/* * 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)); } AVRational av_gcd_q(AVRational a, AVRational b, int max_den, AVRational def) { int64_t gcd, lcm; gcd = av_gcd(a.den, b.den); lcm = (a.den / gcd) * b.den; return lcm < max_den ? av_make_q(av_gcd(a.num, b.num), lcm) : def; }