208 lines
6.4 KiB
C
208 lines
6.4 KiB
C
/*
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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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* @file
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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 "avassert.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_num, int *dst_den,
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int64_t num, int64_t den, int64_t max)
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{
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AVRational a0 = { 0, 1 }, a1 = { 1, 0 };
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int sign = (num < 0) ^ (den < 0);
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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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}
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if (num <= max && den <= max) {
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a1 = (AVRational) { num, den };
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den = 0;
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}
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while (den) {
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uint64_t x = num / den;
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int64_t next_den = num - 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) > num * 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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num = den;
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den = next_den;
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}
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av_assert2(av_gcd(a1.num, a1.den) <= 1U);
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av_assert2(a1.num <= max && a1.den <= max);
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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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}
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AVRational av_mul_q(AVRational b, AVRational c)
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{
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av_reduce(&b.num, &b.den,
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b.num * (int64_t) c.num,
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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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{
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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,
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b.num * (int64_t) c.den +
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c.num * (int64_t) b.den,
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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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{
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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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{
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AVRational a;
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#define LOG2 0.69314718055994530941723212145817656807550013436025
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int exponent;
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int64_t den;
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if (isnan(d))
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return (AVRational) { 0,0 };
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if (fabs(d) > INT_MAX + 3LL)
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return (AVRational) { d < 0 ? -1 : 1, 0 };
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exponent = FFMAX( (int)(log(fabs(d) + 1e-20)/LOG2), 0);
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den = 1LL << (61 - exponent);
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// (int64_t)rint() and llrint() do not work with gcc on ia64 and sparc64
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av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, max);
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if ((!a.num || !a.den) && d && max>0 && max<INT_MAX)
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av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, INT_MAX);
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return a;
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}
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int av_nearer_q(AVRational q, AVRational q1, AVRational q2)
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{
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/* n/d is q, a/b is the median between q1 and q2 */
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int64_t a = q1.num * (int64_t)q2.den + q2.num * (int64_t)q1.den;
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int64_t b = 2 * (int64_t)q1.den * q2.den;
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/* rnd_up(a*d/b) > n => a*d/b > n */
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int64_t x_up = av_rescale_rnd(a, q.den, b, AV_ROUND_UP);
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/* rnd_down(a*d/b) < n => a*d/b < n */
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int64_t x_down = av_rescale_rnd(a, q.den, b, AV_ROUND_DOWN);
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return ((x_up > q.num) - (x_down < q.num)) * av_cmp_q(q2, q1);
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}
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int av_find_nearest_q_idx(AVRational q, const AVRational* q_list)
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{
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int i, nearest_q_idx = 0;
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for (i = 0; q_list[i].den; i++)
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if (av_nearer_q(q, q_list[i], q_list[nearest_q_idx]) > 0)
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nearest_q_idx = i;
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return nearest_q_idx;
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}
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#ifdef TEST
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int main(void)
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{
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AVRational a,b,r;
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for (a.num = -2; a.num <= 2; a.num++) {
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for (a.den = -2; a.den <= 2; a.den++) {
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for (b.num = -2; b.num <= 2; b.num++) {
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for (b.den = -2; b.den <= 2; b.den++) {
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int c = av_cmp_q(a,b);
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double d = av_q2d(a) == av_q2d(b) ?
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0 : (av_q2d(a) - av_q2d(b));
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if (d > 0) d = 1;
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else if (d < 0) d = -1;
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else if (d != d) d = INT_MIN;
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if (c != d)
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av_log(NULL, AV_LOG_ERROR, "%d/%d %d/%d, %d %f\n", a.num,
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a.den, b.num, b.den, c,d);
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r = av_sub_q(av_add_q(b,a), b);
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if(b.den && (r.num*a.den != a.num*r.den || !r.num != !a.num || !r.den != !a.den))
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av_log(NULL, AV_LOG_ERROR, "%d/%d ", r.num, r.den);
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}
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}
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}
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}
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for (a.num = 1; a.num <= 10; a.num++) {
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for (a.den = 1; a.den <= 10; a.den++) {
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if (av_gcd(a.num, a.den) > 1)
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continue;
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for (b.num = 1; b.num <= 10; b.num++) {
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for (b.den = 1; b.den <= 10; b.den++) {
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int start;
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if (av_gcd(b.num, b.den) > 1)
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continue;
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if (av_cmp_q(b, a) < 0)
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continue;
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for (start = 0; start < 10 ; start++) {
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int acc= start;
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int i;
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for (i = 0; i<100; i++) {
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int exact = start + av_rescale_q(i+1, b, a);
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acc = av_add_stable(a, acc, b, 1);
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if (FFABS(acc - exact) > 2) {
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av_log(NULL, AV_LOG_ERROR, "%d/%d %d/%d, %d %d\n", a.num,
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a.den, b.num, b.den, acc, exact);
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return 1;
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}
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}
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}
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}
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}
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}
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}
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return 0;
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}
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#endif
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