/* * rational numbers * Copyright (c) 2003 Michael Niedermayer <michaelni@gmx.at> * * This file is part of Libav. * * Libav 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. * * Libav 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 Libav; 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); *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; }