1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
|
/*
* Copyright (c) 2005-2012 Michael Niedermayer <michaelni@gmx.at>
*
* This file is part of FFmpeg.
*
* FFmpeg is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* FFmpeg is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with FFmpeg; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
/**
* @file
* miscellaneous math routines and tables
*/
#include <stdint.h>
#include <limits.h>
#include "mathematics.h"
#include "libavutil/intmath.h"
#include "libavutil/common.h"
#include "avassert.h"
#include "version.h"
/* Stein's binary GCD algorithm:
* https://en.wikipedia.org/wiki/Binary_GCD_algorithm */
int64_t av_gcd(int64_t a, int64_t b) {
int za, zb, k;
int64_t u, v;
if (a == 0)
return b;
if (b == 0)
return a;
za = ff_ctzll(a);
zb = ff_ctzll(b);
k = FFMIN(za, zb);
u = llabs(a >> za);
v = llabs(b >> zb);
while (u != v) {
if (u > v)
FFSWAP(int64_t, v, u);
v -= u;
v >>= ff_ctzll(v);
}
return (uint64_t)u << k;
}
int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd)
{
int64_t r = 0;
av_assert2(c > 0);
av_assert2(b >=0);
av_assert2((unsigned)(rnd&~AV_ROUND_PASS_MINMAX)<=5 && (rnd&~AV_ROUND_PASS_MINMAX)!=4);
if (c <= 0 || b < 0 || !((unsigned)(rnd&~AV_ROUND_PASS_MINMAX)<=5 && (rnd&~AV_ROUND_PASS_MINMAX)!=4))
return INT64_MIN;
if (rnd & AV_ROUND_PASS_MINMAX) {
if (a == INT64_MIN || a == INT64_MAX)
return a;
rnd -= AV_ROUND_PASS_MINMAX;
}
if (a < 0)
return -(uint64_t)av_rescale_rnd(-FFMAX(a, -INT64_MAX), b, c, rnd ^ ((rnd >> 1) & 1));
if (rnd == AV_ROUND_NEAR_INF)
r = c / 2;
else if (rnd & 1)
r = c - 1;
if (b <= INT_MAX && c <= INT_MAX) {
if (a <= INT_MAX)
return (a * b + r) / c;
else {
int64_t ad = a / c;
int64_t a2 = (a % c * b + r) / c;
if (ad >= INT32_MAX && b && ad > (INT64_MAX - a2) / b)
return INT64_MIN;
return ad * b + a2;
}
} else {
#if 1
uint64_t a0 = a & 0xFFFFFFFF;
uint64_t a1 = a >> 32;
uint64_t b0 = b & 0xFFFFFFFF;
uint64_t b1 = b >> 32;
uint64_t t1 = a0 * b1 + a1 * b0;
uint64_t t1a = t1 << 32;
int i;
a0 = a0 * b0 + t1a;
a1 = a1 * b1 + (t1 >> 32) + (a0 < t1a);
a0 += r;
a1 += a0 < r;
for (i = 63; i >= 0; i--) {
a1 += a1 + ((a0 >> i) & 1);
t1 += t1;
if (c <= a1) {
a1 -= c;
t1++;
}
}
if (t1 > INT64_MAX)
return INT64_MIN;
return t1;
#else
/* reference code doing (a*b + r) / c, requires libavutil/integer.h */
AVInteger ai;
ai = av_mul_i(av_int2i(a), av_int2i(b));
ai = av_add_i(ai, av_int2i(r));
return av_i2int(av_div_i(ai, av_int2i(c)));
#endif
}
}
int64_t av_rescale(int64_t a, int64_t b, int64_t c)
{
return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
}
int64_t av_rescale_q_rnd(int64_t a, AVRational bq, AVRational cq,
enum AVRounding rnd)
{
int64_t b = bq.num * (int64_t)cq.den;
int64_t c = cq.num * (int64_t)bq.den;
return av_rescale_rnd(a, b, c, rnd);
}
int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq)
{
return av_rescale_q_rnd(a, bq, cq, AV_ROUND_NEAR_INF);
}
int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b)
{
int64_t a = tb_a.num * (int64_t)tb_b.den;
int64_t b = tb_b.num * (int64_t)tb_a.den;
if ((FFABS64U(ts_a)|a|FFABS64U(ts_b)|b) <= INT_MAX)
return (ts_a*a > ts_b*b) - (ts_a*a < ts_b*b);
if (av_rescale_rnd(ts_a, a, b, AV_ROUND_DOWN) < ts_b)
return -1;
if (av_rescale_rnd(ts_b, b, a, AV_ROUND_DOWN) < ts_a)
return 1;
return 0;
}
int64_t av_compare_mod(uint64_t a, uint64_t b, uint64_t mod)
{
int64_t c = (a - b) & (mod - 1);
if (c > (mod >> 1))
c -= mod;
return c;
}
int64_t av_rescale_delta(AVRational in_tb, int64_t in_ts, AVRational fs_tb, int duration, int64_t *last, AVRational out_tb){
int64_t a, b, this;
av_assert0(in_ts != AV_NOPTS_VALUE);
av_assert0(duration >= 0);
if (*last == AV_NOPTS_VALUE || !duration || in_tb.num*(int64_t)out_tb.den <= out_tb.num*(int64_t)in_tb.den) {
simple_round:
*last = av_rescale_q(in_ts, in_tb, fs_tb) + duration;
return av_rescale_q(in_ts, in_tb, out_tb);
}
a = av_rescale_q_rnd(2*in_ts-1, in_tb, fs_tb, AV_ROUND_DOWN) >>1;
b = (av_rescale_q_rnd(2*in_ts+1, in_tb, fs_tb, AV_ROUND_UP )+1)>>1;
if (*last < 2*a - b || *last > 2*b - a)
goto simple_round;
this = av_clip64(*last, a, b);
*last = this + duration;
return av_rescale_q(this, fs_tb, out_tb);
}
int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, int64_t inc)
{
int64_t m, d;
if (inc != 1)
inc_tb = av_mul_q(inc_tb, (AVRational) {inc, 1});
m = inc_tb.num * (int64_t)ts_tb.den;
d = inc_tb.den * (int64_t)ts_tb.num;
if (m % d == 0 && ts <= INT64_MAX - m / d)
return ts + m / d;
if (m < d)
return ts;
{
int64_t old = av_rescale_q(ts, ts_tb, inc_tb);
int64_t old_ts = av_rescale_q(old, inc_tb, ts_tb);
if (old == INT64_MAX || old == AV_NOPTS_VALUE || old_ts == AV_NOPTS_VALUE)
return ts;
return av_sat_add64(av_rescale_q(old + 1, inc_tb, ts_tb), ts - old_ts);
}
}
|
