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