Line data Source code
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 :
35 0 : int av_reduce(int *dst_num, int *dst_den,
36 : int64_t num, int64_t den, int64_t max)
37 : {
38 0 : AVRational a0 = { 0, 1 }, a1 = { 1, 0 };
39 0 : int sign = (num < 0) ^ (den < 0);
40 0 : int64_t gcd = av_gcd(FFABS(num), FFABS(den));
41 :
42 0 : if (gcd) {
43 0 : num = FFABS(num) / gcd;
44 0 : den = FFABS(den) / gcd;
45 : }
46 0 : if (num <= max && den <= max) {
47 0 : a1 = (AVRational) { num, den };
48 0 : den = 0;
49 : }
50 :
51 0 : while (den) {
52 0 : uint64_t x = num / den;
53 0 : int64_t next_den = num - den * x;
54 0 : int64_t a2n = x * a1.num + a0.num;
55 0 : int64_t a2d = x * a1.den + a0.den;
56 :
57 0 : if (a2n > max || a2d > max) {
58 0 : if (a1.num) x = (max - a0.num) / a1.num;
59 0 : if (a1.den) x = FFMIN(x, (max - a0.den) / a1.den);
60 :
61 0 : if (den * (2 * x * a1.den + a0.den) > num * a1.den)
62 0 : a1 = (AVRational) { x * a1.num + a0.num, x * a1.den + a0.den };
63 0 : break;
64 : }
65 :
66 0 : a0 = a1;
67 0 : a1 = (AVRational) { a2n, a2d };
68 0 : num = den;
69 0 : den = next_den;
70 : }
71 0 : av_assert2(av_gcd(a1.num, a1.den) <= 1U);
72 :
73 0 : *dst_num = sign ? -a1.num : a1.num;
74 0 : *dst_den = a1.den;
75 :
76 0 : return den == 0;
77 : }
78 :
79 0 : AVRational av_mul_q(AVRational b, AVRational c)
80 : {
81 0 : av_reduce(&b.num, &b.den,
82 0 : b.num * (int64_t) c.num,
83 0 : b.den * (int64_t) c.den, INT_MAX);
84 0 : return b;
85 : }
86 :
87 0 : AVRational av_div_q(AVRational b, AVRational c)
88 : {
89 0 : return av_mul_q(b, (AVRational) { c.den, c.num });
90 : }
91 :
92 0 : AVRational av_add_q(AVRational b, AVRational c) {
93 0 : av_reduce(&b.num, &b.den,
94 0 : b.num * (int64_t) c.den +
95 0 : c.num * (int64_t) b.den,
96 0 : b.den * (int64_t) c.den, INT_MAX);
97 0 : return b;
98 : }
99 :
100 0 : AVRational av_sub_q(AVRational b, AVRational c)
101 : {
102 0 : return av_add_q(b, (AVRational) { -c.num, c.den });
103 : }
104 :
105 0 : AVRational av_d2q(double d, int max)
106 : {
107 : AVRational a;
108 : #define LOG2 0.69314718055994530941723212145817656807550013436025
109 : int exponent;
110 : int64_t den;
111 0 : if (isnan(d))
112 0 : return (AVRational) { 0,0 };
113 0 : if (isinf(d))
114 0 : return (AVRational) { d < 0 ? -1 : 1, 0 };
115 0 : exponent = FFMAX( (int)(log(fabs(d) + 1e-20)/LOG2), 0);
116 0 : den = 1LL << (61 - exponent);
117 0 : av_reduce(&a.num, &a.den, (int64_t)(d * den + 0.5), den, max);
118 :
119 0 : return a;
120 : }
121 :
122 0 : 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 0 : int64_t a = q1.num * (int64_t)q2.den + q2.num * (int64_t)q1.den;
126 0 : int64_t b = 2 * (int64_t)q1.den * q2.den;
127 :
128 : /* rnd_up(a*d/b) > n => a*d/b > n */
129 0 : 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 0 : int64_t x_down = av_rescale_rnd(a, q.den, b, AV_ROUND_DOWN);
133 :
134 0 : return ((x_up > q.num) - (x_down < q.num)) * av_cmp_q(q2, q1);
135 : }
136 :
137 0 : int av_find_nearest_q_idx(AVRational q, const AVRational* q_list)
138 : {
139 0 : int i, nearest_q_idx = 0;
140 0 : for (i = 0; q_list[i].den; i++)
141 0 : if (av_nearer_q(q, q_list[i], q_list[nearest_q_idx]) > 0)
142 0 : nearest_q_idx = i;
143 :
144 0 : return nearest_q_idx;
145 : }
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