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/libavutil/rational.c

http://github.com/FFmpeg/FFmpeg
C | 184 lines | 123 code | 31 blank | 30 comment | 30 complexity | f4f950b39d52fdfc40ec501180f260e4 MD5 | raw file
  1/*
  2 * rational numbers
  3 * Copyright (c) 2003 Michael Niedermayer <michaelni@gmx.at>
  4 *
  5 * This file is part of FFmpeg.
  6 *
  7 * FFmpeg is free software; you can redistribute it and/or
  8 * modify it under the terms of the GNU Lesser General Public
  9 * License as published by the Free Software Foundation; either
 10 * version 2.1 of the License, or (at your option) any later version.
 11 *
 12 * FFmpeg is distributed in the hope that it will be useful,
 13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 15 * Lesser General Public License for more details.
 16 *
 17 * You should have received a copy of the GNU Lesser General Public
 18 * License along with FFmpeg; if not, write to the Free Software
 19 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
 20 */
 21
 22/**
 23 * @file
 24 * rational numbers
 25 * @author Michael Niedermayer <michaelni@gmx.at>
 26 */
 27
 28#include "avassert.h"
 29#include <limits.h>
 30
 31#include "common.h"
 32#include "mathematics.h"
 33#include "rational.h"
 34
 35int av_reduce(int *dst_num, int *dst_den,
 36              int64_t num, int64_t den, int64_t max)
 37{
 38    AVRational a0 = { 0, 1 }, a1 = { 1, 0 };
 39    int sign = (num < 0) ^ (den < 0);
 40    int64_t gcd = av_gcd(FFABS(num), FFABS(den));
 41
 42    if (gcd) {
 43        num = FFABS(num) / gcd;
 44        den = FFABS(den) / gcd;
 45    }
 46    if (num <= max && den <= max) {
 47        a1 = (AVRational) { num, den };
 48        den = 0;
 49    }
 50
 51    while (den) {
 52        uint64_t x        = num / den;
 53        int64_t next_den  = num - den * x;
 54        int64_t a2n       = x * a1.num + a0.num;
 55        int64_t a2d       = x * a1.den + a0.den;
 56
 57        if (a2n > max || a2d > max) {
 58            if (a1.num) x =          (max - a0.num) / a1.num;
 59            if (a1.den) x = FFMIN(x, (max - a0.den) / a1.den);
 60
 61            if (den * (2 * x * a1.den + a0.den) > num * a1.den)
 62                a1 = (AVRational) { x * a1.num + a0.num, x * a1.den + a0.den };
 63            break;
 64        }
 65
 66        a0  = a1;
 67        a1  = (AVRational) { a2n, a2d };
 68        num = den;
 69        den = next_den;
 70    }
 71    av_assert2(av_gcd(a1.num, a1.den) <= 1U);
 72    av_assert2(a1.num <= max && a1.den <= max);
 73
 74    *dst_num = sign ? -a1.num : a1.num;
 75    *dst_den = a1.den;
 76
 77    return den == 0;
 78}
 79
 80AVRational av_mul_q(AVRational b, AVRational c)
 81{
 82    av_reduce(&b.num, &b.den,
 83               b.num * (int64_t) c.num,
 84               b.den * (int64_t) c.den, INT_MAX);
 85    return b;
 86}
 87
 88AVRational av_div_q(AVRational b, AVRational c)
 89{
 90    return av_mul_q(b, (AVRational) { c.den, c.num });
 91}
 92
 93AVRational av_add_q(AVRational b, AVRational c) {
 94    av_reduce(&b.num, &b.den,
 95               b.num * (int64_t) c.den +
 96               c.num * (int64_t) b.den,
 97               b.den * (int64_t) c.den, INT_MAX);
 98    return b;
 99}
100
101AVRational av_sub_q(AVRational b, AVRational c)
102{
103    return av_add_q(b, (AVRational) { -c.num, c.den });
104}
105
106AVRational av_d2q(double d, int max)
107{
108    AVRational a;
109    int exponent;
110    int64_t den;
111    if (isnan(d))
112        return (AVRational) { 0,0 };
113    if (fabs(d) > INT_MAX + 3LL)
114        return (AVRational) { d < 0 ? -1 : 1, 0 };
115    frexp(d, &exponent);
116    exponent = FFMAX(exponent-1, 0);
117    den = 1LL << (61 - exponent);
118    // (int64_t)rint() and llrint() do not work with gcc on ia64 and sparc64,
119    // see Ticket2713 for affected gcc/glibc versions
120    av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, max);
121    if ((!a.num || !a.den) && d && max>0 && max<INT_MAX)
122        av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, INT_MAX);
123
124    return a;
125}
126
127int av_nearer_q(AVRational q, AVRational q1, AVRational q2)
128{
129    /* n/d is q, a/b is the median between q1 and q2 */
130    int64_t a = q1.num * (int64_t)q2.den + q2.num * (int64_t)q1.den;
131    int64_t b = 2 * (int64_t)q1.den * q2.den;
132
133    /* rnd_up(a*d/b) > n => a*d/b > n */
134    int64_t x_up = av_rescale_rnd(a, q.den, b, AV_ROUND_UP);
135
136    /* rnd_down(a*d/b) < n => a*d/b < n */
137    int64_t x_down = av_rescale_rnd(a, q.den, b, AV_ROUND_DOWN);
138
139    return ((x_up > q.num) - (x_down < q.num)) * av_cmp_q(q2, q1);
140}
141
142int av_find_nearest_q_idx(AVRational q, const AVRational* q_list)
143{
144    int i, nearest_q_idx = 0;
145    for (i = 0; q_list[i].den; i++)
146        if (av_nearer_q(q, q_list[i], q_list[nearest_q_idx]) > 0)
147            nearest_q_idx = i;
148
149    return nearest_q_idx;
150}
151
152uint32_t av_q2intfloat(AVRational q) {
153    int64_t n;
154    int shift;
155    int sign = 0;
156
157    if (q.den < 0) {
158        q.den *= -1;
159        q.num *= -1;
160    }
161    if (q.num < 0) {
162        q.num *= -1;
163        sign = 1;
164    }
165
166    if (!q.num && !q.den) return 0xFFC00000;
167    if (!q.num) return 0;
168    if (!q.den) return 0x7F800000 | (q.num & 0x80000000);
169
170    shift = 23 + av_log2(q.den) - av_log2(q.num);
171    if (shift >= 0) n = av_rescale(q.num, 1LL<<shift, q.den);
172    else            n = av_rescale(q.num, 1, ((int64_t)q.den) << -shift);
173
174    shift -= n >= (1<<24);
175    shift += n <  (1<<23);
176
177    if (shift >= 0) n = av_rescale(q.num, 1LL<<shift, q.den);
178    else            n = av_rescale(q.num, 1, ((int64_t)q.den) << -shift);
179
180    av_assert1(n <  (1<<24));
181    av_assert1(n >= (1<<23));
182
183    return sign<<31 | (150-shift)<<23 | (n - (1<<23));
184}