-
Notifications
You must be signed in to change notification settings - Fork 315
Expand file tree
/
Copy pathinfinity.cpp
More file actions
537 lines (508 loc) · 16.2 KB
/
Copy pathinfinity.cpp
File metadata and controls
537 lines (508 loc) · 16.2 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
#include <symengine/complex.h>
#include <symengine/complex_double.h>
#include <symengine/constants.h>
#include <symengine/infinity.h>
#include <symengine/functions.h>
#include <symengine/symengine_exception.h>
#include <symengine/complex_mpc.h>
using SymEngine::ComplexMPC;
namespace SymEngine
{
Infty::Infty(const RCP<const Number> &direction)
{
SYMENGINE_ASSIGN_TYPEID()
_direction = direction;
SYMENGINE_ASSERT(is_canonical(_direction));
}
Infty::Infty(const Infty &inf)
{
SYMENGINE_ASSIGN_TYPEID()
_direction = inf.get_direction();
SYMENGINE_ASSERT(is_canonical(_direction))
}
RCP<const Infty> Infty::from_direction(const RCP<const Number> &direction)
{
return make_rcp<Infty>(direction);
}
RCP<const Infty> Infty::from_int(const int val)
{
SYMENGINE_ASSERT(val >= -1 && val <= 1)
return make_rcp<Infty>(integer(val));
}
//! Canonical when the direction is -1, 0 or 1.
bool Infty::is_canonical(const RCP<const Number> &num) const
{
if (is_a<Complex>(*num) || is_a<ComplexDouble>(*num))
throw NotImplementedError("Not implemented for all directions");
if (num->is_one() || num->is_zero() || num->is_minus_one())
return true;
return false;
}
hash_t Infty::__hash__() const
{
hash_t seed = SYMENGINE_INFTY;
hash_combine<Basic>(seed, *_direction);
return seed;
}
bool Infty::__eq__(const Basic &o) const
{
if (is_a<Infty>(o)) {
const Infty &s = down_cast<const Infty &>(o);
return eq(*_direction, *(s.get_direction()));
}
return false;
}
int Infty::compare(const Basic &o) const
{
SYMENGINE_ASSERT(is_a<Infty>(o))
const Infty &s = down_cast<const Infty &>(o);
return _direction->compare(*(s.get_direction()));
}
bool Infty::is_unsigned_infinity() const
{
return _direction->is_zero();
}
bool Infty::is_positive_infinity() const
{
return _direction->is_positive();
}
bool Infty::is_negative_infinity() const
{
return _direction->is_negative();
}
RCP<const Basic> Infty::conjugate() const
{
if (is_positive_infinity() or is_negative_infinity()) {
return infty(_direction);
}
return make_rcp<const Conjugate>(ComplexInf);
}
RCP<const Number> Infty::add(const Number &other) const
{
if (not is_a<Infty>(other))
return rcp_from_this_cast<Number>();
const Infty &s = down_cast<const Infty &>(other);
if (not eq(*s.get_direction(), *_direction))
return Nan;
else if (is_unsigned_infinity())
return Nan;
else
return rcp_from_this_cast<Number>();
}
RCP<const Number> Infty::mul(const Number &other) const
{
if (is_a<Complex>(other))
throw NotImplementedError(
"Multiplication with Complex not implemented");
if (is_a<Infty>(other)) {
const Infty &s = down_cast<const Infty &>(other);
return make_rcp<const Infty>(this->_direction->mul(*(s._direction)));
} else {
if (other.is_positive())
return rcp_from_this_cast<Number>();
else if (other.is_negative())
return make_rcp<const Infty>(this->_direction->mul(*minus_one));
else
return Nan;
}
}
RCP<const Number> Infty::div(const Number &other) const
{
if (is_a<Infty>(other)) {
return Nan;
} else {
if (other.is_positive())
return rcp_from_this_cast<Number>();
else if (other.is_zero())
return infty(0);
else
return infty(this->_direction->mul(*minus_one));
}
}
RCP<const Number> Infty::pow(const Number &other) const
{
if (is_a<Infty>(other)) {
if (is_positive_infinity()) {
if (other.is_negative()) {
return zero;
} else if (other.is_positive()) {
return rcp_from_this_cast<Number>();
} else {
return Nan;
}
} else if (is_negative_infinity()) {
return Nan;
} else {
if (other.is_positive()) {
return infty(0);
} else if (other.is_negative()) {
return zero;
} else {
return Nan;
}
}
} else if (is_a<Complex>(other)) {
throw NotImplementedError(
"Raising to the Complex powers not yet implemented");
} else {
if (other.is_negative()) {
return zero;
} else if (other.is_zero()) {
return one;
} else {
if (is_positive_infinity()) {
return rcp_from_this_cast<Number>();
} else if (is_negative_infinity()) {
throw NotImplementedError("Raising Negative Infty to the "
"Positive Real powers not yet "
"implemented");
} else {
return infty(0);
}
}
}
}
RCP<const Number> Infty::rpow(const Number &other) const
{
if (is_a_Complex(other)) {
throw NotImplementedError(
"Raising Complex powers to Infty not yet implemented");
} else {
if (other.is_negative()) {
throw NotImplementedError("Raising Negative numbers to infinite "
"powers not yet implemented");
} else if (other.is_zero()) {
throw SymEngineException("Indeterminate Expression: `0 ** +- "
"unsigned Infty` encountered");
} else {
const Number &s = down_cast<const Number &>(other);
if (s.is_one()) {
return Nan;
} else if (is_positive_infinity()) {
if (s.sub(*one)->is_negative()) {
return zero;
} else {
return rcp_from_this_cast<Number>();
}
} else if (is_negative_infinity()) {
if (s.sub(*one)->is_negative()) {
return infty(0);
} else {
return zero;
}
} else {
throw SymEngineException("Indeterminate Expression: `Positive "
"Real Number ** unsigned Infty` "
"encountered");
}
}
}
}
inline RCP<const Infty> infty(const RCP<const Number> &direction)
{
return make_rcp<Infty>(direction);
}
class EvaluateInfty : public Evaluate
{
RCP<const Basic> sin(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
throw DomainError("sin is not defined for infinite values");
}
RCP<const Basic> cos(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
throw DomainError("cos is not defined for infinite values");
}
RCP<const Basic> tan(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
throw DomainError("tan is not defined for infinite values");
}
RCP<const Basic> cot(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
throw DomainError("cot is not defined for infinite values");
}
RCP<const Basic> sec(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
throw DomainError("sec is not defined for infinite values");
}
RCP<const Basic> csc(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
throw DomainError("csc is not defined for infinite values");
}
RCP<const Basic> asin(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
throw DomainError("asin is not defined for infinite values");
}
RCP<const Basic> acos(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
throw DomainError("acos is not defined for infinite values");
}
RCP<const Basic> acsc(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
throw DomainError("acsc is not defined for infinite values");
}
RCP<const Basic> asec(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
throw DomainError("asec is not defined for infinite values");
}
RCP<const Basic> atan(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
const Infty &s = down_cast<const Infty &>(x);
if (s.is_positive()) {
return div(pi, integer(2));
} else if (s.is_negative()) {
return mul(minus_one, (div(pi, integer(2))));
} else {
throw DomainError("atan is not defined for Complex Infinity");
}
}
RCP<const Basic> acot(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
const Infty &s = down_cast<const Infty &>(x);
if (s.is_positive() or s.is_negative()) {
return zero;
} else {
throw DomainError("acot is not defined for Complex Infinity");
}
}
RCP<const Basic> sinh(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
const Infty &s = down_cast<const Infty &>(x);
if (s.is_positive() or s.is_negative()) {
return infty(s.get_direction());
} else {
throw DomainError("sinh is not defined for Complex Infinity");
}
}
RCP<const Basic> csch(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
const Infty &s = down_cast<const Infty &>(x);
if (s.is_positive() or s.is_negative()) {
return zero;
} else {
throw DomainError("csch is not defined for Complex Infinity");
}
}
RCP<const Basic> cosh(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
const Infty &s = down_cast<const Infty &>(x);
if (s.is_positive() or s.is_negative()) {
return Inf;
} else {
throw DomainError("cosh is not defined for Complex Infinity");
}
}
RCP<const Basic> sech(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
const Infty &s = down_cast<const Infty &>(x);
if (s.is_positive() or s.is_negative()) {
return zero;
} else {
throw DomainError("sech is not defined for Complex Infinity");
}
}
RCP<const Basic> tanh(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
const Infty &s = down_cast<const Infty &>(x);
if (s.is_positive()) {
return one;
} else if (s.is_negative()) {
return minus_one;
} else {
throw DomainError("tanh is not defined for Complex Infinity");
}
}
RCP<const Basic> coth(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
const Infty &s = down_cast<const Infty &>(x);
if (s.is_positive()) {
return one;
} else if (s.is_negative()) {
return minus_one;
} else {
throw DomainError("coth is not defined for Complex Infinity");
}
}
RCP<const Basic> asinh(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
const Infty &s = down_cast<const Infty &>(x);
if (s.is_positive() or s.is_negative()) {
return infty(s.get_direction());
} else {
throw DomainError("asinh is not defined for Complex Infinity");
}
}
RCP<const Basic> acosh(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
const Infty &s = down_cast<const Infty &>(x);
if (s.is_positive() or s.is_negative()) {
return Inf;
} else {
throw DomainError("acosh is not defined for Complex Infinity");
}
}
RCP<const Basic> acsch(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
const Infty &s = down_cast<const Infty &>(x);
if (s.is_positive() or s.is_negative()) {
return zero;
} else {
throw DomainError("acsch is not defined for Complex Infinity");
}
}
RCP<const Basic> asech(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
const Infty &s = down_cast<const Infty &>(x);
if (s.is_positive() or s.is_negative()) {
return mul(mul(I, pi), div(one, integer(2)));
} else {
throw DomainError("asech is not defined for Complex Infinity");
}
}
RCP<const Basic> atanh(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
const Infty &s = down_cast<const Infty &>(x);
if (s.is_positive()) {
return mul(minus_one, div(mul(pi, I), integer(2)));
} else if (s.is_negative()) {
return div(mul(pi, I), integer(2));
} else {
throw DomainError("atanh is not defined for Complex Infinity");
}
}
RCP<const Basic> acoth(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
const Infty &s = down_cast<const Infty &>(x);
if (s.is_positive() or s.is_negative()) {
return zero;
} else {
throw DomainError("acoth is not defined for Complex Infinity");
}
}
RCP<const Basic> abs(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
return Inf;
}
RCP<const Basic> log(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
const Infty &s = down_cast<const Infty &>(x);
if (s.is_positive() or s.is_negative()) {
return Inf;
} else {
return ComplexInf;
}
}
RCP<const Basic> gamma(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
const Infty &s = down_cast<const Infty &>(x);
if (s.is_positive()) {
return Inf;
} else {
return ComplexInf;
}
}
RCP<const Basic> exp(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
const Infty &s = down_cast<const Infty &>(x);
if (s.is_positive()) {
return Inf;
} else if (s.is_negative()) {
return zero;
} else {
throw DomainError("exp is not defined for Complex Infinity");
}
}
RCP<const Basic> floor(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
const Infty &s = down_cast<const Infty &>(x);
if (s.is_positive()) {
return Inf;
} else if (s.is_negative()) {
return NegInf;
} else {
throw DomainError("floor is not defined for Complex Infinity");
}
}
RCP<const Basic> ceiling(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
const Infty &s = down_cast<const Infty &>(x);
if (s.is_positive()) {
return Inf;
} else if (s.is_negative()) {
return NegInf;
} else {
throw DomainError("ceiling is not defined for Complex Infinity");
}
}
RCP<const Basic> truncate(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
const Infty &s = down_cast<const Infty &>(x);
if (s.is_positive()) {
return Inf;
} else if (s.is_negative()) {
return NegInf;
} else {
throw DomainError("truncate is not defined for Complex Infinity");
}
}
RCP<const Basic> erf(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
const Infty &s = down_cast<const Infty &>(x);
if (s.is_positive()) {
return one;
} else if (s.is_negative()) {
return minus_one;
} else {
throw DomainError("erf is not defined for Complex Infinity");
}
}
RCP<const Basic> erfc(const Basic &x) const override
{
SYMENGINE_ASSERT(is_a<Infty>(x))
const Infty &s = down_cast<const Infty &>(x);
if (s.is_positive()) {
return zero;
} else if (s.is_negative()) {
return integer(2);
} else {
throw DomainError("erfc is not defined for Complex Infinity");
}
}
};
Evaluate &Infty::get_eval() const
{
static EvaluateInfty evaluate_infty;
return evaluate_infty;
}
} // namespace SymEngine