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/*
* rational numbers
* Copyright (c) 2003 Michael Niedermayer <michaelni@gmx.at>
*
* This file is part of FFmpeg.
*
* FFmpeg is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* FFmpeg is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with FFmpeg; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
/**
* @file rational.c
* rational numbers
* @author Michael Niedermayer <michaelni@gmx.at>
*/
#include <assert.h>
//#include <math.h>
#include <limits.h>
#include "common.h"
#include "mathematics.h"
#include "rational.h"
int av_reduce(int *dst_num, int *dst_den, int64_t num, int64_t den, int64_t max){
AVRational a0={0,1}, a1={1,0};
int sign= (num<0) ^ (den<0);
int64_t gcd= av_gcd(FFABS(num), FFABS(den));
if(gcd){
num = FFABS(num)/gcd;
den = FFABS(den)/gcd;
}
if(num<=max && den<=max){
a1= (AVRational){num, den};
den=0;
}
while(den){
uint64_t x = num / den;
int64_t next_den= num - den*x;
int64_t a2n= x*a1.num + a0.num;
int64_t a2d= x*a1.den + a0.den;
if(a2n > max || a2d > max){
if(a1.num) x= (max - a0.num) / a1.num;
if(a1.den) x= FFMIN(x, (max - a0.den) / a1.den);
if (den*(2*x*a1.den + a0.den) > num*a1.den)
a1 = (AVRational){x*a1.num + a0.num, x*a1.den + a0.den};
break;
}
a0= a1;
a1= (AVRational){a2n, a2d};
num= den;
den= next_den;
}
assert(av_gcd(a1.num, a1.den) <= 1U);
*dst_num = sign ? -a1.num : a1.num;
*dst_den = a1.den;
return den==0;
}
AVRational av_mul_q(AVRational b, AVRational c){
av_reduce(&b.num, &b.den, b.num * (int64_t)c.num, b.den * (int64_t)c.den, INT_MAX);
return b;
}
AVRational av_div_q(AVRational b, AVRational c){
return av_mul_q(b, (AVRational){c.den, c.num});
}
AVRational av_add_q(AVRational b, AVRational c){
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);
return b;
}
AVRational av_sub_q(AVRational b, AVRational c){
return av_add_q(b, (AVRational){-c.num, c.den});
}
AVRational av_d2q(double d, int max){
AVRational a;
#define LOG2 0.69314718055994530941723212145817656807550013436025
int exponent= FFMAX( (int)(log(fabs(d) + 1e-20)/LOG2), 0);
int64_t den= 1LL << (61 - exponent);
av_reduce(&a.num, &a.den, (int64_t)(d * den + 0.5), den, max);
return a;
}
int av_nearer_q(AVRational q, AVRational q1, AVRational q2)
{
/* n/d is q, a/b is the median between q1 and q2 */
int64_t a = q1.num * (int64_t)q2.den + q2.num * (int64_t)q1.den;
int64_t b = 2 * (int64_t)q1.den * q2.den;
/* rnd_up(a*d/b) > n => a*d/b > n */
int64_t x_up = av_rescale_rnd(a, q.den, b, AV_ROUND_UP);
/* rnd_down(a*d/b) < n => a*d/b < n */
int64_t x_down = av_rescale_rnd(a, q.den, b, AV_ROUND_DOWN);
return ((x_up > q.num) - (x_down < q.num)) * av_cmp_q(q2, q1);
}
int av_find_nearest_q_idx(AVRational q, const AVRational* q_list)
{
int i, nearest_q_idx = 0;
for(i=0; q_list[i].den; i++)
if (av_nearer_q(q, q_list[i], q_list[nearest_q_idx]) > 0)
nearest_q_idx = i;
return nearest_q_idx;
}
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