FFmpeg
 All Data Structures Namespaces Files Functions Variables Typedefs Enumerations Enumerator Macros Groups Pages
mathematics.c
Go to the documentation of this file.
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 "mathematics.h"
30 #include "libavutil/intmath.h"
31 #include "libavutil/common.h"
32 #include "avassert.h"
33 #include "version.h"
34 
35 /* Stein's binary GCD algorithm:
36  * https://en.wikipedia.org/wiki/Binary_GCD_algorithm */
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 
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  }
119 #else
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  }
126 #endif
127 }
128 
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 
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 
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 
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 ((FFABS(ts_a)|a|FFABS(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 
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 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 
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)
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  return av_rescale_q(old + 1, inc_tb, ts_tb) + (ts - old_ts);
210  }
211 }
int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd)
Rescale a 64-bit integer with specified rounding.
Definition: mathematics.c:58
#define a0
Definition: regdef.h:46
int num
numerator
Definition: rational.h:44
const char * b
Definition: vf_curves.c:109
#define a1
Definition: regdef.h:47
AVRounding
Definition: mathematics.h:70
#define av_assert0(cond)
assert() equivalent, that is always enabled.
Definition: avassert.h:37
Round toward +infinity.
Definition: mathematics.h:74
#define av_assert2(cond)
assert() equivalent, that does lie in speed critical code.
Definition: avassert.h:63
AVRational av_mul_q(AVRational b, AVRational c)
Multiply two rationals.
Definition: rational.c:80
int64_t av_i2int(AVInteger a)
Convert the given AVInteger to an int64_t.
Definition: integer.c:158
unsigned m
Definition: audioconvert.c:187
int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq)
Rescale a 64-bit integer by 2 rational numbers.
Definition: mathematics.c:142
AVInteger av_int2i(int64_t a)
Convert the given int64_t to an AVInteger.
Definition: integer.c:147
const char * r
Definition: vf_curves.c:107
#define t1
Definition: regdef.h:29
Round to nearest and halfway cases away from zero.
Definition: mathematics.h:75
AVInteger av_mul_i(AVInteger a, AVInteger b)
Definition: integer.c:64
simple assert() macros that are a bit more flexible than ISO C assert().
int64_t av_gcd(int64_t a, int64_t b)
Compute the greatest common divisor of a and b.
Definition: mathematics.c:37
Libavutil version macros.
#define FFMAX(a, b)
Definition: common.h:94
int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b)
Compare 2 timestamps each in its own timebases.
Definition: mathematics.c:147
int64_t av_rescale_q_rnd(int64_t a, AVRational bq, AVRational cq, enum AVRounding rnd)
Rescale a 64-bit integer by 2 rational numbers with specified rounding.
Definition: mathematics.c:134
int64_t av_rescale(int64_t a, int64_t b, int64_t c)
Rescale a 64-bit integer with rounding to nearest.
Definition: mathematics.c:129
#define FFMIN(a, b)
Definition: common.h:96
#define ff_ctzll
Definition: intmath.h:126
#define a2
Definition: regdef.h:48
int64_t duration
Definition: movenc-test.c:63
AVInteger av_add_i(AVInteger a, AVInteger b)
Definition: integer.c:34
#define FFABS(a)
Absolute value, Note, INT_MIN / INT64_MIN result in undefined behavior as they are not representable ...
Definition: common.h:72
int64_t av_rescale_delta(AVRational in_tb, int64_t in_ts, AVRational fs_tb, int duration, int64_t *last, AVRational out_tb)
Rescale a timestamp while preserving known durations.
Definition: mathematics.c:168
rational number numerator/denominator
Definition: rational.h:43
#define u(width,...)
Round toward -infinity.
Definition: mathematics.h:73
common internal and external API header
int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, int64_t inc)
Add a value to a timestamp.
Definition: mathematics.c:191
static double c[64]
#define rnd()
Definition: checkasm.h:66
AVInteger av_div_i(AVInteger a, AVInteger b)
Return a/b.
Definition: integer.c:141
int den
denominator
Definition: rational.h:45
Flag to pass INT64_MIN/MAX through instead of rescaling, this avoids special cases for AV_NOPTS_VALUE...
Definition: mathematics.h:76
#define FFSWAP(type, a, b)
Definition: common.h:99
#define AV_NOPTS_VALUE
Undefined timestamp value.
Definition: avutil.h:240
int64_t av_compare_mod(uint64_t a, uint64_t b, uint64_t mod)
Compare 2 integers modulo mod.
Definition: mathematics.c:160