libavutil/rational.h

   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  */
 128 AVRational 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  */
 136 AVRational 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  */
 144 AVRational 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  */
 152 AVRational av_sub_q(AVRational b, AVRational c) av_const;
 153
 154 /**
 155  * Invert a rational.
 156  * @param q value
 157  * @return 1 / q
 158  */
 159 static av_always_inline AVRational av_inv_q(AVRational q)
 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  * 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  */
 180 AVRational 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  */
 193 int 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  */
 202 int 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  */
 213 uint32_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  */
 219 AVRational av_gcd_q(AVRational a, AVRational b, int max_den, AVRational def);
 220
 221 /**
 222  * @}
 223  */
 224
 225 #endif /* AVUTIL_RATIONAL_H */