File size: 19,935 Bytes
64772a4
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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

cdef extern from "<cmath>" namespace "std" nogil:
    # all C99 functions
    float acos(float x) except +
    double acos(double x) except +
    long double acos(long double x) except +
    float acosf(float x) except +
    long double acosl(long double x) except +

    float asin(float x) except +
    double asin(double x) except +
    long double asin(long double x) except +
    float asinf(float x) except +
    long double asinl(long double x) except +

    float atan(float x) except +
    double atan(double x) except +
    long double atan(long double x) except +
    float atanf(float x) except +
    long double atanl(long double x) except +

    float atan2(float y, float x) except +
    double atan2(double y, double x) except +
    long double atan2(long double y, long double x) except +
    float atan2f(float y, float x) except +
    long double atan2l(long double y, long double x) except +

    float cos(float x) except +
    double cos(double x) except +
    long double cos(long double x) except +
    float cosf(float x) except +
    long double cosl(long double x) except +

    float sin(float x) except +
    double sin(double x) except +
    long double sin(long double x) except +
    float sinf(float x) except +
    long double sinl(long double x) except +

    float tan(float x) except +
    double tan(double x) except +
    long double tan(long double x) except +
    float tanf(float x) except +
    long double tanl(long double x) except +

    float acosh(float x) except +
    double acosh(double x) except +
    long double acosh(long double x) except +
    float acoshf(float x) except +
    long double acoshl(long double x) except +

    float asinh(float x) except +
    double asinh(double x) except +
    long double asinh(long double x) except +
    float asinhf(float x) except +
    long double asinhl(long double x) except +

    float atanh(float x) except +
    double atanh(double x) except +
    long double atanh(long double x) except +
    float atanhf(float x) except +
    long double atanhl(long double x) except +

    float cosh(float x) except +
    double cosh(double x) except +
    long double cosh(long double x) except +
    float coshf(float x) except +
    long double coshl(long double x) except +

    float sinh(float x) except +
    double sinh(double x) except +
    long double sinh(long double x) except +
    float sinhf(float x) except +
    long double sinhl(long double x) except +

    float tanh(float x) except +
    double tanh(double x) except +
    long double tanh(long double x) except +
    float tanhf(float x) except +
    long double tanhl(long double x) except +

    float exp(float x) except +
    double exp(double x) except +
    long double exp(long double x) except +
    float expf(float x) except +
    long double expl(long double x) except +

    float exp2(float x) except +
    double exp2(double x) except +
    long double exp2(long double x) except +
    float exp2f(float x) except +
    long double exp2l(long double x) except +

    float expm1(float x) except +
    double expm1(double x) except +
    long double expm1(long double x) except +
    float expm1f(float x) except +
    long double expm1l(long double x) except +

    float frexp(float value, int* exp) except +
    double frexp(double value, int* exp) except +
    long double frexp(long double value, int* exp) except +
    float frexpf(float value, int* exp) except +
    long double frexpl(long double value, int* exp) except +

    int ilogb(float x) except +
    int ilogb(double x) except +
    int ilogb(long double x) except +
    int ilogbf(float x) except +
    int ilogbl(long double x) except +

    float ldexp(float x, int exp) except +
    double ldexp(double x, int exp) except +
    long double ldexp(long double x, int exp) except +
    float ldexpf(float x, int exp) except +
    long double ldexpl(long double x, int exp) except +

    float log(float x) except +
    double log(double x) except +
    long double log(long double x) except +
    float logf(float x) except +
    long double logl(long double x) except +

    float log10(float x) except +
    double log10(double x) except +
    long double log10(long double x) except +
    float log10f(float x) except +
    long double log10l(long double x) except +

    float log1p(float x) except +
    double log1p(double x) except +
    long double log1p(long double x) except +
    float log1pf(float x) except +
    long double log1pl(long double x) except +

    float log2(float x) except +
    double log2(double x) except +
    long double log2(long double x) except +
    float log2f(float x) except +
    long double log2l(long double x) except +

    float logb(float x) except +
    double logb(double x) except +
    long double logb(long double x) except +
    float logbf(float x) except +
    long double logbl(long double x) except +

    float modf(float value, float* iptr) except +
    double modf(double value, double* iptr) except +
    long double modf(long double value, long double* iptr) except +
    float modff(float value, float* iptr) except +
    long double modfl(long double value, long double* iptr) except +

    float scalbn(float x, int n) except +
    double scalbn(double x, int n) except +
    long double scalbn(long double x, int n) except +
    float scalbnf(float x, int n) except +
    long double scalbnl(long double x, int n) except +

    float scalbln(float x, long int n) except +
    double scalbln(double x, long int n) except +
    long double scalbln(long double x, long int n) except +
    float scalblnf(float x, long int n) except +
    long double scalblnl(long double x, long int n) except +

    float cbrt(float x) except +
    double cbrt(double x) except +
    long double cbrt(long double x) except +
    float cbrtf(float x) except +
    long double cbrtl(long double x) except +

    # absolute values
    int abs(int j) except +
    long int abs(long int j) except +
    long long int abs(long long int j) except +
    float abs(float j) except +
    double abs(double j) except +
    long double abs(long double j) except +

    float fabs(float x) except +
    double fabs(double x) except +
    long double fabs(long double x) except +
    float fabsf(float x) except +
    long double fabsl(long double x) except +

    float hypot(float x, float y) except +
    double hypot(double x, double y) except +
    long double hypot(long double x, long double y) except +
    float hypotf(float x, float y) except +
    long double hypotl(long double x, long double y) except +

    # C++17 three-dimensional hypotenuse
    float hypot(float x, float y, float z) except +
    double hypot(double x, double y, double z) except +
    long double hypot(long double x, long double y, long double z) except +

    float pow(float x, float y) except +
    double pow(double x, double y) except +
    long double pow(long double x, long double y) except +
    float powf(float x, float y) except +
    long double powl(long double x, long double y) except +

    float sqrt(float x) except +
    double sqrt(double x) except +
    long double sqrt(long double x) except +
    float sqrtf(float x) except +
    long double sqrtl(long double x) except +

    float erf(float x) except +
    double erf(double x) except +
    long double erf(long double x) except +
    float erff(float x) except +
    long double erfl(long double x) except +

    float erfc(float x) except +
    double erfc(double x) except +
    long double erfc(long double x) except +
    float erfcf(float x) except +
    long double erfcl(long double x) except +

    float lgamma(float x) except +
    double lgamma(double x) except +
    long double lgamma(long double x) except +
    float lgammaf(float x) except +
    long double lgammal(long double x) except +

    float tgamma(float x) except +
    double tgamma(double x) except +
    long double tgamma(long double x) except +
    float tgammaf(float x) except +
    long double tgammal(long double x) except +

    float ceil(float x) except +
    double ceil(double x) except +
    long double ceil(long double x) except +
    float ceilf(float x) except +
    long double ceill(long double x) except +

    float floor(float x) except +
    double floor(double x) except +
    long double floor(long double x) except +
    float floorf(float x) except +
    long double floorl(long double x) except +

    float nearbyint(float x) except +
    double nearbyint(double x) except +
    long double nearbyint(long double x) except +
    float nearbyintf(float x) except +
    long double nearbyintl(long double x) except +

    float rint(float x) except +
    double rint(double x) except +
    long double rint(long double x) except +
    float rintf(float x) except +
    long double rintl(long double x) except +

    long int lrint(float x) except +
    long int lrint(double x) except +
    long int lrint(long double x) except +
    long int lrintf(float x) except +
    long int lrintl(long double x) except +

    long long int llrint(float x) except +
    long long int llrint(double x) except +
    long long int llrint(long double x) except +
    long long int llrintf(float x) except +
    long long int llrintl(long double x) except +

    float round(float x) except +
    double round(double x) except +
    long double round(long double x) except +
    float roundf(float x) except +
    long double roundl(long double x) except +

    long int lround(float x) except +
    long int lround(double x) except +
    long int lround(long double x) except +
    long int lroundf(float x) except +
    long int lroundl(long double x) except +

    long long int llround(float x) except +
    long long int llround(double x) except +
    long long int llround(long double x) except +
    long long int llroundf(float x) except +
    long long int llroundl(long double x) except +

    float trunc(float x) except +
    double trunc(double x) except +
    long double trunc(long double x) except +
    float truncf(float x) except +
    long double truncl(long double x) except +

    float fmod(float x, float y) except +
    double fmod(double x, double y) except +
    long double fmod(long double x, long double y) except +
    float fmodf(float x, float y) except +
    long double fmodl(long double x, long double y) except +

    float remainder(float x, float y) except +
    double remainder(double x, double y) except +
    long double remainder(long double x, long double y) except +
    float remainderf(float x, float y) except +
    long double remainderl(long double x, long double y) except +

    float remquo(float x, float y, int* quo) except +
    double remquo(double x, double y, int* quo) except +
    long double remquo(long double x, long double y, int* quo) except +
    float remquof(float x, float y, int* quo) except +
    long double remquol(long double x, long double y, int* quo) except +

    float copysign(float x, float y) except +
    double copysign(double x, double y) except +
    long double copysign(long double x, long double y) except +
    float copysignf(float x, float y) except +
    long double copysignl(long double x, long double y) except +

    double nan(const char* tagp) except +
    float nanf(const char* tagp) except +
    long double nanl(const char* tagp) except +

    float nextafter(float x, float y) except +
    double nextafter(double x, double y) except +
    long double nextafter(long double x, long double y) except +
    float nextafterf(float x, float y) except +
    long double nextafterl(long double x, long double y) except +

    float nexttoward(float x, long double y) except +
    double nexttoward(double x, long double y) except +
    long double nexttoward(long double x, long double y) except +
    float nexttowardf(float x, long double y) except +
    long double nexttowardl(long double x, long double y) except +

    float fdim(float x, float y) except +
    double fdim(double x, double y) except +
    long double fdim(long double x, long double y) except +
    float fdimf(float x, float y) except +
    long double fdiml(long double x, long double y) except +

    float fmax(float x, float y) except +
    double fmax(double x, double y) except +
    long double fmax(long double x, long double y) except +
    float fmaxf(float x, float y) except +
    long double fmaxl(long double x, long double y) except +

    float fmin(float x, float y) except +
    double fmin(double x, double y) except +
    long double fmin(long double x, long double y) except +
    float fminf(float x, float y) except +
    long double fminl(long double x, long double y) except +

    float fma(float x, float y, float z) except +
    double fma(double x, double y, double z) except +
    long double fma(long double x, long double y, long double z) except +
    float fmaf(float x, float y, float z) except +
    long double fmal(long double x, long double y, long double z) except +

    # C++20 linear interpolation
    float lerp(float a, float b, float t)
    double lerp(double a, double b, double t)
    long double lerp(long double a, long double b, long double t)

    # classification / comparison functions
    int fpclassify(float x) except +
    int fpclassify(double x) except +
    int fpclassify(long double x) except +

    bint isfinite(float x) except +
    bint isfinite(double x) except +
    bint isfinite(long double x) except +

    bint isinf(float x) except +
    bint isinf(double x) except +
    bint isinf(long double x) except +

    bint isnan(float x) except +
    bint isnan(double x) except +
    bint isnan(long double x) except +

    bint isnormal(float x) except +
    bint isnormal(double x) except +
    bint isnormal(long double x) except +

    bint signbit(float x) except +
    bint signbit(double x) except +
    bint signbit(long double x) except +

    bint isgreater(float x, float y) except +
    bint isgreater(double x, double y) except +
    bint isgreater(long double x, long double y) except +

    bint isgreaterequal(float x, float y) except +
    bint isgreaterequal(double x, double y) except +
    bint isgreaterequal(long double x, long double y) except +

    bint isless(float x, float y) except +
    bint isless(double x, double y) except +
    bint isless(long double x, long double y) except +

    bint islessequal(float x, float y) except +
    bint islessequal(double x, double y) except +
    bint islessequal(long double x, long double y) except +

    bint islessgreater(float x, float y) except +
    bint islessgreater(double x, double y) except +
    bint islessgreater(long double x, long double y) except +

    bint isunordered(float x, float y) except +
    bint isunordered(double x, double y) except +
    bint isunordered(long double x, long double y) except +

    # C++17 mathematical special functions

    # associated Laguerre polynomials
    double       assoc_laguerre(unsigned int n, unsigned int m, double x) except +
    float        assoc_laguerref(unsigned int n, unsigned int m, float x) except +
    long double  assoc_laguerrel(unsigned int n, unsigned int m, long double x) except +

    # associated Legendre functions
    double       assoc_legendre(unsigned int l, unsigned int m, double x) except +
    float        assoc_legendref(unsigned int l, unsigned int m, float x) except +
    long double  assoc_legendrel(unsigned int l, unsigned int m, long double x) except +

    # beta function
    double       beta(double x, double y) except +
    float        betaf(float x, float y) except +
    long double  betal(long double x, long double y) except +

    # complete elliptic integral of the first kind
    double       comp_ellint_1(double k) except +
    float        comp_ellint_1f(float k) except +
    long double  comp_ellint_1l(long double k) except +

    # complete elliptic integral of the second kind
    double       comp_ellint_2(double k) except +
    float        comp_ellint_2f(float k) except +
    long double  comp_ellint_2l(long double k) except +

    # complete elliptic integral of the third kind
    double       comp_ellint_3(double k, double nu) except +
    float        comp_ellint_3f(float k, float nu) except +
    long double  comp_ellint_3l(long double k, long double nu) except +

    # regular modified cylindrical Bessel functions
    double       cyl_bessel_i(double nu, double x) except +
    float        cyl_bessel_if(float nu, float x) except +
    long double  cyl_bessel_il(long double nu, long double x) except +

    # cylindrical Bessel functions of the first kind
    double       cyl_bessel_j(double nu, double x) except +
    float        cyl_bessel_jf(float nu, float x) except +
    long double  cyl_bessel_jl(long double nu, long double x) except +

    # irregular modified cylindrical Bessel functions
    double       cyl_bessel_k(double nu, double x) except +
    float        cyl_bessel_kf(float nu, float x) except +
    long double  cyl_bessel_kl(long double nu, long double x) except +

    # cylindrical Neumann functions
    # cylindrical Bessel functions of the second kind
    double       cyl_neumann(double nu, double x) except +
    float        cyl_neumannf(float nu, float x) except +
    long double  cyl_neumannl(long double nu, long double x) except +

    # incomplete elliptic integral of the first kind
    double       ellint_1(double k, double phi) except +
    float        ellint_1f(float k, float phi) except +
    long double  ellint_1l(long double k, long double phi) except +

    # incomplete elliptic integral of the second kind
    double       ellint_2(double k, double phi) except +
    float        ellint_2f(float k, float phi) except +
    long double  ellint_2l(long double k, long double phi) except +

    # incomplete elliptic integral of the third kind
    double       ellint_3(double k, double nu, double phi) except +
    float        ellint_3f(float k, float nu, float phi) except +
    long double  ellint_3l(long double k, long double nu, long double phi) except +

    # exponential integral
    double       expint(double x) except +
    float        expintf(float x) except +
    long double  expintl(long double x) except +

    # Hermite polynomials
    double       hermite(unsigned int n, double x) except +
    float        hermitef(unsigned int n, float x) except +
    long double  hermitel(unsigned int n, long double x) except +

    # Laguerre polynomials
    double       laguerre(unsigned int n, double x) except +
    float        laguerref(unsigned int n, float x) except +
    long double  laguerrel(unsigned int n, long double x) except +

    # Legendre polynomials
    double       legendre(unsigned int l, double x) except +
    float        legendref(unsigned int l, float x) except +
    long double  legendrel(unsigned int l, long double x) except +

    # Riemann zeta function
    double       riemann_zeta(double x) except +
    float        riemann_zetaf(float x) except +
    long double  riemann_zetal(long double x) except +

    # spherical Bessel functions of the first kind
    double       sph_bessel(unsigned int n, double x) except +
    float        sph_besself(unsigned int n, float x) except +
    long double  sph_bessell(unsigned int n, long double x) except +

    # spherical associated Legendre functions
    double       sph_legendre(unsigned int l, unsigned int m, double theta) except +
    float        sph_legendref(unsigned int l, unsigned int m, float theta) except +
    long double  sph_legendrel(unsigned int l, unsigned int m, long double theta) except +

    # spherical Neumann functions
    # spherical Bessel functions of the second kind
    double       sph_neumann(unsigned int n, double x) except +
    float        sph_neumannf(unsigned int n, float x) except +
    long double  sph_neumannl(unsigned int n, long double x) except +