1 /*
2 * rational numbers
3 * Copyright (c) 2003 Michael Niedermayer <michaelni@gmx.at>
4 *
5 * This file is part of Libav.
6 *
7 * Libav 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 * Libav 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 Libav; 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
av_reduce(int * dst_num,int * dst_den,int64_t num,int64_t den,int64_t max)35 int 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
73 *dst_num = sign ? -a1.num : a1.num;
74 *dst_den = a1.den;
75
76 return den == 0;
77 }
78
av_mul_q(AVRational b,AVRational c)79 AVRational av_mul_q(AVRational b, AVRational c)
80 {
81 av_reduce(&b.num, &b.den,
82 b.num * (int64_t) c.num,
83 b.den * (int64_t) c.den, INT_MAX);
84 return b;
85 }
86
av_div_q(AVRational b,AVRational c)87 AVRational av_div_q(AVRational b, AVRational c)
88 {
89 return av_mul_q(b, (AVRational) { c.den, c.num });
90 }
91
av_add_q(AVRational b,AVRational c)92 AVRational av_add_q(AVRational b, AVRational c) {
93 av_reduce(&b.num, &b.den,
94 b.num * (int64_t) c.den +
95 c.num * (int64_t) b.den,
96 b.den * (int64_t) c.den, INT_MAX);
97 return b;
98 }
99
av_sub_q(AVRational b,AVRational c)100 AVRational av_sub_q(AVRational b, AVRational c)
101 {
102 return av_add_q(b, (AVRational) { -c.num, c.den });
103 }
104
av_d2q(double d,int max)105 AVRational av_d2q(double d, int max)
106 {
107 AVRational a;
108 #define LOG2 0.69314718055994530941723212145817656807550013436025
109 int exponent;
110 int64_t den;
111 if (isnan(d))
112 return (AVRational) { 0,0 };
113 if (isinf(d))
114 return (AVRational) { d < 0 ? -1 : 1, 0 };
115 exponent = FFMAX( (int)(log(fabs(d) + 1e-20)/LOG2), 0);
116 den = 1LL << (61 - exponent);
117 av_reduce(&a.num, &a.den, (int64_t)(d * den + 0.5), den, max);
118
119 return a;
120 }
121
av_nearer_q(AVRational q,AVRational q1,AVRational q2)122 int av_nearer_q(AVRational q, AVRational q1, AVRational q2)
123 {
124 /* n/d is q, a/b is the median between q1 and q2 */
125 int64_t a = q1.num * (int64_t)q2.den + q2.num * (int64_t)q1.den;
126 int64_t b = 2 * (int64_t)q1.den * q2.den;
127
128 /* rnd_up(a*d/b) > n => a*d/b > n */
129 int64_t x_up = av_rescale_rnd(a, q.den, b, AV_ROUND_UP);
130
131 /* rnd_down(a*d/b) < n => a*d/b < n */
132 int64_t x_down = av_rescale_rnd(a, q.den, b, AV_ROUND_DOWN);
133
134 return ((x_up > q.num) - (x_down < q.num)) * av_cmp_q(q2, q1);
135 }
136
av_find_nearest_q_idx(AVRational q,const AVRational * q_list)137 int av_find_nearest_q_idx(AVRational q, const AVRational* q_list)
138 {
139 int i, nearest_q_idx = 0;
140 for (i = 0; q_list[i].den; i++)
141 if (av_nearer_q(q, q_list[i], q_list[nearest_q_idx]) > 0)
142 nearest_q_idx = i;
143
144 return nearest_q_idx;
145 }
146