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1/*
2 * erf function: Copyright (c) 2006 John Maddock
3 * This file is part of FFmpeg.
4 *
5 * FFmpeg is free software; you can redistribute it and/or
6 * modify it under the terms of the GNU Lesser General Public
7 * License as published by the Free Software Foundation; either
8 * version 2.1 of the License, or (at your option) any later version.
9 *
10 * FFmpeg is distributed in the hope that it will be useful,
11 * but WITHOUT ANY WARRANTY; without even the implied warranty of
12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 * Lesser General Public License for more details.
14 *
15 * You should have received a copy of the GNU Lesser General Public
16 * License along with FFmpeg; if not, write to the Free Software
17 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
18 */
19
20/**
21 * @file
22 * Replacements for frequently missing libm functions
23 */
24
25#ifndef AVUTIL_LIBM_H
26#define AVUTIL_LIBM_H
27
28#include <math.h>
29#include "config.h"
30#include "attributes.h"
31#include "intfloat.h"
32#include "mathematics.h"
33
34#if HAVE_MIPSFPU && HAVE_INLINE_ASM
35#include "libavutil/mips/libm_mips.h"
36#endif /* HAVE_MIPSFPU && HAVE_INLINE_ASM*/
37
38#if !HAVE_ATANF
39#undef atanf
40#define atanf(x) ((float)atan(x))
41#endif /* HAVE_ATANF */
42
43#if !HAVE_ATAN2F
44#undef atan2f
45#define atan2f(y, x) ((float)atan2(y, x))
46#endif /* HAVE_ATAN2F */
47
48#if !HAVE_POWF
49#undef powf
50#define powf(x, y) ((float)pow(x, y))
51#endif /* HAVE_POWF */
52
53#if !HAVE_CBRT
54static av_always_inline double cbrt(double x)
55{
56 return x < 0 ? -pow(-x, 1.0 / 3.0) : pow(x, 1.0 / 3.0);
57}
58#endif /* HAVE_CBRT */
59
60#if !HAVE_CBRTF
61static av_always_inline float cbrtf(float x)
62{
63 return x < 0 ? -powf(-x, 1.0 / 3.0) : powf(x, 1.0 / 3.0);
64}
65#endif /* HAVE_CBRTF */
66
67#if !HAVE_COPYSIGN
68static av_always_inline double copysign(double x, double y)
69{
70 uint64_t vx = av_double2int(x);
71 uint64_t vy = av_double2int(y);
72 return av_int2double((vx & UINT64_C(0x7fffffffffffffff)) | (vy & UINT64_C(0x8000000000000000)));
73}
74#endif /* HAVE_COPYSIGN */
75
76#if !HAVE_COSF
77#undef cosf
78#define cosf(x) ((float)cos(x))
79#endif /* HAVE_COSF */
80
81#if !HAVE_ERF
82static inline double ff_eval_poly(const double *coeff, int size, double x) {
83 double sum = coeff[size-1];
84 int i;
85 for (i = size-2; i >= 0; --i) {
86 sum *= x;
87 sum += coeff[i];
88 }
89 return sum;
90}
91
92/**
93 * erf function
94 * Algorithm taken from the Boost project, source:
95 * http://www.boost.org/doc/libs/1_46_1/boost/math/special_functions/erf.hpp
96 * Use, modification and distribution are subject to the
97 * Boost Software License, Version 1.0 (see notice below).
98 * Boost Software License - Version 1.0 - August 17th, 2003
99Permission is hereby granted, free of charge, to any person or organization
100obtaining a copy of the software and accompanying documentation covered by
101this license (the "Software") to use, reproduce, display, distribute,
102execute, and transmit the Software, and to prepare derivative works of the
103Software, and to permit third-parties to whom the Software is furnished to
104do so, all subject to the following:
105
106The copyright notices in the Software and this entire statement, including
107the above license grant, this restriction and the following disclaimer,
108must be included in all copies of the Software, in whole or in part, and
109all derivative works of the Software, unless such copies or derivative
110works are solely in the form of machine-executable object code generated by
111a source language processor.
112
113THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
114IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
115FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
116SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
117FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
118ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
119DEALINGS IN THE SOFTWARE.
120 */
121static inline double erf(double z)
122{
123#ifndef FF_ARRAY_ELEMS
124#define FF_ARRAY_ELEMS(a) (sizeof(a) / sizeof((a)[0]))
125#endif
126 double result;
127
128 /* handle the symmetry: erf(-x) = -erf(x) */
129 if (z < 0)
130 return -erf(-z);
131
132 /* branch based on range of z, and pick appropriate approximation */
133 if (z == 0)
134 return 0;
135 else if (z < 1e-10)
136 return z * 1.125 + z * 0.003379167095512573896158903121545171688;
137 else if (z < 0.5) {
138 // Maximum Deviation Found: 1.561e-17
139 // Expected Error Term: 1.561e-17
140 // Maximum Relative Change in Control Points: 1.155e-04
141 // Max Error found at double precision = 2.961182e-17
142
143 static const double y = 1.044948577880859375;
144 static const double p[] = {
145 0.0834305892146531832907,
146 -0.338165134459360935041,
147 -0.0509990735146777432841,
148 -0.00772758345802133288487,
149 -0.000322780120964605683831,
150 };
151 static const double q[] = {
152 1,
153 0.455004033050794024546,
154 0.0875222600142252549554,
155 0.00858571925074406212772,
156 0.000370900071787748000569,
157 };
158 double zz = z * z;
159 return z * (y + ff_eval_poly(p, FF_ARRAY_ELEMS(p), zz) / ff_eval_poly(q, FF_ARRAY_ELEMS(q), zz));
160 }
161 /* here onwards compute erfc */
162 else if (z < 1.5) {
163 // Maximum Deviation Found: 3.702e-17
164 // Expected Error Term: 3.702e-17
165 // Maximum Relative Change in Control Points: 2.845e-04
166 // Max Error found at double precision = 4.841816e-17
167 static const double y = 0.405935764312744140625;
168 static const double p[] = {
169 -0.098090592216281240205,
170 0.178114665841120341155,
171 0.191003695796775433986,
172 0.0888900368967884466578,
173 0.0195049001251218801359,
174 0.00180424538297014223957,
175 };
176 static const double q[] = {
177 1,
178 1.84759070983002217845,
179 1.42628004845511324508,
180 0.578052804889902404909,
181 0.12385097467900864233,
182 0.0113385233577001411017,
183 0.337511472483094676155e-5,
184 };
185 result = y + ff_eval_poly(p, FF_ARRAY_ELEMS(p), z - 0.5) / ff_eval_poly(q, FF_ARRAY_ELEMS(q), z - 0.5);
186 result *= exp(-z * z) / z;
187 return 1 - result;
188 }
189 else if (z < 2.5) {
190 // Max Error found at double precision = 6.599585e-18
191 // Maximum Deviation Found: 3.909e-18
192 // Expected Error Term: 3.909e-18
193 // Maximum Relative Change in Control Points: 9.886e-05
194 static const double y = 0.50672817230224609375;
195 static const double p[] = {
196 -0.0243500476207698441272,
197 0.0386540375035707201728,
198 0.04394818964209516296,
199 0.0175679436311802092299,
200 0.00323962406290842133584,
201 0.000235839115596880717416,
202 };
203 static const double q[] = {
204 1,
205 1.53991494948552447182,
206 0.982403709157920235114,
207 0.325732924782444448493,
208 0.0563921837420478160373,
209 0.00410369723978904575884,
210 };
211 result = y + ff_eval_poly(p, FF_ARRAY_ELEMS(p), z - 1.5) / ff_eval_poly(q, FF_ARRAY_ELEMS(q), z - 1.5);
212 result *= exp(-z * z) / z;
213 return 1 - result;
214 }
215 else if (z < 4.5) {
216 // Maximum Deviation Found: 1.512e-17
217 // Expected Error Term: 1.512e-17
218 // Maximum Relative Change in Control Points: 2.222e-04
219 // Max Error found at double precision = 2.062515e-17
220 static const double y = 0.5405750274658203125;
221 static const double p[] = {
222 0.00295276716530971662634,
223 0.0137384425896355332126,
224 0.00840807615555585383007,
225 0.00212825620914618649141,
226 0.000250269961544794627958,
227 0.113212406648847561139e-4,
228 };
229 static const double q[] = {
230 1,
231 1.04217814166938418171,
232 0.442597659481563127003,
233 0.0958492726301061423444,
234 0.0105982906484876531489,
235 0.000479411269521714493907,
236 };
237 result = y + ff_eval_poly(p, FF_ARRAY_ELEMS(p), z - 3.5) / ff_eval_poly(q, FF_ARRAY_ELEMS(q), z - 3.5);
238 result *= exp(-z * z) / z;
239 return 1 - result;
240 }
241 /* differ from Boost here, the claim of underflow of erfc(x) past 5.8 is
242 * slightly incorrect, change to 5.92
243 * (really somewhere between 5.9125 and 5.925 is when it saturates) */
244 else if (z < 5.92) {
245 // Max Error found at double precision = 2.997958e-17
246 // Maximum Deviation Found: 2.860e-17
247 // Expected Error Term: 2.859e-17
248 // Maximum Relative Change in Control Points: 1.357e-05
249 static const double y = 0.5579090118408203125;
250 static const double p[] = {
251 0.00628057170626964891937,
252 0.0175389834052493308818,
253 -0.212652252872804219852,
254 -0.687717681153649930619,
255 -2.5518551727311523996,
256 -3.22729451764143718517,
257 -2.8175401114513378771,
258 };
259 static const double q[] = {
260 1,
261 2.79257750980575282228,
262 11.0567237927800161565,
263 15.930646027911794143,
264 22.9367376522880577224,
265 13.5064170191802889145,
266 5.48409182238641741584,
267 };
268 result = y + ff_eval_poly(p, FF_ARRAY_ELEMS(p), 1 / z) / ff_eval_poly(q, FF_ARRAY_ELEMS(q), 1 / z);
269 result *= exp(-z * z) / z;
270 return 1 - result;
271 }
272 /* handle the nan case, but don't use isnan for max portability */
273 else if (z != z)
274 return z;
275 /* finally return saturated result */
276 else
277 return 1;
278}
279#endif /* HAVE_ERF */
280
281#if !HAVE_EXPF
282#undef expf
283#define expf(x) ((float)exp(x))
284#endif /* HAVE_EXPF */
285
286#if !HAVE_EXP2
287#undef exp2
288#define exp2(x) exp((x) * M_LN2)
289#endif /* HAVE_EXP2 */
290
291#if !HAVE_EXP2F
292#undef exp2f
293#define exp2f(x) ((float)exp2(x))
294#endif /* HAVE_EXP2F */
295
296#if !HAVE_ISINF
297#undef isinf
298/* Note: these do not follow the BSD/Apple/GNU convention of returning -1 for
299-Inf, +1 for Inf, 0 otherwise, but merely follow the POSIX/ISO mandated spec of
300returning a non-zero value for +/-Inf, 0 otherwise. */
301static av_always_inline av_const int avpriv_isinff(float x)
302{
303 uint32_t v = av_float2int(x);
304 if ((v & 0x7f800000) != 0x7f800000)
305 return 0;
306 return !(v & 0x007fffff);
307}
308
309static av_always_inline av_const int avpriv_isinf(double x)
310{
311 uint64_t v = av_double2int(x);
312 if ((v & 0x7ff0000000000000) != 0x7ff0000000000000)
313 return 0;
314 return !(v & 0x000fffffffffffff);
315}
316
317#define isinf(x) \
318 (sizeof(x) == sizeof(float) \
319 ? avpriv_isinff(x) \
320 : avpriv_isinf(x))
321#endif /* HAVE_ISINF */
322
323#if !HAVE_ISNAN
324static av_always_inline av_const int avpriv_isnanf(float x)
325{
326 uint32_t v = av_float2int(x);
327 if ((v & 0x7f800000) != 0x7f800000)
328 return 0;
329 return v & 0x007fffff;
330}
331
332static av_always_inline av_const int avpriv_isnan(double x)
333{
334 uint64_t v = av_double2int(x);
335 if ((v & 0x7ff0000000000000) != 0x7ff0000000000000)
336 return 0;
337 return (v & 0x000fffffffffffff) && 1;
338}
339
340#define isnan(x) \
341 (sizeof(x) == sizeof(float) \
342 ? avpriv_isnanf(x) \
343 : avpriv_isnan(x))
344#endif /* HAVE_ISNAN */
345
346#if !HAVE_ISFINITE
347static av_always_inline av_const int avpriv_isfinitef(float x)
348{
349 uint32_t v = av_float2int(x);
350 return (v & 0x7f800000) != 0x7f800000;
351}
352
353static av_always_inline av_const int avpriv_isfinite(double x)
354{
355 uint64_t v = av_double2int(x);
356 return (v & 0x7ff0000000000000) != 0x7ff0000000000000;
357}
358
359#define isfinite(x) \
360 (sizeof(x) == sizeof(float) \
361 ? avpriv_isfinitef(x) \
362 : avpriv_isfinite(x))
363#endif /* HAVE_ISFINITE */
364
365#if !HAVE_HYPOT
366static inline av_const double hypot(double x, double y)
367{
368 double ret, temp;
369 x = fabs(x);
370 y = fabs(y);
371
372 if (isinf(x) || isinf(y))
373 return av_int2double(0x7ff0000000000000);
374 if (x == 0 || y == 0)
375 return x + y;
376 if (x < y) {
377 temp = x;
378 x = y;
379 y = temp;
380 }
381
382 y = y/x;
383 return x*sqrt(1 + y*y);
384}
385#endif /* HAVE_HYPOT */
386
387#if !HAVE_LDEXPF
388#undef ldexpf
389#define ldexpf(x, exp) ((float)ldexp(x, exp))
390#endif /* HAVE_LDEXPF */
391
392#if !HAVE_LLRINT
393#undef llrint
394#define llrint(x) ((long long)rint(x))
395#endif /* HAVE_LLRINT */
396
397#if !HAVE_LLRINTF
398#undef llrintf
399#define llrintf(x) ((long long)rint(x))
400#endif /* HAVE_LLRINT */
401
402#if !HAVE_LOG2
403#undef log2
404#define log2(x) (log(x) * 1.44269504088896340736)
405#endif /* HAVE_LOG2 */
406
407#if !HAVE_LOG2F
408#undef log2f
409#define log2f(x) ((float)log2(x))
410#endif /* HAVE_LOG2F */
411
412#if !HAVE_LOG10F
413#undef log10f
414#define log10f(x) ((float)log10(x))
415#endif /* HAVE_LOG10F */
416
417#if !HAVE_SINF
418#undef sinf
419#define sinf(x) ((float)sin(x))
420#endif /* HAVE_SINF */
421
422#if !HAVE_RINT
423static inline double rint(double x)
424{
425 return x >= 0 ? floor(x + 0.5) : ceil(x - 0.5);
426}
427#endif /* HAVE_RINT */
428
429#if !HAVE_LRINT
430static av_always_inline av_const long int lrint(double x)
431{
432 return rint(x);
433}
434#endif /* HAVE_LRINT */
435
436#if !HAVE_LRINTF
437static av_always_inline av_const long int lrintf(float x)
438{
439 return (int)(rint(x));
440}
441#endif /* HAVE_LRINTF */
442
443#if !HAVE_ROUND
444static av_always_inline av_const double round(double x)
445{
446 return (x > 0) ? floor(x + 0.5) : ceil(x - 0.5);
447}
448#endif /* HAVE_ROUND */
449
450#if !HAVE_ROUNDF
451static av_always_inline av_const float roundf(float x)
452{
453 return (x > 0) ? floor(x + 0.5) : ceil(x - 0.5);
454}
455#endif /* HAVE_ROUNDF */
456
457#if !HAVE_TRUNC
458static av_always_inline av_const double trunc(double x)
459{
460 return (x > 0) ? floor(x) : ceil(x);
461}
462#endif /* HAVE_TRUNC */
463
464#if !HAVE_TRUNCF
465static av_always_inline av_const float truncf(float x)
466{
467 return (x > 0) ? floor(x) : ceil(x);
468}
469#endif /* HAVE_TRUNCF */
470
471#endif /* AVUTIL_LIBM_H */
472
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