FFmpeg coverage

Directory: ../../../ffmpeg/
File: src/libavutil/mathematics.c
Date: 2026-08-30 18:45:47
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 13408650 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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 13408650 if (a == 0)
41 1612248 return b;
42
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 11796402 if (b == 0)
43 3823 return a;
44 11792579 za = ff_ctzll(a);
45 11792579 zb = ff_ctzll(b);
46 11792579 k = FFMIN(za, zb);
47 11792579 u = llabs(a >> za);
48 11792579 v = llabs(b >> zb);
49
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 75832434 while (u != v) {
50
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 64039855 if (u > v)
51 37802705 FFSWAP(int64_t, v, u);
52 64039855 v -= u;
53 64039855 v >>= ff_ctzll(v);
54 }
55 11792579 return (uint64_t)u << k;
56 }
57
58 17707269 int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd)
59 {
60 17707269 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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 17707269 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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 17707269 if (rnd & AV_ROUND_PASS_MINMAX) {
69
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 736443 if (a == INT64_MIN || a == INT64_MAX)
70 1556 return a;
71 734887 rnd -= AV_ROUND_PASS_MINMAX;
72 }
73
74
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 17705713 if (a < 0)
75 127899 return -(uint64_t)av_rescale_rnd(-FFMAX(a, -INT64_MAX), b, c, rnd ^ ((rnd >> 1) & 1));
76
77
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 17577814 if (rnd == AV_ROUND_NEAR_INF)
78 16251099 r = c / 2;
79
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 1326715 else if (rnd & 1)
80 359197 r = c - 1;
81
82
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 17577814 if (b <= INT_MAX && c <= INT_MAX) {
83
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 17309255 if (a <= INT_MAX)
84 17223427 return (a * b + r) / c;
85 else {
86 85828 int64_t ad = a / c;
87 85828 int64_t a2 = (a % c * b + r) / c;
88
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 85828 if (ad >= INT32_MAX && b && ad > (INT64_MAX - a2) / b)
89 1 return INT64_MIN;
90 85827 return ad * b + a2;
91 }
92 } else {
93 #if 1
94 268559 uint64_t a0 = a & 0xFFFFFFFF;
95 268559 uint64_t a1 = a >> 32;
96 268559 uint64_t b0 = b & 0xFFFFFFFF;
97 268559 uint64_t b1 = b >> 32;
98 268559 uint64_t t1 = a0 * b1 + a1 * b0;
99 268559 uint64_t t1a = t1 << 32;
100 int i;
101
102 268559 a0 = a0 * b0 + t1a;
103 268559 a1 = a1 * b1 + (t1 >> 32) + (a0 < t1a);
104 268559 a0 += r;
105 268559 a1 += a0 < r;
106
107
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 17456335 for (i = 63; i >= 0; i--) {
108 17187776 a1 += a1 + ((a0 >> i) & 1);
109 17187776 t1 += t1;
110
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 17187776 if (c <= a1) {
111 2166784 a1 -= c;
112 2166784 t1++;
113 }
114 }
115
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 268559 if (t1 > INT64_MAX)
116 ✗ return INT64_MIN;
117 268559 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 1258281 int64_t av_rescale(int64_t a, int64_t b, int64_t c)
130 {
131 1258281 return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
132 }
133
134 15501469 int64_t av_rescale_q_rnd(int64_t a, AVRational bq, AVRational cq,
135 enum AVRounding rnd)
136 {
137 15501469 int64_t b = bq.num * (int64_t)cq.den;
138 15501469 int64_t c = cq.num * (int64_t)bq.den;
139 15501469 return av_rescale_rnd(a, b, c, rnd);
140 }
141
142 14258004 int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq)
143 {
144 14258004 return av_rescale_q_rnd(a, bq, cq, AV_ROUND_NEAR_INF);
145 }
146
147 1077473 int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b)
148 {
149 1077473 int64_t a = tb_a.num * (int64_t)tb_b.den;
150 1077473 int64_t b = tb_b.num * (int64_t)tb_a.den;
151
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 1077473 if ((FFABS64U(ts_a)|a|FFABS64U(ts_b)|b) <= INT_MAX)
152 1069861 return (ts_a*a > ts_b*b) - (ts_a*a < ts_b*b);
153
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 7612 if (av_rescale_rnd(ts_a, a, b, AV_ROUND_DOWN) < ts_b)
154 6341 return -1;
155
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 1271 if (av_rescale_rnd(ts_b, b, a, AV_ROUND_DOWN) < ts_a)
156 202 return 1;
157 1069 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 360831 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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 360831 av_assert0(in_ts != AV_NOPTS_VALUE);
172
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 360831 av_assert0(duration >= 0);
173
174
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 360831 if (*last == AV_NOPTS_VALUE || !duration || in_tb.num*(int64_t)out_tb.den <= out_tb.num*(int64_t)in_tb.den) {
175 307185 simple_round:
176 307835 *last = av_rescale_q(in_ts, in_tb, fs_tb) + duration;
177 307835 return av_rescale_q(in_ts, in_tb, out_tb);
178 }
179
180 53646 a = av_rescale_q_rnd(2*in_ts-1, in_tb, fs_tb, AV_ROUND_DOWN) >>1;
181 53646 b = (av_rescale_q_rnd(2*in_ts+1, in_tb, fs_tb, AV_ROUND_UP )+1)>>1;
182
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 53646 if (*last < 2*a - b || *last > 2*b - a)
183 650 goto simple_round;
184
185 52996 this = av_clip64(*last, a, b);
186 52996 *last = this + duration;
187
188 52996 return av_rescale_q(this, fs_tb, out_tb);
189 }
190
191 588131 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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 588131 if (inc != 1)
196 10004 inc_tb = av_mul_q(inc_tb, (AVRational) {inc, 1});
197
198 588131 m = inc_tb.num * (int64_t)ts_tb.den;
199 588131 d = inc_tb.den * (int64_t)ts_tb.num;
200
201
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 588131 if (m % d == 0 && ts <= INT64_MAX - m / d)
202 574298 return ts + m / d;
203
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 13833 if (m < d)
204 2823 return ts;
205
206 {
207 11010 int64_t old = av_rescale_q(ts, ts_tb, inc_tb);
208 11010 int64_t old_ts = av_rescale_q(old, inc_tb, ts_tb);
209
210
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 11010 if (old == INT64_MAX || old == AV_NOPTS_VALUE || old_ts == AV_NOPTS_VALUE)
211 ✗ return ts;
212
213 11010 return av_sat_add64(av_rescale_q(old + 1, inc_tb, ts_tb), ts - old_ts);
214 }
215 }
216
217 85190780 static inline double eval_poly(const double *coeff, int size, double x) {
218 85190780 double sum = coeff[size-1];
219 int i;
220
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 894313236 for (i = size-2; i >= 0; --i) {
221 809122456 sum *= x;
222 809122456 sum += coeff[i];
223 }
224 85190780 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 42597532 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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 42597532 if (x == 0)
307 2142 return 1.0;
308 42595390 x = fabs(x);
309
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 42595390 if (x <= 15) {
310 42563731 y = x * x;
311 42563731 return eval_poly(p1, FF_ARRAY_ELEMS(p1), y) / eval_poly(q1, FF_ARRAY_ELEMS(q1), y);
312 }
313 else {
314 31659 y = 1 / x - 1.0 / 15;
315 31659 r = eval_poly(p2, FF_ARRAY_ELEMS(p2), y) / eval_poly(q2, FF_ARRAY_ELEMS(q2), y);
316 31659 factor = exp(x) / sqrt(x);
317 31659 return factor * r;
318 }
319 }
320