libavutil/mathematics.c

   1 /*
   2  * Copyright (c) 2005 Michael Niedermayer <michaelni@gmx.at>
   3  *
   4  * This library is free software; you can redistribute it and/or
   5  * modify it under the terms of the GNU Lesser General Public
   6  * License as published by the Free Software Foundation; either
   7  * version 2 of the License, or (at your option) any later version.
   8  *
   9  * This library is distributed in the hope that it will be useful,
  10  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  11  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  12  * Lesser General Public License for more details.
  13  *
  14  * You should have received a copy of the GNU Lesser General Public
  15  * License along with this library; if not, write to the Free Software
  16  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
  17  */
  18
  19 /**
  20  * @file mathematics.c
  21  * Miscellaneous math routines and tables.
  22  */
  23
  24 #include "common.h"
  25 #include "mathematics.h"
  26
  27 const uint8_t ff_sqrt_tab[128]={
  28         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,
  29         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,
  30         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,
  31         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
  32 };
  33
  34 const uint8_t ff_log2_tab[256]={
  35         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,
  36         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,
  37         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,
  38         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,
  39         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,
  40         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,
  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 };
  44
  45 int64_t ff_gcd(int64_t a, int64_t b){
  46     if(b) return ff_gcd(b, a%b);
  47     else  return a;
  48 }
  49
  50 int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd){
  51     int64_t r=0;
  52     assert(c > 0);
  53     assert(b >=0);
  54     assert(rnd >=0 && rnd<=5 && rnd!=4);
  55
  56     if(a<0 && a != INT64_MIN) return -av_rescale_rnd(-a, b, c, rnd ^ ((rnd>>1)&1));
  57
  58     if(rnd==AV_ROUND_NEAR_INF) r= c/2;
  59     else if(rnd&1)             r= c-1;
  60
  61     if(b<=INT_MAX && c<=INT_MAX){
  62         if(a<=INT_MAX)
  63             return (a * b + r)/c;
  64         else
  65             return a/c*b + (a%c*b + r)/c;
  66     }else{
  67 #if 1
  68         uint64_t a0= a&0xFFFFFFFF;
  69         uint64_t a1= a>>32;
  70         uint64_t b0= b&0xFFFFFFFF;
  71         uint64_t b1= b>>32;
  72         uint64_t t1= a0*b1 + a1*b0;
  73         uint64_t t1a= t1<<32;
  74         int i;
  75
  76         a0 = a0*b0 + t1a;
  77         a1 = a1*b1 + (t1>>32) + (a0<t1a);
  78         a0 += r;
  79         a1 += a0<r;
  80
  81         for(i=63; i>=0; i--){
  82 //            int o= a1 & 0x8000000000000000ULL;
  83             a1+= a1 + ((a0>>i)&1);
  84             t1+=t1;
  85             if(/*o || */c <= a1){
  86                 a1 -= c;
  87                 t1++;
  88             }
  89         }
  90         return t1;
  91     }
  92 #else
  93         AVInteger ai;
  94         ai= av_mul_i(av_int2i(a), av_int2i(b));
  95         ai= av_add_i(ai, av_int2i(r));
  96
  97         return av_i2int(av_div_i(ai, av_int2i(c)));
  98     }
  99 #endif
 100 }
 101
 102 int64_t av_rescale(int64_t a, int64_t b, int64_t c){
 103     return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
 104 }
 105
 106 int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq){
 107     int64_t b= bq.num * (int64_t)cq.den;
 108     int64_t c= cq.num * (int64_t)bq.den;
 109     return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF);
 110 }
 111 #if 0
 112 #undef printf
 113 main(){
 114     int64_t a,b,c,d,e;
 115
 116     for(a=7; a<256LL*256*256*256*128; a=(a*3)+1){
 117         for(b=3; b<256LL*256*256*256*128; b=(b*5)/4+1){
 118             for(c=9; c<256LL*256*256*256*128; c=(c*7)/5+3 ){
 119                 int64_t r= c/2;
 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                 d= av_i2int(av_div_i(ai, av_int2i(c)));
 125
 126                 e= av_rescale(a,b,c);
 127
 128                 if((double)a * (double)b / (double)c > (1LL<<63))
 129                     continue;
 130
 131                 if(d!=e) printf("%Ld*%Ld/%Ld= %Ld=%Ld\n", a, b, c, d, e);
 132             }
 133         }
 134     }
 135 }
 136 #endif