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 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 36int 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 78AVRational 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 83AVRational av_div_q(AVRational b, AVRational c){ 84 return av_mul_q(b, (AVRational){c.den, c.num}); 85} 86 87AVRational 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 92AVRational av_sub_q(AVRational b, AVRational c){ 93 return av_add_q(b, (AVRational){-c.num, c.den}); 94} 95 96AVRational 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 if (isnan(d)) 102 return (AVRational){0,0}; 103 av_reduce(&a.num, &a.den, (int64_t)(d * den + 0.5), den, max); 104 105 return a; 106} 107 108int av_nearer_q(AVRational q, AVRational q1, AVRational q2) 109{ 110 /* n/d is q, a/b is the median between q1 and q2 */ 111 int64_t a = q1.num * (int64_t)q2.den + q2.num * (int64_t)q1.den; 112 int64_t b = 2 * (int64_t)q1.den * q2.den; 113 114 /* rnd_up(a*d/b) > n => a*d/b > n */ 115 int64_t x_up = av_rescale_rnd(a, q.den, b, AV_ROUND_UP); 116 117 /* rnd_down(a*d/b) < n => a*d/b < n */ 118 int64_t x_down = av_rescale_rnd(a, q.den, b, AV_ROUND_DOWN); 119 120 return ((x_up > q.num) - (x_down < q.num)) * av_cmp_q(q2, q1); 121} 122 123int av_find_nearest_q_idx(AVRational q, const AVRational* q_list) 124{ 125 int i, nearest_q_idx = 0; 126 for(i=0; q_list[i].den; i++) 127 if (av_nearer_q(q, q_list[i], q_list[nearest_q_idx]) > 0) 128 nearest_q_idx = i; 129 130 return nearest_q_idx; 131} 132