FFmpeg coverage

Directory: ../../../ffmpeg/
File: src/libavutil/mathematics.c
Date: 2026-09-29 17:04:06
Exec Total Coverage
Lines: 122 125 97.6%
Functions: 11 11 100.0%
Branches: 79 92 85.9%
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1 /*
2 * Copyright (c) 2005-2012 Michael Niedermayer <michaelni@gmx.at>
3 *
4 * This file is part of FFmpeg.
5 *
6 * FFmpeg is free software; you can redistribute it and/or
7 * modify it under the terms of the GNU Lesser General Public
8 * License as published by the Free Software Foundation; either
9 * version 2.1 of the License, or (at your option) any later version.
10 *
11 * FFmpeg is distributed in the hope that it will be useful,
12 * but WITHOUT ANY WARRANTY; without even the implied warranty of
13 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 * Lesser General Public License for more details.
15 *
16 * You should have received a copy of the GNU Lesser General Public
17 * License along with FFmpeg; if not, write to the Free Software
18 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
19 */
20
21 /**
22 * @file
23 * miscellaneous math routines and tables
24 */
25
26 #include <stdint.h>
27 #include <limits.h>
28
29 #include "avutil.h"
30 #include "mathematics.h"
31 #include "libavutil/intmath.h"
32 #include "libavutil/common.h"
33 #include "avassert.h"
34
35 /* Stein's binary GCD algorithm:
36 * https://en.wikipedia.org/wiki/Binary_GCD_algorithm */
37 13420656 int64_t av_gcd(int64_t a, int64_t b) {
38 int za, zb, k;
39 int64_t u, v;
40
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 13420656 if (a == 0)
41 1619700 return b;
42
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 11800956 if (b == 0)
43 3846 return a;
44 11797110 za = ff_ctzll(a);
45 11797110 zb = ff_ctzll(b);
46 11797110 k = FFMIN(za, zb);
47 11797110 u = llabs(a >> za);
48 11797110 v = llabs(b >> zb);
49
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 75847896 while (u != v) {
50
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 64050786 if (u > v)
51 37804444 FFSWAP(int64_t, v, u);
52 64050786 v -= u;
53 64050786 v >>= ff_ctzll(v);
54 }
55 11797110 return (uint64_t)u << k;
56 }
57
58 17673693 int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd)
59 {
60 17673693 int64_t r = 0;
61 av_assert2(c > 0);
62 av_assert2(b >=0);
63 av_assert2((unsigned)(rnd&~AV_ROUND_PASS_MINMAX)<=5 && (rnd&~AV_ROUND_PASS_MINMAX)!=4);
64
65
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 17673693 if (c <= 0 || b < 0 || !((unsigned)(rnd&~AV_ROUND_PASS_MINMAX)<=5 && (rnd&~AV_ROUND_PASS_MINMAX)!=4))
66 ✗ return INT64_MIN;
67
68
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 17673693 if (rnd & AV_ROUND_PASS_MINMAX) {
69
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 720564 if (a == INT64_MIN || a == INT64_MAX)
70 1587 return a;
71 718977 rnd -= AV_ROUND_PASS_MINMAX;
72 }
73
74
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 17672106 if (a < 0)
75 127795 return -(uint64_t)av_rescale_rnd(-FFMAX(a, -INT64_MAX), b, c, rnd ^ ((rnd >> 1) & 1));
76
77
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 17544311 if (rnd == AV_ROUND_NEAR_INF)
78 16212284 r = c / 2;
79
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 1332027 else if (rnd & 1)
80 359940 r = c - 1;
81
82
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 17544311 if (b <= INT_MAX && c <= INT_MAX) {
83
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 17274994 if (a <= INT_MAX)
84 17189204 return (a * b + r) / c;
85 else {
86 85790 int64_t ad = a / c;
87 85790 int64_t a2 = (a % c * b + r) / c;
88
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 85790 if (ad >= INT32_MAX && b && ad > (INT64_MAX - a2) / b)
89 1 return INT64_MIN;
90 85789 return ad * b + a2;
91 }
92 } else {
93 #if 1
94 269317 uint64_t a0 = a & 0xFFFFFFFF;
95 269317 uint64_t a1 = a >> 32;
96 269317 uint64_t b0 = b & 0xFFFFFFFF;
97 269317 uint64_t b1 = b >> 32;
98 269317 uint64_t t1 = a0 * b1 + a1 * b0;
99 269317 uint64_t t1a = t1 << 32;
100 int i;
101
102 269317 a0 = a0 * b0 + t1a;
103 269317 a1 = a1 * b1 + (t1 >> 32) + (a0 < t1a);
104 269317 a0 += r;
105 269317 a1 += a0 < r;
106
107
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 17505605 for (i = 63; i >= 0; i--) {
108 17236288 a1 += a1 + ((a0 >> i) & 1);
109 17236288 t1 += t1;
110
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 17236288 if (c <= a1) {
111 2171222 a1 -= c;
112 2171222 t1++;
113 }
114 }
115
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 269317 if (t1 > INT64_MAX)
116 ✗ return INT64_MIN;
117 269317 return t1;
118 #else
119 /* reference code doing (a*b + r) / c, requires libavutil/integer.h */
120 AVInteger ai;
121 ai = av_mul_i(av_int2i(a), av_int2i(b));
122 ai = av_add_i(ai, av_int2i(r));
123
124 return av_i2int(av_div_i(ai, av_int2i(c)));
125 #endif
126 }
127 }
128
129 1259738 int64_t av_rescale(int64_t a, int64_t b, int64_t c)
130 {
131 1259738 return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
132 }
133
134 15462243 int64_t av_rescale_q_rnd(int64_t a, AVRational bq, AVRational cq,
135 enum AVRounding rnd)
136 {
137 15462243 int64_t b = bq.num * (int64_t)cq.den;
138 15462243 int64_t c = cq.num * (int64_t)bq.den;
139 15462243 return av_rescale_rnd(a, b, c, rnd);
140 }
141
142 14233642 int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq)
143 {
144 14233642 return av_rescale_q_rnd(a, bq, cq, AV_ROUND_NEAR_INF);
145 }
146
147 1048743 int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b)
148 {
149 1048743 int64_t a = tb_a.num * (int64_t)tb_b.den;
150 1048743 int64_t b = tb_b.num * (int64_t)tb_a.den;
151
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 1048743 if ((FFABS64U(ts_a)|a|FFABS64U(ts_b)|b) <= INT_MAX)
152 1041188 return (ts_a*a > ts_b*b) - (ts_a*a < ts_b*b);
153
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 7555 if (av_rescale_rnd(ts_a, a, b, AV_ROUND_DOWN) < ts_b)
154 6281 return -1;
155
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 1274 if (av_rescale_rnd(ts_b, b, a, AV_ROUND_DOWN) < ts_a)
156 202 return 1;
157 1072 return 0;
158 }
159
160 124 int64_t av_compare_mod(uint64_t a, uint64_t b, uint64_t mod)
161 {
162 124 int64_t c = (a - b) & (mod - 1);
163
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 124 if (c > (mod >> 1))
164 40 c -= mod;
165 124 return c;
166 }
167
168 365448 int64_t av_rescale_delta(AVRational in_tb, int64_t in_ts, AVRational fs_tb, int duration, int64_t *last, AVRational out_tb){
169 int64_t a, b, this;
170
171
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 365448 av_assert0(in_ts != AV_NOPTS_VALUE);
172
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 365448 av_assert0(duration >= 0);
173
174
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 365448 if (*last == AV_NOPTS_VALUE || !duration || in_tb.num*(int64_t)out_tb.den <= out_tb.num*(int64_t)in_tb.den) {
175 311757 simple_round:
176 312408 *last = av_rescale_q(in_ts, in_tb, fs_tb) + duration;
177 312408 return av_rescale_q(in_ts, in_tb, out_tb);
178 }
179
180 53691 a = av_rescale_q_rnd(2*in_ts-1, in_tb, fs_tb, AV_ROUND_DOWN) >>1;
181 53691 b = (av_rescale_q_rnd(2*in_ts+1, in_tb, fs_tb, AV_ROUND_UP )+1)>>1;
182
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 53691 if (*last < 2*a - b || *last > 2*b - a)
183 651 goto simple_round;
184
185 53040 this = av_clip64(*last, a, b);
186 53040 *last = this + duration;
187
188 53040 return av_rescale_q(this, fs_tb, out_tb);
189 }
190
191 592231 int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, int64_t inc)
192 {
193 int64_t m, d;
194
195
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 592231 if (inc != 1)
196 10004 inc_tb = av_mul_q(inc_tb, (AVRational) {inc, 1});
197
198 592231 m = inc_tb.num * (int64_t)ts_tb.den;
199 592231 d = inc_tb.den * (int64_t)ts_tb.num;
200
201
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 592231 if (m % d == 0 && ts <= INT64_MAX - m / d)
202 578442 return ts + m / d;
203
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 13789 if (m < d)
204 2823 return ts;
205
206 {
207 10966 int64_t old = av_rescale_q(ts, ts_tb, inc_tb);
208 10966 int64_t old_ts = av_rescale_q(old, inc_tb, ts_tb);
209
210
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 10966 if (old == INT64_MAX || old == AV_NOPTS_VALUE || old_ts == AV_NOPTS_VALUE)
211 ✗ return ts;
212
213 10966 return av_sat_add64(av_rescale_q(old + 1, inc_tb, ts_tb), ts - old_ts);
214 }
215 }
216
217 85282530 static inline double eval_poly(const double *coeff, int size, double x) {
218 85282530 double sum = coeff[size-1];
219 int i;
220
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221 809975451 sum *= x;
222 809975451 sum += coeff[i];
223 }
224 85282530 return sum;
225 }
226
227 /**
228 * 0th order modified bessel function of the first kind.
229 * Algorithm taken from the Boost project, source:
230 * https://searchcode.com/codesearch/view/14918379/
231 * Use, modification and distribution are subject to the
232 * Boost Software License, Version 1.0 (see notice below).
233 * Boost Software License - Version 1.0 - August 17th, 2003
234 Permission is hereby granted, free of charge, to any person or organization
235 obtaining a copy of the software and accompanying documentation covered by
236 this license (the "Software") to use, reproduce, display, distribute,
237 execute, and transmit the Software, and to prepare derivative works of the
238 Software, and to permit third-parties to whom the Software is furnished to
239 do so, all subject to the following:
240
241 The copyright notices in the Software and this entire statement, including
242 the above license grant, this restriction and the following disclaimer,
243 must be included in all copies of the Software, in whole or in part, and
244 all derivative works of the Software, unless such copies or derivative
245 works are solely in the form of machine-executable object code generated by
246 a source language processor.
247
248 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
249 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
250 FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
251 SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
252 FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
253 ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
254 DEALINGS IN THE SOFTWARE.
255 */
256
257 42643572 double av_bessel_i0(double x) {
258 // Modified Bessel function of the first kind of order zero
259 // minimax rational approximations on intervals, see
260 // Blair and Edwards, Chalk River Report AECL-4928, 1974
261 static const double p1[] = {
262 -2.2335582639474375249e+15,
263 -5.5050369673018427753e+14,
264 -3.2940087627407749166e+13,
265 -8.4925101247114157499e+11,
266 -1.1912746104985237192e+10,
267 -1.0313066708737980747e+08,
268 -5.9545626019847898221e+05,
269 -2.4125195876041896775e+03,
270 -7.0935347449210549190e+00,
271 -1.5453977791786851041e-02,
272 -2.5172644670688975051e-05,
273 -3.0517226450451067446e-08,
274 -2.6843448573468483278e-11,
275 -1.5982226675653184646e-14,
276 -5.2487866627945699800e-18,
277 };
278 static const double q1[] = {
279 -2.2335582639474375245e+15,
280 7.8858692566751002988e+12,
281 -1.2207067397808979846e+10,
282 1.0377081058062166144e+07,
283 -4.8527560179962773045e+03,
284 1.0,
285 };
286 static const double p2[] = {
287 -2.2210262233306573296e-04,
288 1.3067392038106924055e-02,
289 -4.4700805721174453923e-01,
290 5.5674518371240761397e+00,
291 -2.3517945679239481621e+01,
292 3.1611322818701131207e+01,
293 -9.6090021968656180000e+00,
294 };
295 static const double q2[] = {
296 -5.5194330231005480228e-04,
297 3.2547697594819615062e-02,
298 -1.1151759188741312645e+00,
299 1.3982595353892851542e+01,
300 -6.0228002066743340583e+01,
301 8.5539563258012929600e+01,
302 -3.1446690275135491500e+01,
303 1.0,
304 };
305 double y, r, factor;
306
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 42643572 if (x == 0)
307 2307 return 1.0;
308 42641265 x = fabs(x);
309
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 42641265 if (x <= 15) {
310 42606501 y = x * x;
311 42606501 return eval_poly(p1, FF_ARRAY_ELEMS(p1), y) / eval_poly(q1, FF_ARRAY_ELEMS(q1), y);
312 }
313 else {
314 34764 y = 1 / x - 1.0 / 15;
315 34764 r = eval_poly(p2, FF_ARRAY_ELEMS(p2), y) / eval_poly(q2, FF_ARRAY_ELEMS(q2), y);
316 34764 factor = exp(x) / sqrt(x);
317 34764 return factor * r;
318 }
319 }
320