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 */
av_gcd(int64_t a,int64_t b)37 int64_t av_gcd(int64_t a, int64_t b) {
38 int za, zb, k;
39 int64_t u, v;
40 if (a == 0)
41 return b;
42 if (b == 0)
43 return a;
44 za = ff_ctzll(a);
45 zb = ff_ctzll(b);
46 k = FFMIN(za, zb);
47 u = llabs(a >> za);
48 v = llabs(b >> zb);
49 while (u != v) {
50 if (u > v)
51 FFSWAP(int64_t, v, u);
52 v -= u;
53 v >>= ff_ctzll(v);
54 }
55 return (uint64_t)u << k;
56 }
57
av_rescale_rnd(int64_t a,int64_t b,int64_t c,enum AVRounding rnd)58 int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd)
59 {
60 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 if (c <= 0 || b < 0 || !((unsigned)(rnd&~AV_ROUND_PASS_MINMAX)<=5 && (rnd&~AV_ROUND_PASS_MINMAX)!=4))
66 return INT64_MIN;
67
68 if (rnd & AV_ROUND_PASS_MINMAX) {
69 if (a == INT64_MIN || a == INT64_MAX)
70 return a;
71 rnd -= AV_ROUND_PASS_MINMAX;
72 }
73
74 if (a < 0)
75 return -(uint64_t)av_rescale_rnd(-FFMAX(a, -INT64_MAX), b, c, rnd ^ ((rnd >> 1) & 1));
76
77 if (rnd == AV_ROUND_NEAR_INF)
78 r = c / 2;
79 else if (rnd & 1)
80 r = c - 1;
81
82 if (b <= INT_MAX && c <= INT_MAX) {
83 if (a <= INT_MAX)
84 return (a * b + r) / c;
85 else {
86 int64_t ad = a / c;
87 int64_t a2 = (a % c * b + r) / c;
88 if (ad >= INT32_MAX && b && ad > (INT64_MAX - a2) / b)
89 return INT64_MIN;
90 return ad * b + a2;
91 }
92 } else {
93 #if 1
94 uint64_t a0 = a & 0xFFFFFFFF;
95 uint64_t a1 = a >> 32;
96 uint64_t b0 = b & 0xFFFFFFFF;
97 uint64_t b1 = b >> 32;
98 uint64_t t1 = a0 * b1 + a1 * b0;
99 uint64_t t1a = t1 << 32;
100 int i;
101
102 a0 = a0 * b0 + t1a;
103 a1 = a1 * b1 + (t1 >> 32) + (a0 < t1a);
104 a0 += r;
105 a1 += a0 < r;
106
107 for (i = 63; i >= 0; i--) {
108 a1 += a1 + ((a0 >> i) & 1);
109 t1 += t1;
110 if (c <= a1) {
111 a1 -= c;
112 t1++;
113 }
114 }
115 if (t1 > INT64_MAX)
116 return INT64_MIN;
117 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
av_rescale(int64_t a,int64_t b,int64_t c)129 int64_t av_rescale(int64_t a, int64_t b, int64_t c)
130 {
131 return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
132 }
133
av_rescale_q_rnd(int64_t a,AVRational bq,AVRational cq,enum AVRounding rnd)134 int64_t av_rescale_q_rnd(int64_t a, AVRational bq, AVRational cq,
135 enum AVRounding rnd)
136 {
137 int64_t b = bq.num * (int64_t)cq.den;
138 int64_t c = cq.num * (int64_t)bq.den;
139 return av_rescale_rnd(a, b, c, rnd);
140 }
141
av_rescale_q(int64_t a,AVRational bq,AVRational cq)142 int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq)
143 {
144 return av_rescale_q_rnd(a, bq, cq, AV_ROUND_NEAR_INF);
145 }
146
av_compare_ts(int64_t ts_a,AVRational tb_a,int64_t ts_b,AVRational tb_b)147 int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b)
148 {
149 int64_t a = tb_a.num * (int64_t)tb_b.den;
150 int64_t b = tb_b.num * (int64_t)tb_a.den;
151 if ((FFABS64U(ts_a)|a|FFABS64U(ts_b)|b) <= INT_MAX)
152 return (ts_a*a > ts_b*b) - (ts_a*a < ts_b*b);
153 if (av_rescale_rnd(ts_a, a, b, AV_ROUND_DOWN) < ts_b)
154 return -1;
155 if (av_rescale_rnd(ts_b, b, a, AV_ROUND_DOWN) < ts_a)
156 return 1;
157 return 0;
158 }
159
av_compare_mod(uint64_t a,uint64_t b,uint64_t mod)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
av_rescale_delta(AVRational in_tb,int64_t in_ts,AVRational fs_tb,int duration,int64_t * last,AVRational out_tb)168 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 av_assert0(in_ts != AV_NOPTS_VALUE);
172 av_assert0(duration >= 0);
173
174 if (*last == AV_NOPTS_VALUE || !duration || in_tb.num*(int64_t)out_tb.den <= out_tb.num*(int64_t)in_tb.den) {
175 simple_round:
176 *last = av_rescale_q(in_ts, in_tb, fs_tb) + duration;
177 return av_rescale_q(in_ts, in_tb, out_tb);
178 }
179
180 a = av_rescale_q_rnd(2*in_ts-1, in_tb, fs_tb, AV_ROUND_DOWN) >>1;
181 b = (av_rescale_q_rnd(2*in_ts+1, in_tb, fs_tb, AV_ROUND_UP )+1)>>1;
182 if (*last < 2*a - b || *last > 2*b - a)
183 goto simple_round;
184
185 this = av_clip64(*last, a, b);
186 *last = this + duration;
187
188 return av_rescale_q(this, fs_tb, out_tb);
189 }
190
av_add_stable(AVRational ts_tb,int64_t ts,AVRational inc_tb,int64_t inc)191 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 if (inc != 1)
196 inc_tb = av_mul_q(inc_tb, (AVRational) {inc, 1});
197
198 m = inc_tb.num * (int64_t)ts_tb.den;
199 d = inc_tb.den * (int64_t)ts_tb.num;
200
201 if (m % d == 0 && ts <= INT64_MAX - m / d)
202 return ts + m / d;
203 if (m < d)
204 return ts;
205
206 {
207 int64_t old = av_rescale_q(ts, ts_tb, inc_tb);
208 int64_t old_ts = av_rescale_q(old, inc_tb, ts_tb);
209
210 if (old == INT64_MAX || old == AV_NOPTS_VALUE || old_ts == AV_NOPTS_VALUE)
211 return ts;
212
213 return av_sat_add64(av_rescale_q(old + 1, inc_tb, ts_tb), ts - old_ts);
214 }
215 }
216