glucat  0.8.2
PyClical.cpp
Go to the documentation of this file.
1 /* Generated by Cython 0.28.5 */
2 
3 /* BEGIN: Cython Metadata
4 {
5  "distutils": {
6  "depends": [
7  "PyClical.h"
8  ],
9  "extra_compile_args": [
10  "-I.",
11  "-I..",
12  "-fno-strict-aliasing",
13  "-Wno-unused",
14  "-Wall",
15  "-std=c++11",
16  "-g",
17  "-O3",
18  "-O2",
19  "-Wall",
20  "-D_FORTIFY_SOURCE=2",
21  "-fstack-protector-strong",
22  "-funwind-tables",
23  "-fasynchronous-unwind-tables",
24  "-fstack-clash-protection",
25  "-g",
26  "-finline-limit=4000",
27  "--param",
28  "inline-unit-growth=200",
29  "-funroll-loops",
30  "-fvariable-expansion-in-unroller",
31  "-DNDEBUG",
32  "-DHAVE_BITS_WORDSIZE_H",
33  "-D_GLUCAT_USE_STD_UNORDERED_MAP",
34  "-D_GLUCAT_USE_DENSE_MATRICES",
35  "-D_GLUCAT_CHECK_ISNAN",
36  "-Wno-unused-local-typedefs",
37  "-Wno-misleading-indentation",
38  "-fno-check-new",
39  "-fexceptions"
40  ],
41  "include_dirs": [
42  ".",
43  ".."
44  ],
45  "language": "c++",
46  "name": "PyClical",
47  "sources": [
48  "PyClical.pyx"
49  ]
50  },
51  "module_name": "PyClical"
52 }
53 END: Cython Metadata */
54 
55 #define PY_SSIZE_T_CLEAN
56 #include "Python.h"
57 #ifndef Py_PYTHON_H
58  #error Python headers needed to compile C extensions, please install development version of Python.
59 #elif PY_VERSION_HEX < 0x02060000 || (0x03000000 <= PY_VERSION_HEX && PY_VERSION_HEX < 0x03030000)
60  #error Cython requires Python 2.6+ or Python 3.3+.
61 #else
62 #define CYTHON_ABI "0_28_5"
63 #define CYTHON_FUTURE_DIVISION 0
64 #include <stddef.h>
65 #ifndef offsetof
66  #define offsetof(type, member) ( (size_t) & ((type*)0) -> member )
67 #endif
68 #if !defined(WIN32) && !defined(MS_WINDOWS)
69  #ifndef __stdcall
70  #define __stdcall
71  #endif
72  #ifndef __cdecl
73  #define __cdecl
74  #endif
75  #ifndef __fastcall
76  #define __fastcall
77  #endif
78 #endif
79 #ifndef DL_IMPORT
80  #define DL_IMPORT(t) t
81 #endif
82 #ifndef DL_EXPORT
83  #define DL_EXPORT(t) t
84 #endif
85 #define __PYX_COMMA ,
86 #ifndef HAVE_LONG_LONG
87  #if PY_VERSION_HEX >= 0x02070000
88  #define HAVE_LONG_LONG
89  #endif
90 #endif
91 #ifndef PY_LONG_LONG
92  #define PY_LONG_LONG LONG_LONG
93 #endif
94 #ifndef Py_HUGE_VAL
95  #define Py_HUGE_VAL HUGE_VAL
96 #endif
97 #ifdef PYPY_VERSION
98  #define CYTHON_COMPILING_IN_PYPY 1
99  #define CYTHON_COMPILING_IN_PYSTON 0
100  #define CYTHON_COMPILING_IN_CPYTHON 0
101  #undef CYTHON_USE_TYPE_SLOTS
102  #define CYTHON_USE_TYPE_SLOTS 0
103  #undef CYTHON_USE_PYTYPE_LOOKUP
104  #define CYTHON_USE_PYTYPE_LOOKUP 0
105  #if PY_VERSION_HEX < 0x03050000
106  #undef CYTHON_USE_ASYNC_SLOTS
107  #define CYTHON_USE_ASYNC_SLOTS 0
108  #elif !defined(CYTHON_USE_ASYNC_SLOTS)
109  #define CYTHON_USE_ASYNC_SLOTS 1
110  #endif
111  #undef CYTHON_USE_PYLIST_INTERNALS
112  #define CYTHON_USE_PYLIST_INTERNALS 0
113  #undef CYTHON_USE_UNICODE_INTERNALS
114  #define CYTHON_USE_UNICODE_INTERNALS 0
115  #undef CYTHON_USE_UNICODE_WRITER
116  #define CYTHON_USE_UNICODE_WRITER 0
117  #undef CYTHON_USE_PYLONG_INTERNALS
118  #define CYTHON_USE_PYLONG_INTERNALS 0
119  #undef CYTHON_AVOID_BORROWED_REFS
120  #define CYTHON_AVOID_BORROWED_REFS 1
121  #undef CYTHON_ASSUME_SAFE_MACROS
122  #define CYTHON_ASSUME_SAFE_MACROS 0
123  #undef CYTHON_UNPACK_METHODS
124  #define CYTHON_UNPACK_METHODS 0
125  #undef CYTHON_FAST_THREAD_STATE
126  #define CYTHON_FAST_THREAD_STATE 0
127  #undef CYTHON_FAST_PYCALL
128  #define CYTHON_FAST_PYCALL 0
129  #undef CYTHON_PEP489_MULTI_PHASE_INIT
130  #define CYTHON_PEP489_MULTI_PHASE_INIT 0
131  #undef CYTHON_USE_TP_FINALIZE
132  #define CYTHON_USE_TP_FINALIZE 0
133 #elif defined(PYSTON_VERSION)
134  #define CYTHON_COMPILING_IN_PYPY 0
135  #define CYTHON_COMPILING_IN_PYSTON 1
136  #define CYTHON_COMPILING_IN_CPYTHON 0
137  #ifndef CYTHON_USE_TYPE_SLOTS
138  #define CYTHON_USE_TYPE_SLOTS 1
139  #endif
140  #undef CYTHON_USE_PYTYPE_LOOKUP
141  #define CYTHON_USE_PYTYPE_LOOKUP 0
142  #undef CYTHON_USE_ASYNC_SLOTS
143  #define CYTHON_USE_ASYNC_SLOTS 0
144  #undef CYTHON_USE_PYLIST_INTERNALS
145  #define CYTHON_USE_PYLIST_INTERNALS 0
146  #ifndef CYTHON_USE_UNICODE_INTERNALS
147  #define CYTHON_USE_UNICODE_INTERNALS 1
148  #endif
149  #undef CYTHON_USE_UNICODE_WRITER
150  #define CYTHON_USE_UNICODE_WRITER 0
151  #undef CYTHON_USE_PYLONG_INTERNALS
152  #define CYTHON_USE_PYLONG_INTERNALS 0
153  #ifndef CYTHON_AVOID_BORROWED_REFS
154  #define CYTHON_AVOID_BORROWED_REFS 0
155  #endif
156  #ifndef CYTHON_ASSUME_SAFE_MACROS
157  #define CYTHON_ASSUME_SAFE_MACROS 1
158  #endif
159  #ifndef CYTHON_UNPACK_METHODS
160  #define CYTHON_UNPACK_METHODS 1
161  #endif
162  #undef CYTHON_FAST_THREAD_STATE
163  #define CYTHON_FAST_THREAD_STATE 0
164  #undef CYTHON_FAST_PYCALL
165  #define CYTHON_FAST_PYCALL 0
166  #undef CYTHON_PEP489_MULTI_PHASE_INIT
167  #define CYTHON_PEP489_MULTI_PHASE_INIT 0
168  #undef CYTHON_USE_TP_FINALIZE
169  #define CYTHON_USE_TP_FINALIZE 0
170 #else
171  #define CYTHON_COMPILING_IN_PYPY 0
172  #define CYTHON_COMPILING_IN_PYSTON 0
173  #define CYTHON_COMPILING_IN_CPYTHON 1
174  #ifndef CYTHON_USE_TYPE_SLOTS
175  #define CYTHON_USE_TYPE_SLOTS 1
176  #endif
177  #if PY_VERSION_HEX < 0x02070000
178  #undef CYTHON_USE_PYTYPE_LOOKUP
179  #define CYTHON_USE_PYTYPE_LOOKUP 0
180  #elif !defined(CYTHON_USE_PYTYPE_LOOKUP)
181  #define CYTHON_USE_PYTYPE_LOOKUP 1
182  #endif
183  #if PY_MAJOR_VERSION < 3
184  #undef CYTHON_USE_ASYNC_SLOTS
185  #define CYTHON_USE_ASYNC_SLOTS 0
186  #elif !defined(CYTHON_USE_ASYNC_SLOTS)
187  #define CYTHON_USE_ASYNC_SLOTS 1
188  #endif
189  #if PY_VERSION_HEX < 0x02070000
190  #undef CYTHON_USE_PYLONG_INTERNALS
191  #define CYTHON_USE_PYLONG_INTERNALS 0
192  #elif !defined(CYTHON_USE_PYLONG_INTERNALS)
193  #define CYTHON_USE_PYLONG_INTERNALS 1
194  #endif
195  #ifndef CYTHON_USE_PYLIST_INTERNALS
196  #define CYTHON_USE_PYLIST_INTERNALS 1
197  #endif
198  #ifndef CYTHON_USE_UNICODE_INTERNALS
199  #define CYTHON_USE_UNICODE_INTERNALS 1
200  #endif
201  #if PY_VERSION_HEX < 0x030300F0
202  #undef CYTHON_USE_UNICODE_WRITER
203  #define CYTHON_USE_UNICODE_WRITER 0
204  #elif !defined(CYTHON_USE_UNICODE_WRITER)
205  #define CYTHON_USE_UNICODE_WRITER 1
206  #endif
207  #ifndef CYTHON_AVOID_BORROWED_REFS
208  #define CYTHON_AVOID_BORROWED_REFS 0
209  #endif
210  #ifndef CYTHON_ASSUME_SAFE_MACROS
211  #define CYTHON_ASSUME_SAFE_MACROS 1
212  #endif
213  #ifndef CYTHON_UNPACK_METHODS
214  #define CYTHON_UNPACK_METHODS 1
215  #endif
216  #ifndef CYTHON_FAST_THREAD_STATE
217  #define CYTHON_FAST_THREAD_STATE 1
218  #endif
219  #ifndef CYTHON_FAST_PYCALL
220  #define CYTHON_FAST_PYCALL 1
221  #endif
222  #ifndef CYTHON_PEP489_MULTI_PHASE_INIT
223  #define CYTHON_PEP489_MULTI_PHASE_INIT (0 && PY_VERSION_HEX >= 0x03050000)
224  #endif
225  #ifndef CYTHON_USE_TP_FINALIZE
226  #define CYTHON_USE_TP_FINALIZE (PY_VERSION_HEX >= 0x030400a1)
227  #endif
228 #endif
229 #if !defined(CYTHON_FAST_PYCCALL)
230 #define CYTHON_FAST_PYCCALL (CYTHON_FAST_PYCALL && PY_VERSION_HEX >= 0x030600B1)
231 #endif
232 #if CYTHON_USE_PYLONG_INTERNALS
233  #include "longintrepr.h"
234  #undef SHIFT
235  #undef BASE
236  #undef MASK
237 #endif
238 #ifndef __has_attribute
239  #define __has_attribute(x) 0
240 #endif
241 #ifndef __has_cpp_attribute
242  #define __has_cpp_attribute(x) 0
243 #endif
244 #ifndef CYTHON_RESTRICT
245  #if defined(__GNUC__)
246  #define CYTHON_RESTRICT __restrict__
247  #elif defined(_MSC_VER) && _MSC_VER >= 1400
248  #define CYTHON_RESTRICT __restrict
249  #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
250  #define CYTHON_RESTRICT restrict
251  #else
252  #define CYTHON_RESTRICT
253  #endif
254 #endif
255 #ifndef CYTHON_UNUSED
256 # if defined(__GNUC__)
257 # if !(defined(__cplusplus)) || (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 4))
258 # define CYTHON_UNUSED __attribute__ ((__unused__))
259 # else
260 # define CYTHON_UNUSED
261 # endif
262 # elif defined(__ICC) || (defined(__INTEL_COMPILER) && !defined(_MSC_VER))
263 # define CYTHON_UNUSED __attribute__ ((__unused__))
264 # else
265 # define CYTHON_UNUSED
266 # endif
267 #endif
268 #ifndef CYTHON_MAYBE_UNUSED_VAR
269 # if defined(__cplusplus)
270  template<class T> void CYTHON_MAYBE_UNUSED_VAR( const T& ) { }
271 # else
272 # define CYTHON_MAYBE_UNUSED_VAR(x) (void)(x)
273 # endif
274 #endif
275 #ifndef CYTHON_NCP_UNUSED
276 # if CYTHON_COMPILING_IN_CPYTHON
277 # define CYTHON_NCP_UNUSED
278 # else
279 # define CYTHON_NCP_UNUSED CYTHON_UNUSED
280 # endif
281 #endif
282 #define __Pyx_void_to_None(void_result) ((void)(void_result), Py_INCREF(Py_None), Py_None)
283 #ifdef _MSC_VER
284  #ifndef _MSC_STDINT_H_
285  #if _MSC_VER < 1300
286  typedef unsigned char uint8_t;
287  typedef unsigned int uint32_t;
288  #else
289  typedef unsigned __int8 uint8_t;
290  typedef unsigned __int32 uint32_t;
291  #endif
292  #endif
293 #else
294  #include <stdint.h>
295 #endif
296 #ifndef CYTHON_FALLTHROUGH
297  #if defined(__cplusplus) && __cplusplus >= 201103L
298  #if __has_cpp_attribute(fallthrough)
299  #define CYTHON_FALLTHROUGH [[fallthrough]]
300  #elif __has_cpp_attribute(clang::fallthrough)
301  #define CYTHON_FALLTHROUGH [[clang::fallthrough]]
302  #elif __has_cpp_attribute(gnu::fallthrough)
303  #define CYTHON_FALLTHROUGH [[gnu::fallthrough]]
304  #endif
305  #endif
306  #ifndef CYTHON_FALLTHROUGH
307  #if __has_attribute(fallthrough)
308  #define CYTHON_FALLTHROUGH __attribute__((fallthrough))
309  #else
310  #define CYTHON_FALLTHROUGH
311  #endif
312  #endif
313  #if defined(__clang__ ) && defined(__apple_build_version__)
314  #if __apple_build_version__ < 7000000
315  #undef CYTHON_FALLTHROUGH
316  #define CYTHON_FALLTHROUGH
317  #endif
318  #endif
319 #endif
320 
321 #ifndef __cplusplus
322  #error "Cython files generated with the C++ option must be compiled with a C++ compiler."
323 #endif
324 #ifndef CYTHON_INLINE
325  #if defined(__clang__)
326  #define CYTHON_INLINE __inline__ __attribute__ ((__unused__))
327  #else
328  #define CYTHON_INLINE inline
329  #endif
330 #endif
331 template<typename T>
332 void __Pyx_call_destructor(T& x) {
333  x.~T();
334 }
335 template<typename T>
336 class __Pyx_FakeReference {
337  public:
338  __Pyx_FakeReference() : ptr(NULL) { }
339  __Pyx_FakeReference(const T& ref) : ptr(const_cast<T*>(&ref)) { }
340  T *operator->() { return ptr; }
341  T *operator&() { return ptr; }
342  operator T&() { return *ptr; }
343  template<typename U> bool operator ==(U other) { return *ptr == other; }
344  template<typename U> bool operator !=(U other) { return *ptr != other; }
345  private:
346  T *ptr;
347 };
348 
349 #if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x02070600 && !defined(Py_OptimizeFlag)
350  #define Py_OptimizeFlag 0
351 #endif
352 #define __PYX_BUILD_PY_SSIZE_T "n"
353 #define CYTHON_FORMAT_SSIZE_T "z"
354 #if PY_MAJOR_VERSION < 3
355  #define __Pyx_BUILTIN_MODULE_NAME "__builtin__"
356  #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
357  PyCode_New(a+k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)
358  #define __Pyx_DefaultClassType PyClass_Type
359 #else
360  #define __Pyx_BUILTIN_MODULE_NAME "builtins"
361  #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
362  PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)
363  #define __Pyx_DefaultClassType PyType_Type
364 #endif
365 #ifndef Py_TPFLAGS_CHECKTYPES
366  #define Py_TPFLAGS_CHECKTYPES 0
367 #endif
368 #ifndef Py_TPFLAGS_HAVE_INDEX
369  #define Py_TPFLAGS_HAVE_INDEX 0
370 #endif
371 #ifndef Py_TPFLAGS_HAVE_NEWBUFFER
372  #define Py_TPFLAGS_HAVE_NEWBUFFER 0
373 #endif
374 #ifndef Py_TPFLAGS_HAVE_FINALIZE
375  #define Py_TPFLAGS_HAVE_FINALIZE 0
376 #endif
377 #if PY_VERSION_HEX <= 0x030700A3 || !defined(METH_FASTCALL)
378  #ifndef METH_FASTCALL
379  #define METH_FASTCALL 0x80
380  #endif
381  typedef PyObject *(*__Pyx_PyCFunctionFast) (PyObject *self, PyObject *const *args, Py_ssize_t nargs);
382  typedef PyObject *(*__Pyx_PyCFunctionFastWithKeywords) (PyObject *self, PyObject *const *args,
383  Py_ssize_t nargs, PyObject *kwnames);
384 #else
385  #define __Pyx_PyCFunctionFast _PyCFunctionFast
386  #define __Pyx_PyCFunctionFastWithKeywords _PyCFunctionFastWithKeywords
387 #endif
388 #if CYTHON_FAST_PYCCALL
389 #define __Pyx_PyFastCFunction_Check(func)\
390  ((PyCFunction_Check(func) && (METH_FASTCALL == (PyCFunction_GET_FLAGS(func) & ~(METH_CLASS | METH_STATIC | METH_COEXIST | METH_KEYWORDS)))))
391 #else
392 #define __Pyx_PyFastCFunction_Check(func) 0
393 #endif
394 #if CYTHON_COMPILING_IN_PYPY && !defined(PyObject_Malloc)
395  #define PyObject_Malloc(s) PyMem_Malloc(s)
396  #define PyObject_Free(p) PyMem_Free(p)
397  #define PyObject_Realloc(p) PyMem_Realloc(p)
398 #endif
399 #if CYTHON_COMPILING_IN_PYSTON
400  #define __Pyx_PyCode_HasFreeVars(co) PyCode_HasFreeVars(co)
401  #define __Pyx_PyFrame_SetLineNumber(frame, lineno) PyFrame_SetLineNumber(frame, lineno)
402 #else
403  #define __Pyx_PyCode_HasFreeVars(co) (PyCode_GetNumFree(co) > 0)
404  #define __Pyx_PyFrame_SetLineNumber(frame, lineno) (frame)->f_lineno = (lineno)
405 #endif
406 #if !CYTHON_FAST_THREAD_STATE || PY_VERSION_HEX < 0x02070000
407  #define __Pyx_PyThreadState_Current PyThreadState_GET()
408 #elif PY_VERSION_HEX >= 0x03060000
409  #define __Pyx_PyThreadState_Current _PyThreadState_UncheckedGet()
410 #elif PY_VERSION_HEX >= 0x03000000
411  #define __Pyx_PyThreadState_Current PyThreadState_GET()
412 #else
413  #define __Pyx_PyThreadState_Current _PyThreadState_Current
414 #endif
415 #if PY_VERSION_HEX < 0x030700A2 && !defined(PyThread_tss_create) && !defined(Py_tss_NEEDS_INIT)
416 #include "pythread.h"
417 #define Py_tss_NEEDS_INIT 0
418 typedef int Py_tss_t;
419 static CYTHON_INLINE int PyThread_tss_create(Py_tss_t *key) {
420  *key = PyThread_create_key();
421  return 0; // PyThread_create_key reports success always
422 }
423 static CYTHON_INLINE Py_tss_t * PyThread_tss_alloc(void) {
424  Py_tss_t *key = (Py_tss_t *)PyObject_Malloc(sizeof(Py_tss_t));
425  *key = Py_tss_NEEDS_INIT;
426  return key;
427 }
428 static CYTHON_INLINE void PyThread_tss_free(Py_tss_t *key) {
429  PyObject_Free(key);
430 }
431 static CYTHON_INLINE int PyThread_tss_is_created(Py_tss_t *key) {
432  return *key != Py_tss_NEEDS_INIT;
433 }
434 static CYTHON_INLINE void PyThread_tss_delete(Py_tss_t *key) {
435  PyThread_delete_key(*key);
436  *key = Py_tss_NEEDS_INIT;
437 }
438 static CYTHON_INLINE int PyThread_tss_set(Py_tss_t *key, void *value) {
439  return PyThread_set_key_value(*key, value);
440 }
441 static CYTHON_INLINE void * PyThread_tss_get(Py_tss_t *key) {
442  return PyThread_get_key_value(*key);
443 }
444 #endif // TSS (Thread Specific Storage) API
445 #if CYTHON_COMPILING_IN_CPYTHON || defined(_PyDict_NewPresized)
446 #define __Pyx_PyDict_NewPresized(n) ((n <= 8) ? PyDict_New() : _PyDict_NewPresized(n))
447 #else
448 #define __Pyx_PyDict_NewPresized(n) PyDict_New()
449 #endif
450 #if PY_MAJOR_VERSION >= 3 || CYTHON_FUTURE_DIVISION
451  #define __Pyx_PyNumber_Divide(x,y) PyNumber_TrueDivide(x,y)
452  #define __Pyx_PyNumber_InPlaceDivide(x,y) PyNumber_InPlaceTrueDivide(x,y)
453 #else
454  #define __Pyx_PyNumber_Divide(x,y) PyNumber_Divide(x,y)
455  #define __Pyx_PyNumber_InPlaceDivide(x,y) PyNumber_InPlaceDivide(x,y)
456 #endif
457 #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030500A1 && CYTHON_USE_UNICODE_INTERNALS
458 #define __Pyx_PyDict_GetItemStr(dict, name) _PyDict_GetItem_KnownHash(dict, name, ((PyASCIIObject *) name)->hash)
459 #else
460 #define __Pyx_PyDict_GetItemStr(dict, name) PyDict_GetItem(dict, name)
461 #endif
462 #if PY_VERSION_HEX > 0x03030000 && defined(PyUnicode_KIND)
463  #define CYTHON_PEP393_ENABLED 1
464  #define __Pyx_PyUnicode_READY(op) (likely(PyUnicode_IS_READY(op)) ?\
465  0 : _PyUnicode_Ready((PyObject *)(op)))
466  #define __Pyx_PyUnicode_GET_LENGTH(u) PyUnicode_GET_LENGTH(u)
467  #define __Pyx_PyUnicode_READ_CHAR(u, i) PyUnicode_READ_CHAR(u, i)
468  #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u) PyUnicode_MAX_CHAR_VALUE(u)
469  #define __Pyx_PyUnicode_KIND(u) PyUnicode_KIND(u)
470  #define __Pyx_PyUnicode_DATA(u) PyUnicode_DATA(u)
471  #define __Pyx_PyUnicode_READ(k, d, i) PyUnicode_READ(k, d, i)
472  #define __Pyx_PyUnicode_WRITE(k, d, i, ch) PyUnicode_WRITE(k, d, i, ch)
473  #define __Pyx_PyUnicode_IS_TRUE(u) (0 != (likely(PyUnicode_IS_READY(u)) ? PyUnicode_GET_LENGTH(u) : PyUnicode_GET_SIZE(u)))
474 #else
475  #define CYTHON_PEP393_ENABLED 0
476  #define PyUnicode_1BYTE_KIND 1
477  #define PyUnicode_2BYTE_KIND 2
478  #define PyUnicode_4BYTE_KIND 4
479  #define __Pyx_PyUnicode_READY(op) (0)
480  #define __Pyx_PyUnicode_GET_LENGTH(u) PyUnicode_GET_SIZE(u)
481  #define __Pyx_PyUnicode_READ_CHAR(u, i) ((Py_UCS4)(PyUnicode_AS_UNICODE(u)[i]))
482  #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u) ((sizeof(Py_UNICODE) == 2) ? 65535 : 1114111)
483  #define __Pyx_PyUnicode_KIND(u) (sizeof(Py_UNICODE))
484  #define __Pyx_PyUnicode_DATA(u) ((void*)PyUnicode_AS_UNICODE(u))
485  #define __Pyx_PyUnicode_READ(k, d, i) ((void)(k), (Py_UCS4)(((Py_UNICODE*)d)[i]))
486  #define __Pyx_PyUnicode_WRITE(k, d, i, ch) (((void)(k)), ((Py_UNICODE*)d)[i] = ch)
487  #define __Pyx_PyUnicode_IS_TRUE(u) (0 != PyUnicode_GET_SIZE(u))
488 #endif
489 #if CYTHON_COMPILING_IN_PYPY
490  #define __Pyx_PyUnicode_Concat(a, b) PyNumber_Add(a, b)
491  #define __Pyx_PyUnicode_ConcatSafe(a, b) PyNumber_Add(a, b)
492 #else
493  #define __Pyx_PyUnicode_Concat(a, b) PyUnicode_Concat(a, b)
494  #define __Pyx_PyUnicode_ConcatSafe(a, b) ((unlikely((a) == Py_None) || unlikely((b) == Py_None)) ?\
495  PyNumber_Add(a, b) : __Pyx_PyUnicode_Concat(a, b))
496 #endif
497 #if CYTHON_COMPILING_IN_PYPY && !defined(PyUnicode_Contains)
498  #define PyUnicode_Contains(u, s) PySequence_Contains(u, s)
499 #endif
500 #if CYTHON_COMPILING_IN_PYPY && !defined(PyByteArray_Check)
501  #define PyByteArray_Check(obj) PyObject_TypeCheck(obj, &PyByteArray_Type)
502 #endif
503 #if CYTHON_COMPILING_IN_PYPY && !defined(PyObject_Format)
504  #define PyObject_Format(obj, fmt) PyObject_CallMethod(obj, "__format__", "O", fmt)
505 #endif
506 #define __Pyx_PyString_FormatSafe(a, b) ((unlikely((a) == Py_None)) ? PyNumber_Remainder(a, b) : __Pyx_PyString_Format(a, b))
507 #define __Pyx_PyUnicode_FormatSafe(a, b) ((unlikely((a) == Py_None)) ? PyNumber_Remainder(a, b) : PyUnicode_Format(a, b))
508 #if PY_MAJOR_VERSION >= 3
509  #define __Pyx_PyString_Format(a, b) PyUnicode_Format(a, b)
510 #else
511  #define __Pyx_PyString_Format(a, b) PyString_Format(a, b)
512 #endif
513 #if PY_MAJOR_VERSION < 3 && !defined(PyObject_ASCII)
514  #define PyObject_ASCII(o) PyObject_Repr(o)
515 #endif
516 #if PY_MAJOR_VERSION >= 3
517  #define PyBaseString_Type PyUnicode_Type
518  #define PyStringObject PyUnicodeObject
519  #define PyString_Type PyUnicode_Type
520  #define PyString_Check PyUnicode_Check
521  #define PyString_CheckExact PyUnicode_CheckExact
522  #define PyObject_Unicode PyObject_Str
523 #endif
524 #if PY_MAJOR_VERSION >= 3
525  #define __Pyx_PyBaseString_Check(obj) PyUnicode_Check(obj)
526  #define __Pyx_PyBaseString_CheckExact(obj) PyUnicode_CheckExact(obj)
527 #else
528  #define __Pyx_PyBaseString_Check(obj) (PyString_Check(obj) || PyUnicode_Check(obj))
529  #define __Pyx_PyBaseString_CheckExact(obj) (PyString_CheckExact(obj) || PyUnicode_CheckExact(obj))
530 #endif
531 #ifndef PySet_CheckExact
532  #define PySet_CheckExact(obj) (Py_TYPE(obj) == &PySet_Type)
533 #endif
534 #if CYTHON_ASSUME_SAFE_MACROS
535  #define __Pyx_PySequence_SIZE(seq) Py_SIZE(seq)
536 #else
537  #define __Pyx_PySequence_SIZE(seq) PySequence_Size(seq)
538 #endif
539 #if PY_MAJOR_VERSION >= 3
540  #define PyIntObject PyLongObject
541  #define PyInt_Type PyLong_Type
542  #define PyInt_Check(op) PyLong_Check(op)
543  #define PyInt_CheckExact(op) PyLong_CheckExact(op)
544  #define PyInt_FromString PyLong_FromString
545  #define PyInt_FromUnicode PyLong_FromUnicode
546  #define PyInt_FromLong PyLong_FromLong
547  #define PyInt_FromSize_t PyLong_FromSize_t
548  #define PyInt_FromSsize_t PyLong_FromSsize_t
549  #define PyInt_AsLong PyLong_AsLong
550  #define PyInt_AS_LONG PyLong_AS_LONG
551  #define PyInt_AsSsize_t PyLong_AsSsize_t
552  #define PyInt_AsUnsignedLongMask PyLong_AsUnsignedLongMask
553  #define PyInt_AsUnsignedLongLongMask PyLong_AsUnsignedLongLongMask
554  #define PyNumber_Int PyNumber_Long
555 #endif
556 #if PY_MAJOR_VERSION >= 3
557  #define PyBoolObject PyLongObject
558 #endif
559 #if PY_MAJOR_VERSION >= 3 && CYTHON_COMPILING_IN_PYPY
560  #ifndef PyUnicode_InternFromString
561  #define PyUnicode_InternFromString(s) PyUnicode_FromString(s)
562  #endif
563 #endif
564 #if PY_VERSION_HEX < 0x030200A4
565  typedef long Py_hash_t;
566  #define __Pyx_PyInt_FromHash_t PyInt_FromLong
567  #define __Pyx_PyInt_AsHash_t PyInt_AsLong
568 #else
569  #define __Pyx_PyInt_FromHash_t PyInt_FromSsize_t
570  #define __Pyx_PyInt_AsHash_t PyInt_AsSsize_t
571 #endif
572 #if PY_MAJOR_VERSION >= 3
573  #define __Pyx_PyMethod_New(func, self, klass) ((self) ? PyMethod_New(func, self) : (Py_INCREF(func), func))
574 #else
575  #define __Pyx_PyMethod_New(func, self, klass) PyMethod_New(func, self, klass)
576 #endif
577 #if CYTHON_USE_ASYNC_SLOTS
578  #if PY_VERSION_HEX >= 0x030500B1
579  #define __Pyx_PyAsyncMethodsStruct PyAsyncMethods
580  #define __Pyx_PyType_AsAsync(obj) (Py_TYPE(obj)->tp_as_async)
581  #else
582  #define __Pyx_PyType_AsAsync(obj) ((__Pyx_PyAsyncMethodsStruct*) (Py_TYPE(obj)->tp_reserved))
583  #endif
584 #else
585  #define __Pyx_PyType_AsAsync(obj) NULL
586 #endif
587 #ifndef __Pyx_PyAsyncMethodsStruct
588  typedef struct {
589  unaryfunc am_await;
590  unaryfunc am_aiter;
591  unaryfunc am_anext;
592  } __Pyx_PyAsyncMethodsStruct;
593 #endif
594 
595 #if defined(WIN32) || defined(MS_WINDOWS)
596  #define _USE_MATH_DEFINES
597 #endif
598 #include <math.h>
599 #ifdef NAN
600 #define __PYX_NAN() ((float) NAN)
601 #else
602 static CYTHON_INLINE float __PYX_NAN() {
603  float value;
604  memset(&value, 0xFF, sizeof(value));
605  return value;
606 }
607 #endif
608 #if defined(__CYGWIN__) && defined(_LDBL_EQ_DBL)
609 #define __Pyx_truncl trunc
610 #else
611 #define __Pyx_truncl truncl
612 #endif
613 
614 
615 #define __PYX_ERR(f_index, lineno, Ln_error) \
616 { \
617  __pyx_filename = __pyx_f[f_index]; __pyx_lineno = lineno; __pyx_clineno = __LINE__; goto Ln_error; \
618 }
619 
620 #ifndef __PYX_EXTERN_C
621  #ifdef __cplusplus
622  #define __PYX_EXTERN_C extern "C"
623  #else
624  #define __PYX_EXTERN_C extern
625  #endif
626 #endif
627 
628 #define __PYX_HAVE__PyClical
629 #define __PYX_HAVE_API__PyClical
630 /* Early includes */
631 #include "ios"
632 #include "new"
633 #include "stdexcept"
634 #include "typeinfo"
635 #include <vector>
636 #include "PyClical.h"
637 #ifdef _OPENMP
638 #include <omp.h>
639 #endif /* _OPENMP */
640 
641 #if defined(PYREX_WITHOUT_ASSERTIONS) && !defined(CYTHON_WITHOUT_ASSERTIONS)
642 #define CYTHON_WITHOUT_ASSERTIONS
643 #endif
644 
645 typedef struct {PyObject **p; const char *s; const Py_ssize_t n; const char* encoding;
646  const char is_unicode; const char is_str; const char intern; } __Pyx_StringTabEntry;
647 
648 #define __PYX_DEFAULT_STRING_ENCODING_IS_ASCII 0
649 #define __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT 0
650 #define __PYX_DEFAULT_STRING_ENCODING ""
651 #define __Pyx_PyObject_FromString __Pyx_PyBytes_FromString
652 #define __Pyx_PyObject_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
653 #define __Pyx_uchar_cast(c) ((unsigned char)c)
654 #define __Pyx_long_cast(x) ((long)x)
655 #define __Pyx_fits_Py_ssize_t(v, type, is_signed) (\
656  (sizeof(type) < sizeof(Py_ssize_t)) ||\
657  (sizeof(type) > sizeof(Py_ssize_t) &&\
658  likely(v < (type)PY_SSIZE_T_MAX ||\
659  v == (type)PY_SSIZE_T_MAX) &&\
660  (!is_signed || likely(v > (type)PY_SSIZE_T_MIN ||\
661  v == (type)PY_SSIZE_T_MIN))) ||\
662  (sizeof(type) == sizeof(Py_ssize_t) &&\
663  (is_signed || likely(v < (type)PY_SSIZE_T_MAX ||\
664  v == (type)PY_SSIZE_T_MAX))) )
665 #if defined (__cplusplus) && __cplusplus >= 201103L
666  #include <cstdlib>
667  #define __Pyx_sst_abs(value) std::abs(value)
668 #elif SIZEOF_INT >= SIZEOF_SIZE_T
669  #define __Pyx_sst_abs(value) abs(value)
670 #elif SIZEOF_LONG >= SIZEOF_SIZE_T
671  #define __Pyx_sst_abs(value) labs(value)
672 #elif defined (_MSC_VER)
673  #define __Pyx_sst_abs(value) ((Py_ssize_t)_abs64(value))
674 #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
675  #define __Pyx_sst_abs(value) llabs(value)
676 #elif defined (__GNUC__)
677  #define __Pyx_sst_abs(value) __builtin_llabs(value)
678 #else
679  #define __Pyx_sst_abs(value) ((value<0) ? -value : value)
680 #endif
681 static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject*);
682 static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject*, Py_ssize_t* length);
683 #define __Pyx_PyByteArray_FromString(s) PyByteArray_FromStringAndSize((const char*)s, strlen((const char*)s))
684 #define __Pyx_PyByteArray_FromStringAndSize(s, l) PyByteArray_FromStringAndSize((const char*)s, l)
685 #define __Pyx_PyBytes_FromString PyBytes_FromString
686 #define __Pyx_PyBytes_FromStringAndSize PyBytes_FromStringAndSize
687 static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char*);
688 #if PY_MAJOR_VERSION < 3
689  #define __Pyx_PyStr_FromString __Pyx_PyBytes_FromString
690  #define __Pyx_PyStr_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
691 #else
692  #define __Pyx_PyStr_FromString __Pyx_PyUnicode_FromString
693  #define __Pyx_PyStr_FromStringAndSize __Pyx_PyUnicode_FromStringAndSize
694 #endif
695 #define __Pyx_PyBytes_AsWritableString(s) ((char*) PyBytes_AS_STRING(s))
696 #define __Pyx_PyBytes_AsWritableSString(s) ((signed char*) PyBytes_AS_STRING(s))
697 #define __Pyx_PyBytes_AsWritableUString(s) ((unsigned char*) PyBytes_AS_STRING(s))
698 #define __Pyx_PyBytes_AsString(s) ((const char*) PyBytes_AS_STRING(s))
699 #define __Pyx_PyBytes_AsSString(s) ((const signed char*) PyBytes_AS_STRING(s))
700 #define __Pyx_PyBytes_AsUString(s) ((const unsigned char*) PyBytes_AS_STRING(s))
701 #define __Pyx_PyObject_AsWritableString(s) ((char*) __Pyx_PyObject_AsString(s))
702 #define __Pyx_PyObject_AsWritableSString(s) ((signed char*) __Pyx_PyObject_AsString(s))
703 #define __Pyx_PyObject_AsWritableUString(s) ((unsigned char*) __Pyx_PyObject_AsString(s))
704 #define __Pyx_PyObject_AsSString(s) ((const signed char*) __Pyx_PyObject_AsString(s))
705 #define __Pyx_PyObject_AsUString(s) ((const unsigned char*) __Pyx_PyObject_AsString(s))
706 #define __Pyx_PyObject_FromCString(s) __Pyx_PyObject_FromString((const char*)s)
707 #define __Pyx_PyBytes_FromCString(s) __Pyx_PyBytes_FromString((const char*)s)
708 #define __Pyx_PyByteArray_FromCString(s) __Pyx_PyByteArray_FromString((const char*)s)
709 #define __Pyx_PyStr_FromCString(s) __Pyx_PyStr_FromString((const char*)s)
710 #define __Pyx_PyUnicode_FromCString(s) __Pyx_PyUnicode_FromString((const char*)s)
711 static CYTHON_INLINE size_t __Pyx_Py_UNICODE_strlen(const Py_UNICODE *u) {
712  const Py_UNICODE *u_end = u;
713  while (*u_end++) ;
714  return (size_t)(u_end - u - 1);
715 }
716 #define __Pyx_PyUnicode_FromUnicode(u) PyUnicode_FromUnicode(u, __Pyx_Py_UNICODE_strlen(u))
717 #define __Pyx_PyUnicode_FromUnicodeAndLength PyUnicode_FromUnicode
718 #define __Pyx_PyUnicode_AsUnicode PyUnicode_AsUnicode
719 #define __Pyx_NewRef(obj) (Py_INCREF(obj), obj)
720 #define __Pyx_Owned_Py_None(b) __Pyx_NewRef(Py_None)
721 static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b);
722 static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*);
723 static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x);
724 #define __Pyx_PySequence_Tuple(obj)\
725  (likely(PyTuple_CheckExact(obj)) ? __Pyx_NewRef(obj) : PySequence_Tuple(obj))
726 static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject*);
727 static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t);
728 #if CYTHON_ASSUME_SAFE_MACROS
729 #define __pyx_PyFloat_AsDouble(x) (PyFloat_CheckExact(x) ? PyFloat_AS_DOUBLE(x) : PyFloat_AsDouble(x))
730 #else
731 #define __pyx_PyFloat_AsDouble(x) PyFloat_AsDouble(x)
732 #endif
733 #define __pyx_PyFloat_AsFloat(x) ((float) __pyx_PyFloat_AsDouble(x))
734 #if PY_MAJOR_VERSION >= 3
735 #define __Pyx_PyNumber_Int(x) (PyLong_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Long(x))
736 #else
737 #define __Pyx_PyNumber_Int(x) (PyInt_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Int(x))
738 #endif
739 #define __Pyx_PyNumber_Float(x) (PyFloat_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Float(x))
740 #if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
741 static int __Pyx_sys_getdefaultencoding_not_ascii;
742 static int __Pyx_init_sys_getdefaultencoding_params(void) {
743  PyObject* sys;
744  PyObject* default_encoding = NULL;
745  PyObject* ascii_chars_u = NULL;
746  PyObject* ascii_chars_b = NULL;
747  const char* default_encoding_c;
748  sys = PyImport_ImportModule("sys");
749  if (!sys) goto bad;
750  default_encoding = PyObject_CallMethod(sys, (char*) "getdefaultencoding", NULL);
751  Py_DECREF(sys);
752  if (!default_encoding) goto bad;
753  default_encoding_c = PyBytes_AsString(default_encoding);
754  if (!default_encoding_c) goto bad;
755  if (strcmp(default_encoding_c, "ascii") == 0) {
756  __Pyx_sys_getdefaultencoding_not_ascii = 0;
757  } else {
758  char ascii_chars[128];
759  int c;
760  for (c = 0; c < 128; c++) {
761  ascii_chars[c] = c;
762  }
763  __Pyx_sys_getdefaultencoding_not_ascii = 1;
764  ascii_chars_u = PyUnicode_DecodeASCII(ascii_chars, 128, NULL);
765  if (!ascii_chars_u) goto bad;
766  ascii_chars_b = PyUnicode_AsEncodedString(ascii_chars_u, default_encoding_c, NULL);
767  if (!ascii_chars_b || !PyBytes_Check(ascii_chars_b) || memcmp(ascii_chars, PyBytes_AS_STRING(ascii_chars_b), 128) != 0) {
768  PyErr_Format(
769  PyExc_ValueError,
770  "This module compiled with c_string_encoding=ascii, but default encoding '%.200s' is not a superset of ascii.",
771  default_encoding_c);
772  goto bad;
773  }
774  Py_DECREF(ascii_chars_u);
775  Py_DECREF(ascii_chars_b);
776  }
777  Py_DECREF(default_encoding);
778  return 0;
779 bad:
780  Py_XDECREF(default_encoding);
781  Py_XDECREF(ascii_chars_u);
782  Py_XDECREF(ascii_chars_b);
783  return -1;
784 }
785 #endif
786 #if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT && PY_MAJOR_VERSION >= 3
787 #define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_DecodeUTF8(c_str, size, NULL)
788 #else
789 #define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_Decode(c_str, size, __PYX_DEFAULT_STRING_ENCODING, NULL)
790 #if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
791 static char* __PYX_DEFAULT_STRING_ENCODING;
792 static int __Pyx_init_sys_getdefaultencoding_params(void) {
793  PyObject* sys;
794  PyObject* default_encoding = NULL;
795  char* default_encoding_c;
796  sys = PyImport_ImportModule("sys");
797  if (!sys) goto bad;
798  default_encoding = PyObject_CallMethod(sys, (char*) (const char*) "getdefaultencoding", NULL);
799  Py_DECREF(sys);
800  if (!default_encoding) goto bad;
801  default_encoding_c = PyBytes_AsString(default_encoding);
802  if (!default_encoding_c) goto bad;
803  __PYX_DEFAULT_STRING_ENCODING = (char*) malloc(strlen(default_encoding_c));
804  if (!__PYX_DEFAULT_STRING_ENCODING) goto bad;
805  strcpy(__PYX_DEFAULT_STRING_ENCODING, default_encoding_c);
806  Py_DECREF(default_encoding);
807  return 0;
808 bad:
809  Py_XDECREF(default_encoding);
810  return -1;
811 }
812 #endif
813 #endif
814 
815 
816 /* Test for GCC > 2.95 */
817 #if defined(__GNUC__) && (__GNUC__ > 2 || (__GNUC__ == 2 && (__GNUC_MINOR__ > 95)))
818  #define likely(x) __builtin_expect(!!(x), 1)
819  #define unlikely(x) __builtin_expect(!!(x), 0)
820 #else /* !__GNUC__ or GCC < 2.95 */
821  #define likely(x) (x)
822  #define unlikely(x) (x)
823 #endif /* __GNUC__ */
824 static CYTHON_INLINE void __Pyx_pretend_to_initialize(void* ptr) { (void)ptr; }
825 
826 static PyObject *__pyx_m = NULL;
827 static PyObject *__pyx_d;
828 static PyObject *__pyx_b;
829 static PyObject *__pyx_cython_runtime = NULL;
830 static PyObject *__pyx_empty_tuple;
831 static PyObject *__pyx_empty_bytes;
832 static PyObject *__pyx_empty_unicode;
833 static int __pyx_lineno;
834 static int __pyx_clineno = 0;
835 static const char * __pyx_cfilenm= __FILE__;
836 static const char *__pyx_filename;
837 
838 
839 static const char *__pyx_f[] = {
840  "PyClical.pyx",
841  "stringsource",
842 };
843 
844 /*--- Type declarations ---*/
845 struct __pyx_obj_8PyClical_index_set;
846 struct __pyx_obj_8PyClical_clifford;
847 struct __pyx_obj_8PyClical___pyx_scope_struct____iter__;
848 struct __pyx_opt_args_8PyClical_sqrt;
849 struct __pyx_opt_args_8PyClical_log;
850 struct __pyx_opt_args_8PyClical_cos;
851 struct __pyx_opt_args_8PyClical_acos;
852 struct __pyx_opt_args_8PyClical_acosh;
853 struct __pyx_opt_args_8PyClical_sin;
854 struct __pyx_opt_args_8PyClical_asin;
855 struct __pyx_opt_args_8PyClical_asinh;
856 struct __pyx_opt_args_8PyClical_tan;
857 struct __pyx_opt_args_8PyClical_atan;
858 struct __pyx_opt_args_8PyClical_atanh;
859 struct __pyx_opt_args_8PyClical_random_clifford;
860 
861 /* "PyClical.pyx":1542
862  * return clifford().wrap( glucat.complexifier(toClifford(obj)) )
863  *
864  * cpdef inline sqrt(obj, i = None): # <<<<<<<<<<<<<<
865  * """
866  * Square root of multivector with optional complexifier.
867  */
868 struct __pyx_opt_args_8PyClical_sqrt {
869  int __pyx_n;
870  PyObject *i;
871 };
872 
873 /* "PyClical.pyx":1579
874  * return clifford().wrap( glucat.exp(toClifford(obj)) )
875  *
876  * cpdef inline log(obj,i = None): # <<<<<<<<<<<<<<
877  * """
878  * Natural logarithm of multivector with optional complexifier.
879  */
880 struct __pyx_opt_args_8PyClical_log {
881  int __pyx_n;
882  PyObject *i;
883 };
884 
885 /* "PyClical.pyx":1602
886  * return clifford().wrap( glucat.log(toClifford(obj)) )
887  *
888  * cpdef inline cos(obj,i = None): # <<<<<<<<<<<<<<
889  * """
890  * Cosine of multivector with optional complexifier.
891  */
892 struct __pyx_opt_args_8PyClical_cos {
893  int __pyx_n;
894  PyObject *i;
895 };
896 
897 /* "PyClical.pyx":1619
898  * return clifford().wrap( glucat.cos(toClifford(obj)) )
899  *
900  * cpdef inline acos(obj,i = None): # <<<<<<<<<<<<<<
901  * """
902  * Inverse cosine of multivector with optional complexifier.
903  */
904 struct __pyx_opt_args_8PyClical_acos {
905  int __pyx_n;
906  PyObject *i;
907 };
908 
909 /* "PyClical.pyx":1656
910  * return clifford().wrap( glucat.cosh(toClifford(obj)) )
911  *
912  * cpdef inline acosh(obj,i = None): # <<<<<<<<<<<<<<
913  * """
914  * Inverse hyperbolic cosine of multivector with optional complexifier.
915  */
916 struct __pyx_opt_args_8PyClical_acosh {
917  int __pyx_n;
918  PyObject *i;
919 };
920 
921 /* "PyClical.pyx":1679
922  * return clifford().wrap( glucat.acosh(toClifford(obj)) )
923  *
924  * cpdef inline sin(obj,i = None): # <<<<<<<<<<<<<<
925  * """
926  * Sine of multivector with optional complexifier.
927  */
928 struct __pyx_opt_args_8PyClical_sin {
929  int __pyx_n;
930  PyObject *i;
931 };
932 
933 /* "PyClical.pyx":1698
934  * return clifford().wrap( glucat.sin(toClifford(obj)) )
935  *
936  * cpdef inline asin(obj,i = None): # <<<<<<<<<<<<<<
937  * """
938  * Inverse sine of multivector with optional complexifier.
939  */
940 struct __pyx_opt_args_8PyClical_asin {
941  int __pyx_n;
942  PyObject *i;
943 };
944 
945 /* "PyClical.pyx":1733
946  * return clifford().wrap( glucat.sinh(toClifford(obj)) )
947  *
948  * cpdef inline asinh(obj,i = None): # <<<<<<<<<<<<<<
949  * """
950  * Inverse hyperbolic sine of multivector with optional complexifier.
951  */
952 struct __pyx_opt_args_8PyClical_asinh {
953  int __pyx_n;
954  PyObject *i;
955 };
956 
957 /* "PyClical.pyx":1752
958  * return clifford().wrap( glucat.asinh(toClifford(obj)) )
959  *
960  * cpdef inline tan(obj,i = None): # <<<<<<<<<<<<<<
961  * """
962  * Tangent of multivector with optional complexifier.
963  */
964 struct __pyx_opt_args_8PyClical_tan {
965  int __pyx_n;
966  PyObject *i;
967 };
968 
969 /* "PyClical.pyx":1769
970  * return clifford().wrap( glucat.tan(toClifford(obj)) )
971  *
972  * cpdef inline atan(obj,i = None): # <<<<<<<<<<<<<<
973  * """
974  * Inverse tangent of multivector with optional complexifier.
975  */
976 struct __pyx_opt_args_8PyClical_atan {
977  int __pyx_n;
978  PyObject *i;
979 };
980 
981 /* "PyClical.pyx":1798
982  * return clifford().wrap( glucat.tanh(toClifford(obj)) )
983  *
984  * cpdef inline atanh(obj,i = None): # <<<<<<<<<<<<<<
985  * """
986  * Inverse hyperbolic tangent of multivector with optional complexifier.
987  */
988 struct __pyx_opt_args_8PyClical_atanh {
989  int __pyx_n;
990  PyObject *i;
991 };
992 
993 /* "PyClical.pyx":1815
994  * return clifford().wrap( glucat.atanh(toClifford(obj)) )
995  *
996  * cpdef inline random_clifford(index_set ixt, fill = 1.0): # <<<<<<<<<<<<<<
997  * """
998  * Random multivector within a frame.
999  */
1000 struct __pyx_opt_args_8PyClical_random_clifford {
1001  int __pyx_n;
1002  PyObject *fill;
1003 };
1004 
1005 /* "PyClical.pyx":37
1006  *
1007  * # Forward reference
1008  * cdef class index_set # <<<<<<<<<<<<<<
1009  *
1010  * cdef inline IndexSet toIndexSet(obj):
1011  */
1012 struct __pyx_obj_8PyClical_index_set {
1013  PyObject_HEAD
1014  struct __pyx_vtabstruct_8PyClical_index_set *__pyx_vtab;
1015  IndexSet *instance;
1016 };
1017 
1018 
1019 /* "PyClical.pyx":530
1020  *
1021  * # Forward reference.
1022  * cdef class clifford # <<<<<<<<<<<<<<
1023  *
1024  * cdef inline Clifford toClifford(obj):
1025  */
1026 struct __pyx_obj_8PyClical_clifford {
1027  PyObject_HEAD
1028  struct __pyx_vtabstruct_8PyClical_clifford *__pyx_vtab;
1029  Clifford *instance;
1030 };
1031 
1032 
1033 /* "PyClical.pyx":227
1034  * return self.instance.getitem(idx)
1035  *
1036  * def __iter__(self): # <<<<<<<<<<<<<<
1037  * """
1038  * Iterate over the indices of an index_set.
1039  */
1040 struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ {
1041  PyObject_HEAD
1042  PyObject *__pyx_v_idx;
1043  struct __pyx_obj_8PyClical_index_set *__pyx_v_self;
1044  PyObject *__pyx_t_0;
1045  Py_ssize_t __pyx_t_1;
1046  PyObject *(*__pyx_t_2)(PyObject *);
1047 };
1048 
1049 
1050 
1051 /* "PyClical.pyx":45
1052  * return index_set(obj).instance[0]
1053  *
1054  * cdef class index_set: # <<<<<<<<<<<<<<
1055  * """
1056  * Python class index_set wraps C++ class IndexSet.
1057  */
1058 
1059 struct __pyx_vtabstruct_8PyClical_index_set {
1060  PyObject *(*wrap)(struct __pyx_obj_8PyClical_index_set *, IndexSet);
1061  IndexSet (*unwrap)(struct __pyx_obj_8PyClical_index_set *);
1062  PyObject *(*copy)(struct __pyx_obj_8PyClical_index_set *, int __pyx_skip_dispatch);
1063 };
1064 static struct __pyx_vtabstruct_8PyClical_index_set *__pyx_vtabptr_8PyClical_index_set;
1065 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_9index_set_wrap(struct __pyx_obj_8PyClical_index_set *, IndexSet);
1066 static CYTHON_INLINE IndexSet __pyx_f_8PyClical_9index_set_unwrap(struct __pyx_obj_8PyClical_index_set *);
1067 
1068 
1069 /* "PyClical.pyx":535
1070  * return clifford(obj).instance[0]
1071  *
1072  * cdef class clifford: # <<<<<<<<<<<<<<
1073  * """
1074  * Python class clifford wraps C++ class Clifford.
1075  */
1076 
1077 struct __pyx_vtabstruct_8PyClical_clifford {
1078  PyObject *(*wrap)(struct __pyx_obj_8PyClical_clifford *, Clifford);
1079  Clifford (*unwrap)(struct __pyx_obj_8PyClical_clifford *);
1080  PyObject *(*copy)(struct __pyx_obj_8PyClical_clifford *, int __pyx_skip_dispatch);
1081 };
1082 static struct __pyx_vtabstruct_8PyClical_clifford *__pyx_vtabptr_8PyClical_clifford;
1083 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_8clifford_wrap(struct __pyx_obj_8PyClical_clifford *, Clifford);
1084 static CYTHON_INLINE Clifford __pyx_f_8PyClical_8clifford_unwrap(struct __pyx_obj_8PyClical_clifford *);
1085 
1086 /* --- Runtime support code (head) --- */
1087 /* Refnanny.proto */
1088 #ifndef CYTHON_REFNANNY
1089  #define CYTHON_REFNANNY 0
1090 #endif
1091 #if CYTHON_REFNANNY
1092  typedef struct {
1093  void (*INCREF)(void*, PyObject*, int);
1094  void (*DECREF)(void*, PyObject*, int);
1095  void (*GOTREF)(void*, PyObject*, int);
1096  void (*GIVEREF)(void*, PyObject*, int);
1097  void* (*SetupContext)(const char*, int, const char*);
1098  void (*FinishContext)(void**);
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1100  static __Pyx_RefNannyAPIStruct *__Pyx_RefNanny = NULL;
1101  static __Pyx_RefNannyAPIStruct *__Pyx_RefNannyImportAPI(const char *modname);
1102  #define __Pyx_RefNannyDeclarations void *__pyx_refnanny = NULL;
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1106  PyGILState_STATE __pyx_gilstate_save = PyGILState_Ensure();\
1107  __pyx_refnanny = __Pyx_RefNanny->SetupContext((name), __LINE__, __FILE__);\
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1113  #define __Pyx_RefNannySetupContext(name, acquire_gil)\
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1115 #endif
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1118  #define __Pyx_INCREF(r) __Pyx_RefNanny->INCREF(__pyx_refnanny, (PyObject *)(r), __LINE__)
1119  #define __Pyx_DECREF(r) __Pyx_RefNanny->DECREF(__pyx_refnanny, (PyObject *)(r), __LINE__)
1120  #define __Pyx_GOTREF(r) __Pyx_RefNanny->GOTREF(__pyx_refnanny, (PyObject *)(r), __LINE__)
1121  #define __Pyx_GIVEREF(r) __Pyx_RefNanny->GIVEREF(__pyx_refnanny, (PyObject *)(r), __LINE__)
1122  #define __Pyx_XINCREF(r) do { if((r) != NULL) {__Pyx_INCREF(r); }} while(0)
1123  #define __Pyx_XDECREF(r) do { if((r) != NULL) {__Pyx_DECREF(r); }} while(0)
1124  #define __Pyx_XGOTREF(r) do { if((r) != NULL) {__Pyx_GOTREF(r); }} while(0)
1125  #define __Pyx_XGIVEREF(r) do { if((r) != NULL) {__Pyx_GIVEREF(r);}} while(0)
1126 #else
1127  #define __Pyx_RefNannyDeclarations
1128  #define __Pyx_RefNannySetupContext(name, acquire_gil)
1129  #define __Pyx_RefNannyFinishContext()
1130  #define __Pyx_INCREF(r) Py_INCREF(r)
1131  #define __Pyx_DECREF(r) Py_DECREF(r)
1132  #define __Pyx_GOTREF(r)
1133  #define __Pyx_GIVEREF(r)
1134  #define __Pyx_XINCREF(r) Py_XINCREF(r)
1135  #define __Pyx_XDECREF(r) Py_XDECREF(r)
1136  #define __Pyx_XGOTREF(r)
1137  #define __Pyx_XGIVEREF(r)
1138 #endif
1139 #define __Pyx_XDECREF_SET(r, v) do {\
1140  PyObject *tmp = (PyObject *) r;\
1141  r = v; __Pyx_XDECREF(tmp);\
1142  } while (0)
1143 #define __Pyx_DECREF_SET(r, v) do {\
1144  PyObject *tmp = (PyObject *) r;\
1145  r = v; __Pyx_DECREF(tmp);\
1146  } while (0)
1147 #define __Pyx_CLEAR(r) do { PyObject* tmp = ((PyObject*)(r)); r = NULL; __Pyx_DECREF(tmp);} while(0)
1148 #define __Pyx_XCLEAR(r) do { if((r) != NULL) {PyObject* tmp = ((PyObject*)(r)); r = NULL; __Pyx_DECREF(tmp);}} while(0)
1149 
1150 /* PyObjectGetAttrStr.proto */
1151 #if CYTHON_USE_TYPE_SLOTS
1152 static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStr(PyObject* obj, PyObject* attr_name);
1153 #else
1154 #define __Pyx_PyObject_GetAttrStr(o,n) PyObject_GetAttr(o,n)
1155 #endif
1156 
1157 /* GetBuiltinName.proto */
1158 static PyObject *__Pyx_GetBuiltinName(PyObject *name);
1159 
1160 /* PyCFunctionFastCall.proto */
1161 #if CYTHON_FAST_PYCCALL
1162 static CYTHON_INLINE PyObject *__Pyx_PyCFunction_FastCall(PyObject *func, PyObject **args, Py_ssize_t nargs);
1163 #else
1164 #define __Pyx_PyCFunction_FastCall(func, args, nargs) (assert(0), NULL)
1165 #endif
1166 
1167 /* PyFunctionFastCall.proto */
1168 #if CYTHON_FAST_PYCALL
1169 #define __Pyx_PyFunction_FastCall(func, args, nargs)\
1170  __Pyx_PyFunction_FastCallDict((func), (args), (nargs), NULL)
1171 #if 1 || PY_VERSION_HEX < 0x030600B1
1172 static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, int nargs, PyObject *kwargs);
1173 #else
1174 #define __Pyx_PyFunction_FastCallDict(func, args, nargs, kwargs) _PyFunction_FastCallDict(func, args, nargs, kwargs)
1175 #endif
1176 #endif
1177 
1178 /* PyObjectCall.proto */
1179 #if CYTHON_COMPILING_IN_CPYTHON
1180 static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw);
1181 #else
1182 #define __Pyx_PyObject_Call(func, arg, kw) PyObject_Call(func, arg, kw)
1183 #endif
1184 
1185 /* PyObjectCallMethO.proto */
1186 #if CYTHON_COMPILING_IN_CPYTHON
1187 static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg);
1188 #endif
1189 
1190 /* PyObjectCallOneArg.proto */
1191 static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg);
1192 
1193 /* PyThreadStateGet.proto */
1194 #if CYTHON_FAST_THREAD_STATE
1195 #define __Pyx_PyThreadState_declare PyThreadState *__pyx_tstate;
1196 #define __Pyx_PyThreadState_assign __pyx_tstate = __Pyx_PyThreadState_Current;
1197 #define __Pyx_PyErr_Occurred() __pyx_tstate->curexc_type
1198 #else
1199 #define __Pyx_PyThreadState_declare
1200 #define __Pyx_PyThreadState_assign
1201 #define __Pyx_PyErr_Occurred() PyErr_Occurred()
1202 #endif
1203 
1204 /* PyErrFetchRestore.proto */
1205 #if CYTHON_FAST_THREAD_STATE
1206 #define __Pyx_PyErr_Clear() __Pyx_ErrRestore(NULL, NULL, NULL)
1207 #define __Pyx_ErrRestoreWithState(type, value, tb) __Pyx_ErrRestoreInState(PyThreadState_GET(), type, value, tb)
1208 #define __Pyx_ErrFetchWithState(type, value, tb) __Pyx_ErrFetchInState(PyThreadState_GET(), type, value, tb)
1209 #define __Pyx_ErrRestore(type, value, tb) __Pyx_ErrRestoreInState(__pyx_tstate, type, value, tb)
1210 #define __Pyx_ErrFetch(type, value, tb) __Pyx_ErrFetchInState(__pyx_tstate, type, value, tb)
1211 static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb);
1212 static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
1213 #if CYTHON_COMPILING_IN_CPYTHON
1214 #define __Pyx_PyErr_SetNone(exc) (Py_INCREF(exc), __Pyx_ErrRestore((exc), NULL, NULL))
1215 #else
1216 #define __Pyx_PyErr_SetNone(exc) PyErr_SetNone(exc)
1217 #endif
1218 #else
1219 #define __Pyx_PyErr_Clear() PyErr_Clear()
1220 #define __Pyx_PyErr_SetNone(exc) PyErr_SetNone(exc)
1221 #define __Pyx_ErrRestoreWithState(type, value, tb) PyErr_Restore(type, value, tb)
1222 #define __Pyx_ErrFetchWithState(type, value, tb) PyErr_Fetch(type, value, tb)
1223 #define __Pyx_ErrRestoreInState(tstate, type, value, tb) PyErr_Restore(type, value, tb)
1224 #define __Pyx_ErrFetchInState(tstate, type, value, tb) PyErr_Fetch(type, value, tb)
1225 #define __Pyx_ErrRestore(type, value, tb) PyErr_Restore(type, value, tb)
1226 #define __Pyx_ErrFetch(type, value, tb) PyErr_Fetch(type, value, tb)
1227 #endif
1228 
1229 /* WriteUnraisableException.proto */
1230 static void __Pyx_WriteUnraisable(const char *name, int clineno,
1231  int lineno, const char *filename,
1232  int full_traceback, int nogil);
1233 
1234 /* PyObjectCallNoArg.proto */
1235 #if CYTHON_COMPILING_IN_CPYTHON
1236 static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func);
1237 #else
1238 #define __Pyx_PyObject_CallNoArg(func) __Pyx_PyObject_Call(func, __pyx_empty_tuple, NULL)
1239 #endif
1240 
1241 /* RaiseDoubleKeywords.proto */
1242 static void __Pyx_RaiseDoubleKeywordsError(const char* func_name, PyObject* kw_name);
1243 
1244 /* ParseKeywords.proto */
1245 static int __Pyx_ParseOptionalKeywords(PyObject *kwds, PyObject **argnames[],\
1246  PyObject *kwds2, PyObject *values[], Py_ssize_t num_pos_args,\
1247  const char* function_name);
1248 
1249 /* RaiseArgTupleInvalid.proto */
1250 static void __Pyx_RaiseArgtupleInvalid(const char* func_name, int exact,
1251  Py_ssize_t num_min, Py_ssize_t num_max, Py_ssize_t num_found);
1252 
1253 /* GetModuleGlobalName.proto */
1254 static CYTHON_INLINE PyObject *__Pyx_GetModuleGlobalName(PyObject *name);
1255 
1256 /* SaveResetException.proto */
1257 #if CYTHON_FAST_THREAD_STATE
1258 #define __Pyx_ExceptionSave(type, value, tb) __Pyx__ExceptionSave(__pyx_tstate, type, value, tb)
1259 static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
1260 #define __Pyx_ExceptionReset(type, value, tb) __Pyx__ExceptionReset(__pyx_tstate, type, value, tb)
1261 static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb);
1262 #else
1263 #define __Pyx_ExceptionSave(type, value, tb) PyErr_GetExcInfo(type, value, tb)
1264 #define __Pyx_ExceptionReset(type, value, tb) PyErr_SetExcInfo(type, value, tb)
1265 #endif
1266 
1267 /* PyErrExceptionMatches.proto */
1268 #if CYTHON_FAST_THREAD_STATE
1269 #define __Pyx_PyErr_ExceptionMatches(err) __Pyx_PyErr_ExceptionMatchesInState(__pyx_tstate, err)
1270 static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err);
1271 #else
1272 #define __Pyx_PyErr_ExceptionMatches(err) PyErr_ExceptionMatches(err)
1273 #endif
1274 
1275 /* GetException.proto */
1276 #if CYTHON_FAST_THREAD_STATE
1277 #define __Pyx_GetException(type, value, tb) __Pyx__GetException(__pyx_tstate, type, value, tb)
1278 static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
1279 #else
1280 static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb);
1281 #endif
1282 
1283 /* RaiseException.proto */
1284 static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause);
1285 
1286 /* PyIntBinop.proto */
1287 #if !CYTHON_COMPILING_IN_PYPY
1288 static PyObject* __Pyx_PyInt_AddObjC(PyObject *op1, PyObject *op2, long intval, int inplace);
1289 #else
1290 #define __Pyx_PyInt_AddObjC(op1, op2, intval, inplace)\
1291  (inplace ? PyNumber_InPlaceAdd(op1, op2) : PyNumber_Add(op1, op2))
1292 #endif
1293 
1294 /* PySequenceContains.proto */
1295 static CYTHON_INLINE int __Pyx_PySequence_ContainsTF(PyObject* item, PyObject* seq, int eq) {
1296  int result = PySequence_Contains(seq, item);
1297  return unlikely(result < 0) ? result : (result == (eq == Py_EQ));
1298 }
1299 
1300 /* SetItemInt.proto */
1301 #define __Pyx_SetItemInt(o, i, v, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
1302  (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\
1303  __Pyx_SetItemInt_Fast(o, (Py_ssize_t)i, v, is_list, wraparound, boundscheck) :\
1304  (is_list ? (PyErr_SetString(PyExc_IndexError, "list assignment index out of range"), -1) :\
1305  __Pyx_SetItemInt_Generic(o, to_py_func(i), v)))
1306 static int __Pyx_SetItemInt_Generic(PyObject *o, PyObject *j, PyObject *v);
1307 static CYTHON_INLINE int __Pyx_SetItemInt_Fast(PyObject *o, Py_ssize_t i, PyObject *v,
1308  int is_list, int wraparound, int boundscheck);
1309 
1310 /* ArgTypeTest.proto */
1311 #define __Pyx_ArgTypeTest(obj, type, none_allowed, name, exact)\
1312  ((likely((Py_TYPE(obj) == type) | (none_allowed && (obj == Py_None)))) ? 1 :\
1313  __Pyx__ArgTypeTest(obj, type, name, exact))
1314 static int __Pyx__ArgTypeTest(PyObject *obj, PyTypeObject *type, const char *name, int exact);
1315 
1316 /* Import.proto */
1317 static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level);
1318 
1319 /* IncludeStringH.proto */
1320 #include <string.h>
1321 
1322 /* PyObject_GenericGetAttrNoDict.proto */
1323 #if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000
1324 static CYTHON_INLINE PyObject* __Pyx_PyObject_GenericGetAttrNoDict(PyObject* obj, PyObject* attr_name);
1325 #else
1326 #define __Pyx_PyObject_GenericGetAttrNoDict PyObject_GenericGetAttr
1327 #endif
1328 
1329 /* PyObject_GenericGetAttr.proto */
1330 #if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000
1331 static PyObject* __Pyx_PyObject_GenericGetAttr(PyObject* obj, PyObject* attr_name);
1332 #else
1333 #define __Pyx_PyObject_GenericGetAttr PyObject_GenericGetAttr
1334 #endif
1335 
1336 /* SetVTable.proto */
1337 static int __Pyx_SetVtable(PyObject *dict, void *vtable);
1338 
1339 /* SetupReduce.proto */
1340 static int __Pyx_setup_reduce(PyObject* type_obj);
1341 
1342 /* PyFloatBinop.proto */
1343 #if !CYTHON_COMPILING_IN_PYPY
1344 static PyObject* __Pyx_PyFloat_DivideObjC(PyObject *op1, PyObject *op2, double floatval, int inplace);
1345 #else
1346 #define __Pyx_PyFloat_DivideObjC(op1, op2, floatval, inplace)\
1347  ((inplace ? __Pyx_PyNumber_InPlaceDivide(op1, op2) : __Pyx_PyNumber_Divide(op1, op2)))
1348  #endif
1349 
1350 /* BytesEquals.proto */
1351 static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals);
1352 
1353 /* UnicodeEquals.proto */
1354 static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals);
1355 
1356 /* StrEquals.proto */
1357 #if PY_MAJOR_VERSION >= 3
1358 #define __Pyx_PyString_Equals __Pyx_PyUnicode_Equals
1359 #else
1360 #define __Pyx_PyString_Equals __Pyx_PyBytes_Equals
1361 #endif
1362 
1363 /* CLineInTraceback.proto */
1364 #ifdef CYTHON_CLINE_IN_TRACEBACK
1365 #define __Pyx_CLineForTraceback(tstate, c_line) (((CYTHON_CLINE_IN_TRACEBACK)) ? c_line : 0)
1366 #else
1367 static int __Pyx_CLineForTraceback(PyThreadState *tstate, int c_line);
1368 #endif
1369 
1370 /* CodeObjectCache.proto */
1371 typedef struct {
1372  PyCodeObject* code_object;
1373  int code_line;
1374 } __Pyx_CodeObjectCacheEntry;
1375 struct __Pyx_CodeObjectCache {
1376  int count;
1377  int max_count;
1378  __Pyx_CodeObjectCacheEntry* entries;
1379 };
1380 static struct __Pyx_CodeObjectCache __pyx_code_cache = {0,0,NULL};
1381 static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line);
1382 static PyCodeObject *__pyx_find_code_object(int code_line);
1383 static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object);
1384 
1385 /* AddTraceback.proto */
1386 static void __Pyx_AddTraceback(const char *funcname, int c_line,
1387  int py_line, const char *filename);
1388 
1389 /* CppExceptionConversion.proto */
1390 #ifndef __Pyx_CppExn2PyErr
1391 #include <new>
1392 #include <typeinfo>
1393 #include <stdexcept>
1394 #include <ios>
1395 static void __Pyx_CppExn2PyErr() {
1396  try {
1397  if (PyErr_Occurred())
1398  ; // let the latest Python exn pass through and ignore the current one
1399  else
1400  throw;
1401  } catch (const std::bad_alloc& exn) {
1402  PyErr_SetString(PyExc_MemoryError, exn.what());
1403  } catch (const std::bad_cast& exn) {
1404  PyErr_SetString(PyExc_TypeError, exn.what());
1405  } catch (const std::bad_typeid& exn) {
1406  PyErr_SetString(PyExc_TypeError, exn.what());
1407  } catch (const std::domain_error& exn) {
1408  PyErr_SetString(PyExc_ValueError, exn.what());
1409  } catch (const std::invalid_argument& exn) {
1410  PyErr_SetString(PyExc_ValueError, exn.what());
1411  } catch (const std::ios_base::failure& exn) {
1412  PyErr_SetString(PyExc_IOError, exn.what());
1413  } catch (const std::out_of_range& exn) {
1414  PyErr_SetString(PyExc_IndexError, exn.what());
1415  } catch (const std::overflow_error& exn) {
1416  PyErr_SetString(PyExc_OverflowError, exn.what());
1417  } catch (const std::range_error& exn) {
1418  PyErr_SetString(PyExc_ArithmeticError, exn.what());
1419  } catch (const std::underflow_error& exn) {
1420  PyErr_SetString(PyExc_ArithmeticError, exn.what());
1421  } catch (const std::exception& exn) {
1422  PyErr_SetString(PyExc_RuntimeError, exn.what());
1423  }
1424  catch (...)
1425  {
1426  PyErr_SetString(PyExc_RuntimeError, "Unknown exception");
1427  }
1428 }
1429 #endif
1430 
1431 /* CIntToPy.proto */
1432 static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value);
1433 
1434 /* CIntFromPy.proto */
1435 static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *);
1436 
1437 /* CIntToPy.proto */
1438 static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value);
1439 
1440 /* CIntFromPy.proto */
1441 static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *);
1442 
1443 /* FastTypeChecks.proto */
1444 #if CYTHON_COMPILING_IN_CPYTHON
1445 #define __Pyx_TypeCheck(obj, type) __Pyx_IsSubtype(Py_TYPE(obj), (PyTypeObject *)type)
1446 static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b);
1447 static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject *type);
1448 static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *type1, PyObject *type2);
1449 #else
1450 #define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type)
1451 #define __Pyx_PyErr_GivenExceptionMatches(err, type) PyErr_GivenExceptionMatches(err, type)
1452 #define __Pyx_PyErr_GivenExceptionMatches2(err, type1, type2) (PyErr_GivenExceptionMatches(err, type1) || PyErr_GivenExceptionMatches(err, type2))
1453 #endif
1454 #define __Pyx_PyException_Check(obj) __Pyx_TypeCheck(obj, PyExc_Exception)
1455 
1456 /* FetchCommonType.proto */
1457 static PyTypeObject* __Pyx_FetchCommonType(PyTypeObject* type);
1458 
1459 /* SwapException.proto */
1460 #if CYTHON_FAST_THREAD_STATE
1461 #define __Pyx_ExceptionSwap(type, value, tb) __Pyx__ExceptionSwap(__pyx_tstate, type, value, tb)
1462 static CYTHON_INLINE void __Pyx__ExceptionSwap(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
1463 #else
1464 static CYTHON_INLINE void __Pyx_ExceptionSwap(PyObject **type, PyObject **value, PyObject **tb);
1465 #endif
1466 
1467 /* PyObjectCallMethod1.proto */
1468 static PyObject* __Pyx_PyObject_CallMethod1(PyObject* obj, PyObject* method_name, PyObject* arg);
1469 static PyObject* __Pyx__PyObject_CallMethod1(PyObject* method, PyObject* arg);
1470 
1471 /* CoroutineBase.proto */
1472 typedef PyObject *(*__pyx_coroutine_body_t)(PyObject *, PyThreadState *, PyObject *);
1473 typedef struct {
1474  PyObject_HEAD
1475  __pyx_coroutine_body_t body;
1476  PyObject *closure;
1477  PyObject *exc_type;
1478  PyObject *exc_value;
1479  PyObject *exc_traceback;
1480  PyObject *gi_weakreflist;
1481  PyObject *classobj;
1482  PyObject *yieldfrom;
1483  PyObject *gi_name;
1484  PyObject *gi_qualname;
1485  PyObject *gi_modulename;
1486  PyObject *gi_code;
1487  int resume_label;
1488  char is_running;
1489 } __pyx_CoroutineObject;
1490 static __pyx_CoroutineObject *__Pyx__Coroutine_New(
1491  PyTypeObject *type, __pyx_coroutine_body_t body, PyObject *code, PyObject *closure,
1492  PyObject *name, PyObject *qualname, PyObject *module_name);
1493 static __pyx_CoroutineObject *__Pyx__Coroutine_NewInit(
1494  __pyx_CoroutineObject *gen, __pyx_coroutine_body_t body, PyObject *code, PyObject *closure,
1495  PyObject *name, PyObject *qualname, PyObject *module_name);
1496 static int __Pyx_Coroutine_clear(PyObject *self);
1497 static PyObject *__Pyx_Coroutine_Send(PyObject *self, PyObject *value);
1498 static PyObject *__Pyx_Coroutine_Close(PyObject *self);
1499 static PyObject *__Pyx_Coroutine_Throw(PyObject *gen, PyObject *args);
1500 #define __Pyx_Coroutine_SwapException(self) {\
1501  __Pyx_ExceptionSwap(&(self)->exc_type, &(self)->exc_value, &(self)->exc_traceback);\
1502  __Pyx_Coroutine_ResetFrameBackpointer(self);\
1503  }
1504 #define __Pyx_Coroutine_ResetAndClearException(self) {\
1505  __Pyx_ExceptionReset((self)->exc_type, (self)->exc_value, (self)->exc_traceback);\
1506  (self)->exc_type = (self)->exc_value = (self)->exc_traceback = NULL;\
1507  }
1508 #if CYTHON_FAST_THREAD_STATE
1509 #define __Pyx_PyGen_FetchStopIterationValue(pvalue)\
1510  __Pyx_PyGen__FetchStopIterationValue(__pyx_tstate, pvalue)
1511 #else
1512 #define __Pyx_PyGen_FetchStopIterationValue(pvalue)\
1513  __Pyx_PyGen__FetchStopIterationValue(__Pyx_PyThreadState_Current, pvalue)
1514 #endif
1515 static int __Pyx_PyGen__FetchStopIterationValue(PyThreadState *tstate, PyObject **pvalue);
1516 static CYTHON_INLINE void __Pyx_Coroutine_ResetFrameBackpointer(__pyx_CoroutineObject *self);
1517 
1518 /* PatchModuleWithCoroutine.proto */
1519 static PyObject* __Pyx_Coroutine_patch_module(PyObject* module, const char* py_code);
1520 
1521 /* PatchGeneratorABC.proto */
1522 static int __Pyx_patch_abc(void);
1523 
1524 /* Generator.proto */
1525 #define __Pyx_Generator_USED
1526 static PyTypeObject *__pyx_GeneratorType = 0;
1527 #define __Pyx_Generator_CheckExact(obj) (Py_TYPE(obj) == __pyx_GeneratorType)
1528 #define __Pyx_Generator_New(body, code, closure, name, qualname, module_name)\
1529  __Pyx__Coroutine_New(__pyx_GeneratorType, body, code, closure, name, qualname, module_name)
1530 static PyObject *__Pyx_Generator_Next(PyObject *self);
1531 static int __pyx_Generator_init(void);
1532 
1533 /* CheckBinaryVersion.proto */
1534 static int __Pyx_check_binary_version(void);
1535 
1536 /* InitStrings.proto */
1537 static int __Pyx_InitStrings(__Pyx_StringTabEntry *t);
1538 
1539 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_9index_set_wrap(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, IndexSet __pyx_v_other); /* proto*/
1540 static CYTHON_INLINE IndexSet __pyx_f_8PyClical_9index_set_unwrap(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto*/
1541 static PyObject *__pyx_f_8PyClical_9index_set_copy(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, int __pyx_skip_dispatch); /* proto*/
1542 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_8clifford_wrap(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, Clifford __pyx_v_other); /* proto*/
1543 static CYTHON_INLINE Clifford __pyx_f_8PyClical_8clifford_unwrap(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto*/
1544 static PyObject *__pyx_f_8PyClical_8clifford_copy(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, int __pyx_skip_dispatch); /* proto*/
1545 
1546 /* Module declarations from 'libcpp.vector' */
1547 
1548 /* Module declarations from 'glucat' */
1549 
1550 /* Module declarations from 'PyClical' */
1551 static PyTypeObject *__pyx_ptype_8PyClical_index_set = 0;
1552 static PyTypeObject *__pyx_ptype_8PyClical_clifford = 0;
1553 static PyTypeObject *__pyx_ptype_8PyClical___pyx_scope_struct____iter__ = 0;
1554 static CYTHON_INLINE IndexSet __pyx_f_8PyClical_toIndexSet(PyObject *); /*proto*/
1555 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_compare(PyObject *, PyObject *, int __pyx_skip_dispatch); /*proto*/
1556 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_min_neg(PyObject *, int __pyx_skip_dispatch); /*proto*/
1557 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_max_pos(PyObject *, int __pyx_skip_dispatch); /*proto*/
1558 static CYTHON_INLINE std::vector<scalar_t> __pyx_f_8PyClical_list_to_vector(PyObject *); /*proto*/
1559 static CYTHON_INLINE Clifford __pyx_f_8PyClical_toClifford(PyObject *); /*proto*/
1560 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_inv(PyObject *, int __pyx_skip_dispatch); /*proto*/
1561 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_scalar(PyObject *, int __pyx_skip_dispatch); /*proto*/
1562 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_real(PyObject *, int __pyx_skip_dispatch); /*proto*/
1563 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_imag(PyObject *, int __pyx_skip_dispatch); /*proto*/
1564 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_pure(PyObject *, int __pyx_skip_dispatch); /*proto*/
1565 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_even(PyObject *, int __pyx_skip_dispatch); /*proto*/
1566 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_odd(PyObject *, int __pyx_skip_dispatch); /*proto*/
1567 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_involute(PyObject *, int __pyx_skip_dispatch); /*proto*/
1568 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_reverse(PyObject *, int __pyx_skip_dispatch); /*proto*/
1569 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_conj(PyObject *, int __pyx_skip_dispatch); /*proto*/
1570 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_quad(PyObject *, int __pyx_skip_dispatch); /*proto*/
1571 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_norm(PyObject *, int __pyx_skip_dispatch); /*proto*/
1572 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_abs(PyObject *, int __pyx_skip_dispatch); /*proto*/
1573 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_max_abs(PyObject *, int __pyx_skip_dispatch); /*proto*/
1574 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_pow(PyObject *, PyObject *, int __pyx_skip_dispatch); /*proto*/
1575 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_outer_pow(PyObject *, PyObject *, int __pyx_skip_dispatch); /*proto*/
1576 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_complexifier(PyObject *, int __pyx_skip_dispatch); /*proto*/
1577 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_sqrt(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_sqrt *__pyx_optional_args); /*proto*/
1578 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_exp(PyObject *, int __pyx_skip_dispatch); /*proto*/
1579 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_log(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_log *__pyx_optional_args); /*proto*/
1580 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_cos(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_cos *__pyx_optional_args); /*proto*/
1581 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_acos(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_acos *__pyx_optional_args); /*proto*/
1582 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_cosh(PyObject *, int __pyx_skip_dispatch); /*proto*/
1583 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_acosh(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_acosh *__pyx_optional_args); /*proto*/
1584 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_sin(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_sin *__pyx_optional_args); /*proto*/
1585 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_asin(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_asin *__pyx_optional_args); /*proto*/
1586 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_sinh(PyObject *, int __pyx_skip_dispatch); /*proto*/
1587 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_asinh(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_asinh *__pyx_optional_args); /*proto*/
1588 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_tan(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_tan *__pyx_optional_args); /*proto*/
1589 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_atan(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_atan *__pyx_optional_args); /*proto*/
1590 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_tanh(PyObject *, int __pyx_skip_dispatch); /*proto*/
1591 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_atanh(PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_8PyClical_atanh *__pyx_optional_args); /*proto*/
1592 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*/
1593 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_cga3(PyObject *, int __pyx_skip_dispatch); /*proto*/
1594 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_cga3std(PyObject *, int __pyx_skip_dispatch); /*proto*/
1595 static CYTHON_INLINE PyObject *__pyx_f_8PyClical_agc3(PyObject *, int __pyx_skip_dispatch); /*proto*/
1596 #define __Pyx_MODULE_NAME "PyClical"
1597 extern int __pyx_module_is_main_PyClical;
1598 int __pyx_module_is_main_PyClical = 0;
1599 
1600 /* Implementation of 'PyClical' */
1601 static PyObject *__pyx_builtin_IndexError;
1602 static PyObject *__pyx_builtin_RuntimeError;
1603 static PyObject *__pyx_builtin_TypeError;
1604 static PyObject *__pyx_builtin_ValueError;
1605 static PyObject *__pyx_builtin_NotImplemented;
1606 static PyObject *__pyx_builtin_range;
1607 static PyObject *__pyx_builtin_xrange;
1608 static const char __pyx_k_[] = ".";
1609 static const char __pyx_k_e[] = "e";
1610 static const char __pyx_k_i[] = "i";
1611 static const char __pyx_k_m[] = "m";
1612 static const char __pyx_k_p[] = "p";
1613 static const char __pyx_k_q[] = "q";
1614 static const char __pyx_k__2[] = " ";
1615 static const char __pyx_k__5[] = ":";
1616 static const char __pyx_k__6[] = "\n\t";
1617 static const char __pyx_k__7[] = " (";
1618 static const char __pyx_k__8[] = ", ";
1619 static const char __pyx_k__9[] = ").";
1620 static const char __pyx_k_cl[] = "cl";
1621 static const char __pyx_k_pi[] = "pi";
1622 static const char __pyx_k_cos[] = "cos";
1623 static const char __pyx_k_exp[] = "exp";
1624 static const char __pyx_k_frm[] = "frm";
1625 static const char __pyx_k_inv[] = "inv";
1626 static const char __pyx_k_ist[] = "ist";
1627 static const char __pyx_k_ixt[] = "ixt";
1628 static const char __pyx_k_lhs[] = "lhs";
1629 static const char __pyx_k_log[] = "log";
1630 static const char __pyx_k_max[] = "max";
1631 static const char __pyx_k_min[] = "min";
1632 static const char __pyx_k_obj[] = "obj";
1633 static const char __pyx_k_odd[] = "odd";
1634 static const char __pyx_k_pow[] = "pow";
1635 static const char __pyx_k_rhs[] = "rhs";
1636 static const char __pyx_k_sin[] = "sin";
1637 static const char __pyx_k_tan[] = "tan";
1638 static const char __pyx_k_tau[] = "tau";
1639 static const char __pyx_k_Real[] = "Real";
1640 static const char __pyx_k_acos[] = "acos";
1641 static const char __pyx_k_args[] = "args";
1642 static const char __pyx_k_asin[] = "asin";
1643 static const char __pyx_k_atan[] = "atan";
1644 static const char __pyx_k_conj[] = "conj";
1645 static const char __pyx_k_copy[] = "copy";
1646 static const char __pyx_k_cosh[] = "cosh";
1647 static const char __pyx_k_even[] = "even";
1648 static const char __pyx_k_fill[] = "fill";
1649 static const char __pyx_k_from[] = " from ";
1650 static const char __pyx_k_iter[] = "__iter__";
1651 static const char __pyx_k_main[] = "__main__";
1652 static const char __pyx_k_math[] = "math";
1653 static const char __pyx_k_name[] = "__name__";
1654 static const char __pyx_k_norm[] = "norm";
1655 static const char __pyx_k_pure[] = "pure";
1656 static const char __pyx_k_quad[] = "quad";
1657 static const char __pyx_k_send[] = "send";
1658 static const char __pyx_k_sinh[] = "sinh";
1659 static const char __pyx_k_sqrt[] = "sqrt";
1660 static const char __pyx_k_tanh[] = "tanh";
1661 static const char __pyx_k_test[] = "_test";
1662 static const char __pyx_k_0_8_2[] = "0.8.2";
1663 static const char __pyx_k_acosh[] = "acosh";
1664 static const char __pyx_k_asinh[] = "asinh";
1665 static const char __pyx_k_atanh[] = "atanh";
1666 static const char __pyx_k_close[] = "close";
1667 static const char __pyx_k_grade[] = "grade";
1668 static const char __pyx_k_istpq[] = "istpq";
1669 static const char __pyx_k_nbar3[] = "nbar3";
1670 static const char __pyx_k_ninf3[] = "ninf3";
1671 static const char __pyx_k_other[] = "other";
1672 static const char __pyx_k_range[] = "range";
1673 static const char __pyx_k_throw[] = "throw";
1674 static const char __pyx_k_using[] = " using (";
1675 static const char __pyx_k_value[] = " value ";
1676 static const char __pyx_k_import[] = "__import__";
1677 static const char __pyx_k_reduce[] = "__reduce__";
1678 static const char __pyx_k_scalar[] = "scalar";
1679 static const char __pyx_k_test_2[] = "__test__";
1680 static const char __pyx_k_xrange[] = "xrange";
1681 static const char __pyx_k_doctest[] = "doctest";
1682 static const char __pyx_k_invalid[] = " invalid ";
1683 static const char __pyx_k_numbers[] = "numbers";
1684 static const char __pyx_k_reverse[] = "reverse";
1685 static const char __pyx_k_testmod[] = "testmod";
1686 static const char __pyx_k_version[] = "__version__";
1687 static const char __pyx_k_Integral[] = "Integral";
1688 static const char __pyx_k_PyClical[] = "PyClical";
1689 static const char __pyx_k_Sequence[] = "Sequence";
1690 static const char __pyx_k_as_frame[] = " as frame:\n\t";
1691 static const char __pyx_k_getstate[] = "__getstate__";
1692 static const char __pyx_k_involute[] = "involute";
1693 static const char __pyx_k_setstate[] = "__setstate__";
1694 static const char __pyx_k_to_frame[] = " to frame ";
1695 static const char __pyx_k_TypeError[] = "TypeError";
1696 static const char __pyx_k_outer_pow[] = "outer_pow";
1697 static const char __pyx_k_reduce_ex[] = "__reduce_ex__";
1698 static const char __pyx_k_IndexError[] = "IndexError";
1699 static const char __pyx_k_ValueError[] = "ValueError";
1700 static const char __pyx_k_pyx_vtable[] = "__pyx_vtable__";
1701 static const char __pyx_k_collections[] = "collections";
1702 static const char __pyx_k_e_line_1887[] = "e (line 1887)";
1703 static const char __pyx_k_PyClical_pyx[] = "PyClical.pyx";
1704 static const char __pyx_k_RuntimeError[] = "RuntimeError";
1705 static const char __pyx_k_abs_line_1473[] = "abs (line 1473)";
1706 static const char __pyx_k_cos_line_1602[] = "cos (line 1602)";
1707 static const char __pyx_k_exp_line_1565[] = "exp (line 1565)";
1708 static const char __pyx_k_inv_line_1329[] = "inv (line 1329)";
1709 static const char __pyx_k_log_line_1579[] = "log (line 1579)";
1710 static const char __pyx_k_odd_line_1397[] = "odd (line 1397)";
1711 static const char __pyx_k_pow_line_1494[] = "pow (line 1494)";
1712 static const char __pyx_k_reduce_cython[] = "__reduce_cython__";
1713 static const char __pyx_k_sin_line_1679[] = "sin (line 1679)";
1714 static const char __pyx_k_tan_line_1752[] = "tan (line 1752)";
1715 static const char __pyx_k_using_invalid[] = " using invalid ";
1716 static const char __pyx_k_Cannot_reframe[] = "Cannot reframe";
1717 static const char __pyx_k_NotImplemented[] = "NotImplemented";
1718 static const char __pyx_k_Not_applicable[] = "Not applicable.";
1719 static const char __pyx_k_acos_line_1619[] = "acos (line 1619)";
1720 static const char __pyx_k_agc3_line_1844[] = "agc3 (line 1844)";
1721 static const char __pyx_k_asin_line_1698[] = "asin (line 1698)";
1722 static const char __pyx_k_atan_line_1769[] = "atan (line 1769)";
1723 static const char __pyx_k_cga3_line_1824[] = "cga3 (line 1824)";
1724 static const char __pyx_k_conj_line_1436[] = "conj (line 1436)";
1725 static const char __pyx_k_cosh_line_1640[] = "cosh (line 1640)";
1726 static const char __pyx_k_even_line_1388[] = "even (line 1388)";
1727 static const char __pyx_k_imag_line_1366[] = "imag (line 1366)";
1728 static const char __pyx_k_invalid_string[] = " invalid string ";
1729 static const char __pyx_k_norm_line_1462[] = "norm (line 1462)";
1730 static const char __pyx_k_pure_line_1377[] = "pure (line 1377)";
1731 static const char __pyx_k_quad_line_1451[] = "quad (line 1451)";
1732 static const char __pyx_k_real_line_1355[] = "real (line 1355)";
1733 static const char __pyx_k_sinh_line_1719[] = "sinh (line 1719)";
1734 static const char __pyx_k_sqrt_line_1542[] = "sqrt (line 1542)";
1735 static const char __pyx_k_tanh_line_1786[] = "tanh (line 1786)";
1736 static const char __pyx_k_acosh_line_1656[] = "acosh (line 1656)";
1737 static const char __pyx_k_asinh_line_1733[] = "asinh (line 1733)";
1738 static const char __pyx_k_atanh_line_1798[] = "atanh (line 1798)";
1739 static const char __pyx_k_istpq_line_1900[] = "istpq (line 1900)";
1740 static const char __pyx_k_setstate_cython[] = "__setstate_cython__";
1741 static const char __pyx_k_compare_line_490[] = "compare (line 490)";
1742 static const char __pyx_k_index_set___iter[] = "index_set.__iter__";
1743 static const char __pyx_k_max_pos_line_511[] = "max_pos (line 511)";
1744 static const char __pyx_k_min_neg_line_502[] = "min_neg (line 502)";
1745 static const char __pyx_k_scalar_line_1344[] = "scalar (line 1344)";
1746 static const char __pyx_k_cga3std_line_1833[] = "cga3std (line 1833)";
1747 static const char __pyx_k_max_abs_line_1482[] = "max_abs (line 1482)";
1748 static const char __pyx_k_reverse_line_1421[] = "reverse (line 1421)";
1749 static const char __pyx_k_cline_in_traceback[] = "cline_in_traceback";
1750 static const char __pyx_k_involute_line_1406[] = "involute (line 1406)";
1751 static const char __pyx_k_outer_pow_line_1518[] = "outer_pow (line 1518)";
1752 static const char __pyx_k_clifford_inv_line_925[] = "clifford.inv (line 925)";
1753 static const char __pyx_k_clifford_pow_line_979[] = "clifford.pow (line 979)";
1754 static const char __pyx_k_clifford_abs_line_1174[] = "clifford.abs (line 1174)";
1755 static const char __pyx_k_clifford_copy_line_554[] = "clifford.copy (line 554)";
1756 static const char __pyx_k_clifford_odd_line_1069[] = "clifford.odd (line 1069)";
1757 static const char __pyx_k_complexifier_line_1527[] = "complexifier (line 1527)";
1758 static const char __pyx_k_index_set_copy_line_64[] = "index_set.copy (line 64)";
1759 static const char __pyx_k_index_set_max_line_349[] = "index_set.max (line 349)";
1760 static const char __pyx_k_index_set_min_line_340[] = "index_set.min (line 340)";
1761 static const char __pyx_k_clifford_conj_line_1137[] = "clifford.conj (line 1137)";
1762 static const char __pyx_k_clifford_even_line_1060[] = "clifford.even (line 1060)";
1763 static const char __pyx_k_clifford_norm_line_1163[] = "clifford.norm (line 1163)";
1764 static const char __pyx_k_clifford_pure_line_1049[] = "clifford.pure (line 1049)";
1765 static const char __pyx_k_clifford_quad_line_1152[] = "clifford.quad (line 1152)";
1766 static const char __pyx_k_Unary_print_clifford_1_1[] = "\n Unary -.\n\n >>> print -clifford(\"{1}\")\n -{1}\n ";
1767 static const char __pyx_k_clifford___or___line_938[] = "clifford.__or__ (line 938)";
1768 static const char __pyx_k_clifford_frame_line_1214[] = "clifford.frame (line 1214)";
1769 static const char __pyx_k_clifford_hidden_doctests[] = "clifford_hidden_doctests";
1770 static const char __pyx_k_clifford_isnan_line_1205[] = "clifford.isnan (line 1205)";
1771 static const char __pyx_k_index_set_count_line_313[] = "index_set.count (line 313)";
1772 static const char __pyx_k_clifford___add___line_739[] = "clifford.__add__ (line 739)";
1773 static const char __pyx_k_clifford___and___line_835[] = "clifford.__and__ (line 835)";
1774 static const char __pyx_k_clifford___div___line_895[] = "clifford.__div__ (line 895)";
1775 static const char __pyx_k_clifford___ior___line_949[] = "clifford.__ior__ (line 949)";
1776 static const char __pyx_k_clifford___mod___line_805[] = "clifford.__mod__ (line 805)";
1777 static const char __pyx_k_clifford___mul___line_779[] = "clifford.__mul__ (line 779)";
1778 static const char __pyx_k_clifford___neg___line_721[] = "clifford.__neg__ (line 721)";
1779 static const char __pyx_k_clifford___pos___line_730[] = "clifford.__pos__ (line 730)";
1780 static const char __pyx_k_clifford___pow___line_960[] = "clifford.__pow__ (line 960)";
1781 static const char __pyx_k_clifford___sub___line_759[] = "clifford.__sub__ (line 759)";
1782 static const char __pyx_k_clifford___xor___line_865[] = "clifford.__xor__ (line 865)";
1783 static const char __pyx_k_clifford_reframe_line_648[] = "clifford.reframe (line 648)";
1784 static const char __pyx_k_clifford_scalar_line_1038[] = "clifford.scalar (line 1038)";
1785 static const char __pyx_k_index_set___or___line_291[] = "index_set.__or__ (line 291)";
1786 static const char __pyx_k_index_set_hidden_doctests[] = "index_set_hidden_doctests";
1787 static const char __pyx_k_random_clifford_line_1815[] = "random_clifford (line 1815)";
1788 static const char __pyx_k_Cannot_take_vector_part_of[] = "Cannot take vector part of ";
1789 static const char __pyx_k_Unary_print_clifford_1_1_2[] = "\n Unary +.\n\n >>> print +clifford(\"{1}\")\n {1}\n ";
1790 static const char __pyx_k_clifford___iadd___line_750[] = "clifford.__iadd__ (line 750)";
1791 static const char __pyx_k_clifford___iand___line_850[] = "clifford.__iand__ (line 850)";
1792 static const char __pyx_k_clifford___idiv___line_910[] = "clifford.__idiv__ (line 910)";
1793 static const char __pyx_k_clifford___imod___line_820[] = "clifford.__imod__ (line 820)";
1794 static const char __pyx_k_clifford___imul___line_792[] = "clifford.__imul__ (line 792)";
1795 static const char __pyx_k_clifford___isub___line_770[] = "clifford.__isub__ (line 770)";
1796 static const char __pyx_k_clifford___iter___line_637[] = "clifford.__iter__ (line 637)";
1797 static const char __pyx_k_clifford___ixor___line_880[] = "clifford.__ixor__ (line 880)";
1798 static const char __pyx_k_clifford___str___line_1234[] = "clifford.__str__ (line 1234)";
1799 static const char __pyx_k_clifford_max_abs_line_1183[] = "clifford.max_abs (line 1183)";
1800 static const char __pyx_k_clifford_reverse_line_1122[] = "clifford.reverse (line 1122)";
1801 static const char __pyx_k_index_set___and___line_269[] = "index_set.__and__ (line 269)";
1802 static const char __pyx_k_index_set___ior___line_302[] = "index_set.__ior__ (line 302)";
1803 static const char __pyx_k_index_set___str___line_393[] = "index_set.__str__ (line 393)";
1804 static const char __pyx_k_index_set___xor___line_247[] = "index_set.__xor__ (line 247)";
1805 static const char __pyx_k_clifford___call___line_1019[] = "clifford.__call__ (line 1019)";
1806 static const char __pyx_k_clifford___repr___line_1225[] = "clifford.__repr__ (line 1225)";
1807 static const char __pyx_k_clifford_involute_line_1106[] = "clifford.involute (line 1106)";
1808 static const char __pyx_k_index_set___iand___line_280[] = "index_set.__iand__ (line 280)";
1809 static const char __pyx_k_index_set___iter___line_227[] = "index_set.__iter__ (line 227)";
1810 static const char __pyx_k_index_set___ixor___line_258[] = "index_set.__ixor__ (line 258)";
1811 static const char __pyx_k_index_set___repr___line_382[] = "index_set.__repr__ (line 382)";
1812 static const char __pyx_k_clifford_outer_pow_line_1003[] = "clifford.outer_pow (line 1003)";
1813 static const char __pyx_k_clifford_truncated_line_1194[] = "clifford.truncated (line 1194)";
1814 static const char __pyx_k_index_set_count_neg_line_322[] = "index_set.count_neg (line 322)";
1815 static const char __pyx_k_index_set_count_pos_line_331[] = "index_set.count_pos (line 331)";
1816 static const char __pyx_k_clifford___getitem___line_706[] = "clifford.__getitem__ (line 706)";
1817 static const char __pyx_k_index_set___invert___line_238[] = "index_set.__invert__ (line 238)";
1818 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 ";
1819 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 ";
1820 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 ";
1821 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 ";
1822 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 ";
1823 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 ";
1824 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 ";
1825 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 ";
1826 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 ";
1827 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 ";
1828 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 ";
1829 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 ";
1830 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 ";
1831 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 ";
1832 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 ";
1833 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 ";
1834 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 ";
1835 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 ";
1836 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 ";
1837 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 ";
1838 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 ";
1839 static const char __pyx_k_clifford_vector_part_line_1078[] = "clifford.vector_part (line 1078)";
1840 static const char __pyx_k_index_set___getitem___line_189[] = "index_set.__getitem__ (line 189)";
1841 static const char __pyx_k_index_set___setitem___line_177[] = "index_set.__setitem__ (line 177)";
1842 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 ";
1843 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 ";
1844 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 ";
1845 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 ";
1846 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 ";
1847 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 ";
1848 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 ";
1849 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 ";
1850 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 ";
1851 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 ";
1852 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 ";
1853 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 ";
1854 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 ";
1855 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 ";
1856 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 ";
1857 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 ";
1858 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 ";
1859 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 ";
1860 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 ";
1861 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 ";
1862 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 ";
1863 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 ";
1864 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 ";
1865 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 ";
1866 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 ";
1867 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 ";
1868 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 ";
1869 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 ";
1870 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 ";
1871 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 ";
1872 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 ";
1873 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 ";
1874 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 ";
1875 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 ";
1876 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 ";
1877 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 ";
1878 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 ";
1879 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 ";
1880 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 ";
1881 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 ";
1882 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 ";
1883 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 ";
1884 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 ";
1885 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 ";
1886 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 ";
1887 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 ";
1888 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 ";
1889 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 ";
1890 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 ";
1891 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 ";
1892 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 ";
1893 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 ";
1894 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 ";
1895 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 ";
1896 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 ";
1897 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 ";
1898 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 ";
1899 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 ";
1900 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 ";
1901 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 ";
1902 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 ";
1903 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 ";
1904 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 ";
1905 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 ";
1906 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 ";
1907 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 ";
1908 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 ";
1909 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 ";
1910  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 ";
1911  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 ";
1912  static const char __pyx_k_This_comparison_operator_is_not[] = "This comparison operator is not implemented for ";
1913  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 ";
1914  static const char __pyx_k_index_set_sign_of_mult_line_364[] = "index_set.sign_of_mult (line 364)";
1915  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 ";
1916  static const char __pyx_k_Cannot_initialize_clifford_objec[] = "Cannot initialize clifford object from";
1917  static const char __pyx_k_Cannot_initialize_index_set_obje[] = "Cannot initialize index_set object from";
1918  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 ";
1919  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 ";
1920  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 ";
1921  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 ";
1922  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 ";
1923  static const char __pyx_k_clifford_hidden_doctests_line_12[] = "clifford_hidden_doctests (line 1243)";
1924  static const char __pyx_k_index_set_hidden_doctests_line_4[] = "index_set_hidden_doctests (line 404)";
1925  static const char __pyx_k_index_set_sign_of_square_line_37[] = "index_set.sign_of_square (line 373)";
1926  static const char __pyx_k_no_default___reduce___due_to_non[] = "no default __reduce__ due to non-trivial __cinit__";
1927  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 ";
1928  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 ";
1929  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 ";
1930  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 ";
1931  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 ";
1932  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 ";
1933  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 ";
1934  static PyObject *__pyx_kp_s_;
1935  static PyObject *__pyx_kp_s_0_8_2;
1936  static PyObject *__pyx_kp_u_Abbreviation_for_clifford_index;
1937  static PyObject *__pyx_kp_u_Abbreviation_for_index_set_q_p;
1938  static PyObject *__pyx_kp_u_Absolute_value_of_multivector_m;
1939  static PyObject *__pyx_kp_u_Absolute_value_square_root_of_n;
1940  static PyObject *__pyx_kp_s_Cannot_initialize_clifford_objec;
1941  static PyObject *__pyx_kp_s_Cannot_initialize_index_set_obje;
1942  static PyObject *__pyx_kp_s_Cannot_reframe;
1943  static PyObject *__pyx_kp_s_Cannot_take_vector_part_of;
1944  static PyObject *__pyx_kp_u_Cardinality_Number_of_indices_i;
1945  static PyObject *__pyx_kp_u_Check_if_a_multivector_contains;
1946  static PyObject *__pyx_kp_u_Conjugation_reverse_o_involute;
1947  static PyObject *__pyx_kp_u_Conjugation_reverse_o_involute_2;
1948  static PyObject *__pyx_kp_u_Contraction_print_clifford_1_cl;
1949  static PyObject *__pyx_kp_u_Contraction_x_clifford_1_x_clif;
1950  static PyObject *__pyx_kp_u_Convert_CGA3_null_vector_to_Euc;
1951  static PyObject *__pyx_kp_u_Convert_CGA3_null_vector_to_sta;
1952  static PyObject *__pyx_kp_u_Convert_Euclidean_3D_multivecto;
1953  static PyObject *__pyx_kp_u_Copy_this_clifford_object_x_cli;
1954  static PyObject *__pyx_kp_u_Copy_this_index_set_object_s_in;
1955  static PyObject *__pyx_kp_u_Cosine_of_multivector_with_opti;
1956  static PyObject *__pyx_kp_u_Even_part_of_multivector_sum_of;
1957  static PyObject *__pyx_kp_u_Even_part_of_multivector_sum_of_2;
1958  static PyObject *__pyx_kp_u_Exponential_of_multivector_x_cl;
1959  static PyObject *__pyx_kp_u_Geometric_difference_print_clif;
1960  static PyObject *__pyx_kp_u_Geometric_difference_x_clifford;
1961  static PyObject *__pyx_kp_u_Geometric_multiplicative_invers;
1962  static PyObject *__pyx_kp_u_Geometric_multiplicative_invers_2;
1963  static PyObject *__pyx_kp_u_Geometric_product_print_cliffor;
1964  static PyObject *__pyx_kp_u_Geometric_product_x_clifford_2;
1965  static PyObject *__pyx_kp_u_Geometric_quotient_print_cliffo;
1966  static PyObject *__pyx_kp_u_Geometric_quotient_x_clifford_1;
1967  static PyObject *__pyx_kp_u_Geometric_sum_print_clifford_1;
1968  static PyObject *__pyx_kp_u_Geometric_sum_x_clifford_1_x_cl;
1969  static PyObject *__pyx_kp_u_Get_the_value_of_an_index_set_o;
1970  static PyObject *__pyx_kp_u_Hyperbolic_cosine_of_multivecto;
1971  static PyObject *__pyx_kp_u_Hyperbolic_sine_of_multivector;
1972  static PyObject *__pyx_kp_u_Hyperbolic_tangent_of_multivect;
1973  static PyObject *__pyx_kp_u_Imaginary_part_deprecated_alway;
1974  static PyObject *__pyx_n_s_IndexError;
1975  static PyObject *__pyx_kp_u_Inner_product_print_clifford_1;
1976  static PyObject *__pyx_kp_u_Inner_product_x_clifford_1_x_cl;
1977  static PyObject *__pyx_kp_u_Integer_power_of_multivector_ob;
1978  static PyObject *__pyx_n_s_Integral;
1979  static PyObject *__pyx_kp_u_Inverse_cosine_of_multivector_w;
1980  static PyObject *__pyx_kp_u_Inverse_hyperbolic_cosine_of_mu;
1981  static PyObject *__pyx_kp_u_Inverse_hyperbolic_sine_of_mult;
1982  static PyObject *__pyx_kp_u_Inverse_hyperbolic_tangent_of_m;
1983  static PyObject *__pyx_kp_u_Inverse_sine_of_multivector_wit;
1984  static PyObject *__pyx_kp_u_Inverse_tangent_of_multivector;
1985  static PyObject *__pyx_kp_u_Iterate_over_the_indices_of_an;
1986  static PyObject *__pyx_kp_u_Main_involution_each_i_is_repla;
1987  static PyObject *__pyx_kp_u_Main_involution_each_i_is_repla_2;
1988  static PyObject *__pyx_kp_u_Maximum_absolute_value_of_coord;
1989  static PyObject *__pyx_kp_u_Maximum_member_index_set_1_1_2;
1990  static PyObject *__pyx_kp_u_Maximum_of_absolute_values_of_c;
1991  static PyObject *__pyx_kp_u_Maximum_positive_index_or_0_if;
1992  static PyObject *__pyx_kp_u_Minimum_member_index_set_1_1_2;
1993  static PyObject *__pyx_kp_u_Minimum_negative_index_or_0_if;
1994  static PyObject *__pyx_kp_u_Natural_logarithm_of_multivecto;
1995  static PyObject *__pyx_kp_u_Norm_sum_of_squares_of_coordina;
1996  static PyObject *__pyx_n_s_NotImplemented;
1997  static PyObject *__pyx_kp_s_Not_applicable;
1998  static PyObject *__pyx_kp_u_Not_applicable_for_a_in_cliffor;
1999  static PyObject *__pyx_kp_u_Number_of_negative_indices_incl;
2000  static PyObject *__pyx_kp_u_Number_of_positive_indices_incl;
2001  static PyObject *__pyx_kp_u_Odd_part_of_multivector_sum_of;
2002  static PyObject *__pyx_kp_u_Odd_part_of_multivector_sum_of_2;
2003  static PyObject *__pyx_kp_u_Outer_product_power_of_multivec;
2004  static PyObject *__pyx_kp_u_Outer_product_power_x_clifford;
2005  static PyObject *__pyx_kp_u_Outer_product_print_clifford_1;
2006  static PyObject *__pyx_kp_u_Outer_product_x_clifford_1_x_cl;
2007  static PyObject *__pyx_kp_u_Power_self_to_the_m_x_clifford;
2008  static PyObject *__pyx_kp_u_Power_self_to_the_m_x_clifford_2;
2009  static PyObject *__pyx_kp_u_Pure_grade_vector_part_print_cl;
2010  static PyObject *__pyx_kp_u_Pure_part_print_clifford_1_1_1;
2011  static PyObject *__pyx_kp_u_Pure_part_print_pure_clifford_1;
2012  static PyObject *__pyx_kp_u_Put_self_into_a_larger_frame_co;
2013  static PyObject *__pyx_n_s_PyClical;
2014  static PyObject *__pyx_kp_s_PyClical_pyx;
2015  static PyObject *__pyx_kp_u_Quadratic_form_rev_x_x_0_print;
2016  static PyObject *__pyx_kp_u_Quadratic_form_rev_x_x_0_print_2;
2017  static PyObject *__pyx_kp_u_Random_multivector_within_a_fra;
2018  static PyObject *__pyx_n_s_Real;
2019  static PyObject *__pyx_kp_u_Real_part_synonym_for_scalar_pa;
2020  static PyObject *__pyx_kp_u_Remove_all_terms_of_self_with_r;
2021  static PyObject *__pyx_kp_u_Reversion_eg_1_2_2_1_print_reve;
2022  static PyObject *__pyx_kp_u_Reversion_eg_clifford_1_cliffor;
2023  static PyObject *__pyx_n_s_RuntimeError;
2024  static PyObject *__pyx_kp_u_Scalar_part_clifford_1_1_1_2_sc;
2025  static PyObject *__pyx_kp_u_Scalar_part_scalar_clifford_1_1;
2026  static PyObject *__pyx_n_s_Sequence;
2027  static PyObject *__pyx_kp_u_Set_complement_not_print_index;
2028  static PyObject *__pyx_kp_u_Set_intersection_and_print_inde;
2029  static PyObject *__pyx_kp_u_Set_intersection_and_x_index_se;
2030  static PyObject *__pyx_kp_u_Set_the_value_of_an_index_set_o;
2031  static PyObject *__pyx_kp_u_Set_union_or_print_index_set_1;
2032  static PyObject *__pyx_kp_u_Set_union_or_x_index_set_1_x_in;
2033  static PyObject *__pyx_kp_u_Sign_of_geometric_product_of_tw;
2034  static PyObject *__pyx_kp_u_Sign_of_geometric_square_of_a_C;
2035  static PyObject *__pyx_kp_u_Sine_of_multivector_with_option;
2036  static PyObject *__pyx_kp_u_Square_root_of_1_which_commutes;
2037  static PyObject *__pyx_kp_u_Square_root_of_multivector_with;
2038  static PyObject *__pyx_kp_u_Subalgebra_generated_by_all_gen;
2039  static PyObject *__pyx_kp_u_Subscripting_map_from_index_set;
2040  static PyObject *__pyx_kp_u_Symmetric_set_difference_exclus;
2041  static PyObject *__pyx_kp_u_Symmetric_set_difference_exclus_2;
2042  static PyObject *__pyx_kp_u_Tangent_of_multivector_with_opt;
2043  static PyObject *__pyx_kp_u_Tests_for_functions_that_Doctes;
2044  static PyObject *__pyx_kp_u_Tests_for_functions_that_Doctes_2;
2045  static PyObject *__pyx_kp_u_The_informal_string_representat;
2046  static PyObject *__pyx_kp_u_The_informal_string_representat_2;
2047  static PyObject *__pyx_kp_u_The_official_string_representat;
2048  static PyObject *__pyx_kp_u_The_official_string_representat_2;
2049  static PyObject *__pyx_kp_s_This_comparison_operator_is_not;
2050  static PyObject *__pyx_kp_u_Transform_left_hand_side_using;
2051  static PyObject *__pyx_kp_u_Transform_left_hand_side_using_2;
2052  static PyObject *__pyx_n_s_TypeError;
2053  static PyObject *__pyx_kp_u_Unary_print_clifford_1_1;
2054  static PyObject *__pyx_kp_u_Unary_print_clifford_1_1_2;
2055  static PyObject *__pyx_n_s_ValueError;
2056  static PyObject *__pyx_kp_u_Vector_part_of_multivector_as_a;
2057  static PyObject *__pyx_kp_s__2;
2058  static PyObject *__pyx_kp_s__5;
2059  static PyObject *__pyx_kp_s__6;
2060  static PyObject *__pyx_kp_s__7;
2061  static PyObject *__pyx_kp_s__8;
2062  static PyObject *__pyx_kp_s__9;
2063  static PyObject *__pyx_kp_u_abs_line_1473;
2064  static PyObject *__pyx_n_s_acos;
2065  static PyObject *__pyx_kp_u_acos_line_1619;
2066  static PyObject *__pyx_n_s_acosh;
2067  static PyObject *__pyx_kp_u_acosh_line_1656;
2068  static PyObject *__pyx_kp_u_agc3_line_1844;
2069  static PyObject *__pyx_n_s_args;
2070  static PyObject *__pyx_kp_s_as_frame;
2071  static PyObject *__pyx_n_s_asin;
2072  static PyObject *__pyx_kp_u_asin_line_1698;
2073  static PyObject *__pyx_n_s_asinh;
2074  static PyObject *__pyx_kp_u_asinh_line_1733;
2075  static PyObject *__pyx_n_s_atan;
2076  static PyObject *__pyx_kp_u_atan_line_1769;
2077  static PyObject *__pyx_n_s_atanh;
2078  static PyObject *__pyx_kp_u_atanh_line_1798;
2079  static PyObject *__pyx_kp_u_cga3_line_1824;
2080  static PyObject *__pyx_kp_u_cga3std_line_1833;
2081  static PyObject *__pyx_n_s_cl;
2082  static PyObject *__pyx_kp_u_clifford___add___line_739;
2083  static PyObject *__pyx_kp_u_clifford___and___line_835;
2084  static PyObject *__pyx_kp_u_clifford___call___line_1019;
2085  static PyObject *__pyx_kp_u_clifford___div___line_895;
2086  static PyObject *__pyx_kp_u_clifford___getitem___line_706;
2087  static PyObject *__pyx_kp_u_clifford___iadd___line_750;
2088  static PyObject *__pyx_kp_u_clifford___iand___line_850;
2089  static PyObject *__pyx_kp_u_clifford___idiv___line_910;
2090  static PyObject *__pyx_kp_u_clifford___imod___line_820;
2091  static PyObject *__pyx_kp_u_clifford___imul___line_792;
2092  static PyObject *__pyx_kp_u_clifford___ior___line_949;
2093  static PyObject *__pyx_kp_u_clifford___isub___line_770;
2094  static PyObject *__pyx_kp_u_clifford___iter___line_637;
2095  static PyObject *__pyx_kp_u_clifford___ixor___line_880;
2096  static PyObject *__pyx_kp_u_clifford___mod___line_805;
2097  static PyObject *__pyx_kp_u_clifford___mul___line_779;
2098  static PyObject *__pyx_kp_u_clifford___neg___line_721;
2099  static PyObject *__pyx_kp_u_clifford___or___line_938;
2100  static PyObject *__pyx_kp_u_clifford___pos___line_730;
2101  static PyObject *__pyx_kp_u_clifford___pow___line_960;
2102  static PyObject *__pyx_kp_u_clifford___repr___line_1225;
2103  static PyObject *__pyx_kp_u_clifford___str___line_1234;
2104  static PyObject *__pyx_kp_u_clifford___sub___line_759;
2105  static PyObject *__pyx_kp_u_clifford___xor___line_865;
2106  static PyObject *__pyx_kp_u_clifford_abs_line_1174;
2107  static PyObject *__pyx_kp_u_clifford_conj_line_1137;
2108  static PyObject *__pyx_kp_u_clifford_copy_line_554;
2109  static PyObject *__pyx_kp_u_clifford_even_line_1060;
2110  static PyObject *__pyx_kp_u_clifford_frame_line_1214;
2111  static PyObject *__pyx_n_s_clifford_hidden_doctests;
2112  static PyObject *__pyx_kp_u_clifford_hidden_doctests_line_12;
2113  static PyObject *__pyx_kp_u_clifford_inv_line_925;
2114  static PyObject *__pyx_kp_u_clifford_involute_line_1106;
2115  static PyObject *__pyx_kp_u_clifford_isnan_line_1205;
2116  static PyObject *__pyx_kp_u_clifford_max_abs_line_1183;
2117  static PyObject *__pyx_kp_u_clifford_norm_line_1163;
2118  static PyObject *__pyx_kp_u_clifford_odd_line_1069;
2119  static PyObject *__pyx_kp_u_clifford_outer_pow_line_1003;
2120  static PyObject *__pyx_kp_u_clifford_pow_line_979;
2121  static PyObject *__pyx_kp_u_clifford_pure_line_1049;
2122  static PyObject *__pyx_kp_u_clifford_quad_line_1152;
2123  static PyObject *__pyx_kp_u_clifford_reframe_line_648;
2124  static PyObject *__pyx_kp_u_clifford_reverse_line_1122;
2125  static PyObject *__pyx_kp_u_clifford_scalar_line_1038;
2126  static PyObject *__pyx_kp_u_clifford_truncated_line_1194;
2127  static PyObject *__pyx_kp_u_clifford_vector_part_line_1078;
2128  static PyObject *__pyx_n_s_cline_in_traceback;
2129  static PyObject *__pyx_n_s_close;
2130  static PyObject *__pyx_n_s_collections;
2131  static PyObject *__pyx_kp_u_compare_line_490;
2132  static PyObject *__pyx_kp_u_complexifier_line_1527;
2133  static PyObject *__pyx_n_s_conj;
2134  static PyObject *__pyx_kp_u_conj_line_1436;
2135  static PyObject *__pyx_n_s_copy;
2136  static PyObject *__pyx_n_s_cos;
2137  static PyObject *__pyx_kp_u_cos_line_1602;
2138  static PyObject *__pyx_n_s_cosh;
2139  static PyObject *__pyx_kp_u_cosh_line_1640;
2140  static PyObject *__pyx_n_s_doctest;
2141  static PyObject *__pyx_n_s_e;
2142  static PyObject *__pyx_kp_u_e_line_1887;
2143  static PyObject *__pyx_n_s_even;
2144  static PyObject *__pyx_kp_u_even_line_1388;
2145  static PyObject *__pyx_n_s_exp;
2146  static PyObject *__pyx_kp_u_exp_line_1565;
2147  static PyObject *__pyx_n_s_fill;
2148  static PyObject *__pyx_n_s_frm;
2149  static PyObject *__pyx_kp_s_from;
2150  static PyObject *__pyx_n_s_getstate;
2151  static PyObject *__pyx_n_s_grade;
2152  static PyObject *__pyx_n_s_i;
2153  static PyObject *__pyx_kp_u_imag_line_1366;
2154  static PyObject *__pyx_n_s_import;
2155  static PyObject *__pyx_kp_u_index_set___and___line_269;
2156  static PyObject *__pyx_kp_u_index_set___getitem___line_189;
2157  static PyObject *__pyx_kp_u_index_set___iand___line_280;
2158  static PyObject *__pyx_kp_u_index_set___invert___line_238;
2159  static PyObject *__pyx_kp_u_index_set___ior___line_302;
2160  static PyObject *__pyx_n_s_index_set___iter;
2161  static PyObject *__pyx_kp_u_index_set___iter___line_227;
2162  static PyObject *__pyx_kp_u_index_set___ixor___line_258;
2163  static PyObject *__pyx_kp_u_index_set___or___line_291;
2164  static PyObject *__pyx_kp_u_index_set___repr___line_382;
2165  static PyObject *__pyx_kp_u_index_set___setitem___line_177;
2166  static PyObject *__pyx_kp_u_index_set___str___line_393;
2167  static PyObject *__pyx_kp_u_index_set___xor___line_247;
2168  static PyObject *__pyx_kp_u_index_set_copy_line_64;
2169  static PyObject *__pyx_kp_u_index_set_count_line_313;
2170  static PyObject *__pyx_kp_u_index_set_count_neg_line_322;
2171  static PyObject *__pyx_kp_u_index_set_count_pos_line_331;
2172  static PyObject *__pyx_n_s_index_set_hidden_doctests;
2173  static PyObject *__pyx_kp_u_index_set_hidden_doctests_line_4;
2174  static PyObject *__pyx_kp_u_index_set_max_line_349;
2175  static PyObject *__pyx_kp_u_index_set_min_line_340;
2176  static PyObject *__pyx_kp_u_index_set_sign_of_mult_line_364;
2177  static PyObject *__pyx_kp_u_index_set_sign_of_square_line_37;
2178  static PyObject *__pyx_n_s_inv;
2179  static PyObject *__pyx_kp_u_inv_line_1329;
2180  static PyObject *__pyx_kp_s_invalid;
2181  static PyObject *__pyx_kp_s_invalid_string;
2182  static PyObject *__pyx_n_s_involute;
2183  static PyObject *__pyx_kp_u_involute_line_1406;
2184  static PyObject *__pyx_n_s_ist;
2185  static PyObject *__pyx_n_s_istpq;
2186  static PyObject *__pyx_kp_u_istpq_line_1900;
2187  static PyObject *__pyx_n_s_iter;
2188  static PyObject *__pyx_n_s_ixt;
2189  static PyObject *__pyx_kp_u_lexicographic_compare_eg_3_4_5;
2190  static PyObject *__pyx_n_s_lhs;
2191  static PyObject *__pyx_n_s_log;
2192  static PyObject *__pyx_kp_u_log_line_1579;
2193  static PyObject *__pyx_n_s_m;
2194  static PyObject *__pyx_n_s_main;
2195  static PyObject *__pyx_n_s_math;
2196  static PyObject *__pyx_n_s_max;
2197  static PyObject *__pyx_kp_u_max_abs_line_1482;
2198  static PyObject *__pyx_kp_u_max_pos_line_511;
2199  static PyObject *__pyx_n_s_min;
2200  static PyObject *__pyx_kp_u_min_neg_line_502;
2201  static PyObject *__pyx_n_s_name;
2202  static PyObject *__pyx_n_s_nbar3;
2203  static PyObject *__pyx_n_s_ninf3;
2204  static PyObject *__pyx_kp_s_no_default___reduce___due_to_non;
2205  static PyObject *__pyx_n_s_norm;
2206  static PyObject *__pyx_kp_u_norm_line_1462;
2207  static PyObject *__pyx_kp_u_norm_sum_of_squares_of_coordina;
2208  static PyObject *__pyx_n_s_numbers;
2209  static PyObject *__pyx_n_s_obj;
2210  static PyObject *__pyx_n_s_odd;
2211  static PyObject *__pyx_kp_u_odd_line_1397;
2212  static PyObject *__pyx_n_s_other;
2213  static PyObject *__pyx_n_s_outer_pow;
2214  static PyObject *__pyx_kp_u_outer_pow_line_1518;
2215  static PyObject *__pyx_n_s_p;
2216  static PyObject *__pyx_n_s_pi;
2217  static PyObject *__pyx_n_s_pow;
2218  static PyObject *__pyx_kp_u_pow_line_1494;
2219  static PyObject *__pyx_n_s_pure;
2220  static PyObject *__pyx_kp_u_pure_line_1377;
2221  static PyObject *__pyx_n_s_pyx_vtable;
2222  static PyObject *__pyx_n_s_q;
2223  static PyObject *__pyx_n_s_quad;
2224  static PyObject *__pyx_kp_u_quad_line_1451;
2225  static PyObject *__pyx_kp_u_random_clifford_line_1815;
2226  static PyObject *__pyx_n_s_range;
2227  static PyObject *__pyx_kp_u_real_line_1355;
2228  static PyObject *__pyx_n_s_reduce;
2229  static PyObject *__pyx_n_s_reduce_cython;
2230  static PyObject *__pyx_n_s_reduce_ex;
2231  static PyObject *__pyx_n_s_reverse;
2232  static PyObject *__pyx_kp_u_reverse_line_1421;
2233  static PyObject *__pyx_n_s_rhs;
2234  static PyObject *__pyx_n_s_scalar;
2235  static PyObject *__pyx_kp_u_scalar_line_1344;
2236  static PyObject *__pyx_n_s_send;
2237  static PyObject *__pyx_n_s_setstate;
2238  static PyObject *__pyx_n_s_setstate_cython;
2239  static PyObject *__pyx_n_s_sin;
2240  static PyObject *__pyx_kp_u_sin_line_1679;
2241  static PyObject *__pyx_n_s_sinh;
2242  static PyObject *__pyx_kp_u_sinh_line_1719;
2243  static PyObject *__pyx_n_s_sqrt;
2244  static PyObject *__pyx_kp_u_sqrt_line_1542;
2245  static PyObject *__pyx_n_s_tan;
2246  static PyObject *__pyx_kp_u_tan_line_1752;
2247  static PyObject *__pyx_n_s_tanh;
2248  static PyObject *__pyx_kp_u_tanh_line_1786;
2249  static PyObject *__pyx_n_s_tau;
2250  static PyObject *__pyx_n_s_test;
2251  static PyObject *__pyx_n_s_test_2;
2252  static PyObject *__pyx_n_s_testmod;
2253  static PyObject *__pyx_n_s_throw;
2254  static PyObject *__pyx_kp_s_to_frame;
2255  static PyObject *__pyx_kp_s_using;
2256  static PyObject *__pyx_kp_s_using_invalid;
2257  static PyObject *__pyx_kp_s_value;
2258  static PyObject *__pyx_n_s_version;
2259  static PyObject *__pyx_n_s_xrange;
2260 static PyObject *__pyx_pf_8PyClical_9index_set_copy(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2261 static int __pyx_pf_8PyClical_9index_set_2__cinit__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_other); /* proto */
2262 static void __pyx_pf_8PyClical_9index_set_4__dealloc__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2263 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 */
2264 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 */
2265 static PyObject *__pyx_pf_8PyClical_9index_set_10__getitem__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_idx); /* proto */
2266 static int __pyx_pf_8PyClical_9index_set_12__contains__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_idx); /* proto */
2267 static PyObject *__pyx_pf_8PyClical_9index_set_14__iter__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2268 static PyObject *__pyx_pf_8PyClical_9index_set_17__invert__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2269 static PyObject *__pyx_pf_8PyClical_9index_set_19__xor__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2270 static PyObject *__pyx_pf_8PyClical_9index_set_21__ixor__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2271 static PyObject *__pyx_pf_8PyClical_9index_set_23__and__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2272 static PyObject *__pyx_pf_8PyClical_9index_set_25__iand__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2273 static PyObject *__pyx_pf_8PyClical_9index_set_27__or__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2274 static PyObject *__pyx_pf_8PyClical_9index_set_29__ior__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2275 static PyObject *__pyx_pf_8PyClical_9index_set_31count(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2276 static PyObject *__pyx_pf_8PyClical_9index_set_33count_neg(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2277 static PyObject *__pyx_pf_8PyClical_9index_set_35count_pos(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2278 static PyObject *__pyx_pf_8PyClical_9index_set_37min(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2279 static PyObject *__pyx_pf_8PyClical_9index_set_39max(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2280 static PyObject *__pyx_pf_8PyClical_9index_set_41hash_fn(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2281 static PyObject *__pyx_pf_8PyClical_9index_set_43sign_of_mult(struct __pyx_obj_8PyClical_index_set *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2282 static PyObject *__pyx_pf_8PyClical_9index_set_45sign_of_square(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2283 static PyObject *__pyx_pf_8PyClical_9index_set_47__repr__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2284 static PyObject *__pyx_pf_8PyClical_9index_set_49__str__(struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2285 static PyObject *__pyx_pf_8PyClical_9index_set_51__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_8PyClical_index_set *__pyx_v_self); /* proto */
2286 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 */
2287 static PyObject *__pyx_pf_8PyClical_index_set_hidden_doctests(CYTHON_UNUSED PyObject *__pyx_self); /* proto */
2288 static PyObject *__pyx_pf_8PyClical_2compare(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2289 static PyObject *__pyx_pf_8PyClical_4min_neg(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2290 static PyObject *__pyx_pf_8PyClical_6max_pos(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2291 static PyObject *__pyx_pf_8PyClical_8clifford_copy(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2292 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 */
2293 static void __pyx_pf_8PyClical_8clifford_4__dealloc__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2294 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 */
2295 static PyObject *__pyx_pf_8PyClical_8clifford_8__iter__(CYTHON_UNUSED struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2296 static PyObject *__pyx_pf_8PyClical_8clifford_10reframe(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_ixt); /* proto */
2297 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 */
2298 static PyObject *__pyx_pf_8PyClical_8clifford_14__getitem__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_ixt); /* proto */
2299 static PyObject *__pyx_pf_8PyClical_8clifford_16__neg__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2300 static PyObject *__pyx_pf_8PyClical_8clifford_18__pos__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2301 static PyObject *__pyx_pf_8PyClical_8clifford_20__add__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2302 static PyObject *__pyx_pf_8PyClical_8clifford_22__iadd__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2303 static PyObject *__pyx_pf_8PyClical_8clifford_24__sub__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2304 static PyObject *__pyx_pf_8PyClical_8clifford_26__isub__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2305 static PyObject *__pyx_pf_8PyClical_8clifford_28__mul__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2306 static PyObject *__pyx_pf_8PyClical_8clifford_30__imul__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2307 static PyObject *__pyx_pf_8PyClical_8clifford_32__mod__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2308 static PyObject *__pyx_pf_8PyClical_8clifford_34__imod__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2309 static PyObject *__pyx_pf_8PyClical_8clifford_36__and__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2310 static PyObject *__pyx_pf_8PyClical_8clifford_38__iand__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2311 static PyObject *__pyx_pf_8PyClical_8clifford_40__xor__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2312 static PyObject *__pyx_pf_8PyClical_8clifford_42__ixor__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2313 #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
2314 static PyObject *__pyx_pf_8PyClical_8clifford_44__div__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2315 #endif
2316 #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
2317 static PyObject *__pyx_pf_8PyClical_8clifford_46__idiv__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2318 #endif
2319 static PyObject *__pyx_pf_8PyClical_8clifford_48inv(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2320 static PyObject *__pyx_pf_8PyClical_8clifford_50__or__(PyObject *__pyx_v_lhs, PyObject *__pyx_v_rhs); /* proto */
2321 static PyObject *__pyx_pf_8PyClical_8clifford_52__ior__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_rhs); /* proto */
2322 static PyObject *__pyx_pf_8PyClical_8clifford_54__pow__(PyObject *__pyx_v_self, PyObject *__pyx_v_m, CYTHON_UNUSED PyObject *__pyx_v_dummy); /* proto */
2323 static PyObject *__pyx_pf_8PyClical_8clifford_56pow(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_m); /* proto */
2324 static PyObject *__pyx_pf_8PyClical_8clifford_58outer_pow(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_m); /* proto */
2325 static PyObject *__pyx_pf_8PyClical_8clifford_60__call__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_grade); /* proto */
2326 static PyObject *__pyx_pf_8PyClical_8clifford_62scalar(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2327 static PyObject *__pyx_pf_8PyClical_8clifford_64pure(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2328 static PyObject *__pyx_pf_8PyClical_8clifford_66even(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2329 static PyObject *__pyx_pf_8PyClical_8clifford_68odd(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2330 static PyObject *__pyx_pf_8PyClical_8clifford_70vector_part(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_frm); /* proto */
2331 static PyObject *__pyx_pf_8PyClical_8clifford_72involute(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2332 static PyObject *__pyx_pf_8PyClical_8clifford_74reverse(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2333 static PyObject *__pyx_pf_8PyClical_8clifford_76conj(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2334 static PyObject *__pyx_pf_8PyClical_8clifford_78quad(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2335 static PyObject *__pyx_pf_8PyClical_8clifford_80norm(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2336 static PyObject *__pyx_pf_8PyClical_8clifford_82abs(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2337 static PyObject *__pyx_pf_8PyClical_8clifford_84max_abs(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2338 static PyObject *__pyx_pf_8PyClical_8clifford_86truncated(struct __pyx_obj_8PyClical_clifford *__pyx_v_self, PyObject *__pyx_v_limit); /* proto */
2339 static PyObject *__pyx_pf_8PyClical_8clifford_88isnan(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2340 static PyObject *__pyx_pf_8PyClical_8clifford_90frame(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2341 static PyObject *__pyx_pf_8PyClical_8clifford_92__repr__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2342 static PyObject *__pyx_pf_8PyClical_8clifford_94__str__(struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2343 static PyObject *__pyx_pf_8PyClical_8clifford_96__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_8PyClical_clifford *__pyx_v_self); /* proto */
2344 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 */
2345 static PyObject *__pyx_pf_8PyClical_8clifford_hidden_doctests(CYTHON_UNUSED PyObject *__pyx_self); /* proto */
2346 static PyObject *__pyx_pf_8PyClical_10inv(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2347 static PyObject *__pyx_pf_8PyClical_12scalar(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2348 static PyObject *__pyx_pf_8PyClical_14real(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2349 static PyObject *__pyx_pf_8PyClical_16imag(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2350 static PyObject *__pyx_pf_8PyClical_18pure(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2351 static PyObject *__pyx_pf_8PyClical_20even(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2352 static PyObject *__pyx_pf_8PyClical_22odd(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2353 static PyObject *__pyx_pf_8PyClical_24involute(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2354 static PyObject *__pyx_pf_8PyClical_26reverse(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2355 static PyObject *__pyx_pf_8PyClical_28conj(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2356 static PyObject *__pyx_pf_8PyClical_30quad(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2357 static PyObject *__pyx_pf_8PyClical_32norm(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2358 static PyObject *__pyx_pf_8PyClical_34abs(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2359 static PyObject *__pyx_pf_8PyClical_36max_abs(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2360 static PyObject *__pyx_pf_8PyClical_38pow(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_m); /* proto */
2361 static PyObject *__pyx_pf_8PyClical_40outer_pow(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_m); /* proto */
2362 static PyObject *__pyx_pf_8PyClical_42complexifier(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2363 static PyObject *__pyx_pf_8PyClical_44sqrt(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2364 static PyObject *__pyx_pf_8PyClical_46exp(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2365 static PyObject *__pyx_pf_8PyClical_48log(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2366 static PyObject *__pyx_pf_8PyClical_50cos(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2367 static PyObject *__pyx_pf_8PyClical_52acos(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2368 static PyObject *__pyx_pf_8PyClical_54cosh(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
2369 static PyObject *__pyx_pf_8PyClical_56acosh(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2370 static PyObject *__pyx_pf_8PyClical_58sin(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2371 static PyObject *__pyx_pf_8PyClical_60asin(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj, PyObject *__pyx_v_i); /* proto */
2372 static PyObject *__pyx_pf_8PyClical_62sinh(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_obj); /* proto */
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2800  * if isinstance(other, index_set): # <<<<<<<<<<<<<<
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2802  * elif isinstance(other, numbers.Integral):
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2806 
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2824  /* "PyClical.pyx":96
2825  * self.instance = new IndexSet((<index_set>other).unwrap())
2826  * elif isinstance(other, numbers.Integral):
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2831  __pyx_t_6 = __Pyx_PyInt_As_int(__pyx_v_other); if (unlikely((__pyx_t_6 == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 96, __pyx_L1_error)
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2838  __pyx_v_self->instance = __pyx_t_3;
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2840  /* "PyClical.pyx":95
2841  * if isinstance(other, index_set):
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2843  * elif isinstance(other, numbers.Integral): # <<<<<<<<<<<<<<
2844  * self.instance = new IndexSet(<int>other)
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2847  goto __pyx_L3;
2848  }
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2850  /* "PyClical.pyx":97
2851  * elif isinstance(other, numbers.Integral):
2852  * self.instance = new IndexSet(<int>other)
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2865  __pyx_t_2 = (__pyx_t_7 != 0);
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2867  __pyx_L4_bool_binop_done:;
2868  __pyx_t_2 = (__pyx_t_1 != 0);
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2871  /* "PyClical.pyx":98
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2873  * elif isinstance(other, (set, frozenset)):
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2879  __Pyx_PyThreadState_declare
2880  __Pyx_PyThreadState_assign
2881  __Pyx_ExceptionSave(&__pyx_t_8, &__pyx_t_9, &__pyx_t_10);
2882  __Pyx_XGOTREF(__pyx_t_8);
2883  __Pyx_XGOTREF(__pyx_t_9);
2884  __Pyx_XGOTREF(__pyx_t_10);
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2897  /* "PyClical.pyx":100
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2955  /* "PyClical.pyx":100
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2958  * for idx in other: # <<<<<<<<<<<<<<
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2962  }
2963  __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
2964 
2965  /* "PyClical.pyx":98
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2969  * self.instance = new IndexSet()
2970  * for idx in other:
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2979  __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
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2992  __Pyx_GOTREF(__pyx_t_5);
2993  __Pyx_GOTREF(__pyx_t_4);
2994  __Pyx_GOTREF(__pyx_t_13);
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3008  __Pyx_GOTREF(__pyx_t_16);
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3010  __Pyx_DECREF(__pyx_t_15); __pyx_t_15 = 0;
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3018  __Pyx_DECREF(__pyx_t_16); __pyx_t_16 = 0;
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3025  * except (RuntimeError, TypeError): # <<<<<<<<<<<<<<
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3032  if (__Pyx_GetException(&__pyx_t_13, &__pyx_t_4, &__pyx_t_5) < 0) __PYX_ERR(0, 104, __pyx_L8_except_error)
3033  __Pyx_GOTREF(__pyx_t_13);
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3077  __pyx_L11_try_end:;
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3149  __Pyx_XDECREF(__pyx_t_13); __pyx_t_13 = 0;
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3489 
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3534  * return eq
3535  * elif op == 4: # > # <<<<<<<<<<<<<<
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3701  * if op == 0: # <
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4349  * def __invert__(self): # <<<<<<<<<<<<<<
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4418  * def __xor__(lhs, rhs): # <<<<<<<<<<<<<<
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4421  */
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4467  * def __xor__(lhs, rhs): # <<<<<<<<<<<<<<
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6280  */
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6364  scalar_t __pyx_t_9;
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6366  PyObject *__pyx_t_11 = NULL;
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6442  * if isinstance(other, clifford): # <<<<<<<<<<<<<<
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6681  __pyx_L10:;
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6684  * error_msg_prefix = "Cannot initialize clifford object from"
6685  * if ixt is None:
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6687  * if isinstance(other, clifford):
6688  * self.instance = new Clifford((<clifford>other).unwrap())
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6692  __Pyx_XDECREF(__pyx_t_4); __pyx_t_4 = 0;
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6695  __pyx_L4_error:;
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6697  __Pyx_XDECREF(__pyx_t_17); __pyx_t_17 = 0;
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6701  __Pyx_XDECREF(__pyx_t_8); __pyx_t_8 = 0;
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6734  __Pyx_DECREF(__pyx_t_17); __pyx_t_17 = 0;
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6789 
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6792  * if ixt is None:
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6798  __Pyx_XGIVEREF(__pyx_t_4);
6799  __Pyx_XGIVEREF(__pyx_t_5);
6800  __Pyx_ExceptionReset(__pyx_t_3, __pyx_t_4, __pyx_t_5);
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6802  __pyx_L9_try_end:;
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6808  * if ixt is None: # <<<<<<<<<<<<<<
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6810  * if isinstance(other, clifford):
6811  */
6812  goto __pyx_L3;
6813  }
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6823  __pyx_t_1 = (__pyx_t_2 != 0);
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6830  * self.instance = new Clifford((<index_set>ixt).unwrap(), <scalar_t>other)
6831  * elif isinstance(other, collections.Sequence):
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6841  if (__pyx_t_2) {
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6843  /* "PyClical.pyx":610
6844  * elif isinstance(ixt, index_set):
6845  * if isinstance(other, numbers.Real):
6846  * self.instance = new Clifford((<index_set>ixt).unwrap(), <scalar_t>other) # <<<<<<<<<<<<<<
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6852  __pyx_t_6 = new Clifford(__pyx_f_8PyClical_9index_set_unwrap(((struct __pyx_obj_8PyClical_index_set *)__pyx_v_ixt)), ((scalar_t)__pyx_t_9));
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6863  * self.instance = new Clifford((<index_set>ixt).unwrap(), <scalar_t>other)
6864  * elif isinstance(other, collections.Sequence):
6865  */
6866  goto __pyx_L21;
6867  }
6868 
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6870  * if isinstance(other, numbers.Real):
6871  * self.instance = new Clifford((<index_set>ixt).unwrap(), <scalar_t>other)
6872  * elif isinstance(other, collections.Sequence): # <<<<<<<<<<<<<<
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6888  * elif isinstance(other, collections.Sequence):
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6902  * if isinstance(other, numbers.Real):
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6904  * elif isinstance(other, collections.Sequence): # <<<<<<<<<<<<<<
6905  * self.instance = new Clifford(list_to_vector(other), (<index_set>ixt).unwrap())
6906  * else:
6907  */
6908  goto __pyx_L21;
6909  }
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6968  * if isinstance(other, numbers.Real):
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6971  goto __pyx_L3;
6972  }
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7016  *
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7060  */
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7062  /* Python wrapper */
7063  static void __pyx_pw_8PyClical_8clifford_5__dealloc__(PyObject *__pyx_v_self); /*proto*/
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7212  __pyx_L1_error:;
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7258  PyObject *__pyx_t_10 = NULL;
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7277  * if isinstance(ixt, index_set): # <<<<<<<<<<<<<<
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7330  * if isinstance(ixt, index_set):
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7411  __Pyx_DECREF(__pyx_t_13); __pyx_t_13 = 0;
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7416  * raise ValueError(error_msg_prefix + " from " + str(self) + " to frame " # <<<<<<<<<<<<<<
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7428  __pyx_L6_except_error:;
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7430  /* "PyClical.pyx":660
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9872  * cdef int i
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18613  return o;
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18618 
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18622  if (PyObject_CallFinalizerFromDealloc(o)) return;
18623  }
18624  #endif
18625  {
18626  PyObject *etype, *eval, *etb;
18627  PyErr_Fetch(&etype, &eval, &etb);
18628  ++Py_REFCNT(o);
18629  __pyx_pw_8PyClical_9index_set_5__dealloc__(o);
18630  --Py_REFCNT(o);
18631  PyErr_Restore(etype, eval, etb);
18632  }
18633  (*Py_TYPE(o)->tp_free)(o);
18634  }
18635  static PyObject *__pyx_sq_item_8PyClical_index_set(PyObject *o, Py_ssize_t i) {
18636  PyObject *r;
18637  PyObject *x = PyInt_FromSsize_t(i); if(!x) return 0;
18638  r = Py_TYPE(o)->tp_as_mapping->mp_subscript(o, x);
18639  Py_DECREF(x);
18640  return r;
18641  }
18642 
18643  static int __pyx_mp_ass_subscript_8PyClical_index_set(PyObject *o, PyObject *i, PyObject *v) {
18644  if (v) {
18645  return __pyx_pw_8PyClical_9index_set_9__setitem__(o, i, v);
18646  }
18647  else {
18648  PyErr_Format(PyExc_NotImplementedError,
18649  "Subscript deletion not supported by %.200s", Py_TYPE(o)->tp_name);
18650  return -1;
18651  }
18652  }
18653 
18654  static PyMethodDef __pyx_methods_8PyClical_index_set[] = {
18655  {"copy", (PyCFunction)__pyx_pw_8PyClical_9index_set_1copy, METH_NOARGS, __pyx_doc_8PyClical_9index_set_copy},
18656  {"count", (PyCFunction)__pyx_pw_8PyClical_9index_set_32count, METH_NOARGS, __pyx_doc_8PyClical_9index_set_31count},
18657  {"count_neg", (PyCFunction)__pyx_pw_8PyClical_9index_set_34count_neg, METH_NOARGS, __pyx_doc_8PyClical_9index_set_33count_neg},
18658  {"count_pos", (PyCFunction)__pyx_pw_8PyClical_9index_set_36count_pos, METH_NOARGS, __pyx_doc_8PyClical_9index_set_35count_pos},
18659  {"min", (PyCFunction)__pyx_pw_8PyClical_9index_set_38min, METH_NOARGS, __pyx_doc_8PyClical_9index_set_37min},
18660  {"max", (PyCFunction)__pyx_pw_8PyClical_9index_set_40max, METH_NOARGS, __pyx_doc_8PyClical_9index_set_39max},
18661  {"hash_fn", (PyCFunction)__pyx_pw_8PyClical_9index_set_42hash_fn, METH_NOARGS, __pyx_doc_8PyClical_9index_set_41hash_fn},
18662  {"sign_of_mult", (PyCFunction)__pyx_pw_8PyClical_9index_set_44sign_of_mult, METH_O, __pyx_doc_8PyClical_9index_set_43sign_of_mult},
18663  {"sign_of_square", (PyCFunction)__pyx_pw_8PyClical_9index_set_46sign_of_square, METH_NOARGS, __pyx_doc_8PyClical_9index_set_45sign_of_square},
18664  {"__reduce_cython__", (PyCFunction)__pyx_pw_8PyClical_9index_set_52__reduce_cython__, METH_NOARGS, 0},
18665  {"__setstate_cython__", (PyCFunction)__pyx_pw_8PyClical_9index_set_54__setstate_cython__, METH_O, 0},
18666  {0, 0, 0, 0}
18667  };
18668 
18669  static PyNumberMethods __pyx_tp_as_number_index_set = {
18670  0, /*nb_add*/
18671  0, /*nb_subtract*/
18672  0, /*nb_multiply*/
18673  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18674  0, /*nb_divide*/
18675  #endif
18676  0, /*nb_remainder*/
18677  0, /*nb_divmod*/
18678  0, /*nb_power*/
18679  0, /*nb_negative*/
18680  0, /*nb_positive*/
18681  0, /*nb_absolute*/
18682  0, /*nb_nonzero*/
18683  __pyx_pw_8PyClical_9index_set_18__invert__, /*nb_invert*/
18684  0, /*nb_lshift*/
18685  0, /*nb_rshift*/
18686  __pyx_pw_8PyClical_9index_set_24__and__, /*nb_and*/
18687  __pyx_pw_8PyClical_9index_set_20__xor__, /*nb_xor*/
18688  __pyx_pw_8PyClical_9index_set_28__or__, /*nb_or*/
18689  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18690  0, /*nb_coerce*/
18691  #endif
18692  0, /*nb_int*/
18693  #if PY_MAJOR_VERSION < 3
18694  0, /*nb_long*/
18695  #else
18696  0, /*reserved*/
18697  #endif
18698  0, /*nb_float*/
18699  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18700  0, /*nb_oct*/
18701  #endif
18702  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18703  0, /*nb_hex*/
18704  #endif
18705  0, /*nb_inplace_add*/
18706  0, /*nb_inplace_subtract*/
18707  0, /*nb_inplace_multiply*/
18708  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18709  0, /*nb_inplace_divide*/
18710  #endif
18711  0, /*nb_inplace_remainder*/
18712  0, /*nb_inplace_power*/
18713  0, /*nb_inplace_lshift*/
18714  0, /*nb_inplace_rshift*/
18715  __pyx_pw_8PyClical_9index_set_26__iand__, /*nb_inplace_and*/
18716  __pyx_pw_8PyClical_9index_set_22__ixor__, /*nb_inplace_xor*/
18717  __pyx_pw_8PyClical_9index_set_30__ior__, /*nb_inplace_or*/
18718  0, /*nb_floor_divide*/
18719  0, /*nb_true_divide*/
18720  0, /*nb_inplace_floor_divide*/
18721  0, /*nb_inplace_true_divide*/
18722  0, /*nb_index*/
18723  #if PY_VERSION_HEX >= 0x03050000
18724  0, /*nb_matrix_multiply*/
18725  #endif
18726  #if PY_VERSION_HEX >= 0x03050000
18727  0, /*nb_inplace_matrix_multiply*/
18728  #endif
18729  };
18730 
18731  static PySequenceMethods __pyx_tp_as_sequence_index_set = {
18732  0, /*sq_length*/
18733  0, /*sq_concat*/
18734  0, /*sq_repeat*/
18735  __pyx_sq_item_8PyClical_index_set, /*sq_item*/
18736  0, /*sq_slice*/
18737  0, /*sq_ass_item*/
18738  0, /*sq_ass_slice*/
18739  __pyx_pw_8PyClical_9index_set_13__contains__, /*sq_contains*/
18740  0, /*sq_inplace_concat*/
18741  0, /*sq_inplace_repeat*/
18742  };
18743 
18744  static PyMappingMethods __pyx_tp_as_mapping_index_set = {
18745  0, /*mp_length*/
18746  __pyx_pw_8PyClical_9index_set_11__getitem__, /*mp_subscript*/
18747  __pyx_mp_ass_subscript_8PyClical_index_set, /*mp_ass_subscript*/
18748  };
18749 
18750  static PyTypeObject __pyx_type_8PyClical_index_set = {
18751  PyVarObject_HEAD_INIT(0, 0)
18752  "PyClical.index_set", /*tp_name*/
18753  sizeof(struct __pyx_obj_8PyClical_index_set), /*tp_basicsize*/
18754  0, /*tp_itemsize*/
18755  __pyx_tp_dealloc_8PyClical_index_set, /*tp_dealloc*/
18756  0, /*tp_print*/
18757  0, /*tp_getattr*/
18758  0, /*tp_setattr*/
18759  #if PY_MAJOR_VERSION < 3
18760  0, /*tp_compare*/
18761  #endif
18762  #if PY_MAJOR_VERSION >= 3
18763  0, /*tp_as_async*/
18764  #endif
18765  __pyx_pw_8PyClical_9index_set_48__repr__, /*tp_repr*/
18766  &__pyx_tp_as_number_index_set, /*tp_as_number*/
18767  &__pyx_tp_as_sequence_index_set, /*tp_as_sequence*/
18768  &__pyx_tp_as_mapping_index_set, /*tp_as_mapping*/
18769  0, /*tp_hash*/
18770  0, /*tp_call*/
18771  __pyx_pw_8PyClical_9index_set_50__str__, /*tp_str*/
18772  0, /*tp_getattro*/
18773  0, /*tp_setattro*/
18774  0, /*tp_as_buffer*/
18775  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE, /*tp_flags*/
18776  "\n Python class index_set wraps C++ class IndexSet.\n ", /*tp_doc*/
18777  0, /*tp_traverse*/
18778  0, /*tp_clear*/
18779  __pyx_pw_8PyClical_9index_set_7__richcmp__, /*tp_richcompare*/
18780  0, /*tp_weaklistoffset*/
18781  __pyx_pw_8PyClical_9index_set_15__iter__, /*tp_iter*/
18782  0, /*tp_iternext*/
18783  __pyx_methods_8PyClical_index_set, /*tp_methods*/
18784  0, /*tp_members*/
18785  0, /*tp_getset*/
18786  0, /*tp_base*/
18787  0, /*tp_dict*/
18788  0, /*tp_descr_get*/
18789  0, /*tp_descr_set*/
18790  0, /*tp_dictoffset*/
18791  0, /*tp_init*/
18792  0, /*tp_alloc*/
18793  __pyx_tp_new_8PyClical_index_set, /*tp_new*/
18794  0, /*tp_free*/
18795  0, /*tp_is_gc*/
18796  0, /*tp_bases*/
18797  0, /*tp_mro*/
18798  0, /*tp_cache*/
18799  0, /*tp_subclasses*/
18800  0, /*tp_weaklist*/
18801  0, /*tp_del*/
18802  0, /*tp_version_tag*/
18803  #if PY_VERSION_HEX >= 0x030400a1
18804  0, /*tp_finalize*/
18805  #endif
18806  };
18807  static struct __pyx_vtabstruct_8PyClical_clifford __pyx_vtable_8PyClical_clifford;
18808 
18809  static PyObject *__pyx_tp_new_8PyClical_clifford(PyTypeObject *t, PyObject *a, PyObject *k) {
18810  struct __pyx_obj_8PyClical_clifford *p;
18811  PyObject *o;
18812  if (likely((t->tp_flags & Py_TPFLAGS_IS_ABSTRACT) == 0)) {
18813  o = (*t->tp_alloc)(t, 0);
18814  } else {
18815  o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_empty_tuple, 0);
18816  }
18817  if (unlikely(!o)) return 0;
18818  p = ((struct __pyx_obj_8PyClical_clifford *)o);
18819  p->__pyx_vtab = __pyx_vtabptr_8PyClical_clifford;
18820  if (unlikely(__pyx_pw_8PyClical_8clifford_3__cinit__(o, a, k) < 0)) goto bad;
18821  return o;
18822  bad:
18823  Py_DECREF(o); o = 0;
18824  return NULL;
18825  }
18826 
18827  static void __pyx_tp_dealloc_8PyClical_clifford(PyObject *o) {
18828  #if CYTHON_USE_TP_FINALIZE
18829  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))) {
18830  if (PyObject_CallFinalizerFromDealloc(o)) return;
18831  }
18832  #endif
18833  {
18834  PyObject *etype, *eval, *etb;
18835  PyErr_Fetch(&etype, &eval, &etb);
18836  ++Py_REFCNT(o);
18837  __pyx_pw_8PyClical_8clifford_5__dealloc__(o);
18838  --Py_REFCNT(o);
18839  PyErr_Restore(etype, eval, etb);
18840  }
18841  (*Py_TYPE(o)->tp_free)(o);
18842  }
18843  static PyObject *__pyx_sq_item_8PyClical_clifford(PyObject *o, Py_ssize_t i) {
18844  PyObject *r;
18845  PyObject *x = PyInt_FromSsize_t(i); if(!x) return 0;
18846  r = Py_TYPE(o)->tp_as_mapping->mp_subscript(o, x);
18847  Py_DECREF(x);
18848  return r;
18849  }
18850 
18851  static PyMethodDef __pyx_methods_8PyClical_clifford[] = {
18852  {"copy", (PyCFunction)__pyx_pw_8PyClical_8clifford_1copy, METH_NOARGS, __pyx_doc_8PyClical_8clifford_copy},
18853  {"reframe", (PyCFunction)__pyx_pw_8PyClical_8clifford_11reframe, METH_O, __pyx_doc_8PyClical_8clifford_10reframe},
18854  {"inv", (PyCFunction)__pyx_pw_8PyClical_8clifford_49inv, METH_NOARGS, __pyx_doc_8PyClical_8clifford_48inv},
18855  {"pow", (PyCFunction)__pyx_pw_8PyClical_8clifford_57pow, METH_O, __pyx_doc_8PyClical_8clifford_56pow},
18856  {"outer_pow", (PyCFunction)__pyx_pw_8PyClical_8clifford_59outer_pow, METH_O, __pyx_doc_8PyClical_8clifford_58outer_pow},
18857  {"scalar", (PyCFunction)__pyx_pw_8PyClical_8clifford_63scalar, METH_NOARGS, __pyx_doc_8PyClical_8clifford_62scalar},
18858  {"pure", (PyCFunction)__pyx_pw_8PyClical_8clifford_65pure, METH_NOARGS, __pyx_doc_8PyClical_8clifford_64pure},
18859  {"even", (PyCFunction)__pyx_pw_8PyClical_8clifford_67even, METH_NOARGS, __pyx_doc_8PyClical_8clifford_66even},
18860  {"odd", (PyCFunction)__pyx_pw_8PyClical_8clifford_69odd, METH_NOARGS, __pyx_doc_8PyClical_8clifford_68odd},
18861  {"vector_part", (PyCFunction)__pyx_pw_8PyClical_8clifford_71vector_part, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_8clifford_70vector_part},
18862  {"involute", (PyCFunction)__pyx_pw_8PyClical_8clifford_73involute, METH_NOARGS, __pyx_doc_8PyClical_8clifford_72involute},
18863  {"reverse", (PyCFunction)__pyx_pw_8PyClical_8clifford_75reverse, METH_NOARGS, __pyx_doc_8PyClical_8clifford_74reverse},
18864  {"conj", (PyCFunction)__pyx_pw_8PyClical_8clifford_77conj, METH_NOARGS, __pyx_doc_8PyClical_8clifford_76conj},
18865  {"quad", (PyCFunction)__pyx_pw_8PyClical_8clifford_79quad, METH_NOARGS, __pyx_doc_8PyClical_8clifford_78quad},
18866  {"norm", (PyCFunction)__pyx_pw_8PyClical_8clifford_81norm, METH_NOARGS, __pyx_doc_8PyClical_8clifford_80norm},
18867  {"abs", (PyCFunction)__pyx_pw_8PyClical_8clifford_83abs, METH_NOARGS, __pyx_doc_8PyClical_8clifford_82abs},
18868  {"max_abs", (PyCFunction)__pyx_pw_8PyClical_8clifford_85max_abs, METH_NOARGS, __pyx_doc_8PyClical_8clifford_84max_abs},
18869  {"truncated", (PyCFunction)__pyx_pw_8PyClical_8clifford_87truncated, METH_O, __pyx_doc_8PyClical_8clifford_86truncated},
18870  {"isnan", (PyCFunction)__pyx_pw_8PyClical_8clifford_89isnan, METH_NOARGS, __pyx_doc_8PyClical_8clifford_88isnan},
18871  {"frame", (PyCFunction)__pyx_pw_8PyClical_8clifford_91frame, METH_NOARGS, __pyx_doc_8PyClical_8clifford_90frame},
18872  {"__reduce_cython__", (PyCFunction)__pyx_pw_8PyClical_8clifford_97__reduce_cython__, METH_NOARGS, 0},
18873  {"__setstate_cython__", (PyCFunction)__pyx_pw_8PyClical_8clifford_99__setstate_cython__, METH_O, 0},
18874  {0, 0, 0, 0}
18875  };
18876 
18877  static PyNumberMethods __pyx_tp_as_number_clifford = {
18878  __pyx_pw_8PyClical_8clifford_21__add__, /*nb_add*/
18879  __pyx_pw_8PyClical_8clifford_25__sub__, /*nb_subtract*/
18880  __pyx_pw_8PyClical_8clifford_29__mul__, /*nb_multiply*/
18881  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18882  __pyx_pw_8PyClical_8clifford_45__div__, /*nb_divide*/
18883  #endif
18884  __pyx_pw_8PyClical_8clifford_33__mod__, /*nb_remainder*/
18885  0, /*nb_divmod*/
18886  __pyx_pw_8PyClical_8clifford_55__pow__, /*nb_power*/
18887  __pyx_pw_8PyClical_8clifford_17__neg__, /*nb_negative*/
18888  __pyx_pw_8PyClical_8clifford_19__pos__, /*nb_positive*/
18889  0, /*nb_absolute*/
18890  0, /*nb_nonzero*/
18891  0, /*nb_invert*/
18892  0, /*nb_lshift*/
18893  0, /*nb_rshift*/
18894  __pyx_pw_8PyClical_8clifford_37__and__, /*nb_and*/
18895  __pyx_pw_8PyClical_8clifford_41__xor__, /*nb_xor*/
18896  __pyx_pw_8PyClical_8clifford_51__or__, /*nb_or*/
18897  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18898  0, /*nb_coerce*/
18899  #endif
18900  0, /*nb_int*/
18901  #if PY_MAJOR_VERSION < 3
18902  0, /*nb_long*/
18903  #else
18904  0, /*reserved*/
18905  #endif
18906  0, /*nb_float*/
18907  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18908  0, /*nb_oct*/
18909  #endif
18910  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18911  0, /*nb_hex*/
18912  #endif
18913  __pyx_pw_8PyClical_8clifford_23__iadd__, /*nb_inplace_add*/
18914  __pyx_pw_8PyClical_8clifford_27__isub__, /*nb_inplace_subtract*/
18915  __pyx_pw_8PyClical_8clifford_31__imul__, /*nb_inplace_multiply*/
18916  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
18917  __pyx_pw_8PyClical_8clifford_47__idiv__, /*nb_inplace_divide*/
18918  #endif
18919  __pyx_pw_8PyClical_8clifford_35__imod__, /*nb_inplace_remainder*/
18920  0, /*nb_inplace_power*/
18921  0, /*nb_inplace_lshift*/
18922  0, /*nb_inplace_rshift*/
18923  __pyx_pw_8PyClical_8clifford_39__iand__, /*nb_inplace_and*/
18924  __pyx_pw_8PyClical_8clifford_43__ixor__, /*nb_inplace_xor*/
18925  __pyx_pw_8PyClical_8clifford_53__ior__, /*nb_inplace_or*/
18926  0, /*nb_floor_divide*/
18927  0, /*nb_true_divide*/
18928  0, /*nb_inplace_floor_divide*/
18929  0, /*nb_inplace_true_divide*/
18930  0, /*nb_index*/
18931  #if PY_VERSION_HEX >= 0x03050000
18932  0, /*nb_matrix_multiply*/
18933  #endif
18934  #if PY_VERSION_HEX >= 0x03050000
18935  0, /*nb_inplace_matrix_multiply*/
18936  #endif
18937  };
18938 
18939  static PySequenceMethods __pyx_tp_as_sequence_clifford = {
18940  0, /*sq_length*/
18941  0, /*sq_concat*/
18942  0, /*sq_repeat*/
18943  __pyx_sq_item_8PyClical_clifford, /*sq_item*/
18944  0, /*sq_slice*/
18945  0, /*sq_ass_item*/
18946  0, /*sq_ass_slice*/
18947  __pyx_pw_8PyClical_8clifford_7__contains__, /*sq_contains*/
18948  0, /*sq_inplace_concat*/
18949  0, /*sq_inplace_repeat*/
18950  };
18951 
18952  static PyMappingMethods __pyx_tp_as_mapping_clifford = {
18953  0, /*mp_length*/
18954  __pyx_pw_8PyClical_8clifford_15__getitem__, /*mp_subscript*/
18955  0, /*mp_ass_subscript*/
18956  };
18957 
18958  static PyTypeObject __pyx_type_8PyClical_clifford = {
18959  PyVarObject_HEAD_INIT(0, 0)
18960  "PyClical.clifford", /*tp_name*/
18961  sizeof(struct __pyx_obj_8PyClical_clifford), /*tp_basicsize*/
18962  0, /*tp_itemsize*/
18963  __pyx_tp_dealloc_8PyClical_clifford, /*tp_dealloc*/
18964  0, /*tp_print*/
18965  0, /*tp_getattr*/
18966  0, /*tp_setattr*/
18967  #if PY_MAJOR_VERSION < 3
18968  0, /*tp_compare*/
18969  #endif
18970  #if PY_MAJOR_VERSION >= 3
18971  0, /*tp_as_async*/
18972  #endif
18973  __pyx_pw_8PyClical_8clifford_93__repr__, /*tp_repr*/
18974  &__pyx_tp_as_number_clifford, /*tp_as_number*/
18975  &__pyx_tp_as_sequence_clifford, /*tp_as_sequence*/
18976  &__pyx_tp_as_mapping_clifford, /*tp_as_mapping*/
18977  0, /*tp_hash*/
18978  __pyx_pw_8PyClical_8clifford_61__call__, /*tp_call*/
18979  __pyx_pw_8PyClical_8clifford_95__str__, /*tp_str*/
18980  0, /*tp_getattro*/
18981  0, /*tp_setattro*/
18982  0, /*tp_as_buffer*/
18983  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE, /*tp_flags*/
18984  "\n Python class clifford wraps C++ class Clifford.\n ", /*tp_doc*/
18985  0, /*tp_traverse*/
18986  0, /*tp_clear*/
18987  __pyx_pw_8PyClical_8clifford_13__richcmp__, /*tp_richcompare*/
18988  0, /*tp_weaklistoffset*/
18989  __pyx_pw_8PyClical_8clifford_9__iter__, /*tp_iter*/
18990  0, /*tp_iternext*/
18991  __pyx_methods_8PyClical_clifford, /*tp_methods*/
18992  0, /*tp_members*/
18993  0, /*tp_getset*/
18994  0, /*tp_base*/
18995  0, /*tp_dict*/
18996  0, /*tp_descr_get*/
18997  0, /*tp_descr_set*/
18998  0, /*tp_dictoffset*/
18999  0, /*tp_init*/
19000  0, /*tp_alloc*/
19001  __pyx_tp_new_8PyClical_clifford, /*tp_new*/
19002  0, /*tp_free*/
19003  0, /*tp_is_gc*/
19004  0, /*tp_bases*/
19005  0, /*tp_mro*/
19006  0, /*tp_cache*/
19007  0, /*tp_subclasses*/
19008  0, /*tp_weaklist*/
19009  0, /*tp_del*/
19010  0, /*tp_version_tag*/
19011  #if PY_VERSION_HEX >= 0x030400a1
19012  0, /*tp_finalize*/
19013  #endif
19014  };
19015 
19016  static struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *__pyx_freelist_8PyClical___pyx_scope_struct____iter__[8];
19017  static int __pyx_freecount_8PyClical___pyx_scope_struct____iter__ = 0;
19018 
19019  static PyObject *__pyx_tp_new_8PyClical___pyx_scope_struct____iter__(PyTypeObject *t, CYTHON_UNUSED PyObject *a, CYTHON_UNUSED PyObject *k) {
19020  PyObject *o;
19021  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__)))) {
19022  o = (PyObject*)__pyx_freelist_8PyClical___pyx_scope_struct____iter__[--__pyx_freecount_8PyClical___pyx_scope_struct____iter__];
19023  memset(o, 0, sizeof(struct __pyx_obj_8PyClical___pyx_scope_struct____iter__));
19024  (void) PyObject_INIT(o, t);
19025  PyObject_GC_Track(o);
19026  } else {
19027  o = (*t->tp_alloc)(t, 0);
19028  if (unlikely(!o)) return 0;
19029  }
19030  return o;
19031  }
19032 
19033  static void __pyx_tp_dealloc_8PyClical___pyx_scope_struct____iter__(PyObject *o) {
19034  struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *p = (struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *)o;
19035  PyObject_GC_UnTrack(o);
19036  Py_CLEAR(p->__pyx_v_idx);
19037  Py_CLEAR(p->__pyx_v_self);
19038  Py_CLEAR(p->__pyx_t_0);
19039  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__)))) {
19040  __pyx_freelist_8PyClical___pyx_scope_struct____iter__[__pyx_freecount_8PyClical___pyx_scope_struct____iter__++] = ((struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *)o);
19041  } else {
19042  (*Py_TYPE(o)->tp_free)(o);
19043  }
19044  }
19045 
19046  static int __pyx_tp_traverse_8PyClical___pyx_scope_struct____iter__(PyObject *o, visitproc v, void *a) {
19047  int e;
19048  struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *p = (struct __pyx_obj_8PyClical___pyx_scope_struct____iter__ *)o;
19049  if (p->__pyx_v_idx) {
19050  e = (*v)(p->__pyx_v_idx, a); if (e) return e;
19051  }
19052  if (p->__pyx_v_self) {
19053  e = (*v)(((PyObject *)p->__pyx_v_self), a); if (e) return e;
19054  }
19055  if (p->__pyx_t_0) {
19056  e = (*v)(p->__pyx_t_0, a); if (e) return e;
19057  }
19058  return 0;
19059  }
19060 
19061  static PyTypeObject __pyx_type_8PyClical___pyx_scope_struct____iter__ = {
19062  PyVarObject_HEAD_INIT(0, 0)
19063  "PyClical.__pyx_scope_struct____iter__", /*tp_name*/
19064  sizeof(struct __pyx_obj_8PyClical___pyx_scope_struct____iter__), /*tp_basicsize*/
19065  0, /*tp_itemsize*/
19066  __pyx_tp_dealloc_8PyClical___pyx_scope_struct____iter__, /*tp_dealloc*/
19067  0, /*tp_print*/
19068  0, /*tp_getattr*/
19069  0, /*tp_setattr*/
19070  #if PY_MAJOR_VERSION < 3
19071  0, /*tp_compare*/
19072  #endif
19073  #if PY_MAJOR_VERSION >= 3
19074  0, /*tp_as_async*/
19075  #endif
19076  0, /*tp_repr*/
19077  0, /*tp_as_number*/
19078  0, /*tp_as_sequence*/
19079  0, /*tp_as_mapping*/
19080  0, /*tp_hash*/
19081  0, /*tp_call*/
19082  0, /*tp_str*/
19083  0, /*tp_getattro*/
19084  0, /*tp_setattro*/
19085  0, /*tp_as_buffer*/
19086  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_HAVE_GC, /*tp_flags*/
19087  0, /*tp_doc*/
19088  __pyx_tp_traverse_8PyClical___pyx_scope_struct____iter__, /*tp_traverse*/
19089  0, /*tp_clear*/
19090  0, /*tp_richcompare*/
19091  0, /*tp_weaklistoffset*/
19092  0, /*tp_iter*/
19093  0, /*tp_iternext*/
19094  0, /*tp_methods*/
19095  0, /*tp_members*/
19096  0, /*tp_getset*/
19097  0, /*tp_base*/
19098  0, /*tp_dict*/
19099  0, /*tp_descr_get*/
19100  0, /*tp_descr_set*/
19101  0, /*tp_dictoffset*/
19102  0, /*tp_init*/
19103  0, /*tp_alloc*/
19104  __pyx_tp_new_8PyClical___pyx_scope_struct____iter__, /*tp_new*/
19105  0, /*tp_free*/
19106  0, /*tp_is_gc*/
19107  0, /*tp_bases*/
19108  0, /*tp_mro*/
19109  0, /*tp_cache*/
19110  0, /*tp_subclasses*/
19111  0, /*tp_weaklist*/
19112  0, /*tp_del*/
19113  0, /*tp_version_tag*/
19114  #if PY_VERSION_HEX >= 0x030400a1
19115  0, /*tp_finalize*/
19116  #endif
19117  };
19118 
19119  static PyMethodDef __pyx_methods[] = {
19120  {"compare", (PyCFunction)__pyx_pw_8PyClical_3compare, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_2compare},
19121  {"min_neg", (PyCFunction)__pyx_pw_8PyClical_5min_neg, METH_O, __pyx_doc_8PyClical_4min_neg},
19122  {"max_pos", (PyCFunction)__pyx_pw_8PyClical_7max_pos, METH_O, __pyx_doc_8PyClical_6max_pos},
19123  {"inv", (PyCFunction)__pyx_pw_8PyClical_11inv, METH_O, __pyx_doc_8PyClical_10inv},
19124  {"scalar", (PyCFunction)__pyx_pw_8PyClical_13scalar, METH_O, __pyx_doc_8PyClical_12scalar},
19125  {"real", (PyCFunction)__pyx_pw_8PyClical_15real, METH_O, __pyx_doc_8PyClical_14real},
19126  {"imag", (PyCFunction)__pyx_pw_8PyClical_17imag, METH_O, __pyx_doc_8PyClical_16imag},
19127  {"pure", (PyCFunction)__pyx_pw_8PyClical_19pure, METH_O, __pyx_doc_8PyClical_18pure},
19128  {"even", (PyCFunction)__pyx_pw_8PyClical_21even, METH_O, __pyx_doc_8PyClical_20even},
19129  {"odd", (PyCFunction)__pyx_pw_8PyClical_23odd, METH_O, __pyx_doc_8PyClical_22odd},
19130  {"involute", (PyCFunction)__pyx_pw_8PyClical_25involute, METH_O, __pyx_doc_8PyClical_24involute},
19131  {"reverse", (PyCFunction)__pyx_pw_8PyClical_27reverse, METH_O, __pyx_doc_8PyClical_26reverse},
19132  {"conj", (PyCFunction)__pyx_pw_8PyClical_29conj, METH_O, __pyx_doc_8PyClical_28conj},
19133  {"quad", (PyCFunction)__pyx_pw_8PyClical_31quad, METH_O, __pyx_doc_8PyClical_30quad},
19134  {"norm", (PyCFunction)__pyx_pw_8PyClical_33norm, METH_O, __pyx_doc_8PyClical_32norm},
19135  {"abs", (PyCFunction)__pyx_pw_8PyClical_35abs, METH_O, __pyx_doc_8PyClical_34abs},
19136  {"max_abs", (PyCFunction)__pyx_pw_8PyClical_37max_abs, METH_O, __pyx_doc_8PyClical_36max_abs},
19137  {"pow", (PyCFunction)__pyx_pw_8PyClical_39pow, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_38pow},
19138  {"outer_pow", (PyCFunction)__pyx_pw_8PyClical_41outer_pow, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_40outer_pow},
19139  {"complexifier", (PyCFunction)__pyx_pw_8PyClical_43complexifier, METH_O, __pyx_doc_8PyClical_42complexifier},
19140  {"sqrt", (PyCFunction)__pyx_pw_8PyClical_45sqrt, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_44sqrt},
19141  {"exp", (PyCFunction)__pyx_pw_8PyClical_47exp, METH_O, __pyx_doc_8PyClical_46exp},
19142  {"log", (PyCFunction)__pyx_pw_8PyClical_49log, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_48log},
19143  {"cos", (PyCFunction)__pyx_pw_8PyClical_51cos, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_50cos},
19144  {"acos", (PyCFunction)__pyx_pw_8PyClical_53acos, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_52acos},
19145  {"cosh", (PyCFunction)__pyx_pw_8PyClical_55cosh, METH_O, __pyx_doc_8PyClical_54cosh},
19146  {"acosh", (PyCFunction)__pyx_pw_8PyClical_57acosh, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_56acosh},
19147  {"sin", (PyCFunction)__pyx_pw_8PyClical_59sin, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_58sin},
19148  {"asin", (PyCFunction)__pyx_pw_8PyClical_61asin, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_60asin},
19149  {"sinh", (PyCFunction)__pyx_pw_8PyClical_63sinh, METH_O, __pyx_doc_8PyClical_62sinh},
19150  {"asinh", (PyCFunction)__pyx_pw_8PyClical_65asinh, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_64asinh},
19151  {"tan", (PyCFunction)__pyx_pw_8PyClical_67tan, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_66tan},
19152  {"atan", (PyCFunction)__pyx_pw_8PyClical_69atan, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_68atan},
19153  {"tanh", (PyCFunction)__pyx_pw_8PyClical_71tanh, METH_O, __pyx_doc_8PyClical_70tanh},
19154  {"atanh", (PyCFunction)__pyx_pw_8PyClical_73atanh, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_72atanh},
19155  {"random_clifford", (PyCFunction)__pyx_pw_8PyClical_75random_clifford, METH_VARARGS|METH_KEYWORDS, __pyx_doc_8PyClical_74random_clifford},
19156  {"cga3", (PyCFunction)__pyx_pw_8PyClical_77cga3, METH_O, __pyx_doc_8PyClical_76cga3},
19157  {"cga3std", (PyCFunction)__pyx_pw_8PyClical_79cga3std, METH_O, __pyx_doc_8PyClical_78cga3std},
19158  {"agc3", (PyCFunction)__pyx_pw_8PyClical_81agc3, METH_O, __pyx_doc_8PyClical_80agc3},
19159  {0, 0, 0, 0}
19160  };
19161 
19162  #if PY_MAJOR_VERSION >= 3
19163  #if CYTHON_PEP489_MULTI_PHASE_INIT
19164  static PyObject* __pyx_pymod_create(PyObject *spec, PyModuleDef *def); /*proto*/
19165  static int __pyx_pymod_exec_PyClical(PyObject* module); /*proto*/
19166  static PyModuleDef_Slot __pyx_moduledef_slots[] = {
19167  {Py_mod_create, (void*)__pyx_pymod_create},
19168  {Py_mod_exec, (void*)__pyx_pymod_exec_PyClical},
19169  {0, NULL}
19170  };
19171  #endif
19172 
19173  static struct PyModuleDef __pyx_moduledef = {
19174  PyModuleDef_HEAD_INIT,
19175  "PyClical",
19176  0, /* m_doc */
19177  #if CYTHON_PEP489_MULTI_PHASE_INIT
19178  0, /* m_size */
19179  #else
19180  -1, /* m_size */
19181  #endif
19182  __pyx_methods /* m_methods */,
19183  #if CYTHON_PEP489_MULTI_PHASE_INIT
19184  __pyx_moduledef_slots, /* m_slots */
19185  #else
19186  NULL, /* m_reload */
19187  #endif
19188  NULL, /* m_traverse */
19189  NULL, /* m_clear */
19190  NULL /* m_free */
19191  };
19192  #endif
19193 
19194 static __Pyx_StringTabEntry __pyx_string_tab[] = {
19195  {&__pyx_kp_s_, __pyx_k_, sizeof(__pyx_k_), 0, 0, 1, 0},
19196  {&__pyx_kp_s_0_8_2, __pyx_k_0_8_2, sizeof(__pyx_k_0_8_2), 0, 0, 1, 0},
19197  {&__pyx_kp_u_Abbreviation_for_clifford_index, __pyx_k_Abbreviation_for_clifford_index, sizeof(__pyx_k_Abbreviation_for_clifford_index), 0, 1, 0, 0},
19198  {&__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},
19199  {&__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},
19200  {&__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},
19201  {&__pyx_kp_s_Cannot_initialize_clifford_objec, __pyx_k_Cannot_initialize_clifford_objec, sizeof(__pyx_k_Cannot_initialize_clifford_objec), 0, 0, 1, 0},
19202  {&__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},
19203  {&__pyx_kp_s_Cannot_reframe, __pyx_k_Cannot_reframe, sizeof(__pyx_k_Cannot_reframe), 0, 0, 1, 0},
19204  {&__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},
19205  {&__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},
19206  {&__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},
19207  {&__pyx_kp_u_Conjugation_reverse_o_involute, __pyx_k_Conjugation_reverse_o_involute, sizeof(__pyx_k_Conjugation_reverse_o_involute), 0, 1, 0, 0},
19208  {&__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},
19209  {&__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},
19210  {&__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},
19211  {&__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},
19212  {&__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},
19213  {&__pyx_kp_u_Convert_Euclidean_3D_multivecto, __pyx_k_Convert_Euclidean_3D_multivecto, sizeof(__pyx_k_Convert_Euclidean_3D_multivecto), 0, 1, 0, 0},
19214  {&__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},
19215  {&__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},
19216  {&__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},
19217  {&__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},
19218  {&__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},
19219  {&__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},
19220  {&__pyx_kp_u_Geometric_difference_print_clif, __pyx_k_Geometric_difference_print_clif, sizeof(__pyx_k_Geometric_difference_print_clif), 0, 1, 0, 0},
19221  {&__pyx_kp_u_Geometric_difference_x_clifford, __pyx_k_Geometric_difference_x_clifford, sizeof(__pyx_k_Geometric_difference_x_clifford), 0, 1, 0, 0},
19222  {&__pyx_kp_u_Geometric_multiplicative_invers, __pyx_k_Geometric_multiplicative_invers, sizeof(__pyx_k_Geometric_multiplicative_invers), 0, 1, 0, 0},
19223  {&__pyx_kp_u_Geometric_multiplicative_invers_2, __pyx_k_Geometric_multiplicative_invers_2, sizeof(__pyx_k_Geometric_multiplicative_invers_2), 0, 1, 0, 0},
19224  {&__pyx_kp_u_Geometric_product_print_cliffor, __pyx_k_Geometric_product_print_cliffor, sizeof(__pyx_k_Geometric_product_print_cliffor), 0, 1, 0, 0},
19225  {&__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},
19226  {&__pyx_kp_u_Geometric_quotient_print_cliffo, __pyx_k_Geometric_quotient_print_cliffo, sizeof(__pyx_k_Geometric_quotient_print_cliffo), 0, 1, 0, 0},
19227  {&__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},
19228  {&__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},
19229  {&__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},
19230  {&__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},
19231  {&__pyx_kp_u_Hyperbolic_cosine_of_multivecto, __pyx_k_Hyperbolic_cosine_of_multivecto, sizeof(__pyx_k_Hyperbolic_cosine_of_multivecto), 0, 1, 0, 0},
19232  {&__pyx_kp_u_Hyperbolic_sine_of_multivector, __pyx_k_Hyperbolic_sine_of_multivector, sizeof(__pyx_k_Hyperbolic_sine_of_multivector), 0, 1, 0, 0},
19233  {&__pyx_kp_u_Hyperbolic_tangent_of_multivect, __pyx_k_Hyperbolic_tangent_of_multivect, sizeof(__pyx_k_Hyperbolic_tangent_of_multivect), 0, 1, 0, 0},
19234  {&__pyx_kp_u_Imaginary_part_deprecated_alway, __pyx_k_Imaginary_part_deprecated_alway, sizeof(__pyx_k_Imaginary_part_deprecated_alway), 0, 1, 0, 0},
19235  {&__pyx_n_s_IndexError, __pyx_k_IndexError, sizeof(__pyx_k_IndexError), 0, 0, 1, 1},
19236  {&__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},
19237  {&__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},
19238  {&__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},
19239  {&__pyx_n_s_Integral, __pyx_k_Integral, sizeof(__pyx_k_Integral), 0, 0, 1, 1},
19240  {&__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},
19241  {&__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},
19242  {&__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},
19243  {&__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},
19244  {&__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},
19245  {&__pyx_kp_u_Inverse_tangent_of_multivector, __pyx_k_Inverse_tangent_of_multivector, sizeof(__pyx_k_Inverse_tangent_of_multivector), 0, 1, 0, 0},
19246  {&__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},
19247  {&__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},
19248  {&__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},
19249  {&__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},
19250  {&__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},
19251  {&__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},
19252  {&__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},
19253  {&__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},
19254  {&__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},
19255  {&__pyx_kp_u_Natural_logarithm_of_multivecto, __pyx_k_Natural_logarithm_of_multivecto, sizeof(__pyx_k_Natural_logarithm_of_multivecto), 0, 1, 0, 0},
19256  {&__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},
19257  {&__pyx_n_s_NotImplemented, __pyx_k_NotImplemented, sizeof(__pyx_k_NotImplemented), 0, 0, 1, 1},
19258  {&__pyx_kp_s_Not_applicable, __pyx_k_Not_applicable, sizeof(__pyx_k_Not_applicable), 0, 0, 1, 0},
19259  {&__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},
19260  {&__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},
19261  {&__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},
19262  {&__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},
19263  {&__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},
19264  {&__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},
19265  {&__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},
19266  {&__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},
19267  {&__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},
19268  {&__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},
19269  {&__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},
19270  {&__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},
19271  {&__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},
19272  {&__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},
19273  {&__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},
19274  {&__pyx_n_s_PyClical, __pyx_k_PyClical, sizeof(__pyx_k_PyClical), 0, 0, 1, 1},
19275  {&__pyx_kp_s_PyClical_pyx, __pyx_k_PyClical_pyx, sizeof(__pyx_k_PyClical_pyx), 0, 0, 1, 0},
19276  {&__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},
19277  {&__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},
19278  {&__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},
19279  {&__pyx_n_s_Real, __pyx_k_Real, sizeof(__pyx_k_Real), 0, 0, 1, 1},
19280  {&__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},
19281  {&__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},
19282  {&__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},
19283  {&__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},
19284  {&__pyx_n_s_RuntimeError, __pyx_k_RuntimeError, sizeof(__pyx_k_RuntimeError), 0, 0, 1, 1},
19285  {&__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},
19286  {&__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},
19287  {&__pyx_n_s_Sequence, __pyx_k_Sequence, sizeof(__pyx_k_Sequence), 0, 0, 1, 1},
19288  {&__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},
19289  {&__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},
19290  {&__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},
19291  {&__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},
19292  {&__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},
19293  {&__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},
19294  {&__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},
19295  {&__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},
19296  {&__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},
19297  {&__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},
19298  {&__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},
19299  {&__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},
19300  {&__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},
19301  {&__pyx_kp_u_Symmetric_set_difference_exclus, __pyx_k_Symmetric_set_difference_exclus, sizeof(__pyx_k_Symmetric_set_difference_exclus), 0, 1, 0, 0},
19302  {&__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},
19303  {&__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},
19304  {&__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},
19305  {&__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},
19306  {&__pyx_kp_u_The_informal_string_representat, __pyx_k_The_informal_string_representat, sizeof(__pyx_k_The_informal_string_representat), 0, 1, 0, 0},
19307  {&__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},
19308  {&__pyx_kp_u_The_official_string_representat, __pyx_k_The_official_string_representat, sizeof(__pyx_k_The_official_string_representat), 0, 1, 0, 0},
19309  {&__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},
19310  {&__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},
19311  {&__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},
19312  {&__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},
19313  {&__pyx_n_s_TypeError, __pyx_k_TypeError, sizeof(__pyx_k_TypeError), 0, 0, 1, 1},
19314  {&__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},
19315  {&__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},
19316  {&__pyx_n_s_ValueError, __pyx_k_ValueError, sizeof(__pyx_k_ValueError), 0, 0, 1, 1},
19317  {&__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},
19318  {&__pyx_kp_s__2, __pyx_k__2, sizeof(__pyx_k__2), 0, 0, 1, 0},
19319  {&__pyx_kp_s__5, __pyx_k__5, sizeof(__pyx_k__5), 0, 0, 1, 0},
19320  {&__pyx_kp_s__6, __pyx_k__6, sizeof(__pyx_k__6), 0, 0, 1, 0},
19321  {&__pyx_kp_s__7, __pyx_k__7, sizeof(__pyx_k__7), 0, 0, 1, 0},
19322  {&__pyx_kp_s__8, __pyx_k__8, sizeof(__pyx_k__8), 0, 0, 1, 0},
19323  {&__pyx_kp_s__9, __pyx_k__9, sizeof(__pyx_k__9), 0, 0, 1, 0},
19324  {&__pyx_kp_u_abs_line_1473, __pyx_k_abs_line_1473, sizeof(__pyx_k_abs_line_1473), 0, 1, 0, 0},
19325  {&__pyx_n_s_acos, __pyx_k_acos, sizeof(__pyx_k_acos), 0, 0, 1, 1},
19326  {&__pyx_kp_u_acos_line_1619, __pyx_k_acos_line_1619, sizeof(__pyx_k_acos_line_1619), 0, 1, 0, 0},
19327  {&__pyx_n_s_acosh, __pyx_k_acosh, sizeof(__pyx_k_acosh), 0, 0, 1, 1},
19328  {&__pyx_kp_u_acosh_line_1656, __pyx_k_acosh_line_1656, sizeof(__pyx_k_acosh_line_1656), 0, 1, 0, 0},
19329  {&__pyx_kp_u_agc3_line_1844, __pyx_k_agc3_line_1844, sizeof(__pyx_k_agc3_line_1844), 0, 1, 0, 0},
19330  {&__pyx_n_s_args, __pyx_k_args, sizeof(__pyx_k_args), 0, 0, 1, 1},
19331  {&__pyx_kp_s_as_frame, __pyx_k_as_frame, sizeof(__pyx_k_as_frame), 0, 0, 1, 0},
19332  {&__pyx_n_s_asin, __pyx_k_asin, sizeof(__pyx_k_asin), 0, 0, 1, 1},
19333  {&__pyx_kp_u_asin_line_1698, __pyx_k_asin_line_1698, sizeof(__pyx_k_asin_line_1698), 0, 1, 0, 0},
19334  {&__pyx_n_s_asinh, __pyx_k_asinh, sizeof(__pyx_k_asinh), 0, 0, 1, 1},
19335  {&__pyx_kp_u_asinh_line_1733, __pyx_k_asinh_line_1733, sizeof(__pyx_k_asinh_line_1733), 0, 1, 0, 0},
19336  {&__pyx_n_s_atan, __pyx_k_atan, sizeof(__pyx_k_atan), 0, 0, 1, 1},
19337  {&__pyx_kp_u_atan_line_1769, __pyx_k_atan_line_1769, sizeof(__pyx_k_atan_line_1769), 0, 1, 0, 0},
19338  {&__pyx_n_s_atanh, __pyx_k_atanh, sizeof(__pyx_k_atanh), 0, 0, 1, 1},
19339  {&__pyx_kp_u_atanh_line_1798, __pyx_k_atanh_line_1798, sizeof(__pyx_k_atanh_line_1798), 0, 1, 0, 0},
19340  {&__pyx_kp_u_cga3_line_1824, __pyx_k_cga3_line_1824, sizeof(__pyx_k_cga3_line_1824), 0, 1, 0, 0},
19341  {&__pyx_kp_u_cga3std_line_1833, __pyx_k_cga3std_line_1833, sizeof(__pyx_k_cga3std_line_1833), 0, 1, 0, 0},
19342  {&__pyx_n_s_cl, __pyx_k_cl, sizeof(__pyx_k_cl), 0, 0, 1, 1},
19343  {&__pyx_kp_u_clifford___add___line_739, __pyx_k_clifford___add___line_739, sizeof(__pyx_k_clifford___add___line_739), 0, 1, 0, 0},
19344  {&__pyx_kp_u_clifford___and___line_835, __pyx_k_clifford___and___line_835, sizeof(__pyx_k_clifford___and___line_835), 0, 1, 0, 0},
19345  {&__pyx_kp_u_clifford___call___line_1019, __pyx_k_clifford___call___line_1019, sizeof(__pyx_k_clifford___call___line_1019), 0, 1, 0, 0},
19346  {&__pyx_kp_u_clifford___div___line_895, __pyx_k_clifford___div___line_895, sizeof(__pyx_k_clifford___div___line_895), 0, 1, 0, 0},
19347  {&__pyx_kp_u_clifford___getitem___line_706, __pyx_k_clifford___getitem___line_706, sizeof(__pyx_k_clifford___getitem___line_706), 0, 1, 0, 0},
19348  {&__pyx_kp_u_clifford___iadd___line_750, __pyx_k_clifford___iadd___line_750, sizeof(__pyx_k_clifford___iadd___line_750), 0, 1, 0, 0},
19349  {&__pyx_kp_u_clifford___iand___line_850, __pyx_k_clifford___iand___line_850, sizeof(__pyx_k_clifford___iand___line_850), 0, 1, 0, 0},
19350  {&__pyx_kp_u_clifford___idiv___line_910, __pyx_k_clifford___idiv___line_910, sizeof(__pyx_k_clifford___idiv___line_910), 0, 1, 0, 0},
19351  {&__pyx_kp_u_clifford___imod___line_820, __pyx_k_clifford___imod___line_820, sizeof(__pyx_k_clifford___imod___line_820), 0, 1, 0, 0},
19352  {&__pyx_kp_u_clifford___imul___line_792, __pyx_k_clifford___imul___line_792, sizeof(__pyx_k_clifford___imul___line_792), 0, 1, 0, 0},
19353  {&__pyx_kp_u_clifford___ior___line_949, __pyx_k_clifford___ior___line_949, sizeof(__pyx_k_clifford___ior___line_949), 0, 1, 0, 0},
19354  {&__pyx_kp_u_clifford___isub___line_770, __pyx_k_clifford___isub___line_770, sizeof(__pyx_k_clifford___isub___line_770), 0, 1, 0, 0},
19355  {&__pyx_kp_u_clifford___iter___line_637, __pyx_k_clifford___iter___line_637, sizeof(__pyx_k_clifford___iter___line_637), 0, 1, 0, 0},
19356  {&__pyx_kp_u_clifford___ixor___line_880, __pyx_k_clifford___ixor___line_880, sizeof(__pyx_k_clifford___ixor___line_880), 0, 1, 0, 0},
19357  {&__pyx_kp_u_clifford___mod___line_805, __pyx_k_clifford___mod___line_805, sizeof(__pyx_k_clifford___mod___line_805), 0, 1, 0, 0},
19358  {&__pyx_kp_u_clifford___mul___line_779, __pyx_k_clifford___mul___line_779, sizeof(__pyx_k_clifford___mul___line_779), 0, 1, 0, 0},
19359  {&__pyx_kp_u_clifford___neg___line_721, __pyx_k_clifford___neg___line_721, sizeof(__pyx_k_clifford___neg___line_721), 0, 1, 0, 0},
19360  {&__pyx_kp_u_clifford___or___line_938, __pyx_k_clifford___or___line_938, sizeof(__pyx_k_clifford___or___line_938), 0, 1, 0, 0},
19361  {&__pyx_kp_u_clifford___pos___line_730, __pyx_k_clifford___pos___line_730, sizeof(__pyx_k_clifford___pos___line_730), 0, 1, 0, 0},
19362  {&__pyx_kp_u_clifford___pow___line_960, __pyx_k_clifford___pow___line_960, sizeof(__pyx_k_clifford___pow___line_960), 0, 1, 0, 0},
19363  {&__pyx_kp_u_clifford___repr___line_1225, __pyx_k_clifford___repr___line_1225, sizeof(__pyx_k_clifford___repr___line_1225), 0, 1, 0, 0},
19364  {&__pyx_kp_u_clifford___str___line_1234, __pyx_k_clifford___str___line_1234, sizeof(__pyx_k_clifford___str___line_1234), 0, 1, 0, 0},
19365  {&__pyx_kp_u_clifford___sub___line_759, __pyx_k_clifford___sub___line_759, sizeof(__pyx_k_clifford___sub___line_759), 0, 1, 0, 0},
19366  {&__pyx_kp_u_clifford___xor___line_865, __pyx_k_clifford___xor___line_865, sizeof(__pyx_k_clifford___xor___line_865), 0, 1, 0, 0},
19367  {&__pyx_kp_u_clifford_abs_line_1174, __pyx_k_clifford_abs_line_1174, sizeof(__pyx_k_clifford_abs_line_1174), 0, 1, 0, 0},
19368  {&__pyx_kp_u_clifford_conj_line_1137, __pyx_k_clifford_conj_line_1137, sizeof(__pyx_k_clifford_conj_line_1137), 0, 1, 0, 0},
19369  {&__pyx_kp_u_clifford_copy_line_554, __pyx_k_clifford_copy_line_554, sizeof(__pyx_k_clifford_copy_line_554), 0, 1, 0, 0},
19370  {&__pyx_kp_u_clifford_even_line_1060, __pyx_k_clifford_even_line_1060, sizeof(__pyx_k_clifford_even_line_1060), 0, 1, 0, 0},
19371  {&__pyx_kp_u_clifford_frame_line_1214, __pyx_k_clifford_frame_line_1214, sizeof(__pyx_k_clifford_frame_line_1214), 0, 1, 0, 0},
19372  {&__pyx_n_s_clifford_hidden_doctests, __pyx_k_clifford_hidden_doctests, sizeof(__pyx_k_clifford_hidden_doctests), 0, 0, 1, 1},
19373  {&__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},
19374  {&__pyx_kp_u_clifford_inv_line_925, __pyx_k_clifford_inv_line_925, sizeof(__pyx_k_clifford_inv_line_925), 0, 1, 0, 0},
19375  {&__pyx_kp_u_clifford_involute_line_1106, __pyx_k_clifford_involute_line_1106, sizeof(__pyx_k_clifford_involute_line_1106), 0, 1, 0, 0},
19376  {&__pyx_kp_u_clifford_isnan_line_1205, __pyx_k_clifford_isnan_line_1205, sizeof(__pyx_k_clifford_isnan_line_1205), 0, 1, 0, 0},
19377  {&__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},
19378  {&__pyx_kp_u_clifford_norm_line_1163, __pyx_k_clifford_norm_line_1163, sizeof(__pyx_k_clifford_norm_line_1163), 0, 1, 0, 0},
19379  {&__pyx_kp_u_clifford_odd_line_1069, __pyx_k_clifford_odd_line_1069, sizeof(__pyx_k_clifford_odd_line_1069), 0, 1, 0, 0},
19380  {&__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},
19381  {&__pyx_kp_u_clifford_pow_line_979, __pyx_k_clifford_pow_line_979, sizeof(__pyx_k_clifford_pow_line_979), 0, 1, 0, 0},
19382  {&__pyx_kp_u_clifford_pure_line_1049, __pyx_k_clifford_pure_line_1049, sizeof(__pyx_k_clifford_pure_line_1049), 0, 1, 0, 0},
19383  {&__pyx_kp_u_clifford_quad_line_1152, __pyx_k_clifford_quad_line_1152, sizeof(__pyx_k_clifford_quad_line_1152), 0, 1, 0, 0},
19384  {&__pyx_kp_u_clifford_reframe_line_648, __pyx_k_clifford_reframe_line_648, sizeof(__pyx_k_clifford_reframe_line_648), 0, 1, 0, 0},
19385  {&__pyx_kp_u_clifford_reverse_line_1122, __pyx_k_clifford_reverse_line_1122, sizeof(__pyx_k_clifford_reverse_line_1122), 0, 1, 0, 0},
19386  {&__pyx_kp_u_clifford_scalar_line_1038, __pyx_k_clifford_scalar_line_1038, sizeof(__pyx_k_clifford_scalar_line_1038), 0, 1, 0, 0},
19387  {&__pyx_kp_u_clifford_truncated_line_1194, __pyx_k_clifford_truncated_line_1194, sizeof(__pyx_k_clifford_truncated_line_1194), 0, 1, 0, 0},
19388  {&__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},
19389  {&__pyx_n_s_cline_in_traceback, __pyx_k_cline_in_traceback, sizeof(__pyx_k_cline_in_traceback), 0, 0, 1, 1},
19390  {&__pyx_n_s_close, __pyx_k_close, sizeof(__pyx_k_close), 0, 0, 1, 1},
19391  {&__pyx_n_s_collections, __pyx_k_collections, sizeof(__pyx_k_collections), 0, 0, 1, 1},
19392  {&__pyx_kp_u_compare_line_490, __pyx_k_compare_line_490, sizeof(__pyx_k_compare_line_490), 0, 1, 0, 0},
19393  {&__pyx_kp_u_complexifier_line_1527, __pyx_k_complexifier_line_1527, sizeof(__pyx_k_complexifier_line_1527), 0, 1, 0, 0},
19394  {&__pyx_n_s_conj, __pyx_k_conj, sizeof(__pyx_k_conj), 0, 0, 1, 1},
19395  {&__pyx_kp_u_conj_line_1436, __pyx_k_conj_line_1436, sizeof(__pyx_k_conj_line_1436), 0, 1, 0, 0},
19396  {&__pyx_n_s_copy, __pyx_k_copy, sizeof(__pyx_k_copy), 0, 0, 1, 1},
19397  {&__pyx_n_s_cos, __pyx_k_cos, sizeof(__pyx_k_cos), 0, 0, 1, 1},
19398  {&__pyx_kp_u_cos_line_1602, __pyx_k_cos_line_1602, sizeof(__pyx_k_cos_line_1602), 0, 1, 0, 0},
19399  {&__pyx_n_s_cosh, __pyx_k_cosh, sizeof(__pyx_k_cosh), 0, 0, 1, 1},
19400  {&__pyx_kp_u_cosh_line_1640, __pyx_k_cosh_line_1640, sizeof(__pyx_k_cosh_line_1640), 0, 1, 0, 0},
19401  {&__pyx_n_s_doctest, __pyx_k_doctest, sizeof(__pyx_k_doctest), 0, 0, 1, 1},
19402  {&__pyx_n_s_e, __pyx_k_e, sizeof(__pyx_k_e), 0, 0, 1, 1},
19403  {&__pyx_kp_u_e_line_1887, __pyx_k_e_line_1887, sizeof(__pyx_k_e_line_1887), 0, 1, 0, 0},
19404  {&__pyx_n_s_even, __pyx_k_even, sizeof(__pyx_k_even), 0, 0, 1, 1},
19405  {&__pyx_kp_u_even_line_1388, __pyx_k_even_line_1388, sizeof(__pyx_k_even_line_1388), 0, 1, 0, 0},
19406  {&__pyx_n_s_exp, __pyx_k_exp, sizeof(__pyx_k_exp), 0, 0, 1, 1},
19407  {&__pyx_kp_u_exp_line_1565, __pyx_k_exp_line_1565, sizeof(__pyx_k_exp_line_1565), 0, 1, 0, 0},
19408  {&__pyx_n_s_fill, __pyx_k_fill, sizeof(__pyx_k_fill), 0, 0, 1, 1},
19409  {&__pyx_n_s_frm, __pyx_k_frm, sizeof(__pyx_k_frm), 0, 0, 1, 1},
19410  {&__pyx_kp_s_from, __pyx_k_from, sizeof(__pyx_k_from), 0, 0, 1, 0},
19411  {&__pyx_n_s_getstate, __pyx_k_getstate, sizeof(__pyx_k_getstate), 0, 0, 1, 1},
19412  {&__pyx_n_s_grade, __pyx_k_grade, sizeof(__pyx_k_grade), 0, 0, 1, 1},
19413  {&__pyx_n_s_i, __pyx_k_i, sizeof(__pyx_k_i), 0, 0, 1, 1},
19414  {&__pyx_kp_u_imag_line_1366, __pyx_k_imag_line_1366, sizeof(__pyx_k_imag_line_1366), 0, 1, 0, 0},
19415  {&__pyx_n_s_import, __pyx_k_import, sizeof(__pyx_k_import), 0, 0, 1, 1},
19416  {&__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},
19417  {&__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},
19418  {&__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},
19419  {&__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},
19420  {&__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},
19421  {&__pyx_n_s_index_set___iter, __pyx_k_index_set___iter, sizeof(__pyx_k_index_set___iter), 0, 0, 1, 1},
19422  {&__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},
19423  {&__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},
19424  {&__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},
19425  {&__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},
19426  {&__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},
19427  {&__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},
19428  {&__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},
19429  {&__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},
19430  {&__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},
19431  {&__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},
19432  {&__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},
19433  {&__pyx_n_s_index_set_hidden_doctests, __pyx_k_index_set_hidden_doctests, sizeof(__pyx_k_index_set_hidden_doctests), 0, 0, 1, 1},
19434  {&__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},
19435  {&__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},
19436  {&__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},
19437  {&__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},
19438  {&__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},
19439  {&__pyx_n_s_inv, __pyx_k_inv, sizeof(__pyx_k_inv), 0, 0, 1, 1},
19440  {&__pyx_kp_u_inv_line_1329, __pyx_k_inv_line_1329, sizeof(__pyx_k_inv_line_1329), 0, 1, 0, 0},
19441  {&__pyx_kp_s_invalid, __pyx_k_invalid, sizeof(__pyx_k_invalid), 0, 0, 1, 0},
19442  {&__pyx_kp_s_invalid_string, __pyx_k_invalid_string, sizeof(__pyx_k_invalid_string), 0, 0, 1, 0},
19443  {&__pyx_n_s_involute, __pyx_k_involute, sizeof(__pyx_k_involute), 0, 0, 1, 1},
19444  {&__pyx_kp_u_involute_line_1406, __pyx_k_involute_line_1406, sizeof(__pyx_k_involute_line_1406), 0, 1, 0, 0},
19445  {&__pyx_n_s_ist, __pyx_k_ist, sizeof(__pyx_k_ist), 0, 0, 1, 1},
19446  {&__pyx_n_s_istpq, __pyx_k_istpq, sizeof(__pyx_k_istpq), 0, 0, 1, 1},
19447  {&__pyx_kp_u_istpq_line_1900, __pyx_k_istpq_line_1900, sizeof(__pyx_k_istpq_line_1900), 0, 1, 0, 0},
19448  {&__pyx_n_s_iter, __pyx_k_iter, sizeof(__pyx_k_iter), 0, 0, 1, 1},
19449  {&__pyx_n_s_ixt, __pyx_k_ixt, sizeof(__pyx_k_ixt), 0, 0, 1, 1},
19450  {&__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},
19451  {&__pyx_n_s_lhs, __pyx_k_lhs, sizeof(__pyx_k_lhs), 0, 0, 1, 1},
19452  {&__pyx_n_s_log, __pyx_k_log, sizeof(__pyx_k_log), 0, 0, 1, 1},
19453  {&__pyx_kp_u_log_line_1579, __pyx_k_log_line_1579, sizeof(__pyx_k_log_line_1579), 0, 1, 0, 0},
19454  {&__pyx_n_s_m, __pyx_k_m, sizeof(__pyx_k_m), 0, 0, 1, 1},
19455  {&__pyx_n_s_main, __pyx_k_main, sizeof(__pyx_k_main), 0, 0, 1, 1},
19456  {&__pyx_n_s_math, __pyx_k_math, sizeof(__pyx_k_math), 0, 0, 1, 1},
19457  {&__pyx_n_s_max, __pyx_k_max, sizeof(__pyx_k_max), 0, 0, 1, 1},
19458  {&__pyx_kp_u_max_abs_line_1482, __pyx_k_max_abs_line_1482, sizeof(__pyx_k_max_abs_line_1482), 0, 1, 0, 0},
19459  {&__pyx_kp_u_max_pos_line_511, __pyx_k_max_pos_line_511, sizeof(__pyx_k_max_pos_line_511), 0, 1, 0, 0},
19460  {&__pyx_n_s_min, __pyx_k_min, sizeof(__pyx_k_min), 0, 0, 1, 1},
19461  {&__pyx_kp_u_min_neg_line_502, __pyx_k_min_neg_line_502, sizeof(__pyx_k_min_neg_line_502), 0, 1, 0, 0},
19462  {&__pyx_n_s_name, __pyx_k_name, sizeof(__pyx_k_name), 0, 0, 1, 1},
19463  {&__pyx_n_s_nbar3, __pyx_k_nbar3, sizeof(__pyx_k_nbar3), 0, 0, 1, 1},
19464  {&__pyx_n_s_ninf3, __pyx_k_ninf3, sizeof(__pyx_k_ninf3), 0, 0, 1, 1},
19465  {&__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},
19466  {&__pyx_n_s_norm, __pyx_k_norm, sizeof(__pyx_k_norm), 0, 0, 1, 1},
19467  {&__pyx_kp_u_norm_line_1462, __pyx_k_norm_line_1462, sizeof(__pyx_k_norm_line_1462), 0, 1, 0, 0},
19468  {&__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},
19469  {&__pyx_n_s_numbers, __pyx_k_numbers, sizeof(__pyx_k_numbers), 0, 0, 1, 1},
19470  {&__pyx_n_s_obj, __pyx_k_obj, sizeof(__pyx_k_obj), 0, 0, 1, 1},
19471  {&__pyx_n_s_odd, __pyx_k_odd, sizeof(__pyx_k_odd), 0, 0, 1, 1},
19472  {&__pyx_kp_u_odd_line_1397, __pyx_k_odd_line_1397, sizeof(__pyx_k_odd_line_1397), 0, 1, 0, 0},
19473  {&__pyx_n_s_other, __pyx_k_other, sizeof(__pyx_k_other), 0, 0, 1, 1},
19474  {&__pyx_n_s_outer_pow, __pyx_k_outer_pow, sizeof(__pyx_k_outer_pow), 0, 0, 1, 1},
19475  {&__pyx_kp_u_outer_pow_line_1518, __pyx_k_outer_pow_line_1518, sizeof(__pyx_k_outer_pow_line_1518), 0, 1, 0, 0},
19476  {&__pyx_n_s_p, __pyx_k_p, sizeof(__pyx_k_p), 0, 0, 1, 1},
19477  {&__pyx_n_s_pi, __pyx_k_pi, sizeof(__pyx_k_pi), 0, 0, 1, 1},
19478  {&__pyx_n_s_pow, __pyx_k_pow, sizeof(__pyx_k_pow), 0, 0, 1, 1},
19479  {&__pyx_kp_u_pow_line_1494, __pyx_k_pow_line_1494, sizeof(__pyx_k_pow_line_1494), 0, 1, 0, 0},
19480  {&__pyx_n_s_pure, __pyx_k_pure, sizeof(__pyx_k_pure), 0, 0, 1, 1},
19481  {&__pyx_kp_u_pure_line_1377, __pyx_k_pure_line_1377, sizeof(__pyx_k_pure_line_1377), 0, 1, 0, 0},
19482  {&__pyx_n_s_pyx_vtable, __pyx_k_pyx_vtable, sizeof(__pyx_k_pyx_vtable), 0, 0, 1, 1},
19483  {&__pyx_n_s_q, __pyx_k_q, sizeof(__pyx_k_q), 0, 0, 1, 1},
19484  {&__pyx_n_s_quad, __pyx_k_quad, sizeof(__pyx_k_quad), 0, 0, 1, 1},
19485  {&__pyx_kp_u_quad_line_1451, __pyx_k_quad_line_1451, sizeof(__pyx_k_quad_line_1451), 0, 1, 0, 0},
19486  {&__pyx_kp_u_random_clifford_line_1815, __pyx_k_random_clifford_line_1815, sizeof(__pyx_k_random_clifford_line_1815), 0, 1, 0, 0},
19487  {&__pyx_n_s_range, __pyx_k_range, sizeof(__pyx_k_range), 0, 0, 1, 1},
19488  {&__pyx_kp_u_real_line_1355, __pyx_k_real_line_1355, sizeof(__pyx_k_real_line_1355), 0, 1, 0, 0},
19489  {&__pyx_n_s_reduce, __pyx_k_reduce, sizeof(__pyx_k_reduce), 0, 0, 1, 1},
19490  {&__pyx_n_s_reduce_cython, __pyx_k_reduce_cython, sizeof(__pyx_k_reduce_cython), 0, 0, 1, 1},
19491  {&__pyx_n_s_reduce_ex, __pyx_k_reduce_ex, sizeof(__pyx_k_reduce_ex), 0, 0, 1, 1},
19492  {&__pyx_n_s_reverse, __pyx_k_reverse, sizeof(__pyx_k_reverse), 0, 0, 1, 1},
19493  {&__pyx_kp_u_reverse_line_1421, __pyx_k_reverse_line_1421, sizeof(__pyx_k_reverse_line_1421), 0, 1, 0, 0},
19494  {&__pyx_n_s_rhs, __pyx_k_rhs, sizeof(__pyx_k_rhs), 0, 0, 1, 1},
19495  {&__pyx_n_s_scalar, __pyx_k_scalar, sizeof(__pyx_k_scalar), 0, 0, 1, 1},
19496  {&__pyx_kp_u_scalar_line_1344, __pyx_k_scalar_line_1344, sizeof(__pyx_k_scalar_line_1344), 0, 1, 0, 0},
19497  {&__pyx_n_s_send, __pyx_k_send, sizeof(__pyx_k_send), 0, 0, 1, 1},
19498  {&__pyx_n_s_setstate, __pyx_k_setstate, sizeof(__pyx_k_setstate), 0, 0, 1, 1},
19499  {&__pyx_n_s_setstate_cython, __pyx_k_setstate_cython, sizeof(__pyx_k_setstate_cython), 0, 0, 1, 1},
19500  {&__pyx_n_s_sin, __pyx_k_sin, sizeof(__pyx_k_sin), 0, 0, 1, 1},
19501  {&__pyx_kp_u_sin_line_1679, __pyx_k_sin_line_1679, sizeof(__pyx_k_sin_line_1679), 0, 1, 0, 0},
19502  {&__pyx_n_s_sinh, __pyx_k_sinh, sizeof(__pyx_k_sinh), 0, 0, 1, 1},
19503  {&__pyx_kp_u_sinh_line_1719, __pyx_k_sinh_line_1719, sizeof(__pyx_k_sinh_line_1719), 0, 1, 0, 0},
19504  {&__pyx_n_s_sqrt, __pyx_k_sqrt, sizeof(__pyx_k_sqrt), 0, 0, 1, 1},
19505  {&__pyx_kp_u_sqrt_line_1542, __pyx_k_sqrt_line_1542, sizeof(__pyx_k_sqrt_line_1542), 0, 1, 0, 0},
19506  {&__pyx_n_s_tan, __pyx_k_tan, sizeof(__pyx_k_tan), 0, 0, 1, 1},
19507  {&__pyx_kp_u_tan_line_1752, __pyx_k_tan_line_1752, sizeof(__pyx_k_tan_line_1752), 0, 1, 0, 0},
19508  {&__pyx_n_s_tanh, __pyx_k_tanh, sizeof(__pyx_k_tanh), 0, 0, 1, 1},
19509  {&__pyx_kp_u_tanh_line_1786, __pyx_k_tanh_line_1786, sizeof(__pyx_k_tanh_line_1786), 0, 1, 0, 0},
19510  {&__pyx_n_s_tau, __pyx_k_tau, sizeof(__pyx_k_tau), 0, 0, 1, 1},
19511  {&__pyx_n_s_test, __pyx_k_test, sizeof(__pyx_k_test), 0, 0, 1, 1},
19512  {&__pyx_n_s_test_2, __pyx_k_test_2, sizeof(__pyx_k_test_2), 0, 0, 1, 1},
19513  {&__pyx_n_s_testmod, __pyx_k_testmod, sizeof(__pyx_k_testmod), 0, 0, 1, 1},
19514  {&__pyx_n_s_throw, __pyx_k_throw, sizeof(__pyx_k_throw), 0, 0, 1, 1},
19515  {&__pyx_kp_s_to_frame, __pyx_k_to_frame, sizeof(__pyx_k_to_frame), 0, 0, 1, 0},
19516  {&__pyx_kp_s_using, __pyx_k_using, sizeof(__pyx_k_using), 0, 0, 1, 0},
19517  {&__pyx_kp_s_using_invalid, __pyx_k_using_invalid, sizeof(__pyx_k_using_invalid), 0, 0, 1, 0},
19518  {&__pyx_kp_s_value, __pyx_k_value, sizeof(__pyx_k_value), 0, 0, 1, 0},
19519  {&__pyx_n_s_version, __pyx_k_version, sizeof(__pyx_k_version), 0, 0, 1, 1},
19520  {&__pyx_n_s_xrange, __pyx_k_xrange, sizeof(__pyx_k_xrange), 0, 0, 1, 1},
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19523 static int __Pyx_InitCachedBuiltins(void) {
19524  __pyx_builtin_IndexError = __Pyx_GetBuiltinName(__pyx_n_s_IndexError); if (!__pyx_builtin_IndexError) __PYX_ERR(0, 102, __pyx_L1_error)
19525  __pyx_builtin_RuntimeError = __Pyx_GetBuiltinName(__pyx_n_s_RuntimeError); if (!__pyx_builtin_RuntimeError) __PYX_ERR(0, 104, __pyx_L1_error)
19526  __pyx_builtin_TypeError = __Pyx_GetBuiltinName(__pyx_n_s_TypeError); if (!__pyx_builtin_TypeError) __PYX_ERR(0, 104, __pyx_L1_error)
19527  __pyx_builtin_ValueError = __Pyx_GetBuiltinName(__pyx_n_s_ValueError); if (!__pyx_builtin_ValueError) __PYX_ERR(0, 105, __pyx_L1_error)
19528  __pyx_builtin_NotImplemented = __Pyx_GetBuiltinName(__pyx_n_s_NotImplemented); if (!__pyx_builtin_NotImplemented) __PYX_ERR(0, 157, __pyx_L1_error)
19529  __pyx_builtin_range = __Pyx_GetBuiltinName(__pyx_n_s_range); if (!__pyx_builtin_range) __PYX_ERR(0, 234, __pyx_L1_error)
19530  #if PY_MAJOR_VERSION >= 3
19531  __pyx_builtin_xrange = __Pyx_GetBuiltinName(__pyx_n_s_range); if (!__pyx_builtin_xrange) __PYX_ERR(0, 1098, __pyx_L1_error)
19532  #else
19533  __pyx_builtin_xrange = __Pyx_GetBuiltinName(__pyx_n_s_xrange); if (!__pyx_builtin_xrange) __PYX_ERR(0, 1098, __pyx_L1_error)
19534  #endif
19535  return 0;
19536  __pyx_L1_error:;
19537  return -1;
19538 }
19539 
19540 static int __Pyx_InitCachedConstants(void) {
19541  __Pyx_RefNannyDeclarations
19542  __Pyx_RefNannySetupContext("__Pyx_InitCachedConstants", 0);
19543 
19544  /* "(tree fragment)":2
19545  * def __reduce_cython__(self):
19546  * raise TypeError("no default __reduce__ due to non-trivial __cinit__") # <<<<<<<<<<<<<<
19547  * def __setstate_cython__(self, __pyx_state):
19548  * raise TypeError("no default __reduce__ due to non-trivial __cinit__")
19549  */
19550  __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)
19551  __Pyx_GOTREF(__pyx_tuple__3);
19552  __Pyx_GIVEREF(__pyx_tuple__3);
19553 
19554  /* "(tree fragment)":4
19555  * raise TypeError("no default __reduce__ due to non-trivial __cinit__")
19556  * def __setstate_cython__(self, __pyx_state):
19557  * raise TypeError("no default __reduce__ due to non-trivial __cinit__") # <<<<<<<<<<<<<<
19558  */
19559  __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)
19560  __Pyx_GOTREF(__pyx_tuple__4);
19561  __Pyx_GIVEREF(__pyx_tuple__4);
19562 
19563  /* "PyClical.pyx":635
19564  * TypeError: Not applicable.
19565  * """
19566  * raise TypeError("Not applicable.") # <<<<<<<<<<<<<<
19567  *
19568  * def __iter__(self):
19569  */
19570  __pyx_tuple__10 = PyTuple_Pack(1, __pyx_kp_s_Not_applicable); if (unlikely(!__pyx_tuple__10)) __PYX_ERR(0, 635, __pyx_L1_error)
19571  __Pyx_GOTREF(__pyx_tuple__10);
19572  __Pyx_GIVEREF(__pyx_tuple__10);
19573 
19574  /* "PyClical.pyx":646
19575  * TypeError: Not applicable.
19576  * """
19577  * raise TypeError("Not applicable.") # <<<<<<<<<<<<<<
19578  *
19579  * def reframe(self, ixt):
19580  */
19581  __pyx_tuple__11 = PyTuple_Pack(1, __pyx_kp_s_Not_applicable); if (unlikely(!__pyx_tuple__11)) __PYX_ERR(0, 646, __pyx_L1_error)
19582  __Pyx_GOTREF(__pyx_tuple__11);
19583  __Pyx_GIVEREF(__pyx_tuple__11);
19584 
19585  /* "(tree fragment)":2
19586  * def __reduce_cython__(self):
19587  * raise TypeError("no default __reduce__ due to non-trivial __cinit__") # <<<<<<<<<<<<<<
19588  * def __setstate_cython__(self, __pyx_state):
19589  * raise TypeError("no default __reduce__ due to non-trivial __cinit__")
19590  */
19591  __pyx_tuple__12 = PyTuple_Pack(1, __pyx_kp_s_no_default___reduce___due_to_non); if (unlikely(!__pyx_tuple__12)) __PYX_ERR(1, 2, __pyx_L1_error)
19592  __Pyx_GOTREF(__pyx_tuple__12);
19593  __Pyx_GIVEREF(__pyx_tuple__12);
19594 
19595  /* "(tree fragment)":4
19596  * raise TypeError("no default __reduce__ due to non-trivial __cinit__")
19597  * def __setstate_cython__(self, __pyx_state):
19598  * raise TypeError("no default __reduce__ due to non-trivial __cinit__") # <<<<<<<<<<<<<<
19599  */
19600  __pyx_tuple__13 = PyTuple_Pack(1, __pyx_kp_s_no_default___reduce___due_to_non); if (unlikely(!__pyx_tuple__13)) __PYX_ERR(1, 4, __pyx_L1_error)
19601  __Pyx_GOTREF(__pyx_tuple__13);
19602  __Pyx_GIVEREF(__pyx_tuple__13);
19603 
19604  /* "PyClical.pyx":404
19605  * return index_set_to_str( self.unwrap() ).c_str()
19606  *
19607  * def index_set_hidden_doctests(): # <<<<<<<<<<<<<<
19608  * """
19609  * Tests for functions that Doctest cannot see.
19610  */
19611  __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_index_set_hidden_doctests, 404, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__14)) __PYX_ERR(0, 404, __pyx_L1_error)
19612 
19613  /* "PyClical.pyx":1243
19614  * return clifford_to_str( self.unwrap() ).c_str()
19615  *
19616  * def clifford_hidden_doctests(): # <<<<<<<<<<<<<<
19617  * """
19618  * Tests for functions that Doctest cannot see.
19619  */
19620  __pyx_codeobj__15 = (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__15)) __PYX_ERR(0, 1243, __pyx_L1_error)
19621 
19622  /* "PyClical.pyx":1856
19623  *
19624  * # Some abbreviations.
19625  * tau = atan(clifford(1.0)) * 8.0 # <<<<<<<<<<<<<<
19626  * pi = tau / 2.0
19627  *
19628  */
19629  __pyx_tuple__16 = PyTuple_Pack(1, __pyx_float_1_0); if (unlikely(!__pyx_tuple__16)) __PYX_ERR(0, 1856, __pyx_L1_error)
19630  __Pyx_GOTREF(__pyx_tuple__16);
19631  __Pyx_GIVEREF(__pyx_tuple__16);
19632 
19633  /* "PyClical.pyx":1887
19634  * """
19635  *
19636  * def e(obj): # <<<<<<<<<<<<<<
19637  * """
19638  * Abbreviation for clifford(index_set(obj)).
19639  */
19640  __pyx_tuple__17 = PyTuple_Pack(1, __pyx_n_s_obj); if (unlikely(!__pyx_tuple__17)) __PYX_ERR(0, 1887, __pyx_L1_error)
19641  __Pyx_GOTREF(__pyx_tuple__17);
19642  __Pyx_GIVEREF(__pyx_tuple__17);
19643  __pyx_codeobj__18 = (PyObject*)__Pyx_PyCode_New(1, 0, 1, 0, CO_OPTIMIZED|CO_NEWLOCALS, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__17, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_PyClical_pyx, __pyx_n_s_e, 1887, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__18)) __PYX_ERR(0, 1887, __pyx_L1_error)
19644 
19645  /* "PyClical.pyx":1900
19646  * return clifford(index_set(obj))
19647  *
19648  * def istpq(p, q): # <<<<<<<<<<<<<<
19649  * """
19650  * Abbreviation for index_set({-q,...p}).
19651  */
19652  __pyx_tuple__19 = PyTuple_Pack(2, __pyx_n_s_p, __pyx_n_s_q); if (unlikely(!__pyx_tuple__19)) __PYX_ERR(0, 1900, __pyx_L1_error)
19653  __Pyx_GOTREF(__pyx_tuple__19);
19654  __Pyx_GIVEREF(__pyx_tuple__19);
19655  __pyx_codeobj__20 = (PyObject*)__Pyx_PyCode_New(2, 0, 2, 0, CO_OPTIMIZED|CO_NEWLOCALS, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__19, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_PyClical_pyx, __pyx_n_s_istpq, 1900, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__20)) __PYX_ERR(0, 1900, __pyx_L1_error)
19656 
19657  /* "PyClical.pyx":1909
19658  * return index_set(set(range(-q,p+1)))
19659  *
19660  * ninf3 = e(4) + e(-1) # Null infinity point in 3D Conformal Geometric Algebra [DL]. # <<<<<<<<<<<<<<
19661  * nbar3 = e(4) - e(-1) # Null bar point in 3D Conformal Geometric Algebra [DL].
19662  *
19663  */
19664  __pyx_tuple__21 = PyTuple_Pack(1, __pyx_int_4); if (unlikely(!__pyx_tuple__21)) __PYX_ERR(0, 1909, __pyx_L1_error)
19665  __Pyx_GOTREF(__pyx_tuple__21);
19666  __Pyx_GIVEREF(__pyx_tuple__21);
19667  __pyx_tuple__22 = PyTuple_Pack(1, __pyx_int_neg_1); if (unlikely(!__pyx_tuple__22)) __PYX_ERR(0, 1909, __pyx_L1_error)
19668  __Pyx_GOTREF(__pyx_tuple__22);
19669  __Pyx_GIVEREF(__pyx_tuple__22);
19670 
19671  /* "PyClical.pyx":1910
19672  *
19673  * ninf3 = e(4) + e(-1) # Null infinity point in 3D Conformal Geometric Algebra [DL].
19674  * nbar3 = e(4) - e(-1) # Null bar point in 3D Conformal Geometric Algebra [DL]. # <<<<<<<<<<<<<<
19675  *
19676  * # Doctest interface.
19677  */
19678  __pyx_tuple__23 = PyTuple_Pack(1, __pyx_int_4); if (unlikely(!__pyx_tuple__23)) __PYX_ERR(0, 1910, __pyx_L1_error)
19679  __Pyx_GOTREF(__pyx_tuple__23);
19680  __Pyx_GIVEREF(__pyx_tuple__23);
19681  __pyx_tuple__24 = PyTuple_Pack(1, __pyx_int_neg_1); if (unlikely(!__pyx_tuple__24)) __PYX_ERR(0, 1910, __pyx_L1_error)
19682  __Pyx_GOTREF(__pyx_tuple__24);
19683  __Pyx_GIVEREF(__pyx_tuple__24);
19684 
19685  /* "PyClical.pyx":1913
19686  *
19687  * # Doctest interface.
19688  * def _test(): # <<<<<<<<<<<<<<
19689  * import PyClical, doctest
19690  * return doctest.testmod(PyClical)
19691  */
19692  __pyx_tuple__25 = PyTuple_Pack(2, __pyx_n_s_PyClical, __pyx_n_s_doctest); if (unlikely(!__pyx_tuple__25)) __PYX_ERR(0, 1913, __pyx_L1_error)
19693  __Pyx_GOTREF(__pyx_tuple__25);
19694  __Pyx_GIVEREF(__pyx_tuple__25);
19695  __pyx_codeobj__26 = (PyObject*)__Pyx_PyCode_New(0, 0, 2, 0, CO_OPTIMIZED|CO_NEWLOCALS, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__25, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_PyClical_pyx, __pyx_n_s_test, 1913, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__26)) __PYX_ERR(0, 1913, __pyx_L1_error)
19696  __Pyx_RefNannyFinishContext();
19697  return 0;
19698  __pyx_L1_error:;
19699  __Pyx_RefNannyFinishContext();
19700  return -1;
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19702 
19703 static int __Pyx_InitGlobals(void) {
19704  if (__Pyx_InitStrings(__pyx_string_tab) < 0) __PYX_ERR(0, 1, __pyx_L1_error);
19705  __pyx_float_0_0 = PyFloat_FromDouble(0.0); if (unlikely(!__pyx_float_0_0)) __PYX_ERR(0, 1, __pyx_L1_error)
19706  __pyx_float_1_0 = PyFloat_FromDouble(1.0); if (unlikely(!__pyx_float_1_0)) __PYX_ERR(0, 1, __pyx_L1_error)
19707  __pyx_float_2_0 = PyFloat_FromDouble(2.0); if (unlikely(!__pyx_float_2_0)) __PYX_ERR(0, 1, __pyx_L1_error)
19708  __pyx_float_8_0 = PyFloat_FromDouble(8.0); if (unlikely(!__pyx_float_8_0)) __PYX_ERR(0, 1, __pyx_L1_error)
19709  __pyx_int_0 = PyInt_FromLong(0); if (unlikely(!__pyx_int_0)) __PYX_ERR(0, 1, __pyx_L1_error)
19710  __pyx_int_1 = PyInt_FromLong(1); if (unlikely(!__pyx_int_1)) __PYX_ERR(0, 1, __pyx_L1_error)
19711  __pyx_int_4 = PyInt_FromLong(4); if (unlikely(!__pyx_int_4)) __PYX_ERR(0, 1, __pyx_L1_error)
19712  __pyx_int_neg_1 = PyInt_FromLong(-1); if (unlikely(!__pyx_int_neg_1)) __PYX_ERR(0, 1, __pyx_L1_error)
19713  return 0;
19714  __pyx_L1_error:;
19715  return -1;
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19719 static int __Pyx_modinit_variable_export_code(void); /*proto*/
19720 static int __Pyx_modinit_function_export_code(void); /*proto*/
19721 static int __Pyx_modinit_type_init_code(void); /*proto*/
19722 static int __Pyx_modinit_type_import_code(void); /*proto*/
19723 static int __Pyx_modinit_variable_import_code(void); /*proto*/
19724 static int __Pyx_modinit_function_import_code(void); /*proto*/
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19726 static int __Pyx_modinit_global_init_code(void) {
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19752  __Pyx_RefNannySetupContext("__Pyx_modinit_type_init_code", 0);
19753  /*--- Type init code ---*/
19754  __pyx_vtabptr_8PyClical_index_set = &__pyx_vtable_8PyClical_index_set;
19755  __pyx_vtable_8PyClical_index_set.wrap = (PyObject *(*)(struct __pyx_obj_8PyClical_index_set *, IndexSet))__pyx_f_8PyClical_9index_set_wrap;
19756  __pyx_vtable_8PyClical_index_set.unwrap = (IndexSet (*)(struct __pyx_obj_8PyClical_index_set *))__pyx_f_8PyClical_9index_set_unwrap;
19757  __pyx_vtable_8PyClical_index_set.copy = (PyObject *(*)(struct __pyx_obj_8PyClical_index_set *, int __pyx_skip_dispatch))__pyx_f_8PyClical_9index_set_copy;
19758  if (PyType_Ready(&__pyx_type_8PyClical_index_set) < 0) __PYX_ERR(0, 45, __pyx_L1_error)
19759  __pyx_type_8PyClical_index_set.tp_print = 0;
19760  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)) {
19761  __pyx_type_8PyClical_index_set.tp_getattro = __Pyx_PyObject_GenericGetAttr;
19762  }
19763  #if CYTHON_COMPILING_IN_CPYTHON
19764  {
19765  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__setitem__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
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19767  __pyx_wrapperbase_8PyClical_9index_set_8__setitem__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19768  __pyx_wrapperbase_8PyClical_9index_set_8__setitem__.doc = __pyx_doc_8PyClical_9index_set_8__setitem__;
19769  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_8__setitem__;
19770  }
19771  }
19772  #endif
19773  #if CYTHON_COMPILING_IN_CPYTHON
19774  {
19775  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__getitem__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19776  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19777  __pyx_wrapperbase_8PyClical_9index_set_10__getitem__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19778  __pyx_wrapperbase_8PyClical_9index_set_10__getitem__.doc = __pyx_doc_8PyClical_9index_set_10__getitem__;
19779  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_10__getitem__;
19780  }
19781  }
19782  #endif
19783  #if CYTHON_COMPILING_IN_CPYTHON
19784  {
19785  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__contains__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19786  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19787  __pyx_wrapperbase_8PyClical_9index_set_12__contains__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19788  __pyx_wrapperbase_8PyClical_9index_set_12__contains__.doc = __pyx_doc_8PyClical_9index_set_12__contains__;
19789  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_12__contains__;
19790  }
19791  }
19792  #endif
19793  #if CYTHON_COMPILING_IN_CPYTHON
19794  {
19795  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__iter__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19796  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19797  __pyx_wrapperbase_8PyClical_9index_set_14__iter__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19798  __pyx_wrapperbase_8PyClical_9index_set_14__iter__.doc = __pyx_doc_8PyClical_9index_set_14__iter__;
19799  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_14__iter__;
19800  }
19801  }
19802  #endif
19803  #if CYTHON_COMPILING_IN_CPYTHON
19804  {
19805  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__invert__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19806  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19807  __pyx_wrapperbase_8PyClical_9index_set_17__invert__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19808  __pyx_wrapperbase_8PyClical_9index_set_17__invert__.doc = __pyx_doc_8PyClical_9index_set_17__invert__;
19809  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_17__invert__;
19810  }
19811  }
19812  #endif
19813  #if CYTHON_COMPILING_IN_CPYTHON
19814  {
19815  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__xor__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19816  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19817  __pyx_wrapperbase_8PyClical_9index_set_19__xor__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19818  __pyx_wrapperbase_8PyClical_9index_set_19__xor__.doc = __pyx_doc_8PyClical_9index_set_19__xor__;
19819  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_19__xor__;
19820  }
19821  }
19822  #endif
19823  #if CYTHON_COMPILING_IN_CPYTHON
19824  {
19825  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__ixor__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19826  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19827  __pyx_wrapperbase_8PyClical_9index_set_21__ixor__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19828  __pyx_wrapperbase_8PyClical_9index_set_21__ixor__.doc = __pyx_doc_8PyClical_9index_set_21__ixor__;
19829  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_21__ixor__;
19830  }
19831  }
19832  #endif
19833  #if CYTHON_COMPILING_IN_CPYTHON
19834  {
19835  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__and__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19836  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19837  __pyx_wrapperbase_8PyClical_9index_set_23__and__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19838  __pyx_wrapperbase_8PyClical_9index_set_23__and__.doc = __pyx_doc_8PyClical_9index_set_23__and__;
19839  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_23__and__;
19840  }
19841  }
19842  #endif
19843  #if CYTHON_COMPILING_IN_CPYTHON
19844  {
19845  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__iand__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19846  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19847  __pyx_wrapperbase_8PyClical_9index_set_25__iand__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19848  __pyx_wrapperbase_8PyClical_9index_set_25__iand__.doc = __pyx_doc_8PyClical_9index_set_25__iand__;
19849  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_25__iand__;
19850  }
19851  }
19852  #endif
19853  #if CYTHON_COMPILING_IN_CPYTHON
19854  {
19855  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__or__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19856  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19857  __pyx_wrapperbase_8PyClical_9index_set_27__or__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19858  __pyx_wrapperbase_8PyClical_9index_set_27__or__.doc = __pyx_doc_8PyClical_9index_set_27__or__;
19859  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_27__or__;
19860  }
19861  }
19862  #endif
19863  #if CYTHON_COMPILING_IN_CPYTHON
19864  {
19865  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__ior__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19866  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19867  __pyx_wrapperbase_8PyClical_9index_set_29__ior__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19868  __pyx_wrapperbase_8PyClical_9index_set_29__ior__.doc = __pyx_doc_8PyClical_9index_set_29__ior__;
19869  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_29__ior__;
19870  }
19871  }
19872  #endif
19873  #if CYTHON_COMPILING_IN_CPYTHON
19874  {
19875  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__repr__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19876  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19877  __pyx_wrapperbase_8PyClical_9index_set_47__repr__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19878  __pyx_wrapperbase_8PyClical_9index_set_47__repr__.doc = __pyx_doc_8PyClical_9index_set_47__repr__;
19879  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_47__repr__;
19880  }
19881  }
19882  #endif
19883  #if CYTHON_COMPILING_IN_CPYTHON
19884  {
19885  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_index_set, "__str__"); if (unlikely(!wrapper)) __PYX_ERR(0, 45, __pyx_L1_error)
19886  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19887  __pyx_wrapperbase_8PyClical_9index_set_49__str__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19888  __pyx_wrapperbase_8PyClical_9index_set_49__str__.doc = __pyx_doc_8PyClical_9index_set_49__str__;
19889  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_9index_set_49__str__;
19890  }
19891  }
19892  #endif
19893  if (__Pyx_SetVtable(__pyx_type_8PyClical_index_set.tp_dict, __pyx_vtabptr_8PyClical_index_set) < 0) __PYX_ERR(0, 45, __pyx_L1_error)
19894  if (PyObject_SetAttrString(__pyx_m, "index_set", (PyObject *)&__pyx_type_8PyClical_index_set) < 0) __PYX_ERR(0, 45, __pyx_L1_error)
19895  if (__Pyx_setup_reduce((PyObject*)&__pyx_type_8PyClical_index_set) < 0) __PYX_ERR(0, 45, __pyx_L1_error)
19896  __pyx_ptype_8PyClical_index_set = &__pyx_type_8PyClical_index_set;
19897  __pyx_vtabptr_8PyClical_clifford = &__pyx_vtable_8PyClical_clifford;
19898  __pyx_vtable_8PyClical_clifford.wrap = (PyObject *(*)(struct __pyx_obj_8PyClical_clifford *, Clifford))__pyx_f_8PyClical_8clifford_wrap;
19899  __pyx_vtable_8PyClical_clifford.unwrap = (Clifford (*)(struct __pyx_obj_8PyClical_clifford *))__pyx_f_8PyClical_8clifford_unwrap;
19900  __pyx_vtable_8PyClical_clifford.copy = (PyObject *(*)(struct __pyx_obj_8PyClical_clifford *, int __pyx_skip_dispatch))__pyx_f_8PyClical_8clifford_copy;
19901  if (PyType_Ready(&__pyx_type_8PyClical_clifford) < 0) __PYX_ERR(0, 535, __pyx_L1_error)
19902  __pyx_type_8PyClical_clifford.tp_print = 0;
19903  if ((CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP) && likely(!__pyx_type_8PyClical_clifford.tp_dictoffset && __pyx_type_8PyClical_clifford.tp_getattro == PyObject_GenericGetAttr)) {
19904  __pyx_type_8PyClical_clifford.tp_getattro = __Pyx_PyObject_GenericGetAttr;
19905  }
19906  #if CYTHON_COMPILING_IN_CPYTHON
19907  {
19908  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__contains__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19909  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19910  __pyx_wrapperbase_8PyClical_8clifford_6__contains__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19911  __pyx_wrapperbase_8PyClical_8clifford_6__contains__.doc = __pyx_doc_8PyClical_8clifford_6__contains__;
19912  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_6__contains__;
19913  }
19914  }
19915  #endif
19916  #if CYTHON_COMPILING_IN_CPYTHON
19917  {
19918  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__iter__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19919  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19920  __pyx_wrapperbase_8PyClical_8clifford_8__iter__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19921  __pyx_wrapperbase_8PyClical_8clifford_8__iter__.doc = __pyx_doc_8PyClical_8clifford_8__iter__;
19922  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_8__iter__;
19923  }
19924  }
19925  #endif
19926  #if CYTHON_COMPILING_IN_CPYTHON
19927  {
19928  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__getitem__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19929  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19930  __pyx_wrapperbase_8PyClical_8clifford_14__getitem__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19931  __pyx_wrapperbase_8PyClical_8clifford_14__getitem__.doc = __pyx_doc_8PyClical_8clifford_14__getitem__;
19932  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_14__getitem__;
19933  }
19934  }
19935  #endif
19936  #if CYTHON_COMPILING_IN_CPYTHON
19937  {
19938  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__neg__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19939  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19940  __pyx_wrapperbase_8PyClical_8clifford_16__neg__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19941  __pyx_wrapperbase_8PyClical_8clifford_16__neg__.doc = __pyx_doc_8PyClical_8clifford_16__neg__;
19942  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_16__neg__;
19943  }
19944  }
19945  #endif
19946  #if CYTHON_COMPILING_IN_CPYTHON
19947  {
19948  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__pos__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19949  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19950  __pyx_wrapperbase_8PyClical_8clifford_18__pos__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19951  __pyx_wrapperbase_8PyClical_8clifford_18__pos__.doc = __pyx_doc_8PyClical_8clifford_18__pos__;
19952  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_18__pos__;
19953  }
19954  }
19955  #endif
19956  #if CYTHON_COMPILING_IN_CPYTHON
19957  {
19958  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__add__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19959  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19960  __pyx_wrapperbase_8PyClical_8clifford_20__add__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19961  __pyx_wrapperbase_8PyClical_8clifford_20__add__.doc = __pyx_doc_8PyClical_8clifford_20__add__;
19962  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_20__add__;
19963  }
19964  }
19965  #endif
19966  #if CYTHON_COMPILING_IN_CPYTHON
19967  {
19968  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__iadd__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19969  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19970  __pyx_wrapperbase_8PyClical_8clifford_22__iadd__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19971  __pyx_wrapperbase_8PyClical_8clifford_22__iadd__.doc = __pyx_doc_8PyClical_8clifford_22__iadd__;
19972  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_22__iadd__;
19973  }
19974  }
19975  #endif
19976  #if CYTHON_COMPILING_IN_CPYTHON
19977  {
19978  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__sub__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19979  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19980  __pyx_wrapperbase_8PyClical_8clifford_24__sub__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19981  __pyx_wrapperbase_8PyClical_8clifford_24__sub__.doc = __pyx_doc_8PyClical_8clifford_24__sub__;
19982  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_24__sub__;
19983  }
19984  }
19985  #endif
19986  #if CYTHON_COMPILING_IN_CPYTHON
19987  {
19988  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__isub__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19989  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
19990  __pyx_wrapperbase_8PyClical_8clifford_26__isub__ = *((PyWrapperDescrObject *)wrapper)->d_base;
19991  __pyx_wrapperbase_8PyClical_8clifford_26__isub__.doc = __pyx_doc_8PyClical_8clifford_26__isub__;
19992  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_26__isub__;
19993  }
19994  }
19995  #endif
19996  #if CYTHON_COMPILING_IN_CPYTHON
19997  {
19998  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__mul__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
19999  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
20000  __pyx_wrapperbase_8PyClical_8clifford_28__mul__ = *((PyWrapperDescrObject *)wrapper)->d_base;
20001  __pyx_wrapperbase_8PyClical_8clifford_28__mul__.doc = __pyx_doc_8PyClical_8clifford_28__mul__;
20002  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_28__mul__;
20003  }
20004  }
20005  #endif
20006  #if CYTHON_COMPILING_IN_CPYTHON
20007  {
20008  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__imul__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
20009  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
20010  __pyx_wrapperbase_8PyClical_8clifford_30__imul__ = *((PyWrapperDescrObject *)wrapper)->d_base;
20011  __pyx_wrapperbase_8PyClical_8clifford_30__imul__.doc = __pyx_doc_8PyClical_8clifford_30__imul__;
20012  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_30__imul__;
20013  }
20014  }
20015  #endif
20016  #if CYTHON_COMPILING_IN_CPYTHON
20017  {
20018  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__mod__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
20019  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
20020  __pyx_wrapperbase_8PyClical_8clifford_32__mod__ = *((PyWrapperDescrObject *)wrapper)->d_base;
20021  __pyx_wrapperbase_8PyClical_8clifford_32__mod__.doc = __pyx_doc_8PyClical_8clifford_32__mod__;
20022  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_32__mod__;
20023  }
20024  }
20025  #endif
20026  #if CYTHON_COMPILING_IN_CPYTHON
20027  {
20028  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__imod__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
20029  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
20030  __pyx_wrapperbase_8PyClical_8clifford_34__imod__ = *((PyWrapperDescrObject *)wrapper)->d_base;
20031  __pyx_wrapperbase_8PyClical_8clifford_34__imod__.doc = __pyx_doc_8PyClical_8clifford_34__imod__;
20032  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_34__imod__;
20033  }
20034  }
20035  #endif
20036  #if CYTHON_COMPILING_IN_CPYTHON
20037  {
20038  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__and__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
20039  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
20040  __pyx_wrapperbase_8PyClical_8clifford_36__and__ = *((PyWrapperDescrObject *)wrapper)->d_base;
20041  __pyx_wrapperbase_8PyClical_8clifford_36__and__.doc = __pyx_doc_8PyClical_8clifford_36__and__;
20042  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_36__and__;
20043  }
20044  }
20045  #endif
20046  #if CYTHON_COMPILING_IN_CPYTHON
20047  {
20048  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__iand__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
20049  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
20050  __pyx_wrapperbase_8PyClical_8clifford_38__iand__ = *((PyWrapperDescrObject *)wrapper)->d_base;
20051  __pyx_wrapperbase_8PyClical_8clifford_38__iand__.doc = __pyx_doc_8PyClical_8clifford_38__iand__;
20052  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_38__iand__;
20053  }
20054  }
20055  #endif
20056  #if CYTHON_COMPILING_IN_CPYTHON
20057  {
20058  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__xor__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
20059  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
20060  __pyx_wrapperbase_8PyClical_8clifford_40__xor__ = *((PyWrapperDescrObject *)wrapper)->d_base;
20061  __pyx_wrapperbase_8PyClical_8clifford_40__xor__.doc = __pyx_doc_8PyClical_8clifford_40__xor__;
20062  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_40__xor__;
20063  }
20064  }
20065  #endif
20066  #if CYTHON_COMPILING_IN_CPYTHON
20067  {
20068  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__ixor__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
20069  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
20070  __pyx_wrapperbase_8PyClical_8clifford_42__ixor__ = *((PyWrapperDescrObject *)wrapper)->d_base;
20071  __pyx_wrapperbase_8PyClical_8clifford_42__ixor__.doc = __pyx_doc_8PyClical_8clifford_42__ixor__;
20072  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_42__ixor__;
20073  }
20074  }
20075  #endif
20076  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
20077  #if CYTHON_COMPILING_IN_CPYTHON
20078  {
20079  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__div__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
20080  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
20081  __pyx_wrapperbase_8PyClical_8clifford_44__div__ = *((PyWrapperDescrObject *)wrapper)->d_base;
20082  __pyx_wrapperbase_8PyClical_8clifford_44__div__.doc = __pyx_doc_8PyClical_8clifford_44__div__;
20083  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_44__div__;
20084  }
20085  }
20086  #endif
20087  #endif
20088  #if PY_MAJOR_VERSION < 3 || (CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03050000)
20089  #if CYTHON_COMPILING_IN_CPYTHON
20090  {
20091  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__idiv__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
20092  if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
20093  __pyx_wrapperbase_8PyClical_8clifford_46__idiv__ = *((PyWrapperDescrObject *)wrapper)->d_base;
20094  __pyx_wrapperbase_8PyClical_8clifford_46__idiv__.doc = __pyx_doc_8PyClical_8clifford_46__idiv__;
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20105  __pyx_wrapperbase_8PyClical_8clifford_50__or__.doc = __pyx_doc_8PyClical_8clifford_50__or__;
20106  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_50__or__;
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20110  #if CYTHON_COMPILING_IN_CPYTHON
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20112  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__ior__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
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20114  __pyx_wrapperbase_8PyClical_8clifford_52__ior__ = *((PyWrapperDescrObject *)wrapper)->d_base;
20115  __pyx_wrapperbase_8PyClical_8clifford_52__ior__.doc = __pyx_doc_8PyClical_8clifford_52__ior__;
20116  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_52__ior__;
20117  }
20118  }
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20120  #if CYTHON_COMPILING_IN_CPYTHON
20121  {
20122  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__pow__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
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20124  __pyx_wrapperbase_8PyClical_8clifford_54__pow__ = *((PyWrapperDescrObject *)wrapper)->d_base;
20125  __pyx_wrapperbase_8PyClical_8clifford_54__pow__.doc = __pyx_doc_8PyClical_8clifford_54__pow__;
20126  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_54__pow__;
20127  }
20128  }
20129  #endif
20130  #if CYTHON_COMPILING_IN_CPYTHON
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20146  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_92__repr__;
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20148  }
20149  #endif
20150  #if CYTHON_COMPILING_IN_CPYTHON
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20152  PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_8PyClical_clifford, "__str__"); if (unlikely(!wrapper)) __PYX_ERR(0, 535, __pyx_L1_error)
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20156  ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_8PyClical_8clifford_94__str__;
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20158  }
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20185 static int __Pyx_modinit_variable_import_code(void) {
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20193 static int __Pyx_modinit_function_import_code(void) {
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20200 
20201 
20202 #if PY_MAJOR_VERSION < 3
20203 #ifdef CYTHON_NO_PYINIT_EXPORT
20204 #define __Pyx_PyMODINIT_FUNC void
20205 #else
20206 #define __Pyx_PyMODINIT_FUNC PyMODINIT_FUNC
20207 #endif
20208 #else
20209 #ifdef CYTHON_NO_PYINIT_EXPORT
20210 #define __Pyx_PyMODINIT_FUNC PyObject *
20211 #else
20212 #define __Pyx_PyMODINIT_FUNC PyMODINIT_FUNC
20213 #endif
20214 #endif
20215 #ifndef CYTHON_SMALL_CODE
20216 #if defined(__clang__)
20217  #define CYTHON_SMALL_CODE
20218 #elif defined(__GNUC__) && (!(defined(__cplusplus)) || (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ > 4)))
20219  #define CYTHON_SMALL_CODE __attribute__((cold))
20220 #else
20221  #define CYTHON_SMALL_CODE
20222 #endif
20223 #endif
20224 
20225 
20226 #if PY_MAJOR_VERSION < 3
20227 __Pyx_PyMODINIT_FUNC initPyClical(void) CYTHON_SMALL_CODE; /*proto*/
20228 __Pyx_PyMODINIT_FUNC initPyClical(void)
20229 #else
20230 __Pyx_PyMODINIT_FUNC PyInit_PyClical(void) CYTHON_SMALL_CODE; /*proto*/
20231 __Pyx_PyMODINIT_FUNC PyInit_PyClical(void)
20232 #if CYTHON_PEP489_MULTI_PHASE_INIT
20233 {
20234  return PyModuleDef_Init(&__pyx_moduledef);
20235 }
20236 static int __Pyx_copy_spec_to_module(PyObject *spec, PyObject *moddict, const char* from_name, const char* to_name) {
20237  PyObject *value = PyObject_GetAttrString(spec, from_name);
20238  int result = 0;
20239  if (likely(value)) {
20240  result = PyDict_SetItemString(moddict, to_name, value);
20241  Py_DECREF(value);
20242  } else if (PyErr_ExceptionMatches(PyExc_AttributeError)) {
20243  PyErr_Clear();
20244  } else {
20245  result = -1;
20246  }
20247  return result;
20248 }
20249 static PyObject* __pyx_pymod_create(PyObject *spec, CYTHON_UNUSED PyModuleDef *def) {
20250  PyObject *module = NULL, *moddict, *modname;
20251  if (__pyx_m)
20252  return __Pyx_NewRef(__pyx_m);
20253  modname = PyObject_GetAttrString(spec, "name");
20254  if (unlikely(!modname)) goto bad;
20255  module = PyModule_NewObject(modname);
20256  Py_DECREF(modname);
20257  if (unlikely(!module)) goto bad;
20258  moddict = PyModule_GetDict(module);
20259  if (unlikely(!moddict)) goto bad;
20260  if (unlikely(__Pyx_copy_spec_to_module(spec, moddict, "loader", "__loader__") < 0)) goto bad;
20261  if (unlikely(__Pyx_copy_spec_to_module(spec, moddict, "origin", "__file__") < 0)) goto bad;
20262  if (unlikely(__Pyx_copy_spec_to_module(spec, moddict, "parent", "__package__") < 0)) goto bad;
20263  if (unlikely(__Pyx_copy_spec_to_module(spec, moddict, "submodule_search_locations", "__path__") < 0)) goto bad;
20264  return module;
20265 bad:
20266  Py_XDECREF(module);
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20268 }
20269 
20270 
20271 static int __pyx_pymod_exec_PyClical(PyObject *__pyx_pyinit_module)
20272 #endif
20273 #endif
20274 {
20275  PyObject *__pyx_t_1 = NULL;
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20277  PyObject *__pyx_t_3 = NULL;
20278  int __pyx_t_4;
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20280  #if CYTHON_PEP489_MULTI_PHASE_INIT
20281  if (__pyx_m && __pyx_m == __pyx_pyinit_module) return 0;
20282  #elif PY_MAJOR_VERSION >= 3
20283  if (__pyx_m) return __Pyx_NewRef(__pyx_m);
20284  #endif
20285  #if CYTHON_REFNANNY
20286 __Pyx_RefNanny = __Pyx_RefNannyImportAPI("refnanny");
20287 if (!__Pyx_RefNanny) {
20288  PyErr_Clear();
20289  __Pyx_RefNanny = __Pyx_RefNannyImportAPI("Cython.Runtime.refnanny");
20290  if (!__Pyx_RefNanny)
20291  Py_FatalError("failed to import 'refnanny' module");
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20297  __pyx_empty_bytes = PyBytes_FromStringAndSize("", 0); if (unlikely(!__pyx_empty_bytes)) __PYX_ERR(0, 1, __pyx_L1_error)
20298  __pyx_empty_unicode = PyUnicode_FromStringAndSize("", 0); if (unlikely(!__pyx_empty_unicode)) __PYX_ERR(0, 1, __pyx_L1_error)
20299  #ifdef __Pyx_CyFunction_USED
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20314  #ifdef __Pyx_StopAsyncIteration_USED
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20317  /*--- Library function declarations ---*/
20318  /*--- Threads initialization code ---*/
20319  #if defined(__PYX_FORCE_INIT_THREADS) && __PYX_FORCE_INIT_THREADS
20320  #ifdef WITH_THREAD /* Python build with threading support? */
20321  PyEval_InitThreads();
20322  #endif
20323  #endif
20324  /*--- Module creation code ---*/
20325  #if CYTHON_PEP489_MULTI_PHASE_INIT
20326  __pyx_m = __pyx_pyinit_module;
20327  Py_INCREF(__pyx_m);
20328  #else
20329  #if PY_MAJOR_VERSION < 3
20330  __pyx_m = Py_InitModule4("PyClical", __pyx_methods, 0, 0, PYTHON_API_VERSION); Py_XINCREF(__pyx_m);
20331  #else
20332  __pyx_m = PyModule_Create(&__pyx_moduledef);
20333  #endif
20334  if (unlikely(!__pyx_m)) __PYX_ERR(0, 1, __pyx_L1_error)
20335  #endif
20336  __pyx_d = PyModule_GetDict(__pyx_m); if (unlikely(!__pyx_d)) __PYX_ERR(0, 1, __pyx_L1_error)
20337  Py_INCREF(__pyx_d);
20338  __pyx_b = PyImport_AddModule(__Pyx_BUILTIN_MODULE_NAME); if (unlikely(!__pyx_b)) __PYX_ERR(0, 1, __pyx_L1_error)
20339  __pyx_cython_runtime = PyImport_AddModule((char *) "cython_runtime"); if (unlikely(!__pyx_cython_runtime)) __PYX_ERR(0, 1, __pyx_L1_error)
20340  #if CYTHON_COMPILING_IN_PYPY
20341  Py_INCREF(__pyx_b);
20342  #endif
20343  if (PyObject_SetAttrString(__pyx_m, "__builtins__", __pyx_b) < 0) __PYX_ERR(0, 1, __pyx_L1_error);
20344  /*--- Initialize various global constants etc. ---*/
20345  if (__Pyx_InitGlobals() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20346  #if PY_MAJOR_VERSION < 3 && (__PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT)
20347  if (__Pyx_init_sys_getdefaultencoding_params() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
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20350  if (PyObject_SetAttrString(__pyx_m, "__name__", __pyx_n_s_main) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20351  }
20352  #if PY_MAJOR_VERSION >= 3
20353  {
20354  PyObject *modules = PyImport_GetModuleDict(); if (unlikely(!modules)) __PYX_ERR(0, 1, __pyx_L1_error)
20355  if (!PyDict_GetItemString(modules, "PyClical")) {
20356  if (unlikely(PyDict_SetItemString(modules, "PyClical", __pyx_m) < 0)) __PYX_ERR(0, 1, __pyx_L1_error)
20357  }
20358  }
20359  #endif
20360  /*--- Builtin init code ---*/
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20362  /*--- Constants init code ---*/
20363  if (__Pyx_InitCachedConstants() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20364  /*--- Global type/function init code ---*/
20365  (void)__Pyx_modinit_global_init_code();
20366  (void)__Pyx_modinit_variable_export_code();
20367  (void)__Pyx_modinit_function_export_code();
20368  if (unlikely(__Pyx_modinit_type_init_code() != 0)) goto __pyx_L1_error;
20369  (void)__Pyx_modinit_type_import_code();
20370  (void)__Pyx_modinit_variable_import_code();
20371  (void)__Pyx_modinit_function_import_code();
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20375  #endif
20376 
20377  /* "PyClical.pyx":28
20378  * # C. Doran and A. Lasenby, "Geometric algebra for physicists", Cambridge, 2003.
20379  *
20380  * import math # <<<<<<<<<<<<<<
20381  * import numbers
20382  * import collections
20383  */
20384  __pyx_t_1 = __Pyx_Import(__pyx_n_s_math, 0, -1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 28, __pyx_L1_error)
20385  __Pyx_GOTREF(__pyx_t_1);
20386  if (PyDict_SetItem(__pyx_d, __pyx_n_s_math, __pyx_t_1) < 0) __PYX_ERR(0, 28, __pyx_L1_error)
20387  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
20388 
20389  /* "PyClical.pyx":29
20390  *
20391  * import math
20392  * import numbers # <<<<<<<<<<<<<<
20393  * import collections
20394  *
20395  */
20396  __pyx_t_1 = __Pyx_Import(__pyx_n_s_numbers, 0, -1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 29, __pyx_L1_error)
20397  __Pyx_GOTREF(__pyx_t_1);
20398  if (PyDict_SetItem(__pyx_d, __pyx_n_s_numbers, __pyx_t_1) < 0) __PYX_ERR(0, 29, __pyx_L1_error)
20399  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
20400 
20401  /* "PyClical.pyx":30
20402  * import math
20403  * import numbers
20404  * import collections # <<<<<<<<<<<<<<
20405  *
20406  * __version__ = "0.8.2"
20407  */
20408  __pyx_t_1 = __Pyx_Import(__pyx_n_s_collections, 0, -1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 30, __pyx_L1_error)
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20411  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
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20413  /* "PyClical.pyx":32
20414  * import collections
20415  *
20416  * __version__ = "0.8.2" # <<<<<<<<<<<<<<
20417  *
20418  * from PyClical cimport *
20419  */
20420  if (PyDict_SetItem(__pyx_d, __pyx_n_s_version, __pyx_kp_s_0_8_2) < 0) __PYX_ERR(0, 32, __pyx_L1_error)
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20423  * return index_set_to_str( self.unwrap() ).c_str()
20424  *
20425  * def index_set_hidden_doctests(): # <<<<<<<<<<<<<<
20426  * """
20427  * Tests for functions that Doctest cannot see.
20428  */
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20432  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
20433 
20434  /* "PyClical.pyx":1243
20435  * return clifford_to_str( self.unwrap() ).c_str()
20436  *
20437  * def clifford_hidden_doctests(): # <<<<<<<<<<<<<<
20438  * """
20439  * Tests for functions that Doctest cannot see.
20440  */
20441  __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)
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20444  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
20445 
20446  /* "PyClical.pyx":1856
20447  *
20448  * # Some abbreviations.
20449  * tau = atan(clifford(1.0)) * 8.0 # <<<<<<<<<<<<<<
20450  * pi = tau / 2.0
20451  *
20452  */
20453  __pyx_t_1 = __Pyx_PyObject_Call(((PyObject *)__pyx_ptype_8PyClical_clifford), __pyx_tuple__16, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 1856, __pyx_L1_error)
20454  __Pyx_GOTREF(__pyx_t_1);
20455  __pyx_t_2 = __pyx_f_8PyClical_atan(__pyx_t_1, 0, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 1856, __pyx_L1_error)
20456  __Pyx_GOTREF(__pyx_t_2);
20457  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
20458  __pyx_t_1 = PyNumber_Multiply(__pyx_t_2, __pyx_float_8_0); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 1856, __pyx_L1_error)
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20465  * # Some abbreviations.
20466  * tau = atan(clifford(1.0)) * 8.0
20467  * pi = tau / 2.0 # <<<<<<<<<<<<<<
20468  *
20469  * cl = clifford
20470  */
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20480  * pi = tau / 2.0
20481  *
20482  * cl = clifford # <<<<<<<<<<<<<<
20483  * """
20484  * Abbreviation for clifford.
20485  */
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20489  * """
20490  *
20491  * ist = index_set # <<<<<<<<<<<<<<
20492  * """
20493  * Abbreviation for index_set.
20494  */
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20498  * """
20499  *
20500  * def e(obj): # <<<<<<<<<<<<<<
20501  * """
20502  * Abbreviation for clifford(index_set(obj)).
20503  */
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20510  * return clifford(index_set(obj))
20511  *
20512  * def istpq(p, q): # <<<<<<<<<<<<<<
20513  * """
20514  * Abbreviation for index_set({-q,...p}).
20515  */
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20522  * return index_set(set(range(-q,p+1)))
20523  *
20524  * ninf3 = e(4) + e(-1) # Null infinity point in 3D Conformal Geometric Algebra [DL]. # <<<<<<<<<<<<<<
20525  * nbar3 = e(4) - e(-1) # Null bar point in 3D Conformal Geometric Algebra [DL].
20526  *
20527  */
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20545  /* "PyClical.pyx":1910
20546  *
20547  * ninf3 = e(4) + e(-1) # Null infinity point in 3D Conformal Geometric Algebra [DL].
20548  * nbar3 = e(4) - e(-1) # Null bar point in 3D Conformal Geometric Algebra [DL]. # <<<<<<<<<<<<<<
20549  *
20550  * # Doctest interface.
20551  */
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20569  /* "PyClical.pyx":1913
20570  *
20571  * # Doctest interface.
20572  * def _test(): # <<<<<<<<<<<<<<
20573  * import PyClical, doctest
20574  * return doctest.testmod(PyClical)
20575  */
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20582  * return doctest.testmod(PyClical)
20583  *
20584  * if __name__ == "__main__": # <<<<<<<<<<<<<<
20585  * _test()
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20593  /* "PyClical.pyx":1918
20594  *
20595  * if __name__ == "__main__":
20596  * _test() # <<<<<<<<<<<<<<
20597  */
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20606  * return doctest.testmod(PyClical)
20607  *
20608  * if __name__ == "__main__": # <<<<<<<<<<<<<<
20609  * _test()
20610  */
20611  }
20612 
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20614  * # -*- coding: utf-8 -*- # <<<<<<<<<<<<<<
20615  * # distutils: language = c++
20616  * #
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20670  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_clifford___call___line_1019, __pyx_kp_u_Pure_grade_vector_part_print_cl) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20671  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_clifford_scalar_line_1038, __pyx_kp_u_Scalar_part_clifford_1_1_1_2_sc) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20672  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_clifford_pure_line_1049, __pyx_kp_u_Pure_part_print_clifford_1_1_1) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20673  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_clifford_even_line_1060, __pyx_kp_u_Even_part_of_multivector_sum_of) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20674  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_clifford_odd_line_1069, __pyx_kp_u_Odd_part_of_multivector_sum_of) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20675  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_clifford_vector_part_line_1078, __pyx_kp_u_Vector_part_of_multivector_as_a) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20676  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_clifford_involute_line_1106, __pyx_kp_u_Main_involution_each_i_is_repla) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20677  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_clifford_reverse_line_1122, __pyx_kp_u_Reversion_eg_clifford_1_cliffor) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20678  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_clifford_conj_line_1137, __pyx_kp_u_Conjugation_reverse_o_involute) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20679  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_clifford_quad_line_1152, __pyx_kp_u_Quadratic_form_rev_x_x_0_print) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20680  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_clifford_norm_line_1163, __pyx_kp_u_Norm_sum_of_squares_of_coordina) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20681  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_clifford_abs_line_1174, __pyx_kp_u_Absolute_value_square_root_of_n) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20682  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_clifford_max_abs_line_1183, __pyx_kp_u_Maximum_of_absolute_values_of_c) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20683  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_clifford_truncated_line_1194, __pyx_kp_u_Remove_all_terms_of_self_with_r) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20684  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_clifford_isnan_line_1205, __pyx_kp_u_Check_if_a_multivector_contains) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20685  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_clifford_frame_line_1214, __pyx_kp_u_Subalgebra_generated_by_all_gen) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20686  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_clifford___repr___line_1225, __pyx_kp_u_The_official_string_representat_2) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20687  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_clifford___str___line_1234, __pyx_kp_u_The_informal_string_representat_2) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20688  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_clifford_hidden_doctests_line_12, __pyx_kp_u_Tests_for_functions_that_Doctes_2) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20689  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_inv_line_1329, __pyx_kp_u_Geometric_multiplicative_invers_2) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20690  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_scalar_line_1344, __pyx_kp_u_Scalar_part_scalar_clifford_1_1) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20691  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_real_line_1355, __pyx_kp_u_Real_part_synonym_for_scalar_pa) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20692  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_imag_line_1366, __pyx_kp_u_Imaginary_part_deprecated_alway) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20693  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_pure_line_1377, __pyx_kp_u_Pure_part_print_pure_clifford_1) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20694  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_even_line_1388, __pyx_kp_u_Even_part_of_multivector_sum_of_2) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20695  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_odd_line_1397, __pyx_kp_u_Odd_part_of_multivector_sum_of_2) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20696  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_involute_line_1406, __pyx_kp_u_Main_involution_each_i_is_repla_2) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20697  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_reverse_line_1421, __pyx_kp_u_Reversion_eg_1_2_2_1_print_reve) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20698  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_conj_line_1436, __pyx_kp_u_Conjugation_reverse_o_involute_2) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20699  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_quad_line_1451, __pyx_kp_u_Quadratic_form_rev_x_x_0_print_2) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20700  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_norm_line_1462, __pyx_kp_u_norm_sum_of_squares_of_coordina) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20701  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_abs_line_1473, __pyx_kp_u_Absolute_value_of_multivector_m) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20702  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_max_abs_line_1482, __pyx_kp_u_Maximum_absolute_value_of_coord) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20703  if (PyDict_SetItem(__pyx_t_1, __pyx_kp_u_pow_line_1494, __pyx_kp_u_Integer_power_of_multivector_ob) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20704  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)
20705  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)
20706  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)
20707  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)
20708  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)
20709  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)
20710  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)
20711  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)
20712  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)
20713  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)
20714  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)
20715  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)
20716  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)
20717  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)
20718  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)
20719  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)
20720  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)
20721  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)
20722  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)
20723  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)
20724  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)
20725  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)
20726  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)
20727  if (PyDict_SetItem(__pyx_d, __pyx_n_s_test_2, __pyx_t_1) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
20728  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
20729 
20730  /*--- Wrapped vars code ---*/
20731 
20732  goto __pyx_L0;
20733  __pyx_L1_error:;
20734  __Pyx_XDECREF(__pyx_t_1);
20735  __Pyx_XDECREF(__pyx_t_2);
20736  __Pyx_XDECREF(__pyx_t_3);
20737  if (__pyx_m) {
20738  if (__pyx_d) {
20739  __Pyx_AddTraceback("init PyClical", 0, __pyx_lineno, __pyx_filename);
20740  }
20741  Py_DECREF(__pyx_m); __pyx_m = 0;
20742  } else if (!PyErr_Occurred()) {
20743  PyErr_SetString(PyExc_ImportError, "init PyClical");
20744  }
20745  __pyx_L0:;
20746  __Pyx_RefNannyFinishContext();
20747  #if CYTHON_PEP489_MULTI_PHASE_INIT
20748  return (__pyx_m != NULL) ? 0 : -1;
20749  #elif PY_MAJOR_VERSION >= 3
20750  return __pyx_m;
20751  #else
20752  return;
20753  #endif
20754 }
20755 
20756 /* --- Runtime support code --- */
20757 /* Refnanny */
20758 #if CYTHON_REFNANNY
20759 static __Pyx_RefNannyAPIStruct *__Pyx_RefNannyImportAPI(const char *modname) {
20760  PyObject *m = NULL, *p = NULL;
20761  void *r = NULL;
20762  m = PyImport_ImportModule((char *)modname);
20763  if (!m) goto end;
20764  p = PyObject_GetAttrString(m, (char *)"RefNannyAPI");
20765  if (!p) goto end;
20766  r = PyLong_AsVoidPtr(p);
20767 end:
20768  Py_XDECREF(p);
20769  Py_XDECREF(m);
20770  return (__Pyx_RefNannyAPIStruct *)r;
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20774 /* PyObjectGetAttrStr */
20775 #if CYTHON_USE_TYPE_SLOTS
20776 static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStr(PyObject* obj, PyObject* attr_name) {
20777  PyTypeObject* tp = Py_TYPE(obj);
20778  if (likely(tp->tp_getattro))
20779  return tp->tp_getattro(obj, attr_name);
20780 #if PY_MAJOR_VERSION < 3
20781  if (likely(tp->tp_getattr))
20782  return tp->tp_getattr(obj, PyString_AS_STRING(attr_name));
20783 #endif
20784  return PyObject_GetAttr(obj, attr_name);
20785 }
20786 #endif
20787 
20788 /* GetBuiltinName */
20789 static PyObject *__Pyx_GetBuiltinName(PyObject *name) {
20790  PyObject* result = __Pyx_PyObject_GetAttrStr(__pyx_b, name);
20791  if (unlikely(!result)) {
20792  PyErr_Format(PyExc_NameError,
20793 #if PY_MAJOR_VERSION >= 3
20794  "name '%U' is not defined", name);
20795 #else
20796  "name '%.200s' is not defined", PyString_AS_STRING(name));
20797 #endif
20798  }
20799  return result;
20800 }
20801 
20802 /* PyCFunctionFastCall */
20803 #if CYTHON_FAST_PYCCALL
20804 static CYTHON_INLINE PyObject * __Pyx_PyCFunction_FastCall(PyObject *func_obj, PyObject **args, Py_ssize_t nargs) {
20805  PyCFunctionObject *func = (PyCFunctionObject*)func_obj;
20806  PyCFunction meth = PyCFunction_GET_FUNCTION(func);
20807  PyObject *self = PyCFunction_GET_SELF(func);
20808  int flags = PyCFunction_GET_FLAGS(func);
20809  assert(PyCFunction_Check(func));
20810  assert(METH_FASTCALL == (flags & ~(METH_CLASS | METH_STATIC | METH_COEXIST | METH_KEYWORDS)));
20811  assert(nargs >= 0);
20812  assert(nargs == 0 || args != NULL);
20813  /* _PyCFunction_FastCallDict() must not be called with an exception set,
20814  because it may clear it (directly or indirectly) and so the
20815  caller loses its exception */
20816  assert(!PyErr_Occurred());
20817  if ((PY_VERSION_HEX < 0x030700A0) || unlikely(flags & METH_KEYWORDS)) {
20818  return (*((__Pyx_PyCFunctionFastWithKeywords)meth)) (self, args, nargs, NULL);
20819  } else {
20820  return (*((__Pyx_PyCFunctionFast)meth)) (self, args, nargs);
20821  }
20822 }
20823 #endif
20824 
20825 /* PyFunctionFastCall */
20826 #if CYTHON_FAST_PYCALL
20827 #include "frameobject.h"
20828 static PyObject* __Pyx_PyFunction_FastCallNoKw(PyCodeObject *co, PyObject **args, Py_ssize_t na,
20829  PyObject *globals) {
20830  PyFrameObject *f;
20831  PyThreadState *tstate = __Pyx_PyThreadState_Current;
20832  PyObject **fastlocals;
20833  Py_ssize_t i;
20834  PyObject *result;
20835  assert(globals != NULL);
20836  /* XXX Perhaps we should create a specialized
20837  PyFrame_New() that doesn't take locals, but does
20838  take builtins without sanity checking them.
20839  */
20840  assert(tstate != NULL);
20841  f = PyFrame_New(tstate, co, globals, NULL);
20842  if (f == NULL) {
20843  return NULL;
20844  }
20845  fastlocals = f->f_localsplus;
20846  for (i = 0; i < na; i++) {
20847  Py_INCREF(*args);
20848  fastlocals[i] = *args++;
20849  }
20850  result = PyEval_EvalFrameEx(f,0);
20851  ++tstate->recursion_depth;
20852  Py_DECREF(f);
20853  --tstate->recursion_depth;
20854  return result;
20855 }
20856 #if 1 || PY_VERSION_HEX < 0x030600B1
20857 static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, int nargs, PyObject *kwargs) {
20858  PyCodeObject *co = (PyCodeObject *)PyFunction_GET_CODE(func);
20859  PyObject *globals = PyFunction_GET_GLOBALS(func);
20860  PyObject *argdefs = PyFunction_GET_DEFAULTS(func);
20861  PyObject *closure;
20862 #if PY_MAJOR_VERSION >= 3
20863  PyObject *kwdefs;
20864 #endif
20865  PyObject *kwtuple, **k;
20866  PyObject **d;
20867  Py_ssize_t nd;
20868  Py_ssize_t nk;
20869  PyObject *result;
20870  assert(kwargs == NULL || PyDict_Check(kwargs));
20871  nk = kwargs ? PyDict_Size(kwargs) : 0;
20872  if (Py_EnterRecursiveCall((char*)" while calling a Python object")) {
20873  return NULL;
20874  }
20875  if (
20876 #if PY_MAJOR_VERSION >= 3
20877  co->co_kwonlyargcount == 0 &&
20878 #endif
20879  likely(kwargs == NULL || nk == 0) &&
20880  co->co_flags == (CO_OPTIMIZED | CO_NEWLOCALS | CO_NOFREE)) {
20881  if (argdefs == NULL && co->co_argcount == nargs) {
20882  result = __Pyx_PyFunction_FastCallNoKw(co, args, nargs, globals);
20883  goto done;
20884  }
20885  else if (nargs == 0 && argdefs != NULL
20886  && co->co_argcount == Py_SIZE(argdefs)) {
20887  /* function called with no arguments, but all parameters have
20888  a default value: use default values as arguments .*/
20889  args = &PyTuple_GET_ITEM(argdefs, 0);
20890  result =__Pyx_PyFunction_FastCallNoKw(co, args, Py_SIZE(argdefs), globals);
20891  goto done;
20892  }
20893  }
20894  if (kwargs != NULL) {
20895  Py_ssize_t pos, i;
20896  kwtuple = PyTuple_New(2 * nk);
20897  if (kwtuple == NULL) {
20898  result = NULL;
20899  goto done;
20900  }
20901  k = &PyTuple_GET_ITEM(kwtuple, 0);
20902  pos = i = 0;
20903  while (PyDict_Next(kwargs, &pos, &k[i], &k[i+1])) {
20904  Py_INCREF(k[i]);
20905  Py_INCREF(k[i+1]);
20906  i += 2;
20907  }
20908  nk = i / 2;
20909  }
20910  else {
20911  kwtuple = NULL;
20912  k = NULL;
20913  }
20914  closure = PyFunction_GET_CLOSURE(func);
20915 #if PY_MAJOR_VERSION >= 3
20916  kwdefs = PyFunction_GET_KW_DEFAULTS(func);
20917 #endif
20918  if (argdefs != NULL) {
20919  d = &PyTuple_GET_ITEM(argdefs, 0);
20920  nd = Py_SIZE(argdefs);
20921  }
20922  else {
20923  d = NULL;
20924  nd = 0;
20925  }
20926 #if PY_MAJOR_VERSION >= 3
20927  result = PyEval_EvalCodeEx((PyObject*)co, globals, (PyObject *)NULL,
20928  args, nargs,
20929  k, (int)nk,
20930  d, (int)nd, kwdefs, closure);
20931 #else
20932  result = PyEval_EvalCodeEx(co, globals, (PyObject *)NULL,
20933  args, nargs,
20934  k, (int)nk,
20935  d, (int)nd, closure);
20936 #endif
20937  Py_XDECREF(kwtuple);
20938 done:
20939  Py_LeaveRecursiveCall();
20940  return result;
20941 }
20942 #endif
20943 #endif
20944 
20945 /* PyObjectCall */
20946 #if CYTHON_COMPILING_IN_CPYTHON
20947 static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw) {
20948  PyObject *result;
20949  ternaryfunc call = func->ob_type->tp_call;
20950  if (unlikely(!call))
20951  return PyObject_Call(func, arg, kw);
20952  if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
20953  return NULL;
20954  result = (*call)(func, arg, kw);
20955  Py_LeaveRecursiveCall();
20956  if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
20957  PyErr_SetString(
20958  PyExc_SystemError,
20959  "NULL result without error in PyObject_Call");
20960  }
20961  return result;
20962 }
20963 #endif
20964 
20965 /* PyObjectCallMethO */
20966 #if CYTHON_COMPILING_IN_CPYTHON
20967 static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg) {
20968  PyObject *self, *result;
20969  PyCFunction cfunc;
20970  cfunc = PyCFunction_GET_FUNCTION(func);
20971  self = PyCFunction_GET_SELF(func);
20972  if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
20973  return NULL;
20974  result = cfunc(self, arg);
20975  Py_LeaveRecursiveCall();
20976  if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
20977  PyErr_SetString(
20978  PyExc_SystemError,
20979  "NULL result without error in PyObject_Call");
20980  }
20981  return result;
20982 }
20983 #endif
20984 
20985 /* PyObjectCallOneArg */
20986 #if CYTHON_COMPILING_IN_CPYTHON
20987 static PyObject* __Pyx__PyObject_CallOneArg(PyObject *func, PyObject *arg) {
20988  PyObject *result;
20989  PyObject *args = PyTuple_New(1);
20990  if (unlikely(!args)) return NULL;
20991  Py_INCREF(arg);
20992  PyTuple_SET_ITEM(args, 0, arg);
20993  result = __Pyx_PyObject_Call(func, args, NULL);
20994  Py_DECREF(args);
20995  return result;
20996 }
20997 static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
20998 #if CYTHON_FAST_PYCALL
20999  if (PyFunction_Check(func)) {
21000  return __Pyx_PyFunction_FastCall(func, &arg, 1);
21001  }
21002 #endif
21003  if (likely(PyCFunction_Check(func))) {
21004  if (likely(PyCFunction_GET_FLAGS(func) & METH_O)) {
21005  return __Pyx_PyObject_CallMethO(func, arg);
21006 #if CYTHON_FAST_PYCCALL
21007  } else if (PyCFunction_GET_FLAGS(func) & METH_FASTCALL) {
21008  return __Pyx_PyCFunction_FastCall(func, &arg, 1);
21009 #endif
21010  }
21011  }
21012  return __Pyx__PyObject_CallOneArg(func, arg);
21013 }
21014 #else
21015 static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
21016  PyObject *result;
21017  PyObject *args = PyTuple_Pack(1, arg);
21018  if (unlikely(!args)) return NULL;
21019  result = __Pyx_PyObject_Call(func, args, NULL);
21020  Py_DECREF(args);
21021  return result;
21022 }
21023 #endif
21024 
21025 /* PyErrFetchRestore */
21026 #if CYTHON_FAST_THREAD_STATE
21027 static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {
21028  PyObject *tmp_type, *tmp_value, *tmp_tb;
21029  tmp_type = tstate->curexc_type;
21030  tmp_value = tstate->curexc_value;
21031  tmp_tb = tstate->curexc_traceback;
21032  tstate->curexc_type = type;
21033  tstate->curexc_value = value;
21034  tstate->curexc_traceback = tb;
21035  Py_XDECREF(tmp_type);
21036  Py_XDECREF(tmp_value);
21037  Py_XDECREF(tmp_tb);
21038 }
21039 static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
21040  *type = tstate->curexc_type;
21041  *value = tstate->curexc_value;
21042  *tb = tstate->curexc_traceback;
21043  tstate->curexc_type = 0;
21044  tstate->curexc_value = 0;
21045  tstate->curexc_traceback = 0;
21046 }
21047 #endif
21048 
21049 /* WriteUnraisableException */
21050 static void __Pyx_WriteUnraisable(const char *name, CYTHON_UNUSED int clineno,
21051  CYTHON_UNUSED int lineno, CYTHON_UNUSED const char *filename,
21052  int full_traceback, CYTHON_UNUSED int nogil) {
21053  PyObject *old_exc, *old_val, *old_tb;
21054  PyObject *ctx;
21055  __Pyx_PyThreadState_declare
21056 #ifdef WITH_THREAD
21057  PyGILState_STATE state;
21058  if (nogil)
21059  state = PyGILState_Ensure();
21060 #ifdef _MSC_VER
21061  else state = (PyGILState_STATE)-1;
21062 #endif
21063 #endif
21064  __Pyx_PyThreadState_assign
21065  __Pyx_ErrFetch(&old_exc, &old_val, &old_tb);
21066  if (full_traceback) {
21067  Py_XINCREF(old_exc);
21068  Py_XINCREF(old_val);
21069  Py_XINCREF(old_tb);
21070  __Pyx_ErrRestore(old_exc, old_val, old_tb);
21071  PyErr_PrintEx(1);
21072  }
21073  #if PY_MAJOR_VERSION < 3
21074  ctx = PyString_FromString(name);
21075  #else
21076  ctx = PyUnicode_FromString(name);
21077  #endif
21078  __Pyx_ErrRestore(old_exc, old_val, old_tb);
21079  if (!ctx) {
21080  PyErr_WriteUnraisable(Py_None);
21081  } else {
21082  PyErr_WriteUnraisable(ctx);
21083  Py_DECREF(ctx);
21084  }
21085 #ifdef WITH_THREAD
21086  if (nogil)
21087  PyGILState_Release(state);
21088 #endif
21089 }
21090 
21091 /* PyObjectCallNoArg */
21092 #if CYTHON_COMPILING_IN_CPYTHON
21093 static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func) {
21094 #if CYTHON_FAST_PYCALL
21095  if (PyFunction_Check(func)) {
21096  return __Pyx_PyFunction_FastCall(func, NULL, 0);
21097  }
21098 #endif
21099 #ifdef __Pyx_CyFunction_USED
21100  if (likely(PyCFunction_Check(func) || __Pyx_TypeCheck(func, __pyx_CyFunctionType))) {
21101 #else
21102  if (likely(PyCFunction_Check(func))) {
21103 #endif
21104  if (likely(PyCFunction_GET_FLAGS(func) & METH_NOARGS)) {
21105  return __Pyx_PyObject_CallMethO(func, NULL);
21106  }
21107  }
21108  return __Pyx_PyObject_Call(func, __pyx_empty_tuple, NULL);
21109 }
21110 #endif
21111 
21112 /* RaiseDoubleKeywords */
21113  static void __Pyx_RaiseDoubleKeywordsError(
21114  const char* func_name,
21115  PyObject* kw_name)
21116 {
21117  PyErr_Format(PyExc_TypeError,
21118  #if PY_MAJOR_VERSION >= 3
21119  "%s() got multiple values for keyword argument '%U'", func_name, kw_name);
21120  #else
21121  "%s() got multiple values for keyword argument '%s'", func_name,
21122  PyString_AsString(kw_name));
21123  #endif
21124 }
21125 
21126 /* ParseKeywords */
21127  static int __Pyx_ParseOptionalKeywords(
21128  PyObject *kwds,
21129  PyObject **argnames[],
21130  PyObject *kwds2,
21131  PyObject *values[],
21132  Py_ssize_t num_pos_args,
21133  const char* function_name)
21134 {
21135  PyObject *key = 0, *value = 0;
21136  Py_ssize_t pos = 0;
21137  PyObject*** name;
21138  PyObject*** first_kw_arg = argnames + num_pos_args;
21139  while (PyDict_Next(kwds, &pos, &key, &value)) {
21140  name = first_kw_arg;
21141  while (*name && (**name != key)) name++;
21142  if (*name) {
21143  values[name-argnames] = value;
21144  continue;
21145  }
21146  name = first_kw_arg;
21147  #if PY_MAJOR_VERSION < 3
21148  if (likely(PyString_CheckExact(key)) || likely(PyString_Check(key))) {
21149  while (*name) {
21150  if ((CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**name) == PyString_GET_SIZE(key))
21151  && _PyString_Eq(**name, key)) {
21152  values[name-argnames] = value;
21153  break;
21154  }
21155  name++;
21156  }
21157  if (*name) continue;
21158  else {
21159  PyObject*** argname = argnames;
21160  while (argname != first_kw_arg) {
21161  if ((**argname == key) || (
21162  (CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**argname) == PyString_GET_SIZE(key))
21163  && _PyString_Eq(**argname, key))) {
21164  goto arg_passed_twice;
21165  }
21166  argname++;
21167  }
21168  }
21169  } else
21170  #endif
21171  if (likely(PyUnicode_Check(key))) {
21172  while (*name) {
21173  int cmp = (**name == key) ? 0 :
21174  #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
21175  (PyUnicode_GET_SIZE(**name) != PyUnicode_GET_SIZE(key)) ? 1 :
21176  #endif
21177  PyUnicode_Compare(**name, key);
21178  if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
21179  if (cmp == 0) {
21180  values[name-argnames] = value;
21181  break;
21182  }
21183  name++;
21184  }
21185  if (*name) continue;
21186  else {
21187  PyObject*** argname = argnames;
21188  while (argname != first_kw_arg) {
21189  int cmp = (**argname == key) ? 0 :
21190  #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
21191  (PyUnicode_GET_SIZE(**argname) != PyUnicode_GET_SIZE(key)) ? 1 :
21192  #endif
21193  PyUnicode_Compare(**argname, key);
21194  if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
21195  if (cmp == 0) goto arg_passed_twice;
21196  argname++;
21197  }
21198  }
21199  } else
21200  goto invalid_keyword_type;
21201  if (kwds2) {
21202  if (unlikely(PyDict_SetItem(kwds2, key, value))) goto bad;
21203  } else {
21204  goto invalid_keyword;
21205  }
21206  }
21207  return 0;
21208 arg_passed_twice:
21209  __Pyx_RaiseDoubleKeywordsError(function_name, key);
21210  goto bad;
21211 invalid_keyword_type:
21212  PyErr_Format(PyExc_TypeError,
21213  "%.200s() keywords must be strings", function_name);
21214  goto bad;
21215 invalid_keyword:
21216  PyErr_Format(PyExc_TypeError,
21217  #if PY_MAJOR_VERSION < 3
21218  "%.200s() got an unexpected keyword argument '%.200s'",
21219  function_name, PyString_AsString(key));
21220  #else
21221  "%s() got an unexpected keyword argument '%U'",
21222  function_name, key);
21223  #endif
21224 bad:
21225  return -1;
21226 }
21227 
21228 /* RaiseArgTupleInvalid */
21229  static void __Pyx_RaiseArgtupleInvalid(
21230  const char* func_name,
21231  int exact,
21232  Py_ssize_t num_min,
21233  Py_ssize_t num_max,
21234  Py_ssize_t num_found)
21235 {
21236  Py_ssize_t num_expected;
21237  const char *more_or_less;
21238  if (num_found < num_min) {
21239  num_expected = num_min;
21240  more_or_less = "at least";
21241  } else {
21242  num_expected = num_max;
21243  more_or_less = "at most";
21244  }
21245  if (exact) {
21246  more_or_less = "exactly";
21247  }
21248  PyErr_Format(PyExc_TypeError,
21249  "%.200s() takes %.8s %" CYTHON_FORMAT_SSIZE_T "d positional argument%.1s (%" CYTHON_FORMAT_SSIZE_T "d given)",
21250  func_name, more_or_less, num_expected,
21251  (num_expected == 1) ? "" : "s", num_found);
21252 }
21253 
21254 /* GetModuleGlobalName */
21255  static CYTHON_INLINE PyObject *__Pyx_GetModuleGlobalName(PyObject *name) {
21256  PyObject *result;
21257 #if !CYTHON_AVOID_BORROWED_REFS
21258 #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030500A1
21259  result = _PyDict_GetItem_KnownHash(__pyx_d, name, ((PyASCIIObject *) name)->hash);
21260  if (likely(result)) {
21261  Py_INCREF(result);
21262  } else if (unlikely(PyErr_Occurred())) {
21263  result = NULL;
21264  } else {
21265 #else
21266  result = PyDict_GetItem(__pyx_d, name);
21267  if (likely(result)) {
21268  Py_INCREF(result);
21269  } else {
21270 #endif
21271 #else
21272  result = PyObject_GetItem(__pyx_d, name);
21273  if (!result) {
21274  PyErr_Clear();
21275 #endif
21276  result = __Pyx_GetBuiltinName(name);
21277  }
21278  return result;
21279 }
21280 
21281 /* SaveResetException */
21282  #if CYTHON_FAST_THREAD_STATE
21283 static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
21284  #if PY_VERSION_HEX >= 0x030700A3
21285  *type = tstate->exc_state.exc_type;
21286  *value = tstate->exc_state.exc_value;
21287  *tb = tstate->exc_state.exc_traceback;
21288  #else
21289  *type = tstate->exc_type;
21290  *value = tstate->exc_value;
21291  *tb = tstate->exc_traceback;
21292  #endif
21293  Py_XINCREF(*type);
21294  Py_XINCREF(*value);
21295  Py_XINCREF(*tb);
21296 }
21297 static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {
21298  PyObject *tmp_type, *tmp_value, *tmp_tb;
21299  #if PY_VERSION_HEX >= 0x030700A3
21300  tmp_type = tstate->exc_state.exc_type;
21301  tmp_value = tstate->exc_state.exc_value;
21302  tmp_tb = tstate->exc_state.exc_traceback;
21303  tstate->exc_state.exc_type = type;
21304  tstate->exc_state.exc_value = value;
21305  tstate->exc_state.exc_traceback = tb;
21306  #else
21307  tmp_type = tstate->exc_type;
21308  tmp_value = tstate->exc_value;
21309  tmp_tb = tstate->exc_traceback;
21310  tstate->exc_type = type;
21311  tstate->exc_value = value;
21312  tstate->exc_traceback = tb;
21313  #endif
21314  Py_XDECREF(tmp_type);
21315  Py_XDECREF(tmp_value);
21316  Py_XDECREF(tmp_tb);
21317 }
21318 #endif
21319 
21320 /* PyErrExceptionMatches */
21321  #if CYTHON_FAST_THREAD_STATE
21322 static int __Pyx_PyErr_ExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) {
21323  Py_ssize_t i, n;
21324  n = PyTuple_GET_SIZE(tuple);
21325 #if PY_MAJOR_VERSION >= 3
21326  for (i=0; i<n; i++) {
21327  if (exc_type == PyTuple_GET_ITEM(tuple, i)) return 1;
21328  }
21329 #endif
21330  for (i=0; i<n; i++) {
21331  if (__Pyx_PyErr_GivenExceptionMatches(exc_type, PyTuple_GET_ITEM(tuple, i))) return 1;
21332  }
21333  return 0;
21334 }
21335 static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err) {
21336  PyObject *exc_type = tstate->curexc_type;
21337  if (exc_type == err) return 1;
21338  if (unlikely(!exc_type)) return 0;
21339  if (unlikely(PyTuple_Check(err)))
21340  return __Pyx_PyErr_ExceptionMatchesTuple(exc_type, err);
21341  return __Pyx_PyErr_GivenExceptionMatches(exc_type, err);
21342 }
21343 #endif
21344 
21345 /* GetException */
21346  #if CYTHON_FAST_THREAD_STATE
21347 static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
21348 #else
21349 static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb) {
21350 #endif
21351  PyObject *local_type, *local_value, *local_tb;
21352 #if CYTHON_FAST_THREAD_STATE
21353  PyObject *tmp_type, *tmp_value, *tmp_tb;
21354  local_type = tstate->curexc_type;
21355  local_value = tstate->curexc_value;
21356  local_tb = tstate->curexc_traceback;
21357  tstate->curexc_type = 0;
21358  tstate->curexc_value = 0;
21359  tstate->curexc_traceback = 0;
21360 #else
21361  PyErr_Fetch(&local_type, &local_value, &local_tb);
21362 #endif
21363  PyErr_NormalizeException(&local_type, &local_value, &local_tb);
21364 #if CYTHON_FAST_THREAD_STATE
21365  if (unlikely(tstate->curexc_type))
21366 #else
21367  if (unlikely(PyErr_Occurred()))
21368 #endif
21369  goto bad;
21370  #if PY_MAJOR_VERSION >= 3
21371  if (local_tb) {
21372  if (unlikely(PyException_SetTraceback(local_value, local_tb) < 0))
21373  goto bad;
21374  }
21375  #endif
21376  Py_XINCREF(local_tb);
21377  Py_XINCREF(local_type);
21378  Py_XINCREF(local_value);
21379  *type = local_type;
21380  *value = local_value;
21381  *tb = local_tb;
21382 #if CYTHON_FAST_THREAD_STATE
21383  #if PY_VERSION_HEX >= 0x030700A3
21384  tmp_type = tstate->exc_state.exc_type;
21385  tmp_value = tstate->exc_state.exc_value;
21386  tmp_tb = tstate->exc_state.exc_traceback;
21387  tstate->exc_state.exc_type = local_type;
21388  tstate->exc_state.exc_value = local_value;
21389  tstate->exc_state.exc_traceback = local_tb;
21390  #else
21391  tmp_type = tstate->exc_type;
21392  tmp_value = tstate->exc_value;
21393  tmp_tb = tstate->exc_traceback;
21394  tstate->exc_type = local_type;
21395  tstate->exc_value = local_value;
21396  tstate->exc_traceback = local_tb;
21397  #endif
21398  Py_XDECREF(tmp_type);
21399  Py_XDECREF(tmp_value);
21400  Py_XDECREF(tmp_tb);
21401 #else
21402  PyErr_SetExcInfo(local_type, local_value, local_tb);
21403 #endif
21404  return 0;
21405 bad:
21406  *type = 0;
21407  *value = 0;
21408  *tb = 0;
21409  Py_XDECREF(local_type);
21410  Py_XDECREF(local_value);
21411  Py_XDECREF(local_tb);
21412  return -1;
21413 }
21414 
21415 /* RaiseException */
21416  #if PY_MAJOR_VERSION < 3
21417 static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb,
21418  CYTHON_UNUSED PyObject *cause) {
21419  __Pyx_PyThreadState_declare
21420  Py_XINCREF(type);
21421  if (!value || value == Py_None)
21422  value = NULL;
21423  else
21424  Py_INCREF(value);
21425  if (!tb || tb == Py_None)
21426  tb = NULL;
21427  else {
21428  Py_INCREF(tb);
21429  if (!PyTraceBack_Check(tb)) {
21430  PyErr_SetString(PyExc_TypeError,
21431  "raise: arg 3 must be a traceback or None");
21432  goto raise_error;
21433  }
21434  }
21435  if (PyType_Check(type)) {
21436 #if CYTHON_COMPILING_IN_PYPY
21437  if (!value) {
21438  Py_INCREF(Py_None);
21439  value = Py_None;
21440  }
21441 #endif
21442  PyErr_NormalizeException(&type, &value, &tb);
21443  } else {
21444  if (value) {
21445  PyErr_SetString(PyExc_TypeError,
21446  "instance exception may not have a separate value");
21447  goto raise_error;
21448  }
21449  value = type;
21450  type = (PyObject*) Py_TYPE(type);
21451  Py_INCREF(type);
21452  if (!PyType_IsSubtype((PyTypeObject *)type, (PyTypeObject *)PyExc_BaseException)) {
21453  PyErr_SetString(PyExc_TypeError,
21454  "raise: exception class must be a subclass of BaseException");
21455  goto raise_error;
21456  }
21457  }
21458  __Pyx_PyThreadState_assign
21459  __Pyx_ErrRestore(type, value, tb);
21460  return;
21461 raise_error:
21462  Py_XDECREF(value);
21463  Py_XDECREF(type);
21464  Py_XDECREF(tb);
21465  return;
21466 }
21467 #else
21468 static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause) {
21469  PyObject* owned_instance = NULL;
21470  if (tb == Py_None) {
21471  tb = 0;
21472  } else if (tb && !PyTraceBack_Check(tb)) {
21473  PyErr_SetString(PyExc_TypeError,
21474  "raise: arg 3 must be a traceback or None");
21475  goto bad;
21476  }
21477  if (value == Py_None)
21478  value = 0;
21479  if (PyExceptionInstance_Check(type)) {
21480  if (value) {
21481  PyErr_SetString(PyExc_TypeError,
21482  "instance exception may not have a separate value");
21483  goto bad;
21484  }
21485  value = type;
21486  type = (PyObject*) Py_TYPE(value);
21487  } else if (PyExceptionClass_Check(type)) {
21488  PyObject *instance_class = NULL;
21489  if (value && PyExceptionInstance_Check(value)) {
21490  instance_class = (PyObject*) Py_TYPE(value);
21491  if (instance_class != type) {
21492  int is_subclass = PyObject_IsSubclass(instance_class, type);
21493  if (!is_subclass) {
21494  instance_class = NULL;
21495  } else if (unlikely(is_subclass == -1)) {
21496  goto bad;
21497  } else {
21498  type = instance_class;
21499  }
21500  }
21501  }
21502  if (!instance_class) {
21503  PyObject *args;
21504  if (!value)
21505  args = PyTuple_New(0);
21506  else if (PyTuple_Check(value)) {
21507  Py_INCREF(value);
21508  args = value;
21509  } else
21510  args = PyTuple_Pack(1, value);
21511  if (!args)
21512  goto bad;
21513  owned_instance = PyObject_Call(type, args, NULL);
21514  Py_DECREF(args);
21515  if (!owned_instance)
21516  goto bad;
21517  value = owned_instance;
21518  if (!PyExceptionInstance_Check(value)) {
21519  PyErr_Format(PyExc_TypeError,
21520  "calling %R should have returned an instance of "
21521  "BaseException, not %R",
21522  type, Py_TYPE(value));
21523  goto bad;
21524  }
21525  }
21526  } else {
21527  PyErr_SetString(PyExc_TypeError,
21528  "raise: exception class must be a subclass of BaseException");
21529  goto bad;
21530  }
21531  if (cause) {
21532  PyObject *fixed_cause;
21533  if (cause == Py_None) {
21534  fixed_cause = NULL;
21535  } else if (PyExceptionClass_Check(cause)) {
21536  fixed_cause = PyObject_CallObject(cause, NULL);
21537  if (fixed_cause == NULL)
21538  goto bad;
21539  } else if (PyExceptionInstance_Check(cause)) {
21540  fixed_cause = cause;
21541  Py_INCREF(fixed_cause);
21542  } else {
21543  PyErr_SetString(PyExc_TypeError,
21544  "exception causes must derive from "
21545  "BaseException");
21546  goto bad;
21547  }
21548  PyException_SetCause(value, fixed_cause);
21549  }
21550  PyErr_SetObject(type, value);
21551  if (tb) {
21552 #if CYTHON_COMPILING_IN_PYPY
21553  PyObject *tmp_type, *tmp_value, *tmp_tb;
21554  PyErr_Fetch(&tmp_type, &tmp_value, &tmp_tb);
21555  Py_INCREF(tb);
21556  PyErr_Restore(tmp_type, tmp_value, tb);
21557  Py_XDECREF(tmp_tb);
21558 #else
21559  PyThreadState *tstate = __Pyx_PyThreadState_Current;
21560  PyObject* tmp_tb = tstate->curexc_traceback;
21561  if (tb != tmp_tb) {
21562  Py_INCREF(tb);
21563  tstate->curexc_traceback = tb;
21564  Py_XDECREF(tmp_tb);
21565  }
21566 #endif
21567  }
21568 bad:
21569  Py_XDECREF(owned_instance);
21570  return;
21571 }
21572 #endif
21573 
21574 /* PyIntBinop */
21575  #if !CYTHON_COMPILING_IN_PYPY
21576 static PyObject* __Pyx_PyInt_AddObjC(PyObject *op1, PyObject *op2, CYTHON_UNUSED long intval, CYTHON_UNUSED int inplace) {
21577  #if PY_MAJOR_VERSION < 3
21578  if (likely(PyInt_CheckExact(op1))) {
21579  const long b = intval;
21580  long x;
21581  long a = PyInt_AS_LONG(op1);
21582  x = (long)((unsigned long)a + b);
21583  if (likely((x^a) >= 0 || (x^b) >= 0))
21584  return PyInt_FromLong(x);
21585  return PyLong_Type.tp_as_number->nb_add(op1, op2);
21586  }
21587  #endif
21588  #if CYTHON_USE_PYLONG_INTERNALS
21589  if (likely(PyLong_CheckExact(op1))) {
21590  const long b = intval;
21591  long a, x;
21592 #ifdef HAVE_LONG_LONG
21593  const PY_LONG_LONG llb = intval;
21594  PY_LONG_LONG lla, llx;
21595 #endif
21596  const digit* digits = ((PyLongObject*)op1)->ob_digit;
21597  const Py_ssize_t size = Py_SIZE(op1);
21598  if (likely(__Pyx_sst_abs(size) <= 1)) {
21599  a = likely(size) ? digits[0] : 0;
21600  if (size == -1) a = -a;
21601  } else {
21602  switch (size) {
21603  case -2:
21604  if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
21605  a = -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
21606  break;
21607 #ifdef HAVE_LONG_LONG
21608  } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
21609  lla = -(PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
21610  goto long_long;
21611 #endif
21612  }
21613  CYTHON_FALLTHROUGH;
21614  case 2:
21615  if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
21616  a = (long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
21617  break;
21618 #ifdef HAVE_LONG_LONG
21619  } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
21620  lla = (PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
21621  goto long_long;
21622 #endif
21623  }
21624  CYTHON_FALLTHROUGH;
21625  case -3:
21626  if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
21627  a = -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
21628  break;
21629 #ifdef HAVE_LONG_LONG
21630  } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
21631  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]));
21632  goto long_long;
21633 #endif
21634  }
21635  CYTHON_FALLTHROUGH;
21636  case 3:
21637  if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
21638  a = (long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
21639  break;
21640 #ifdef HAVE_LONG_LONG
21641  } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
21642  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]));
21643  goto long_long;
21644 #endif
21645  }
21646  CYTHON_FALLTHROUGH;
21647  case -4:
21648  if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
21649  a = -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
21650  break;
21651 #ifdef HAVE_LONG_LONG
21652  } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
21653  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]));
21654  goto long_long;
21655 #endif
21656  }
21657  CYTHON_FALLTHROUGH;
21658  case 4:
21659  if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
21660  a = (long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
21661  break;
21662 #ifdef HAVE_LONG_LONG
21663  } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
21664  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]));
21665  goto long_long;
21666 #endif
21667  }
21668  CYTHON_FALLTHROUGH;
21669  default: return PyLong_Type.tp_as_number->nb_add(op1, op2);
21670  }
21671  }
21672  x = a + b;
21673  return PyLong_FromLong(x);
21674 #ifdef HAVE_LONG_LONG
21675  long_long:
21676  llx = lla + llb;
21677  return PyLong_FromLongLong(llx);
21678 #endif
21679 
21680 
21681  }
21682  #endif
21683  if (PyFloat_CheckExact(op1)) {
21684  const long b = intval;
21685  double a = PyFloat_AS_DOUBLE(op1);
21686  double result;
21687  PyFPE_START_PROTECT("add", return NULL)
21688  result = ((double)a) + (double)b;
21689  PyFPE_END_PROTECT(result)
21690  return PyFloat_FromDouble(result);
21691  }
21692  return (inplace ? PyNumber_InPlaceAdd : PyNumber_Add)(op1, op2);
21693 }
21694 #endif
21695 
21696 /* SetItemInt */
21697  static int __Pyx_SetItemInt_Generic(PyObject *o, PyObject *j, PyObject *v) {
21698  int r;
21699  if (!j) return -1;
21700  r = PyObject_SetItem(o, j, v);
21701  Py_DECREF(j);
21702  return r;
21703 }
21704 static CYTHON_INLINE int __Pyx_SetItemInt_Fast(PyObject *o, Py_ssize_t i, PyObject *v, int is_list,
21705  CYTHON_NCP_UNUSED int wraparound, CYTHON_NCP_UNUSED int boundscheck) {
21706 #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS && CYTHON_USE_TYPE_SLOTS
21707  if (is_list || PyList_CheckExact(o)) {
21708  Py_ssize_t n = (!wraparound) ? i : ((likely(i >= 0)) ? i : i + PyList_GET_SIZE(o));
21709  if ((!boundscheck) || likely((n >= 0) & (n < PyList_GET_SIZE(o)))) {
21710  PyObject* old = PyList_GET_ITEM(o, n);
21711  Py_INCREF(v);
21712  PyList_SET_ITEM(o, n, v);
21713  Py_DECREF(old);
21714  return 1;
21715  }
21716  } else {
21717  PySequenceMethods *m = Py_TYPE(o)->tp_as_sequence;
21718  if (likely(m && m->sq_ass_item)) {
21719  if (wraparound && unlikely(i < 0) && likely(m->sq_length)) {
21720  Py_ssize_t l = m->sq_length(o);
21721  if (likely(l >= 0)) {
21722  i += l;
21723  } else {
21724  if (!PyErr_ExceptionMatches(PyExc_OverflowError))
21725  return -1;
21726  PyErr_Clear();
21727  }
21728  }
21729  return m->sq_ass_item(o, i, v);
21730  }
21731  }
21732 #else
21733 #if CYTHON_COMPILING_IN_PYPY
21734  if (is_list || (PySequence_Check(o) && !PyDict_Check(o))) {
21735 #else
21736  if (is_list || PySequence_Check(o)) {
21737 #endif
21738  return PySequence_SetItem(o, i, v);
21739  }
21740 #endif
21741  return __Pyx_SetItemInt_Generic(o, PyInt_FromSsize_t(i), v);
21742 }
21743 
21744 /* ArgTypeTest */
21745  static int __Pyx__ArgTypeTest(PyObject *obj, PyTypeObject *type, const char *name, int exact)
21746 {
21747  if (unlikely(!type)) {
21748  PyErr_SetString(PyExc_SystemError, "Missing type object");
21749  return 0;
21750  }
21751  else if (exact) {
21752  #if PY_MAJOR_VERSION == 2
21753  if ((type == &PyBaseString_Type) && likely(__Pyx_PyBaseString_CheckExact(obj))) return 1;
21754  #endif
21755  }
21756  else {
21757  if (likely(__Pyx_TypeCheck(obj, type))) return 1;
21758  }
21759  PyErr_Format(PyExc_TypeError,
21760  "Argument '%.200s' has incorrect type (expected %.200s, got %.200s)",
21761  name, type->tp_name, Py_TYPE(obj)->tp_name);
21762  return 0;
21763 }
21764 
21765 /* Import */
21766  static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level) {
21767  PyObject *empty_list = 0;
21768  PyObject *module = 0;
21769  PyObject *global_dict = 0;
21770  PyObject *empty_dict = 0;
21771  PyObject *list;
21772  #if PY_MAJOR_VERSION < 3
21773  PyObject *py_import;
21774  py_import = __Pyx_PyObject_GetAttrStr(__pyx_b, __pyx_n_s_import);
21775  if (!py_import)
21776  goto bad;
21777  #endif
21778  if (from_list)
21779  list = from_list;
21780  else {
21781  empty_list = PyList_New(0);
21782  if (!empty_list)
21783  goto bad;
21784  list = empty_list;
21785  }
21786  global_dict = PyModule_GetDict(__pyx_m);
21787  if (!global_dict)
21788  goto bad;
21789  empty_dict = PyDict_New();
21790  if (!empty_dict)
21791  goto bad;
21792  {
21793  #if PY_MAJOR_VERSION >= 3
21794  if (level == -1) {
21795  if (strchr(__Pyx_MODULE_NAME, '.')) {
21796  module = PyImport_ImportModuleLevelObject(
21797  name, global_dict, empty_dict, list, 1);
21798  if (!module) {
21799  if (!PyErr_ExceptionMatches(PyExc_ImportError))
21800  goto bad;
21801  PyErr_Clear();
21802  }
21803  }
21804  level = 0;
21805  }
21806  #endif
21807  if (!module) {
21808  #if PY_MAJOR_VERSION < 3
21809  PyObject *py_level = PyInt_FromLong(level);
21810  if (!py_level)
21811  goto bad;
21812  module = PyObject_CallFunctionObjArgs(py_import,
21813  name, global_dict, empty_dict, list, py_level, NULL);
21814  Py_DECREF(py_level);
21815  #else
21816  module = PyImport_ImportModuleLevelObject(
21817  name, global_dict, empty_dict, list, level);
21818  #endif
21819  }
21820  }
21821 bad:
21822  #if PY_MAJOR_VERSION < 3
21823  Py_XDECREF(py_import);
21824  #endif
21825  Py_XDECREF(empty_list);
21826  Py_XDECREF(empty_dict);
21827  return module;
21828 }
21829 
21830 /* PyObject_GenericGetAttrNoDict */
21831  #if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000
21832 static PyObject *__Pyx_RaiseGenericGetAttributeError(PyTypeObject *tp, PyObject *attr_name) {
21833  PyErr_Format(PyExc_AttributeError,
21834 #if PY_MAJOR_VERSION >= 3
21835  "'%.50s' object has no attribute '%U'",
21836  tp->tp_name, attr_name);
21837 #else
21838  "'%.50s' object has no attribute '%.400s'",
21839  tp->tp_name, PyString_AS_STRING(attr_name));
21840 #endif
21841  return NULL;
21842 }
21843 static CYTHON_INLINE PyObject* __Pyx_PyObject_GenericGetAttrNoDict(PyObject* obj, PyObject* attr_name) {
21844  PyObject *descr;
21845  PyTypeObject *tp = Py_TYPE(obj);
21846  if (unlikely(!PyString_Check(attr_name))) {
21847  return PyObject_GenericGetAttr(obj, attr_name);
21848  }
21849  assert(!tp->tp_dictoffset);
21850  descr = _PyType_Lookup(tp, attr_name);
21851  if (unlikely(!descr)) {
21852  return __Pyx_RaiseGenericGetAttributeError(tp, attr_name);
21853  }
21854  Py_INCREF(descr);
21855  #if PY_MAJOR_VERSION < 3
21856  if (likely(PyType_HasFeature(Py_TYPE(descr), Py_TPFLAGS_HAVE_CLASS)))
21857  #endif
21858  {
21859  descrgetfunc f = Py_TYPE(descr)->tp_descr_get;
21860  if (unlikely(f)) {
21861  PyObject *res = f(descr, obj, (PyObject *)tp);
21862  Py_DECREF(descr);
21863  return res;
21864  }
21865  }
21866  return descr;
21867 }
21868 #endif
21869 
21870 /* PyObject_GenericGetAttr */
21871  #if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000
21872 static PyObject* __Pyx_PyObject_GenericGetAttr(PyObject* obj, PyObject* attr_name) {
21873  if (unlikely(Py_TYPE(obj)->tp_dictoffset)) {
21874  return PyObject_GenericGetAttr(obj, attr_name);
21875  }
21876  return __Pyx_PyObject_GenericGetAttrNoDict(obj, attr_name);
21877 }
21878 #endif
21879 
21880 /* SetVTable */
21881  static int __Pyx_SetVtable(PyObject *dict, void *vtable) {
21882 #if PY_VERSION_HEX >= 0x02070000
21883  PyObject *ob = PyCapsule_New(vtable, 0, 0);
21884 #else
21885  PyObject *ob = PyCObject_FromVoidPtr(vtable, 0);
21886 #endif
21887  if (!ob)
21888  goto bad;
21889  if (PyDict_SetItem(dict, __pyx_n_s_pyx_vtable, ob) < 0)
21890  goto bad;
21891  Py_DECREF(ob);
21892  return 0;
21893 bad:
21894  Py_XDECREF(ob);
21895  return -1;
21896 }
21897 
21898 /* SetupReduce */
21899  static int __Pyx_setup_reduce_is_named(PyObject* meth, PyObject* name) {
21900  int ret;
21901  PyObject *name_attr;
21902  name_attr = __Pyx_PyObject_GetAttrStr(meth, __pyx_n_s_name);
21903  if (likely(name_attr)) {
21904  ret = PyObject_RichCompareBool(name_attr, name, Py_EQ);
21905  } else {
21906  ret = -1;
21907  }
21908  if (unlikely(ret < 0)) {
21909  PyErr_Clear();
21910  ret = 0;
21911  }
21912  Py_XDECREF(name_attr);
21913  return ret;
21914 }
21915 static int __Pyx_setup_reduce(PyObject* type_obj) {
21916  int ret = 0;
21917  PyObject *object_reduce = NULL;
21918  PyObject *object_reduce_ex = NULL;
21919  PyObject *reduce = NULL;
21920  PyObject *reduce_ex = NULL;
21921  PyObject *reduce_cython = NULL;
21922  PyObject *setstate = NULL;
21923  PyObject *setstate_cython = NULL;
21924 #if CYTHON_USE_PYTYPE_LOOKUP
21925  if (_PyType_Lookup((PyTypeObject*)type_obj, __pyx_n_s_getstate)) goto GOOD;
21926 #else
21927  if (PyObject_HasAttr(type_obj, __pyx_n_s_getstate)) goto GOOD;
21928 #endif
21929 #if CYTHON_USE_PYTYPE_LOOKUP
21930  object_reduce_ex = _PyType_Lookup(&PyBaseObject_Type, __pyx_n_s_reduce_ex); if (!object_reduce_ex) goto BAD;
21931 #else
21932  object_reduce_ex = __Pyx_PyObject_GetAttrStr((PyObject*)&PyBaseObject_Type, __pyx_n_s_reduce_ex); if (!object_reduce_ex) goto BAD;
21933 #endif
21934  reduce_ex = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_n_s_reduce_ex); if (unlikely(!reduce_ex)) goto BAD;
21935  if (reduce_ex == object_reduce_ex) {
21936 #if CYTHON_USE_PYTYPE_LOOKUP
21937  object_reduce = _PyType_Lookup(&PyBaseObject_Type, __pyx_n_s_reduce); if (!object_reduce) goto BAD;
21938 #else
21939  object_reduce = __Pyx_PyObject_GetAttrStr((PyObject*)&PyBaseObject_Type, __pyx_n_s_reduce); if (!object_reduce) goto BAD;
21940 #endif
21941  reduce = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_n_s_reduce); if (unlikely(!reduce)) goto BAD;
21942  if (reduce == object_reduce || __Pyx_setup_reduce_is_named(reduce, __pyx_n_s_reduce_cython)) {
21943  reduce_cython = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_n_s_reduce_cython); if (unlikely(!reduce_cython)) goto BAD;
21944  ret = PyDict_SetItem(((PyTypeObject*)type_obj)->tp_dict, __pyx_n_s_reduce, reduce_cython); if (unlikely(ret < 0)) goto BAD;
21945  ret = PyDict_DelItem(((PyTypeObject*)type_obj)->tp_dict, __pyx_n_s_reduce_cython); if (unlikely(ret < 0)) goto BAD;
21946  setstate = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_n_s_setstate);
21947  if (!setstate) PyErr_Clear();
21948  if (!setstate || __Pyx_setup_reduce_is_named(setstate, __pyx_n_s_setstate_cython)) {
21949  setstate_cython = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_n_s_setstate_cython); if (unlikely(!setstate_cython)) goto BAD;
21950  ret = PyDict_SetItem(((PyTypeObject*)type_obj)->tp_dict, __pyx_n_s_setstate, setstate_cython); if (unlikely(ret < 0)) goto BAD;
21951  ret = PyDict_DelItem(((PyTypeObject*)type_obj)->tp_dict, __pyx_n_s_setstate_cython); if (unlikely(ret < 0)) goto BAD;
21952  }
21953  PyType_Modified((PyTypeObject*)type_obj);
21954  }
21955  }
21956  goto GOOD;
21957 BAD:
21958  if (!PyErr_Occurred())
21959  PyErr_Format(PyExc_RuntimeError, "Unable to initialize pickling for %s", ((PyTypeObject*)type_obj)->tp_name);
21960  ret = -1;
21961 GOOD:
21962 #if !CYTHON_USE_PYTYPE_LOOKUP
21963  Py_XDECREF(object_reduce);
21964  Py_XDECREF(object_reduce_ex);
21965 #endif
21966  Py_XDECREF(reduce);
21967  Py_XDECREF(reduce_ex);
21968  Py_XDECREF(reduce_cython);
21969  Py_XDECREF(setstate);
21970  Py_XDECREF(setstate_cython);
21971  return ret;
21972 }
21973 
21974 /* PyFloatBinop */
21975  #if !CYTHON_COMPILING_IN_PYPY
21976 static PyObject* __Pyx_PyFloat_DivideObjC(PyObject *op1, PyObject *op2, double floatval, CYTHON_UNUSED int inplace) {
21977  const double b = floatval;
21978  double a, result;
21979  if (likely(PyFloat_CheckExact(op1))) {
21980  a = PyFloat_AS_DOUBLE(op1);
21981  } else
21982  #if PY_MAJOR_VERSION < 3
21983  if (likely(PyInt_CheckExact(op1))) {
21984  a = (double) PyInt_AS_LONG(op1);
21985  } else
21986  #endif
21987  if (likely(PyLong_CheckExact(op1))) {
21988  #if CYTHON_USE_PYLONG_INTERNALS
21989  const digit* digits = ((PyLongObject*)op1)->ob_digit;
21990  const Py_ssize_t size = Py_SIZE(op1);
21991  switch (size) {
21992  case 0: a = 0.0; break;
21993  case -1: a = -(double) digits[0]; break;
21994  case 1: a = (double) digits[0]; break;
21995  case -2:
21996  case 2:
21997  if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (1 * PyLong_SHIFT < 53))) {
21998  a = (double) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
21999  if ((8 * sizeof(unsigned long) < 53) || (2 * PyLong_SHIFT < 53) || (a < (double) ((PY_LONG_LONG)1 << 53))) {
22000  if (size == -2)
22001  a = -a;
22002  break;
22003  }
22004  }
22005  CYTHON_FALLTHROUGH;
22006  case -3:
22007  case 3:
22008  if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (2 * PyLong_SHIFT < 53))) {
22009  a = (double) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
22010  if ((8 * sizeof(unsigned long) < 53) || (3 * PyLong_SHIFT < 53) || (a < (double) ((PY_LONG_LONG)1 << 53))) {
22011  if (size == -3)
22012  a = -a;
22013  break;
22014  }
22015  }
22016  CYTHON_FALLTHROUGH;
22017  case -4:
22018  case 4:
22019  if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (3 * PyLong_SHIFT < 53))) {
22020  a = (double) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
22021  if ((8 * sizeof(unsigned long) < 53) || (4 * PyLong_SHIFT < 53) || (a < (double) ((PY_LONG_LONG)1 << 53))) {
22022  if (size == -4)
22023  a = -a;
22024  break;
22025  }
22026  }
22027  CYTHON_FALLTHROUGH;
22028  default:
22029  #else
22030  {
22031  #endif
22032  a = PyLong_AsDouble(op1);
22033  if (unlikely(a == -1.0 && PyErr_Occurred())) return NULL;
22034  }
22035  } else {
22036  return (inplace ? __Pyx_PyNumber_InPlaceDivide(op1, op2) : __Pyx_PyNumber_Divide(op1, op2));
22037  }
22038  PyFPE_START_PROTECT("divide", return NULL)
22039  result = a / b;
22040  PyFPE_END_PROTECT(result)
22041  return PyFloat_FromDouble(result);
22042 }
22043 #endif
22044 
22045 /* BytesEquals */
22046  static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals) {
22047 #if CYTHON_COMPILING_IN_PYPY
22048  return PyObject_RichCompareBool(s1, s2, equals);
22049 #else
22050  if (s1 == s2) {
22051  return (equals == Py_EQ);
22052  } else if (PyBytes_CheckExact(s1) & PyBytes_CheckExact(s2)) {
22053  const char *ps1, *ps2;
22054  Py_ssize_t length = PyBytes_GET_SIZE(s1);
22055  if (length != PyBytes_GET_SIZE(s2))
22056  return (equals == Py_NE);
22057  ps1 = PyBytes_AS_STRING(s1);
22058  ps2 = PyBytes_AS_STRING(s2);
22059  if (ps1[0] != ps2[0]) {
22060  return (equals == Py_NE);
22061  } else if (length == 1) {
22062  return (equals == Py_EQ);
22063  } else {
22064  int result;
22065 #if CYTHON_USE_UNICODE_INTERNALS
22066  Py_hash_t hash1, hash2;
22067  hash1 = ((PyBytesObject*)s1)->ob_shash;
22068  hash2 = ((PyBytesObject*)s2)->ob_shash;
22069  if (hash1 != hash2 && hash1 != -1 && hash2 != -1) {
22070  return (equals == Py_NE);
22071  }
22072 #endif
22073  result = memcmp(ps1, ps2, (size_t)length);
22074  return (equals == Py_EQ) ? (result == 0) : (result != 0);
22075  }
22076  } else if ((s1 == Py_None) & PyBytes_CheckExact(s2)) {
22077  return (equals == Py_NE);
22078  } else if ((s2 == Py_None) & PyBytes_CheckExact(s1)) {
22079  return (equals == Py_NE);
22080  } else {
22081  int result;
22082  PyObject* py_result = PyObject_RichCompare(s1, s2, equals);
22083  if (!py_result)
22084  return -1;
22085  result = __Pyx_PyObject_IsTrue(py_result);
22086  Py_DECREF(py_result);
22087  return result;
22088  }
22089 #endif
22090 }
22091 
22092 /* UnicodeEquals */
22093  static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals) {
22094 #if CYTHON_COMPILING_IN_PYPY
22095  return PyObject_RichCompareBool(s1, s2, equals);
22096 #else
22097 #if PY_MAJOR_VERSION < 3
22098  PyObject* owned_ref = NULL;
22099 #endif
22100  int s1_is_unicode, s2_is_unicode;
22101  if (s1 == s2) {
22102  goto return_eq;
22103  }
22104  s1_is_unicode = PyUnicode_CheckExact(s1);
22105  s2_is_unicode = PyUnicode_CheckExact(s2);
22106 #if PY_MAJOR_VERSION < 3
22107  if ((s1_is_unicode & (!s2_is_unicode)) && PyString_CheckExact(s2)) {
22108  owned_ref = PyUnicode_FromObject(s2);
22109  if (unlikely(!owned_ref))
22110  return -1;
22111  s2 = owned_ref;
22112  s2_is_unicode = 1;
22113  } else if ((s2_is_unicode & (!s1_is_unicode)) && PyString_CheckExact(s1)) {
22114  owned_ref = PyUnicode_FromObject(s1);
22115  if (unlikely(!owned_ref))
22116  return -1;
22117  s1 = owned_ref;
22118  s1_is_unicode = 1;
22119  } else if (((!s2_is_unicode) & (!s1_is_unicode))) {
22120  return __Pyx_PyBytes_Equals(s1, s2, equals);
22121  }
22122 #endif
22123  if (s1_is_unicode & s2_is_unicode) {
22124  Py_ssize_t length;
22125  int kind;
22126  void *data1, *data2;
22127  if (unlikely(__Pyx_PyUnicode_READY(s1) < 0) || unlikely(__Pyx_PyUnicode_READY(s2) < 0))
22128  return -1;
22129  length = __Pyx_PyUnicode_GET_LENGTH(s1);
22130  if (length != __Pyx_PyUnicode_GET_LENGTH(s2)) {
22131  goto return_ne;
22132  }
22133 #if CYTHON_USE_UNICODE_INTERNALS
22134  {
22135  Py_hash_t hash1, hash2;
22136  #if CYTHON_PEP393_ENABLED
22137  hash1 = ((PyASCIIObject*)s1)->hash;
22138  hash2 = ((PyASCIIObject*)s2)->hash;
22139  #else
22140  hash1 = ((PyUnicodeObject*)s1)->hash;
22141  hash2 = ((PyUnicodeObject*)s2)->hash;
22142  #endif
22143  if (hash1 != hash2 && hash1 != -1 && hash2 != -1) {
22144  goto return_ne;
22145  }
22146  }
22147 #endif
22148  kind = __Pyx_PyUnicode_KIND(s1);
22149  if (kind != __Pyx_PyUnicode_KIND(s2)) {
22150  goto return_ne;
22151  }
22152  data1 = __Pyx_PyUnicode_DATA(s1);
22153  data2 = __Pyx_PyUnicode_DATA(s2);
22154  if (__Pyx_PyUnicode_READ(kind, data1, 0) != __Pyx_PyUnicode_READ(kind, data2, 0)) {
22155  goto return_ne;
22156  } else if (length == 1) {
22157  goto return_eq;
22158  } else {
22159  int result = memcmp(data1, data2, (size_t)(length * kind));
22160  #if PY_MAJOR_VERSION < 3
22161  Py_XDECREF(owned_ref);
22162  #endif
22163  return (equals == Py_EQ) ? (result == 0) : (result != 0);
22164  }
22165  } else if ((s1 == Py_None) & s2_is_unicode) {
22166  goto return_ne;
22167  } else if ((s2 == Py_None) & s1_is_unicode) {
22168  goto return_ne;
22169  } else {
22170  int result;
22171  PyObject* py_result = PyObject_RichCompare(s1, s2, equals);
22172  #if PY_MAJOR_VERSION < 3
22173  Py_XDECREF(owned_ref);
22174  #endif
22175  if (!py_result)
22176  return -1;
22177  result = __Pyx_PyObject_IsTrue(py_result);
22178  Py_DECREF(py_result);
22179  return result;
22180  }
22181 return_eq:
22182  #if PY_MAJOR_VERSION < 3
22183  Py_XDECREF(owned_ref);
22184  #endif
22185  return (equals == Py_EQ);
22186 return_ne:
22187  #if PY_MAJOR_VERSION < 3
22188  Py_XDECREF(owned_ref);
22189  #endif
22190  return (equals == Py_NE);
22191 #endif
22192 }
22193 
22194 /* CLineInTraceback */
22195  #ifndef CYTHON_CLINE_IN_TRACEBACK
22196 static int __Pyx_CLineForTraceback(CYTHON_UNUSED PyThreadState *tstate, int c_line) {
22197  PyObject *use_cline;
22198  PyObject *ptype, *pvalue, *ptraceback;
22199 #if CYTHON_COMPILING_IN_CPYTHON
22200  PyObject **cython_runtime_dict;
22201 #endif
22202  if (unlikely(!__pyx_cython_runtime)) {
22203  return c_line;
22204  }
22205  __Pyx_ErrFetchInState(tstate, &ptype, &pvalue, &ptraceback);
22206 #if CYTHON_COMPILING_IN_CPYTHON
22207  cython_runtime_dict = _PyObject_GetDictPtr(__pyx_cython_runtime);
22208  if (likely(cython_runtime_dict)) {
22209  use_cline = __Pyx_PyDict_GetItemStr(*cython_runtime_dict, __pyx_n_s_cline_in_traceback);
22210  } else
22211 #endif
22212  {
22213  PyObject *use_cline_obj = __Pyx_PyObject_GetAttrStr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback);
22214  if (use_cline_obj) {
22215  use_cline = PyObject_Not(use_cline_obj) ? Py_False : Py_True;
22216  Py_DECREF(use_cline_obj);
22217  } else {
22218  PyErr_Clear();
22219  use_cline = NULL;
22220  }
22221  }
22222  if (!use_cline) {
22223  c_line = 0;
22224  PyObject_SetAttr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback, Py_False);
22225  }
22226  else if (PyObject_Not(use_cline) != 0) {
22227  c_line = 0;
22228  }
22229  __Pyx_ErrRestoreInState(tstate, ptype, pvalue, ptraceback);
22230  return c_line;
22231 }
22232 #endif
22233 
22234 /* CodeObjectCache */
22235  static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line) {
22236  int start = 0, mid = 0, end = count - 1;
22237  if (end >= 0 && code_line > entries[end].code_line) {
22238  return count;
22239  }
22240  while (start < end) {
22241  mid = start + (end - start) / 2;
22242  if (code_line < entries[mid].code_line) {
22243  end = mid;
22244  } else if (code_line > entries[mid].code_line) {
22245  start = mid + 1;
22246  } else {
22247  return mid;
22248  }
22249  }
22250  if (code_line <= entries[mid].code_line) {
22251  return mid;
22252  } else {
22253  return mid + 1;
22254  }
22255 }
22256 static PyCodeObject *__pyx_find_code_object(int code_line) {
22257  PyCodeObject* code_object;
22258  int pos;
22259  if (unlikely(!code_line) || unlikely(!__pyx_code_cache.entries)) {
22260  return NULL;
22261  }
22262  pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
22263  if (unlikely(pos >= __pyx_code_cache.count) || unlikely(__pyx_code_cache.entries[pos].code_line != code_line)) {
22264  return NULL;
22265  }
22266  code_object = __pyx_code_cache.entries[pos].code_object;
22267  Py_INCREF(code_object);
22268  return code_object;
22269 }
22270 static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object) {
22271  int pos, i;
22272  __Pyx_CodeObjectCacheEntry* entries = __pyx_code_cache.entries;
22273  if (unlikely(!code_line)) {
22274  return;
22275  }
22276  if (unlikely(!entries)) {
22277  entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Malloc(64*sizeof(__Pyx_CodeObjectCacheEntry));
22278  if (likely(entries)) {
22279  __pyx_code_cache.entries = entries;
22280  __pyx_code_cache.max_count = 64;
22281  __pyx_code_cache.count = 1;
22282  entries[0].code_line = code_line;
22283  entries[0].code_object = code_object;
22284  Py_INCREF(code_object);
22285  }
22286  return;
22287  }
22288  pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
22289  if ((pos < __pyx_code_cache.count) && unlikely(__pyx_code_cache.entries[pos].code_line == code_line)) {
22290  PyCodeObject* tmp = entries[pos].code_object;
22291  entries[pos].code_object = code_object;
22292  Py_DECREF(tmp);
22293  return;
22294  }
22295  if (__pyx_code_cache.count == __pyx_code_cache.max_count) {
22296  int new_max = __pyx_code_cache.max_count + 64;
22297  entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Realloc(
22298  __pyx_code_cache.entries, (size_t)new_max*sizeof(__Pyx_CodeObjectCacheEntry));
22299  if (unlikely(!entries)) {
22300  return;
22301  }
22302  __pyx_code_cache.entries = entries;
22303  __pyx_code_cache.max_count = new_max;
22304  }
22305  for (i=__pyx_code_cache.count; i>pos; i--) {
22306  entries[i] = entries[i-1];
22307  }
22308  entries[pos].code_line = code_line;
22309  entries[pos].code_object = code_object;
22310  __pyx_code_cache.count++;
22311  Py_INCREF(code_object);
22312 }
22313 
22314 /* AddTraceback */
22315  #include "compile.h"
22316 #include "frameobject.h"
22317 #include "traceback.h"
22318 static PyCodeObject* __Pyx_CreateCodeObjectForTraceback(
22319  const char *funcname, int c_line,
22320  int py_line, const char *filename) {
22321  PyCodeObject *py_code = 0;
22322  PyObject *py_srcfile = 0;
22323  PyObject *py_funcname = 0;
22324  #if PY_MAJOR_VERSION < 3
22325  py_srcfile = PyString_FromString(filename);
22326  #else
22327  py_srcfile = PyUnicode_FromString(filename);
22328  #endif
22329  if (!py_srcfile) goto bad;
22330  if (c_line) {
22331  #if PY_MAJOR_VERSION < 3
22332  py_funcname = PyString_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
22333  #else
22334  py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
22335  #endif
22336  }
22337  else {
22338  #if PY_MAJOR_VERSION < 3
22339  py_funcname = PyString_FromString(funcname);
22340  #else
22341  py_funcname = PyUnicode_FromString(funcname);
22342  #endif
22343  }
22344  if (!py_funcname) goto bad;
22345  py_code = __Pyx_PyCode_New(
22346  0,
22347  0,
22348  0,
22349  0,
22350  0,
22351  __pyx_empty_bytes, /*PyObject *code,*/
22352  __pyx_empty_tuple, /*PyObject *consts,*/
22353  __pyx_empty_tuple, /*PyObject *names,*/
22354  __pyx_empty_tuple, /*PyObject *varnames,*/
22355  __pyx_empty_tuple, /*PyObject *freevars,*/
22356  __pyx_empty_tuple, /*PyObject *cellvars,*/
22357  py_srcfile, /*PyObject *filename,*/
22358  py_funcname, /*PyObject *name,*/
22359  py_line,
22360  __pyx_empty_bytes /*PyObject *lnotab*/
22361  );
22362  Py_DECREF(py_srcfile);
22363  Py_DECREF(py_funcname);
22364  return py_code;
22365 bad:
22366  Py_XDECREF(py_srcfile);
22367  Py_XDECREF(py_funcname);
22368  return NULL;
22369 }
22370 static void __Pyx_AddTraceback(const char *funcname, int c_line,
22371  int py_line, const char *filename) {
22372  PyCodeObject *py_code = 0;
22373  PyFrameObject *py_frame = 0;
22374  PyThreadState *tstate = __Pyx_PyThreadState_Current;
22375  if (c_line) {
22376  c_line = __Pyx_CLineForTraceback(tstate, c_line);
22377  }
22378  py_code = __pyx_find_code_object(c_line ? -c_line : py_line);
22379  if (!py_code) {
22380  py_code = __Pyx_CreateCodeObjectForTraceback(
22381  funcname, c_line, py_line, filename);
22382  if (!py_code) goto bad;
22383  __pyx_insert_code_object(c_line ? -c_line : py_line, py_code);
22384  }
22385  py_frame = PyFrame_New(
22386  tstate, /*PyThreadState *tstate,*/
22387  py_code, /*PyCodeObject *code,*/
22388  __pyx_d, /*PyObject *globals,*/
22389  0 /*PyObject *locals*/
22390  );
22391  if (!py_frame) goto bad;
22392  __Pyx_PyFrame_SetLineNumber(py_frame, py_line);
22393  PyTraceBack_Here(py_frame);
22394 bad:
22395  Py_XDECREF(py_code);
22396  Py_XDECREF(py_frame);
22397 }
22398 
22399 /* CIntFromPyVerify */
22400  #define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)\
22401  __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 0)
22402 #define __PYX_VERIFY_RETURN_INT_EXC(target_type, func_type, func_value)\
22403  __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 1)
22404 #define __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, exc)\
22405  {\
22406  func_type value = func_value;\
22407  if (sizeof(target_type) < sizeof(func_type)) {\
22408  if (unlikely(value != (func_type) (target_type) value)) {\
22409  func_type zero = 0;\
22410  if (exc && unlikely(value == (func_type)-1 && PyErr_Occurred()))\
22411  return (target_type) -1;\
22412  if (is_unsigned && unlikely(value < zero))\
22413  goto raise_neg_overflow;\
22414  else\
22415  goto raise_overflow;\
22416  }\
22417  }\
22418  return (target_type) value;\
22419  }
22420 
22421 /* CIntToPy */
22422  static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value) {
22423  const int neg_one = (int) -1, const_zero = (int) 0;
22424  const int is_unsigned = neg_one > const_zero;
22425  if (is_unsigned) {
22426  if (sizeof(int) < sizeof(long)) {
22427  return PyInt_FromLong((long) value);
22428  } else if (sizeof(int) <= sizeof(unsigned long)) {
22429  return PyLong_FromUnsignedLong((unsigned long) value);
22430 #ifdef HAVE_LONG_LONG
22431  } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {
22432  return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
22433 #endif
22434  }
22435  } else {
22436  if (sizeof(int) <= sizeof(long)) {
22437  return PyInt_FromLong((long) value);
22438 #ifdef HAVE_LONG_LONG
22439  } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
22440  return PyLong_FromLongLong((PY_LONG_LONG) value);
22441 #endif
22442  }
22443  }
22444  {
22445  int one = 1; int little = (int)*(unsigned char *)&one;
22446  unsigned char *bytes = (unsigned char *)&value;
22447  return _PyLong_FromByteArray(bytes, sizeof(int),
22448  little, !is_unsigned);
22449  }
22450 }
22451 
22452 /* CIntFromPy */
22453  static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) {
22454  const int neg_one = (int) -1, const_zero = (int) 0;
22455  const int is_unsigned = neg_one > const_zero;
22456 #if PY_MAJOR_VERSION < 3
22457  if (likely(PyInt_Check(x))) {
22458  if (sizeof(int) < sizeof(long)) {
22459  __PYX_VERIFY_RETURN_INT(int, long, PyInt_AS_LONG(x))
22460  } else {
22461  long val = PyInt_AS_LONG(x);
22462  if (is_unsigned && unlikely(val < 0)) {
22463  goto raise_neg_overflow;
22464  }
22465  return (int) val;
22466  }
22467  } else
22468 #endif
22469  if (likely(PyLong_Check(x))) {
22470  if (is_unsigned) {
22471 #if CYTHON_USE_PYLONG_INTERNALS
22472  const digit* digits = ((PyLongObject*)x)->ob_digit;
22473  switch (Py_SIZE(x)) {
22474  case 0: return (int) 0;
22475  case 1: __PYX_VERIFY_RETURN_INT(int, digit, digits[0])
22476  case 2:
22477  if (8 * sizeof(int) > 1 * PyLong_SHIFT) {
22478  if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
22479  __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22480  } else if (8 * sizeof(int) >= 2 * PyLong_SHIFT) {
22481  return (int) (((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
22482  }
22483  }
22484  break;
22485  case 3:
22486  if (8 * sizeof(int) > 2 * PyLong_SHIFT) {
22487  if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
22488  __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22489  } else if (8 * sizeof(int) >= 3 * PyLong_SHIFT) {
22490  return (int) (((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
22491  }
22492  }
22493  break;
22494  case 4:
22495  if (8 * sizeof(int) > 3 * PyLong_SHIFT) {
22496  if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
22497  __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])))
22498  } else if (8 * sizeof(int) >= 4 * PyLong_SHIFT) {
22499  return (int) (((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
22500  }
22501  }
22502  break;
22503  }
22504 #endif
22505 #if CYTHON_COMPILING_IN_CPYTHON
22506  if (unlikely(Py_SIZE(x) < 0)) {
22507  goto raise_neg_overflow;
22508  }
22509 #else
22510  {
22511  int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
22512  if (unlikely(result < 0))
22513  return (int) -1;
22514  if (unlikely(result == 1))
22515  goto raise_neg_overflow;
22516  }
22517 #endif
22518  if (sizeof(int) <= sizeof(unsigned long)) {
22519  __PYX_VERIFY_RETURN_INT_EXC(int, unsigned long, PyLong_AsUnsignedLong(x))
22520 #ifdef HAVE_LONG_LONG
22521  } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {
22522  __PYX_VERIFY_RETURN_INT_EXC(int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
22523 #endif
22524  }
22525  } else {
22526 #if CYTHON_USE_PYLONG_INTERNALS
22527  const digit* digits = ((PyLongObject*)x)->ob_digit;
22528  switch (Py_SIZE(x)) {
22529  case 0: return (int) 0;
22530  case -1: __PYX_VERIFY_RETURN_INT(int, sdigit, (sdigit) (-(sdigit)digits[0]))
22531  case 1: __PYX_VERIFY_RETURN_INT(int, digit, +digits[0])
22532  case -2:
22533  if (8 * sizeof(int) - 1 > 1 * PyLong_SHIFT) {
22534  if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
22535  __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22536  } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
22537  return (int) (((int)-1)*(((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
22538  }
22539  }
22540  break;
22541  case 2:
22542  if (8 * sizeof(int) > 1 * PyLong_SHIFT) {
22543  if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
22544  __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22545  } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
22546  return (int) ((((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
22547  }
22548  }
22549  break;
22550  case -3:
22551  if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
22552  if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
22553  __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22554  } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
22555  return (int) (((int)-1)*(((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
22556  }
22557  }
22558  break;
22559  case 3:
22560  if (8 * sizeof(int) > 2 * PyLong_SHIFT) {
22561  if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
22562  __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22563  } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
22564  return (int) ((((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
22565  }
22566  }
22567  break;
22568  case -4:
22569  if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
22570  if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
22571  __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])))
22572  } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) {
22573  return (int) (((int)-1)*(((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
22574  }
22575  }
22576  break;
22577  case 4:
22578  if (8 * sizeof(int) > 3 * PyLong_SHIFT) {
22579  if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
22580  __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])))
22581  } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) {
22582  return (int) ((((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
22583  }
22584  }
22585  break;
22586  }
22587 #endif
22588  if (sizeof(int) <= sizeof(long)) {
22589  __PYX_VERIFY_RETURN_INT_EXC(int, long, PyLong_AsLong(x))
22590 #ifdef HAVE_LONG_LONG
22591  } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
22592  __PYX_VERIFY_RETURN_INT_EXC(int, PY_LONG_LONG, PyLong_AsLongLong(x))
22593 #endif
22594  }
22595  }
22596  {
22597 #if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
22598  PyErr_SetString(PyExc_RuntimeError,
22599  "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
22600 #else
22601  int val;
22602  PyObject *v = __Pyx_PyNumber_IntOrLong(x);
22603  #if PY_MAJOR_VERSION < 3
22604  if (likely(v) && !PyLong_Check(v)) {
22605  PyObject *tmp = v;
22606  v = PyNumber_Long(tmp);
22607  Py_DECREF(tmp);
22608  }
22609  #endif
22610  if (likely(v)) {
22611  int one = 1; int is_little = (int)*(unsigned char *)&one;
22612  unsigned char *bytes = (unsigned char *)&val;
22613  int ret = _PyLong_AsByteArray((PyLongObject *)v,
22614  bytes, sizeof(val),
22615  is_little, !is_unsigned);
22616  Py_DECREF(v);
22617  if (likely(!ret))
22618  return val;
22619  }
22620 #endif
22621  return (int) -1;
22622  }
22623  } else {
22624  int val;
22625  PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
22626  if (!tmp) return (int) -1;
22627  val = __Pyx_PyInt_As_int(tmp);
22628  Py_DECREF(tmp);
22629  return val;
22630  }
22631 raise_overflow:
22632  PyErr_SetString(PyExc_OverflowError,
22633  "value too large to convert to int");
22634  return (int) -1;
22635 raise_neg_overflow:
22636  PyErr_SetString(PyExc_OverflowError,
22637  "can't convert negative value to int");
22638  return (int) -1;
22639 }
22640 
22641 /* CIntToPy */
22642  static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) {
22643  const long neg_one = (long) -1, const_zero = (long) 0;
22644  const int is_unsigned = neg_one > const_zero;
22645  if (is_unsigned) {
22646  if (sizeof(long) < sizeof(long)) {
22647  return PyInt_FromLong((long) value);
22648  } else if (sizeof(long) <= sizeof(unsigned long)) {
22649  return PyLong_FromUnsignedLong((unsigned long) value);
22650 #ifdef HAVE_LONG_LONG
22651  } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
22652  return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
22653 #endif
22654  }
22655  } else {
22656  if (sizeof(long) <= sizeof(long)) {
22657  return PyInt_FromLong((long) value);
22658 #ifdef HAVE_LONG_LONG
22659  } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
22660  return PyLong_FromLongLong((PY_LONG_LONG) value);
22661 #endif
22662  }
22663  }
22664  {
22665  int one = 1; int little = (int)*(unsigned char *)&one;
22666  unsigned char *bytes = (unsigned char *)&value;
22667  return _PyLong_FromByteArray(bytes, sizeof(long),
22668  little, !is_unsigned);
22669  }
22670 }
22671 
22672 /* CIntFromPy */
22673  static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *x) {
22674  const long neg_one = (long) -1, const_zero = (long) 0;
22675  const int is_unsigned = neg_one > const_zero;
22676 #if PY_MAJOR_VERSION < 3
22677  if (likely(PyInt_Check(x))) {
22678  if (sizeof(long) < sizeof(long)) {
22679  __PYX_VERIFY_RETURN_INT(long, long, PyInt_AS_LONG(x))
22680  } else {
22681  long val = PyInt_AS_LONG(x);
22682  if (is_unsigned && unlikely(val < 0)) {
22683  goto raise_neg_overflow;
22684  }
22685  return (long) val;
22686  }
22687  } else
22688 #endif
22689  if (likely(PyLong_Check(x))) {
22690  if (is_unsigned) {
22691 #if CYTHON_USE_PYLONG_INTERNALS
22692  const digit* digits = ((PyLongObject*)x)->ob_digit;
22693  switch (Py_SIZE(x)) {
22694  case 0: return (long) 0;
22695  case 1: __PYX_VERIFY_RETURN_INT(long, digit, digits[0])
22696  case 2:
22697  if (8 * sizeof(long) > 1 * PyLong_SHIFT) {
22698  if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
22699  __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22700  } else if (8 * sizeof(long) >= 2 * PyLong_SHIFT) {
22701  return (long) (((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
22702  }
22703  }
22704  break;
22705  case 3:
22706  if (8 * sizeof(long) > 2 * PyLong_SHIFT) {
22707  if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
22708  __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22709  } else if (8 * sizeof(long) >= 3 * PyLong_SHIFT) {
22710  return (long) (((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
22711  }
22712  }
22713  break;
22714  case 4:
22715  if (8 * sizeof(long) > 3 * PyLong_SHIFT) {
22716  if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
22717  __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])))
22718  } else if (8 * sizeof(long) >= 4 * PyLong_SHIFT) {
22719  return (long) (((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
22720  }
22721  }
22722  break;
22723  }
22724 #endif
22725 #if CYTHON_COMPILING_IN_CPYTHON
22726  if (unlikely(Py_SIZE(x) < 0)) {
22727  goto raise_neg_overflow;
22728  }
22729 #else
22730  {
22731  int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
22732  if (unlikely(result < 0))
22733  return (long) -1;
22734  if (unlikely(result == 1))
22735  goto raise_neg_overflow;
22736  }
22737 #endif
22738  if (sizeof(long) <= sizeof(unsigned long)) {
22739  __PYX_VERIFY_RETURN_INT_EXC(long, unsigned long, PyLong_AsUnsignedLong(x))
22740 #ifdef HAVE_LONG_LONG
22741  } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
22742  __PYX_VERIFY_RETURN_INT_EXC(long, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
22743 #endif
22744  }
22745  } else {
22746 #if CYTHON_USE_PYLONG_INTERNALS
22747  const digit* digits = ((PyLongObject*)x)->ob_digit;
22748  switch (Py_SIZE(x)) {
22749  case 0: return (long) 0;
22750  case -1: __PYX_VERIFY_RETURN_INT(long, sdigit, (sdigit) (-(sdigit)digits[0]))
22751  case 1: __PYX_VERIFY_RETURN_INT(long, digit, +digits[0])
22752  case -2:
22753  if (8 * sizeof(long) - 1 > 1 * PyLong_SHIFT) {
22754  if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
22755  __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22756  } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
22757  return (long) (((long)-1)*(((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
22758  }
22759  }
22760  break;
22761  case 2:
22762  if (8 * sizeof(long) > 1 * PyLong_SHIFT) {
22763  if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
22764  __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22765  } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
22766  return (long) ((((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
22767  }
22768  }
22769  break;
22770  case -3:
22771  if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
22772  if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
22773  __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22774  } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
22775  return (long) (((long)-1)*(((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
22776  }
22777  }
22778  break;
22779  case 3:
22780  if (8 * sizeof(long) > 2 * PyLong_SHIFT) {
22781  if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
22782  __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
22783  } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
22784  return (long) ((((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
22785  }
22786  }
22787  break;
22788  case -4:
22789  if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
22790  if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
22791  __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])))
22792  } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
22793  return (long) (((long)-1)*(((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
22794  }
22795  }
22796  break;
22797  case 4:
22798  if (8 * sizeof(long) > 3 * PyLong_SHIFT) {
22799  if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
22800  __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])))
22801  } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
22802  return (long) ((((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
22803  }
22804  }
22805  break;
22806  }
22807 #endif
22808  if (sizeof(long) <= sizeof(long)) {
22809  __PYX_VERIFY_RETURN_INT_EXC(long, long, PyLong_AsLong(x))
22810 #ifdef HAVE_LONG_LONG
22811  } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
22812  __PYX_VERIFY_RETURN_INT_EXC(long, PY_LONG_LONG, PyLong_AsLongLong(x))
22813 #endif
22814  }
22815  }
22816  {
22817 #if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
22818  PyErr_SetString(PyExc_RuntimeError,
22819  "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
22820 #else
22821  long val;
22822  PyObject *v = __Pyx_PyNumber_IntOrLong(x);
22823  #if PY_MAJOR_VERSION < 3
22824  if (likely(v) && !PyLong_Check(v)) {
22825  PyObject *tmp = v;
22826  v = PyNumber_Long(tmp);
22827  Py_DECREF(tmp);
22828  }
22829  #endif
22830  if (likely(v)) {
22831  int one = 1; int is_little = (int)*(unsigned char *)&one;
22832  unsigned char *bytes = (unsigned char *)&val;
22833  int ret = _PyLong_AsByteArray((PyLongObject *)v,
22834  bytes, sizeof(val),
22835  is_little, !is_unsigned);
22836  Py_DECREF(v);
22837  if (likely(!ret))
22838  return val;
22839  }
22840 #endif
22841  return (long) -1;
22842  }
22843  } else {
22844  long val;
22845  PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
22846  if (!tmp) return (long) -1;
22847  val = __Pyx_PyInt_As_long(tmp);
22848  Py_DECREF(tmp);
22849  return val;
22850  }
22851 raise_overflow:
22852  PyErr_SetString(PyExc_OverflowError,
22853  "value too large to convert to long");
22854  return (long) -1;
22855 raise_neg_overflow:
22856  PyErr_SetString(PyExc_OverflowError,
22857  "can't convert negative value to long");
22858  return (long) -1;
22859 }
22860 
22861 /* FastTypeChecks */
22862  #if CYTHON_COMPILING_IN_CPYTHON
22863 static int __Pyx_InBases(PyTypeObject *a, PyTypeObject *b) {
22864  while (a) {
22865  a = a->tp_base;
22866  if (a == b)
22867  return 1;
22868  }
22869  return b == &PyBaseObject_Type;
22870 }
22871 static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b) {
22872  PyObject *mro;
22873  if (a == b) return 1;
22874  mro = a->tp_mro;
22875  if (likely(mro)) {
22876  Py_ssize_t i, n;
22877  n = PyTuple_GET_SIZE(mro);
22878  for (i = 0; i < n; i++) {
22879  if (PyTuple_GET_ITEM(mro, i) == (PyObject *)b)
22880  return 1;
22881  }
22882  return 0;
22883  }
22884  return __Pyx_InBases(a, b);
22885 }
22886 #if PY_MAJOR_VERSION == 2
22887 static int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject* exc_type2) {
22888  PyObject *exception, *value, *tb;
22889  int res;
22890  __Pyx_PyThreadState_declare
22891  __Pyx_PyThreadState_assign
22892  __Pyx_ErrFetch(&exception, &value, &tb);
22893  res = exc_type1 ? PyObject_IsSubclass(err, exc_type1) : 0;
22894  if (unlikely(res == -1)) {
22895  PyErr_WriteUnraisable(err);
22896  res = 0;
22897  }
22898  if (!res) {
22899  res = PyObject_IsSubclass(err, exc_type2);
22900  if (unlikely(res == -1)) {
22901  PyErr_WriteUnraisable(err);
22902  res = 0;
22903  }
22904  }
22905  __Pyx_ErrRestore(exception, value, tb);
22906  return res;
22907 }
22908 #else
22909 static CYTHON_INLINE int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject *exc_type2) {
22910  int res = exc_type1 ? __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type1) : 0;
22911  if (!res) {
22912  res = __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type2);
22913  }
22914  return res;
22915 }
22916 #endif
22917 static int __Pyx_PyErr_GivenExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) {
22918  Py_ssize_t i, n;
22919  assert(PyExceptionClass_Check(exc_type));
22920  n = PyTuple_GET_SIZE(tuple);
22921 #if PY_MAJOR_VERSION >= 3
22922  for (i=0; i<n; i++) {
22923  if (exc_type == PyTuple_GET_ITEM(tuple, i)) return 1;
22924  }
22925 #endif
22926  for (i=0; i<n; i++) {
22927  PyObject *t = PyTuple_GET_ITEM(tuple, i);
22928  #if PY_MAJOR_VERSION < 3
22929  if (likely(exc_type == t)) return 1;
22930  #endif
22931  if (likely(PyExceptionClass_Check(t))) {
22932  if (__Pyx_inner_PyErr_GivenExceptionMatches2(exc_type, NULL, t)) return 1;
22933  } else {
22934  }
22935  }
22936  return 0;
22937 }
22938 static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject* exc_type) {
22939  if (likely(err == exc_type)) return 1;
22940  if (likely(PyExceptionClass_Check(err))) {
22941  if (likely(PyExceptionClass_Check(exc_type))) {
22942  return __Pyx_inner_PyErr_GivenExceptionMatches2(err, NULL, exc_type);
22943  } else if (likely(PyTuple_Check(exc_type))) {
22944  return __Pyx_PyErr_GivenExceptionMatchesTuple(err, exc_type);
22945  } else {
22946  }
22947  }
22948  return PyErr_GivenExceptionMatches(err, exc_type);
22949 }
22950 static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *exc_type1, PyObject *exc_type2) {
22951  assert(PyExceptionClass_Check(exc_type1));
22952  assert(PyExceptionClass_Check(exc_type2));
22953  if (likely(err == exc_type1 || err == exc_type2)) return 1;
22954  if (likely(PyExceptionClass_Check(err))) {
22955  return __Pyx_inner_PyErr_GivenExceptionMatches2(err, exc_type1, exc_type2);
22956  }
22957  return (PyErr_GivenExceptionMatches(err, exc_type1) || PyErr_GivenExceptionMatches(err, exc_type2));
22958 }
22959 #endif
22960 
22961 /* FetchCommonType */
22962  static PyTypeObject* __Pyx_FetchCommonType(PyTypeObject* type) {
22963  PyObject* fake_module;
22964  PyTypeObject* cached_type = NULL;
22965  fake_module = PyImport_AddModule((char*) "_cython_" CYTHON_ABI);
22966  if (!fake_module) return NULL;
22967  Py_INCREF(fake_module);
22968  cached_type = (PyTypeObject*) PyObject_GetAttrString(fake_module, type->tp_name);
22969  if (cached_type) {
22970  if (!PyType_Check((PyObject*)cached_type)) {
22971  PyErr_Format(PyExc_TypeError,
22972  "Shared Cython type %.200s is not a type object",
22973  type->tp_name);
22974  goto bad;
22975  }
22976  if (cached_type->tp_basicsize != type->tp_basicsize) {
22977  PyErr_Format(PyExc_TypeError,
22978  "Shared Cython type %.200s has the wrong size, try recompiling",
22979  type->tp_name);
22980  goto bad;
22981  }
22982  } else {
22983  if (!PyErr_ExceptionMatches(PyExc_AttributeError)) goto bad;
22984  PyErr_Clear();
22985  if (PyType_Ready(type) < 0) goto bad;
22986  if (PyObject_SetAttrString(fake_module, type->tp_name, (PyObject*) type) < 0)
22987  goto bad;
22988  Py_INCREF(type);
22989  cached_type = type;
22990  }
22991 done:
22992  Py_DECREF(fake_module);
22993  return cached_type;
22994 bad:
22995  Py_XDECREF(cached_type);
22996  cached_type = NULL;
22997  goto done;
22998 }
22999 
23000 /* SwapException */
23001  #if CYTHON_FAST_THREAD_STATE
23002 static CYTHON_INLINE void __Pyx__ExceptionSwap(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
23003  PyObject *tmp_type, *tmp_value, *tmp_tb;
23004  #if PY_VERSION_HEX >= 0x030700A3
23005  tmp_type = tstate->exc_state.exc_type;
23006  tmp_value = tstate->exc_state.exc_value;
23007  tmp_tb = tstate->exc_state.exc_traceback;
23008  tstate->exc_state.exc_type = *type;
23009  tstate->exc_state.exc_value = *value;
23010  tstate->exc_state.exc_traceback = *tb;
23011  #else
23012  tmp_type = tstate->exc_type;
23013  tmp_value = tstate->exc_value;
23014  tmp_tb = tstate->exc_traceback;
23015  tstate->exc_type = *type;
23016  tstate->exc_value = *value;
23017  tstate->exc_traceback = *tb;
23018  #endif
23019  *type = tmp_type;
23020  *value = tmp_value;
23021  *tb = tmp_tb;
23022 }
23023 #else
23024 static CYTHON_INLINE void __Pyx_ExceptionSwap(PyObject **type, PyObject **value, PyObject **tb) {
23025  PyObject *tmp_type, *tmp_value, *tmp_tb;
23026  PyErr_GetExcInfo(&tmp_type, &tmp_value, &tmp_tb);
23027  PyErr_SetExcInfo(*type, *value, *tb);
23028  *type = tmp_type;
23029  *value = tmp_value;
23030  *tb = tmp_tb;
23031 }
23032 #endif
23033 
23034 /* PyObjectCallMethod1 */
23035  static PyObject* __Pyx__PyObject_CallMethod1(PyObject* method, PyObject* arg) {
23036  PyObject *result = NULL;
23037 #if CYTHON_UNPACK_METHODS
23038  if (likely(PyMethod_Check(method))) {
23039  PyObject *self = PyMethod_GET_SELF(method);
23040  if (likely(self)) {
23041  PyObject *args;
23042  PyObject *function = PyMethod_GET_FUNCTION(method);
23043  #if CYTHON_FAST_PYCALL
23044  if (PyFunction_Check(function)) {
23045  PyObject *args[2] = {self, arg};
23046  result = __Pyx_PyFunction_FastCall(function, args, 2);
23047  goto done;
23048  }
23049  #endif
23050  #if CYTHON_FAST_PYCCALL
23051  if (__Pyx_PyFastCFunction_Check(function)) {
23052  PyObject *args[2] = {self, arg};
23053  result = __Pyx_PyCFunction_FastCall(function, args, 2);
23054  goto done;
23055  }
23056  #endif
23057  args = PyTuple_New(2);
23058  if (unlikely(!args)) goto done;
23059  Py_INCREF(self);
23060  PyTuple_SET_ITEM(args, 0, self);
23061  Py_INCREF(arg);
23062  PyTuple_SET_ITEM(args, 1, arg);
23063  Py_INCREF(function);
23064  result = __Pyx_PyObject_Call(function, args, NULL);
23065  Py_DECREF(args);
23066  Py_DECREF(function);
23067  return result;
23068  }
23069  }
23070 #endif
23071  result = __Pyx_PyObject_CallOneArg(method, arg);
23072  goto done;
23073 done:
23074  return result;
23075 }
23076 static PyObject* __Pyx_PyObject_CallMethod1(PyObject* obj, PyObject* method_name, PyObject* arg) {
23077  PyObject *method, *result;
23078  method = __Pyx_PyObject_GetAttrStr(obj, method_name);
23079  if (unlikely(!method)) return NULL;
23080  result = __Pyx__PyObject_CallMethod1(method, arg);
23081  Py_DECREF(method);
23082  return result;
23083 }
23084 
23085 /* CoroutineBase */
23086  #include <structmember.h>
23087 #include <frameobject.h>
23088 #define __Pyx_Coroutine_Undelegate(gen) Py_CLEAR((gen)->yieldfrom)
23089 static int __Pyx_PyGen__FetchStopIterationValue(CYTHON_UNUSED PyThreadState *__pyx_tstate, PyObject **pvalue) {
23090  PyObject *et, *ev, *tb;
23091  PyObject *value = NULL;
23092  __Pyx_ErrFetch(&et, &ev, &tb);
23093  if (!et) {
23094  Py_XDECREF(tb);
23095  Py_XDECREF(ev);
23096  Py_INCREF(Py_None);
23097  *pvalue = Py_None;
23098  return 0;
23099  }
23100  if (likely(et == PyExc_StopIteration)) {
23101  if (!ev) {
23102  Py_INCREF(Py_None);
23103  value = Py_None;
23104  }
23105 #if PY_VERSION_HEX >= 0x030300A0
23106  else if (Py_TYPE(ev) == (PyTypeObject*)PyExc_StopIteration) {
23107  value = ((PyStopIterationObject *)ev)->value;
23108  Py_INCREF(value);
23109  Py_DECREF(ev);
23110  }
23111 #endif
23112  else if (unlikely(PyTuple_Check(ev))) {
23113  if (PyTuple_GET_SIZE(ev) >= 1) {
23114 #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
23115  value = PyTuple_GET_ITEM(ev, 0);
23116  Py_INCREF(value);
23117 #else
23118  value = PySequence_ITEM(ev, 0);
23119 #endif
23120  } else {
23121  Py_INCREF(Py_None);
23122  value = Py_None;
23123  }
23124  Py_DECREF(ev);
23125  }
23126  else if (!__Pyx_TypeCheck(ev, (PyTypeObject*)PyExc_StopIteration)) {
23127  value = ev;
23128  }
23129  if (likely(value)) {
23130  Py_XDECREF(tb);
23131  Py_DECREF(et);
23132  *pvalue = value;
23133  return 0;
23134  }
23135  } else if (!__Pyx_PyErr_GivenExceptionMatches(et, PyExc_StopIteration)) {
23136  __Pyx_ErrRestore(et, ev, tb);
23137  return -1;
23138  }
23139  PyErr_NormalizeException(&et, &ev, &tb);
23140  if (unlikely(!PyObject_TypeCheck(ev, (PyTypeObject*)PyExc_StopIteration))) {
23141  __Pyx_ErrRestore(et, ev, tb);
23142  return -1;
23143  }
23144  Py_XDECREF(tb);
23145  Py_DECREF(et);
23146 #if PY_VERSION_HEX >= 0x030300A0
23147  value = ((PyStopIterationObject *)ev)->value;
23148  Py_INCREF(value);
23149  Py_DECREF(ev);
23150 #else
23151  {
23152  PyObject* args = __Pyx_PyObject_GetAttrStr(ev, __pyx_n_s_args);
23153  Py_DECREF(ev);
23154  if (likely(args)) {
23155  value = PySequence_GetItem(args, 0);
23156  Py_DECREF(args);
23157  }
23158  if (unlikely(!value)) {
23159  __Pyx_ErrRestore(NULL, NULL, NULL);
23160  Py_INCREF(Py_None);
23161  value = Py_None;
23162  }
23163  }
23164 #endif
23165  *pvalue = value;
23166  return 0;
23167 }
23168 static CYTHON_INLINE
23169 void __Pyx_Coroutine_ExceptionClear(__pyx_CoroutineObject *self) {
23170  PyObject *exc_type = self->exc_type;
23171  PyObject *exc_value = self->exc_value;
23172  PyObject *exc_traceback = self->exc_traceback;
23173  self->exc_type = NULL;
23174  self->exc_value = NULL;
23175  self->exc_traceback = NULL;
23176  Py_XDECREF(exc_type);
23177  Py_XDECREF(exc_value);
23178  Py_XDECREF(exc_traceback);
23179 }
23180 #define __Pyx_Coroutine_AlreadyRunningError(gen) (__Pyx__Coroutine_AlreadyRunningError(gen), (PyObject*)NULL)
23181 static void __Pyx__Coroutine_AlreadyRunningError(CYTHON_UNUSED __pyx_CoroutineObject *gen) {
23182  const char *msg;
23183  if (0) {
23184  #ifdef __Pyx_Coroutine_USED
23185  } else if (__Pyx_Coroutine_Check((PyObject*)gen)) {
23186  msg = "coroutine already executing";
23187  #endif
23188  #ifdef __Pyx_AsyncGen_USED
23189  } else if (__Pyx_AsyncGen_CheckExact((PyObject*)gen)) {
23190  msg = "async generator already executing";
23191  #endif
23192  } else {
23193  msg = "generator already executing";
23194  }
23195  PyErr_SetString(PyExc_ValueError, msg);
23196 }
23197 #define __Pyx_Coroutine_NotStartedError(gen) (__Pyx__Coroutine_NotStartedError(gen), (PyObject*)NULL)
23198 static void __Pyx__Coroutine_NotStartedError(CYTHON_UNUSED PyObject *gen) {
23199  const char *msg;
23200  if (0) {
23201  #ifdef __Pyx_Coroutine_USED
23202  } else if (__Pyx_Coroutine_Check(gen)) {
23203  msg = "can't send non-None value to a just-started coroutine";
23204  #endif
23205  #ifdef __Pyx_AsyncGen_USED
23206  } else if (__Pyx_AsyncGen_CheckExact(gen)) {
23207  msg = "can't send non-None value to a just-started async generator";
23208  #endif
23209  } else {
23210  msg = "can't send non-None value to a just-started generator";
23211  }
23212  PyErr_SetString(PyExc_TypeError, msg);
23213 }
23214 #define __Pyx_Coroutine_AlreadyTerminatedError(gen, value, closing) (__Pyx__Coroutine_AlreadyTerminatedError(gen, value, closing), (PyObject*)NULL)
23215 static void __Pyx__Coroutine_AlreadyTerminatedError(CYTHON_UNUSED PyObject *gen, PyObject *value, CYTHON_UNUSED int closing) {
23216  #ifdef __Pyx_Coroutine_USED
23217  if (!closing && __Pyx_Coroutine_Check(gen)) {
23218  PyErr_SetString(PyExc_RuntimeError, "cannot reuse already awaited coroutine");
23219  } else
23220  #endif
23221  if (value) {
23222  #ifdef __Pyx_AsyncGen_USED
23223  if (__Pyx_AsyncGen_CheckExact(gen))
23224  PyErr_SetNone(__Pyx_PyExc_StopAsyncIteration);
23225  else
23226  #endif
23227  PyErr_SetNone(PyExc_StopIteration);
23228  }
23229 }
23230 static
23231 PyObject *__Pyx_Coroutine_SendEx(__pyx_CoroutineObject *self, PyObject *value, int closing) {
23232  __Pyx_PyThreadState_declare
23233  PyThreadState *tstate;
23234  PyObject *retval;
23235  assert(!self->is_running);
23236  if (unlikely(self->resume_label == 0)) {
23237  if (unlikely(value && value != Py_None)) {
23238  return __Pyx_Coroutine_NotStartedError((PyObject*)self);
23239  }
23240  }
23241  if (unlikely(self->resume_label == -1)) {
23242  return __Pyx_Coroutine_AlreadyTerminatedError((PyObject*)self, value, closing);
23243  }
23244 #if CYTHON_FAST_THREAD_STATE
23245  __Pyx_PyThreadState_assign
23246  tstate = __pyx_tstate;
23247 #else
23248  tstate = __Pyx_PyThreadState_Current;
23249 #endif
23250  if (self->exc_type) {
23251 #if CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_PYSTON
23252 #else
23253  if (self->exc_traceback) {
23254  PyTracebackObject *tb = (PyTracebackObject *) self->exc_traceback;
23255  PyFrameObject *f = tb->tb_frame;
23256  Py_XINCREF(tstate->frame);
23257  assert(f->f_back == NULL);
23258  f->f_back = tstate->frame;
23259  }
23260 #endif
23261  __Pyx_ExceptionSwap(&self->exc_type, &self->exc_value,
23262  &self->exc_traceback);
23263  } else {
23264  __Pyx_Coroutine_ExceptionClear(self);
23265  __Pyx_ExceptionSave(&self->exc_type, &self->exc_value, &self->exc_traceback);
23266  }
23267  self->is_running = 1;
23268  retval = self->body((PyObject *) self, tstate, value);
23269  self->is_running = 0;
23270  return retval;
23271 }
23272 static CYTHON_INLINE void __Pyx_Coroutine_ResetFrameBackpointer(__pyx_CoroutineObject *self) {
23273  if (likely(self->exc_traceback)) {
23274 #if CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_PYSTON
23275 #else
23276  PyTracebackObject *tb = (PyTracebackObject *) self->exc_traceback;
23277  PyFrameObject *f = tb->tb_frame;
23278  Py_CLEAR(f->f_back);
23279 #endif
23280  }
23281 }
23282 static CYTHON_INLINE
23283 PyObject *__Pyx_Coroutine_MethodReturn(CYTHON_UNUSED PyObject* gen, PyObject *retval) {
23284  if (unlikely(!retval)) {
23285  __Pyx_PyThreadState_declare
23286  __Pyx_PyThreadState_assign
23287  if (!__Pyx_PyErr_Occurred()) {
23288  PyObject *exc = PyExc_StopIteration;
23289  #ifdef __Pyx_AsyncGen_USED
23290  if (__Pyx_AsyncGen_CheckExact(gen))
23291  exc = __Pyx_PyExc_StopAsyncIteration;
23292  #endif
23293  __Pyx_PyErr_SetNone(exc);
23294  }
23295  }
23296  return retval;
23297 }
23298 static CYTHON_INLINE
23299 PyObject *__Pyx_Coroutine_FinishDelegation(__pyx_CoroutineObject *gen) {
23300  PyObject *ret;
23301  PyObject *val = NULL;
23302  __Pyx_Coroutine_Undelegate(gen);
23303  __Pyx_PyGen__FetchStopIterationValue(__Pyx_PyThreadState_Current, &val);
23304  ret = __Pyx_Coroutine_SendEx(gen, val, 0);
23305  Py_XDECREF(val);
23306  return ret;
23307 }
23308 static PyObject *__Pyx_Coroutine_Send(PyObject *self, PyObject *value) {
23309  PyObject *retval;
23310  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject*) self;
23311  PyObject *yf = gen->yieldfrom;
23312  if (unlikely(gen->is_running))
23313  return __Pyx_Coroutine_AlreadyRunningError(gen);
23314  if (yf) {
23315  PyObject *ret;
23316  gen->is_running = 1;
23317  #ifdef __Pyx_Generator_USED
23318  if (__Pyx_Generator_CheckExact(yf)) {
23319  ret = __Pyx_Coroutine_Send(yf, value);
23320  } else
23321  #endif
23322  #ifdef __Pyx_Coroutine_USED
23323  if (__Pyx_Coroutine_Check(yf)) {
23324  ret = __Pyx_Coroutine_Send(yf, value);
23325  } else
23326  #endif
23327  #ifdef __Pyx_AsyncGen_USED
23328  if (__pyx_PyAsyncGenASend_CheckExact(yf)) {
23329  ret = __Pyx_async_gen_asend_send(yf, value);
23330  } else
23331  #endif
23332  #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x03030000 && (defined(__linux__) || PY_VERSION_HEX >= 0x030600B3)
23333  if (PyGen_CheckExact(yf)) {
23334  ret = _PyGen_Send((PyGenObject*)yf, value == Py_None ? NULL : value);
23335  } else
23336  #endif
23337  #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x03050000 && defined(PyCoro_CheckExact) && (defined(__linux__) || PY_VERSION_HEX >= 0x030600B3)
23338  if (PyCoro_CheckExact(yf)) {
23339  ret = _PyGen_Send((PyGenObject*)yf, value == Py_None ? NULL : value);
23340  } else
23341  #endif
23342  {
23343  if (value == Py_None)
23344  ret = Py_TYPE(yf)->tp_iternext(yf);
23345  else
23346  ret = __Pyx_PyObject_CallMethod1(yf, __pyx_n_s_send, value);
23347  }
23348  gen->is_running = 0;
23349  if (likely(ret)) {
23350  return ret;
23351  }
23352  retval = __Pyx_Coroutine_FinishDelegation(gen);
23353  } else {
23354  retval = __Pyx_Coroutine_SendEx(gen, value, 0);
23355  }
23356  return __Pyx_Coroutine_MethodReturn(self, retval);
23357 }
23358 static int __Pyx_Coroutine_CloseIter(__pyx_CoroutineObject *gen, PyObject *yf) {
23359  PyObject *retval = NULL;
23360  int err = 0;
23361  #ifdef __Pyx_Generator_USED
23362  if (__Pyx_Generator_CheckExact(yf)) {
23363  retval = __Pyx_Coroutine_Close(yf);
23364  if (!retval)
23365  return -1;
23366  } else
23367  #endif
23368  #ifdef __Pyx_Coroutine_USED
23369  if (__Pyx_Coroutine_Check(yf)) {
23370  retval = __Pyx_Coroutine_Close(yf);
23371  if (!retval)
23372  return -1;
23373  } else
23374  if (__Pyx_CoroutineAwait_CheckExact(yf)) {
23375  retval = __Pyx_CoroutineAwait_Close((__pyx_CoroutineAwaitObject*)yf);
23376  if (!retval)
23377  return -1;
23378  } else
23379  #endif
23380  #ifdef __Pyx_AsyncGen_USED
23381  if (__pyx_PyAsyncGenASend_CheckExact(yf)) {
23382  retval = __Pyx_async_gen_asend_close(yf, NULL);
23383  } else
23384  if (__pyx_PyAsyncGenAThrow_CheckExact(yf)) {
23385  retval = __Pyx_async_gen_athrow_close(yf, NULL);
23386  } else
23387  #endif
23388  {
23389  PyObject *meth;
23390  gen->is_running = 1;
23391  meth = __Pyx_PyObject_GetAttrStr(yf, __pyx_n_s_close);
23392  if (unlikely(!meth)) {
23393  if (!PyErr_ExceptionMatches(PyExc_AttributeError)) {
23394  PyErr_WriteUnraisable(yf);
23395  }
23396  PyErr_Clear();
23397  } else {
23398  retval = PyObject_CallFunction(meth, NULL);
23399  Py_DECREF(meth);
23400  if (!retval)
23401  err = -1;
23402  }
23403  gen->is_running = 0;
23404  }
23405  Py_XDECREF(retval);
23406  return err;
23407 }
23408 static PyObject *__Pyx_Generator_Next(PyObject *self) {
23409  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject*) self;
23410  PyObject *yf = gen->yieldfrom;
23411  if (unlikely(gen->is_running))
23412  return __Pyx_Coroutine_AlreadyRunningError(gen);
23413  if (yf) {
23414  PyObject *ret;
23415  gen->is_running = 1;
23416  #ifdef __Pyx_Generator_USED
23417  if (__Pyx_Generator_CheckExact(yf)) {
23418  ret = __Pyx_Generator_Next(yf);
23419  } else
23420  #endif
23421  #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x03030000 && (defined(__linux__) || PY_VERSION_HEX >= 0x030600B3)
23422  if (PyGen_CheckExact(yf)) {
23423  ret = _PyGen_Send((PyGenObject*)yf, NULL);
23424  } else
23425  #endif
23426  #ifdef __Pyx_Coroutine_USED
23427  if (__Pyx_Coroutine_Check(yf)) {
23428  ret = __Pyx_Coroutine_Send(yf, Py_None);
23429  } else
23430  #endif
23431  ret = Py_TYPE(yf)->tp_iternext(yf);
23432  gen->is_running = 0;
23433  if (likely(ret)) {
23434  return ret;
23435  }
23436  return __Pyx_Coroutine_FinishDelegation(gen);
23437  }
23438  return __Pyx_Coroutine_SendEx(gen, Py_None, 0);
23439 }
23440 static PyObject *__Pyx_Coroutine_Close(PyObject *self) {
23441  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
23442  PyObject *retval, *raised_exception;
23443  PyObject *yf = gen->yieldfrom;
23444  int err = 0;
23445  if (unlikely(gen->is_running))
23446  return __Pyx_Coroutine_AlreadyRunningError(gen);
23447  if (yf) {
23448  Py_INCREF(yf);
23449  err = __Pyx_Coroutine_CloseIter(gen, yf);
23450  __Pyx_Coroutine_Undelegate(gen);
23451  Py_DECREF(yf);
23452  }
23453  if (err == 0)
23454  PyErr_SetNone(PyExc_GeneratorExit);
23455  retval = __Pyx_Coroutine_SendEx(gen, NULL, 1);
23456  if (unlikely(retval)) {
23457  const char *msg;
23458  Py_DECREF(retval);
23459  if ((0)) {
23460  #ifdef __Pyx_Coroutine_USED
23461  } else if (__Pyx_Coroutine_Check(self)) {
23462  msg = "coroutine ignored GeneratorExit";
23463  #endif
23464  #ifdef __Pyx_AsyncGen_USED
23465  } else if (__Pyx_AsyncGen_CheckExact(self)) {
23466 #if PY_VERSION_HEX < 0x03060000
23467  msg = "async generator ignored GeneratorExit - might require Python 3.6+ finalisation (PEP 525)";
23468 #else
23469  msg = "async generator ignored GeneratorExit";
23470 #endif
23471  #endif
23472  } else {
23473  msg = "generator ignored GeneratorExit";
23474  }
23475  PyErr_SetString(PyExc_RuntimeError, msg);
23476  return NULL;
23477  }
23478  raised_exception = PyErr_Occurred();
23479  if (likely(!raised_exception || __Pyx_PyErr_GivenExceptionMatches2(raised_exception, PyExc_GeneratorExit, PyExc_StopIteration))) {
23480  if (raised_exception) PyErr_Clear();
23481  Py_INCREF(Py_None);
23482  return Py_None;
23483  }
23484  return NULL;
23485 }
23486 static PyObject *__Pyx__Coroutine_Throw(PyObject *self, PyObject *typ, PyObject *val, PyObject *tb,
23487  PyObject *args, int close_on_genexit) {
23488  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
23489  PyObject *yf = gen->yieldfrom;
23490  if (unlikely(gen->is_running))
23491  return __Pyx_Coroutine_AlreadyRunningError(gen);
23492  if (yf) {
23493  PyObject *ret;
23494  Py_INCREF(yf);
23495  if (__Pyx_PyErr_GivenExceptionMatches(typ, PyExc_GeneratorExit) && close_on_genexit) {
23496  int err = __Pyx_Coroutine_CloseIter(gen, yf);
23497  Py_DECREF(yf);
23498  __Pyx_Coroutine_Undelegate(gen);
23499  if (err < 0)
23500  return __Pyx_Coroutine_MethodReturn(self, __Pyx_Coroutine_SendEx(gen, NULL, 0));
23501  goto throw_here;
23502  }
23503  gen->is_running = 1;
23504  if (0
23505  #ifdef __Pyx_Generator_USED
23506  || __Pyx_Generator_CheckExact(yf)
23507  #endif
23508  #ifdef __Pyx_Coroutine_USED
23509  || __Pyx_Coroutine_Check(yf)
23510  #endif
23511  ) {
23512  ret = __Pyx__Coroutine_Throw(yf, typ, val, tb, args, close_on_genexit);
23513  #ifdef __Pyx_Coroutine_USED
23514  } else if (__Pyx_CoroutineAwait_CheckExact(yf)) {
23515  ret = __Pyx__Coroutine_Throw(((__pyx_CoroutineAwaitObject*)yf)->coroutine, typ, val, tb, args, close_on_genexit);
23516  #endif
23517  } else {
23518  PyObject *meth = __Pyx_PyObject_GetAttrStr(yf, __pyx_n_s_throw);
23519  if (unlikely(!meth)) {
23520  Py_DECREF(yf);
23521  if (!PyErr_ExceptionMatches(PyExc_AttributeError)) {
23522  gen->is_running = 0;
23523  return NULL;
23524  }
23525  PyErr_Clear();
23526  __Pyx_Coroutine_Undelegate(gen);
23527  gen->is_running = 0;
23528  goto throw_here;
23529  }
23530  if (likely(args)) {
23531  ret = PyObject_CallObject(meth, args);
23532  } else {
23533  ret = PyObject_CallFunctionObjArgs(meth, typ, val, tb, NULL);
23534  }
23535  Py_DECREF(meth);
23536  }
23537  gen->is_running = 0;
23538  Py_DECREF(yf);
23539  if (!ret) {
23540  ret = __Pyx_Coroutine_FinishDelegation(gen);
23541  }
23542  return __Pyx_Coroutine_MethodReturn(self, ret);
23543  }
23544 throw_here:
23545  __Pyx_Raise(typ, val, tb, NULL);
23546  return __Pyx_Coroutine_MethodReturn(self, __Pyx_Coroutine_SendEx(gen, NULL, 0));
23547 }
23548 static PyObject *__Pyx_Coroutine_Throw(PyObject *self, PyObject *args) {
23549  PyObject *typ;
23550  PyObject *val = NULL;
23551  PyObject *tb = NULL;
23552  if (!PyArg_UnpackTuple(args, (char *)"throw", 1, 3, &typ, &val, &tb))
23553  return NULL;
23554  return __Pyx__Coroutine_Throw(self, typ, val, tb, args, 1);
23555 }
23556 static int __Pyx_Coroutine_traverse(__pyx_CoroutineObject *gen, visitproc visit, void *arg) {
23557  Py_VISIT(gen->closure);
23558  Py_VISIT(gen->classobj);
23559  Py_VISIT(gen->yieldfrom);
23560  Py_VISIT(gen->exc_type);
23561  Py_VISIT(gen->exc_value);
23562  Py_VISIT(gen->exc_traceback);
23563  return 0;
23564 }
23565 static int __Pyx_Coroutine_clear(PyObject *self) {
23566  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
23567  Py_CLEAR(gen->closure);
23568  Py_CLEAR(gen->classobj);
23569  Py_CLEAR(gen->yieldfrom);
23570  Py_CLEAR(gen->exc_type);
23571  Py_CLEAR(gen->exc_value);
23572  Py_CLEAR(gen->exc_traceback);
23573 #ifdef __Pyx_AsyncGen_USED
23574  if (__Pyx_AsyncGen_CheckExact(self)) {
23575  Py_CLEAR(((__pyx_PyAsyncGenObject*)gen)->ag_finalizer);
23576  }
23577 #endif
23578  Py_CLEAR(gen->gi_code);
23579  Py_CLEAR(gen->gi_name);
23580  Py_CLEAR(gen->gi_qualname);
23581  Py_CLEAR(gen->gi_modulename);
23582  return 0;
23583 }
23584 static void __Pyx_Coroutine_dealloc(PyObject *self) {
23585  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
23586  PyObject_GC_UnTrack(gen);
23587  if (gen->gi_weakreflist != NULL)
23588  PyObject_ClearWeakRefs(self);
23589  if (gen->resume_label >= 0) {
23590  PyObject_GC_Track(self);
23591 #if PY_VERSION_HEX >= 0x030400a1 && CYTHON_USE_TP_FINALIZE
23592  if (PyObject_CallFinalizerFromDealloc(self))
23593 #else
23594  Py_TYPE(gen)->tp_del(self);
23595  if (self->ob_refcnt > 0)
23596 #endif
23597  {
23598  return;
23599  }
23600  PyObject_GC_UnTrack(self);
23601  }
23602 #ifdef __Pyx_AsyncGen_USED
23603  if (__Pyx_AsyncGen_CheckExact(self)) {
23604  /* We have to handle this case for asynchronous generators
23605  right here, because this code has to be between UNTRACK
23606  and GC_Del. */
23607  Py_CLEAR(((__pyx_PyAsyncGenObject*)self)->ag_finalizer);
23608  }
23609 #endif
23610  __Pyx_Coroutine_clear(self);
23611  PyObject_GC_Del(gen);
23612 }
23613 static void __Pyx_Coroutine_del(PyObject *self) {
23614  PyObject *error_type, *error_value, *error_traceback;
23615  __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
23616  __Pyx_PyThreadState_declare
23617  if (gen->resume_label < 0) {
23618  return;
23619  }
23620 #if !CYTHON_USE_TP_FINALIZE
23621  assert(self->ob_refcnt == 0);
23622  self->ob_refcnt = 1;
23623 #endif
23624  __Pyx_PyThreadState_assign
23625  __Pyx_ErrFetch(&error_type, &error_value, &error_traceback);
23626 #ifdef __Pyx_AsyncGen_USED
23627  if (__Pyx_AsyncGen_CheckExact(self)) {
23628  __pyx_PyAsyncGenObject *agen = (__pyx_PyAsyncGenObject*)self;
23629  PyObject *finalizer = agen->ag_finalizer;
23630  if (finalizer && !agen->ag_closed) {
23631  PyObject *res = __Pyx_PyObject_CallOneArg(finalizer, self);
23632  if (unlikely(!res)) {
23633  PyErr_WriteUnraisable(self);
23634  } else {
23635  Py_DECREF(res);
23636  }
23637  __Pyx_ErrRestore(error_type, error_value, error_traceback);
23638  return;
23639  }
23640  }
23641 #endif
23642  if (unlikely(gen->resume_label == 0 && !error_value)) {
23643 #ifdef __Pyx_Coroutine_USED
23644 #ifdef __Pyx_Generator_USED
23645  if (!__Pyx_Generator_CheckExact(self))
23646 #endif
23647  {
23648  PyObject_GC_UnTrack(self);
23649 #if PY_MAJOR_VERSION >= 3 || defined(PyErr_WarnFormat)
23650  if (unlikely(PyErr_WarnFormat(PyExc_RuntimeWarning, 1, "coroutine '%.50S' was never awaited", gen->gi_qualname) < 0))
23651  PyErr_WriteUnraisable(self);
23652 #else
23653  {PyObject *msg;
23654  char *cmsg;
23655  #if CYTHON_COMPILING_IN_PYPY
23656  msg = NULL;
23657  cmsg = (char*) "coroutine was never awaited";
23658  #else
23659  char *cname;
23660  PyObject *qualname;
23661  qualname = gen->gi_qualname;
23662  cname = PyString_AS_STRING(qualname);
23663  msg = PyString_FromFormat("coroutine '%.50s' was never awaited", cname);
23664  if (unlikely(!msg)) {
23665  PyErr_Clear();
23666  cmsg = (char*) "coroutine was never awaited";
23667  } else {
23668  cmsg = PyString_AS_STRING(msg);
23669  }
23670  #endif
23671  if (unlikely(PyErr_WarnEx(PyExc_RuntimeWarning, cmsg, 1) < 0))
23672  PyErr_WriteUnraisable(self);
23673  Py_XDECREF(msg);}
23674 #endif
23675  PyObject_GC_Track(self);
23676  }
23677 #endif
23678  } else {
23679  PyObject *res = __Pyx_Coroutine_Close(self);
23680  if (unlikely(!res)) {
23681  if (PyErr_Occurred())
23682  PyErr_WriteUnraisable(self);
23683  } else {
23684  Py_DECREF(res);
23685  }
23686  }
23687  __Pyx_ErrRestore(error_type, error_value, error_traceback);
23688 #if !CYTHON_USE_TP_FINALIZE
23689  assert(self->ob_refcnt > 0);
23690  if (--self->ob_refcnt == 0) {
23691  return;
23692  }
23693  {
23694  Py_ssize_t refcnt = self->ob_refcnt;
23695  _Py_NewReference(self);
23696  self->ob_refcnt = refcnt;
23697  }
23698 #if CYTHON_COMPILING_IN_CPYTHON
23699  assert(PyType_IS_GC(self->ob_type) &&
23700  _Py_AS_GC(self)->gc.gc_refs != _PyGC_REFS_UNTRACKED);
23701  _Py_DEC_REFTOTAL;
23702 #endif
23703 #ifdef COUNT_ALLOCS
23704  --Py_TYPE(self)->tp_frees;
23705  --Py_TYPE(self)->tp_allocs;
23706 #endif
23707 #endif
23708 }
23709 static PyObject *
23710 __Pyx_Coroutine_get_name(__pyx_CoroutineObject *self)
23711 {
23712  PyObject *name = self->gi_name;
23713  if (unlikely(!name)) name = Py_None;
23714  Py_INCREF(name);
23715  return name;
23716 }
23717 static int
23718 __Pyx_Coroutine_set_name(__pyx_CoroutineObject *self, PyObject *value)
23719 {
23720  PyObject *tmp;
23721 #if PY_MAJOR_VERSION >= 3
23722  if (unlikely(value == NULL || !PyUnicode_Check(value))) {
23723 #else
23724  if (unlikely(value == NULL || !PyString_Check(value))) {
23725 #endif
23726  PyErr_SetString(PyExc_TypeError,
23727  "__name__ must be set to a string object");
23728  return -1;
23729  }
23730  tmp = self->gi_name;
23731  Py_INCREF(value);
23732  self->gi_name = value;
23733  Py_XDECREF(tmp);
23734  return 0;
23735 }
23736 static PyObject *
23737 __Pyx_Coroutine_get_qualname(__pyx_CoroutineObject *self)
23738 {
23739  PyObject *name = self->gi_qualname;
23740  if (unlikely(!name)) name = Py_None;
23741  Py_INCREF(name);
23742  return name;
23743 }
23744 static int
23745 __Pyx_Coroutine_set_qualname(__pyx_CoroutineObject *self, PyObject *value)
23746 {
23747  PyObject *tmp;
23748 #if PY_MAJOR_VERSION >= 3
23749  if (unlikely(value == NULL || !PyUnicode_Check(value))) {
23750 #else
23751  if (unlikely(value == NULL || !PyString_Check(value))) {
23752 #endif
23753  PyErr_SetString(PyExc_TypeError,
23754  "__qualname__ must be set to a string object");
23755  return -1;
23756  }
23757  tmp = self->gi_qualname;
23758  Py_INCREF(value);
23759  self->gi_qualname = value;
23760  Py_XDECREF(tmp);
23761  return 0;
23762 }
23763 static __pyx_CoroutineObject *__Pyx__Coroutine_New(
23764  PyTypeObject* type, __pyx_coroutine_body_t body, PyObject *code, PyObject *closure,
23765  PyObject *name, PyObject *qualname, PyObject *module_name) {
23766  __pyx_CoroutineObject *gen = PyObject_GC_New(__pyx_CoroutineObject, type);
23767  if (unlikely(!gen))
23768  return NULL;
23769  return __Pyx__Coroutine_NewInit(gen, body, code, closure, name, qualname, module_name);
23770 }
23771 static __pyx_CoroutineObject *__Pyx__Coroutine_NewInit(
23772  __pyx_CoroutineObject *gen, __pyx_coroutine_body_t body, PyObject *code, PyObject *closure,
23773  PyObject *name, PyObject *qualname, PyObject *module_name) {
23774  gen->body = body;
23775  gen->closure = closure;
23776  Py_XINCREF(closure);
23777  gen->is_running = 0;
23778  gen->resume_label = 0;
23779  gen->classobj = NULL;
23780  gen->yieldfrom = NULL;
23781  gen->exc_type = NULL;
23782  gen->exc_value = NULL;
23783  gen->exc_traceback = NULL;
23784  gen->gi_weakreflist = NULL;
23785  Py_XINCREF(qualname);
23786  gen->gi_qualname = qualname;
23787  Py_XINCREF(name);
23788  gen->gi_name = name;
23789  Py_XINCREF(module_name);
23790  gen->gi_modulename = module_name;
23791  Py_XINCREF(code);
23792  gen->gi_code = code;
23793  PyObject_GC_Track(gen);
23794  return gen;
23795 }
23796 
23797 /* PatchModuleWithCoroutine */
23798  static PyObject* __Pyx_Coroutine_patch_module(PyObject* module, const char* py_code) {
23799 #if defined(__Pyx_Generator_USED) || defined(__Pyx_Coroutine_USED)
23800  int result;
23801  PyObject *globals, *result_obj;
23802  globals = PyDict_New(); if (unlikely(!globals)) goto ignore;
23803  result = PyDict_SetItemString(globals, "_cython_coroutine_type",
23804  #ifdef __Pyx_Coroutine_USED
23805  (PyObject*)__pyx_CoroutineType);
23806  #else
23807  Py_None);
23808  #endif
23809  if (unlikely(result < 0)) goto ignore;
23810  result = PyDict_SetItemString(globals, "_cython_generator_type",
23811  #ifdef __Pyx_Generator_USED
23812  (PyObject*)__pyx_GeneratorType);
23813  #else
23814  Py_None);
23815  #endif
23816  if (unlikely(result < 0)) goto ignore;
23817  if (unlikely(PyDict_SetItemString(globals, "_module", module) < 0)) goto ignore;
23818  if (unlikely(PyDict_SetItemString(globals, "__builtins__", __pyx_b) < 0)) goto ignore;
23819  result_obj = PyRun_String(py_code, Py_file_input, globals, globals);
23820  if (unlikely(!result_obj)) goto ignore;
23821  Py_DECREF(result_obj);
23822  Py_DECREF(globals);
23823  return module;
23824 ignore:
23825  Py_XDECREF(globals);
23826  PyErr_WriteUnraisable(module);
23827  if (unlikely(PyErr_WarnEx(PyExc_RuntimeWarning, "Cython module failed to patch module with custom type", 1) < 0)) {
23828  Py_DECREF(module);
23829  module = NULL;
23830  }
23831 #else
23832  py_code++;
23833 #endif
23834  return module;
23835 }
23836 
23837 /* PatchGeneratorABC */
23838  #ifndef CYTHON_REGISTER_ABCS
23839 #define CYTHON_REGISTER_ABCS 1
23840 #endif
23841 #if defined(__Pyx_Generator_USED) || defined(__Pyx_Coroutine_USED)
23842 static PyObject* __Pyx_patch_abc_module(PyObject *module);
23843 static PyObject* __Pyx_patch_abc_module(PyObject *module) {
23844  module = __Pyx_Coroutine_patch_module(
23845  module, ""
23846 "if _cython_generator_type is not None:\n"
23847 " try: Generator = _module.Generator\n"
23848 " except AttributeError: pass\n"
23849 " else: Generator.register(_cython_generator_type)\n"
23850 "if _cython_coroutine_type is not None:\n"
23851 " try: Coroutine = _module.Coroutine\n"
23852 " except AttributeError: pass\n"
23853 " else: Coroutine.register(_cython_coroutine_type)\n"
23854  );
23855  return module;
23856 }
23857 #endif
23858 static int __Pyx_patch_abc(void) {
23859 #if defined(__Pyx_Generator_USED) || defined(__Pyx_Coroutine_USED)
23860  static int abc_patched = 0;
23861  if (CYTHON_REGISTER_ABCS && !abc_patched) {
23862  PyObject *module;
23863  module = PyImport_ImportModule((PY_MAJOR_VERSION >= 3) ? "collections.abc" : "collections");
23864  if (!module) {
23865  PyErr_WriteUnraisable(NULL);
23866  if (unlikely(PyErr_WarnEx(PyExc_RuntimeWarning,
23867  ((PY_MAJOR_VERSION >= 3) ?
23868  "Cython module failed to register with collections.abc module" :
23869  "Cython module failed to register with collections module"), 1) < 0)) {
23870  return -1;
23871  }
23872  } else {
23873  module = __Pyx_patch_abc_module(module);
23874  abc_patched = 1;
23875  if (unlikely(!module))
23876  return -1;
23877  Py_DECREF(module);
23878  }
23879  module = PyImport_ImportModule("backports_abc");
23880  if (module) {
23881  module = __Pyx_patch_abc_module(module);
23882  Py_XDECREF(module);
23883  }
23884  if (!module) {
23885  PyErr_Clear();
23886  }
23887  }
23888 #else
23889  if ((0)) __Pyx_Coroutine_patch_module(NULL, NULL);
23890 #endif
23891  return 0;
23892 }
23893 
23894 /* Generator */
23895  static PyMethodDef __pyx_Generator_methods[] = {
23896  {"send", (PyCFunction) __Pyx_Coroutine_Send, METH_O,
23897  (char*) PyDoc_STR("send(arg) -> send 'arg' into generator,\nreturn next yielded value or raise StopIteration.")},
23898  {"throw", (PyCFunction) __Pyx_Coroutine_Throw, METH_VARARGS,
23899  (char*) PyDoc_STR("throw(typ[,val[,tb]]) -> raise exception in generator,\nreturn next yielded value or raise StopIteration.")},
23900  {"close", (PyCFunction) __Pyx_Coroutine_Close, METH_NOARGS,
23901  (char*) PyDoc_STR("close() -> raise GeneratorExit inside generator.")},
23902  {0, 0, 0, 0}
23903 };
23904 static PyMemberDef __pyx_Generator_memberlist[] = {
23905  {(char *) "gi_running", T_BOOL, offsetof(__pyx_CoroutineObject, is_running), READONLY, NULL},
23906  {(char*) "gi_yieldfrom", T_OBJECT, offsetof(__pyx_CoroutineObject, yieldfrom), READONLY,
23907  (char*) PyDoc_STR("object being iterated by 'yield from', or None")},
23908  {(char*) "gi_code", T_OBJECT, offsetof(__pyx_CoroutineObject, gi_code), READONLY, NULL},
23909  {0, 0, 0, 0, 0}
23910 };
23911 static PyGetSetDef __pyx_Generator_getsets[] = {
23912  {(char *) "__name__", (getter)__Pyx_Coroutine_get_name, (setter)__Pyx_Coroutine_set_name,
23913  (char*) PyDoc_STR("name of the generator"), 0},
23914  {(char *) "__qualname__", (getter)__Pyx_Coroutine_get_qualname, (setter)__Pyx_Coroutine_set_qualname,
23915  (char*) PyDoc_STR("qualified name of the generator"), 0},
23916  {0, 0, 0, 0, 0}
23917 };
23918 static PyTypeObject __pyx_GeneratorType_type = {
23919  PyVarObject_HEAD_INIT(0, 0)
23920  "generator",
23921  sizeof(__pyx_CoroutineObject),
23922  0,
23923  (destructor) __Pyx_Coroutine_dealloc,
23924  0,
23925  0,
23926  0,
23927  0,
23928  0,
23929  0,
23930  0,
23931  0,
23932  0,
23933  0,
23934  0,
23935  0,
23936  0,
23937  0,
23938  Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC | Py_TPFLAGS_HAVE_FINALIZE,
23939  0,
23940  (traverseproc) __Pyx_Coroutine_traverse,
23941  0,
23942  0,
23943  offsetof(__pyx_CoroutineObject, gi_weakreflist),
23944  0,
23945  (iternextfunc) __Pyx_Generator_Next,
23946  __pyx_Generator_methods,
23947  __pyx_Generator_memberlist,
23948  __pyx_Generator_getsets,
23949  0,
23950  0,
23951  0,
23952  0,
23953  0,
23954  0,
23955  0,
23956  0,
23957  0,
23958  0,
23959  0,
23960  0,
23961  0,
23962  0,
23963  0,
23964 #if CYTHON_USE_TP_FINALIZE
23965  0,
23966 #else
23967  __Pyx_Coroutine_del,
23968 #endif
23969  0,
23970 #if CYTHON_USE_TP_FINALIZE
23971  __Pyx_Coroutine_del,
23972 #elif PY_VERSION_HEX >= 0x030400a1
23973  0,
23974 #endif
23975 };
23976 static int __pyx_Generator_init(void) {
23977  __pyx_GeneratorType_type.tp_getattro = __Pyx_PyObject_GenericGetAttrNoDict;
23978  __pyx_GeneratorType_type.tp_iter = PyObject_SelfIter;
23979  __pyx_GeneratorType = __Pyx_FetchCommonType(&__pyx_GeneratorType_type);
23980  if (unlikely(!__pyx_GeneratorType)) {
23981  return -1;
23982  }
23983  return 0;
23984 }
23985 
23986 /* CheckBinaryVersion */
23987  static int __Pyx_check_binary_version(void) {
23988  char ctversion[4], rtversion[4];
23989  PyOS_snprintf(ctversion, 4, "%d.%d", PY_MAJOR_VERSION, PY_MINOR_VERSION);
23990  PyOS_snprintf(rtversion, 4, "%s", Py_GetVersion());
23991  if (ctversion[0] != rtversion[0] || ctversion[2] != rtversion[2]) {
23992  char message[200];
23993  PyOS_snprintf(message, sizeof(message),
23994  "compiletime version %s of module '%.100s' "
23995  "does not match runtime version %s",
23996  ctversion, __Pyx_MODULE_NAME, rtversion);
23997  return PyErr_WarnEx(NULL, message, 1);
23998  }
23999  return 0;
24000 }
24001 
24002 /* InitStrings */
24003  static int __Pyx_InitStrings(__Pyx_StringTabEntry *t) {
24004  while (t->p) {
24005  #if PY_MAJOR_VERSION < 3
24006  if (t->is_unicode) {
24007  *t->p = PyUnicode_DecodeUTF8(t->s, t->n - 1, NULL);
24008  } else if (t->intern) {
24009  *t->p = PyString_InternFromString(t->s);
24010  } else {
24011  *t->p = PyString_FromStringAndSize(t->s, t->n - 1);
24012  }
24013  #else
24014  if (t->is_unicode | t->is_str) {
24015  if (t->intern) {
24016  *t->p = PyUnicode_InternFromString(t->s);
24017  } else if (t->encoding) {
24018  *t->p = PyUnicode_Decode(t->s, t->n - 1, t->encoding, NULL);
24019  } else {
24020  *t->p = PyUnicode_FromStringAndSize(t->s, t->n - 1);
24021  }
24022  } else {
24023  *t->p = PyBytes_FromStringAndSize(t->s, t->n - 1);
24024  }
24025  #endif
24026  if (!*t->p)
24027  return -1;
24028  if (PyObject_Hash(*t->p) == -1)
24029  return -1;
24030  ++t;
24031  }
24032  return 0;
24033 }
24034 
24035 static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char* c_str) {
24036  return __Pyx_PyUnicode_FromStringAndSize(c_str, (Py_ssize_t)strlen(c_str));
24037 }
24038 static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject* o) {
24039  Py_ssize_t ignore;
24040  return __Pyx_PyObject_AsStringAndSize(o, &ignore);
24041 }
24042 #if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
24043 #if !CYTHON_PEP393_ENABLED
24044 static const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
24045  char* defenc_c;
24046  PyObject* defenc = _PyUnicode_AsDefaultEncodedString(o, NULL);
24047  if (!defenc) return NULL;
24048  defenc_c = PyBytes_AS_STRING(defenc);
24049 #if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
24050  {
24051  char* end = defenc_c + PyBytes_GET_SIZE(defenc);
24052  char* c;
24053  for (c = defenc_c; c < end; c++) {
24054  if ((unsigned char) (*c) >= 128) {
24055  PyUnicode_AsASCIIString(o);
24056  return NULL;
24057  }
24058  }
24059  }
24060 #endif
24061  *length = PyBytes_GET_SIZE(defenc);
24062  return defenc_c;
24063 }
24064 #else
24065 static CYTHON_INLINE const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
24066  if (unlikely(__Pyx_PyUnicode_READY(o) == -1)) return NULL;
24067 #if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
24068  if (likely(PyUnicode_IS_ASCII(o))) {
24069  *length = PyUnicode_GET_LENGTH(o);
24070  return PyUnicode_AsUTF8(o);
24071  } else {
24072  PyUnicode_AsASCIIString(o);
24073  return NULL;
24074  }
24075 #else
24076  return PyUnicode_AsUTF8AndSize(o, length);
24077 #endif
24078 }
24079 #endif
24080 #endif
24081 static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
24082 #if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
24083  if (
24084 #if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
24085  __Pyx_sys_getdefaultencoding_not_ascii &&
24086 #endif
24087  PyUnicode_Check(o)) {
24088  return __Pyx_PyUnicode_AsStringAndSize(o, length);
24089  } else
24090 #endif
24091 #if (!CYTHON_COMPILING_IN_PYPY) || (defined(PyByteArray_AS_STRING) && defined(PyByteArray_GET_SIZE))
24092  if (PyByteArray_Check(o)) {
24093  *length = PyByteArray_GET_SIZE(o);
24094  return PyByteArray_AS_STRING(o);
24095  } else
24096 #endif
24097  {
24098  char* result;
24099  int r = PyBytes_AsStringAndSize(o, &result, length);
24100  if (unlikely(r < 0)) {
24101  return NULL;
24102  } else {
24103  return result;
24104  }
24105  }
24106 }
24107 static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) {
24108  int is_true = x == Py_True;
24109  if (is_true | (x == Py_False) | (x == Py_None)) return is_true;
24110  else return PyObject_IsTrue(x);
24111 }
24112 static PyObject* __Pyx_PyNumber_IntOrLongWrongResultType(PyObject* result, const char* type_name) {
24113 #if PY_MAJOR_VERSION >= 3
24114  if (PyLong_Check(result)) {
24115  if (PyErr_WarnFormat(PyExc_DeprecationWarning, 1,
24116  "__int__ returned non-int (type %.200s). "
24117  "The ability to return an instance of a strict subclass of int "
24118  "is deprecated, and may be removed in a future version of Python.",
24119  Py_TYPE(result)->tp_name)) {
24120  Py_DECREF(result);
24121  return NULL;
24122  }
24123  return result;
24124  }
24125 #endif
24126  PyErr_Format(PyExc_TypeError,
24127  "__%.4s__ returned non-%.4s (type %.200s)",
24128  type_name, type_name, Py_TYPE(result)->tp_name);
24129  Py_DECREF(result);
24130  return NULL;
24131 }
24132 static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x) {
24133 #if CYTHON_USE_TYPE_SLOTS
24134  PyNumberMethods *m;
24135 #endif
24136  const char *name = NULL;
24137  PyObject *res = NULL;
24138 #if PY_MAJOR_VERSION < 3
24139  if (likely(PyInt_Check(x) || PyLong_Check(x)))
24140 #else
24141  if (likely(PyLong_Check(x)))
24142 #endif
24143  return __Pyx_NewRef(x);
24144 #if CYTHON_USE_TYPE_SLOTS
24145  m = Py_TYPE(x)->tp_as_number;
24146  #if PY_MAJOR_VERSION < 3
24147  if (m && m->nb_int) {
24148  name = "int";
24149  res = m->nb_int(x);
24150  }
24151  else if (m && m->nb_long) {
24152  name = "long";
24153  res = m->nb_long(x);
24154  }
24155  #else
24156  if (likely(m && m->nb_int)) {
24157  name = "int";
24158  res = m->nb_int(x);
24159  }
24160  #endif
24161 #else
24162  if (!PyBytes_CheckExact(x) && !PyUnicode_CheckExact(x)) {
24163  res = PyNumber_Int(x);
24164  }
24165 #endif
24166  if (likely(res)) {
24167 #if PY_MAJOR_VERSION < 3
24168  if (unlikely(!PyInt_Check(res) && !PyLong_Check(res))) {
24169 #else
24170  if (unlikely(!PyLong_CheckExact(res))) {
24171 #endif
24172  return __Pyx_PyNumber_IntOrLongWrongResultType(res, name);
24173  }
24174  }
24175  else if (!PyErr_Occurred()) {
24176  PyErr_SetString(PyExc_TypeError,
24177  "an integer is required");
24178  }
24179  return res;
24180 }
24181 static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject* b) {
24182  Py_ssize_t ival;
24183  PyObject *x;
24184 #if PY_MAJOR_VERSION < 3
24185  if (likely(PyInt_CheckExact(b))) {
24186  if (sizeof(Py_ssize_t) >= sizeof(long))
24187  return PyInt_AS_LONG(b);
24188  else
24189  return PyInt_AsSsize_t(x);
24190  }
24191 #endif
24192  if (likely(PyLong_CheckExact(b))) {
24193  #if CYTHON_USE_PYLONG_INTERNALS
24194  const digit* digits = ((PyLongObject*)b)->ob_digit;
24195  const Py_ssize_t size = Py_SIZE(b);
24196  if (likely(__Pyx_sst_abs(size) <= 1)) {
24197  ival = likely(size) ? digits[0] : 0;
24198  if (size == -1) ival = -ival;
24199  return ival;
24200  } else {
24201  switch (size) {
24202  case 2:
24203  if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
24204  return (Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
24205  }
24206  break;
24207  case -2:
24208  if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
24209  return -(Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
24210  }
24211  break;
24212  case 3:
24213  if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
24214  return (Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
24215  }
24216  break;
24217  case -3:
24218  if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
24219  return -(Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
24220  }
24221  break;
24222  case 4:
24223  if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
24224  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]));
24225  }
24226  break;
24227  case -4:
24228  if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
24229  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]));
24230  }
24231  break;
24232  }
24233  }
24234  #endif
24235  return PyLong_AsSsize_t(b);
24236  }
24237  x = PyNumber_Index(b);
24238  if (!x) return -1;
24239  ival = PyInt_AsSsize_t(x);
24240  Py_DECREF(x);
24241  return ival;
24242 }
24243 static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b) {
24244  return b ? __Pyx_NewRef(Py_True) : __Pyx_NewRef(Py_False);
24245 }
24246 static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) {
24247  return PyInt_FromSize_t(ival);
24248 }
24249 
24250 
24251 #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
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::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
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
glucat::operator!=
bool operator!=(const Multivector< Scalar_T, LO, HI > &lhs, const RHS< Scalar_T, LO, HI > &rhs)
Test for inequality of multivectors.
Definition: clifford_algebra_imp.h:78
cga3::cga3std
Multivector_T cga3std(const Multivector_T &X)
Convert CGA3 null vector to standard Conformal Geometric Algebra null vector [DL (10.52)].
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
Generated on Tue Jul 10 2018 12:00:00 for glucat by   doxygen 1.8.14