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 libavutil/rational.c
  24  * rational numbers
  25  * @author Michael Niedermayer <michaelni@gmx.at>
  26  */
  27
  28 #include <assert.h>
  29 //#include <math.h>
  30 #include <limits.h>
  31
  32 #include "common.h"
  33 #include "mathematics.h"
  34 #include "rational.h"
  35
  36 int av_reduce(int *dst_num, int *dst_den, int64_t num, int64_t den, int64_t max){
  37     AVRational a0={0,1}, a1={1,0};
  38     int sign= (num<0) ^ (den<0);
  39     int64_t gcd= av_gcd(FFABS(num), FFABS(den));
  40
  41     if(gcd){
  42         num = FFABS(num)/gcd;
  43         den = FFABS(den)/gcd;
  44     }
  45     if(num<=max && den<=max){
  46         a1= (AVRational){num, den};
  47         den=0;
  48     }
  49
  50     while(den){
  51         uint64_t x      = num / den;
  52         int64_t next_den= num - den*x;
  53         int64_t a2n= x*a1.num + a0.num;
  54         int64_t a2d= x*a1.den + a0.den;
  55
  56         if(a2n > max || a2d > max){
  57             if(a1.num) x= (max - a0.num) / a1.num;
  58             if(a1.den) x= FFMIN(x, (max - a0.den) / a1.den);
  59
  60             if (den*(2*x*a1.den + a0.den) > num*a1.den)
  61                 a1 = (AVRational){x*a1.num + a0.num, x*a1.den + a0.den};
  62             break;
  63         }
  64
  65         a0= a1;
  66         a1= (AVRational){a2n, a2d};
  67         num= den;
  68         den= next_den;
  69     }
  70     assert(av_gcd(a1.num, a1.den) <= 1U);
  71
  72     *dst_num = sign ? -a1.num : a1.num;
  73     *dst_den = a1.den;
  74
  75     return den==0;
  76 }
  77
  78 AVRational av_mul_q(AVRational b, AVRational c){
  79     av_reduce(&b.num, &b.den, b.num * (int64_t)c.num, b.den * (int64_t)c.den, INT_MAX);
  80     return b;
  81 }
  82
  83 AVRational av_div_q(AVRational b, AVRational c){
  84     return av_mul_q(b, (AVRational){c.den, c.num});
  85 }
  86
  87 AVRational av_add_q(AVRational b, AVRational c){
  88     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);
  89     return b;
  90 }
  91
  92 AVRational av_sub_q(AVRational b, AVRational c){
  93     return av_add_q(b, (AVRational){-c.num, c.den});
  94 }
  95
  96 AVRational av_d2q(double d, int max){
  97     AVRational a;
  98 #define LOG2  0.69314718055994530941723212145817656807550013436025
  99     int exponent= FFMAX( (int)(log(fabs(d) + 1e-20)/LOG2), 0);
 100     int64_t den= 1LL << (61 - exponent);
 101     av_reduce(&a.num, &a.den, (int64_t)(d * den + 0.5), den, max);
 102
 103     return a;
 104 }
 105
 106 int av_nearer_q(AVRational q, AVRational q1, AVRational q2)
 107 {
 108     /* n/d is q, a/b is the median between q1 and q2 */
 109     int64_t a = q1.num * (int64_t)q2.den + q2.num * (int64_t)q1.den;
 110     int64_t b = 2 * (int64_t)q1.den * q2.den;
 111
 112     /* rnd_up(a*d/b) > n => a*d/b > n */
 113     int64_t x_up = av_rescale_rnd(a, q.den, b, AV_ROUND_UP);
 114
 115     /* rnd_down(a*d/b) < n => a*d/b < n */
 116     int64_t x_down = av_rescale_rnd(a, q.den, b, AV_ROUND_DOWN);
 117
 118     return ((x_up > q.num) - (x_down < q.num)) * av_cmp_q(q2, q1);
 119 }
 120
 121 int av_find_nearest_q_idx(AVRational q, const AVRational* q_list)
 122 {
 123     int i, nearest_q_idx = 0;
 124     for(i=0; q_list[i].den; i++)
 125         if (av_nearer_q(q, q_list[i], q_list[nearest_q_idx]) > 0)
 126             nearest_q_idx = i;
 127
 128     return nearest_q_idx;
 129 }