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
24 * rational numbers
25 * @author Michael Niedermayer <michaelni@gmx.at>
26 */
27
30
34
36 int64_t num, int64_t den, int64_t max)
37 {
39 int sign = (num < 0) ^ (den < 0);
41
42 if (gcd) {
43 num =
FFABS(num) / gcd;
44 den =
FFABS(den) / gcd;
45 }
46 if (num <= max && den <= max) {
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;
60
61 if (den * (2 * x *
a1.den + a0.
den) > num *
a1.den)
63 break;
64 }
65
68 num = den;
69 den = next_den;
70 }
73
74 *dst_num = sign ? -
a1.num :
a1.num;
76
77 return den == 0;
78 }
79
81 {
84 b.
den * (int64_t) c.
den, INT_MAX);
86 }
87
89 {
91 }
92
97 b.
den * (int64_t) c.
den, INT_MAX);
99 }
100
102 {
104 }
105
107 {
109 int exponent;
110 int64_t den;
113 if (fabs(d) > INT_MAX + 3LL)
115 frexp(d, &exponent);
116 exponent =
FFMAX(exponent-1, 0);
117 den = 1LL << (61 - exponent);
118 // (int64_t)rint() and llrint() do not work with gcc on ia64 and sparc64,
119 // see Ticket2713 for affected gcc/glibc versions
121 if ((!a.
num || !a.
den) && d && max>0 && max<INT_MAX)
123
125 }
126
128 {
129 /* n/d is q, a/b is the median between q1 and q2 */
130 int64_t
a = q1.
num * (int64_t)q2.
den + q2.
num * (int64_t)q1.
den;
131 int64_t
b = 2 * (int64_t)q1.
den * q2.
den;
132
133 /* rnd_up(a*d/b) > n => a*d/b > n */
135
136 /* rnd_down(a*d/b) < n => a*d/b < n */
138
140 }
141
143 {
144 int i, nearest_q_idx = 0;
145 for (i = 0; q_list[i].
den; i++)
146 if (
av_nearer_q(q, q_list[i], q_list[nearest_q_idx]) > 0)
147 nearest_q_idx = i;
148
149 return nearest_q_idx;
150 }
151
155 int sign = 0;
156
160 }
163 sign = 1;
164 }
165
166 if (!q.
num && !q.
den)
return 0xFFC00000;
167 if (!q.
num)
return 0;
168 if (!q.
den)
return 0x7F800000 | (q.
num & 0x80000000);
169
173
174 shift -= n >= (1<<24);
175 shift += n < (1<<23);
176
179
182
183 return sign<<31 | (150-
shift)<<23 | (n - (1<<23));
184 }
static int shift(int a, int b)
AVRational av_div_q(AVRational b, AVRational c)
Divide one rational by another.
static const uint8_t q1[256]
uint32_t av_q2intfloat(AVRational q)
Convert an AVRational to a IEEE 32-bit float expressed in fixed-point format.
AVRational av_sub_q(AVRational b, AVRational c)
Subtract one rational from another.
#define av_assert2(cond)
assert() equivalent, that does lie in speed critical code.
int av_reduce(int *dst_num, int *dst_den, int64_t num, int64_t den, int64_t max)
Reduce a fraction.
simple assert() macros that are a bit more flexible than ISO C assert().
int64_t av_gcd(int64_t a, int64_t b)
Compute the greatest common divisor of two integer operands.
#define av_assert1(cond)
assert() equivalent, that does not lie in speed critical code.
int64_t av_rescale(int64_t a, int64_t b, int64_t c)
Rescale a 64-bit integer with rounding to nearest.
#define FFABS(a)
Absolute value, Note, INT_MIN / INT64_MIN result in undefined behavior as they are not representable ...
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.
int av_find_nearest_q_idx(AVRational q, const AVRational *q_list)
Find the value in a list of rationals nearest a given reference rational.
Rational number (pair of numerator and denominator).
AVRational av_d2q(double d, int max)
Convert a double precision floating point number to a rational.
static int av_cmp_q(AVRational a, AVRational b)
Compare two rationals.
common internal and external API header
Utilties for rational number calculation.
AVRational av_add_q(AVRational b, AVRational c)
Add two rationals.
int av_nearer_q(AVRational q, AVRational q1, AVRational q2)
Find which of the two rationals is closer to another rational.
AVRational av_mul_q(AVRational b, AVRational c)
Multiply two rationals.