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 /* * rational numbers * Copyright (c) 2003 Michael Niedermayer * * 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 */ #ifndef AVUTIL_RATIONAL_H #define AVUTIL_RATIONAL_H #include #include #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 */