libavutil/mathematics.c

   1 /*
   2  * Copyright (c) 2005 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 mathematics.c
  23  * Miscellaneous math routines and tables.
  24  */
  25
  26 #include "common.h"
  27 #include "mathematics.h"
  28
  29 const uint8_t ff_sqrt_tab[256]={
  30   0, 16, 23, 28, 32, 36, 40, 43, 46, 48, 51, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 77, 79, 80, 82, 84, 85, 87, 88, 90,
  31  91, 92, 94, 95, 96, 98, 99,100,102,103,104,105,107,108,109,110,111,112,114,115,116,117,118,119,120,121,122,123,124,125,126,127,
  32 128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,144,145,146,147,148,149,150,151,151,152,153,154,155,156,156,
  33 157,158,159,160,160,161,162,163,164,164,165,166,167,168,168,169,170,171,171,172,173,174,174,175,176,176,177,178,179,179,180,181,
  34 182,182,183,184,184,185,186,186,187,188,188,189,190,190,191,192,192,193,194,194,195,196,196,197,198,198,199,200,200,201,202,202,
  35 203,204,204,205,205,206,207,207,208,208,209,210,210,211,212,212,213,213,214,215,215,216,216,217,218,218,219,219,220,220,221,222,
  36 222,223,223,224,224,225,226,226,227,227,228,228,229,230,230,231,231,232,232,233,233,234,235,235,236,236,237,237,238,238,239,239,
  37 240,240,241,242,242,243,243,244,244,245,245,246,246,247,247,248,248,249,249,250,250,251,251,252,252,253,253,254,254,255,255,255
  38 };
  39
  40 const uint8_t ff_log2_tab[256]={
  41         0,0,1,1,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,
  42         5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
  43         6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
  44         6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
  45         7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
  46         7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
  47         7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
  48         7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7
  49 };
  50
  51 int64_t ff_gcd(int64_t a, int64_t b){
  52     if(b) return ff_gcd(b, a%b);
  53     else  return a;
  54 }
  55
  56 int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd){
  57     int64_t r=0;
  58     assert(c > 0);
  59     assert(b >=0);
  60     assert(rnd >=0 && rnd<=5 && rnd!=4);
  61
  62     if(a<0 && a != INT64_MIN) return -av_rescale_rnd(-a, b, c, rnd ^ ((rnd>>1)&1));
  63
  64     if(rnd==AV_ROUND_NEAR_INF) r= c/2;
  65     else if(rnd&1)             r= c-1;
  66
  67     if(b<=INT_MAX && c<=INT_MAX){
  68         if(a<=INT_MAX)
  69             return (a * b + r)/c;
  70         else
  71             return a/c*b + (a%c*b + r)/c;
  72     }else{
  73 #if 1
  74         uint64_t a0= a&0xFFFFFFFF;
  75         uint64_t a1= a>>32;
  76         uint64_t b0= b&0xFFFFFFFF;
  77         uint64_t b1= b>>32;
  78         uint64_t t1= a0*b1 + a1*b0;
  79         uint64_t t1a= t1<<32;
  80         int i;
  81
  82         a0 = a0*b0 + t1a;
  83         a1 = a1*b1 + (t1>>32) + (a0<t1a);
  84         a0 += r;
  85         a1 += a0<r;
  86
  87         for(i=63; i>=0; i--){
  88 //            int o= a1 & 0x8000000000000000ULL;
  89             a1+= a1 + ((a0>>i)&1);
  90             t1+=t1;
  91             if(/*o || */c <= a1){
  92                 a1 -= c;
  93                 t1++;
  94             }
  95         }
  96         return t1;
  97     }
  98 #else
  99         AVInteger ai;
 100         ai= av_mul_i(av_int2i(a), av_int2i(b));
 101         ai= av_add_i(ai, av_int2i(r));
 102
 103         return av_i2int(av_div_i(ai, av_int2i(c)));
 104     }
 105 #endif
 106 }
 107
 108 int64_t av_rescale(int64_t a, int64_t b, int64_t c){
 109     return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
 110 }
 111
 112 int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq){
 113     int64_t b= bq.num * (int64_t)cq.den;
 114     int64_t c= cq.num * (int64_t)bq.den;
 115     return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
 116 }
 117
 118 #ifdef TEST
 119 #include "integer.h"
 120 #undef printf
 121 int main(void){
 122     int64_t a,b,c,d,e;
 123
 124     for(a=7; a<(1LL<<62); a+=a/3+1){
 125         for(b=3; b<(1LL<<62); b+=b/4+1){
 126             for(c=9; c<(1LL<<62); c+=(c*2)/5+3){
 127                 int64_t r= c/2;
 128                 AVInteger ai;
 129                 ai= av_mul_i(av_int2i(a), av_int2i(b));
 130                 ai= av_add_i(ai, av_int2i(r));
 131
 132                 d= av_i2int(av_div_i(ai, av_int2i(c)));
 133
 134                 e= av_rescale(a,b,c);
 135
 136                 if((double)a * (double)b / (double)c > (1LL<<63))
 137                     continue;
 138
 139                 if(d!=e) printf("%"PRId64"*%"PRId64"/%"PRId64"= %"PRId64"=%"PRId64"\n", a, b, c, d, e);
 140             }
 141         }
 142     }
 143     return 0;
 144 }
 145 #endif