path: root/libavutil/rational.c (plain)
blob: 35ee08877f3497379d383b06a7c424a1c940d1cd

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
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	av_assert2(a1.num <= max && a1.den <= max);
73
74	*dst_num = sign ? -a1.num : a1.num;
75	*dst_den = a1.den;
76
77	return den == 0;
78	}
79
80	AVRational av_mul_q(AVRational b, AVRational c)
81	{
82	av_reduce(&b.num, &b.den,
83	b.num * (int64_t) c.num,
84	b.den * (int64_t) c.den, INT_MAX);
85	return b;
86	}
87
88	AVRational av_div_q(AVRational b, AVRational c)
89	{
90	return av_mul_q(b, (AVRational) { c.den, c.num });
91	}
92
93	AVRational av_add_q(AVRational b, AVRational c) {
94	av_reduce(&b.num, &b.den,
95	b.num * (int64_t) c.den +
96	c.num * (int64_t) b.den,
97	b.den * (int64_t) c.den, INT_MAX);
98	return b;
99	}
100
101	AVRational av_sub_q(AVRational b, AVRational c)
102	{
103	return av_add_q(b, (AVRational) { -c.num, c.den });
104	}
105
106	AVRational av_d2q(double d, int max)
107	{
108	AVRational a;
109	int exponent;
110	int64_t den;
111	if (isnan(d))
112	return (AVRational) { 0,0 };
113	if (fabs(d) > INT_MAX + 3LL)
114	return (AVRational) { d < 0 ? -1 : 1, 0 };
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
120	av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, max);
121	if ((!a.num || !a.den) && d && max>0 && max<INT_MAX)
122	av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, INT_MAX);
123
124	return a;
125	}
126
127	int av_nearer_q(AVRational q, AVRational q1, AVRational q2)
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 */
134	int64_t x_up = av_rescale_rnd(a, q.den, b, AV_ROUND_UP);
135
136	/* rnd_down(a*d/b) < n => a*d/b < n */
137	int64_t x_down = av_rescale_rnd(a, q.den, b, AV_ROUND_DOWN);
138
139	return ((x_up > q.num) - (x_down < q.num)) * av_cmp_q(q2, q1);
140	}
141
142	int av_find_nearest_q_idx(AVRational q, const AVRational* q_list)
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
152	uint32_t av_q2intfloat(AVRational q) {
153	int64_t n;
154	int shift;
155	int sign = 0;
156
157	if (q.den < 0) {
158	q.den *= -1;
159	q.num *= -1;
160	}
161	if (q.num < 0) {
162	q.num *= -1;
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
170	shift = 23 + av_log2(q.den) - av_log2(q.num);
171	if (shift >= 0) n = av_rescale(q.num, 1LL<<shift, q.den);
172	else n = av_rescale(q.num, 1, ((int64_t)q.den) << -shift);
173
174	shift -= n >= (1<<24);
175	shift += n < (1<<23);
176
177	if (shift >= 0) n = av_rescale(q.num, 1LL<<shift, q.den);
178	else n = av_rescale(q.num, 1, ((int64_t)q.den) << -shift);
179
180	av_assert1(n < (1<<24));
181	av_assert1(n >= (1<<23));
182
183	return sign<<31 | (150-shift)<<23 | (n - (1<<23));
184	}
185