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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 numbers
- * @author Michael Niedermayer <michaelni@gmx.at>
- */
- #include "avassert.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;
- }
- av_assert2(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;
- int64_t den;
- if (isnan(d))
- return (AVRational) { 0,0 };
- if (isinf(d))
- return (AVRational) { d < 0 ? -1 : 1, 0 };
- exponent = FFMAX( (int)(log(fabs(d) + 1e-20)/LOG2), 0);
- 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;
- }
- #ifdef TEST
- int main(void)
- {
- 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);
- }
- }
- }
- }
- return 0;
- }
- #endif
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