/* | |

* rational numbers | |

* Copyright (c) 2003 Michael Niedermayer <michaelni@gmx.at> | |

* | |

* This file is part of FFmpeg. | |

* | |

* FFmpeg is free software; you can redistribute it and/or | |

* modify it under the terms of the GNU Lesser General Public | |

* License as published by the Free Software Foundation; either | |

* version 2.1 of the License, or (at your option) any later version. | |

* | |

* FFmpeg is distributed in the hope that it will be useful, | |

* but WITHOUT ANY WARRANTY; without even the implied warranty of | |

* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |

* Lesser General Public License for more details. | |

* | |

* You should have received a copy of the GNU Lesser General Public | |

* License along with FFmpeg; if not, write to the Free Software | |

* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA | |

*/ | |

/** | |

* @file | |

* @ingroup lavu_math_rational | |

* Utilties for rational number calculation. | |

* @author Michael Niedermayer <michaelni@gmx.at> | |

*/ | |

#ifndef AVUTIL_RATIONAL_H | |

#define AVUTIL_RATIONAL_H | |

#include <stdint.h> | |

#include <limits.h> | |

#include "attributes.h" | |

/** | |

* @defgroup lavu_math_rational AVRational | |

* @ingroup lavu_math | |

* Rational number calculation. | |

* | |

* While rational numbers can be expressed as floating-point numbers, the | |

* conversion process is a lossy one, so are floating-point operations. On the | |

* other hand, the nature of FFmpeg demands highly accurate calculation of | |

* timestamps. This set of rational number utilities serves as a generic | |

* interface for manipulating rational numbers as pairs of numerators and | |

* denominators. | |

* | |

* Many of the functions that operate on AVRational's have the suffix `_q`, in | |

* reference to the mathematical symbol "ℚ" (Q) which denotes the set of all | |

* rational numbers. | |

* | |

* @{ | |

*/ | |

/** | |

* Rational number (pair of numerator and denominator). | |

*/ | |

typedef struct AVRational{ | |

int num; ///< Numerator | |

int den; ///< Denominator | |

} AVRational; | |

/** | |

* Create an AVRational. | |

* | |

* Useful for compilers that do not support compound literals. | |

* | |

* @note The return value is not reduced. | |

* @see av_reduce() | |

*/ | |

static inline AVRational av_make_q(int num, int den) | |

{ | |

AVRational r = { num, den }; | |

return r; | |

} | |

/** | |

* Compare two rationals. | |

* | |

* @param a First rational | |

* @param b Second rational | |

* | |

* @return One of the following values: | |

* - 0 if `a == b` | |

* - 1 if `a > b` | |

* - -1 if `a < b` | |

* - `INT_MIN` if one of the values is of the form `0 / 0` | |

*/ | |

static inline int av_cmp_q(AVRational a, AVRational b){ | |

const int64_t tmp= a.num * (int64_t)b.den - b.num * (int64_t)a.den; | |

if(tmp) return (int)((tmp ^ a.den ^ b.den)>>63)|1; | |

else if(b.den && a.den) return 0; | |

else if(a.num && b.num) return (a.num>>31) - (b.num>>31); | |

else return INT_MIN; | |

} | |

/** | |

* Convert an AVRational to a `double`. | |

* @param a AVRational to convert | |

* @return `a` in floating-point form | |

* @see av_d2q() | |

*/ | |

static inline double av_q2d(AVRational a){ | |

return a.num / (double) a.den; | |

} | |

/** | |

* Reduce a fraction. | |

* | |

* This is useful for framerate calculations. | |

* | |

* @param[out] dst_num Destination numerator | |

* @param[out] dst_den Destination denominator | |

* @param[in] num Source numerator | |

* @param[in] den Source denominator | |

* @param[in] max Maximum allowed values for `dst_num` & `dst_den` | |

* @return 1 if the operation is exact, 0 otherwise | |

*/ | |

int av_reduce(int *dst_num, int *dst_den, int64_t num, int64_t den, int64_t max); | |

/** | |

* Multiply two rationals. | |

* @param b First rational | |

* @param c Second rational | |

* @return b*c | |

*/ | |

AVRational av_mul_q(AVRational b, AVRational c) av_const; | |

/** | |

* Divide one rational by another. | |

* @param b First rational | |

* @param c Second rational | |

* @return b/c | |

*/ | |

AVRational av_div_q(AVRational b, AVRational c) av_const; | |

/** | |

* Add two rationals. | |

* @param b First rational | |

* @param c Second rational | |

* @return b+c | |

*/ | |

AVRational av_add_q(AVRational b, AVRational c) av_const; | |

/** | |

* Subtract one rational from another. | |

* @param b First rational | |

* @param c Second rational | |

* @return b-c | |

*/ | |

AVRational av_sub_q(AVRational b, AVRational c) av_const; | |

/** | |

* Invert a rational. | |

* @param q value | |

* @return 1 / q | |

*/ | |

static av_always_inline AVRational av_inv_q(AVRational q) | |

{ | |

AVRational r = { q.den, q.num }; | |

return r; | |

} | |

/** | |

* Convert a double precision floating point number to a rational. | |

* | |

* In case of infinity, the returned value is expressed as `{1, 0}` or | |

* `{-1, 0}` depending on the sign. | |

* | |

* @param d `double` to convert | |

* @param max Maximum allowed numerator and denominator | |

* @return `d` in AVRational form | |

* @see av_q2d() | |

*/ | |

AVRational av_d2q(double d, int max) av_const; | |

/** | |

* Find which of the two rationals is closer to another rational. | |

* | |

* @param q Rational to be compared against | |

* @param q1,q2 Rationals to be tested | |

* @return One of the following values: | |

* - 1 if `q1` is nearer to `q` than `q2` | |

* - -1 if `q2` is nearer to `q` than `q1` | |

* - 0 if they have the same distance | |

*/ | |

int av_nearer_q(AVRational q, AVRational q1, AVRational q2); | |

/** | |

* Find the value in a list of rationals nearest a given reference rational. | |

* | |

* @param q Reference rational | |

* @param q_list Array of rationals terminated by `{0, 0}` | |

* @return Index of the nearest value found in the array | |

*/ | |

int av_find_nearest_q_idx(AVRational q, const AVRational* q_list); | |

/** | |

* Convert an AVRational to a IEEE 32-bit `float` expressed in fixed-point | |

* format. | |

* | |

* @param q Rational to be converted | |

* @return Equivalent floating-point value, expressed as an unsigned 32-bit | |

* integer. | |

* @note The returned value is platform-indepedant. | |

*/ | |

uint32_t av_q2intfloat(AVRational q); | |

/** | |

* Return the best rational so that a and b are multiple of it. | |

* If the resulting denominator is larger than max_den, return def. | |

*/ | |

AVRational av_gcd_q(AVRational a, AVRational b, int max_den, AVRational def); | |

/** | |

* @} | |

*/ | |

#endif /* AVUTIL_RATIONAL_H */ |