yading@11: /* yading@11: * rational numbers yading@11: * Copyright (c) 2003 Michael Niedermayer yading@11: * yading@11: * This file is part of FFmpeg. yading@11: * yading@11: * FFmpeg is free software; you can redistribute it and/or yading@11: * modify it under the terms of the GNU Lesser General Public yading@11: * License as published by the Free Software Foundation; either yading@11: * version 2.1 of the License, or (at your option) any later version. yading@11: * yading@11: * FFmpeg is distributed in the hope that it will be useful, yading@11: * but WITHOUT ANY WARRANTY; without even the implied warranty of yading@11: * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU yading@11: * Lesser General Public License for more details. yading@11: * yading@11: * You should have received a copy of the GNU Lesser General Public yading@11: * License along with FFmpeg; if not, write to the Free Software yading@11: * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA yading@11: */ yading@11: yading@11: /** yading@11: * @file yading@11: * rational numbers yading@11: * @author Michael Niedermayer yading@11: */ yading@11: yading@11: #include "avassert.h" yading@11: //#include yading@11: #include yading@11: yading@11: #include "common.h" yading@11: #include "mathematics.h" yading@11: #include "rational.h" yading@11: yading@11: int av_reduce(int *dst_num, int *dst_den, yading@11: int64_t num, int64_t den, int64_t max) yading@11: { yading@11: AVRational a0 = { 0, 1 }, a1 = { 1, 0 }; yading@11: int sign = (num < 0) ^ (den < 0); yading@11: int64_t gcd = av_gcd(FFABS(num), FFABS(den)); yading@11: yading@11: if (gcd) { yading@11: num = FFABS(num) / gcd; yading@11: den = FFABS(den) / gcd; yading@11: } yading@11: if (num <= max && den <= max) { yading@11: a1 = (AVRational) { num, den }; yading@11: den = 0; yading@11: } yading@11: yading@11: while (den) { yading@11: uint64_t x = num / den; yading@11: int64_t next_den = num - den * x; yading@11: int64_t a2n = x * a1.num + a0.num; yading@11: int64_t a2d = x * a1.den + a0.den; yading@11: yading@11: if (a2n > max || a2d > max) { yading@11: if (a1.num) x = (max - a0.num) / a1.num; yading@11: if (a1.den) x = FFMIN(x, (max - a0.den) / a1.den); yading@11: yading@11: if (den * (2 * x * a1.den + a0.den) > num * a1.den) yading@11: a1 = (AVRational) { x * a1.num + a0.num, x * a1.den + a0.den }; yading@11: break; yading@11: } yading@11: yading@11: a0 = a1; yading@11: a1 = (AVRational) { a2n, a2d }; yading@11: num = den; yading@11: den = next_den; yading@11: } yading@11: av_assert2(av_gcd(a1.num, a1.den) <= 1U); yading@11: yading@11: *dst_num = sign ? -a1.num : a1.num; yading@11: *dst_den = a1.den; yading@11: yading@11: return den == 0; yading@11: } yading@11: yading@11: AVRational av_mul_q(AVRational b, AVRational c) yading@11: { yading@11: av_reduce(&b.num, &b.den, yading@11: b.num * (int64_t) c.num, yading@11: b.den * (int64_t) c.den, INT_MAX); yading@11: return b; yading@11: } yading@11: yading@11: AVRational av_div_q(AVRational b, AVRational c) yading@11: { yading@11: return av_mul_q(b, (AVRational) { c.den, c.num }); yading@11: } yading@11: yading@11: AVRational av_add_q(AVRational b, AVRational c) { yading@11: av_reduce(&b.num, &b.den, yading@11: b.num * (int64_t) c.den + yading@11: c.num * (int64_t) b.den, yading@11: b.den * (int64_t) c.den, INT_MAX); yading@11: return b; yading@11: } yading@11: yading@11: AVRational av_sub_q(AVRational b, AVRational c) yading@11: { yading@11: return av_add_q(b, (AVRational) { -c.num, c.den }); yading@11: } yading@11: yading@11: AVRational av_d2q(double d, int max) yading@11: { yading@11: AVRational a; yading@11: #define LOG2 0.69314718055994530941723212145817656807550013436025 yading@11: int exponent; yading@11: int64_t den; yading@11: if (isnan(d)) yading@11: return (AVRational) { 0,0 }; yading@11: if (isinf(d)) yading@11: return (AVRational) { d < 0 ? -1 : 1, 0 }; yading@11: exponent = FFMAX( (int)(log(fabs(d) + 1e-20)/LOG2), 0); yading@11: den = 1LL << (61 - exponent); yading@11: av_reduce(&a.num, &a.den, (int64_t)(d * den + 0.5), den, max); yading@11: yading@11: return a; yading@11: } yading@11: yading@11: int av_nearer_q(AVRational q, AVRational q1, AVRational q2) yading@11: { yading@11: /* n/d is q, a/b is the median between q1 and q2 */ yading@11: int64_t a = q1.num * (int64_t)q2.den + q2.num * (int64_t)q1.den; yading@11: int64_t b = 2 * (int64_t)q1.den * q2.den; yading@11: yading@11: /* rnd_up(a*d/b) > n => a*d/b > n */ yading@11: int64_t x_up = av_rescale_rnd(a, q.den, b, AV_ROUND_UP); yading@11: yading@11: /* rnd_down(a*d/b) < n => a*d/b < n */ yading@11: int64_t x_down = av_rescale_rnd(a, q.den, b, AV_ROUND_DOWN); yading@11: yading@11: return ((x_up > q.num) - (x_down < q.num)) * av_cmp_q(q2, q1); yading@11: } yading@11: yading@11: int av_find_nearest_q_idx(AVRational q, const AVRational* q_list) yading@11: { yading@11: int i, nearest_q_idx = 0; yading@11: for (i = 0; q_list[i].den; i++) yading@11: if (av_nearer_q(q, q_list[i], q_list[nearest_q_idx]) > 0) yading@11: nearest_q_idx = i; yading@11: yading@11: return nearest_q_idx; yading@11: } yading@11: yading@11: #ifdef TEST yading@11: int main(void) yading@11: { yading@11: AVRational a,b,r; yading@11: for (a.num = -2; a.num <= 2; a.num++) { yading@11: for (a.den = -2; a.den <= 2; a.den++) { yading@11: for (b.num = -2; b.num <= 2; b.num++) { yading@11: for (b.den = -2; b.den <= 2; b.den++) { yading@11: int c = av_cmp_q(a,b); yading@11: double d = av_q2d(a) == av_q2d(b) ? yading@11: 0 : (av_q2d(a) - av_q2d(b)); yading@11: if (d > 0) d = 1; yading@11: else if (d < 0) d = -1; yading@11: else if (d != d) d = INT_MIN; yading@11: if (c != d) yading@11: av_log(NULL, AV_LOG_ERROR, "%d/%d %d/%d, %d %f\n", a.num, yading@11: a.den, b.num, b.den, c,d); yading@11: r = av_sub_q(av_add_q(b,a), b); yading@11: if(b.den && (r.num*a.den != a.num*r.den || !r.num != !a.num || !r.den != !a.den)) yading@11: av_log(NULL, AV_LOG_ERROR, "%d/%d ", r.num, r.den); yading@11: } yading@11: } yading@11: } yading@11: } yading@11: return 0; yading@11: } yading@11: #endif