rational.c 4.44 KB
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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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 * This file is part of Libav.
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 *
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 * Libav is free software; you can redistribute it and/or
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 * modify it under the terms of the GNU Lesser General Public
 * 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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 * Libav is distributed in the hope that it will be useful,
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 * 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
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 * License along with Libav; 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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 * @file
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 * rational numbers
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 * @author Michael Niedermayer <michaelni@gmx.at>
 */

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#include "avassert.h"
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//#include <math.h>
#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_num, int *dst_den, int64_t num, int64_t den, int64_t max){
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    AVRational a0={0,1}, a1={1,0};
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    int sign= (num<0) ^ (den<0);
    int64_t gcd= av_gcd(FFABS(num), FFABS(den));
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    if(gcd){
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        num = FFABS(num)/gcd;
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        den = FFABS(den)/gcd;
    }
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    if(num<=max && den<=max){
        a1= (AVRational){num, den};
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        den=0;
    }
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    while(den){
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        uint64_t x      = num / den;
        int64_t next_den= num - den*x;
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        int64_t a2n= x*a1.num + a0.num;
        int64_t a2d= x*a1.den + a0.den;

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        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);

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            if (den*(2*x*a1.den + a0.den) > num*a1.den)
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                a1 = (AVRational){x*a1.num + a0.num, x*a1.den + a0.den};
            break;
        }
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        a0= a1;
        a1= (AVRational){a2n, a2d};
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        num= den;
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        den= next_den;
    }
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    av_assert2(av_gcd(a1.num, a1.den) <= 1U);
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    *dst_num = sign ? -a1.num : a1.num;
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    *dst_den = a1.den;
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    return den==0;
}

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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){
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    return av_mul_q(b, (AVRational){c.den, c.num});
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}

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){
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    return av_add_q(b, (AVRational){-c.num, c.den});
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}

AVRational av_d2q(double d, int max){
    AVRational a;
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#define LOG2  0.69314718055994530941723212145817656807550013436025
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    int exponent;
    int64_t den;
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    if (isnan(d))
        return (AVRational){0,0};
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    if (isinf(d))
        return (AVRational){ d<0 ? -1:1, 0 };
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    exponent = FFMAX( (int)(log(fabs(d) + 1e-20)/LOG2), 0);
    den = 1LL << (61 - exponent);
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    av_reduce(&a.num, &a.den, (int64_t)(d * den + 0.5), den, max);

    return a;
}
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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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#ifdef TEST
main(){
    AVRational a,b;
    for(a.num=-2; a.num<=2; a.num++){
        for(a.den=-2; a.den<=2; a.den++){
            for(b.num=-2; b.num<=2; b.num++){
                for(b.den=-2; b.den<=2; b.den++){
                    int c= av_cmp_q(a,b);
                    double d= av_q2d(a) == av_q2d(b) ? 0 : (av_q2d(a) - av_q2d(b));
                    if(d>0) d=1;
                    else if(d<0) d=-1;
                    else if(d != d) d= INT_MIN;
                    if(c!=d) av_log(0, AV_LOG_ERROR, "%d/%d %d/%d, %d %f\n", a.num, a.den, b.num, b.den, c,d);
                }
            }
        }
    }
}
#endif