4c0216e60f802ab3ad63ea162e8eed02e0995be5
[libav.git] / libavutil / rational.c
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 rational.c
24 * Rational numbers
25 * @author Michael Niedermayer <michaelni@gmx.at>
26 */
27
28 //#include <math.h>
29 #include <limits.h>
30
31 #include "common.h"
32 #include "mathematics.h"
33 #include "rational.h"
34
35 int av_reduce(int *dst_nom, int *dst_den, int64_t nom, int64_t den, int64_t max){
36 AVRational a0={0,1}, a1={1,0};
37 int sign= (nom<0) ^ (den<0);
38 int64_t gcd= av_gcd(FFABS(nom), FFABS(den));
39
40 if(gcd){
41 nom = FFABS(nom)/gcd;
42 den = FFABS(den)/gcd;
43 }
44 if(nom<=max && den<=max){
45 a1= (AVRational){nom, den};
46 den=0;
47 }
48
49 while(den){
50 uint64_t x = nom / den;
51 int64_t next_den= nom - den*x;
52 int64_t a2n= x*a1.num + a0.num;
53 int64_t a2d= x*a1.den + a0.den;
54
55 if(a2n > max || a2d > max){
56 if(a1.num) x= (max - a0.num) / a1.num;
57 if(a1.den) x= FFMIN(x, (max - a0.den) / a1.den);
58
59 if (den*(2*x*a1.den + a0.den) > nom*a1.den)
60 a1 = (AVRational){x*a1.num + a0.num, x*a1.den + a0.den};
61 break;
62 }
63
64 a0= a1;
65 a1= (AVRational){a2n, a2d};
66 nom= den;
67 den= next_den;
68 }
69 assert(av_gcd(a1.num, a1.den) <= 1U);
70
71 *dst_nom = sign ? -a1.num : a1.num;
72 *dst_den = a1.den;
73
74 return den==0;
75 }
76
77 AVRational av_mul_q(AVRational b, AVRational c){
78 av_reduce(&b.num, &b.den, b.num * (int64_t)c.num, b.den * (int64_t)c.den, INT_MAX);
79 return b;
80 }
81
82 AVRational av_div_q(AVRational b, AVRational c){
83 return av_mul_q(b, (AVRational){c.den, c.num});
84 }
85
86 AVRational av_add_q(AVRational b, AVRational c){
87 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);
88 return b;
89 }
90
91 AVRational av_sub_q(AVRational b, AVRational c){
92 return av_add_q(b, (AVRational){-c.num, c.den});
93 }
94
95 AVRational av_d2q(double d, int max){
96 AVRational a;
97 #define LOG2 0.69314718055994530941723212145817656807550013436025
98 int exponent= FFMAX( (int)(log(fabs(d) + 1e-20)/LOG2), 0);
99 int64_t den= 1LL << (61 - exponent);
100 av_reduce(&a.num, &a.den, (int64_t)(d * den + 0.5), den, max);
101
102 return a;
103 }
104
105 int av_nearer_q(AVRational q, AVRational q1, AVRational q2)
106 {
107 /* n/d is q, a/b is the median between q1 and q2 */
108 int64_t a = q1.num * (int64_t)q2.den + q2.num * (int64_t)q1.den;
109 int64_t b = 2 * (int64_t)q1.den * q2.den;
110
111 /* rnd_up(a*d/b) > n => a*d/b > n */
112 int64_t x_up = av_rescale_rnd(a, q.den, b, AV_ROUND_UP);
113
114 /* rnd_down(a*d/b) < n => a*d/b < n */
115 int64_t x_down = av_rescale_rnd(a, q.den, b, AV_ROUND_DOWN);
116
117 return ((x_up > q.num) - (x_down < q.num)) * av_cmp_q(q2, q1);
118 }
119
120 int av_find_nearest_q_idx(AVRational q, const AVRational* q_list)
121 {
122 int i, nearest_q_idx = 0;
123 for(i=0; q_list[i].den; i++)
124 if (av_nearer_q(q, q_list[i], q_list[nearest_q_idx]) > 0)
125 nearest_q_idx = i;
126
127 return nearest_q_idx;
128 }