif
20309 
20310 /* GetBuiltinName */
20311 static PyObject *__Pyx_GetBuiltinName(PyObject *name) {
20312  PyObject* result = __Pyx_PyObject_GetAttrStr(__pyx_b, name);
20313  if (unlikely(!result)) {
20314  PyErr_Format(PyExc_NameError,
20315 #if PY_MAJOR_VERSION >= 3
20316  "name '%U' is not defined", name);
20317 #else
20318  "name '%.200s' is not defined", PyString_AS_STRING(name));
20319 #endif
20320  }
20321  return result;
20322 }
20323 
20324 /* PyCFunctionFastCall */
20325 #if CYTHON_FAST_PYCCALL
20326 static CYTHON_INLINE PyObject * __Pyx_PyCFunction_FastCall(PyObject *func_obj, PyObject **args, Py_ssize_t nargs) {
20327  PyCFunctionObject *func = (PyCFunctionObject*)func_obj;
20328  PyCFunction meth = PyCFunction_GET_FUNCTION(func);
20329  PyObject *self = PyCFunction_GET_SELF(func);
20330  int flags = PyCFunction_GET_FLAGS(func);
20331  assert(PyCFunction_Check(func));
20332  assert(METH_FASTCALL == (flags & ~(METH_CLASS | METH_STATIC | METH_COEXIST | METH_KEYWORDS | METH_STACKLESS)));
20333  assert(nargs >= 0);
20334  assert(nargs == 0 || args != NULL);
20335  /* _PyCFunction_FastCallDict() must not be called with an exception set,
20336  because it may clear it (directly or indirectly) and so the
20337  caller loses its exception */
20338  assert(!PyErr_Occurred());
20339  if ((PY_VERSION_HEX < 0x030700A0) || unlikely(flags & METH_KEYWORDS)) {
20340  return (*((__Pyx_PyCFunctionFastWithKeywords)(void*)meth)) (self, args, nargs, NULL);
20341  } else {
20342  return (*((__Pyx_PyCFunctionFast)(void*)meth)) (self, args, nargs);
20343  }
20344 }
20345 #endif
20346 
20347 /* PyFunctionFastCall */
20348 #if CYTHON_FAST_PYCALL
20349 static PyObject* __Pyx_PyFunction_FastCallNoKw(PyCodeObject *co, PyObject **args, Py_ssize_t na,
20350  PyObject *globals) {
20351  PyFrameObject *f;
20352  PyThreadState *tstate = __Pyx_PyThreadState_Current;
20353  PyObject **fastlocals;
20354  Py_ssize_t i;
20355  PyObject *result;
20356  assert(globals != NULL);
20357  /* XXX Perhaps we should create a specialized
20358  PyFrame_New() that doesn't take locals, but does
20359  take builtins without sanity checking them.
20360  */
20361  assert(tstate != NULL);
20362  f = PyFrame_New(tstate, co, globals, NULL);
20363  if (f == NULL) {
20364  return NULL;
20365  }
20366  fastlocals = __Pyx_PyFrame_GetLocalsplus(f);
20367  for (i = 0; i < na; i++) {
20368  Py_INCREF(*args);
20369  fastlocals[i] = *args++;
20370  }
20371  result = PyEval_EvalFrameEx(f,0);
20372  ++tstate->recursion_depth;
20373  Py_DECREF(f);
20374  --tstate->recursion_depth;
20375  return result;
20376 }
20377 #if 1 || PY_VERSION_HEX < 0x030600B1
20378 static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, int nargs, PyObject *kwargs) {
20379  PyCodeObject *co = (PyCodeObject *)PyFunction_GET_CODE(func);
20380  PyObject *globals = PyFunction_GET_GLOBALS(func);
20381  PyObject *argdefs = PyFunction_GET_DEFAULTS(func);
20382  PyObject *closure;
20383 #if PY_MAJOR_VERSION >= 3
20384  PyObject *kwdefs;
20385 #endif
20386  PyObject *kwtuple, **k;
20387  PyObject **d;
20388  Py_ssize_t nd;
20389  Py_ssize_t nk;
20390  PyObject *result;
20391  assert(kwargs == NULL || PyDict_Check(kwargs));
20392  nk = kwargs ? PyDict_Size(kwargs) : 0;
20393  if (Py_EnterRecursiveCall((char*)" while calling a Python object")) {
20394  return NULL;
20395  }
20396  if (
20397 #if PY_MAJOR_VERSION >= 3
20398  co->co_kwonlyargcount == 0 &&
20399 #endif
20400  likely(kwargs == NULL || nk == 0) &&
20401  co->co_flags == (CO_OPTIMIZED | CO_NEWLOCALS | CO_NOFREE)) {
20402  if (argdefs == NULL && co->co_argcount == nargs) {
20403  result = __Pyx_PyFunction_FastCallNoKw(co, args, nargs, globals);
20404  goto done;
20405  }
20406  else if (nargs == 0 && argdefs != NULL
20407  && co->co_argcount == Py_SIZE(argdefs)) {
20408  /* function called with no arguments, but all parameters have
20409  a default value: use default values as arguments .*/
20410  args = &PyTuple_GET_ITEM(argdefs, 0);
20411  result =__Pyx_PyFunction_FastCallNoKw(co, args, Py_SIZE(argdefs), globals);
20412  goto done;
20413  }
20414  }
20415  if (kwargs != NULL) {
20416  Py_ssize_t pos, i;
20417  kwtuple = PyTuple_New(2 * nk);
20418  if (kwtuple == NULL) {
20419  result = NULL;
20420  goto done;
20421  }
20422  k = &PyTuple_GET_ITEM(kwtuple, 0);
20423  pos = i = 0;
20424  while (PyDict_Next(kwargs, &pos, &k[i], &k[i+1])) {
20425  Py_INCREF(k[i]);
20426  Py_INCREF(k[i+1]);
20427  i += 2;
20428  }
20429  nk = i / 2;
20430  }
20431  else {
20432  kwtuple = NULL;
20433  k = NULL;
20434  }
20435  closure = PyFunction_GET_CLOSURE(func);
20436 #if PY_MAJOR_VERSION >= 3
20437  kwdefs = PyFunction_GET_KW_DEFAULTS(func);
20438 #endif
20439  if (argdefs != NULL) {
20440  d = &PyTuple_GET_ITEM(argdefs, 0);
20441  nd = Py_SIZE(argdefs);
20442  }
20443  else {
20444  d = NULL;
20445  nd = 0;
20446  }
20447 #if PY_MAJOR_VERSION >= 3
20448  result = PyEval_EvalCodeEx((PyObject*)co, globals, (PyObject *)NULL,
20449  args, nargs,
20450  k, (int)nk,
20451  d, (int)nd, kwdefs, closure);
20452 #else
20453  result = PyEval_EvalCodeEx(co, globals, (PyObject *)NULL,
20454  args, nargs,
20455  k, (int)nk,
20456  d, (int)nd, closure);
20457 #endif
20458  Py_XDECREF(kwtuple);
20459 done:
20460  Py_LeaveRecursiveCall();
20461  return result;
20462 }
20463 #endif
20464 #endif
20465 
20466 /* PyObjectCall */
20467 #if CYTHON_COMPILING_IN_CPYTHON
20468 static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw) {
20469  PyObject *result;
20470  ternaryfunc call = func->ob_type->tp_call;
20471  if (unlikely(!call))
20472  return PyObject_Call(func, arg, kw);
20473  if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
20474  return NULL;
20475  result = (*call)(func, arg, kw);
20476  Py_LeaveRecursiveCall();
20477  if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
20478  PyErr_SetString(
20479  PyExc_SystemError,
20480  "NULL result without error in PyObject_Call");
20481  }
20482  return result;
20483 }
20484 #endif
20485 
20486 /* PyObjectCallMethO */
20487 #if CYTHON_COMPILING_IN_CPYTHON
20488 static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg) {
20489  PyObject *self, *result;
20490  PyCFunction cfunc;
20491  cfunc = PyCFunction_GET_FUNCTION(func);
20492  self = PyCFunction_GET_SELF(func);
20493  if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
20494  return NULL;
20495  result = cfunc(self, arg);
20496  Py_LeaveRecursiveCall();
20497  if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
20498  PyErr_SetString(
20499  PyExc_SystemError,
20500  "NULL result without error in PyObject_Call");
20501  }
20502  return result;
20503 }
20504 #endif
20505 
20506 /* PyObjectCallOneArg */
20507 #if CYTHON_COMPILING_IN_CPYTHON
20508 static PyObject* __Pyx__PyObject_CallOneArg(PyObject *func, PyObject *arg) {
20509  PyObject *result;
20510  PyObject *args = PyTuple_New(1);
20511  if (unlikely(!args)) return NULL;
20512  Py_INCREF(arg);
20513  PyTuple_SET_ITEM(args, 0, arg);
20514  result = __Pyx_PyObject_Call(func, args, NULL);
20515  Py_DECREF(args);
20516  return result;
20517 }
20518 static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
20519 #if CYTHON_FAST_PYCALL
20520  if (PyFunction_Check(func)) {
20521  return __Pyx_PyFunction_FastCall(func, &arg, 1);
20522  }
20523 #endif
20524  if (likely(PyCFunction_Check(func))) {
20525  if (likely(PyCFunction_GET_FLAGS(func) & METH_O)) {
20526  return __Pyx_PyObject_CallMethO(func, arg);
20527 #if CYTHON_FAST_PYCCALL
20528  } else if (PyCFunction_GET_FLAGS(func) & METH_FASTCALL) {
20529  return __Pyx_PyCFunction_FastCall(func, &arg, 1);
20530 #endif
20531  }
20532  }
20533  return __Pyx__PyObject_CallOneArg(func, arg);
20534 }
20535 #else
20536 static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
20537  PyObject *result;
20538  PyObject *args = PyTuple_Pack(1, arg);
20539  if (unlikely(!args)) return NULL;
20540  result = __Pyx_PyObject_Call(func, args, NULL);
20541  Py_DECREF(args);
20542  return result;
20543 }
20544 #endif
20545 
20546 /* PyErrFetchRestore */
20547 #if CYTHON_FAST_THREAD_STATE
20548 static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {
20549  PyObject *tmp_type, *tmp_value, *tmp_tb;
20550  tmp_type = tstate->curexc_type;
20551  tmp_value = tstate->curexc_value;
20552  tmp_tb = tstate->curexc_traceback;
20553  tstate->curexc_type = type;
20554  tstate->curexc_value = value;
20555  tstate->curexc_traceback = tb;
20556  Py_XDECREF(tmp_type);
20557  Py_XDECREF(tmp_value);
20558  Py_XDECREF(tmp_tb);
20559 }
20560 static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
20561  *type = tstate->curexc_type;
20562  *value = tstate->curexc_value;
20563  *tb = tstate->curexc_traceback;
20564  tstate->curexc_type = 0;
20565  tstate->curexc_value = 0;
20566  tstate->curexc_traceback = 0;
20567 }
20568 #endif
20569 
20570 /* WriteUnraisableException */
20571 static void __Pyx_WriteUnraisable(const char *name, CYTHON_UNUSED int clineno,
20572  CYTHON_UNUSED int lineno, CYTHON_UNUSED const char *filename,
20573  int full_traceback, CYTHON_UNUSED int nogil) {
20574  PyObject *old_exc, *old_val, *old_tb;
20575  PyObject *ctx;
20576  __Pyx_PyThreadState_declare
20577 #ifdef WITH_THREAD
20578  PyGILState_STATE state;
20579  if (nogil)
20580  state = PyGILState_Ensure();
20581 #ifdef _MSC_VER
20582  else state = (PyGILState_STATE)-1;
20583 #endif
20584 #endif
20585  __Pyx_PyThreadState_assign
20586  __Pyx_ErrFetch(&old_exc, &old_val, &old_tb);
20587  if (full_traceback) {
20588  Py_XINCREF(old_exc);
20589  Py_XINCREF(old_val);
20590  Py_XINCREF(old_tb);
20591  __Pyx_ErrRestore(old_exc, old_val, old_tb);
20592  PyErr_PrintEx(1);
20593  }
20594  #if PY_MAJOR_VERSION < 3
20595  ctx = PyString_FromString(name);
20596  #else
20597  ctx = PyUnicode_FromString(name);
20598  #endif
20599  __Pyx_ErrRestore(old_exc, old_val, old_tb);
20600  if (!ctx) {
20601  PyErr_WriteUnraisable(Py_None);
20602  } else {
20603  PyErr_WriteUnraisable(ctx);
20604  Py_DECREF(ctx);
20605  }
20606 #ifdef WITH_THREAD
20607  if (nogil)
20608  PyGILState_Release(state);
20609 #endif
20610 }
20611 
20612 /* PyDictVersioning */
20613 #if CYTHON_USE_DICT_VERSIONS && CYTHON_USE_TYPE_SLOTS
20614 static CYTHON_INLINE PY_UINT64_T __Pyx_get_tp_dict_version(PyObject *obj) {
20615  PyObject *dict = Py_TYPE(obj)->tp_dict;
20616  return likely(dict) ? __PYX_GET_DICT_VERSION(dict) : 0;
20617 }
20618 static CYTHON_INLINE PY_UINT64_T __Pyx_get_object_dict_version(PyObject *obj) {
20619  PyObject **dictptr = NULL;
20620  Py_ssize_t offset = Py_TYPE(obj)->tp_dictoffset;
20621  if (offset) {
20622 #if CYTHON_COMPILING_IN_CPYTHON
20623  dictptr = (likely(offset > 0)) ? (PyObject **) ((char *)obj + offset) : _PyObject_GetDictPtr(obj);
20624 #else
20625  dictptr = _PyObject_GetDictPtr(obj);
20626 #endif
20627  }
20628  return (dictptr && *dictptr) ? __PYX_GET_DICT_VERSION(*dictptr) : 0;
20629 }
20630 static CYTHON_INLINE int __Pyx_object_dict_version_matches(PyObject* obj, PY_UINT64_T tp_dict_version, PY_UINT64_T obj_dict_version) {
20631  PyObject *dict = Py_TYPE(obj)->tp_dict;
20632  if (unlikely(!dict) || unlikely(tp_dict_version != __PYX_GET_DICT_VERSION(dict)))
20633  return 0;
20634  return obj_dict_version == __Pyx_get_object_dict_version(obj);
20635 }
20636 #endif
20637 
20638 /* PyObjectCallNoArg */
20639 #if CYTHON_COMPILING_IN_CPYTHON
20640 static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func) {
20641 #if CYTHON_FAST_PYCALL
20642  if (PyFunction_Check(func)) {
20643  return __Pyx_PyFunction_FastCall(func, NULL, 0);
20644  }
20645 #endif
20646 #ifdef __Pyx_CyFunction_USED
20647  if (likely(PyCFunction_Check(func) || __Pyx_CyFunction_Check(func)))
20648 #else
20649  if (likely(PyCFunction_Check(func)))
20650 #endif
20651  {
20652  if (likely(PyCFunction_GET_FLAGS(func) & METH_NOARGS)) {
20653  return __Pyx_PyObject_CallMethO(func, NULL);
20654  }
20655  }
20656  return __Pyx_PyObject_Call(func, __pyx_empty_tuple, NULL);
20657 }
20658 #endif
20659 
20660 /* RaiseDoubleKeywords */
20661 static void __Pyx_RaiseDoubleKeywordsError(
20662  const char* func_name,
20663  PyObject* kw_name)
20664 {
20665  PyErr_Format(PyExc_TypeError,
20666  #if PY_MAJOR_VERSION >= 3
20667  "%s() got multiple values for keyword argument '%U'", func_name, kw_name);
20668  #else
20669  "%s() got multiple values for keyword argument '%s'", func_name,
20670  PyString_AsString(kw_name));
20671  #endif
20672 }
20673 
20674 /* ParseKeywords */
20675 static int __Pyx_ParseOptionalKeywords(
20676  PyObject *kwds,
20677  PyObject **argnames[],
20678  PyObject *kwds2,
20679  PyObject *values[],
20680  Py_ssize_t num_pos_args,
20681  const char* function_name)
20682 {
20683  PyObject *key = 0, *value = 0;
20684  Py_ssize_t pos = 0;
20685  PyObject*** name;
20686  PyObject*** first_kw_arg = argnames + num_pos_args;
20687  while (PyDict_Next(kwds, &pos, &key, &value)) {
20688  name = first_kw_arg;
20689  while (*name && (**name != key)) name++;
20690  if (*name) {
20691  values[name-argnames] = value;
20692  continue;
20693  }
20694  name = first_kw_arg;
20695  #if PY_MAJOR_VERSION < 3
20696  if (likely(PyString_CheckExact(key)) || likely(PyString_Check(key))) {
20697  while (*name) {
20698  if ((CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**name) == PyString_GET_SIZE(key))
20699  && _PyString_Eq(**name, key)) {
20700  values[name-argnames] = value;
20701  break;
20702  }
20703  name++;
20704  }
20705  if (*name) continue;
20706  else {
20707  PyObject*** argname = argnames;
20708  while (argname != first_kw_arg) {
20709  if ((**argname == key) || (
20710  (CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**argname) == PyString_GET_SIZE(key))
20711  && _PyString_Eq(**argname, key))) {
20712  goto arg_passed_twice;
20713  }
20714  argname++;
20715  }
20716  }
20717  } else
20718  #endif
20719  if (likely(PyUnicode_Check(key))) {
20720  while (*name) {
20721  int cmp = (**name == key) ? 0 :
20722  #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
20723  (PyUnicode_GET_SIZE(**name) != PyUnicode_GET_SIZE(key)) ? 1 :
20724  #endif
20725  PyUnicode_Compare(**name, key);
20726  if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
20727  if (cmp == 0) {
20728  values[name-argnames] = value;
20729  break;
20730  }
20731  name++;
20732  }
20733  if (*name) continue;
20734  else {
20735  PyObject*** argname = argnames;
20736  while (argname != first_kw_arg) {
20737  int cmp = (**argname == key) ? 0 :
20738  #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
20739  (PyUnicode_GET_SIZE(**argname) != PyUnicode_GET_SIZE(key)) ? 1 :
20740  #endif
20741  PyUnicode_Compare(**argname, key);
20742  if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
20743  if (cmp == 0) goto arg_passed_twice;
20744  argname++;
20745  }
20746  }
20747  } else
20748  goto invalid_keyword_type;
20749  if (kwds2) {
20750  if (unlikely(PyDict_SetItem(kwds2, key, value))) goto bad;
20751  } else {
20752  goto invalid_keyword;
20753  }
20754  }
20755  return 0;
20756 arg_passed_twice:
20757  __Pyx_RaiseDoubleKeywordsError(function_name, key);
20758  goto bad;
20759 invalid_keyword_type:
20760  PyErr_Format(PyExc_TypeError,
20761  "%.200s() keywords must be strings", function_name);
20762  goto bad;
20763 invalid_keyword:
20764  PyErr_Format(PyExc_TypeError,
20765  #if PY_MAJOR_VERSION < 3
20766  "%.200s() got an unexpected keyword argument '%.200s'",
20767  function_name, PyString_AsString(key));
20768  #else
20769  "%s() got an unexpected keyword argument '%U'",
20770  function_name, key);
20771  #endif
20772 bad:
20773  return -1;
20774 }
20775 
20776 /* RaiseArgTupleInvalid */
20777 static void __Pyx_RaiseArgtupleInvalid(
20778  const char* func_name,
20779  int exact,
20780  Py_ssize_t num_min,
20781  Py_ssize_t num_max,
20782  Py_ssize_t num_found)
20783 {
20784  Py_ssize_t num_expected;
20785  const char *more_or_less;
20786  if (num_found < num_min) {
20787  num_expected = num_min;
20788  more_or_less = "at least";
20789  } else {
20790  num_expected = num_max;
20791  more_or_less = "at most";
20792  }
20793  if (exact) {
20794  more_or_less = "exactly";
20795  }
20796  PyErr_Format(PyExc_TypeError,
20797  "%.200s() takes %.8s %" CYTHON_FORMAT_SSIZE_T "d positional argument%.1s (%" CYTHON_FORMAT_SSIZE_T "d given)",
20798  func_name, more_or_less, num_expected,
20799  (num_expected == 1) ? "" : "s", num_found);
20800 }
20801 
20802 /* GetModuleGlobalName */
20803 #if CYTHON_USE_DICT_VERSIONS
20804 static PyObject *__Pyx__GetModuleGlobalName(PyObject *name, PY_UINT64_T *dict_version, PyObject **dict_cached_value)
20805 #else
20806 static CYTHON_INLINE PyObject *__Pyx__GetModuleGlobalName(PyObject *name)
20807 #endif
20808 {
20809  PyObject *result;
20810 #if !CYTHON_AVOID_BORROWED_REFS
20811 #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030500A1
20812  result = _PyDict_GetItem_KnownHash(__pyx_d, name, ((PyASCIIObject *) name)->hash);
20813  __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version)
20814  if (likely(result)) {
20815  return __Pyx_NewRef(result);
20816  } else if (unlikely(PyErr_Occurred())) {
20817  return NULL;
20818  }
20819 #else
20820  result = PyDict_GetItem(__pyx_d, name);
20821  __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version)
20822  if (likely(result)) {
20823  return __Pyx_NewRef(result);
20824  }
20825 #endif
20826 #else
20827  result = PyObject_GetItem(__pyx_d, name);
20828  __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version)
20829  if (likely(result)) {
20830  return __Pyx_NewRef(result);
20831  }
20832  PyErr_Clear();
20833 #endif
20834  return __Pyx_GetBuiltinName(name);
20835 }
20836 
20837 /* GetTopmostException */
20838 #if CYTHON_USE_EXC_INFO_STACK
20839 static _PyErr_StackItem *
20840 __Pyx_PyErr_GetTopmostException(PyThreadState *tstate)
20841 {
20842  _PyErr_StackItem *exc_info = tstate->exc_info;
20843  while ((exc_info->exc_type == NULL || exc_info->exc_type == Py_None) &&
20844  exc_info->previous_item != NULL)
20845  {
20846  exc_info = exc_info->previous_item;
20847  }
20848  return exc_info;
20849 }
20850 #endif
20851 
20852 /* SaveResetException */
20853 #if CYTHON_FAST_THREAD_STATE
20854 static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
20855  #if CYTHON_USE_EXC_INFO_STACK
20856  _PyErr_StackItem *exc_info = __Pyx_PyErr_GetTopmostException(tstate);
20857  *type = exc_info->exc_type;
20858  *value = exc_info->exc_value;
20859  *tb = exc_info->exc_traceback;
20860  #else
20861  *type = tstate->exc_type;
20862  *value = tstate->exc_value;
20863  *tb = tstate->exc_traceback;
20864  #endif
20865  Py_XINCREF(*type);
20866  Py_XINCREF(*value);
20867  Py_XINCREF(*tb);
20868 }
20869 static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {
20870  PyObject *tmp_type, *tmp_value, *tmp_tb;
20871  #if CYTHON_USE_EXC_INFO_STACK
20872  _PyErr_StackItem *exc_info = tstate->exc_info;
20873  tmp_type = exc_info->exc_type;
20874  tmp_value = exc_info->exc_value;
20875  tmp_tb = exc_info->exc_traceback;
20876  exc_info->exc_type = type;
20877  exc_info->exc_value = value;
20878  exc_info->exc_traceback = tb;
20879  #else
20880  tmp_type = tstate->exc_type;
20881  tmp_value = tstate->exc_value;
20882  tmp_tb = tstate->exc_traceback;
20883  tstate->exc_type = type;
20884  tstate->exc_value = value;
20885  tstate->exc_traceback = tb;
20886  #endif
20887  Py_XDECREF(tmp_type);
20888  Py_XDECREF(tmp_value);
20889  Py_XDECREF(tmp_tb);
20890 }
20891 #endif
20892 
20893 /* PyErrExceptionMatches */
20894 #if CYTHON_FAST_THREAD_STATE
20895 static int __Pyx_PyErr_ExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) {
20896  Py_ssize_t i, n;
20897  n = PyTuple_GET_SIZE(tuple);
20898 #if PY_MAJOR_VERSION >= 3
20899  for (i=0; i<n; i++) {
20900  if (exc_type == PyTuple_GET_ITEM(tuple, i)) return 1;
20901  }
20902 #endif
20903  for (i=0; i<n; i++) {
20904  if (__Pyx_PyErr_GivenExceptionMatches(exc_type, PyTuple_GET_ITEM(tuple, i))) return 1;
20905  }
20906  return 0;
20907 }
20908 static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err) {
20909  PyObject *exc_type = tstate->curexc_type;
20910  if (exc_type == err) return 1;
20911  if (unlikely(!exc_type)) return 0;
20912  if (unlikely(PyTuple_Check(err)))
20913  return __Pyx_PyErr_ExceptionMatchesTuple(exc_type, err);
20914  return __Pyx_PyErr_GivenExceptionMatches(exc_type, err);
20915 }
20916 #endif
20917 
20918 /* GetException */
20919 #if CYTHON_FAST_THREAD_STATE
20920 static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb)
20921 #else
20922 static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb)
20923 #endif
20924 {
20925  PyObject *local_type, *local_value, *local_tb;
20926 #if CYTHON_FAST_THREAD_STATE
20927  PyObject *tmp_type, *tmp_value, *tmp_tb;
20928  local_type = tstate->curexc_type;
20929  local_value = tstate->curexc_value;
20930  local_tb = tstate->curexc_traceback;
20931  tstate->curexc_type = 0;
20932  tstate->curexc_value = 0;
20933  tstate->curexc_traceback = 0;
20934 #else
20935  PyErr_Fetch(&local_type, &local_value, &local_tb);
20936 #endif
20937  PyErr_NormalizeException(&local_type, &local_value, &local_tb);
20938 #if CYTHON_FAST_THREAD_STATE
20939  if (unlikely(tstate->curexc_type))
20940 #else
20941  if (unlikely(PyErr_Occurred()))
20942 #endif
20943  goto bad;
20944  #if PY_MAJOR_VERSION >= 3
20945  if (local_tb) {
20946  if (unlikely(PyException_SetTraceback(local_value, local_tb) < 0))
20947  goto bad;
20948  }
20949  #endif
20950  Py_XINCREF(local_tb);
20951  Py_XINCREF(local_type);
20952  Py_XINCREF(local_value);
20953  *type = local_type;
20954  *value = local_value;
20955  *tb = local_tb;
20956 #if CYTHON_FAST_THREAD_STATE
20957  #if CYTHON_USE_EXC_INFO_STACK
20958  {
20959  _PyErr_StackItem *exc_info = tstate->exc_info;
20960  tmp_type = exc_info->exc_type;
20961  tmp_value = exc_info->exc_value;
20962  tmp_tb = exc_info->exc_traceback;
20963  exc_info->exc_type = local_type;
20964  exc_info->exc_value = local_value;
20965  exc_info->exc_traceback = local_tb;
20966  }
20967  #else
20968  tmp_type = tstate->exc_type;
20969  tmp_value = tstate->exc_value;
20970  tmp_tb = tstate->exc_traceback;
20971  tstate->exc_type = local_type;
20972  tstate->exc_value = local_value;
20973  tstate->exc_traceback = local_tb;
20974  #endif
20975  Py_XDECREF(tmp_type);
20976  Py_XDECREF(tmp_value);
20977  Py_XDECREF(tmp_tb);
20978 #else
20979  PyErr_SetExcInfo(local_type, local_value, local_tb);
20980 #endif
20981  return 0;
20982 bad:
20983  *type = 0;
20984  *value = 0;
20985  *tb = 0;
20986  Py_XDECREF(local_type);
20987  Py_XDECREF(local_value);
20988  Py_XDECREF(local_tb);
20989  return -1;
20990 }
20991 
20992 /* RaiseException */
20993 #if PY_MAJOR_VERSION < 3
20994 static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb,
20995  CYTHON_UNUSED PyObject *cause) {
20996  __Pyx_PyThreadState_declare
20997  Py_XINCREF(type);
20998  if (!value || value == Py_None)
20999  value = NULL;
21000  else
21001  Py_INCREF(value);
21002  if (!tb || tb == Py_None)
21003  tb = NULL;
21004  else {
21005  Py_INCREF(tb);
21006  if (!PyTraceBack_Check(tb)) {
21007  PyErr_SetString(PyExc_TypeError,
21008  "raise: arg 3 must be a traceback or None");
21009  goto raise_error;
21010  }
21011  }
21012  if (PyType_Check(type)) {
21013 #if CYTHON_COMPILING_IN_PYPY
21014  if (!value) {
21015  Py_INCREF(Py_None);
21016  value = Py_None;
21017  }
21018 #endif
21019  PyErr_NormalizeException(&type, &value, &tb);
21020  } else {
21021  if (value) {
21022  PyErr_SetString(PyExc_TypeError,
21023  "instance exception may not have a separate value");
21024  goto raise_error;
21025  }
21026  value = type;
21027  type = (PyObject*) Py_TYPE(type);
21028  Py_INCREF(type);
21029  if (!PyType_IsSubtype((PyTypeObject *)type, (PyTypeObject *)PyExc_BaseException)) {
21030  PyErr_SetString(PyExc_TypeError,
21031  "raise: exception class must be a subclass of BaseException");
21032  goto raise_error;
21033  }
21034  }
21035  __Pyx_PyThreadState_assign
21036  __Pyx_ErrRestore(type, value, tb);
21037  return;
21038 raise_error:
21039  Py_XDECREF(value);
21040  Py_XDECREF(type);
21041  Py_XDECREF(tb);
21042  return;
21043 }
21044 #else
21045 static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause) {
21046  PyObject* owned_instance = NULL;
21047  if (tb == Py_None) {
21048  tb = 0;
21049  } else if (tb && !PyTraceBack_Check(tb)) {
21050  PyErr_SetString(PyExc_TypeError,
21051  "raise: arg 3 must be a traceback or None");
21052  goto bad;
21053  }
21054  if (value == Py_None)
21055  value = 0;
21056  if (PyExceptionInstance_Check(type)) {
21057  if (value) {
21058  PyErr_SetString(PyExc_TypeError,
21059  "instance exception may not have a separate value");
21060  goto bad;
21061  }
21062  value = type;
21063  type = (PyObject*) Py_TYPE(value);
21064  } else if (PyExceptionClass_Check(type)) {
21065  PyObject *instance_class = NULL;
21066  if (value && PyExceptionInstance_Check(value)) {
21067  instance_class = (PyObject*) Py_TYPE(value);
21068  if (instance_class != type) {
21069  int is_subclass = PyObject_IsSubclass(instance_class, type);
21070  if (!is_subclass) {
21071  instance_class = NULL;
21072  } else if (unlikely(is_subclass == -1)) {
21073  goto bad;
21074  } else {
21075  type = instance_class;
21076  }
21077  }
21078  }
21079  if (!instance_class) {
21080  PyObject *args;
21081  if (!value)
21082  args = PyTuple_New(0);
21083  else if (PyTuple_Check(value)) {
21084  Py_INCREF(value);
21085  args = value;
21086  } else
21087  args = PyTuple_Pack(1, value);
21088  if (!args)
21089  goto bad;
21090  owned_instance = PyObject_Call(type, args, NULL);
21091  Py_DECREF(args);
21092  if (!owned_instance)
21093  goto bad;
21094  value = owned_instance;
21095  if (!PyExceptionInstance_Check(value)) {
21096  PyErr_Format(PyExc_TypeError,
21097  "calling %R should have returned an instance of "
21098  "BaseException, not %R",
21099  type, Py_TYPE(value));
21100  goto bad;
21101  }
21102  }
21103  } else {
21104  PyErr_SetString(PyExc_TypeError,
21105  "raise: exception class must be a subclass of BaseException");
21106  goto bad;
21107  }
21108  if (cause) {
21109  PyObject *fixed_cause;
21110  if (cause == Py_None) {
21111  fixed_cause = NULL;
21112  } else if (PyExceptionClass_Check(cause)) {
21113  fixed_cause = PyObject_CallObject(cause, NULL);
21114  if (fixed_cause == NULL)
21115  goto bad;
21116  } else if (PyExceptionInstance_Check(cause)) {
21117  fixed_cause = cause;
21118  Py_INCREF(fixed_cause);
21119  } else {
21120  PyErr_SetString(PyExc_TypeError,
21121  "exception causes must derive from "
21122  "BaseException");
21123  goto bad;
21124  }
21125  PyException_SetCause(value, fixed_cause);
21126  }
21127  PyErr_SetObject(type, value);
21128  if (tb) {
21129 #if CYTHON_COMPILING_IN_PYPY
21130  PyObject *tmp_type, *tmp_value, *tmp_tb;
21131  PyErr_Fetch(&tmp_type, &tmp_value, &tmp_tb);
21132  Py_INCREF(tb);
21133  PyErr_Restore(tmp_type, tmp_value, tb);
21134  Py_XDECREF(tmp_tb);
21135 #else
21136  PyThreadState *tstate = __Pyx_PyThreadState_Current;
21137  PyObject* tmp_tb = tstate->curexc_traceback;
21138  if (tb != tmp_tb) {
21139  Py_INCREF(tb);
21140  tstate->curexc_traceback = tb;
21141  Py_XDECREF(tmp_tb);
21142  }
21143 #endif
21144  }
21145 bad:
21146  Py_XDECREF(owned_instance);
21147  return;
21148 }
21149 #endif
21150 
21151 /* PyIntBinop */
21152 #if !CYTHON_COMPILING_IN_PYPY
21153 static PyObject* __Pyx_PyInt_AddObjC(PyObject *op1, PyObject *op2, CYTHON_UNUSED long intval, int inplace, int zerodivision_check) {
21154  (void)inplace;
21155  (void)zerodivision_check;
21156  #if PY_MAJOR_VERSION < 3
21157  if (likely(PyInt_CheckExact(op1))) {
21158  const long b = intval;
21159  long x;
21160  long a = PyInt_AS_LONG(op1);
21161  x = (long)((unsigned long)a + b);
21162  if (likely((x^a) >= 0 || (x^b) >= 0))
21163  return PyInt_FromLong(x);
21164  return PyLong_Type.tp_as_number->nb_add(op1, op2);
21165  }
21166  #endif
21167  #if CYTHON_USE_PYLONG_INTERNALS
21168  if (likely(PyLong_CheckExact(op1))) {
21169  const long b = intval;
21170  long a, x;
21171 #ifdef HAVE_LONG_LONG
21172  const PY_LONG_LONG llb = intval;
21173  PY_LONG_LONG lla, llx;
21174 #endif
21175  const digit* digits = ((PyLongObject*)op1)->ob_digit;
21176  const Py_ssize_t size = Py_SIZE(op1);
21177  if (likely(__Pyx_sst_abs(size) <= 1)) {
21178  a = likely(size) ? digits[0] : 0;
21179  if (size == -1) a = -a;
21180  } else {
21181  switch (size) {
21182  case -2:
21183  if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
21184  a = -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
21185  break;
21186 #ifdef HAVE_LONG_LONG
21187  } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
21188  lla = -(PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
21189  goto long_long;
21190 #endif
21191  }
21192  CYTHON_FALLTHROUGH;
21193  case 2:
21194  if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
21195  a = (long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
21196  break;
21197 #ifdef HAVE_LONG_LONG
21198  } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
21199  lla = (PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
21200  goto long_long;
21201 #endif
21202  }
21203  CYTHON_FALLTHROUGH;
21204  case -3:
21205  if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
21206  a = -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
21207  break;
21208 #ifdef HAVE_LONG_LONG
21209  } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
21210  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]));
21211  goto long_long;
21212 #endif
21213  }
21214  CYTHON_FALLTHROUGH;
21215  case 3:
21216  if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
21217  a = (long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
21218  break;
21219 #ifdef HAVE_LONG_LONG
21220  } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
21221  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]));
21222  goto long_long;
21223 #endif
21224  }
21225  CYTHON_FALLTHROUGH;
21226  case -4:
21227  if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
21228  a = -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
21229  break;
21230 #ifdef HAVE_LONG_LONG
21231  } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
21232  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]));
21233  goto long_long;
21234 #endif
21235  }
21236  CYTHON_FALLTHROUGH;
21237  case 4:
21238  if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
21239  a = (long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
21240  break;
21241 #ifdef HAVE_LONG_LONG
21242  } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
21243  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]));
21244  goto long_long;
21245 #endif
21246  }
21247  CYTHON_FALLTHROUGH;
21248  default: return PyLong_Type.tp_as_number->nb_add(op1, op2);
21249  }
21250  }
21251  x = a + b;
21252  return PyLong_FromLong(x);
21253 #ifdef HAVE_LONG_LONG
21254  long_long:
21255  llx = lla + llb;
21256  return PyLong_FromLongLong(llx);
21257 #endif
21258 
21259 
21260  }
21261  #endif
21262  if (PyFloat_CheckExact(op1)) {
21263  const long b = intval;
21264  double a = PyFloat_AS_DOUBLE(op1);
21265  double result;
21266  PyFPE_START_PROTECT("add", return NULL)
21267  result = ((double)a) + (double)b;
21268  PyFPE_END_PROTECT(result)
21269  return PyFloat_FromDouble(result);
21270  }
21271  return (inplace ? PyNumber_InPlaceAdd : PyNumber_Add)(op1, op2);
21272 }
21273 #endif
21274 
21275 /* SetItemInt */
21276 static int __Pyx_SetItemInt_Generic(PyObject *o, PyObject *j, PyObject *v) {
21277  int r;
21278  if (!j) return -1;
21279  r = PyObject_SetItem(o, j, v);
21280  Py_DECREF(j);
21281  return r;
21282 }
21283 static CYTHON_INLINE int __Pyx_SetItemInt_Fast(PyObject *o, Py_ssize_t i, PyObject *v, int is_list,
21284  CYTHON_NCP_UNUSED int wraparound, CYTHON_NCP_UNUSED int boundscheck) {
21285 #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS && CYTHON_USE_TYPE_SLOTS
21286  if (is_list || PyList_CheckExact(o)) {
21287  Py_ssize_t n = (!wraparound) ? i : ((likely(i >= 0)) ? i : i + PyList_GET_SIZE(o));
21288  if ((!boundscheck) || likely(__Pyx_is_valid_index(n, PyList_GET_SIZE(o)))) {
21289  PyObject* old = PyList_GET_ITEM(o, n);
21290  Py_INCREF(v);
21291  PyList_SET_ITEM(o, n, v);
21292  Py_DECREF(old);
21293  return 1;
21294  }
21295  } else {
21296  PySequenceMethods *m = Py_TYPE(o)->tp_as_sequence;
21297  if (likely(m && m->sq_ass_item)) {
21298  if (wraparound && unlikely(i < 0) && likely(m->sq_length)) {
21299  Py_ssize_t l = m->sq_length(o);
21300  if (likely(l >= 0)) {
21301  i += l;
21302  } else {
21303  if (!PyErr_ExceptionMatches(PyExc_OverflowError))
21304  return -1;
21305  PyErr_Clear();
21306  }
21307  }
21308  return m->sq_ass_item(o, i, v);
21309  }
21310  }
21311 #else
21312 #if CYTHON_COMPILING_IN_PYPY
21313  if (is_list || (PySequence_Check(o) && !PyDict_Check(o)))
21314 #else
21315  if (is_list || PySequence_Check(o))
21316 #endif
21317  {
21318  return PySequence_SetItem(o, i, v);
21319  }
21320 #endif
21321  return __Pyx_SetItemInt_Generic(o, PyInt_FromSsize_t(i), v);
21322 }
21323 
21324 /* PyObjectCall2Args */
21325 static CYTHON_UNUSED PyObject* __Pyx_PyObject_Call2Args(PyObject* function, PyObject* arg1, PyObject* arg2) {
21326  PyObject *args, *result = NULL;
21327  #if CYTHON_FAST_PYCALL
21328  if (PyFunction_Check(function)) {
21329  PyObject *args[2] = {arg1, arg2};
21330  return __Pyx_PyFunction_FastCall(function, args, 2);
21331  }
21332  #endif
21333  #if CYTHON_FAST_PYCCALL
21334  if (__Pyx_PyFastCFunction_Check(function)) {
21335  PyObject *args[2] = {arg1, arg2};
21336  return __Pyx_PyCFunction_FastCall(function, args, 2);
21337  }
21338  #endif
21339  args = PyTuple_New(2);
21340  if (unlikely(!args)) goto done;
21341  Py_INCREF(arg1);
21342  PyTuple_SET_ITEM(args, 0, arg1);
21343  Py_INCREF(arg2);
21344  PyTuple_SET_ITEM(args, 1, arg2);
21345  Py_INCREF(function);
21346  result = __Pyx_PyObject_Call(function, args, NULL);
21347  Py_DECREF(args);
21348  Py_DECREF(function);
21349 done:
21350  return result;
21351 }
21352 
21353 /* ArgTypeTest */
21354 static int __Pyx__ArgTypeTest(PyObject *obj, PyTypeObject *type, const char *name, int exact)
21355 {
21356  if (unlikely(!type)) {
21357  PyErr_SetString(PyExc_SystemError, "Missing type object");
21358  return 0;
21359  }
21360  else if (exact) {
21361  #if PY_MAJOR_VERSION == 2
21362  if ((type == &PyBaseString_Type) && likely(__Pyx_PyBaseString_CheckExact(obj))) return 1;
21363  #endif
21364  }
21365  else {
21366  if (likely(__Pyx_TypeCheck(obj, type))) return 1;
21367  }
21368  PyErr_Format(PyExc_TypeError,
21369  "Argument '%.200s' has incorrect type (expected %.200s, got %.200s)",
21370  name, type->tp_name, Py_TYPE(obj)->tp_name);
21371  return 0;
21372 }
21373 
21374 /* Import */
21375 static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level) {
21376  PyObject *empty_list = 0;
21377  PyObject *module = 0;
21378  PyObject *global_dict = 0;
21379  PyObject *empty_dict = 0;
21380  PyObject *list;
21381  #if PY_MAJOR_VERSION < 3
21382  PyObject *py_import;
21383  py_import = __Pyx_PyObject_GetAttrStr(__pyx_b, __pyx_n_s_import);
21384  if (!py_import)
21385  goto bad;
21386  #endif
21387  if (from_list)
21388  list = from_list;
21389  else {
21390  empty_list = PyList_New(0);
21391  if (!empty_list)
21392  goto bad;
21393  list = empty_list;
21394  }
21395  global_dict = PyModule_GetDict(__pyx_m);
21396  if (!global_dict)
21397  goto bad;
21398  empty_dict = PyDict_New();
21399  if (!empty_dict)
21400  goto bad;
21401  {
21402  #if PY_MAJOR_VERSION >= 3
21403  if (level == -1) {
21404  if (strchr(__Pyx_MODULE_NAME, '.')) {
21405  module = PyImport_ImportModuleLevelObject(
21406  name, global_dict, empty_dict, list, 1);
21407  if (!module) {
21408  if (!PyErr_ExceptionMatches(PyExc_ImportError))
21409  goto bad;
21410  PyErr_Clear();
21411  }
21412  }
21413  level = 0;
21414  }
21415  #endif
21416  if (!module) {
21417  #if PY_MAJOR_VERSION < 3
21418  PyObject *py_level = PyInt_FromLong(level);
21419  if (!py_level)
21420  goto bad;
21421  module = PyObject_CallFunctionObjArgs(py_import,
21422  name, global_dict, empty_dict, list, py_level, (PyObject *)NULL);
21423  Py_DECREF(py_level);
21424  #else
21425  module = PyImport_ImportModuleLevelObject(
21426  name, global_dict, empty_dict, list, level);
21427  #endif
21428  }
21429  }
21430 bad:
21431  #if PY_MAJOR_VERSION < 3
21432  Py_XDECREF(py_import);
21433  #endif
21434  Py_XDECREF(empty_list);
21435  Py_XDECREF(empty_dict);
21436  return module;
21437 }
21438 
21439 /* PyObject_GenericGetAttrNoDict */
21440 #if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000
21441 static PyObject *__Pyx_RaiseGenericGetAttributeError(PyTypeObject *tp, PyObject *attr_name) {
21442  PyErr_Format(PyExc_AttributeError,
21443 #if PY_MAJOR_VERSION >= 3
21444  "'%.50s' object has no attribute '%U'",
21445  tp->tp_name, attr_name);
21446 #else
21447  "'%.50s' object has no attribute '%.400s'",
21448  tp->tp_name, PyString_AS_STRING(attr_name));
21449 #endif
21450  return NULL;
21451 }
21452 static CYTHON_INLINE PyObject* __Pyx_PyObject_GenericGetAttrNoDict(PyObject* obj, PyObject* attr_name) {
21453  PyObject *descr;
21454  PyTypeObject *tp = Py_TYPE(obj);
21455  if (unlikely(!PyString_Check(attr_name))) {
21456  return PyObject_GenericGetAttr(obj, attr_name);
21457  }
21458  assert(!tp->tp_dictoffset);
21459  descr = _PyType_Lookup(tp, attr_name);
21460  if (unlikely(!descr)) {
21461  return __Pyx_RaiseGenericGetAttributeError(tp, attr_name);
21462  }
21463  Py_INCREF(descr);
21464  #if PY_MAJOR_VERSION < 3
21465  if (likely(PyType_HasFeature(Py_TYPE(descr), Py_TPFLAGS_HAVE_CLASS)))
21466  #endif
21467  {
21468  descrgetfunc f = Py_TYPE(descr)->tp_descr_get;
21469  if (unlikely(f)) {
21470  PyObject *res = f(descr, obj, (PyObject *)tp);
21471  Py_DECREF(descr);
21472  return res;
21473  }
21474  }
21475  return descr;
21476 }
21477 #endif
21478 
21479 /* PyObject_GenericGetAttr */
21480 #if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000
21481 static PyObject* __Pyx_PyObject_GenericGetAttr(PyObject* obj, PyObject* attr_name) {
21482  if (unlikely(Py_TYPE(obj)->tp_dictoffset)) {
21483  return PyObject_GenericGetAttr(obj, attr_name);
21484  }
21485  return __Pyx_PyObject_GenericGetAttrNoDict(obj, attr_name);
21486 }
21487 #endif
21488 
21489 /* SetVTable */
21490 static int __Pyx_SetVtable(PyObject *dict, void *vtable) {
21491 #if PY_VERSION_HEX >= 0x02070000
21492  PyObject *ob = PyCapsule_New(vtable, 0, 0);
21493 #else
21494  PyObject *ob = PyCObject_FromVoidPtr(vtable, 0);
21495 #endif
21496  if (!ob)
21497  goto bad;
21498  if (PyDict_SetItem(dict, __pyx_n_s_pyx_vtable, ob) < 0)
21499  goto bad;
21500  Py_DECREF(ob);
21501  return 0;
21502 bad:
21503  Py_XDECREF(ob);
21504  return -1;
21505 }
21506 
21507 /* SetupReduce */
21508 static int __Pyx_setup_reduce_is_named(PyObject* meth, PyObject* name) {
21509  int ret;
21510  PyObject *name_attr;
21511  name_attr = __Pyx_PyObject_GetAttrStr(meth, __pyx_n_s_name);
21512  if (likely(name_attr)) {
21513  ret = PyObject_RichCompareBool(name_attr, name, Py_EQ);
21514  } else {
21515  ret = -1;
21516  }
21517  if (unlikely(ret < 0)) {
21518  PyErr_Clear();
21519  ret = 0;
21520  }
21521  Py_XDECREF(name_attr);
21522  return ret;
21523 }
21524 static int __Pyx_setup_reduce(PyObject* type_obj) {
21525  int ret = 0;
21526  PyObject *object_reduce = NULL;
21527  PyObject *object_reduce_ex = NULL;
21528  PyObject *reduce = NULL;
21529  PyObject *reduce_ex = NULL;
21530  PyObject *reduce_cython = NULL;
21531  PyObject *setstate = NULL;
21532  PyObject *setstate_cython = NULL;
21533 #if CYTHON_USE_PYTYPE_LOOKUP
21534  if (_PyType_Lookup((PyTypeObject*)type_obj, __pyx_n_s_getstate)) goto GOOD;
21535 #else
21536  if (PyObject_HasAttr(type_obj, __pyx_n_s_getstate)) goto GOOD;
21537 #endif
21538 #if CYTHON_USE_PYTYPE_LOOKUP
21539  object_reduce_ex = _PyType_Lookup(&PyBaseObject_Type, __pyx_n_s_reduce_ex); if (!object_reduce_ex) goto BAD;
21540 #else
21541  object_reduce_ex = __Pyx_PyObject_GetAttrStr((PyObject*)&PyBaseObject_Type, __pyx_n_s_reduce_ex); if (!object_reduce_ex) goto BAD;
21542 #endif
21543  reduce_ex = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_n_s_reduce_ex); if (unlikely(!reduce_ex)) goto BAD;
21544  if (reduce_ex == object_reduce_ex) {
21545 #if CYTHON_USE_PYTYPE_LOOKUP
21546  object_reduce = _PyType_Lookup(&PyBaseObject_Type, __pyx_n_s_reduce); if (!object_reduce) goto BAD;
21547 #else
21548  object_reduce = __Pyx_PyObject_GetAttrStr((PyObject*)&PyBaseObject_Type, __pyx_n_s_reduce); if (!object_reduce) goto BAD;
21549 #endif
21550  reduce = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_n_s_reduce); if (unlikely(!reduce)) goto BAD;
21551  if (reduce == object_reduce || __Pyx_setup_reduce_is_named(reduce, __pyx_n_s_reduce_cython)) {
21552  reduce_cython = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_n_s_reduce_cython); if (unlikely(!reduce_cython)) goto BAD;
21553  ret = PyDict_SetItem(((PyTypeObject*)type_obj)->tp_dict, __pyx_n_s_reduce, reduce_cython); if (unlikely(ret < 0)) goto BAD;
21554  ret = PyDict_DelItem(((PyTypeObject*)type_obj)->tp_dict, __pyx_n_s_reduce_cython); if (unlikely(ret < 0)) goto BAD;
21555  setstate = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_n_s_setstate);
21556  if (!setstate) PyErr_Clear();
21557  if (!setstate || __Pyx_setup_reduce_is_named(setstate, __pyx_n_s_setstate_cython)) {
21558  setstate_cython = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_n_s_setstate_cython); if (unlikely(!setstate_cython)) goto BAD;
21559  ret = PyDict_SetItem(((PyTypeObject*)type_obj)->tp_dict, __pyx_n_s_setstate, setstate_cython); if (unlikely(ret < 0)) goto BAD;
21560  ret = PyDict_DelItem(((PyTypeObject*)type_obj)->tp_dict, __pyx_n_s_setstate_cython); if (unlikely(ret < 0)) goto BAD;
21561  }
21562  PyType_Modified((PyTypeObject*)type_obj);
21563  }
21564  }
21565  goto GOOD;
21566 BAD:
21567  if (!PyErr_Occurred())
21568  PyErr_Format(PyExc_RuntimeError, "Unable to initialize pickling for %s", ((PyTypeObject*)type_obj)->tp_name);
21569  ret = -1;
21570 GOOD:
21571 #if !CYTHON_USE_PYTYPE_LOOKUP
21572  Py_XDECREF(object_reduce);
21573  Py_XDECREF(object_reduce_ex);
21574 #endif
21575  Py_XDECREF(reduce);
21576  Py_XDECREF(reduce_ex);
21577  Py_XDECREF(reduce_cython);
21578  Py_XDECREF(setstate);
21579  Py_XDECREF(setstate_cython);
21580  return ret;
21581 }
21582 
21583 /* PyFloatBinop */
21584 #if !CYTHON_COMPILING_IN_PYPY
21585 static PyObject* __Pyx_PyFloat_DivideObjC(PyObject *op1, PyObject *op2, double floatval, int inplace, int zerodivision_check) {
21586  const double b = floatval;
21587  double a, result;
21588  (void)inplace;
21589  (void)zerodivision_check;
21590  if (likely(PyFloat_CheckExact(op1))) {
21591  a = PyFloat_AS_DOUBLE(op1);
21592 
21593  } else
21594  #if PY_MAJOR_VERSION < 3
21595  if (likely(PyInt_CheckExact(op1))) {
21596  a = (double) PyInt_AS_LONG(op1);
21597 
21598  } else
21599  #endif
21600  if (likely(PyLong_CheckExact(op1))) {
21601  #if CYTHON_USE_PYLONG_INTERNALS
21602  const digit* digits = ((PyLongObject*)op1)->ob_digit;
21603  const Py_ssize_t size = Py_SIZE(op1);
21604  switch (size) {
21605  case 0: a = 0.0; break;
21606  case -1: a = -(double) digits[0]; break;
21607  case 1: a = (double) digits[0]; break;
21608  case -2:
21609  case 2:
21610  if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (1 * PyLong_SHIFT < 53))) {
21611  a = (double) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
21612  if ((8 * sizeof(unsigned long) < 53) || (2 * PyLong_SHIFT < 53) || (a < (double) ((PY_LONG_LONG)1 << 53))) {
21613  if (size == -2)
21614  a = -a;
21615  break;
21616  }
21617  }
21618  CYTHON_FALLTHROUGH;
21619  case -3:
21620  case 3:
21621  if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (2 * PyLong_SHIFT < 53))) {
21622  a = (double) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
21623  if ((8 * sizeof(unsigned long) < 53) || (3 * PyLong_SHIFT < 53) || (a < (double) ((PY_LONG_LONG)1 << 53))) {
21624  if (size == -3)
21625  a = -a;
21626  break;
21627  }
21628  }
21629  CYTHON_FALLTHROUGH;
21630  case -4:
21631  case 4:
21632  if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (3 * PyLong_SHIFT < 53))) {
21633  a = (double) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
21634  if ((8 * sizeof(unsigned long) < 53) || (4 * PyLong_SHIFT < 53) || (a < (double) ((PY_LONG_LONG)1 << 53))) {
21635  if (size == -4)
21636  a = -a;
21637  break;
21638  }
21639  }
21640  CYTHON_FALLTHROUGH;
21641  default:
21642  #else
21643  {
21644  #endif
21645  a = PyLong_AsDouble(op1);
21646  if (unlikely(a == -1.0 && PyErr_Occurred())) return NULL;
21647 
21648  }
21649  } else {
21650  return (inplace ? __Pyx_PyNumber_InPlaceDivide(op1, op2) : __Pyx_PyNumber_Divide(op1, op2));
21651  }
21652 
21653  PyFPE_START_PROTECT("divide", return NULL)
21654  result = a / b;
21655  PyFPE_END_PROTECT(result)
21656  return PyFloat_FromDouble(result);
21657 }
21658 #endif
21659 
21660 /* BytesEquals */
21661  static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals) {
21662 #if CYTHON_COMPILING_IN_PYPY
21663  return PyObject_RichCompareBool(s1, s2, equals);
21664 #else
21665  if (s1 == s2) {
21666  return (equals == Py_EQ);
21667  } else if (PyBytes_CheckExact(s1) & PyBytes_CheckExact(s2)) {
21668  const char *ps1, *ps2;
21669  Py_ssize_t length = PyBytes_GET_SIZE(s1);
21670  if (length != PyBytes_GET_SIZE(s2))
21671  return (equals == Py_NE);
21672  ps1 = PyBytes_AS_STRING(s1);
21673  ps2 = PyBytes_AS_STRING(s2);
21674  if (ps1[0] != ps2[0]) {
21675  return (equals == Py_NE);
21676  } else if (length == 1) {
21677  return (equals == Py_EQ);
21678  } else {
21679  int result;
21680 #if CYTHON_USE_UNICODE_INTERNALS
21681  Py_hash_t hash1, hash2;
21682  hash1 = ((PyBytesObject*)s1)->ob_shash;
21683  hash2 = ((PyBytesObject*)s2)->ob_shash;
21684  if (hash1 != hash2 && hash1 != -1 && hash2 != -1) {
21685  return (equals == Py_NE);
21686  }
21687 #endif
21688  result = memcmp(ps1, ps2, (size_t)length);
21689  return (equals == Py_EQ) ? (result == 0) : (result != 0);
21690  }
21691  } else if ((s1 == Py_None) & PyBytes_CheckExact(s2)) {
21692  return (equals == Py_NE);
21693  } else if ((s2 == Py_None) & PyBytes_CheckExact(s1)) {
21694  return (equals == Py_NE);
21695  } else {
21696  int result;
21697  PyObject* py_result = PyObject_RichCompare(s1, s2, equals);
21698  if (!py_result)
21699  return -1;
21700  result = __Pyx_PyObject_IsTrue(py_result);
21701  Py_DECREF(py_result);
21702  return result;
21703  }
21704 #endif
21705 }
21706 
21707 /* UnicodeEquals */
21708  static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals) {
21709 #if CYTHON_COMPILING_IN_PYPY
21710  return PyObject_RichCompareBool(s1, s2, equals);
21711 #else
21712 #if PY_MAJOR_VERSION < 3
21713  PyObject* owned_ref = NULL;
21714 #endif
21715  int s1_is_unicode, s2_is_unicode;
21716  if (s1 == s2) {
21717  goto return_eq;
21718  }
21719  s1_is_unicode = PyUnicode_CheckExact(s1);
21720  s2_is_unicode = PyUnicode_CheckExact(s2);
21721 #if PY_MAJOR_VERSION < 3
21722  if ((s1_is_unicode & (!s2_is_unicode)) && PyString_CheckExact(s2)) {
21723  owned_ref = PyUnicode_FromObject(s2);
21724  if (unlikely(!owned_ref))
21725  return -1;
21726  s2 = owned_ref;
21727  s2_is_unicode = 1;
21728  } else if ((s2_is_unicode & (!s1_is_unicode)) && PyString_CheckExact(s1)) {
21729  owned_ref = PyUnicode_FromObject(s1);
21730  if (unlikely(!owned_ref))
21731  return -1;
21732  s1 = owned_ref;
21733  s1_is_unicode = 1;
21734  } else if (((!s2_is_unicode) & (!s1_is_unicode))) {
21735  return __Pyx_PyBytes_Equals(s1, s2, equals);
21736  }
21737 #endif
21738  if (s1_is_unicode & s2_is_unicode) {
21739  Py_ssize_t length;
21740  int kind;
21741  void *data1, *data2;
21742  if (unlikely(__Pyx_PyUnicode_READY(s1) < 0) || unlikely(__Pyx_PyUnicode_READY(s2) < 0))
21743  return -1;
21744  length = __Pyx_PyUnicode_GET_LENGTH(s1);
21745  if (length != __Pyx_PyUnicode_GET_LENGTH(s2)) {
21746  goto return_ne;
21747  }
21748 #if CYTHON_USE_UNICODE_INTERNALS
21749  {
21750  Py_hash_t hash1, hash2;
21751  #if CYTHON_PEP393_ENABLED
21752  hash1 = ((PyASCIIObject*)s1)->hash;
21753  hash2 = ((PyASCIIObject*)s2)->hash;
21754  #else
21755  hash1 = ((PyUnicodeObject*)s1)->hash;
21756  hash2 = ((PyUnicodeObject*)s2)->hash;
21757  #endif
21758  if (hash1 != hash2 && hash1 != -1 && hash2 != -1) {
21759  goto return_ne;
21760  }
21761  }
21762 #endif
21763  kind = __Pyx_PyUnicode_KIND(s1);
21764  if (kind != __Pyx_PyUnicode_KIND(s2)) {
21765  goto return_ne;
21766  }
21767  data1 = __Pyx_PyUnicode_DATA(s1);
21768  data2 = __Pyx_PyUnicode_DATA(s2);
21769  if (__Pyx_PyUnicode_READ(kind, data1, 0) != __Pyx_PyUnicode_READ(kind, data2, 0)) {
21770  goto return_ne;
21771  } else if (length == 1) {
21772  goto return_eq;
21773  } else {
21774  int result = memcmp(data1, data2, (size_t)(length * kind));
21775  #if PY_MAJOR_VERSION < 3
21776  Py_XDECREF(owned_ref);
21777  #endif
21778  return (equals == Py_EQ) ? (result == 0) : (result != 0);
21779  }
21780  } else if ((s1 == Py_None) & s2_is_unicode) {
21781  goto return_ne;
21782  } else if ((s2 == Py_None) & s1_is_unicode) {
21783  goto return_ne;
21784  } else {
21785  int result;
21786  PyObject* py_result = PyObject_RichCompare(s1, s2, equals);
21787  #if PY_MAJOR_VERSION < 3
21788  Py_XDECREF(owned_ref);
21789  #endif
21790  if (!py_result)
21791  return -1;
21792  result = __Pyx_PyObject_IsTrue(py_result);
21793  Py_DECREF(py_result);
21794  return result;
21795  }
21796 return_eq:
21797  #if PY_MAJOR_VERSION < 3
21798  Py_XDECREF(owned_ref);
21799  #endif
21800  return (equals == Py_EQ);
21801 return_ne:
21802  #if PY_MAJOR_VERSION < 3
21803  Py_XDECREF(owned_ref);
21804  #endif
21805  return (equals == Py_NE);
21806 #endif
21807 }
21808 
21809 /* CLineInTraceback */
21810  #ifndef CYTHON_CLINE_IN_TRACEBACK
21811 static int __Pyx_CLineForTraceback(PyThreadState *tstate, int c_line) {
21812  PyObject *use_cline;
21813  PyObject *ptype, *pvalue, *ptraceback;
21814 #if CYTHON_COMPILING_IN_CPYTHON
21815  PyObject **cython_runtime_dict;
21816 #endif
21817  if (unlikely(!__pyx_cython_runtime)) {
21818  return c_line;
21819  }
21820  __Pyx_ErrFetchInState(tstate, &ptype, &pvalue, &ptraceback);
21821 #if CYTHON_COMPILING_IN_CPYTHON
21822  cython_runtime_dict = _PyObject_GetDictPtr(__pyx_cython_runtime);
21823  if (likely(cython_runtime_dict)) {
21824  __PYX_PY_DICT_LOOKUP_IF_MODIFIED(
21825  use_cline, *cython_runtime_dict,
21826  __Pyx_PyDict_GetItemStr(*cython_runtime_dict, __pyx_n_s_cline_in_traceback))
21827  } else
21828 #endif
21829  {
21830  PyObject *use_cline_obj = __Pyx_PyObject_GetAttrStr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback);
21831  if (use_cline_obj) {
21832  use_cline = PyObject_Not(use_cline_obj) ? Py_False : Py_True;
21833  Py_DECREF(use_cline_obj);
21834  } else {
21835  PyErr_Clear();
21836  use_cline = NULL;
21837  }
21838  }
21839  if (!use_cline) {
21840  c_line = 0;
21841  PyObject_SetAttr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback, Py_False);
21842  }
21843  else if (use_cline == Py_False || (use_cline != Py_True && PyObject_Not(use_cline) != 0)) {
21844  c_line = 0;
21845  }
21846  __Pyx_ErrRestoreInState(tstate, ptype, pvalue, ptraceback);
21847  return c_line;
21848 }
21849 #endif
21850 
21851 /* CodeObjectCache */
21852  static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line) {
21853  int start = 0, mid = 0, end = count - 1;
21854  if (end >= 0 && code_line > entries[end].code_line) {
21855  return count;
21856  }
21857  while (start < end) {
21858  mid = start + (end - start) / 2;
21859  if (code_line < entries[mid].code_line) {
21860  end = mid;
21861  } else if (code_line > entries[mid].code_line) {
21862  start = mid + 1;
21863  } else {
21864  return mid;
21865  }
21866  }
21867  if (code_line <= entries[mid].code_line) {
21868  return mid;
21869  } else {
21870  return mid + 1;
21871  }
21872 }
21873 static PyCodeObject *__pyx_find_code_object(int code_line) {
21874  PyCodeObject* code_object;
21875  int pos;
21876  if (unlikely(!code_line) || unlikely(!__pyx_code_cache.entries)) {
21877  return NULL;
21878  }
21879  pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
21880  if (unlikely(pos >= __pyx_code_cache.count) || unlikely(__pyx_code_cache.entries[pos].code_line != code_line)) {
21881  return NULL;
21882  }
21883  code_object = __pyx_code_cache.entries[pos].code_object;
21884  Py_INCREF(code_object);
21885  return code_object;
21886 }
21887 static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object) {
21888  int pos, i;
21889  __Pyx_CodeObjectCacheEntry* entries = __pyx_code_cache.entries;
21890  if (unlikely(!code_line)) {
21891  return;
21892  }
21893  if (unlikely(!entries)) {
21894  entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Malloc(64*sizeof(__Pyx_CodeObjectCacheEntry));
21895  if (likely(entries)) {
21896  __pyx_code_cache.entries = entries;
21897  __pyx_code_cache.max_count = 64;
21898  __pyx_code_cache.count = 1;
21899  entries[0].code_line = code_line;
21900  entries[0].code_object = code_object;
21901  Py_INCREF(code_object);
21902  }
21903  return;
21904  }
21905  pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
21906  if ((pos < __pyx_code_cache.count) && unlikely(__pyx_code_cache.entries[pos].code_line == code_line)) {
21907  PyCodeObject* tmp = entries[pos].code_object;
21908  entries[pos].code_object = code_object;
21909  Py_DECREF(tmp);
21910  return;
21911  }
21912  if (__pyx_code_cache.count == __pyx_code_cache.max_count) {
21913  int new_max = __pyx_code_cache.max_count + 64;
21914  entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Realloc(
21915  __pyx_code_cache.entries, (size_t)new_max*sizeof(__Pyx_CodeObjectCacheEntry));
21916  if (unlikely(!entries)) {
21917  return;
21918  }
21919  __pyx_code_cache.entries = entries;
21920  __pyx_code_cache.max_count = new_max;
21921  }
21922  for (i=__pyx_code_cache.count; i>pos; i--) {
21923  entries[i] = entries[i-1];
21924  }
21925  entries[pos].code_line = code_line;
21926  entries[pos].code_object = code_object;
21927  __pyx_code_cache.count++;
21928  Py_INCREF(code_object);
21929 }
21930 
21931 /* AddTraceback */
21932  #include "compile.h"
21933 #include "frameobject.h"
21934 #include "traceback.h"
21935 static PyCodeObject* __Pyx_CreateCodeObjectForTraceback(
21936  const char *funcname, int c_line,
21937  int py_line, const char *filename) {
21938  PyCodeObject *py_code = 0;
21939  PyObject *py_srcfile = 0;
21940  PyObject *py_funcname = 0;
21941  #if PY_MAJOR_VERSION < 3
21942  py_srcfile = PyString_FromString(filename);
21943  #else
21944  py_srcfile = PyUnicode_FromString(filename);
21945  #endif
21946  if (!py_srcfile) goto bad;
21947  if (c_line) {
21948  #if PY_MAJOR_VERSION < 3
21949  py_funcname = PyString_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
21950  #else
21951  py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
21952  #endif
21953  }
21954  else {
21955  #if PY_MAJOR_VERSION < 3
21956  py_funcname = PyString_FromString(funcname);
21957  #else
21958  py_funcname = PyUnicode_FromString(funcname);
21959  #endif
21960  }
21961  if (!py_funcname) goto bad;
21962  py_code = __Pyx_PyCode_New(
21963  0,
21964  0,
21965  0,
21966  0,
21967  0,
21968  __pyx_empty_bytes, /*PyObject *code,*/
21969  __pyx_empty_tuple, /*PyObject *consts,*/
21970  __pyx_empty_tuple, /*PyObject *names,*/
21971  __pyx_empty_tuple, /*PyObject *varnames,*/
21972  __pyx_empty_tuple, /*PyObject *freevars,*/
21973  __pyx_empty_tuple, /*PyObject *cellvars,*/
21974  py_srcfile, /*PyObject *filename,*/
21975  py_funcname, /*PyObject *name,*/
21976  py_line,
21977  __pyx_empty_bytes /*PyObject *lnotab*/
21978  );
21979  Py_DECREF(py_srcfile);
21980  Py_DECREF(py_funcname);
21981  return py_code;
21982 bad:
21983  Py_XDECREF(py_srcfile);
21984  Py_XDECREF(py_funcname);
21985  return NULL;
21986 }
21987 static void __Pyx_AddTraceback(const char *funcname, int c_line,
21988  int py_line, const char *filename) {
21989  PyCodeObject *py_code = 0;
21990  PyFrameObject *py_frame = 0;
21991  PyThreadState *tstate = __Pyx_PyThreadState_Current;
21992  if (c_line) {
21993  c_line = __Pyx_CLineForTraceback(tstate, c_line);
21994  }
21995  py_code = __pyx_find_code_object(c_line ? -c_line : py_line);
21996  if (!py_code) {
21997  py_code = __Pyx_CreateCodeObjectForTraceback(
21998  funcname, c_line, py_line, filename);
21999  if (!py_code) goto bad;
22000  __pyx_insert_code_object(c_line ? -c_line : py_line, py_code);
22001  }
22002  py_frame = PyFrame_New(
22003  tstate, /*PyThreadState *tstate,*/
22004  py_code, /*PyCodeObject *code,*/
22005  __pyx_d, /*PyObject *globals,*/
22006  0 /*PyObject *locals*/
22007  );
22008  if (!py_frame) goto bad;
22009  __Pyx_PyFrame_SetLineNumber(py_frame, py_line);
22010  PyTraceBack_Here(py_frame);
22011 bad:
22012  Py_XDECREF(py_code);
22013  Py_XDECREF(py_frame);
22014 }
22015 
22016 /* CIntFromPyVerify */
22017  #define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)\
22018  __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 0)
22019 #define __PYX_VERIFY_RETURN_INT_EXC(target_type, func_type, func_value)\
22020  __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 1)
22021 #define __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, exc)\
22022  {\
22023  func_type value = func_value;\
22024  if (sizeof(target_type) < sizeof(func_type)) {\
22025  if (unlikely(value != (func_type) (target_type) value)) {\
22026  func_type zero = 0;\
22027  if (exc && unlikely(value == (func_type)-1 && PyErr_Occurred()))\
22028  return (target_type) -1;\
22029  if (is_unsigned && unlikely(value < zero))\
22030  goto raise_neg_overflow;\
22031  else\
22032  goto raise_overflow;\
22033  }\
22034  }\
22035  return (target_type) value;\
22036  }
22037 
22038 /* CIntToPy */
22039  static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value) {
22040  const int neg_one = (int) ((int) 0 - (int) 1), const_zero = (int) 0;
22041  const int is_unsigned = neg_one > const_zero;
22042  if (is_unsigned) {
22043  if (sizeof(int) < sizeof(long)) {
22044  return PyInt_FromLong((long) value);
22045  } else if (sizeof(int) <= sizeof(unsigned long)) {
22046  return PyLong_FromUnsignedLong((unsigned long) value);
22047 #ifdef HAVE_LONG_LONG
22048  } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {
22049  return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
22050 #endif
22051  }
22052  } else {
22053  if (sizeof(int) <= sizeof(long)) {
22054  return PyInt_FromLong((long) value);
22055 #ifdef HAVE_LONG_LONG
22056  } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
22057  return PyLong_FromLongLong((PY_LONG_LONG) value);
22058 #endif
22059  }
22060  }
22061  {
22062  int one = 1; int little = (int)*(unsigned char *)&one;
22063  unsigned char *bytes = (unsigned char *)&value;
22064  return _PyLong_FromByteArray(bytes, sizeof(int),
22065  little, !is_unsigned);
22066  }
22067 }
22068 
22069 /* CIntFromPy */
22070  static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) {
22071  const int neg_one = (int) ((int) 0 - (int) 1), const_zero = (int) 0;
22072  const int is_unsigned = neg_one > const_zero;
22073 #if PY_MAJOR_VERSION < 3
22074  if (likely(PyInt_Check(x))) {
22075  if (sizeof(int) < sizeof(long)) {
22076  __PYX_VERIFY_RETURN_INT(int, long, PyInt_AS_LONG(x))
22077  } else {
22078  long val = PyInt_AS_LONG(x);
22079  if (is_unsigned && unlikely(val < 0)) {
22080  goto raise_neg_overflow;
22081  }
22082  return (int) val;
22083  }
22084  } else
22085 #endif
22086  if (likely(PyLong_Check(x))) {
22087  if (is_unsigned) {
22088 #if CYTHON_USE_PYLONG_INTERNALS
22089  const digit* digits = ((PyLongObject*)x)->ob_digit;
22090  switch (Py_SIZE(x)) {
22091  case 0: return (int) 0;
22092  case 1: __PYX_VERIFY_RETURN_INT(int, digit, digits[0])
22093  case 2:
22094  if (8 * sizeof(int) > 1 * PyLong_SHIFT) {
22095  if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
22096  __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22097  } else if (8 * sizeof(int) >= 2 * PyLong_SHIFT) {
22098  return (int) (((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
22099  }
22100  }
22101  break;
22102  case 3:
22103  if (8 * sizeof(int) > 2 * PyLong_SHIFT) {
22104  if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
22105  __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22106  } else if (8 * sizeof(int) >= 3 * PyLong_SHIFT) {
22107  return (int) (((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
22108  }
22109  }
22110  break;
22111  case 4:
22112  if (8 * sizeof(int) > 3 * PyLong_SHIFT) {
22113  if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
22114  __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])))
22115  } else if (8 * sizeof(int) >= 4 * PyLong_SHIFT) {
22116  return (int) (((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
22117  }
22118  }
22119  break;
22120  }
22121 #endif
22122 #if CYTHON_COMPILING_IN_CPYTHON
22123  if (unlikely(Py_SIZE(x) < 0)) {
22124  goto raise_neg_overflow;
22125  }
22126 #else
22127  {
22128  int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
22129  if (unlikely(result < 0))
22130  return (int) -1;
22131  if (unlikely(result == 1))
22132  goto raise_neg_overflow;
22133  }
22134 #endif
22135  if (sizeof(int) <= sizeof(unsigned long)) {
22136  __PYX_VERIFY_RETURN_INT_EXC(int, unsigned long, PyLong_AsUnsignedLong(x))
22137 #ifdef HAVE_LONG_LONG
22138  } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {
22139  __PYX_VERIFY_RETURN_INT_EXC(int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
22140 #endif
22141  }
22142  } else {
22143 #if CYTHON_USE_PYLONG_INTERNALS
22144  const digit* digits = ((PyLongObject*)x)->ob_digit;
22145  switch (Py_SIZE(x)) {
22146  case 0: return (int) 0;
22147  case -1: __PYX_VERIFY_RETURN_INT(int, sdigit, (sdigit) (-(sdigit)digits[0]))
22148  case 1: __PYX_VERIFY_RETURN_INT(int, digit, +digits[0])
22149  case -2:
22150  if (8 * sizeof(int) - 1 > 1 * PyLong_SHIFT) {
22151  if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
22152  __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22153  } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
22154  return (int) (((int)-1)*(((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
22155  }
22156  }
22157  break;
22158  case 2:
22159  if (8 * sizeof(int) > 1 * PyLong_SHIFT) {
22160  if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
22161  __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22162  } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
22163  return (int) ((((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
22164  }
22165  }
22166  break;
22167  case -3:
22168  if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
22169  if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
22170  __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22171  } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
22172  return (int) (((int)-1)*(((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
22173  }
22174  }
22175  break;
22176  case 3:
22177  if (8 * sizeof(int) > 2 * PyLong_SHIFT) {
22178  if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
22179  __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22180  } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
22181  return (int) ((((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
22182  }
22183  }
22184  break;
22185  case -4:
22186  if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
22187  if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
22188  __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])))
22189  } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) {
22190  return (int) (((int)-1)*(((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
22191  }
22192  }
22193  break;
22194  case 4:
22195  if (8 * sizeof(int) > 3 * PyLong_SHIFT) {
22196  if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
22197  __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])))
22198  } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) {
22199  return (int) ((((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
22200  }
22201  }
22202  break;
22203  }
22204 #endif
22205  if (sizeof(int) <= sizeof(long)) {
22206  __PYX_VERIFY_RETURN_INT_EXC(int, long, PyLong_AsLong(x))
22207 #ifdef HAVE_LONG_LONG
22208  } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
22209  __PYX_VERIFY_RETURN_INT_EXC(int, PY_LONG_LONG, PyLong_AsLongLong(x))
22210 #endif
22211  }
22212  }
22213  {
22214 #if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
22215  PyErr_SetString(PyExc_RuntimeError,
22216  "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
22217 #else
22218  int val;
22219  PyObject *v = __Pyx_PyNumber_IntOrLong(x);
22220  #if PY_MAJOR_VERSION < 3
22221  if (likely(v) && !PyLong_Check(v)) {
22222  PyObject *tmp = v;
22223  v = PyNumber_Long(tmp);
22224  Py_DECREF(tmp);
22225  }
22226  #endif
22227  if (likely(v)) {
22228  int one = 1; int is_little = (int)*(unsigned char *)&one;
22229  unsigned char *bytes = (unsigned char *)&val;
22230  int ret = _PyLong_AsByteArray((PyLongObject *)v,
22231  bytes, sizeof(val),
22232  is_little, !is_unsigned);
22233  Py_DECREF(v);
22234  if (likely(!ret))
22235  return val;
22236  }
22237 #endif
22238  return (int) -1;
22239  }
22240  } else {
22241  int val;
22242  PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
22243  if (!tmp) return (int) -1;
22244  val = __Pyx_PyInt_As_int(tmp);
22245  Py_DECREF(tmp);
22246  return val;
22247  }
22248 raise_overflow:
22249  PyErr_SetString(PyExc_OverflowError,
22250  "value too large to convert to int");
22251  return (int) -1;
22252 raise_neg_overflow:
22253  PyErr_SetString(PyExc_OverflowError,
22254  "can't convert negative value to int");
22255  return (int) -1;
22256 }
22257 
22258 /* CIntToPy */
22259  static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) {
22260  const long neg_one = (long) ((long) 0 - (long) 1), const_zero = (long) 0;
22261  const int is_unsigned = neg_one > const_zero;
22262  if (is_unsigned) {
22263  if (sizeof(long) < sizeof(long)) {
22264  return PyInt_FromLong((long) value);
22265  } else if (sizeof(long) <= sizeof(unsigned long)) {
22266  return PyLong_FromUnsignedLong((unsigned long) value);
22267 #ifdef HAVE_LONG_LONG
22268  } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
22269  return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
22270 #endif
22271  }
22272  } else {
22273  if (sizeof(long) <= sizeof(long)) {
22274  return PyInt_FromLong((long) value);
22275 #ifdef HAVE_LONG_LONG
22276  } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
22277  return PyLong_FromLongLong((PY_LONG_LONG) value);
22278 #endif
22279  }
22280  }
22281  {
22282  int one = 1; int little = (int)*(unsigned char *)&one;
22283  unsigned char *bytes = (unsigned char *)&value;
22284  return _PyLong_FromByteArray(bytes, sizeof(long),
22285  little, !is_unsigned);
22286  }
22287 }
22288 
22289 /* CIntFromPy */
22290  static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *x) {
22291  const long neg_one = (long) ((long) 0 - (long) 1), const_zero = (long) 0;
22292  const int is_unsigned = neg_one > const_zero;
22293 #if PY_MAJOR_VERSION < 3
22294  if (likely(PyInt_Check(x))) {
22295  if (sizeof(long) < sizeof(long)) {
22296  __PYX_VERIFY_RETURN_INT(long, long, PyInt_AS_LONG(x))
22297  } else {
22298  long val = PyInt_AS_LONG(x);
22299  if (is_unsigned && unlikely(val < 0)) {
22300  goto raise_neg_overflow;
22301  }
22302  return (long) val;
22303  }
22304  } else
22305 #endif
22306  if (likely(PyLong_Check(x))) {
22307  if (is_unsigned) {
22308 #if CYTHON_USE_PYLONG_INTERNALS
22309  const digit* digits = ((PyLongObject*)x)->ob_digit;
22310  switch (Py_SIZE(x)) {
22311  case 0: return (long) 0;
22312  case 1: __PYX_VERIFY_RETURN_INT(long, digit, digits[0])
22313  case 2:
22314  if (8 * sizeof(long) > 1 * PyLong_SHIFT) {
22315  if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
22316  __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22317  } else if (8 * sizeof(long) >= 2 * PyLong_SHIFT) {
22318  return (long) (((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
22319  }
22320  }
22321  break;
22322  case 3:
22323  if (8 * sizeof(long) > 2 * PyLong_SHIFT) {
22324  if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
22325  __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22326  } else if (8 * sizeof(long) >= 3 * PyLong_SHIFT) {
22327  return (long) (((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
22328  }
22329  }
22330  break;
22331  case 4:
22332  if (8 * sizeof(long) > 3 * PyLong_SHIFT) {
22333  if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
22334  __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])))
22335  } else if (8 * sizeof(long) >= 4 * PyLong_SHIFT) {
22336  return (long) (((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
22337  }
22338  }
22339  break;
22340  }
22341 #endif
22342 #if CYTHON_COMPILING_IN_CPYTHON
22343  if (unlikely(Py_SIZE(x) < 0)) {
22344  goto raise_neg_overflow;
22345  }
22346 #else
22347  {
22348  int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
22349  if (unlikely(result < 0))
22350  return (long) -1;
22351  if (unlikely(result == 1))
22352  goto raise_neg_overflow;
22353  }
22354 #endif
22355  if (sizeof(long) <= sizeof(unsigned long)) {
22356  __PYX_VERIFY_RETURN_INT_EXC(long, unsigned long, PyLong_AsUnsignedLong(x))
22357 #ifdef HAVE_LONG_LONG
22358  } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
22359  __PYX_VERIFY_RETURN_INT_EXC(long, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
22360 #endif
22361  }
22362  } else {
22363 #if CYTHON_USE_PYLONG_INTERNALS
22364  const digit* digits = ((PyLongObject*)x)->ob_digit;
22365  switch (Py_SIZE(x)) {
22366  case 0: return (long) 0;
22367  case -1: __PYX_VERIFY_RETURN_INT(long, sdigit, (sdigit) (-(sdigit)digits[0]))
22368  case 1: __PYX_VERIFY_RETURN_INT(long, digit, +digits[0])
22369  case -2:
22370  if (8 * sizeof(long) - 1 > 1 * PyLong_SHIFT) {
22371  if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
22372  __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22373  } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
22374  return (long) (((long)-1)*(((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
22375  }
22376  }
22377  break;
22378  case 2:
22379  if (8 * sizeof(long) > 1 * PyLong_SHIFT) {
22380  if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
22381  __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22382  } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
22383  return (long) ((((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
22384  }
22385  }
22386  break;
22387  case -3:
22388  if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
22389  if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
22390  __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22391  } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
22392  return (long) (((long)-1)*(((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
22393  }
22394  }
22395  break;
22396  case 3:
22397  if (8 * sizeof(long) > 2 * PyLong_SHIFT) {
22398  if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
22399  __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22400  } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
22401  return (long) ((((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
22402  }
22403  }
22404  break;
22405  case -4:
22406  if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
22407  if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
22408  __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])))
22409  } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
22410  return (long) (((long)-1)*(((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
22411  }
22412  }
22413  break;
22414  case 4:
22415  if (8 * sizeof(long) > 3 * PyLong_SHIFT) {
22416  if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
22417  __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])))
22418  } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
22419  return (long) ((((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
22420  }
22421  }
22422  break;
22423  }
22424 #endif
22425  if (sizeof(long) <= sizeof(long)) {
22426  __PYX_VERIFY_RETURN_INT_EXC(long, long, PyLong_AsLong(x))
22427 #ifdef HAVE_LONG_LONG
22428  } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
22429  __PYX_VERIFY_RETURN_INT_EXC(long, PY_LONG_LONG, PyLong_AsLongLong(x))
22430 #endif
22431  }
22432  }
22433  {
22434 #if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
22435  PyErr_SetString(PyExc_RuntimeError,
22436  "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
22437 #else
22438  long val;
22439  PyObject *v = __Pyx_PyNumber_IntOrLong(x);
22440  #if PY_MAJOR_VERSION < 3
22441  if (likely(v) && !PyLong_Check(v)) {
22442  PyObject *tmp = v;
22443  v = PyNumber_Long(tmp);
22444  Py_DECREF(tmp);
22445  }
22446  #endif
22447  if (likely(v)) {
22448  int one = 1; int is_little = (int)*(unsigned char *)&one;
22449  unsigned char *bytes = (unsigned char *)&val;
22450  int ret = _PyLong_AsByteArray((PyLongObject *)v,
22451  bytes, sizeof(val),
22452  is_little, !is_unsigned);
22453  Py_DECREF(v);
22454  if (likely(!ret))
22455  return val;
22456  }
22457 #endif
22458  return (long) -1;
22459  }
22460  } else {
22461  long val;
22462  PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
22463  if (!tmp) return (long) -1;
22464  val = __Pyx_PyInt_As_long(tmp);
22465  Py_DECREF(tmp);
22466  return val;
22467  }
22468 raise_overflow:
22469  PyErr_SetString(PyExc_OverflowError,
22470  "value too large to convert to long");
22471  return (long) -1;
22472 raise_neg_overflow:
22473  PyErr_SetString(PyExc_OverflowError,
22474  "can't convert negative value to long");
22475  return (long) -1;
22476 }
22477 
22478 /* FastTypeChecks */
22479  #if CYTHON_COMPILING_IN_CPYTHON
22480 static int __Pyx_InBases(PyTypeObject *a, PyTypeObject *b) {
22481  while (a) {
22482  a = a->tp_base;
22483  if (a == b)
22484  return 1;
22485  }
22486  return b == &PyBaseObject_Type;
22487 }
22488 static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b) {
22489  PyObject *mro;
22490  if (a == b) return 1;
22491  mro = a->tp_mro;
22492  if (likely(mro)) {
22493  Py_ssize_t i, n;
22494  n = PyTuple_GET_SIZE(mro);
22495  for (i = 0; i < n; i++) {
22496  if (PyTuple_GET_ITEM(mro, i) == (PyObject *)b)
22497  return 1;
22498  }
22499  return 0;
22500  }
22501  return __Pyx_InBases(a, b);
22502 }
22503 #if PY_MAJOR_VERSION == 2
22504 static int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject* exc_type2) {
22505  PyObject *exception, *value, *tb;
22506  int res;
22507  __Pyx_PyThreadState_declare
22508  __Pyx_PyThreadState_assign
22509  __Pyx_ErrFetch(&exception, &value, &tb);
22510  res = exc_type1 ? PyObject_IsSubclass(err, exc_type1) : 0;
22511  if (unlikely(res == -1)) {
22512  PyErr_WriteUnraisable(err);
22513  res = 0;
22514  }
22515  if (!res) {
22516  res = PyObject_IsSubclass(err, exc_type2);
22517  if (unlikely(res == -1)) {
22518  PyErr_WriteUnraisable(err);
22519  res = 0;
22520  }
22521  }
22522  __Pyx_ErrRestore(exception, value, tb);
22523  return res;
22524 }
22525 #else
22526 static CYTHON_INLINE int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject *exc_type2) {
22527  int res = exc_type1 ? __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type1) : 0;
22528  if (!res) {
22529  res = __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type2);
22530  }
22531  return res;
22532 }
22533 #endif
22534 static int __Pyx_PyErr_GivenExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) {
22535  Py_ssize_t i, n;
22536  assert(PyExceptionClass_Check(exc_type));
22537  n = PyTuple_GET_SIZE(tuple);
22538 #if PY_MAJOR_VERSION >= 3
22539  for (i=0; i<n; i++) {
22540  if (exc_type == PyTuple_GET_ITEM(tuple, i)) return 1;
22541  }
22542 #endif
22543  for (i=0; i<n; i++) {
22544  PyObject *t = PyTuple_GET_ITEM(tuple, i);
22545  #if PY_MAJOR_VERSION < 3
22546  if (likely(exc_type == t)) return 1;
22547  #endif
22548  if (likely(PyExceptionClass_Check(t))) {
22549  if (__Pyx_inner_PyErr_GivenExceptionMatches2(exc_type, NULL, t)) return 1;
22550  } else {
22551  }
22552  }
22553  return 0;
22554 }
22555 static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject* exc_type) {
22556  if (likely(err == exc_type)) return 1;
22557  if (likely(PyExceptionClass_Check(err))) {
22558  if (likely(PyExceptionClass_Check(exc_type))) {
22559  return __Pyx_inner_PyErr_GivenExceptionMatches2(err, NULL, exc_type);
22560  } else if (likely(PyTuple_Check(exc_type))) {
22561  return __Pyx_PyErr_GivenExceptionMatchesTuple(err, exc_type);
22562  } else {
22563  }
22564  }
22565  return PyErr_GivenExceptionMatches(err, exc_type);
22566 }
22567 static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *exc_type1, PyObject *exc_type2) {
22568  assert(PyExceptionClass_Check(exc_type1));
22569  assert(PyExceptionClass_Check(exc_type2));
22570  if (likely(err == exc_type1 || err == exc_type2)) return 1;
22571  if (likely(PyExceptionClass_Check(err))) {
22572  return __Pyx_inner_PyErr_GivenExceptionMatches2(err, exc_type1, exc_type2);
22573  }
22574  return (PyErr_GivenExceptionMatches(err, exc_type1) || PyErr_GivenExceptionMatches(err, exc_type2));
22575 }
22576 #endif
22577 
22578 /* FetchCommonType */
22579  static PyTypeObject* __Pyx_FetchCommonType(PyTypeObject* type) {
22580  PyObject* fake_module;
22581  PyTypeObject* cached_type = NULL;
22582  fake_module = PyImport_AddModule((char*) "_cython_" CYTHON_ABI);
22583  if (!fake_module) return NULL;
22584  Py_INCREF(fake_module);
22585  cached_type = (PyTypeObject*) PyObject_GetAttrString(fake_module, type->tp_name);
22586  if (cached_type) {
22587  if (!PyType_Check((PyObject*)cached_type)) {
22588  PyErr_Format(PyExc_TypeError,
22589  "Shared Cython type %.200s is not a type object",
22590  type->tp_name);
22591  goto bad;
22592  }
22593  if (cached_type->tp_basicsize != type->tp_basicsize) {
22594  PyErr_Format(PyExc_TypeError,
22595  "Shared Cython type %.200s has the wrong size, try recompiling",
22596  type->tp_name);
22597  goto bad;
22598  }
22599  } else {
22600  if (!PyErr_ExceptionMatches(PyExc_AttributeError)) goto bad;
22601  PyErr_Clear();
22602  if (PyType_Ready(type) < 0) goto bad;
22603  if (PyObject_SetAttrString(fake_module, type->tp_name, (PyObject*) type) < 0)
22604  goto bad;
22605  Py_INCREF(type);
22606  cached_type = type;
22607  }
22608 done:
22609  Py_DECREF(fake_module);
22610  return cached_type;
22611 bad:
22612  Py_XDECREF(cached_type);
22613  cached_type = NULL;
22614  goto done;
22615 }
22616 
22617 /* SwapException */
22618  #if CYTHON_FAST_THREAD_STATE
22619 static CYTHON_INLINE void __Pyx__ExceptionSwap(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
22620  PyObject *tmp_type, *tmp_value, *tmp_tb;
22621  #if CYTHON_USE_EXC_INFO_STACK
22622  _PyErr_StackItem *exc_info = tstate->exc_info;
22623  tmp_type = exc_info->exc_type;
22624  tmp_value = exc_info->exc_value;
22625  tmp_tb = exc_info->exc_traceback;
22626  exc_info->exc_type = *type;
22627  exc_info->exc_value = *value;
22628  exc_info->exc_traceback = *tb;
22629  #else
22630  tmp_type = tstate->exc_type;
22631  tmp_value = tstate->exc_value;
22632  tmp_tb = tstate->exc_traceback;
22633  tstate->exc_type = *type;
22634  tstate->exc_value = *value;
22635  tstate->exc_traceback = *tb;
22636  #endif
22637  *type = tmp_type;
22638  *value = tmp_value;
22639  *tb = tmp_tb;
22640 }
22641 #else
22642 static CYTHON_INLINE void __Pyx_ExceptionSwap(PyObject **type, PyObject **value, PyObject **tb) {
22643  PyObject *tmp_type, *tmp_value, *tmp_tb;
22644  PyErr_GetExcInfo(&tmp_type, &tmp_value, &tmp_tb);
22645  PyErr_SetExcInfo(*type, *value, *tb);
22646  *type = tmp_type;
22647  *value = tmp_value;
22648  *tb = tmp_tb;
22649 }
22650 #endif
22651 
22652 /* PyObjectGetMethod */
22653  static int __Pyx_PyObject_GetMethod(PyObject *obj, PyObject *name, PyObject **method) {
22654  PyObject *attr;
22655 #if CYTHON_UNPACK_METHODS && CYTHON_COMPILING_IN_CPYTHON && CYTHON_USE_PYTYPE_LOOKUP
22656  PyTypeObject *tp = Py_TYPE(obj);
22657  PyObject *descr;
22658  descrgetfunc f = NULL;
22659  PyObject **dictptr, *dict;
22660  int meth_found = 0;
22661  assert (*method == NULL);
22662  if (unlikely(tp->tp_getattro != PyObject_GenericGetAttr)) {
22663  attr = __Pyx_PyObject_GetAttrStr(obj, name);
22664  goto try_unpack;
22665  }
22666  if (unlikely(tp->tp_dict == NULL) && unlikely(PyType_Ready(tp) < 0)) {
22667  return 0;
22668  }
22669  descr = _PyType_Lookup(tp, name);
22670  if (likely(descr != NULL)) {
22671  Py_INCREF(descr);
22672 #if PY_MAJOR_VERSION >= 3
22673  #ifdef __Pyx_CyFunction_USED
22674  if (likely(PyFunction_Check(descr) || (Py_TYPE(descr) == &PyMethodDescr_Type) || __Pyx_CyFunction_Check(descr)))
22675  #else
22676  if (likely(PyFunction_Check(descr) || (Py_TYPE(descr) == &PyMethodDescr_Type)))
22677  #endif
22678 #else
22679  #ifdef __Pyx_CyFunction_USED
22680  if (likely(PyFunction_Check(descr) || __Pyx_CyFunction_Check(descr)))
22681  #else
22682  if (likely(PyFunction_Check(descr)))
22683  #endif
22684 #endif
22685  {
22686  meth_found = 1;
22687  } else {
22688  f = Py_TYPE(descr)->tp_descr_get;
22689  if (f != NULL && PyDescr_IsData(descr)) {
22690  attr = f(descr, obj, (PyObject *)Py_TYPE(obj));
22691  Py_DECREF(descr);
22692  goto try_unpack;
22693  }
22694  }
22695  }
22696  dictptr = _PyObject_GetDictPtr(obj);
22697  if (dictptr != NULL && (dict = *dictptr) != NULL) {
22698  Py_INCREF(dict);
22699  attr = __Pyx_PyDict_GetItemStr(dict, name);
22700  if (attr != NULL) {
22701  Py_INCREF(attr);
22702  Py_DECREF(dict);
22703  Py_XDECREF(descr);
22704  goto try_unpack;
22705  }
22706  Py_DECREF(dict);
22707  }
22708  if (meth_found) {
22709  *method = descr;
22710  return 1;
22711  }
22712  if (f != NULL) {
22713  attr = f(descr, obj, (PyObject *)Py_TYPE(obj));
22714  Py_DECREF(descr);
22715  goto try_unpack;
22716  }
22717  if (descr != NULL) {
22718  *method = descr;
22719  return 0;
22720  }
22721  PyErr_Format(PyExc_AttributeError,
22722 #if PY_MAJOR_VERSION >= 3
22723  "'%.50s' object has no attribute '%U'",
22724  tp->tp_name, name);
22725 #else
22726  "'%.50s' object has no attribute '%.400s'",
22727  tp->tp_name, PyString_AS_STRING(name));
22728 #endif
22729  return 0;
22730 #else
22731  attr = __Pyx_PyObject_GetAttrStr(obj, name);
22732  goto try_unpack;
22733 #endif
22734 try_unpack:
22735 #if CYTHON_UNPACK_METHODS
22736  if (likely(attr) && PyMethod_Check(attr) && likely(PyMethod_GET_SELF(attr) == obj)) {
22737  PyObject *function = PyMethod_GET_FUNCTION(attr);
22738  Py_INCREF(function);
22739  Py_DECREF(attr);
22740  *method = function;
22741  return 1;
22742  }
22743 #endif
22744  *method = attr;
22745  return 0;
22746 }
22747 
22748 /* PyObjectCallMethod1 */
22749  static PyObject* __Pyx__PyObject_CallMethod1(PyObject* method, PyObject* arg) {
22750  PyObject *result = __Pyx_PyObject_CallOneArg(method, arg);
22751  Py_DECREF(method);
22752  return result;
22753 }
22754 static PyObject* __Pyx_PyObject_CallMethod1(PyObject* obj, PyObject* method_name, PyObject* arg) {
22755  PyObject *method = NULL, *result;
22756  int is_method = __Pyx_PyObject_GetMethod(obj, method_name, &method);
22757  if (likely(is_method)) {
22758  result = __Pyx_PyObject_Call2Args(method, obj, arg);
22759  Py_DECREF(method);
22760  return result;
22761  }
22762  if (unlikely(!method)) return NULL;
22763  return __Pyx__PyObject_CallMethod1(method, arg);
22764 }
22765 
22766 /* CoroutineBase */
22767  #include <structmember.h>
22768 #include <frameobject.h>
22769 #define __Pyx_Coroutine_Undelegate(gen) Py_CLEAR((gen)->yieldfrom)
22770 static int __Pyx_PyGen__FetchStopIterationValue(CYTHON_UNUSED PyThreadState *__pyx_tstate, PyObject **pvalue) {
22771  PyObject *et, *ev, *tb;
22772  PyObject *value = NULL;
22773  __Pyx_ErrFetch(&et, &ev, &tb);
22774  if (!et) {
22775  Py_XDECREF(tb);
22776  Py_XDECREF(ev);
22777  Py_INCREF(Py_None);
22778  *pvalue = Py_None;
22779  return 0;
22780  }
22781  if (likely(et == PyExc_StopIteration)) {
22782  if (!ev) {
22783  Py_INCREF(Py_None);
22784  value = Py_None;
22785  }
22786 #if PY_VERSION_HEX >= 0x030300A0
22787  else if (Py_TYPE(ev) == (PyTypeObject*)PyExc_StopIteration) {
22788  value = ((PyStopIterationObject *)ev)->value;
22789  Py_INCREF(value);
22790  Py_DECREF(ev);
22791  }
22792 #endif
22793  else if (unlikely(PyTuple_Check(ev))) {
22794  if (PyTuple_GET_SIZE(ev) >= 1) {
22795 #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
22796  value = PyTuple_GET_ITEM(ev, 0);
22797  Py_INCREF(value);
22798 #else
22799  value = PySequence_ITEM(ev, 0);
22800 #endif
22801  } else {
22802  Py_INCREF(Py_None);
22803  value = Py_None;
22804  }
22805  Py_DECREF(ev);
22806  }
22807  else if (!__Pyx_TypeCheck(ev, (PyTypeObject*)PyExc_StopIteration)) {
22808  value = ev;
22809  }
22810  if (likely(value)) {
22811  Py_XDECREF(tb);
22812  Py_DECREF(et);
22813  *pvalue = value;
22814  return 0;
22815  }
22816  } else if (!__Pyx_PyErr_GivenExceptionMatches(et, PyExc_StopIteration)) {
22817  __Pyx_ErrRestore(et, ev, tb);
22818  return -1;
22819  }
22820  PyErr_NormalizeException(&et, &ev, &tb);
22821  if (unlikely(!PyObject_TypeCheck(ev, (PyTypeObject*)PyExc_StopIteration))) {
22822  __Pyx_ErrRestore(et, ev, tb);
22823  return -1;
22824  }
22825  Py_XDECREF(tb);
22826  Py_DECREF(et);
22827 #if PY_VERSION_HEX >= 0x030300A0
22828  value = ((PyStopIterationObject *)ev)->value;
22829  Py_INCREF(value);
22830  Py_DECREF(ev);
22831 #else
22832  {
22833  PyObject* args = __Pyx_PyObject_GetAttrStr(ev, __pyx_n_s_args);
22834  Py_DECREF(ev);
22835  if (likely(args)) {
22836  value = PySequence_GetItem(args, 0);
22837  Py_DECREF(args);
22838  }
22839  if (unlikely(!value)) {
22840  __Pyx_ErrRestore(NULL, NULL, NULL);
22841  Py_INCREF(Py_None);
22842  value = Py_None;
22843  }
22844  }
22845 #endif
22846  *pvalue = value;
22847  return 0;
22848 }
22849 static CYTHON_INLINE
22850 void __Pyx_Coroutine_ExceptionClear(__Pyx_ExcInfoStruct *exc_state) {
22851  PyObject *t, *v, *tb;
22852  t = exc_state->exc_type;
22853  v = exc_state->exc_value;
22854  tb = exc_state->exc_traceback;
22855  exc_state->exc_type = NULL;
22856  exc_state->exc_value = NULL;
22857  exc_state->exc_traceback = NULL;
22858  Py_XDECREF(t);
22859  Py_XDECREF(v);
22860  Py_XDECREF(tb);
22861 }
22862 #define __Pyx_Coroutine_AlreadyRunningError(gen) (__Pyx__Coroutine_AlreadyRunningError(gen), (PyObject*)NULL)
22863 static void __Pyx__Coroutine_AlreadyRunningError(CYTHON_UNUSED __pyx_CoroutineObject *gen) {
22864  const char *msg;
22865  if ((0)) {
22866  #ifdef __Pyx_Coroutine_USED
22867  } else if (__Pyx_Coroutine_Check((PyObject*)gen)) {
22868  msg = "coroutine already executing";
22869  #endif
22870  #ifdef __Pyx_AsyncGen_USED
22871  } else if (__Pyx_AsyncGen_CheckExact((PyObject*)gen)) {
22872  msg = "async generator already executing";
22873  #endif
22874  } else {
22875  msg = "generator already executing";
22876  }
22877  PyErr_SetString(PyExc_ValueError, msg);
22878 }
22879 #define __Pyx_Coroutine_NotStartedError(gen) (__Pyx__Coroutine_NotStartedError(gen), (PyObject*)NULL)
22880 static void __Pyx__Coroutine_NotStartedError(CYTHON_UNUSED PyObject *gen) {
22881  const char *msg;
22882  if ((0)) {
22883  #ifdef __Pyx_Coroutine_USED
22884  } else if (__Pyx_Coroutine_Check(gen)) {
22885  msg = "can't send non-None value to a just-started coroutine";
22886  #endif
22887  #ifdef __Pyx_AsyncGen_USED
22888  } else if (__Pyx_AsyncGen_CheckExact(gen)) {
22889  msg = "can't send non-None value to a just-started async generator";
22890  #endif
22891  } else {
22892  msg = "can't send non-None value to a just-started generator";
22893  }
22894  PyErr_SetString(PyExc_TypeError, msg);
22895 }
22896 #define __Pyx_Coroutine_AlreadyTerminatedError(gen, value, closing) (__Pyx__Coroutine_AlreadyTerminatedError(gen, value, closing), (PyObject*)NULL)
22897 static void __Pyx__Coroutine_AlreadyTerminatedError(CYTHON_UNUSED PyObject *gen, PyObject *value, CYTHON_UNUSED int closing) {
22898  #ifdef __Pyx_Coroutine_USED
22899  if (!closing && __Pyx_Coroutine_Check(gen)) {
22900  PyErr_SetString(PyExc_RuntimeError, "cannot reuse already awaited coroutine");
22901  } else
22902  #endif
22903  if (value) {
22904  #ifdef __Pyx_AsyncGen_USED
22905  if (__Pyx_AsyncGen_CheckExact(gen))
22906  PyErr_SetNone(__Pyx_PyExc_StopAsyncIteration);
22907  else
22908  #endif
22909  PyErr_SetNone(PyExc_StopIteration);
22910  }
22911 }
22912 static
22913 PyObject *__Pyx_Coroutine_SendEx(__pyx_CoroutineObject *self, PyObject *value, int closing) {
22914  __Pyx_PyThreadState_declare
22915  PyThreadState *tstate;
22916  __Pyx_ExcInfoStruct *exc_state;
22917  PyObject *retval;
22918  assert(!self->is_running);
22919  if (unlikely(self->resume_label == 0)) {
22920  if (unlikely(value && value != Py_None)) {
22921  return __Pyx_Coroutine_NotStartedError((PyObject*)self);
22922  }
22923  }
22924  if (unlikely(self->resume_label == -1)) {
22925  return __Pyx_Coroutine_AlreadyTerminatedError((PyObject*)self, value, closing);
22926  }
22927 #if CYTHON_FAST_THREAD_STATE
22928  __Pyx_PyThreadState_assign
22929  tstate = __pyx_tstate;
22930 #else
22931  tstate = __Pyx_PyThreadState_Current;
22932 #endif
22933  exc_state = &self->gi_exc_state;
22934  if (exc_state->exc_type) {
22935  #if CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_PYSTON
22936  #else
22937  if (exc_state->exc_traceback) {
22938  PyTracebackObject *tb = (PyTracebackObject *) exc_state->exc_traceback;
22939  PyFrameObject *f = tb->tb_frame;
22940  Py_XINCREF(tstate->frame);
22941  assert(f->f_back == NULL);
22942  f->f_back = tstate->frame;
22943  }
22944  #endif
22945  }
22946 #if CYTHON_USE_EXC_INFO_STACK
22947  exc_state->previous_item = tstate->exc_info;
22948  tstate->exc_info = exc_state;
22949 #else
22950  if (exc_state->exc_type) {
22951  __Pyx_ExceptionSwap(&exc_state->exc_type, &exc_state->exc_value, &exc_state->exc_traceback);
22952  } else {
22953  __Pyx_Coroutine_ExceptionClear(exc_state);
22954  __Pyx_ExceptionSave(&exc_state->exc_type, &exc_state->exc_value, &exc_state->exc_traceback);
22955  }
22956 #endif
22957  self->is_running = 1;
22958  retval = self->body((PyObject *) self, tstate, value);
22959  self->is_running = 0;
22960 #if CYTHON_USE_EXC_INFO_STACK
22961  exc_state = &self->gi_exc_state;
22962  tstate->exc_info = exc_state->previous_item;
22963  exc_state->previous_item = NULL;
22964  __Pyx_Coroutine_ResetFrameBackpointer(exc_state);
22965 #endif
22966  return retval;
22967 }
22968 static CYTHON_INLINE void __Pyx_Coroutine_ResetFrameBackpointer(__Pyx_ExcInfoStruct *exc_state) {
22969  PyObject *exc_tb = exc_state->exc_traceback;
22970  if (likely(exc_tb)) {
22971 #if CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_PYSTON
22972 #else
22973  PyTracebackObject *tb = (PyTracebackObject *) exc_tb;
22974  PyFrameObject *f = tb->tb_frame;
22975  Py_CLEAR(f->f_back);
22976 #endif
22977  }
22978 }
22979 static CYTHON_INLINE
22980 PyObject *__Pyx_Coroutine_MethodReturn(CYTHON_UNUSED PyObject* gen, PyObject *retval) {
22981  if (unlikely(!retval)) {
22982  __Pyx_PyThreadState_declare
22983  __Pyx_PyThreadState_assign
22984  if (!__Pyx_PyErr_Occurred()) {
22985  PyObject *exc = PyExc_StopIteration;
22986  #ifdef __Pyx_AsyncGen_USED
22987  if (__Pyx_AsyncGen_CheckExact(gen))
22988  exc = __Pyx_PyExc_StopAsyncIteration;
22989  #endif
22990  __Pyx_PyErr_SetNone(exc);
22991  }
22992  }
22993  return retval;
22994 }
22995 static CYTHON_INLINE
22996 PyObject *__Pyx_Coroutine_FinishDelegation(__pyx_CoroutineObject *gen) {
22997  PyObject *ret;
22998  PyObject *val = NULL;
22999  __Pyx_Coroutine_Undelegate(gen);
23000  __Pyx_PyGen__FetchStopIterationValue(__Pyx_PyThreadState_Current, &val);
23001  ret = __Pyx_Coroutine_SendEx(gen, val, 0);
23002  Py_XDECREF(val);
23003  return ret;
23004 }
23005 static PyObject *__Pyx_Coroutine_Send(PyObject *self, PyObject *value) {
23006  PyObject *retval;
23007  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject*) self;
23008  PyObject *yf = gen->yieldfrom;
23009  if (unlikely(gen->is_running))
23010  return __Pyx_Coroutine_AlreadyRunningError(gen);
23011  if (yf) {
23012  PyObject *ret;
23013  gen->is_running = 1;
23014  #ifdef __Pyx_Generator_USED
23015  if (__Pyx_Generator_CheckExact(yf)) {
23016  ret = __Pyx_Coroutine_Send(yf, value);
23017  } else
23018  #endif
23019  #ifdef __Pyx_Coroutine_USED
23020  if (__Pyx_Coroutine_Check(yf)) {
23021  ret = __Pyx_Coroutine_Send(yf, value);
23022  } else
23023  #endif
23024  #ifdef __Pyx_AsyncGen_USED
23025  if (__pyx_PyAsyncGenASend_CheckExact(yf)) {
23026  ret = __Pyx_async_gen_asend_send(yf, value);
23027  } else
23028  #endif
23029  #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x03030000 && (defined(__linux__) || PY_VERSION_HEX >= 0x030600B3)
23030  if (PyGen_CheckExact(yf)) {
23031  ret = _PyGen_Send((PyGenObject*)yf, value == Py_None ? NULL : value);
23032  } else
23033  #endif
23034  #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x03050000 && defined(PyCoro_CheckExact) && (defined(__linux__) || PY_VERSION_HEX >= 0x030600B3)
23035  if (PyCoro_CheckExact(yf)) {
23036  ret = _PyGen_Send((PyGenObject*)yf, value == Py_None ? NULL : value);
23037  } else
23038  #endif
23039  {
23040  if (value == Py_None)
23041  ret = Py_TYPE(yf)->tp_iternext(yf);
23042  else
23043  ret = __Pyx_PyObject_CallMethod1(yf, __pyx_n_s_send, value);
23044  }
23045  gen->is_running = 0;
23046  if (likely(ret)) {
23047  return ret;
23048  }
23049  retval = __Pyx_Coroutine_FinishDelegation(gen);
23050  } else {
23051  retval = __Pyx_Coroutine_SendEx(gen, value, 0);
23052  }
23053  return __Pyx_Coroutine_MethodReturn(self, retval);
23054 }
23055 static int __Pyx_Coroutine_CloseIter(__pyx_CoroutineObject *gen, PyObject *yf) {
23056  PyObject *retval = NULL;
23057  int err = 0;
23058  #ifdef __Pyx_Generator_USED
23059  if (__Pyx_Generator_CheckExact(yf)) {
23060  retval = __Pyx_Coroutine_Close(yf);
23061  if (!retval)
23062  return -1;
23063  } else
23064  #endif
23065  #ifdef __Pyx_Coroutine_USED
23066  if (__Pyx_Coroutine_Check(yf)) {
23067  retval = __Pyx_Coroutine_Close(yf);
23068  if (!retval)
23069  return -1;
23070  } else
23071  if (__Pyx_CoroutineAwait_CheckExact(yf)) {
23072  retval = __Pyx_CoroutineAwait_Close((__pyx_CoroutineAwaitObject*)yf, NULL);
23073  if (!retval)
23074  return -1;
23075  } else
23076  #endif
23077  #ifdef __Pyx_AsyncGen_USED
23078  if (__pyx_PyAsyncGenASend_CheckExact(yf)) {
23079  retval = __Pyx_async_gen_asend_close(yf, NULL);
23080  } else
23081  if (__pyx_PyAsyncGenAThrow_CheckExact(yf)) {
23082  retval = __Pyx_async_gen_athrow_close(yf, NULL);
23083  } else
23084  #endif
23085  {
23086  PyObject *meth;
23087  gen->is_running = 1;
23088  meth = __Pyx_PyObject_GetAttrStr(yf, __pyx_n_s_close);
23089  if (unlikely(!meth)) {
23090  if (!PyErr_ExceptionMatches(PyExc_AttributeError)) {
23091  PyErr_WriteUnraisable(yf);
23092  }
23093  PyErr_Clear();
23094  } else {
23095  retval = PyObject_CallFunction(meth, NULL);
23096  Py_DECREF(meth);
23097  if (!retval)
23098  err = -1;
23099  }
23100  gen->is_running = 0;
23101  }
23102  Py_XDECREF(retval);
23103  return err;
23104 }
23105 static PyObject *__Pyx_Generator_Next(PyObject *self) {
23106  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject*) self;
23107  PyObject *yf = gen->yieldfrom;
23108  if (unlikely(gen->is_running))
23109  return __Pyx_Coroutine_AlreadyRunningError(gen);
23110  if (yf) {
23111  PyObject *ret;
23112  gen->is_running = 1;
23113  #ifdef __Pyx_Generator_USED
23114  if (__Pyx_Generator_CheckExact(yf)) {
23115  ret = __Pyx_Generator_Next(yf);
23116  } else
23117  #endif
23118  #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x03030000 && (defined(__linux__) || PY_VERSION_HEX >= 0x030600B3)
23119  if (PyGen_CheckExact(yf)) {
23120  ret = _PyGen_Send((PyGenObject*)yf, NULL);
23121  } else
23122  #endif
23123  #ifdef __Pyx_Coroutine_USED
23124  if (__Pyx_Coroutine_Check(yf)) {
23125  ret = __Pyx_Coroutine_Send(yf, Py_None);
23126  } else
23127  #endif
23128  ret = Py_TYPE(yf)->tp_iternext(yf);
23129  gen->is_running = 0;
23130  if (likely(ret)) {
23131  return ret;
23132  }
23133  return __Pyx_Coroutine_FinishDelegation(gen);
23134  }
23135  return __Pyx_Coroutine_SendEx(gen, Py_None, 0);
23136 }
23137 static PyObject *__Pyx_Coroutine_Close_Method(PyObject *self, CYTHON_UNUSED PyObject *arg) {
23138  return __Pyx_Coroutine_Close(self);
23139 }
23140 static PyObject *__Pyx_Coroutine_Close(PyObject *self) {
23141  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
23142  PyObject *retval, *raised_exception;
23143  PyObject *yf = gen->yieldfrom;
23144  int err = 0;
23145  if (unlikely(gen->is_running))
23146  return __Pyx_Coroutine_AlreadyRunningError(gen);
23147  if (yf) {
23148  Py_INCREF(yf);
23149  err = __Pyx_Coroutine_CloseIter(gen, yf);
23150  __Pyx_Coroutine_Undelegate(gen);
23151  Py_DECREF(yf);
23152  }
23153  if (err == 0)
23154  PyErr_SetNone(PyExc_GeneratorExit);
23155  retval = __Pyx_Coroutine_SendEx(gen, NULL, 1);
23156  if (unlikely(retval)) {
23157  const char *msg;
23158  Py_DECREF(retval);
23159  if ((0)) {
23160  #ifdef __Pyx_Coroutine_USED
23161  } else if (__Pyx_Coroutine_Check(self)) {
23162  msg = "coroutine ignored GeneratorExit";
23163  #endif
23164  #ifdef __Pyx_AsyncGen_USED
23165  } else if (__Pyx_AsyncGen_CheckExact(self)) {
23166 #if PY_VERSION_HEX < 0x03060000
23167  msg = "async generator ignored GeneratorExit - might require Python 3.6+ finalisation (PEP 525)";
23168 #else
23169  msg = "async generator ignored GeneratorExit";
23170 #endif
23171  #endif
23172  } else {
23173  msg = "generator ignored GeneratorExit";
23174  }
23175  PyErr_SetString(PyExc_RuntimeError, msg);
23176  return NULL;
23177  }
23178  raised_exception = PyErr_Occurred();
23179  if (likely(!raised_exception || __Pyx_PyErr_GivenExceptionMatches2(raised_exception, PyExc_GeneratorExit, PyExc_StopIteration))) {
23180  if (raised_exception) PyErr_Clear();
23181  Py_INCREF(Py_None);
23182  return Py_None;
23183  }
23184  return NULL;
23185 }
23186 static PyObject *__Pyx__Coroutine_Throw(PyObject *self, PyObject *typ, PyObject *val, PyObject *tb,
23187  PyObject *args, int close_on_genexit) {
23188  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
23189  PyObject *yf = gen->yieldfrom;
23190  if (unlikely(gen->is_running))
23191  return __Pyx_Coroutine_AlreadyRunningError(gen);
23192  if (yf) {
23193  PyObject *ret;
23194  Py_INCREF(yf);
23195  if (__Pyx_PyErr_GivenExceptionMatches(typ, PyExc_GeneratorExit) && close_on_genexit) {
23196  int err = __Pyx_Coroutine_CloseIter(gen, yf);
23197  Py_DECREF(yf);
23198  __Pyx_Coroutine_Undelegate(gen);
23199  if (err < 0)
23200  return __Pyx_Coroutine_MethodReturn(self, __Pyx_Coroutine_SendEx(gen, NULL, 0));
23201  goto throw_here;
23202  }
23203  gen->is_running = 1;
23204  if (0
23205  #ifdef __Pyx_Generator_USED
23206  || __Pyx_Generator_CheckExact(yf)
23207  #endif
23208  #ifdef __Pyx_Coroutine_USED
23209  || __Pyx_Coroutine_Check(yf)
23210  #endif
23211  ) {
23212  ret = __Pyx__Coroutine_Throw(yf, typ, val, tb, args, close_on_genexit);
23213  #ifdef __Pyx_Coroutine_USED
23214  } else if (__Pyx_CoroutineAwait_CheckExact(yf)) {
23215  ret = __Pyx__Coroutine_Throw(((__pyx_CoroutineAwaitObject*)yf)->coroutine, typ, val, tb, args, close_on_genexit);
23216  #endif
23217  } else {
23218  PyObject *meth = __Pyx_PyObject_GetAttrStr(yf, __pyx_n_s_throw);
23219  if (unlikely(!meth)) {
23220  Py_DECREF(yf);
23221  if (!PyErr_ExceptionMatches(PyExc_AttributeError)) {
23222  gen->is_running = 0;
23223  return NULL;
23224  }
23225  PyErr_Clear();
23226  __Pyx_Coroutine_Undelegate(gen);
23227  gen->is_running = 0;
23228  goto throw_here;
23229  }
23230  if (likely(args)) {
23231  ret = PyObject_CallObject(meth, args);
23232  } else {
23233  ret = PyObject_CallFunctionObjArgs(meth, typ, val, tb, NULL);
23234  }
23235  Py_DECREF(meth);
23236  }
23237  gen->is_running = 0;
23238  Py_DECREF(yf);
23239  if (!ret) {
23240  ret = __Pyx_Coroutine_FinishDelegation(gen);
23241  }
23242  return __Pyx_Coroutine_MethodReturn(self, ret);
23243  }
23244 throw_here:
23245  __Pyx_Raise(typ, val, tb, NULL);
23246  return __Pyx_Coroutine_MethodReturn(self, __Pyx_Coroutine_SendEx(gen, NULL, 0));
23247 }
23248 static PyObject *__Pyx_Coroutine_Throw(PyObject *self, PyObject *args) {
23249  PyObject *typ;
23250  PyObject *val = NULL;
23251  PyObject *tb = NULL;
23252  if (!PyArg_UnpackTuple(args, (char *)"throw", 1, 3, &typ, &val, &tb))
23253  return NULL;
23254  return __Pyx__Coroutine_Throw(self, typ, val, tb, args, 1);
23255 }
23256 static CYTHON_INLINE int __Pyx_Coroutine_traverse_excstate(__Pyx_ExcInfoStruct *exc_state, visitproc visit, void *arg) {
23257  Py_VISIT(exc_state->exc_type);
23258  Py_VISIT(exc_state->exc_value);
23259  Py_VISIT(exc_state->exc_traceback);
23260  return 0;
23261 }
23262 static int __Pyx_Coroutine_traverse(__pyx_CoroutineObject *gen, visitproc visit, void *arg) {
23263  Py_VISIT(gen->closure);
23264  Py_VISIT(gen->classobj);
23265  Py_VISIT(gen->yieldfrom);
23266  return __Pyx_Coroutine_traverse_excstate(&gen->gi_exc_state, visit, arg);
23267 }
23268 static int __Pyx_Coroutine_clear(PyObject *self) {
23269  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
23270  Py_CLEAR(gen->closure);
23271  Py_CLEAR(gen->classobj);
23272  Py_CLEAR(gen->yieldfrom);
23273  __Pyx_Coroutine_ExceptionClear(&gen->gi_exc_state);
23274 #ifdef __Pyx_AsyncGen_USED
23275  if (__Pyx_AsyncGen_CheckExact(self)) {
23276  Py_CLEAR(((__pyx_PyAsyncGenObject*)gen)->ag_finalizer);
23277  }
23278 #endif
23279  Py_CLEAR(gen->gi_code);
23280  Py_CLEAR(gen->gi_name);
23281  Py_CLEAR(gen->gi_qualname);
23282  Py_CLEAR(gen->gi_modulename);
23283  return 0;
23284 }
23285 static void __Pyx_Coroutine_dealloc(PyObject *self) {
23286  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
23287  PyObject_GC_UnTrack(gen);
23288  if (gen->gi_weakreflist != NULL)
23289  PyObject_ClearWeakRefs(self);
23290  if (gen->resume_label >= 0) {
23291  PyObject_GC_Track(self);
23292 #if PY_VERSION_HEX >= 0x030400a1 && CYTHON_USE_TP_FINALIZE
23293  if (PyObject_CallFinalizerFromDealloc(self))
23294 #else
23295  Py_TYPE(gen)->tp_del(self);
23296  if (self->ob_refcnt > 0)
23297 #endif
23298  {
23299  return;
23300  }
23301  PyObject_GC_UnTrack(self);
23302  }
23303 #ifdef __Pyx_AsyncGen_USED
23304  if (__Pyx_AsyncGen_CheckExact(self)) {
23305  /* We have to handle this case for asynchronous generators
23306  right here, because this code has to be between UNTRACK
23307  and GC_Del. */
23308  Py_CLEAR(((__pyx_PyAsyncGenObject*)self)->ag_finalizer);
23309  }
23310 #endif
23311  __Pyx_Coroutine_clear(self);
23312  PyObject_GC_Del(gen);
23313 }
23314 static void __Pyx_Coroutine_del(PyObject *self) {
23315  PyObject *error_type, *error_value, *error_traceback;
23316  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
23317  __Pyx_PyThreadState_declare
23318  if (gen->resume_label < 0) {
23319  return;
23320  }
23321 #if !CYTHON_USE_TP_FINALIZE
23322  assert(self->ob_refcnt == 0);
23323  self->ob_refcnt = 1;
23324 #endif
23325  __Pyx_PyThreadState_assign
23326  __Pyx_ErrFetch(&error_type, &error_value, &error_traceback);
23327 #ifdef __Pyx_AsyncGen_USED
23328  if (__Pyx_AsyncGen_CheckExact(self)) {
23329  __pyx_PyAsyncGenObject *agen = (__pyx_PyAsyncGenObject*)self;
23330  PyObject *finalizer = agen->ag_finalizer;
23331  if (finalizer && !agen->ag_closed) {
23332  PyObject *res = __Pyx_PyObject_CallOneArg(finalizer, self);
23333  if (unlikely(!res)) {
23334  PyErr_WriteUnraisable(self);
23335  } else {
23336  Py_DECREF(res);
23337  }
23338  __Pyx_ErrRestore(error_type, error_value, error_traceback);
23339  return;
23340  }
23341  }
23342 #endif
23343  if (unlikely(gen->resume_label == 0 && !error_value)) {
23344 #ifdef __Pyx_Coroutine_USED
23345 #ifdef __Pyx_Generator_USED
23346  if (!__Pyx_Generator_CheckExact(self))
23347 #endif
23348  {
23349  PyObject_GC_UnTrack(self);
23350 #if PY_MAJOR_VERSION >= 3 || defined(PyErr_WarnFormat)
23351  if (unlikely(PyErr_WarnFormat(PyExc_RuntimeWarning, 1, "coroutine '%.50S' was never awaited", gen->gi_qualname) < 0))
23352  PyErr_WriteUnraisable(self);
23353 #else
23354  {PyObject *msg;
23355  char *cmsg;
23356  #if CYTHON_COMPILING_IN_PYPY
23357  msg = NULL;
23358  cmsg = (char*) "coroutine was never awaited";
23359  #else
23360  char *cname;
23361  PyObject *qualname;
23362  qualname = gen->gi_qualname;
23363  cname = PyString_AS_STRING(qualname);
23364  msg = PyString_FromFormat("coroutine '%.50s' was never awaited", cname);
23365  if (unlikely(!msg)) {
23366  PyErr_Clear();
23367  cmsg = (char*) "coroutine was never awaited";
23368  } else {
23369  cmsg = PyString_AS_STRING(msg);
23370  }
23371  #endif
23372  if (unlikely(PyErr_WarnEx(PyExc_RuntimeWarning, cmsg, 1) < 0))
23373  PyErr_WriteUnraisable(self);
23374  Py_XDECREF(msg);}
23375 #endif
23376  PyObject_GC_Track(self);
23377  }
23378 #endif
23379  } else {
23380  PyObject *res = __Pyx_Coroutine_Close(self);
23381  if (unlikely(!res)) {
23382  if (PyErr_Occurred())
23383  PyErr_WriteUnraisable(self);
23384  } else {
23385  Py_DECREF(res);
23386  }
23387  }
23388  __Pyx_ErrRestore(error_type, error_value, error_traceback);
23389 #if !CYTHON_USE_TP_FINALIZE
23390  assert(self->ob_refcnt > 0);
23391  if (--self->ob_refcnt == 0) {
23392  return;
23393  }
23394  {
23395  Py_ssize_t refcnt = self->ob_refcnt;
23396  _Py_NewReference(self);
23397  self->ob_refcnt = refcnt;
23398  }
23399 #if CYTHON_COMPILING_IN_CPYTHON
23400  assert(PyType_IS_GC(self->ob_type) &&
23401  _Py_AS_GC(self)->gc.gc_refs != _PyGC_REFS_UNTRACKED);
23402  _Py_DEC_REFTOTAL;
23403 #endif
23404 #ifdef COUNT_ALLOCS
23405  --Py_TYPE(self)->tp_frees;
23406  --Py_TYPE(self)->tp_allocs;
23407 #endif
23408 #endif
23409 }
23410 static PyObject *
23411 __Pyx_Coroutine_get_name(__pyx_CoroutineObject *self, CYTHON_UNUSED void *context)
23412 {
23413  PyObject *name = self->gi_name;
23414  if (unlikely(!name)) name = Py_None;
23415  Py_INCREF(name);
23416  return name;
23417 }
23418 static int
23419 __Pyx_Coroutine_set_name(__pyx_CoroutineObject *self, PyObject *value, CYTHON_UNUSED void *context)
23420 {
23421  PyObject *tmp;
23422 #if PY_MAJOR_VERSION >= 3
23423  if (unlikely(value == NULL || !PyUnicode_Check(value)))
23424 #else
23425  if (unlikely(value == NULL || !PyString_Check(value)))
23426 #endif
23427  {
23428  PyErr_SetString(PyExc_TypeError,
23429  "__name__ must be set to a string object");
23430  return -1;
23431  }
23432  tmp = self->gi_name;
23433  Py_INCREF(value);
23434  self->gi_name = value;
23435  Py_XDECREF(tmp);
23436  return 0;
23437 }
23438 static PyObject *
23439 __Pyx_Coroutine_get_qualname(__pyx_CoroutineObject *self, CYTHON_UNUSED void *context)
23440 {
23441  PyObject *name = self->gi_qualname;
23442  if (unlikely(!name)) name = Py_None;
23443  Py_INCREF(name);
23444  return name;
23445 }
23446 static int
23447 __Pyx_Coroutine_set_qualname(__pyx_CoroutineObject *self, PyObject *value, CYTHON_UNUSED void *context)
23448 {
23449  PyObject *tmp;
23450 #if PY_MAJOR_VERSION >= 3
23451  if (unlikely(value == NULL || !PyUnicode_Check(value)))
23452 #else
23453  if (unlikely(value == NULL || !PyString_Check(value)))
23454 #endif
23455  {
23456  PyErr_SetString(PyExc_TypeError,
23457  "__qualname__ must be set to a string object");
23458  return -1;
23459  }
23460  tmp = self->gi_qualname;
23461  Py_INCREF(value);
23462  self->gi_qualname = value;
23463  Py_XDECREF(tmp);
23464  return 0;
23465 }
23466 static __pyx_CoroutineObject *__Pyx__Coroutine_New(
23467  PyTypeObject* type, __pyx_coroutine_body_t body, PyObject *code, PyObject *closure,
23468  PyObject *name, PyObject *qualname, PyObject *module_name) {
23469  __pyx_CoroutineObject *gen = PyObject_GC_New(__pyx_CoroutineObject, type);
23470  if (unlikely(!gen))
23471  return NULL;
23472  return __Pyx__Coroutine_NewInit(gen, body, code, closure, name, qualname, module_name);
23473 }
23474 static __pyx_CoroutineObject *__Pyx__Coroutine_NewInit(
23475  __pyx_CoroutineObject *gen, __pyx_coroutine_body_t body, PyObject *code, PyObject *closure,
23476  PyObject *name, PyObject *qualname, PyObject *module_name) {
23477  gen->body = body;
23478  gen->closure = closure;
23479  Py_XINCREF(closure);
23480  gen->is_running = 0;
23481  gen->resume_label = 0;
23482  gen->classobj = NULL;
23483  gen->yieldfrom = NULL;
23484  gen->gi_exc_state.exc_type = NULL;
23485  gen->gi_exc_state.exc_value = NULL;
23486  gen->gi_exc_state.exc_traceback = NULL;
23487 #if CYTHON_USE_EXC_INFO_STACK
23488  gen->gi_exc_state.previous_item = NULL;
23489 #endif
23490  gen->gi_weakreflist = NULL;
23491  Py_XINCREF(qualname);
23492  gen->gi_qualname = qualname;
23493  Py_XINCREF(name);
23494  gen->gi_name = name;
23495  Py_XINCREF(module_name);
23496  gen->gi_modulename = module_name;
23497  Py_XINCREF(code);
23498  gen->gi_code = code;
23499  PyObject_GC_Track(gen);
23500  return gen;
23501 }
23502 
23503 /* PatchModuleWithCoroutine */
23504  static PyObject* __Pyx_Coroutine_patch_module(PyObject* module, const char* py_code) {
23505 #if defined(__Pyx_Generator_USED) || defined(__Pyx_Coroutine_USED)
23506  int result;
23507  PyObject *globals, *result_obj;
23508  globals = PyDict_New(); if (unlikely(!globals)) goto ignore;
23509  result = PyDict_SetItemString(globals, "_cython_coroutine_type",
23510  #ifdef __Pyx_Coroutine_USED
23511  (PyObject*)__pyx_CoroutineType);
23512  #else
23513  Py_None);
23514  #endif
23515  if (unlikely(result < 0)) goto ignore;
23516  result = PyDict_SetItemString(globals, "_cython_generator_type",
23517  #ifdef __Pyx_Generator_USED
23518  (PyObject*)__pyx_GeneratorType);
23519  #else
23520  Py_None);
23521  #endif
23522  if (unlikely(result < 0)) goto ignore;
23523  if (unlikely(PyDict_SetItemString(globals, "_module", module) < 0)) goto ignore;
23524  if (unlikely(PyDict_SetItemString(globals, "__builtins__", __pyx_b) < 0)) goto ignore;
23525  result_obj = PyRun_String(py_code, Py_file_input, globals, globals);
23526  if (unlikely(!result_obj)) goto ignore;
23527  Py_DECREF(result_obj);
23528  Py_DECREF(globals);
23529  return module;
23530 ignore:
23531  Py_XDECREF(globals);
23532  PyErr_WriteUnraisable(module);
23533  if (unlikely(PyErr_WarnEx(PyExc_RuntimeWarning, "Cython module failed to patch module with custom type", 1) < 0)) {
23534  Py_DECREF(module);
23535  module = NULL;
23536  }
23537 #else
23538  py_code++;
23539 #endif
23540  return module;
23541 }
23542 
23543 /* PatchGeneratorABC */
23544  #ifndef CYTHON_REGISTER_ABCS
23545 #define CYTHON_REGISTER_ABCS 1
23546 #endif
23547 #if defined(__Pyx_Generator_USED) || defined(__Pyx_Coroutine_USED)
23548 static PyObject* __Pyx_patch_abc_module(PyObject *module);
23549 static PyObject* __Pyx_patch_abc_module(PyObject *module) {
23550  module = __Pyx_Coroutine_patch_module(
23551  module, ""
23552 "if _cython_generator_type is not None:\n"
23553 " try: Generator = _module.Generator\n"
23554 " except AttributeError: pass\n"
23555 " else: Generator.register(_cython_generator_type)\n"
23556 "if _cython_coroutine_type is not None:\n"
23557 " try: Coroutine = _module.Coroutine\n"
23558 " except AttributeError: pass\n"
23559 " else: Coroutine.register(_cython_coroutine_type)\n"
23560  );
23561  return module;
23562 }
23563 #endif
23564 static int __Pyx_patch_abc(void) {
23565 #if defined(__Pyx_Generator_USED) || defined(__Pyx_Coroutine_USED)
23566  static int abc_patched = 0;
23567  if (CYTHON_REGISTER_ABCS && !abc_patched) {
23568  PyObject *module;
23569  module = PyImport_ImportModule((PY_MAJOR_VERSION >= 3) ? "collections.abc" : "collections");
23570  if (!module) {
23571  PyErr_WriteUnraisable(NULL);
23572  if (unlikely(PyErr_WarnEx(PyExc_RuntimeWarning,
23573  ((PY_MAJOR_VERSION >= 3) ?
23574  "Cython module failed to register with collections.abc module" :
23575  "Cython module failed to register with collections module"), 1) < 0)) {
23576  return -1;
23577  }
23578  } else {
23579  module = __Pyx_patch_abc_module(module);
23580  abc_patched = 1;
23581  if (unlikely(!module))
23582  return -1;
23583  Py_DECREF(module);
23584  }
23585  module = PyImport_ImportModule("backports_abc");
23586  if (module) {
23587  module = __Pyx_patch_abc_module(module);
23588  Py_XDECREF(module);
23589  }
23590  if (!module) {
23591  PyErr_Clear();
23592  }
23593  }
23594 #else
23595  if ((0)) __Pyx_Coroutine_patch_module(NULL, NULL);
23596 #endif
23597  return 0;
23598 }
23599 
23600 /* Generator */
23601  static PyMethodDef __pyx_Generator_methods[] = {
23602  {"send", (PyCFunction) __Pyx_Coroutine_Send, METH_O,
23603  (char*) PyDoc_STR("send(arg) -> send 'arg' into generator,\nreturn next yielded value or raise StopIteration.")},
23604  {"throw", (PyCFunction) __Pyx_Coroutine_Throw, METH_VARARGS,
23605  (char*) PyDoc_STR("throw(typ[,val[,tb]]) -> raise exception in generator,\nreturn next yielded value or raise StopIteration.")},
23606  {"close", (PyCFunction) __Pyx_Coroutine_Close_Method, METH_NOARGS,
23607  (char*) PyDoc_STR("close() -> raise GeneratorExit inside generator.")},
23608  {0, 0, 0, 0}
23609 };
23610 static PyMemberDef __pyx_Generator_memberlist[] = {
23611  {(char *) "gi_running", T_BOOL, offsetof(__pyx_CoroutineObject, is_running), READONLY, NULL},
23612  {(char*) "gi_yieldfrom", T_OBJECT, offsetof(__pyx_CoroutineObject, yieldfrom), READONLY,
23613  (char*) PyDoc_STR("object being iterated by 'yield from', or None")},
23614  {(char*) "gi_code", T_OBJECT, offsetof(__pyx_CoroutineObject, gi_code), READONLY, NULL},
23615  {0, 0, 0, 0, 0}
23616 };
23617 static PyGetSetDef __pyx_Generator_getsets[] = {
23618  {(char *) "__name__", (getter)__Pyx_Coroutine_get_name, (setter)__Pyx_Coroutine_set_name,
23619  (char*) PyDoc_STR("name of the generator"), 0},
23620  {(char *) "__qualname__", (getter)__Pyx_Coroutine_get_qualname, (setter)__Pyx_Coroutine_set_qualname,
23621  (char*) PyDoc_STR("qualified name of the generator"), 0},
23622  {0, 0, 0, 0, 0}
23623 };
23624 static PyTypeObject __pyx_GeneratorType_type = {
23625  PyVarObject_HEAD_INIT(0, 0)
23626  "generator",
23627  sizeof(__pyx_CoroutineObject),
23628  0,
23629  (destructor) __Pyx_Coroutine_dealloc,
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  0,
23643  0,
23644  Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC | Py_TPFLAGS_HAVE_FINALIZE,
23645  0,
23646  (traverseproc) __Pyx_Coroutine_traverse,
23647  0,
23648  0,
23649  offsetof(__pyx_CoroutineObject, gi_weakreflist),
23650  0,
23651  (iternextfunc) __Pyx_Generator_Next,
23652  __pyx_Generator_methods,
23653  __pyx_Generator_memberlist,
23654  __pyx_Generator_getsets,
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  0,
23669  0,
23670 #if CYTHON_USE_TP_FINALIZE
23671  0,
23672 #else
23673  __Pyx_Coroutine_del,
23674 #endif
23675  0,
23676 #if CYTHON_USE_TP_FINALIZE
23677  __Pyx_Coroutine_del,
23678 #elif PY_VERSION_HEX >= 0x030400a1
23679  0,
23680 #endif
23681 };
23682 static int __pyx_Generator_init(void) {
23683  __pyx_GeneratorType_type.tp_getattro = __Pyx_PyObject_GenericGetAttrNoDict;
23684  __pyx_GeneratorType_type.tp_iter = PyObject_SelfIter;
23685  __pyx_GeneratorType = __Pyx_FetchCommonType(&__pyx_GeneratorType_type);
23686  if (unlikely(!__pyx_GeneratorType)) {
23687  return -1;
23688  }
23689  return 0;
23690 }
23691 
23692 /* CheckBinaryVersion */
23693  static int __Pyx_check_binary_version(void) {
23694  char ctversion[4], rtversion[4];
23695  PyOS_snprintf(ctversion, 4, "%d.%d", PY_MAJOR_VERSION, PY_MINOR_VERSION);
23696  PyOS_snprintf(rtversion, 4, "%s", Py_GetVersion());
23697  if (ctversion[0] != rtversion[0] || ctversion[2] != rtversion[2]) {
23698  char message[200];
23699  PyOS_snprintf(message, sizeof(message),
23700  "compiletime version %s of module '%.100s' "
23701  "does not match runtime version %s",
23702  ctversion, __Pyx_MODULE_NAME, rtversion);
23703  return PyErr_WarnEx(NULL, message, 1);
23704  }
23705  return 0;
23706 }
23707 
23708 /* InitStrings */
23709  static int __Pyx_InitStrings(__Pyx_StringTabEntry *t) {
23710  while (t->p) {
23711  #if PY_MAJOR_VERSION < 3
23712  if (t->is_unicode) {
23713  *t->p = PyUnicode_DecodeUTF8(t->s, t->n - 1, NULL);
23714  } else if (t->intern) {
23715  *t->p = PyString_InternFromString(t->s);
23716  } else {
23717  *t->p = PyString_FromStringAndSize(t->s, t->n - 1);
23718  }
23719  #else
23720  if (t->is_unicode | t->is_str) {
23721  if (t->intern) {
23722  *t->p = PyUnicode_InternFromString(t->s);
23723  } else if (t->encoding) {
23724  *t->p = PyUnicode_Decode(t->s, t->n - 1, t->encoding, NULL);
23725  } else {
23726  *t->p = PyUnicode_FromStringAndSize(t->s, t->n - 1);
23727  }
23728  } else {
23729  *t->p = PyBytes_FromStringAndSize(t->s, t->n - 1);
23730  }
23731  #endif
23732  if (!*t->p)
23733  return -1;
23734  if (PyObject_Hash(*t->p) == -1)
23735  return -1;
23736  ++t;
23737  }
23738  return 0;
23739 }
23740 
23741 static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char* c_str) {
23742  return __Pyx_PyUnicode_FromStringAndSize(c_str, (Py_ssize_t)strlen(c_str));
23743 }
23744 static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject* o) {
23745  Py_ssize_t ignore;
23746  return __Pyx_PyObject_AsStringAndSize(o, &ignore);
23747 }
23748 #if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
23749 #if !CYTHON_PEP393_ENABLED
23750 static const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
23751  char* defenc_c;
23752  PyObject* defenc = _PyUnicode_AsDefaultEncodedString(o, NULL);
23753  if (!defenc) return NULL;
23754  defenc_c = PyBytes_AS_STRING(defenc);
23755 #if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
23756  {
23757  char* end = defenc_c + PyBytes_GET_SIZE(defenc);
23758  char* c;
23759  for (c = defenc_c; c < end; c++) {
23760  if ((unsigned char) (*c) >= 128) {
23761  PyUnicode_AsASCIIString(o);
23762  return NULL;
23763  }
23764  }
23765  }
23766 #endif
23767  *length = PyBytes_GET_SIZE(defenc);
23768  return defenc_c;
23769 }
23770 #else
23771 static CYTHON_INLINE const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
23772  if (unlikely(__Pyx_PyUnicode_READY(o) == -1)) return NULL;
23773 #if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
23774  if (likely(PyUnicode_IS_ASCII(o))) {
23775  *length = PyUnicode_GET_LENGTH(o);
23776  return PyUnicode_AsUTF8(o);
23777  } else {
23778  PyUnicode_AsASCIIString(o);
23779  return NULL;
23780  }
23781 #else
23782  return PyUnicode_AsUTF8AndSize(o, length);
23783 #endif
23784 }
23785 #endif
23786 #endif
23787 static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
23788 #if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
23789  if (
23790 #if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
23791  __Pyx_sys_getdefaultencoding_not_ascii &&
23792 #endif
23793  PyUnicode_Check(o)) {
23794  return __Pyx_PyUnicode_AsStringAndSize(o, length);
23795  } else
23796 #endif
23797 #if (!CYTHON_COMPILING_IN_PYPY) || (defined(PyByteArray_AS_STRING) && defined(PyByteArray_GET_SIZE))
23798  if (PyByteArray_Check(o)) {
23799  *length = PyByteArray_GET_SIZE(o);
23800  return PyByteArray_AS_STRING(o);
23801  } else
23802 #endif
23803  {
23804  char* result;
23805  int r = PyBytes_AsStringAndSize(o, &result, length);
23806  if (unlikely(r < 0)) {
23807  return NULL;
23808  } else {
23809  return result;
23810  }
23811  }
23812 }
23813 static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) {
23814  int is_true = x == Py_True;
23815  if (is_true | (x == Py_False) | (x == Py_None)) return is_true;
23816  else return PyObject_IsTrue(x);
23817 }
23818 static CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject* x) {
23819  int retval;
23820  if (unlikely(!x)) return -1;
23821  retval = __Pyx_PyObject_IsTrue(x);
23822  Py_DECREF(x);
23823  return retval;
23824 }
23825 static PyObject* __Pyx_PyNumber_IntOrLongWrongResultType(PyObject* result, const char* type_name) {
23826 #if PY_MAJOR_VERSION >= 3
23827  if (PyLong_Check(result)) {
23828  if (PyErr_WarnFormat(PyExc_DeprecationWarning, 1,
23829  "__int__ returned non-int (type %.200s). "
23830  "The ability to return an instance of a strict subclass of int "
23831  "is deprecated, and may be removed in a future version of Python.",
23832  Py_TYPE(result)->tp_name)) {
23833  Py_DECREF(result);
23834  return NULL;
23835  }
23836  return result;
23837  }
23838 #endif
23839  PyErr_Format(PyExc_TypeError,
23840  "__%.4s__ returned non-%.4s (type %.200s)",
23841  type_name, type_name, Py_TYPE(result)->tp_name);
23842  Py_DECREF(result);
23843  return NULL;
23844 }
23845 static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x) {
23846 #if CYTHON_USE_TYPE_SLOTS
23847  PyNumberMethods *m;
23848 #endif
23849  const char *name = NULL;
23850  PyObject *res = NULL;
23851 #if PY_MAJOR_VERSION < 3
23852  if (likely(PyInt_Check(x) || PyLong_Check(x)))
23853 #else
23854  if (likely(PyLong_Check(x)))
23855 #endif
23856  return __Pyx_NewRef(x);
23857 #if CYTHON_USE_TYPE_SLOTS
23858  m = Py_TYPE(x)->tp_as_number;
23859  #if PY_MAJOR_VERSION < 3
23860  if (m && m->nb_int) {
23861  name = "int";
23862  res = m->nb_int(x);
23863  }
23864  else if (m && m->nb_long) {
23865  name = "long";
23866  res = m->nb_long(x);
23867  }
23868  #else
23869  if (likely(m && m->nb_int)) {
23870  name = "int";
23871  res = m->nb_int(x);
23872  }
23873  #endif
23874 #else
23875  if (!PyBytes_CheckExact(x) && !PyUnicode_CheckExact(x)) {
23876  res = PyNumber_Int(x);
23877  }
23878 #endif
23879  if (likely(res)) {
23880 #if PY_MAJOR_VERSION < 3
23881  if (unlikely(!PyInt_Check(res) && !PyLong_Check(res))) {
23882 #else
23883  if (unlikely(!PyLong_CheckExact(res))) {
23884 #endif
23885  return __Pyx_PyNumber_IntOrLongWrongResultType(res, name);
23886  }
23887  }
23888  else if (!PyErr_Occurred()) {
23889  PyErr_SetString(PyExc_TypeError,
23890  "an integer is required");
23891  }
23892  return res;
23893 }
23894 static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject* b) {
23895  Py_ssize_t ival;
23896  PyObject *x;
23897 #if PY_MAJOR_VERSION < 3
23898  if (likely(PyInt_CheckExact(b))) {
23899  if (sizeof(Py_ssize_t) >= sizeof(long))
23900  return PyInt_AS_LONG(b);
23901  else
23902  return PyInt_AsSsize_t(b);
23903  }
23904 #endif
23905  if (likely(PyLong_CheckExact(b))) {
23906  #if CYTHON_USE_PYLONG_INTERNALS
23907  const digit* digits = ((PyLongObject*)b)->ob_digit;
23908  const Py_ssize_t size = Py_SIZE(b);
23909  if (likely(__Pyx_sst_abs(size) <= 1)) {
23910  ival = likely(size) ? digits[0] : 0;
23911  if (size == -1) ival = -ival;
23912  return ival;
23913  } else {
23914  switch (size) {
23915  case 2:
23916  if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
23917  return (Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
23918  }
23919  break;
23920  case -2:
23921  if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
23922  return -(Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
23923  }
23924  break;
23925  case 3:
23926  if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
23927  return (Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
23928  }
23929  break;
23930  case -3:
23931  if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
23932  return -(Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
23933  }
23934  break;
23935  case 4:
23936  if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
23937  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]));
23938  }
23939  break;
23940  case -4:
23941  if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
23942  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]));
23943  }
23944  break;
23945  }
23946  }
23947  #endif
23948  return PyLong_AsSsize_t(b);
23949  }
23950  x = PyNumber_Index(b);
23951  if (!x) return -1;
23952  ival = PyInt_AsSsize_t(x);
23953  Py_DECREF(x);
23954  return ival;
23955 }
23956 static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b) {
23957  return b ? __Pyx_NewRef(Py_True) : __Pyx_NewRef(Py_False);
23958 }
23959 static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) {
23960  return PyInt_FromSize_t(ival);
23961 }
23962 
23963 
23964 #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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