libavutil/rational.c

   1 /*
   2  * Rational numbers
   3  * Copyright (c) 2003 Michael Niedermayer <michaelni@gmx.at>
   4  *
   5  * This file is part of FFmpeg.
   6  *
   7  * FFmpeg is free software; you can redistribute it and/or
   8  * modify it under the terms of the GNU Lesser General Public
   9  * License as published by the Free Software Foundation; either
  10  * version 2.1 of the License, or (at your option) any later version.
  11  *
  12  * FFmpeg is distributed in the hope that it will be useful,
  13  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  14  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  15  * Lesser General Public License for more details.
  16  *
  17  * You should have received a copy of the GNU Lesser General Public
  18  * License along with FFmpeg; if not, write to the Free Software
  19  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
  20  */
  21
  22 /**
  23  * @file rational.c
  24  * Rational numbers
  25  * @author Michael Niedermayer <michaelni@gmx.at>
  26  */
  27
  28 //#include <math.h>
  29 #include <limits.h>
  30
  31 #include "common.h"
  32 #include "mathematics.h"
  33 #include "rational.h"
  34
  35 int av_reduce(int *dst_nom, int *dst_den, int64_t nom, int64_t den, int64_t max){
  36     AVRational a0={0,1}, a1={1,0};
  37     int sign= (nom<0) ^ (den<0);
  38     int64_t gcd= ff_gcd(FFABS(nom), FFABS(den));
  39
  40     if(gcd){
  41         nom = FFABS(nom)/gcd;
  42         den = FFABS(den)/gcd;
  43     }
  44     if(nom<=max && den<=max){
  45         a1= (AVRational){nom, den};
  46         den=0;
  47     }
  48
  49     while(den){
  50         uint64_t x      = nom / den;
  51         int64_t next_den= nom - den*x;
  52         int64_t a2n= x*a1.num + a0.num;
  53         int64_t a2d= x*a1.den + a0.den;
  54
  55         if(a2n > max || a2d > max){
  56             if(a1.num) x= (max - a0.num) / a1.num;
  57             if(a1.den) x= FFMIN(x, (max - a0.den) / a1.den);
  58
  59             if (den*(2*x*a1.den + a0.den) > nom*a1.den)
  60                 a1 = (AVRational){x*a1.num + a0.num, x*a1.den + a0.den};
  61             break;
  62         }
  63
  64         a0= a1;
  65         a1= (AVRational){a2n, a2d};
  66         nom= den;
  67         den= next_den;
  68     }
  69     assert(ff_gcd(a1.num, a1.den) <= 1U);
  70
  71     *dst_nom = sign ? -a1.num : a1.num;
  72     *dst_den = a1.den;
  73
  74     return den==0;
  75 }
  76
  77 AVRational av_mul_q(AVRational b, AVRational c){
  78     av_reduce(&b.num, &b.den, b.num * (int64_t)c.num, b.den * (int64_t)c.den, INT_MAX);
  79     return b;
  80 }
  81
  82 AVRational av_div_q(AVRational b, AVRational c){
  83     return av_mul_q(b, (AVRational){c.den, c.num});
  84 }
  85
  86 AVRational av_add_q(AVRational b, AVRational c){
  87     av_reduce(&b.num, &b.den, b.num * (int64_t)c.den + c.num * (int64_t)b.den, b.den * (int64_t)c.den, INT_MAX);
  88     return b;
  89 }
  90
  91 AVRational av_sub_q(AVRational b, AVRational c){
  92     return av_add_q(b, (AVRational){-c.num, c.den});
  93 }
  94
  95 AVRational av_d2q(double d, int max){
  96     AVRational a;
  97 #define LOG2  0.69314718055994530941723212145817656807550013436025
  98     int exponent= FFMAX( (int)(log(fabs(d) + 1e-20)/LOG2), 0);
  99     int64_t den= 1LL << (61 - exponent);
 100     av_reduce(&a.num, &a.den, (int64_t)(d * den + 0.5), den, max);
 101
 102     return a;
 103 }
 104
 105 int av_nearer_q(AVRational q, AVRational q1, AVRational q2)
 106 {
 107     /* n/d is q, a/b is the median between q1 and q2 */
 108     int64_t a = q1.num * (int64_t)q2.den + q2.num * (int64_t)q1.den;
 109     int64_t b = 2 * (int64_t)q1.den * q2.den;
 110
 111     /* rnd_up(a*d/b) > n => a*d/b > n */
 112     int64_t x_up = av_rescale_rnd(a, q.den, b, AV_ROUND_UP);
 113
 114     /* rnd_down(a*d/b) < n => a*d/b < n */
 115     int64_t x_down = av_rescale_rnd(a, q.den, b, AV_ROUND_DOWN);
 116
 117     return ((x_up > q.num) - (x_down < q.num)) * av_cmp_q(q2, q1);
 118 }
 119
 120 int av_find_nearest_q_idx(AVRational q, const AVRational* q_list)
 121 {
 122     int i, nearest_q_idx = 0;
 123     for(i=0; q_list[i].den; i++)
 124         if (av_nearer_q(q, q_list[i], q_list[nearest_q_idx]) > 0)
 125             nearest_q_idx = i;
 126
 127     return nearest_q_idx;
 128 }