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[128]={
  30         0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5,
  31         5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
  32         8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
  33         9, 9, 9, 9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11
  34 };
  35
  36 const uint8_t ff_log2_tab[256]={
  37         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,
  38         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,
  39         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,
  40         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,
  41         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,
  42         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,
  43         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,
  44         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
  45 };
  46
  47 int64_t ff_gcd(int64_t a, int64_t b){
  48     if(b) return ff_gcd(b, a%b);
  49     else  return a;
  50 }
  51
  52 int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd){
  53     int64_t r=0;
  54     assert(c > 0);
  55     assert(b >=0);
  56     assert(rnd >=0 && rnd<=5 && rnd!=4);
  57
  58     if(a<0 && a != INT64_MIN) return -av_rescale_rnd(-a, b, c, rnd ^ ((rnd>>1)&1));
  59
  60     if(rnd==AV_ROUND_NEAR_INF) r= c/2;
  61     else if(rnd&1)             r= c-1;
  62
  63     if(b<=INT_MAX && c<=INT_MAX){
  64         if(a<=INT_MAX)
  65             return (a * b + r)/c;
  66         else
  67             return a/c*b + (a%c*b + r)/c;
  68     }else{
  69 #if 1
  70         uint64_t a0= a&0xFFFFFFFF;
  71         uint64_t a1= a>>32;
  72         uint64_t b0= b&0xFFFFFFFF;
  73         uint64_t b1= b>>32;
  74         uint64_t t1= a0*b1 + a1*b0;
  75         uint64_t t1a= t1<<32;
  76         int i;
  77
  78         a0 = a0*b0 + t1a;
  79         a1 = a1*b1 + (t1>>32) + (a0<t1a);
  80         a0 += r;
  81         a1 += a0<r;
  82
  83         for(i=63; i>=0; i--){
  84 //            int o= a1 & 0x8000000000000000ULL;
  85             a1+= a1 + ((a0>>i)&1);
  86             t1+=t1;
  87             if(/*o || */c <= a1){
  88                 a1 -= c;
  89                 t1++;
  90             }
  91         }
  92         return t1;
  93     }
  94 #else
  95         AVInteger ai;
  96         ai= av_mul_i(av_int2i(a), av_int2i(b));
  97         ai= av_add_i(ai, av_int2i(r));
  98
  99         return av_i2int(av_div_i(ai, av_int2i(c)));
 100     }
 101 #endif
 102 }
 103
 104 int64_t av_rescale(int64_t a, int64_t b, int64_t c){
 105     return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
 106 }
 107
 108 int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq){
 109     int64_t b= bq.num * (int64_t)cq.den;
 110     int64_t c= cq.num * (int64_t)bq.den;
 111     return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
 112 }
 113 #if 0
 114 #include "integer.h"
 115 #undef printf
 116 main(){
 117     int64_t a,b,c,d,e;
 118
 119     for(a=7; a<(1LL<<62); a+=a/3+1){
 120         for(b=3; b<(1LL<<62); b+=b/4+1){
 121             for(c=9; c<(1LL<<62); c+=(c*2)/5+3){
 122                 int64_t r= c/2;
 123                 AVInteger ai;
 124                 ai= av_mul_i(av_int2i(a), av_int2i(b));
 125                 ai= av_add_i(ai, av_int2i(r));
 126
 127                 d= av_i2int(av_div_i(ai, av_int2i(c)));
 128
 129                 e= av_rescale(a,b,c);
 130
 131                 if((double)a * (double)b / (double)c > (1LL<<63))
 132                     continue;
 133
 134                 if(d!=e) printf("%"PRId64"*%"PRId64"/%"PRId64"= %"PRId64"=%"PRId64"\n", a, b, c, d, e);
 135             }
 136         }
 137     }
 138 }
 139 #endif