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rational.h
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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  */
58 typedef 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  */
71 static inline AVRational av_make_q(int num, int den)
72 {
73  AVRational r = { num, 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  */
89 static 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  */
104 static 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  */
120 int 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  */
129 
130 /**
131  * Divide one rational by another.
132  * @param b First rational
133  * @param c Second rational
134  * @return b/c
135  */
137 
138 /**
139  * Add two rationals.
140  * @param b First rational
141  * @param c Second rational
142  * @return b+c
143  */
145 
146 /**
147  * Subtract one rational from another.
148  * @param b First rational
149  * @param c Second rational
150  * @return b-c
151  */
153 
154 /**
155  * Invert a rational.
156  * @param q value
157  * @return 1 / q
158  */
160 {
161  AVRational r = { q.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  * @param d `double` to convert
172  * @param max Maximum allowed numerator and denominator
173  * @return `d` in AVRational form
174  * @see av_q2d()
175  */
176 AVRational av_d2q(double d, int max) av_const;
177 
178 /**
179  * Find which of the two rationals is closer to another rational.
180  *
181  * @param q Rational to be compared against
182  * @param q1,q2 Rationals to be tested
183  * @return One of the following values:
184  * - 1 if `q1` is nearer to `q` than `q2`
185  * - -1 if `q2` is nearer to `q` than `q1`
186  * - 0 if they have the same distance
187  */
189 
190 /**
191  * Find the value in a list of rationals nearest a given reference rational.
192  *
193  * @param q Reference rational
194  * @param q_list Array of rationals terminated by `{0, 0}`
195  * @return Index of the nearest value found in the array
196  */
197 int av_find_nearest_q_idx(AVRational q, const AVRational* q_list);
198 
199 /**
200  * Convert an AVRational to a IEEE 32-bit `float` expressed in fixed-point
201  * format.
202  *
203  * @param q Rational to be converted
204  * @return Equivalent floating-point value, expressed as an unsigned 32-bit
205  * integer.
206  * @note The returned value is platform-indepedant.
207  */
208 uint32_t av_q2intfloat(AVRational q);
209 
210 /**
211  * @}
212  */
213 
214 #endif /* AVUTIL_RATIONAL_H */
#define av_const
Definition: attributes.h:76
AVRational av_div_q(AVRational b, AVRational c) av_const
Divide one rational by another.
Definition: rational.c:88
int num
Numerator.
Definition: rational.h:59
const char * b
Definition: vf_curves.c:113
static const uint8_t q1[256]
Definition: twofish.c:96
uint32_t av_q2intfloat(AVRational q)
Convert an AVRational to a IEEE 32-bit float expressed in fixed-point format.
Definition: rational.c:152
Macro definitions for various function/variable attributes.
AVRational av_sub_q(AVRational b, AVRational c) av_const
Subtract one rational from another.
Definition: rational.c:101
static double av_q2d(AVRational a)
Convert an AVRational to a double.
Definition: rational.h:104
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
const char * r
Definition: vf_curves.c:111
static AVRational av_make_q(int num, int den)
Create an AVRational.
Definition: rational.h:71
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.
Definition: rational.c:142
Rational number (pair of numerator and denominator).
Definition: rational.h:58
AVRational av_d2q(double d, int max) av_const
Convert a double precision floating point number to a rational.
Definition: rational.c:106
static av_always_inline AVRational av_inv_q(AVRational q)
Invert a rational.
Definition: rational.h:159
static int av_cmp_q(AVRational a, AVRational b)
Compare two rationals.
Definition: rational.h:89
AVRational av_add_q(AVRational b, AVRational c) av_const
Add two rationals.
Definition: rational.c:93
int av_nearer_q(AVRational q, AVRational q1, AVRational q2)
Find which of the two rationals is closer to another rational.
Definition: rational.c:127
int den
Denominator.
Definition: rational.h:60
static uint8_t tmp[8]
Definition: des.c:38
static AVCodec * c
AVRational av_mul_q(AVRational b, AVRational c) av_const
Multiply two rationals.
Definition: rational.c:80
#define av_always_inline
Definition: attributes.h:39