FFmpeg coverage

Directory: ../../../ffmpeg/
File: src/libavutil/mathematics.c
Date: 2025-04-25 22:50:00
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 1905016 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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 1905016 if (a == 0)
41 641181 return b;
42
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 1263835 if (b == 0)
43 3542 return a;
44 1260293 za = ff_ctzll(a);
45 1260293 zb = ff_ctzll(b);
46 1260293 k = FFMIN(za, zb);
47 1260293 u = llabs(a >> za);
48 1260293 v = llabs(b >> zb);
49
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 6190640 while (u != v) {
50
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 4930347 if (u > v)
51 2190930 FFSWAP(int64_t, v, u);
52 4930347 v -= u;
53 4930347 v >>= ff_ctzll(v);
54 }
55 1260293 return (uint64_t)u << k;
56 }
57
58 14950066 int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd)
59 {
60 14950066 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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 14950066 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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 14950066 if (rnd & AV_ROUND_PASS_MINMAX) {
69
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 451351 if (a == INT64_MIN || a == INT64_MAX)
70 1394 return a;
71 449957 rnd -= AV_ROUND_PASS_MINMAX;
72 }
73
74
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 14948672 if (a < 0)
75 108035 return -(uint64_t)av_rescale_rnd(-FFMAX(a, -INT64_MAX), b, c, rnd ^ ((rnd >> 1) & 1));
76
77
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 14840637 if (rnd == AV_ROUND_NEAR_INF)
78 13664536 r = c / 2;
79
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 1176101 else if (rnd & 1)
80 283219 r = c - 1;
81
82
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 14840637 if (b <= INT_MAX && c <= INT_MAX) {
83
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 14596555 if (a <= INT_MAX)
84 14511290 return (a * b + r) / c;
85 else {
86 85265 int64_t ad = a / c;
87 85265 int64_t a2 = (a % c * b + r) / c;
88
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 85265 if (ad >= INT32_MAX && b && ad > (INT64_MAX - a2) / b)
89 1 return INT64_MIN;
90 85264 return ad * b + a2;
91 }
92 } else {
93 #if 1
94 244082 uint64_t a0 = a & 0xFFFFFFFF;
95 244082 uint64_t a1 = a >> 32;
96 244082 uint64_t b0 = b & 0xFFFFFFFF;
97 244082 uint64_t b1 = b >> 32;
98 244082 uint64_t t1 = a0 * b1 + a1 * b0;
99 244082 uint64_t t1a = t1 << 32;
100 int i;
101
102 244082 a0 = a0 * b0 + t1a;
103 244082 a1 = a1 * b1 + (t1 >> 32) + (a0 < t1a);
104 244082 a0 += r;
105 244082 a1 += a0 < r;
106
107
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108 15621248 a1 += a1 + ((a0 >> i) & 1);
109 15621248 t1 += t1;
110
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 15621248 if (c <= a1) {
111 1886740 a1 -= c;
112 1886740 t1++;
113 }
114 }
115
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 244082 if (t1 > INT64_MAX)
116 ✗ return INT64_MIN;
117 244082 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 1080356 int64_t av_rescale(int64_t a, int64_t b, int64_t c)
130 {
131 1080356 return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
132 }
133
134 12987729 int64_t av_rescale_q_rnd(int64_t a, AVRational bq, AVRational cq,
135 enum AVRounding rnd)
136 {
137 12987729 int64_t b = bq.num * (int64_t)cq.den;
138 12987729 int64_t c = cq.num * (int64_t)bq.den;
139 12987729 return av_rescale_rnd(a, b, c, rnd);
140 }
141
142 12134298 int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq)
143 {
144 12134298 return av_rescale_q_rnd(a, bq, cq, AV_ROUND_NEAR_INF);
145 }
146
147 959732 int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b)
148 {
149 959732 int64_t a = tb_a.num * (int64_t)tb_b.den;
150 959732 int64_t b = tb_b.num * (int64_t)tb_a.den;
151
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 959732 if ((FFABS64U(ts_a)|a|FFABS64U(ts_b)|b) <= INT_MAX)
152 951777 return (ts_a*a > ts_b*b) - (ts_a*a < ts_b*b);
153
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 7955 if (av_rescale_rnd(ts_a, a, b, AV_ROUND_DOWN) < ts_b)
154 6701 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 303364 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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 303364 av_assert0(in_ts != AV_NOPTS_VALUE);
172
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 303364 av_assert0(duration >= 0);
173
174
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 303364 if (*last == AV_NOPTS_VALUE || !duration || in_tb.num*(int64_t)out_tb.den <= out_tb.num*(int64_t)in_tb.den) {
175 258368 simple_round:
176 258999 *last = av_rescale_q(in_ts, in_tb, fs_tb) + duration;
177 258999 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 508577 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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 508577 if (inc != 1)
196 ✗ inc_tb = av_mul_q(inc_tb, (AVRational) {inc, 1});
197
198 508577 m = inc_tb.num * (int64_t)ts_tb.den;
199 508577 d = inc_tb.den * (int64_t)ts_tb.num;
200
201
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 508577 if (m % d == 0 && ts <= INT64_MAX - m / d)
202 495253 return ts + m / d;
203
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 13324 if (m < d)
204 2822 return ts;
205
206 {
207 10502 int64_t old = av_rescale_q(ts, ts_tb, inc_tb);
208 10502 int64_t old_ts = av_rescale_q(old, inc_tb, ts_tb);
209
210
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 10502 if (old == INT64_MAX || old == AV_NOPTS_VALUE || old_ts == AV_NOPTS_VALUE)
211 ✗ return ts;
212
213 10502 return av_sat_add64(av_rescale_q(old + 1, inc_tb, ts_tb), ts - old_ts);
214 }
215 }
216
217 84998756 static inline double eval_poly(const double *coeff, int size, double x) {
218 84998756 double sum = coeff[size-1];
219 int i;
220
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 892336314 for (i = size-2; i >= 0; --i) {
221 807337558 sum *= x;
222 807337558 sum += coeff[i];
223 }
224 84998756 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 42501202 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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 42501202 if (x == 0)
307 1824 return 1.0;
308 42499378 x = fabs(x);
309
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 42499378 if (x <= 15) {
310 42474274 y = x * x;
311 42474274 return eval_poly(p1, FF_ARRAY_ELEMS(p1), y) / eval_poly(q1, FF_ARRAY_ELEMS(q1), y);
312 }
313 else {
314 25104 y = 1 / x - 1.0 / 15;
315 25104 r = eval_poly(p2, FF_ARRAY_ELEMS(p2), y) / eval_poly(q2, FF_ARRAY_ELEMS(q2), y);
316 25104 factor = exp(x) / sqrt(x);
317 25104 return factor * r;
318 }
319 }
320