FFmpeg coverage

Directory: ../../../ffmpeg/
File: src/libavutil/mathematics.c
Date: 2025-08-19 23:55:23
Exec Total Coverage
Lines: 116 125 92.8%
Functions: 10 11 90.9%
Branches: 75 92 81.5%
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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 1931617 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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 1931617 if (a == 0)
41 655489 return b;
42
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 1276128 if (b == 0)
43 3542 return a;
44 1272586 za = ff_ctzll(a);
45 1272586 zb = ff_ctzll(b);
46 1272586 k = FFMIN(za, zb);
47 1272586 u = llabs(a >> za);
48 1272586 v = llabs(b >> zb);
49
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 6237508 while (u != v) {
50
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 4964922 if (u > v)
51 2212749 FFSWAP(int64_t, v, u);
52 4964922 v -= u;
53 4964922 v >>= ff_ctzll(v);
54 }
55 1272586 return (uint64_t)u << k;
56 }
57
58 15076896 int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd)
59 {
60 15076896 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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 15076896 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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 15076896 if (rnd & AV_ROUND_PASS_MINMAX) {
69
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 458079 if (a == INT64_MIN || a == INT64_MAX)
70 1424 return a;
71 456655 rnd -= AV_ROUND_PASS_MINMAX;
72 }
73
74
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 15075472 if (a < 0)
75 108381 return -(uint64_t)av_rescale_rnd(-FFMAX(a, -INT64_MAX), b, c, rnd ^ ((rnd >> 1) & 1));
76
77
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 14967091 if (rnd == AV_ROUND_NEAR_INF)
78 13785327 r = c / 2;
79
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 1181764 else if (rnd & 1)
80 283389 r = c - 1;
81
82
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 14967091 if (b <= INT_MAX && c <= INT_MAX) {
83
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 14723006 if (a <= INT_MAX)
84 14637744 return (a * b + r) / c;
85 else {
86 85262 int64_t ad = a / c;
87 85262 int64_t a2 = (a % c * b + r) / c;
88
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 85262 if (ad >= INT32_MAX && b && ad > (INT64_MAX - a2) / b)
89 1 return INT64_MIN;
90 85261 return ad * b + a2;
91 }
92 } else {
93 #if 1
94 244085 uint64_t a0 = a & 0xFFFFFFFF;
95 244085 uint64_t a1 = a >> 32;
96 244085 uint64_t b0 = b & 0xFFFFFFFF;
97 244085 uint64_t b1 = b >> 32;
98 244085 uint64_t t1 = a0 * b1 + a1 * b0;
99 244085 uint64_t t1a = t1 << 32;
100 int i;
101
102 244085 a0 = a0 * b0 + t1a;
103 244085 a1 = a1 * b1 + (t1 >> 32) + (a0 < t1a);
104 244085 a0 += r;
105 244085 a1 += a0 < r;
106
107
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 15865525 for (i = 63; i >= 0; i--) {
108 15621440 a1 += a1 + ((a0 >> i) & 1);
109 15621440 t1 += t1;
110
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 15621440 if (c <= a1) {
111 1886509 a1 -= c;
112 1886509 t1++;
113 }
114 }
115
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 244085 if (t1 > INT64_MAX)
116 ✗ return INT64_MIN;
117 244085 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 1080938 int64_t av_rescale(int64_t a, int64_t b, int64_t c)
130 {
131 1080938 return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
132 }
133
134 13108103 int64_t av_rescale_q_rnd(int64_t a, AVRational bq, AVRational cq,
135 enum AVRounding rnd)
136 {
137 13108103 int64_t b = bq.num * (int64_t)cq.den;
138 13108103 int64_t c = cq.num * (int64_t)bq.den;
139 13108103 return av_rescale_rnd(a, b, c, rnd);
140 }
141
142 12247809 int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq)
143 {
144 12247809 return av_rescale_q_rnd(a, bq, cq, AV_ROUND_NEAR_INF);
145 }
146
147 971528 int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b)
148 {
149 971528 int64_t a = tb_a.num * (int64_t)tb_b.den;
150 971528 int64_t b = tb_b.num * (int64_t)tb_a.den;
151
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 971528 if ((FFABS64U(ts_a)|a|FFABS64U(ts_b)|b) <= INT_MAX)
152 963592 return (ts_a*a > ts_b*b) - (ts_a*a < ts_b*b);
153
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 7936 if (av_rescale_rnd(ts_a, a, b, AV_ROUND_DOWN) < ts_b)
154 6682 return -1;
155
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 1254 if (av_rescale_rnd(ts_b, b, a, AV_ROUND_DOWN) < ts_a)
156 193 return 1;
157 1061 return 0;
158 }
159
160 ✗ int64_t av_compare_mod(uint64_t a, uint64_t b, uint64_t mod)
161 {
162 ✗ int64_t c = (a - b) & (mod - 1);
163 ✗ if (c > (mod >> 1))
164 ✗ c -= mod;
165 ✗ return c;
166 }
167
168 303741 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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 303741 av_assert0(in_ts != AV_NOPTS_VALUE);
172
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 303741 av_assert0(duration >= 0);
173
174
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 303741 if (*last == AV_NOPTS_VALUE || !duration || in_tb.num*(int64_t)out_tb.den <= out_tb.num*(int64_t)in_tb.den) {
175 258750 simple_round:
176 259381 *last = av_rescale_q(in_ts, in_tb, fs_tb) + duration;
177 259381 return av_rescale_q(in_ts, in_tb, out_tb);
178 }
179
180 44991 a = av_rescale_q_rnd(2*in_ts-1, in_tb, fs_tb, AV_ROUND_DOWN) >>1;
181 44991 b = (av_rescale_q_rnd(2*in_ts+1, in_tb, fs_tb, AV_ROUND_UP )+1)>>1;
182
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 44991 if (*last < 2*a - b || *last > 2*b - a)
183 631 goto simple_round;
184
185 44360 this = av_clip64(*last, a, b);
186 44360 *last = this + duration;
187
188 44360 return av_rescale_q(this, fs_tb, out_tb);
189 }
190
191 513705 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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 513705 if (inc != 1)
196 ✗ inc_tb = av_mul_q(inc_tb, (AVRational) {inc, 1});
197
198 513705 m = inc_tb.num * (int64_t)ts_tb.den;
199 513705 d = inc_tb.den * (int64_t)ts_tb.num;
200
201
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 513705 if (m % d == 0 && ts <= INT64_MAX - m / d)
202 500393 return ts + m / d;
203
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 13312 if (m < d)
204 2822 return ts;
205
206 {
207 10490 int64_t old = av_rescale_q(ts, ts_tb, inc_tb);
208 10490 int64_t old_ts = av_rescale_q(old, inc_tb, ts_tb);
209
210
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 10490 if (old == INT64_MAX || old == AV_NOPTS_VALUE || old_ts == AV_NOPTS_VALUE)
211 ✗ return ts;
212
213 10490 return av_sat_add64(av_rescale_q(old + 1, inc_tb, ts_tb), ts - old_ts);
214 }
215 }
216
217 85006422 static inline double eval_poly(const double *coeff, int size, double x) {
218 85006422 double sum = coeff[size-1];
219 int i;
220
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221 807408321 sum *= x;
222 807408321 sum += coeff[i];
223 }
224 85006422 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 42505051 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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 42505051 if (x == 0)
307 1840 return 1.0;
308 42503211 x = fabs(x);
309
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 42503211 if (x <= 15) {
310 42477763 y = x * x;
311 42477763 return eval_poly(p1, FF_ARRAY_ELEMS(p1), y) / eval_poly(q1, FF_ARRAY_ELEMS(q1), y);
312 }
313 else {
314 25448 y = 1 / x - 1.0 / 15;
315 25448 r = eval_poly(p2, FF_ARRAY_ELEMS(p2), y) / eval_poly(q2, FF_ARRAY_ELEMS(q2), y);
316 25448 factor = exp(x) / sqrt(x);
317 25448 return factor * r;
318 }
319 }
320