Line data Source code
1 : /* Complex math module */
2 :
3 : /* much code borrowed from mathmodule.c */
4 :
5 : #ifndef Py_BUILD_CORE_BUILTIN
6 : # define Py_BUILD_CORE_MODULE 1
7 : #endif
8 :
9 : #include "Python.h"
10 : #include "pycore_pymath.h" // _PY_SHORT_FLOAT_REPR
11 : #include "pycore_dtoa.h" // _Py_dg_stdnan()
12 : /* we need DBL_MAX, DBL_MIN, DBL_EPSILON, DBL_MANT_DIG and FLT_RADIX from
13 : float.h. We assume that FLT_RADIX is either 2 or 16. */
14 : #include <float.h>
15 :
16 : /* For _Py_log1p with workarounds for buggy handling of zeros. */
17 : #include "_math.h"
18 :
19 : #include "clinic/cmathmodule.c.h"
20 : /*[clinic input]
21 : module cmath
22 : [clinic start generated code]*/
23 : /*[clinic end generated code: output=da39a3ee5e6b4b0d input=308d6839f4a46333]*/
24 :
25 : /*[python input]
26 : class Py_complex_protected_converter(Py_complex_converter):
27 : def modify(self):
28 : return 'errno = 0;'
29 :
30 :
31 : class Py_complex_protected_return_converter(CReturnConverter):
32 : type = "Py_complex"
33 :
34 : def render(self, function, data):
35 : self.declare(data)
36 : data.return_conversion.append("""
37 : if (errno == EDOM) {
38 : PyErr_SetString(PyExc_ValueError, "math domain error");
39 : goto exit;
40 : }
41 : else if (errno == ERANGE) {
42 : PyErr_SetString(PyExc_OverflowError, "math range error");
43 : goto exit;
44 : }
45 : else {
46 : return_value = PyComplex_FromCComplex(_return_value);
47 : }
48 : """.strip())
49 : [python start generated code]*/
50 : /*[python end generated code: output=da39a3ee5e6b4b0d input=8b27adb674c08321]*/
51 :
52 : #if (FLT_RADIX != 2 && FLT_RADIX != 16)
53 : #error "Modules/cmathmodule.c expects FLT_RADIX to be 2 or 16"
54 : #endif
55 :
56 : #ifndef M_LN2
57 : #define M_LN2 (0.6931471805599453094) /* natural log of 2 */
58 : #endif
59 :
60 : #ifndef M_LN10
61 : #define M_LN10 (2.302585092994045684) /* natural log of 10 */
62 : #endif
63 :
64 : /*
65 : CM_LARGE_DOUBLE is used to avoid spurious overflow in the sqrt, log,
66 : inverse trig and inverse hyperbolic trig functions. Its log is used in the
67 : evaluation of exp, cos, cosh, sin, sinh, tan, and tanh to avoid unnecessary
68 : overflow.
69 : */
70 :
71 : #define CM_LARGE_DOUBLE (DBL_MAX/4.)
72 : #define CM_SQRT_LARGE_DOUBLE (sqrt(CM_LARGE_DOUBLE))
73 : #define CM_LOG_LARGE_DOUBLE (log(CM_LARGE_DOUBLE))
74 : #define CM_SQRT_DBL_MIN (sqrt(DBL_MIN))
75 :
76 : /*
77 : CM_SCALE_UP is an odd integer chosen such that multiplication by
78 : 2**CM_SCALE_UP is sufficient to turn a subnormal into a normal.
79 : CM_SCALE_DOWN is (-(CM_SCALE_UP+1)/2). These scalings are used to compute
80 : square roots accurately when the real and imaginary parts of the argument
81 : are subnormal.
82 : */
83 :
84 : #if FLT_RADIX==2
85 : #define CM_SCALE_UP (2*(DBL_MANT_DIG/2) + 1)
86 : #elif FLT_RADIX==16
87 : #define CM_SCALE_UP (4*DBL_MANT_DIG+1)
88 : #endif
89 : #define CM_SCALE_DOWN (-(CM_SCALE_UP+1)/2)
90 :
91 : /* Constants cmath.inf, cmath.infj, cmath.nan, cmath.nanj.
92 : cmath.nan and cmath.nanj are defined only when either
93 : _PY_SHORT_FLOAT_REPR is 1 (which should be
94 : the most common situation on machines using an IEEE 754
95 : representation), or Py_NAN is defined. */
96 :
97 : static double
98 4 : m_inf(void)
99 : {
100 : #if _PY_SHORT_FLOAT_REPR == 1
101 4 : return _Py_dg_infinity(0);
102 : #else
103 : return Py_HUGE_VAL;
104 : #endif
105 : }
106 :
107 : static Py_complex
108 2 : c_infj(void)
109 : {
110 : Py_complex r;
111 2 : r.real = 0.0;
112 2 : r.imag = m_inf();
113 2 : return r;
114 : }
115 :
116 : #if _PY_SHORT_FLOAT_REPR == 1
117 :
118 : static double
119 4 : m_nan(void)
120 : {
121 : #if _PY_SHORT_FLOAT_REPR == 1
122 4 : return _Py_dg_stdnan(0);
123 : #else
124 : return Py_NAN;
125 : #endif
126 : }
127 :
128 : static Py_complex
129 2 : c_nanj(void)
130 : {
131 : Py_complex r;
132 2 : r.real = 0.0;
133 2 : r.imag = m_nan();
134 2 : return r;
135 : }
136 :
137 : #endif
138 :
139 : /* forward declarations */
140 : static Py_complex cmath_asinh_impl(PyObject *, Py_complex);
141 : static Py_complex cmath_atanh_impl(PyObject *, Py_complex);
142 : static Py_complex cmath_cosh_impl(PyObject *, Py_complex);
143 : static Py_complex cmath_sinh_impl(PyObject *, Py_complex);
144 : static Py_complex cmath_sqrt_impl(PyObject *, Py_complex);
145 : static Py_complex cmath_tanh_impl(PyObject *, Py_complex);
146 : static PyObject * math_error(void);
147 :
148 : /* Code to deal with special values (infinities, NaNs, etc.). */
149 :
150 : /* special_type takes a double and returns an integer code indicating
151 : the type of the double as follows:
152 : */
153 :
154 : enum special_types {
155 : ST_NINF, /* 0, negative infinity */
156 : ST_NEG, /* 1, negative finite number (nonzero) */
157 : ST_NZERO, /* 2, -0. */
158 : ST_PZERO, /* 3, +0. */
159 : ST_POS, /* 4, positive finite number (nonzero) */
160 : ST_PINF, /* 5, positive infinity */
161 : ST_NAN /* 6, Not a Number */
162 : };
163 :
164 : static enum special_types
165 1058 : special_type(double d)
166 : {
167 1058 : if (Py_IS_FINITE(d)) {
168 376 : if (d != 0) {
169 172 : if (copysign(1., d) == 1.)
170 86 : return ST_POS;
171 : else
172 86 : return ST_NEG;
173 : }
174 : else {
175 204 : if (copysign(1., d) == 1.)
176 102 : return ST_PZERO;
177 : else
178 102 : return ST_NZERO;
179 : }
180 : }
181 682 : if (Py_IS_NAN(d))
182 238 : return ST_NAN;
183 444 : if (copysign(1., d) == 1.)
184 222 : return ST_PINF;
185 : else
186 222 : return ST_NINF;
187 : }
188 :
189 : #define SPECIAL_VALUE(z, table) \
190 : if (!Py_IS_FINITE((z).real) || !Py_IS_FINITE((z).imag)) { \
191 : errno = 0; \
192 : return table[special_type((z).real)] \
193 : [special_type((z).imag)]; \
194 : }
195 :
196 : #define P Py_MATH_PI
197 : #define P14 0.25*Py_MATH_PI
198 : #define P12 0.5*Py_MATH_PI
199 : #define P34 0.75*Py_MATH_PI
200 : #define INF Py_HUGE_VAL
201 : #define N Py_NAN
202 : #define U -9.5426319407711027e33 /* unlikely value, used as placeholder */
203 :
204 : /* First, the C functions that do the real work. Each of the c_*
205 : functions computes and returns the C99 Annex G recommended result
206 : and also sets errno as follows: errno = 0 if no floating-point
207 : exception is associated with the result; errno = EDOM if C99 Annex
208 : G recommends raising divide-by-zero or invalid for this result; and
209 : errno = ERANGE where the overflow floating-point signal should be
210 : raised.
211 : */
212 :
213 : static Py_complex acos_special_values[7][7];
214 :
215 : /*[clinic input]
216 : cmath.acos -> Py_complex_protected
217 :
218 : z: Py_complex_protected
219 : /
220 :
221 : Return the arc cosine of z.
222 : [clinic start generated code]*/
223 :
224 : static Py_complex
225 186 : cmath_acos_impl(PyObject *module, Py_complex z)
226 : /*[clinic end generated code: output=40bd42853fd460ae input=bd6cbd78ae851927]*/
227 : {
228 : Py_complex s1, s2, r;
229 :
230 186 : SPECIAL_VALUE(z, acos_special_values);
231 :
232 153 : if (fabs(z.real) > CM_LARGE_DOUBLE || fabs(z.imag) > CM_LARGE_DOUBLE) {
233 : /* avoid unnecessary overflow for large arguments */
234 20 : r.real = atan2(fabs(z.imag), z.real);
235 : /* split into cases to make sure that the branch cut has the
236 : correct continuity on systems with unsigned zeros */
237 20 : if (z.real < 0.) {
238 8 : r.imag = -copysign(log(hypot(z.real/2., z.imag/2.)) +
239 : M_LN2*2., z.imag);
240 : } else {
241 12 : r.imag = copysign(log(hypot(z.real/2., z.imag/2.)) +
242 12 : M_LN2*2., -z.imag);
243 : }
244 : } else {
245 133 : s1.real = 1.-z.real;
246 133 : s1.imag = -z.imag;
247 133 : s1 = cmath_sqrt_impl(module, s1);
248 133 : s2.real = 1.+z.real;
249 133 : s2.imag = z.imag;
250 133 : s2 = cmath_sqrt_impl(module, s2);
251 133 : r.real = 2.*atan2(s1.real, s2.real);
252 133 : r.imag = asinh(s2.real*s1.imag - s2.imag*s1.real);
253 : }
254 153 : errno = 0;
255 153 : return r;
256 : }
257 :
258 :
259 : static Py_complex acosh_special_values[7][7];
260 :
261 : /*[clinic input]
262 : cmath.acosh = cmath.acos
263 :
264 : Return the inverse hyperbolic cosine of z.
265 : [clinic start generated code]*/
266 :
267 : static Py_complex
268 171 : cmath_acosh_impl(PyObject *module, Py_complex z)
269 : /*[clinic end generated code: output=3e2454d4fcf404ca input=3f61bee7d703e53c]*/
270 : {
271 : Py_complex s1, s2, r;
272 :
273 171 : SPECIAL_VALUE(z, acosh_special_values);
274 :
275 138 : if (fabs(z.real) > CM_LARGE_DOUBLE || fabs(z.imag) > CM_LARGE_DOUBLE) {
276 : /* avoid unnecessary overflow for large arguments */
277 20 : r.real = log(hypot(z.real/2., z.imag/2.)) + M_LN2*2.;
278 20 : r.imag = atan2(z.imag, z.real);
279 : } else {
280 118 : s1.real = z.real - 1.;
281 118 : s1.imag = z.imag;
282 118 : s1 = cmath_sqrt_impl(module, s1);
283 118 : s2.real = z.real + 1.;
284 118 : s2.imag = z.imag;
285 118 : s2 = cmath_sqrt_impl(module, s2);
286 118 : r.real = asinh(s1.real*s2.real + s1.imag*s2.imag);
287 118 : r.imag = 2.*atan2(s1.imag, s2.real);
288 : }
289 138 : errno = 0;
290 138 : return r;
291 : }
292 :
293 : /*[clinic input]
294 : cmath.asin = cmath.acos
295 :
296 : Return the arc sine of z.
297 : [clinic start generated code]*/
298 :
299 : static Py_complex
300 174 : cmath_asin_impl(PyObject *module, Py_complex z)
301 : /*[clinic end generated code: output=3b264cd1b16bf4e1 input=be0bf0cfdd5239c5]*/
302 : {
303 : /* asin(z) = -i asinh(iz) */
304 : Py_complex s, r;
305 174 : s.real = -z.imag;
306 174 : s.imag = z.real;
307 174 : s = cmath_asinh_impl(module, s);
308 174 : r.real = s.imag;
309 174 : r.imag = -s.real;
310 174 : return r;
311 : }
312 :
313 :
314 : static Py_complex asinh_special_values[7][7];
315 :
316 : /*[clinic input]
317 : cmath.asinh = cmath.acos
318 :
319 : Return the inverse hyperbolic sine of z.
320 : [clinic start generated code]*/
321 :
322 : static Py_complex
323 345 : cmath_asinh_impl(PyObject *module, Py_complex z)
324 : /*[clinic end generated code: output=733d8107841a7599 input=5c09448fcfc89a79]*/
325 : {
326 : Py_complex s1, s2, r;
327 :
328 345 : SPECIAL_VALUE(z, asinh_special_values);
329 :
330 279 : if (fabs(z.real) > CM_LARGE_DOUBLE || fabs(z.imag) > CM_LARGE_DOUBLE) {
331 40 : if (z.imag >= 0.) {
332 24 : r.real = copysign(log(hypot(z.real/2., z.imag/2.)) +
333 : M_LN2*2., z.real);
334 : } else {
335 16 : r.real = -copysign(log(hypot(z.real/2., z.imag/2.)) +
336 16 : M_LN2*2., -z.real);
337 : }
338 40 : r.imag = atan2(z.imag, fabs(z.real));
339 : } else {
340 239 : s1.real = 1.+z.imag;
341 239 : s1.imag = -z.real;
342 239 : s1 = cmath_sqrt_impl(module, s1);
343 239 : s2.real = 1.-z.imag;
344 239 : s2.imag = z.real;
345 239 : s2 = cmath_sqrt_impl(module, s2);
346 239 : r.real = asinh(s1.real*s2.imag-s2.real*s1.imag);
347 239 : r.imag = atan2(z.imag, s1.real*s2.real-s1.imag*s2.imag);
348 : }
349 279 : errno = 0;
350 279 : return r;
351 : }
352 :
353 :
354 : /*[clinic input]
355 : cmath.atan = cmath.acos
356 :
357 : Return the arc tangent of z.
358 : [clinic start generated code]*/
359 :
360 : static Py_complex
361 201 : cmath_atan_impl(PyObject *module, Py_complex z)
362 : /*[clinic end generated code: output=b6bfc497058acba4 input=3b21ff7d5eac632a]*/
363 : {
364 : /* atan(z) = -i atanh(iz) */
365 : Py_complex s, r;
366 201 : s.real = -z.imag;
367 201 : s.imag = z.real;
368 201 : s = cmath_atanh_impl(module, s);
369 201 : r.real = s.imag;
370 201 : r.imag = -s.real;
371 201 : return r;
372 : }
373 :
374 : /* Windows screws up atan2 for inf and nan, and alpha Tru64 5.1 doesn't follow
375 : C99 for atan2(0., 0.). */
376 : static double
377 121 : c_atan2(Py_complex z)
378 : {
379 121 : if (Py_IS_NAN(z.real) || Py_IS_NAN(z.imag))
380 39 : return Py_NAN;
381 82 : if (Py_IS_INFINITY(z.imag)) {
382 36 : if (Py_IS_INFINITY(z.real)) {
383 16 : if (copysign(1., z.real) == 1.)
384 : /* atan2(+-inf, +inf) == +-pi/4 */
385 8 : return copysign(0.25*Py_MATH_PI, z.imag);
386 : else
387 : /* atan2(+-inf, -inf) == +-pi*3/4 */
388 8 : return copysign(0.75*Py_MATH_PI, z.imag);
389 : }
390 : /* atan2(+-inf, x) == +-pi/2 for finite x */
391 20 : return copysign(0.5*Py_MATH_PI, z.imag);
392 : }
393 46 : if (Py_IS_INFINITY(z.real) || z.imag == 0.) {
394 37 : if (copysign(1., z.real) == 1.)
395 : /* atan2(+-y, +inf) = atan2(+-0, +x) = +-0. */
396 20 : return copysign(0., z.imag);
397 : else
398 : /* atan2(+-y, -inf) = atan2(+-0., -x) = +-pi. */
399 17 : return copysign(Py_MATH_PI, z.imag);
400 : }
401 9 : return atan2(z.imag, z.real);
402 : }
403 :
404 :
405 : static Py_complex atanh_special_values[7][7];
406 :
407 : /*[clinic input]
408 : cmath.atanh = cmath.acos
409 :
410 : Return the inverse hyperbolic tangent of z.
411 : [clinic start generated code]*/
412 :
413 : static Py_complex
414 493 : cmath_atanh_impl(PyObject *module, Py_complex z)
415 : /*[clinic end generated code: output=e83355f93a989c9e input=2b3fdb82fb34487b]*/
416 : {
417 : Py_complex r;
418 : double ay, h;
419 :
420 493 : SPECIAL_VALUE(z, atanh_special_values);
421 :
422 : /* Reduce to case where z.real >= 0., using atanh(z) = -atanh(-z). */
423 427 : if (z.real < 0.) {
424 116 : return _Py_c_neg(cmath_atanh_impl(module, _Py_c_neg(z)));
425 : }
426 :
427 311 : ay = fabs(z.imag);
428 311 : if (z.real > CM_SQRT_LARGE_DOUBLE || ay > CM_SQRT_LARGE_DOUBLE) {
429 : /*
430 : if abs(z) is large then we use the approximation
431 : atanh(z) ~ 1/z +/- i*pi/2 (+/- depending on the sign
432 : of z.imag)
433 : */
434 50 : h = hypot(z.real/2., z.imag/2.); /* safe from overflow */
435 50 : r.real = z.real/4./h/h;
436 : /* the two negations in the next line cancel each other out
437 : except when working with unsigned zeros: they're there to
438 : ensure that the branch cut has the correct continuity on
439 : systems that don't support signed zeros */
440 50 : r.imag = -copysign(Py_MATH_PI/2., -z.imag);
441 50 : errno = 0;
442 261 : } else if (z.real == 1. && ay < CM_SQRT_DBL_MIN) {
443 : /* C99 standard says: atanh(1+/-0.) should be inf +/- 0i */
444 16 : if (ay == 0.) {
445 8 : r.real = INF;
446 8 : r.imag = z.imag;
447 8 : errno = EDOM;
448 : } else {
449 8 : r.real = -log(sqrt(ay)/sqrt(hypot(ay, 2.)));
450 8 : r.imag = copysign(atan2(2., -ay)/2, z.imag);
451 8 : errno = 0;
452 : }
453 : } else {
454 245 : r.real = m_log1p(4.*z.real/((1-z.real)*(1-z.real) + ay*ay))/4.;
455 245 : r.imag = -atan2(-2.*z.imag, (1-z.real)*(1+z.real) - ay*ay)/2.;
456 245 : errno = 0;
457 : }
458 311 : return r;
459 : }
460 :
461 :
462 : /*[clinic input]
463 : cmath.cos = cmath.acos
464 :
465 : Return the cosine of z.
466 : [clinic start generated code]*/
467 :
468 : static Py_complex
469 136 : cmath_cos_impl(PyObject *module, Py_complex z)
470 : /*[clinic end generated code: output=fd64918d5b3186db input=6022e39b77127ac7]*/
471 : {
472 : /* cos(z) = cosh(iz) */
473 : Py_complex r;
474 136 : r.real = -z.imag;
475 136 : r.imag = z.real;
476 136 : r = cmath_cosh_impl(module, r);
477 136 : return r;
478 : }
479 :
480 :
481 : /* cosh(infinity + i*y) needs to be dealt with specially */
482 : static Py_complex cosh_special_values[7][7];
483 :
484 : /*[clinic input]
485 : cmath.cosh = cmath.acos
486 :
487 : Return the hyperbolic cosine of z.
488 : [clinic start generated code]*/
489 :
490 : static Py_complex
491 275 : cmath_cosh_impl(PyObject *module, Py_complex z)
492 : /*[clinic end generated code: output=2e969047da601bdb input=d6b66339e9cc332b]*/
493 : {
494 : Py_complex r;
495 : double x_minus_one;
496 :
497 : /* special treatment for cosh(+/-inf + iy) if y is not a NaN */
498 275 : if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) {
499 98 : if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag) &&
500 48 : (z.imag != 0.)) {
501 40 : if (z.real > 0) {
502 20 : r.real = copysign(INF, cos(z.imag));
503 20 : r.imag = copysign(INF, sin(z.imag));
504 : }
505 : else {
506 20 : r.real = copysign(INF, cos(z.imag));
507 20 : r.imag = -copysign(INF, sin(z.imag));
508 : }
509 : }
510 : else {
511 116 : r = cosh_special_values[special_type(z.real)]
512 58 : [special_type(z.imag)];
513 : }
514 : /* need to set errno = EDOM if y is +/- infinity and x is not
515 : a NaN */
516 98 : if (Py_IS_INFINITY(z.imag) && !Py_IS_NAN(z.real))
517 24 : errno = EDOM;
518 : else
519 74 : errno = 0;
520 98 : return r;
521 : }
522 :
523 177 : if (fabs(z.real) > CM_LOG_LARGE_DOUBLE) {
524 : /* deal correctly with cases where cosh(z.real) overflows but
525 : cosh(z) does not. */
526 4 : x_minus_one = z.real - copysign(1., z.real);
527 4 : r.real = cos(z.imag) * cosh(x_minus_one) * Py_MATH_E;
528 4 : r.imag = sin(z.imag) * sinh(x_minus_one) * Py_MATH_E;
529 : } else {
530 173 : r.real = cos(z.imag) * cosh(z.real);
531 173 : r.imag = sin(z.imag) * sinh(z.real);
532 : }
533 : /* detect overflow, and set errno accordingly */
534 177 : if (Py_IS_INFINITY(r.real) || Py_IS_INFINITY(r.imag))
535 0 : errno = ERANGE;
536 : else
537 177 : errno = 0;
538 177 : return r;
539 : }
540 :
541 :
542 : /* exp(infinity + i*y) and exp(-infinity + i*y) need special treatment for
543 : finite y */
544 : static Py_complex exp_special_values[7][7];
545 :
546 : /*[clinic input]
547 : cmath.exp = cmath.acos
548 :
549 : Return the exponential value e**z.
550 : [clinic start generated code]*/
551 :
552 : static Py_complex
553 148 : cmath_exp_impl(PyObject *module, Py_complex z)
554 : /*[clinic end generated code: output=edcec61fb9dfda6c input=8b9e6cf8a92174c3]*/
555 : {
556 : Py_complex r;
557 : double l;
558 :
559 148 : if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) {
560 49 : if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag)
561 24 : && (z.imag != 0.)) {
562 20 : if (z.real > 0) {
563 10 : r.real = copysign(INF, cos(z.imag));
564 10 : r.imag = copysign(INF, sin(z.imag));
565 : }
566 : else {
567 10 : r.real = copysign(0., cos(z.imag));
568 10 : r.imag = copysign(0., sin(z.imag));
569 : }
570 : }
571 : else {
572 58 : r = exp_special_values[special_type(z.real)]
573 29 : [special_type(z.imag)];
574 : }
575 : /* need to set errno = EDOM if y is +/- infinity and x is not
576 : a NaN and not -infinity */
577 49 : if (Py_IS_INFINITY(z.imag) &&
578 14 : (Py_IS_FINITE(z.real) ||
579 6 : (Py_IS_INFINITY(z.real) && z.real > 0)))
580 10 : errno = EDOM;
581 : else
582 39 : errno = 0;
583 49 : return r;
584 : }
585 :
586 99 : if (z.real > CM_LOG_LARGE_DOUBLE) {
587 8 : l = exp(z.real-1.);
588 8 : r.real = l*cos(z.imag)*Py_MATH_E;
589 8 : r.imag = l*sin(z.imag)*Py_MATH_E;
590 : } else {
591 91 : l = exp(z.real);
592 91 : r.real = l*cos(z.imag);
593 91 : r.imag = l*sin(z.imag);
594 : }
595 : /* detect overflow, and set errno accordingly */
596 99 : if (Py_IS_INFINITY(r.real) || Py_IS_INFINITY(r.imag))
597 5 : errno = ERANGE;
598 : else
599 94 : errno = 0;
600 99 : return r;
601 : }
602 :
603 : static Py_complex log_special_values[7][7];
604 :
605 : static Py_complex
606 538 : c_log(Py_complex z)
607 : {
608 : /*
609 : The usual formula for the real part is log(hypot(z.real, z.imag)).
610 : There are four situations where this formula is potentially
611 : problematic:
612 :
613 : (1) the absolute value of z is subnormal. Then hypot is subnormal,
614 : so has fewer than the usual number of bits of accuracy, hence may
615 : have large relative error. This then gives a large absolute error
616 : in the log. This can be solved by rescaling z by a suitable power
617 : of 2.
618 :
619 : (2) the absolute value of z is greater than DBL_MAX (e.g. when both
620 : z.real and z.imag are within a factor of 1/sqrt(2) of DBL_MAX)
621 : Again, rescaling solves this.
622 :
623 : (3) the absolute value of z is close to 1. In this case it's
624 : difficult to achieve good accuracy, at least in part because a
625 : change of 1ulp in the real or imaginary part of z can result in a
626 : change of billions of ulps in the correctly rounded answer.
627 :
628 : (4) z = 0. The simplest thing to do here is to call the
629 : floating-point log with an argument of 0, and let its behaviour
630 : (returning -infinity, signaling a floating-point exception, setting
631 : errno, or whatever) determine that of c_log. So the usual formula
632 : is fine here.
633 :
634 : */
635 :
636 : Py_complex r;
637 : double ax, ay, am, an, h;
638 :
639 538 : SPECIAL_VALUE(z, log_special_values);
640 :
641 472 : ax = fabs(z.real);
642 472 : ay = fabs(z.imag);
643 :
644 472 : if (ax > CM_LARGE_DOUBLE || ay > CM_LARGE_DOUBLE) {
645 40 : r.real = log(hypot(ax/2., ay/2.)) + M_LN2;
646 432 : } else if (ax < DBL_MIN && ay < DBL_MIN) {
647 36 : if (ax > 0. || ay > 0.) {
648 : /* catch cases where hypot(ax, ay) is subnormal */
649 28 : r.real = log(hypot(ldexp(ax, DBL_MANT_DIG),
650 28 : ldexp(ay, DBL_MANT_DIG))) - DBL_MANT_DIG*M_LN2;
651 : }
652 : else {
653 : /* log(+/-0. +/- 0i) */
654 8 : r.real = -INF;
655 8 : r.imag = atan2(z.imag, z.real);
656 8 : errno = EDOM;
657 8 : return r;
658 : }
659 : } else {
660 396 : h = hypot(ax, ay);
661 396 : if (0.71 <= h && h <= 1.73) {
662 65 : am = ax > ay ? ax : ay; /* max(ax, ay) */
663 65 : an = ax > ay ? ay : ax; /* min(ax, ay) */
664 65 : r.real = m_log1p((am-1)*(am+1)+an*an)/2.;
665 : } else {
666 331 : r.real = log(h);
667 : }
668 : }
669 464 : r.imag = atan2(z.imag, z.real);
670 464 : errno = 0;
671 464 : return r;
672 : }
673 :
674 :
675 : /*[clinic input]
676 : cmath.log10 = cmath.acos
677 :
678 : Return the base-10 logarithm of z.
679 : [clinic start generated code]*/
680 :
681 : static Py_complex
682 182 : cmath_log10_impl(PyObject *module, Py_complex z)
683 : /*[clinic end generated code: output=2922779a7c38cbe1 input=cff5644f73c1519c]*/
684 : {
685 : Py_complex r;
686 : int errno_save;
687 :
688 182 : r = c_log(z);
689 182 : errno_save = errno; /* just in case the divisions affect errno */
690 182 : r.real = r.real / M_LN10;
691 182 : r.imag = r.imag / M_LN10;
692 182 : errno = errno_save;
693 182 : return r;
694 : }
695 :
696 :
697 : /*[clinic input]
698 : cmath.sin = cmath.acos
699 :
700 : Return the sine of z.
701 : [clinic start generated code]*/
702 :
703 : static Py_complex
704 136 : cmath_sin_impl(PyObject *module, Py_complex z)
705 : /*[clinic end generated code: output=980370d2ff0bb5aa input=2d3519842a8b4b85]*/
706 : {
707 : /* sin(z) = -i sin(iz) */
708 : Py_complex s, r;
709 136 : s.real = -z.imag;
710 136 : s.imag = z.real;
711 136 : s = cmath_sinh_impl(module, s);
712 136 : r.real = s.imag;
713 136 : r.imag = -s.real;
714 136 : return r;
715 : }
716 :
717 :
718 : /* sinh(infinity + i*y) needs to be dealt with specially */
719 : static Py_complex sinh_special_values[7][7];
720 :
721 : /*[clinic input]
722 : cmath.sinh = cmath.acos
723 :
724 : Return the hyperbolic sine of z.
725 : [clinic start generated code]*/
726 :
727 : static Py_complex
728 276 : cmath_sinh_impl(PyObject *module, Py_complex z)
729 : /*[clinic end generated code: output=38b0a6cce26f3536 input=d2d3fc8c1ddfd2dd]*/
730 : {
731 : Py_complex r;
732 : double x_minus_one;
733 :
734 : /* special treatment for sinh(+/-inf + iy) if y is finite and
735 : nonzero */
736 276 : if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) {
737 98 : if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag)
738 48 : && (z.imag != 0.)) {
739 40 : if (z.real > 0) {
740 20 : r.real = copysign(INF, cos(z.imag));
741 20 : r.imag = copysign(INF, sin(z.imag));
742 : }
743 : else {
744 20 : r.real = -copysign(INF, cos(z.imag));
745 20 : r.imag = copysign(INF, sin(z.imag));
746 : }
747 : }
748 : else {
749 116 : r = sinh_special_values[special_type(z.real)]
750 58 : [special_type(z.imag)];
751 : }
752 : /* need to set errno = EDOM if y is +/- infinity and x is not
753 : a NaN */
754 98 : if (Py_IS_INFINITY(z.imag) && !Py_IS_NAN(z.real))
755 24 : errno = EDOM;
756 : else
757 74 : errno = 0;
758 98 : return r;
759 : }
760 :
761 178 : if (fabs(z.real) > CM_LOG_LARGE_DOUBLE) {
762 4 : x_minus_one = z.real - copysign(1., z.real);
763 4 : r.real = cos(z.imag) * sinh(x_minus_one) * Py_MATH_E;
764 4 : r.imag = sin(z.imag) * cosh(x_minus_one) * Py_MATH_E;
765 : } else {
766 174 : r.real = cos(z.imag) * sinh(z.real);
767 174 : r.imag = sin(z.imag) * cosh(z.real);
768 : }
769 : /* detect overflow, and set errno accordingly */
770 178 : if (Py_IS_INFINITY(r.real) || Py_IS_INFINITY(r.imag))
771 0 : errno = ERANGE;
772 : else
773 178 : errno = 0;
774 178 : return r;
775 : }
776 :
777 :
778 : static Py_complex sqrt_special_values[7][7];
779 :
780 : /*[clinic input]
781 : cmath.sqrt = cmath.acos
782 :
783 : Return the square root of z.
784 : [clinic start generated code]*/
785 :
786 : static Py_complex
787 1146 : cmath_sqrt_impl(PyObject *module, Py_complex z)
788 : /*[clinic end generated code: output=b6507b3029c339fc input=7088b166fc9a58c7]*/
789 : {
790 : /*
791 : Method: use symmetries to reduce to the case when x = z.real and y
792 : = z.imag are nonnegative. Then the real part of the result is
793 : given by
794 :
795 : s = sqrt((x + hypot(x, y))/2)
796 :
797 : and the imaginary part is
798 :
799 : d = (y/2)/s
800 :
801 : If either x or y is very large then there's a risk of overflow in
802 : computation of the expression x + hypot(x, y). We can avoid this
803 : by rewriting the formula for s as:
804 :
805 : s = 2*sqrt(x/8 + hypot(x/8, y/8))
806 :
807 : This costs us two extra multiplications/divisions, but avoids the
808 : overhead of checking for x and y large.
809 :
810 : If both x and y are subnormal then hypot(x, y) may also be
811 : subnormal, so will lack full precision. We solve this by rescaling
812 : x and y by a sufficiently large power of 2 to ensure that x and y
813 : are normal.
814 : */
815 :
816 :
817 : Py_complex r;
818 : double s,d;
819 : double ax, ay;
820 :
821 1146 : SPECIAL_VALUE(z, sqrt_special_values);
822 :
823 1113 : if (z.real == 0. && z.imag == 0.) {
824 29 : r.real = 0.;
825 29 : r.imag = z.imag;
826 29 : return r;
827 : }
828 :
829 1084 : ax = fabs(z.real);
830 1084 : ay = fabs(z.imag);
831 :
832 1084 : if (ax < DBL_MIN && ay < DBL_MIN && (ax > 0. || ay > 0.)) {
833 : /* here we catch cases where hypot(ax, ay) is subnormal */
834 16 : ax = ldexp(ax, CM_SCALE_UP);
835 16 : s = ldexp(sqrt(ax + hypot(ax, ldexp(ay, CM_SCALE_UP))),
836 : CM_SCALE_DOWN);
837 : } else {
838 1068 : ax /= 8.;
839 1068 : s = 2.*sqrt(ax + hypot(ax, ay/8.));
840 : }
841 1084 : d = ay/(2.*s);
842 :
843 1084 : if (z.real >= 0.) {
844 767 : r.real = s;
845 767 : r.imag = copysign(d, z.imag);
846 : } else {
847 317 : r.real = d;
848 317 : r.imag = copysign(s, z.imag);
849 : }
850 1084 : errno = 0;
851 1084 : return r;
852 : }
853 :
854 :
855 : /*[clinic input]
856 : cmath.tan = cmath.acos
857 :
858 : Return the tangent of z.
859 : [clinic start generated code]*/
860 :
861 : static Py_complex
862 139 : cmath_tan_impl(PyObject *module, Py_complex z)
863 : /*[clinic end generated code: output=7c5f13158a72eb13 input=fc167e528767888e]*/
864 : {
865 : /* tan(z) = -i tanh(iz) */
866 : Py_complex s, r;
867 139 : s.real = -z.imag;
868 139 : s.imag = z.real;
869 139 : s = cmath_tanh_impl(module, s);
870 139 : r.real = s.imag;
871 139 : r.imag = -s.real;
872 139 : return r;
873 : }
874 :
875 :
876 : /* tanh(infinity + i*y) needs to be dealt with specially */
877 : static Py_complex tanh_special_values[7][7];
878 :
879 : /*[clinic input]
880 : cmath.tanh = cmath.acos
881 :
882 : Return the hyperbolic tangent of z.
883 : [clinic start generated code]*/
884 :
885 : static Py_complex
886 281 : cmath_tanh_impl(PyObject *module, Py_complex z)
887 : /*[clinic end generated code: output=36d547ef7aca116c input=22f67f9dc6d29685]*/
888 : {
889 : /* Formula:
890 :
891 : tanh(x+iy) = (tanh(x)(1+tan(y)^2) + i tan(y)(1-tanh(x))^2) /
892 : (1+tan(y)^2 tanh(x)^2)
893 :
894 : To avoid excessive roundoff error, 1-tanh(x)^2 is better computed
895 : as 1/cosh(x)^2. When abs(x) is large, we approximate 1-tanh(x)^2
896 : by 4 exp(-2*x) instead, to avoid possible overflow in the
897 : computation of cosh(x).
898 :
899 : */
900 :
901 : Py_complex r;
902 : double tx, ty, cx, txty, denom;
903 :
904 : /* special treatment for tanh(+/-inf + iy) if y is finite and
905 : nonzero */
906 281 : if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) {
907 98 : if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag)
908 48 : && (z.imag != 0.)) {
909 40 : if (z.real > 0) {
910 20 : r.real = 1.0;
911 20 : r.imag = copysign(0.,
912 20 : 2.*sin(z.imag)*cos(z.imag));
913 : }
914 : else {
915 20 : r.real = -1.0;
916 20 : r.imag = copysign(0.,
917 20 : 2.*sin(z.imag)*cos(z.imag));
918 : }
919 : }
920 : else {
921 116 : r = tanh_special_values[special_type(z.real)]
922 58 : [special_type(z.imag)];
923 : }
924 : /* need to set errno = EDOM if z.imag is +/-infinity and
925 : z.real is finite */
926 98 : if (Py_IS_INFINITY(z.imag) && Py_IS_FINITE(z.real))
927 16 : errno = EDOM;
928 : else
929 82 : errno = 0;
930 98 : return r;
931 : }
932 :
933 : /* danger of overflow in 2.*z.imag !*/
934 183 : if (fabs(z.real) > CM_LOG_LARGE_DOUBLE) {
935 10 : r.real = copysign(1., z.real);
936 10 : r.imag = 4.*sin(z.imag)*cos(z.imag)*exp(-2.*fabs(z.real));
937 : } else {
938 173 : tx = tanh(z.real);
939 173 : ty = tan(z.imag);
940 173 : cx = 1./cosh(z.real);
941 173 : txty = tx*ty;
942 173 : denom = 1. + txty*txty;
943 173 : r.real = tx*(1.+ty*ty)/denom;
944 173 : r.imag = ((ty/denom)*cx)*cx;
945 : }
946 183 : errno = 0;
947 183 : return r;
948 : }
949 :
950 :
951 : /*[clinic input]
952 : cmath.log
953 :
954 : z as x: Py_complex
955 : base as y_obj: object = NULL
956 : /
957 :
958 : log(z[, base]) -> the logarithm of z to the given base.
959 :
960 : If the base not specified, returns the natural logarithm (base e) of z.
961 : [clinic start generated code]*/
962 :
963 : static PyObject *
964 281 : cmath_log_impl(PyObject *module, Py_complex x, PyObject *y_obj)
965 : /*[clinic end generated code: output=4effdb7d258e0d94 input=230ed3a71ecd000a]*/
966 : {
967 : Py_complex y;
968 :
969 281 : errno = 0;
970 281 : x = c_log(x);
971 281 : if (y_obj != NULL) {
972 99 : y = PyComplex_AsCComplex(y_obj);
973 99 : if (PyErr_Occurred()) {
974 24 : return NULL;
975 : }
976 75 : y = c_log(y);
977 75 : x = _Py_c_quot(x, y);
978 : }
979 257 : if (errno != 0)
980 4 : return math_error();
981 253 : return PyComplex_FromCComplex(x);
982 : }
983 :
984 :
985 : /* And now the glue to make them available from Python: */
986 :
987 : static PyObject *
988 13 : math_error(void)
989 : {
990 13 : if (errno == EDOM)
991 12 : PyErr_SetString(PyExc_ValueError, "math domain error");
992 1 : else if (errno == ERANGE)
993 1 : PyErr_SetString(PyExc_OverflowError, "math range error");
994 : else /* Unexpected math error */
995 0 : PyErr_SetFromErrno(PyExc_ValueError);
996 13 : return NULL;
997 : }
998 :
999 :
1000 : /*[clinic input]
1001 : cmath.phase
1002 :
1003 : z: Py_complex
1004 : /
1005 :
1006 : Return argument, also known as the phase angle, of a complex.
1007 : [clinic start generated code]*/
1008 :
1009 : static PyObject *
1010 43 : cmath_phase_impl(PyObject *module, Py_complex z)
1011 : /*[clinic end generated code: output=50725086a7bfd253 input=5cf75228ba94b69d]*/
1012 : {
1013 : double phi;
1014 :
1015 43 : errno = 0;
1016 43 : phi = c_atan2(z);
1017 43 : if (errno != 0)
1018 0 : return math_error();
1019 : else
1020 43 : return PyFloat_FromDouble(phi);
1021 : }
1022 :
1023 : /*[clinic input]
1024 : cmath.polar
1025 :
1026 : z: Py_complex
1027 : /
1028 :
1029 : Convert a complex from rectangular coordinates to polar coordinates.
1030 :
1031 : r is the distance from 0 and phi the phase angle.
1032 : [clinic start generated code]*/
1033 :
1034 : static PyObject *
1035 78 : cmath_polar_impl(PyObject *module, Py_complex z)
1036 : /*[clinic end generated code: output=d0a8147c41dbb654 input=26c353574fd1a861]*/
1037 : {
1038 : double r, phi;
1039 :
1040 78 : errno = 0;
1041 78 : phi = c_atan2(z); /* should not cause any exception */
1042 78 : r = _Py_c_abs(z); /* sets errno to ERANGE on overflow */
1043 78 : if (errno != 0)
1044 1 : return math_error();
1045 : else
1046 77 : return Py_BuildValue("dd", r, phi);
1047 : }
1048 :
1049 : /*
1050 : rect() isn't covered by the C99 standard, but it's not too hard to
1051 : figure out 'spirit of C99' rules for special value handing:
1052 :
1053 : rect(x, t) should behave like exp(log(x) + it) for positive-signed x
1054 : rect(x, t) should behave like -exp(log(-x) + it) for negative-signed x
1055 : rect(nan, t) should behave like exp(nan + it), except that rect(nan, 0)
1056 : gives nan +- i0 with the sign of the imaginary part unspecified.
1057 :
1058 : */
1059 :
1060 : static Py_complex rect_special_values[7][7];
1061 :
1062 : /*[clinic input]
1063 : cmath.rect
1064 :
1065 : r: double
1066 : phi: double
1067 : /
1068 :
1069 : Convert from polar coordinates to rectangular coordinates.
1070 : [clinic start generated code]*/
1071 :
1072 : static PyObject *
1073 58 : cmath_rect_impl(PyObject *module, double r, double phi)
1074 : /*[clinic end generated code: output=385a0690925df2d5 input=24c5646d147efd69]*/
1075 : {
1076 : Py_complex z;
1077 58 : errno = 0;
1078 :
1079 : /* deal with special values */
1080 58 : if (!Py_IS_FINITE(r) || !Py_IS_FINITE(phi)) {
1081 : /* if r is +/-infinity and phi is finite but nonzero then
1082 : result is (+-INF +-INF i), but we need to compute cos(phi)
1083 : and sin(phi) to figure out the signs. */
1084 49 : if (Py_IS_INFINITY(r) && (Py_IS_FINITE(phi)
1085 24 : && (phi != 0.))) {
1086 20 : if (r > 0) {
1087 10 : z.real = copysign(INF, cos(phi));
1088 10 : z.imag = copysign(INF, sin(phi));
1089 : }
1090 : else {
1091 10 : z.real = -copysign(INF, cos(phi));
1092 10 : z.imag = -copysign(INF, sin(phi));
1093 : }
1094 : }
1095 : else {
1096 58 : z = rect_special_values[special_type(r)]
1097 29 : [special_type(phi)];
1098 : }
1099 : /* need to set errno = EDOM if r is a nonzero number and phi
1100 : is infinite */
1101 49 : if (r != 0. && !Py_IS_NAN(r) && Py_IS_INFINITY(phi))
1102 8 : errno = EDOM;
1103 : else
1104 41 : errno = 0;
1105 : }
1106 9 : else if (phi == 0.0) {
1107 : /* Workaround for buggy results with phi=-0.0 on OS X 10.8. See
1108 : bugs.python.org/issue18513. */
1109 6 : z.real = r;
1110 6 : z.imag = r * phi;
1111 6 : errno = 0;
1112 : }
1113 : else {
1114 3 : z.real = r * cos(phi);
1115 3 : z.imag = r * sin(phi);
1116 3 : errno = 0;
1117 : }
1118 :
1119 58 : if (errno != 0)
1120 8 : return math_error();
1121 : else
1122 50 : return PyComplex_FromCComplex(z);
1123 : }
1124 :
1125 : /*[clinic input]
1126 : cmath.isfinite = cmath.polar
1127 :
1128 : Return True if both the real and imaginary parts of z are finite, else False.
1129 : [clinic start generated code]*/
1130 :
1131 : static PyObject *
1132 49 : cmath_isfinite_impl(PyObject *module, Py_complex z)
1133 : /*[clinic end generated code: output=ac76611e2c774a36 input=848e7ee701895815]*/
1134 : {
1135 49 : return PyBool_FromLong(Py_IS_FINITE(z.real) && Py_IS_FINITE(z.imag));
1136 : }
1137 :
1138 : /*[clinic input]
1139 : cmath.isnan = cmath.polar
1140 :
1141 : Checks if the real or imaginary part of z not a number (NaN).
1142 : [clinic start generated code]*/
1143 :
1144 : static PyObject *
1145 9 : cmath_isnan_impl(PyObject *module, Py_complex z)
1146 : /*[clinic end generated code: output=e7abf6e0b28beab7 input=71799f5d284c9baf]*/
1147 : {
1148 9 : return PyBool_FromLong(Py_IS_NAN(z.real) || Py_IS_NAN(z.imag));
1149 : }
1150 :
1151 : /*[clinic input]
1152 : cmath.isinf = cmath.polar
1153 :
1154 : Checks if the real or imaginary part of z is infinite.
1155 : [clinic start generated code]*/
1156 :
1157 : static PyObject *
1158 9 : cmath_isinf_impl(PyObject *module, Py_complex z)
1159 : /*[clinic end generated code: output=502a75a79c773469 input=363df155c7181329]*/
1160 : {
1161 14 : return PyBool_FromLong(Py_IS_INFINITY(z.real) ||
1162 5 : Py_IS_INFINITY(z.imag));
1163 : }
1164 :
1165 : /*[clinic input]
1166 : cmath.isclose -> bool
1167 :
1168 : a: Py_complex
1169 : b: Py_complex
1170 : *
1171 : rel_tol: double = 1e-09
1172 : maximum difference for being considered "close", relative to the
1173 : magnitude of the input values
1174 : abs_tol: double = 0.0
1175 : maximum difference for being considered "close", regardless of the
1176 : magnitude of the input values
1177 :
1178 : Determine whether two complex numbers are close in value.
1179 :
1180 : Return True if a is close in value to b, and False otherwise.
1181 :
1182 : For the values to be considered close, the difference between them must be
1183 : smaller than at least one of the tolerances.
1184 :
1185 : -inf, inf and NaN behave similarly to the IEEE 754 Standard. That is, NaN is
1186 : not close to anything, even itself. inf and -inf are only close to themselves.
1187 : [clinic start generated code]*/
1188 :
1189 : static int
1190 82 : cmath_isclose_impl(PyObject *module, Py_complex a, Py_complex b,
1191 : double rel_tol, double abs_tol)
1192 : /*[clinic end generated code: output=8a2486cc6e0014d1 input=df9636d7de1d4ac3]*/
1193 : {
1194 : double diff;
1195 :
1196 : /* sanity check on the inputs */
1197 82 : if (rel_tol < 0.0 || abs_tol < 0.0 ) {
1198 2 : PyErr_SetString(PyExc_ValueError,
1199 : "tolerances must be non-negative");
1200 2 : return -1;
1201 : }
1202 :
1203 80 : if ( (a.real == b.real) && (a.imag == b.imag) ) {
1204 : /* short circuit exact equality -- needed to catch two infinities of
1205 : the same sign. And perhaps speeds things up a bit sometimes.
1206 : */
1207 13 : return 1;
1208 : }
1209 :
1210 : /* This catches the case of two infinities of opposite sign, or
1211 : one infinity and one finite number. Two infinities of opposite
1212 : sign would otherwise have an infinite relative tolerance.
1213 : Two infinities of the same sign are caught by the equality check
1214 : above.
1215 : */
1216 :
1217 67 : if (Py_IS_INFINITY(a.real) || Py_IS_INFINITY(a.imag) ||
1218 63 : Py_IS_INFINITY(b.real) || Py_IS_INFINITY(b.imag)) {
1219 7 : return 0;
1220 : }
1221 :
1222 : /* now do the regular computation
1223 : this is essentially the "weak" test from the Boost library
1224 : */
1225 :
1226 60 : diff = _Py_c_abs(_Py_c_diff(a, b));
1227 :
1228 60 : return (((diff <= rel_tol * _Py_c_abs(b)) ||
1229 60 : (diff <= rel_tol * _Py_c_abs(a))) ||
1230 : (diff <= abs_tol));
1231 : }
1232 :
1233 : PyDoc_STRVAR(module_doc,
1234 : "This module provides access to mathematical functions for complex\n"
1235 : "numbers.");
1236 :
1237 : static PyMethodDef cmath_methods[] = {
1238 : CMATH_ACOS_METHODDEF
1239 : CMATH_ACOSH_METHODDEF
1240 : CMATH_ASIN_METHODDEF
1241 : CMATH_ASINH_METHODDEF
1242 : CMATH_ATAN_METHODDEF
1243 : CMATH_ATANH_METHODDEF
1244 : CMATH_COS_METHODDEF
1245 : CMATH_COSH_METHODDEF
1246 : CMATH_EXP_METHODDEF
1247 : CMATH_ISCLOSE_METHODDEF
1248 : CMATH_ISFINITE_METHODDEF
1249 : CMATH_ISINF_METHODDEF
1250 : CMATH_ISNAN_METHODDEF
1251 : CMATH_LOG_METHODDEF
1252 : CMATH_LOG10_METHODDEF
1253 : CMATH_PHASE_METHODDEF
1254 : CMATH_POLAR_METHODDEF
1255 : CMATH_RECT_METHODDEF
1256 : CMATH_SIN_METHODDEF
1257 : CMATH_SINH_METHODDEF
1258 : CMATH_SQRT_METHODDEF
1259 : CMATH_TAN_METHODDEF
1260 : CMATH_TANH_METHODDEF
1261 : {NULL, NULL} /* sentinel */
1262 : };
1263 :
1264 : static int
1265 2 : cmath_exec(PyObject *mod)
1266 : {
1267 2 : if (PyModule_AddObject(mod, "pi", PyFloat_FromDouble(Py_MATH_PI)) < 0) {
1268 0 : return -1;
1269 : }
1270 2 : if (PyModule_AddObject(mod, "e", PyFloat_FromDouble(Py_MATH_E)) < 0) {
1271 0 : return -1;
1272 : }
1273 : // 2pi
1274 2 : if (PyModule_AddObject(mod, "tau", PyFloat_FromDouble(Py_MATH_TAU)) < 0) {
1275 0 : return -1;
1276 : }
1277 2 : if (PyModule_AddObject(mod, "inf", PyFloat_FromDouble(m_inf())) < 0) {
1278 0 : return -1;
1279 : }
1280 :
1281 2 : if (PyModule_AddObject(mod, "infj",
1282 : PyComplex_FromCComplex(c_infj())) < 0) {
1283 0 : return -1;
1284 : }
1285 : #if _PY_SHORT_FLOAT_REPR == 1
1286 2 : if (PyModule_AddObject(mod, "nan", PyFloat_FromDouble(m_nan())) < 0) {
1287 0 : return -1;
1288 : }
1289 2 : if (PyModule_AddObject(mod, "nanj",
1290 : PyComplex_FromCComplex(c_nanj())) < 0) {
1291 0 : return -1;
1292 : }
1293 : #endif
1294 :
1295 : /* initialize special value tables */
1296 :
1297 : #define INIT_SPECIAL_VALUES(NAME, BODY) { Py_complex* p = (Py_complex*)NAME; BODY }
1298 : #define C(REAL, IMAG) p->real = REAL; p->imag = IMAG; ++p;
1299 :
1300 2 : INIT_SPECIAL_VALUES(acos_special_values, {
1301 : C(P34,INF) C(P,INF) C(P,INF) C(P,-INF) C(P,-INF) C(P34,-INF) C(N,INF)
1302 : C(P12,INF) C(U,U) C(U,U) C(U,U) C(U,U) C(P12,-INF) C(N,N)
1303 : C(P12,INF) C(U,U) C(P12,0.) C(P12,-0.) C(U,U) C(P12,-INF) C(P12,N)
1304 : C(P12,INF) C(U,U) C(P12,0.) C(P12,-0.) C(U,U) C(P12,-INF) C(P12,N)
1305 : C(P12,INF) C(U,U) C(U,U) C(U,U) C(U,U) C(P12,-INF) C(N,N)
1306 : C(P14,INF) C(0.,INF) C(0.,INF) C(0.,-INF) C(0.,-INF) C(P14,-INF) C(N,INF)
1307 : C(N,INF) C(N,N) C(N,N) C(N,N) C(N,N) C(N,-INF) C(N,N)
1308 : })
1309 :
1310 2 : INIT_SPECIAL_VALUES(acosh_special_values, {
1311 : C(INF,-P34) C(INF,-P) C(INF,-P) C(INF,P) C(INF,P) C(INF,P34) C(INF,N)
1312 : C(INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,P12) C(N,N)
1313 : C(INF,-P12) C(U,U) C(0.,-P12) C(0.,P12) C(U,U) C(INF,P12) C(N,N)
1314 : C(INF,-P12) C(U,U) C(0.,-P12) C(0.,P12) C(U,U) C(INF,P12) C(N,N)
1315 : C(INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,P12) C(N,N)
1316 : C(INF,-P14) C(INF,-0.) C(INF,-0.) C(INF,0.) C(INF,0.) C(INF,P14) C(INF,N)
1317 : C(INF,N) C(N,N) C(N,N) C(N,N) C(N,N) C(INF,N) C(N,N)
1318 : })
1319 :
1320 2 : INIT_SPECIAL_VALUES(asinh_special_values, {
1321 : C(-INF,-P14) C(-INF,-0.) C(-INF,-0.) C(-INF,0.) C(-INF,0.) C(-INF,P14) C(-INF,N)
1322 : C(-INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(-INF,P12) C(N,N)
1323 : C(-INF,-P12) C(U,U) C(-0.,-0.) C(-0.,0.) C(U,U) C(-INF,P12) C(N,N)
1324 : C(INF,-P12) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(INF,P12) C(N,N)
1325 : C(INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,P12) C(N,N)
1326 : C(INF,-P14) C(INF,-0.) C(INF,-0.) C(INF,0.) C(INF,0.) C(INF,P14) C(INF,N)
1327 : C(INF,N) C(N,N) C(N,-0.) C(N,0.) C(N,N) C(INF,N) C(N,N)
1328 : })
1329 :
1330 2 : INIT_SPECIAL_VALUES(atanh_special_values, {
1331 : C(-0.,-P12) C(-0.,-P12) C(-0.,-P12) C(-0.,P12) C(-0.,P12) C(-0.,P12) C(-0.,N)
1332 : C(-0.,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(-0.,P12) C(N,N)
1333 : C(-0.,-P12) C(U,U) C(-0.,-0.) C(-0.,0.) C(U,U) C(-0.,P12) C(-0.,N)
1334 : C(0.,-P12) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(0.,P12) C(0.,N)
1335 : C(0.,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(0.,P12) C(N,N)
1336 : C(0.,-P12) C(0.,-P12) C(0.,-P12) C(0.,P12) C(0.,P12) C(0.,P12) C(0.,N)
1337 : C(0.,-P12) C(N,N) C(N,N) C(N,N) C(N,N) C(0.,P12) C(N,N)
1338 : })
1339 :
1340 2 : INIT_SPECIAL_VALUES(cosh_special_values, {
1341 : C(INF,N) C(U,U) C(INF,0.) C(INF,-0.) C(U,U) C(INF,N) C(INF,N)
1342 : C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
1343 : C(N,0.) C(U,U) C(1.,0.) C(1.,-0.) C(U,U) C(N,0.) C(N,0.)
1344 : C(N,0.) C(U,U) C(1.,-0.) C(1.,0.) C(U,U) C(N,0.) C(N,0.)
1345 : C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
1346 : C(INF,N) C(U,U) C(INF,-0.) C(INF,0.) C(U,U) C(INF,N) C(INF,N)
1347 : C(N,N) C(N,N) C(N,0.) C(N,0.) C(N,N) C(N,N) C(N,N)
1348 : })
1349 :
1350 2 : INIT_SPECIAL_VALUES(exp_special_values, {
1351 : C(0.,0.) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(0.,0.) C(0.,0.)
1352 : C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
1353 : C(N,N) C(U,U) C(1.,-0.) C(1.,0.) C(U,U) C(N,N) C(N,N)
1354 : C(N,N) C(U,U) C(1.,-0.) C(1.,0.) C(U,U) C(N,N) C(N,N)
1355 : C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
1356 : C(INF,N) C(U,U) C(INF,-0.) C(INF,0.) C(U,U) C(INF,N) C(INF,N)
1357 : C(N,N) C(N,N) C(N,-0.) C(N,0.) C(N,N) C(N,N) C(N,N)
1358 : })
1359 :
1360 2 : INIT_SPECIAL_VALUES(log_special_values, {
1361 : C(INF,-P34) C(INF,-P) C(INF,-P) C(INF,P) C(INF,P) C(INF,P34) C(INF,N)
1362 : C(INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,P12) C(N,N)
1363 : C(INF,-P12) C(U,U) C(-INF,-P) C(-INF,P) C(U,U) C(INF,P12) C(N,N)
1364 : C(INF,-P12) C(U,U) C(-INF,-0.) C(-INF,0.) C(U,U) C(INF,P12) C(N,N)
1365 : C(INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,P12) C(N,N)
1366 : C(INF,-P14) C(INF,-0.) C(INF,-0.) C(INF,0.) C(INF,0.) C(INF,P14) C(INF,N)
1367 : C(INF,N) C(N,N) C(N,N) C(N,N) C(N,N) C(INF,N) C(N,N)
1368 : })
1369 :
1370 2 : INIT_SPECIAL_VALUES(sinh_special_values, {
1371 : C(INF,N) C(U,U) C(-INF,-0.) C(-INF,0.) C(U,U) C(INF,N) C(INF,N)
1372 : C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
1373 : C(0.,N) C(U,U) C(-0.,-0.) C(-0.,0.) C(U,U) C(0.,N) C(0.,N)
1374 : C(0.,N) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(0.,N) C(0.,N)
1375 : C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
1376 : C(INF,N) C(U,U) C(INF,-0.) C(INF,0.) C(U,U) C(INF,N) C(INF,N)
1377 : C(N,N) C(N,N) C(N,-0.) C(N,0.) C(N,N) C(N,N) C(N,N)
1378 : })
1379 :
1380 2 : INIT_SPECIAL_VALUES(sqrt_special_values, {
1381 : C(INF,-INF) C(0.,-INF) C(0.,-INF) C(0.,INF) C(0.,INF) C(INF,INF) C(N,INF)
1382 : C(INF,-INF) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,INF) C(N,N)
1383 : C(INF,-INF) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(INF,INF) C(N,N)
1384 : C(INF,-INF) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(INF,INF) C(N,N)
1385 : C(INF,-INF) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,INF) C(N,N)
1386 : C(INF,-INF) C(INF,-0.) C(INF,-0.) C(INF,0.) C(INF,0.) C(INF,INF) C(INF,N)
1387 : C(INF,-INF) C(N,N) C(N,N) C(N,N) C(N,N) C(INF,INF) C(N,N)
1388 : })
1389 :
1390 2 : INIT_SPECIAL_VALUES(tanh_special_values, {
1391 : C(-1.,0.) C(U,U) C(-1.,-0.) C(-1.,0.) C(U,U) C(-1.,0.) C(-1.,0.)
1392 : C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
1393 : C(N,N) C(U,U) C(-0.,-0.) C(-0.,0.) C(U,U) C(N,N) C(N,N)
1394 : C(N,N) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(N,N) C(N,N)
1395 : C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
1396 : C(1.,0.) C(U,U) C(1.,-0.) C(1.,0.) C(U,U) C(1.,0.) C(1.,0.)
1397 : C(N,N) C(N,N) C(N,-0.) C(N,0.) C(N,N) C(N,N) C(N,N)
1398 : })
1399 :
1400 2 : INIT_SPECIAL_VALUES(rect_special_values, {
1401 : C(INF,N) C(U,U) C(-INF,0.) C(-INF,-0.) C(U,U) C(INF,N) C(INF,N)
1402 : C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
1403 : C(0.,0.) C(U,U) C(-0.,0.) C(-0.,-0.) C(U,U) C(0.,0.) C(0.,0.)
1404 : C(0.,0.) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(0.,0.) C(0.,0.)
1405 : C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
1406 : C(INF,N) C(U,U) C(INF,-0.) C(INF,0.) C(U,U) C(INF,N) C(INF,N)
1407 : C(N,N) C(N,N) C(N,0.) C(N,0.) C(N,N) C(N,N) C(N,N)
1408 : })
1409 2 : return 0;
1410 : }
1411 :
1412 : static PyModuleDef_Slot cmath_slots[] = {
1413 : {Py_mod_exec, cmath_exec},
1414 : {0, NULL}
1415 : };
1416 :
1417 : static struct PyModuleDef cmathmodule = {
1418 : PyModuleDef_HEAD_INIT,
1419 : .m_name = "cmath",
1420 : .m_doc = module_doc,
1421 : .m_size = 0,
1422 : .m_methods = cmath_methods,
1423 : .m_slots = cmath_slots
1424 : };
1425 :
1426 : PyMODINIT_FUNC
1427 2 : PyInit_cmath(void)
1428 : {
1429 2 : return PyModuleDef_Init(&cmathmodule);
1430 : }
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