src/third_party/ffmpeg/libavutil/mathematics.c

   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 && a != INT64_MIN)
  80         return -av_rescale_rnd(-a, 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             return a / c * b + (a % c * b + r) / c;
  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         return t1;
 116     }
 117 #else
 118         AVInteger ai;
 119         ai = av_mul_i(av_int2i(a), av_int2i(b));
 120         ai = av_add_i(ai, av_int2i(r));
 121
 122         return av_i2int(av_div_i(ai, av_int2i(c)));
 123     }
 124 #endif
 125 }
 126
 127 int64_t av_rescale(int64_t a, int64_t b, int64_t c)
 128 {
 129     return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
 130 }
 131
 132 int64_t av_rescale_q_rnd(int64_t a, AVRational bq, AVRational cq,
 133                          enum AVRounding rnd)
 134 {
 135     int64_t b = bq.num * (int64_t)cq.den;
 136     int64_t c = cq.num * (int64_t)bq.den;
 137     return av_rescale_rnd(a, b, c, rnd);
 138 }
 139
 140 int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq)
 141 {
 142     return av_rescale_q_rnd(a, bq, cq, AV_ROUND_NEAR_INF);
 143 }
 144
 145 int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b)
 146 {
 147     int64_t a = tb_a.num * (int64_t)tb_b.den;
 148     int64_t b = tb_b.num * (int64_t)tb_a.den;
 149     if ((FFABS(ts_a)|a|FFABS(ts_b)|b) <= INT_MAX)
 150         return (ts_a*a > ts_b*b) - (ts_a*a < ts_b*b);
 151     if (av_rescale_rnd(ts_a, a, b, AV_ROUND_DOWN) < ts_b)
 152         return -1;
 153     if (av_rescale_rnd(ts_b, b, a, AV_ROUND_DOWN) < ts_a)
 154         return 1;
 155     return 0;
 156 }
 157
 158 int64_t av_compare_mod(uint64_t a, uint64_t b, uint64_t mod)
 159 {
 160     int64_t c = (a - b) & (mod - 1);
 161     if (c > (mod >> 1))
 162         c -= mod;
 163     return c;
 164 }
 165
 166 int64_t av_rescale_delta(AVRational in_tb, int64_t in_ts,  AVRational fs_tb, int duration, int64_t *last, AVRational out_tb){
 167     int64_t a, b, this;
 168
 169     av_assert0(in_ts != AV_NOPTS_VALUE);
 170     av_assert0(duration >= 0);
 171
 172     if (*last == AV_NOPTS_VALUE || !duration || in_tb.num*(int64_t)out_tb.den <= out_tb.num*(int64_t)in_tb.den) {
 173 simple_round:
 174         *last = av_rescale_q(in_ts, in_tb, fs_tb) + duration;
 175         return av_rescale_q(in_ts, in_tb, out_tb);
 176     }
 177
 178     a =  av_rescale_q_rnd(2*in_ts-1, in_tb, fs_tb, AV_ROUND_DOWN)   >>1;
 179     b = (av_rescale_q_rnd(2*in_ts+1, in_tb, fs_tb, AV_ROUND_UP  )+1)>>1;
 180     if (*last < 2*a - b || *last > 2*b - a)
 181         goto simple_round;
 182
 183     this = av_clip64(*last, a, b);
 184     *last = this + duration;
 185
 186     return av_rescale_q(this, fs_tb, out_tb);
 187 }
 188
 189 int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, int64_t inc)
 190 {
 191     int64_t m, d;
 192
 193     if (inc != 1)
 194         inc_tb = av_mul_q(inc_tb, (AVRational) {inc, 1});
 195
 196     m = inc_tb.num * (int64_t)ts_tb.den;
 197     d = inc_tb.den * (int64_t)ts_tb.num;
 198
 199     if (m % d == 0)
 200         return ts + m / d;
 201     if (m < d)
 202         return ts;
 203
 204     {
 205         int64_t old = av_rescale_q(ts, ts_tb, inc_tb);
 206         int64_t old_ts = av_rescale_q(old, inc_tb, ts_tb);
 207         return av_rescale_q(old + 1, inc_tb, ts_tb) + (ts - old_ts);
 208     }
 209 }