FFmpeg coverage


Directory: ../../../ffmpeg/
File: src/libavutil/mathematics.c
Date: 2024-03-28 14:59:00
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 1450836 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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1450836 if (a == 0)
41 532828 return b;
42
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918008 if (b == 0)
43 3260 return a;
44 914748 za = ff_ctzll(a);
45 914748 zb = ff_ctzll(b);
46 914748 k = FFMIN(za, zb);
47 914748 u = llabs(a >> za);
48 914748 v = llabs(b >> zb);
49
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4775436 while (u != v) {
50
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3860688 if (u > v)
51 1466567 FFSWAP(int64_t, v, u);
52 3860688 v -= u;
53 3860688 v >>= ff_ctzll(v);
54 }
55 914748 return (uint64_t)u << k;
56 }
57
58 13783963 int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd)
59 {
60 13783963 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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13783963 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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13783963 if (rnd & AV_ROUND_PASS_MINMAX) {
69
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432742 if (a == INT64_MIN || a == INT64_MAX)
70 1320 return a;
71 431422 rnd -= AV_ROUND_PASS_MINMAX;
72 }
73
74
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13782643 if (a < 0)
75 104895 return -(uint64_t)av_rescale_rnd(-FFMAX(a, -INT64_MAX), b, c, rnd ^ ((rnd >> 1) & 1));
76
77
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13677748 if (rnd == AV_ROUND_NEAR_INF)
78 12519689 r = c / 2;
79
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1158059 else if (rnd & 1)
80 279465 r = c - 1;
81
82
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13677748 if (b <= INT_MAX && c <= INT_MAX) {
83
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13517872 if (a <= INT_MAX)
84 13513081 return (a * b + r) / c;
85 else {
86 4791 int64_t ad = a / c;
87 4791 int64_t a2 = (a % c * b + r) / c;
88
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4791 if (ad >= INT32_MAX && b && ad > (INT64_MAX - a2) / b)
89 1 return INT64_MIN;
90 4790 return ad * b + a2;
91 }
92 } else {
93 #if 1
94 159876 uint64_t a0 = a & 0xFFFFFFFF;
95 159876 uint64_t a1 = a >> 32;
96 159876 uint64_t b0 = b & 0xFFFFFFFF;
97 159876 uint64_t b1 = b >> 32;
98 159876 uint64_t t1 = a0 * b1 + a1 * b0;
99 159876 uint64_t t1a = t1 << 32;
100 int i;
101
102 159876 a0 = a0 * b0 + t1a;
103 159876 a1 = a1 * b1 + (t1 >> 32) + (a0 < t1a);
104 159876 a0 += r;
105 159876 a1 += a0 < r;
106
107
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10391940 for (i = 63; i >= 0; i--) {
108 10232064 a1 += a1 + ((a0 >> i) & 1);
109 10232064 t1 += t1;
110
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10232064 if (c <= a1) {
111 1188309 a1 -= c;
112 1188309 t1++;
113 }
114 }
115
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159876 if (t1 > INT64_MAX)
116 return INT64_MIN;
117 159876 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 902431 int64_t av_rescale(int64_t a, int64_t b, int64_t c)
130 {
131 902431 return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
132 }
133
134 12016021 int64_t av_rescale_q_rnd(int64_t a, AVRational bq, AVRational cq,
135 enum AVRounding rnd)
136 {
137 12016021 int64_t b = bq.num * (int64_t)cq.den;
138 12016021 int64_t c = cq.num * (int64_t)bq.den;
139 12016021 return av_rescale_rnd(a, b, c, rnd);
140 }
141
142 11185911 int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq)
143 {
144 11185911 return av_rescale_q_rnd(a, bq, cq, AV_ROUND_NEAR_INF);
145 }
146
147 887624 int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b)
148 {
149 887624 int64_t a = tb_a.num * (int64_t)tb_b.den;
150 887624 int64_t b = tb_b.num * (int64_t)tb_a.den;
151
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887624 if ((FFABS64U(ts_a)|a|FFABS64U(ts_b)|b) <= INT_MAX)
152 879682 return (ts_a*a > ts_b*b) - (ts_a*a < ts_b*b);
153
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7942 if (av_rescale_rnd(ts_a, a, b, AV_ROUND_DOWN) < ts_b)
154 6688 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 298835 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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298835 av_assert0(in_ts != AV_NOPTS_VALUE);
172
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298835 av_assert0(duration >= 0);
173
174
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298835 if (*last == AV_NOPTS_VALUE || !duration || in_tb.num*(int64_t)out_tb.den <= out_tb.num*(int64_t)in_tb.den) {
175 253848 simple_round:
176 254481 *last = av_rescale_q(in_ts, in_tb, fs_tb) + duration;
177 254481 return av_rescale_q(in_ts, in_tb, out_tb);
178 }
179
180 44987 a = av_rescale_q_rnd(2*in_ts-1, in_tb, fs_tb, AV_ROUND_DOWN) >>1;
181 44987 b = (av_rescale_q_rnd(2*in_ts+1, in_tb, fs_tb, AV_ROUND_UP )+1)>>1;
182
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44987 if (*last < 2*a - b || *last > 2*b - a)
183 633 goto simple_round;
184
185 44354 this = av_clip64(*last, a, b);
186 44354 *last = this + duration;
187
188 44354 return av_rescale_q(this, fs_tb, out_tb);
189 }
190
191 489365 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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489365 if (inc != 1)
196 inc_tb = av_mul_q(inc_tb, (AVRational) {inc, 1});
197
198 489365 m = inc_tb.num * (int64_t)ts_tb.den;
199 489365 d = inc_tb.den * (int64_t)ts_tb.num;
200
201
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489365 if (m % d == 0 && ts <= INT64_MAX - m / d)
202 476408 return ts + m / d;
203
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12957 if (m < d)
204 2822 return ts;
205
206 {
207 10135 int64_t old = av_rescale_q(ts, ts_tb, inc_tb);
208 10135 int64_t old_ts = av_rescale_q(old, inc_tb, ts_tb);
209
210
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10135 if (old == INT64_MAX || old == AV_NOPTS_VALUE || old_ts == AV_NOPTS_VALUE)
211 return ts;
212
213 10135 return av_sat_add64(av_rescale_q(old + 1, inc_tb, ts_tb), ts - old_ts);
214 }
215 }
216
217 84791316 static inline double eval_poly(const double *coeff, int size, double x) {
218 84791316 double sum = coeff[size-1];
219 int i;
220
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890202282 for (i = size-2; i >= 0; --i) {
221 805410966 sum *= x;
222 805410966 sum += coeff[i];
223 }
224 84791316 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 42397115 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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42397115 if (x == 0)
307 1457 return 1.0;
308 42395658 x = fabs(x);
309
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42395658 if (x <= 15) {
310 42377902 y = x * x;
311 42377902 return eval_poly(p1, FF_ARRAY_ELEMS(p1), y) / eval_poly(q1, FF_ARRAY_ELEMS(q1), y);
312 }
313 else {
314 17756 y = 1 / x - 1.0 / 15;
315 17756 r = eval_poly(p2, FF_ARRAY_ELEMS(p2), y) / eval_poly(q2, FF_ARRAY_ELEMS(q2), y);
316 17756 factor = exp(x) / sqrt(x);
317 17756 return factor * r;
318 }
319 }
320