FFmpeg coverage

Directory: ../../../ffmpeg/
File: src/libavutil/mathematics.c
Date: 2025-06-23 20:06:14
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 1908757 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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 1908757 if (a == 0)
41 642094 return b;
42
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 1266663 if (b == 0)
43 3542 return a;
44 1263121 za = ff_ctzll(a);
45 1263121 zb = ff_ctzll(b);
46 1263121 k = FFMIN(za, zb);
47 1263121 u = llabs(a >> za);
48 1263121 v = llabs(b >> zb);
49
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 6200641 while (u != v) {
50
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 4937520 if (u > v)
51 2195730 FFSWAP(int64_t, v, u);
52 4937520 v -= u;
53 4937520 v >>= ff_ctzll(v);
54 }
55 1263121 return (uint64_t)u << k;
56 }
57
58 14962170 int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd)
59 {
60 14962170 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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 14962170 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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 14962170 if (rnd & AV_ROUND_PASS_MINMAX) {
69
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 451388 if (a == INT64_MIN || a == INT64_MAX)
70 1410 return a;
71 449978 rnd -= AV_ROUND_PASS_MINMAX;
72 }
73
74
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 14960760 if (a < 0)
75 107972 return -(uint64_t)av_rescale_rnd(-FFMAX(a, -INT64_MAX), b, c, rnd ^ ((rnd >> 1) & 1));
76
77
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 14852788 if (rnd == AV_ROUND_NEAR_INF)
78 13676563 r = c / 2;
79
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 1176225 else if (rnd & 1)
80 283368 r = c - 1;
81
82
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 14852788 if (b <= INT_MAX && c <= INT_MAX) {
83
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 14608650 if (a <= INT_MAX)
84 14523387 return (a * b + r) / c;
85 else {
86 85263 int64_t ad = a / c;
87 85263 int64_t a2 = (a % c * b + r) / c;
88
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 85263 if (ad >= INT32_MAX && b && ad > (INT64_MAX - a2) / b)
89 1 return INT64_MIN;
90 85262 return ad * b + a2;
91 }
92 } else {
93 #if 1
94 244138 uint64_t a0 = a & 0xFFFFFFFF;
95 244138 uint64_t a1 = a >> 32;
96 244138 uint64_t b0 = b & 0xFFFFFFFF;
97 244138 uint64_t b1 = b >> 32;
98 244138 uint64_t t1 = a0 * b1 + a1 * b0;
99 244138 uint64_t t1a = t1 << 32;
100 int i;
101
102 244138 a0 = a0 * b0 + t1a;
103 244138 a1 = a1 * b1 + (t1 >> 32) + (a0 < t1a);
104 244138 a0 += r;
105 244138 a1 += a0 < r;
106
107
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 15868970 for (i = 63; i >= 0; i--) {
108 15624832 a1 += a1 + ((a0 >> i) & 1);
109 15624832 t1 += t1;
110
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 15624832 if (c <= a1) {
111 1887194 a1 -= c;
112 1887194 t1++;
113 }
114 }
115
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 244138 if (t1 > INT64_MAX)
116 ✗ return INT64_MIN;
117 244138 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 1080181 int64_t av_rescale(int64_t a, int64_t b, int64_t c)
130 {
131 1080181 return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
132 }
133
134 13000107 int64_t av_rescale_q_rnd(int64_t a, AVRational bq, AVRational cq,
135 enum AVRounding rnd)
136 {
137 13000107 int64_t b = bq.num * (int64_t)cq.den;
138 13000107 int64_t c = cq.num * (int64_t)bq.den;
139 13000107 return av_rescale_rnd(a, b, c, rnd);
140 }
141
142 12146479 int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq)
143 {
144 12146479 return av_rescale_q_rnd(a, bq, cq, AV_ROUND_NEAR_INF);
145 }
146
147 959552 int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b)
148 {
149 959552 int64_t a = tb_a.num * (int64_t)tb_b.den;
150 959552 int64_t b = tb_b.num * (int64_t)tb_a.den;
151
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 959552 if ((FFABS64U(ts_a)|a|FFABS64U(ts_b)|b) <= INT_MAX)
152 951596 return (ts_a*a > ts_b*b) - (ts_a*a < ts_b*b);
153
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 7956 if (av_rescale_rnd(ts_a, a, b, AV_ROUND_DOWN) < ts_b)
154 6702 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 303503 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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 303503 av_assert0(in_ts != AV_NOPTS_VALUE);
172
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 303503 av_assert0(duration >= 0);
173
174
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 303503 if (*last == AV_NOPTS_VALUE || !duration || in_tb.num*(int64_t)out_tb.den <= out_tb.num*(int64_t)in_tb.den) {
175 258507 simple_round:
176 259138 *last = av_rescale_q(in_ts, in_tb, fs_tb) + duration;
177 259138 return av_rescale_q(in_ts, in_tb, out_tb);
178 }
179
180 44996 a = av_rescale_q_rnd(2*in_ts-1, in_tb, fs_tb, AV_ROUND_DOWN) >>1;
181 44996 b = (av_rescale_q_rnd(2*in_ts+1, in_tb, fs_tb, AV_ROUND_UP )+1)>>1;
182
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 44996 if (*last < 2*a - b || *last > 2*b - a)
183 631 goto simple_round;
184
185 44365 this = av_clip64(*last, a, b);
186 44365 *last = this + duration;
187
188 44365 return av_rescale_q(this, fs_tb, out_tb);
189 }
190
191 508549 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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 508549 if (inc != 1)
196 ✗ inc_tb = av_mul_q(inc_tb, (AVRational) {inc, 1});
197
198 508549 m = inc_tb.num * (int64_t)ts_tb.den;
199 508549 d = inc_tb.den * (int64_t)ts_tb.num;
200
201
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 508549 if (m % d == 0 && ts <= INT64_MAX - m / d)
202 495230 return ts + m / d;
203
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 13319 if (m < d)
204 2822 return ts;
205
206 {
207 10497 int64_t old = av_rescale_q(ts, ts_tb, inc_tb);
208 10497 int64_t old_ts = av_rescale_q(old, inc_tb, ts_tb);
209
210
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 10497 if (old == INT64_MAX || old == AV_NOPTS_VALUE || old_ts == AV_NOPTS_VALUE)
211 ✗ return ts;
212
213 10497 return av_sat_add64(av_rescale_q(old + 1, inc_tb, ts_tb), ts - old_ts);
214 }
215 }
216
217 84999524 static inline double eval_poly(const double *coeff, int size, double x) {
218 84999524 double sum = coeff[size-1];
219 int i;
220
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 892343694 for (i = size-2; i >= 0; --i) {
221 807344170 sum *= x;
222 807344170 sum += coeff[i];
223 }
224 84999524 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 42501589 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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 42501589 if (x == 0)
307 1827 return 1.0;
308 42499762 x = fabs(x);
309
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 42499762 if (x <= 15) {
310 42474544 y = x * x;
311 42474544 return eval_poly(p1, FF_ARRAY_ELEMS(p1), y) / eval_poly(q1, FF_ARRAY_ELEMS(q1), y);
312 }
313 else {
314 25218 y = 1 / x - 1.0 / 15;
315 25218 r = eval_poly(p2, FF_ARRAY_ELEMS(p2), y) / eval_poly(q2, FF_ARRAY_ELEMS(q2), y);
316 25218 factor = exp(x) / sqrt(x);
317 25218 return factor * r;
318 }
319 }
320