/* * 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 numbers * @author Michael Niedermayer <michaelni@gmx.at> */ #include "avassert.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;    }    av_assert2(av_gcd(a1.num, a1.den) <= 1U);    av_assert2(a1.num <= max && a1.den <= max);     *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;    int exponent;    int64_t den;    if (isnan(d))        return (AVRational) { 0,0 };    if (fabs(d) > INT_MAX + 3LL)        return (AVRational) { d < 0 ? -1 : 1, 0 };    frexp(d, &exponent);    exponent = FFMAX(exponent-1, 0);    den = 1LL << (61 - exponent);    // (int64_t)rint() and llrint() do not work with gcc on ia64 and sparc64,    // see Ticket2713 for affected gcc/glibc versions    av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, max);    if ((!a.num || !a.den) && d && max>0 && max<INT_MAX)        av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, INT_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;} uint32_t av_q2intfloat(AVRational q) {    int64_t n;    int shift;    int sign = 0;     if (q.den < 0) {        q.den *= -1;        q.num *= -1;    }    if (q.num < 0) {        q.num *= -1;        sign = 1;    }     if (!q.num && !q.den) return 0xFFC00000;    if (!q.num) return 0;    if (!q.den) return 0x7F800000 | (q.num & 0x80000000);     shift = 23 + av_log2(q.den) - av_log2(q.num);    if (shift >= 0) n = av_rescale(q.num, 1LL<<shift, q.den);    else            n = av_rescale(q.num, 1, ((int64_t)q.den) << -shift);     shift -= n >= (1<<24);    shift += n <  (1<<23);     if (shift >= 0) n = av_rescale(q.num, 1LL<<shift, q.den);    else            n = av_rescale(q.num, 1, ((int64_t)q.den) << -shift);     av_assert1(n <  (1<<24));    av_assert1(n >= (1<<23));     return sign<<31 | (150-shift)<<23 | (n - (1<<23));}