1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
|
/*
* rational numbers
* Copyright (c) 2003 Michael Niedermayer <michaelni@gmx.at>
*
* This file is part of Libav.
*
* Libav 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.
*
* Libav 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 Libav; 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);
*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;
#define LOG2 0.69314718055994530941723212145817656807550013436025
int exponent;
int64_t den;
if (isnan(d))
return (AVRational) { 0,0 };
if (isinf(d))
return (AVRational) { d < 0 ? -1 : 1, 0 };
exponent = FFMAX( (int)(log(fabs(d) + 1e-20)/LOG2), 0);
den = 1LL << (61 - exponent);
av_reduce(&a.num, &a.den, (int64_t)(d * den + 0.5), den, 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;
}
|
