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 * @ingroup lavu_math_rational
25 * Utilties for rational number calculation.
26 * @author Michael Niedermayer <michaelni@gmx.at>
27 */
28
29#ifndef AVUTIL_RATIONAL_H
30#define AVUTIL_RATIONAL_H
31
32#include <stdint.h>
33#include <limits.h>
34#include "attributes.h"
35
36/**
37 * @defgroup lavu_math_rational AVRational
38 * @ingroup lavu_math
39 * Rational number calculation.
40 *
41 * While rational numbers can be expressed as floating-point numbers, the
42 * conversion process is a lossy one, so are floating-point operations. On the
43 * other hand, the nature of FFmpeg demands highly accurate calculation of
44 * timestamps. This set of rational number utilities serves as a generic
45 * interface for manipulating rational numbers as pairs of numerators and
46 * denominators.
47 *
48 * Many of the functions that operate on AVRational's have the suffix `_q`, in
49 * reference to the mathematical symbol "ℚ" (Q) which denotes the set of all
50 * rational numbers.
51 *
52 * @{
53 */
54
55/**
56 * Rational number (pair of numerator and denominator).
57 */
58typedef struct AVRational{
59 int num; ///< Numerator
60 int den; ///< Denominator
61} AVRational;
62
63/**
64 * Create an AVRational.
65 *
66 * Useful for compilers that do not support compound literals.
67 *
68 * @note The return value is not reduced.
69 * @see av_reduce()
70 */
71static inline AVRational av_make_q(int num, int den)
72{
73 AVRational r = { .num: num, .den: den };
74 return r;
75}
76
77/**
78 * Compare two rationals.
79 *
80 * @param a First rational
81 * @param b Second rational
82 *
83 * @return One of the following values:
84 * - 0 if `a == b`
85 * - 1 if `a > b`
86 * - -1 if `a < b`
87 * - `INT_MIN` if one of the values is of the form `0 / 0`
88 */
89static inline int av_cmp_q(AVRational a, AVRational b){
90 const int64_t tmp= a.num * (int64_t)b.den - b.num * (int64_t)a.den;
91
92 if(tmp) return (int)((tmp ^ a.den ^ b.den)>>63)|1;
93 else if(b.den && a.den) return 0;
94 else if(a.num && b.num) return (a.num>>31) - (b.num>>31);
95 else return INT_MIN;
96}
97
98/**
99 * Convert an AVRational to a `double`.
100 * @param a AVRational to convert
101 * @return `a` in floating-point form
102 * @see av_d2q()
103 */
104static inline double av_q2d(AVRational a){
105 return a.num / (double) a.den;
106}
107
108/**
109 * Reduce a fraction.
110 *
111 * This is useful for framerate calculations.
112 *
113 * @param[out] dst_num Destination numerator
114 * @param[out] dst_den Destination denominator
115 * @param[in] num Source numerator
116 * @param[in] den Source denominator
117 * @param[in] max Maximum allowed values for `dst_num` & `dst_den`
118 * @return 1 if the operation is exact, 0 otherwise
119 */
120int av_reduce(int *dst_num, int *dst_den, int64_t num, int64_t den, int64_t max);
121
122/**
123 * Multiply two rationals.
124 * @param b First rational
125 * @param c Second rational
126 * @return b*c
127 */
128AVRational av_mul_q(AVRational b, AVRational c) av_const;
129
130/**
131 * Divide one rational by another.
132 * @param b First rational
133 * @param c Second rational
134 * @return b/c
135 */
136AVRational av_div_q(AVRational b, AVRational c) av_const;
137
138/**
139 * Add two rationals.
140 * @param b First rational
141 * @param c Second rational
142 * @return b+c
143 */
144AVRational av_add_q(AVRational b, AVRational c) av_const;
145
146/**
147 * Subtract one rational from another.
148 * @param b First rational
149 * @param c Second rational
150 * @return b-c
151 */
152AVRational av_sub_q(AVRational b, AVRational c) av_const;
153
154/**
155 * Invert a rational.
156 * @param q value
157 * @return 1 / q
158 */
159static av_always_inline AVRational av_inv_q(AVRational q)
160{
161 AVRational r = { .num: q.den, .den: q.num };
162 return r;
163}
164
165/**
166 * Convert a double precision floating point number to a rational.
167 *
168 * In case of infinity, the returned value is expressed as `{1, 0}` or
169 * `{-1, 0}` depending on the sign.
170 *
171 * In general rational numbers with |num| <= 1<<26 && |den| <= 1<<26
172 * can be recovered exactly from their double representation.
173 * (no exceptions were found within 1B random ones)
174 *
175 * @param d `double` to convert
176 * @param max Maximum allowed numerator and denominator
177 * @return `d` in AVRational form
178 * @see av_q2d()
179 */
180AVRational av_d2q(double d, int max) av_const;
181
182/**
183 * Find which of the two rationals is closer to another rational.
184 *
185 * @param q Rational to be compared against
186 * @param q1 Rational to be tested
187 * @param q2 Rational to be tested
188 * @return One of the following values:
189 * - 1 if `q1` is nearer to `q` than `q2`
190 * - -1 if `q2` is nearer to `q` than `q1`
191 * - 0 if they have the same distance
192 */
193int av_nearer_q(AVRational q, AVRational q1, AVRational q2);
194
195/**
196 * Find the value in a list of rationals nearest a given reference rational.
197 *
198 * @param q Reference rational
199 * @param q_list Array of rationals terminated by `{0, 0}`
200 * @return Index of the nearest value found in the array
201 */
202int av_find_nearest_q_idx(AVRational q, const AVRational* q_list);
203
204/**
205 * Convert an AVRational to a IEEE 32-bit `float` expressed in fixed-point
206 * format.
207 *
208 * @param q Rational to be converted
209 * @return Equivalent floating-point value, expressed as an unsigned 32-bit
210 * integer.
211 * @note The returned value is platform-indepedant.
212 */
213uint32_t av_q2intfloat(AVRational q);
214
215/**
216 * Return the best rational so that a and b are multiple of it.
217 * If the resulting denominator is larger than max_den, return def.
218 */
219AVRational av_gcd_q(AVRational a, AVRational b, int max_den, AVRational def);
220
221/**
222 * @}
223 */
224
225#endif /* AVUTIL_RATIONAL_H */
226