Libav
rational.c
Go to the documentation of this file.
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 
28 #include "avassert.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_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 
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 
88 {
89  return av_mul_q(b, (AVRational) { c.den, c.num });
90 }
91 
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 
101 {
102  return av_add_q(b, (AVRational) { -c.num, c.den });
103 }
104 
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 
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 
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 }
int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd)
Rescale a 64-bit integer with specified rounding.
Definition: mathematics.c:58
int num
numerator
Definition: rational.h:44
static int av_cmp_q(AVRational a, AVRational b)
Compare two rationals.
Definition: rational.h:55
Definition: vf_drawbox.c:37
Round toward +infinity.
Definition: mathematics.h:53
#define av_assert2(cond)
assert() equivalent, that does lie in speed critical code.
Definition: avassert.h:63
static av_always_inline av_const int isnan(float x)
Definition: libm.h:85
#define b
Definition: input.c:52
AVRational av_mul_q(AVRational b, AVRational c)
Multiply two rationals.
Definition: rational.c:79
AVRational av_add_q(AVRational b, AVRational c)
Add two rationals.
Definition: rational.c:92
int av_nearer_q(AVRational q, AVRational q1, AVRational q2)
Definition: rational.c:122
AVRational av_div_q(AVRational b, AVRational c)
Divide one rational by another.
Definition: rational.c:87
simple assert() macros that are a bit more flexible than ISO C assert().
int64_t av_gcd(int64_t a, int64_t b)
Return the greatest common divisor of a and b.
Definition: mathematics.c:53
#define FFMAX(a, b)
Definition: common.h:55
int av_reduce(int *dst_num, int *dst_den, int64_t num, int64_t den, int64_t max)
Reduce a fraction.
Definition: rational.c:35
AVRational av_sub_q(AVRational b, AVRational c)
Subtract one rational from another.
Definition: rational.c:100
AVRational av_d2q(double d, int max)
Convert a double precision floating point number to a rational.
Definition: rational.c:105
#define FFMIN(a, b)
Definition: common.h:57
#define FFABS(a)
Definition: common.h:52
int av_find_nearest_q_idx(AVRational q, const AVRational *q_list)
Find the nearest value in q_list to q.
Definition: rational.c:137
if(ac->has_optimized_func)
rational number numerator/denominator
Definition: rational.h:43
#define LOG2
Round toward -infinity.
Definition: mathematics.h:52
common internal and external API header
rational numbers
int den
denominator
Definition: rational.h:45
static av_always_inline av_const int isinf(float x)
Definition: libm.h:75