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mathematics.c
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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 "mathematics.h"
30 #include "libavutil/common.h"
31 #include "avassert.h"
32 #include "version.h"
33 
34 #if FF_API_AV_REVERSE
35 const uint8_t av_reverse[256] = {
36 0x00,0x80,0x40,0xC0,0x20,0xA0,0x60,0xE0,0x10,0x90,0x50,0xD0,0x30,0xB0,0x70,0xF0,
37 0x08,0x88,0x48,0xC8,0x28,0xA8,0x68,0xE8,0x18,0x98,0x58,0xD8,0x38,0xB8,0x78,0xF8,
38 0x04,0x84,0x44,0xC4,0x24,0xA4,0x64,0xE4,0x14,0x94,0x54,0xD4,0x34,0xB4,0x74,0xF4,
39 0x0C,0x8C,0x4C,0xCC,0x2C,0xAC,0x6C,0xEC,0x1C,0x9C,0x5C,0xDC,0x3C,0xBC,0x7C,0xFC,
40 0x02,0x82,0x42,0xC2,0x22,0xA2,0x62,0xE2,0x12,0x92,0x52,0xD2,0x32,0xB2,0x72,0xF2,
41 0x0A,0x8A,0x4A,0xCA,0x2A,0xAA,0x6A,0xEA,0x1A,0x9A,0x5A,0xDA,0x3A,0xBA,0x7A,0xFA,
42 0x06,0x86,0x46,0xC6,0x26,0xA6,0x66,0xE6,0x16,0x96,0x56,0xD6,0x36,0xB6,0x76,0xF6,
43 0x0E,0x8E,0x4E,0xCE,0x2E,0xAE,0x6E,0xEE,0x1E,0x9E,0x5E,0xDE,0x3E,0xBE,0x7E,0xFE,
44 0x01,0x81,0x41,0xC1,0x21,0xA1,0x61,0xE1,0x11,0x91,0x51,0xD1,0x31,0xB1,0x71,0xF1,
45 0x09,0x89,0x49,0xC9,0x29,0xA9,0x69,0xE9,0x19,0x99,0x59,0xD9,0x39,0xB9,0x79,0xF9,
46 0x05,0x85,0x45,0xC5,0x25,0xA5,0x65,0xE5,0x15,0x95,0x55,0xD5,0x35,0xB5,0x75,0xF5,
47 0x0D,0x8D,0x4D,0xCD,0x2D,0xAD,0x6D,0xED,0x1D,0x9D,0x5D,0xDD,0x3D,0xBD,0x7D,0xFD,
48 0x03,0x83,0x43,0xC3,0x23,0xA3,0x63,0xE3,0x13,0x93,0x53,0xD3,0x33,0xB3,0x73,0xF3,
49 0x0B,0x8B,0x4B,0xCB,0x2B,0xAB,0x6B,0xEB,0x1B,0x9B,0x5B,0xDB,0x3B,0xBB,0x7B,0xFB,
50 0x07,0x87,0x47,0xC7,0x27,0xA7,0x67,0xE7,0x17,0x97,0x57,0xD7,0x37,0xB7,0x77,0xF7,
51 0x0F,0x8F,0x4F,0xCF,0x2F,0xAF,0x6F,0xEF,0x1F,0x9F,0x5F,0xDF,0x3F,0xBF,0x7F,0xFF,
52 };
53 #endif
54 
55 int64_t av_gcd(int64_t a, int64_t b)
56 {
57  if (b)
58  return av_gcd(b, a % b);
59  else
60  return a;
61 }
62 
63 int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd)
64 {
65  int64_t r = 0;
66  av_assert2(c > 0);
67  av_assert2(b >=0);
68  av_assert2((unsigned)(rnd&~AV_ROUND_PASS_MINMAX)<=5 && (rnd&~AV_ROUND_PASS_MINMAX)!=4);
69 
70  if (c <= 0 || b < 0 || !((unsigned)(rnd&~AV_ROUND_PASS_MINMAX)<=5 && (rnd&~AV_ROUND_PASS_MINMAX)!=4))
71  return INT64_MIN;
72 
73  if (rnd & AV_ROUND_PASS_MINMAX) {
74  if (a == INT64_MIN || a == INT64_MAX)
75  return a;
76  rnd -= AV_ROUND_PASS_MINMAX;
77  }
78 
79  if (a < 0)
80  return -(uint64_t)av_rescale_rnd(-FFMAX(a, -INT64_MAX), b, c, rnd ^ ((rnd >> 1) & 1));
81 
82  if (rnd == AV_ROUND_NEAR_INF)
83  r = c / 2;
84  else if (rnd & 1)
85  r = c - 1;
86 
87  if (b <= INT_MAX && c <= INT_MAX) {
88  if (a <= INT_MAX)
89  return (a * b + r) / c;
90  else {
91  int64_t ad = a / c;
92  int64_t a2 = (a % c * b + r) / c;
93  if (ad >= INT32_MAX && b && ad > (INT64_MAX - a2) / b)
94  return INT64_MIN;
95  return ad * b + a2;
96  }
97  } else {
98 #if 1
99  uint64_t a0 = a & 0xFFFFFFFF;
100  uint64_t a1 = a >> 32;
101  uint64_t b0 = b & 0xFFFFFFFF;
102  uint64_t b1 = b >> 32;
103  uint64_t t1 = a0 * b1 + a1 * b0;
104  uint64_t t1a = t1 << 32;
105  int i;
106 
107  a0 = a0 * b0 + t1a;
108  a1 = a1 * b1 + (t1 >> 32) + (a0 < t1a);
109  a0 += r;
110  a1 += a0 < r;
111 
112  for (i = 63; i >= 0; i--) {
113  a1 += a1 + ((a0 >> i) & 1);
114  t1 += t1;
115  if (c <= a1) {
116  a1 -= c;
117  t1++;
118  }
119  }
120  if (t1 > INT64_MAX)
121  return INT64_MIN;
122  return t1;
123  }
124 #else
125  AVInteger ai;
126  ai = av_mul_i(av_int2i(a), av_int2i(b));
127  ai = av_add_i(ai, av_int2i(r));
128 
129  return av_i2int(av_div_i(ai, av_int2i(c)));
130  }
131 #endif
132 }
133 
134 int64_t av_rescale(int64_t a, int64_t b, int64_t c)
135 {
136  return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
137 }
138 
139 int64_t av_rescale_q_rnd(int64_t a, AVRational bq, AVRational cq,
140  enum AVRounding rnd)
141 {
142  int64_t b = bq.num * (int64_t)cq.den;
143  int64_t c = cq.num * (int64_t)bq.den;
144  return av_rescale_rnd(a, b, c, rnd);
145 }
146 
147 int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq)
148 {
149  return av_rescale_q_rnd(a, bq, cq, AV_ROUND_NEAR_INF);
150 }
151 
152 int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b)
153 {
154  int64_t a = tb_a.num * (int64_t)tb_b.den;
155  int64_t b = tb_b.num * (int64_t)tb_a.den;
156  if ((FFABS(ts_a)|a|FFABS(ts_b)|b) <= INT_MAX)
157  return (ts_a*a > ts_b*b) - (ts_a*a < ts_b*b);
158  if (av_rescale_rnd(ts_a, a, b, AV_ROUND_DOWN) < ts_b)
159  return -1;
160  if (av_rescale_rnd(ts_b, b, a, AV_ROUND_DOWN) < ts_a)
161  return 1;
162  return 0;
163 }
164 
165 int64_t av_compare_mod(uint64_t a, uint64_t b, uint64_t mod)
166 {
167  int64_t c = (a - b) & (mod - 1);
168  if (c > (mod >> 1))
169  c -= mod;
170  return c;
171 }
172 
173 int64_t av_rescale_delta(AVRational in_tb, int64_t in_ts, AVRational fs_tb, int duration, int64_t *last, AVRational out_tb){
174  int64_t a, b, this;
175 
176  av_assert0(in_ts != AV_NOPTS_VALUE);
177  av_assert0(duration >= 0);
178 
179  if (*last == AV_NOPTS_VALUE || !duration || in_tb.num*(int64_t)out_tb.den <= out_tb.num*(int64_t)in_tb.den) {
180 simple_round:
181  *last = av_rescale_q(in_ts, in_tb, fs_tb) + duration;
182  return av_rescale_q(in_ts, in_tb, out_tb);
183  }
184 
185  a = av_rescale_q_rnd(2*in_ts-1, in_tb, fs_tb, AV_ROUND_DOWN) >>1;
186  b = (av_rescale_q_rnd(2*in_ts+1, in_tb, fs_tb, AV_ROUND_UP )+1)>>1;
187  if (*last < 2*a - b || *last > 2*b - a)
188  goto simple_round;
189 
190  this = av_clip64(*last, a, b);
191  *last = this + duration;
192 
193  return av_rescale_q(this, fs_tb, out_tb);
194 }
195 
196 int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, int64_t inc)
197 {
198  int64_t m, d;
199 
200  if (inc != 1)
201  inc_tb = av_mul_q(inc_tb, (AVRational) {inc, 1});
202 
203  m = inc_tb.num * (int64_t)ts_tb.den;
204  d = inc_tb.den * (int64_t)ts_tb.num;
205 
206  if (m % d == 0)
207  return ts + m / d;
208  if (m < d)
209  return ts;
210 
211  {
212  int64_t old = av_rescale_q(ts, ts_tb, inc_tb);
213  int64_t old_ts = av_rescale_q(old, inc_tb, ts_tb);
214  return av_rescale_q(old + 1, inc_tb, ts_tb) + (ts - old_ts);
215  }
216 }
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:63
#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
uint8_t
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
static int64_t duration
Definition: ffplay.c:326
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:147
AVInteger av_int2i(int64_t a)
Convert the given int64_t to an AVInteger.
Definition: integer.c:147
const uint8_t av_reverse[256]
Reverse the order of the bits of an 8-bits unsigned integer.
Definition: mathematics.c:35
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)
Return the greatest common divisor of a and b.
Definition: mathematics.c:55
Libavutil version macros.
#define FFMAX(a, b)
Definition: common.h:90
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:152
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:139
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:134
#define a2
Definition: regdef.h:48
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:68
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:173
rational number numerator/denominator
Definition: rational.h:43
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:196
static double c[64]
#define rnd()
Definition: checkasm.h:43
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 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:165