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/*
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* rational numbers
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* Copyright (c) 2003 Michael Niedermayer <michaelni@gmx.at>
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*
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* This file is part of FFmpeg.
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*
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* FFmpeg is free software; you can redistribute it and/or
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* modify it under the terms of the GNU Lesser General Public
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* License as published by the Free Software Foundation; either
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* version 2.1 of the License, or (at your option) any later version.
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*
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* FFmpeg is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public
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* License along with FFmpeg; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
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*/
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/**
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* @file
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* @ingroup lavu_math_rational
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* Utilties for rational number calculation.
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* @author Michael Niedermayer <michaelni@gmx.at>
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*/
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#ifndef AVUTIL_RATIONAL_H
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#define AVUTIL_RATIONAL_H
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#include <stdint.h>
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#include <limits.h>
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#include "attributes.h"
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/**
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* @defgroup lavu_math_rational AVRational
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* @ingroup lavu_math
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* Rational number calculation.
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*
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* While rational numbers can be expressed as floating-point numbers, the
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* conversion process is a lossy one, so are floating-point operations. On the
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* other hand, the nature of FFmpeg demands highly accurate calculation of
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* timestamps. This set of rational number utilities serves as a generic
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* interface for manipulating rational numbers as pairs of numerators and
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* denominators.
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*
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* Many of the functions that operate on AVRational's have the suffix `_q`, in
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* reference to the mathematical symbol "ℚ" (Q) which denotes the set of all
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* rational numbers.
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*
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* @{
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*/
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/**
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* Rational number (pair of numerator and denominator).
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*/
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typedef struct AVRational{
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int num; ///< Numerator
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int den; ///< Denominator
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} AVRational;
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/**
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* Create an AVRational.
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*
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* Useful for compilers that do not support compound literals.
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*
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* @note The return value is not reduced.
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* @see av_reduce()
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*/
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static inline AVRational av_make_q(int num, int den)
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{
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AVRational r = { num, den };
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return r;
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}
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/**
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* Compare two rationals.
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*
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* @param a First rational
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* @param b Second rational
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*
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* @return One of the following values:
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* - 0 if `a == b`
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* - 1 if `a > b`
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* - -1 if `a < b`
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* - `INT_MIN` if one of the values is of the form `0 / 0`
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*/
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static inline int av_cmp_q(AVRational a, AVRational b){
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const int64_t tmp= a.num * (int64_t)b.den - b.num * (int64_t)a.den;
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if(tmp) return (int)((tmp ^ a.den ^ b.den)>>63)|1;
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else if(b.den && a.den) return 0;
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else if(a.num && b.num) return (a.num>>31) - (b.num>>31);
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else return INT_MIN;
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}
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/**
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* Convert an AVRational to a `double`.
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* @param a AVRational to convert
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* @return `a` in floating-point form
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* @see av_d2q()
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*/
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static inline double av_q2d(AVRational a){
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return a.num / (double) a.den;
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}
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/**
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* Reduce a fraction.
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*
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* This is useful for framerate calculations.
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*
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* @param[out] dst_num Destination numerator
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* @param[out] dst_den Destination denominator
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* @param[in] num Source numerator
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* @param[in] den Source denominator
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* @param[in] max Maximum allowed values for `dst_num` & `dst_den`
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* @return 1 if the operation is exact, 0 otherwise
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*/
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int av_reduce(int *dst_num, int *dst_den, int64_t num, int64_t den, int64_t max);
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/**
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* Multiply two rationals.
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* @param b First rational
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* @param c Second rational
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* @return b*c
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*/
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AVRational av_mul_q(AVRational b, AVRational c) av_const;
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/**
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* Divide one rational by another.
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* @param b First rational
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* @param c Second rational
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* @return b/c
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*/
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AVRational av_div_q(AVRational b, AVRational c) av_const;
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/**
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* Add two rationals.
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* @param b First rational
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* @param c Second rational
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* @return b+c
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*/
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AVRational av_add_q(AVRational b, AVRational c) av_const;
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/**
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* Subtract one rational from another.
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* @param b First rational
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* @param c Second rational
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* @return b-c
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*/
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AVRational av_sub_q(AVRational b, AVRational c) av_const;
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/**
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* Invert a rational.
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* @param q value
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* @return 1 / q
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*/
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static av_always_inline AVRational av_inv_q(AVRational q)
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{
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AVRational r = { q.den, q.num };
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return r;
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}
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/**
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* Convert a double precision floating point number to a rational.
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*
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* In case of infinity, the returned value is expressed as `{1, 0}` or
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* `{-1, 0}` depending on the sign.
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*
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* In general rational numbers with |num| <= 1<<26 && |den| <= 1<<26
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* can be recovered exactly from their double representation.
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* (no exceptions were found within 1B random ones)
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*
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* @param d `double` to convert
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* @param max Maximum allowed numerator and denominator
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* @return `d` in AVRational form
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* @see av_q2d()
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*/
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AVRational av_d2q(double d, int max) av_const;
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/**
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* Find which of the two rationals is closer to another rational.
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*
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* @param q Rational to be compared against
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* @param q1 Rational to be tested
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* @param q2 Rational to be tested
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* @return One of the following values:
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* - 1 if `q1` is nearer to `q` than `q2`
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* - -1 if `q2` is nearer to `q` than `q1`
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* - 0 if they have the same distance
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*/
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int av_nearer_q(AVRational q, AVRational q1, AVRational q2);
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/**
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* Find the value in a list of rationals nearest a given reference rational.
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*
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* @param q Reference rational
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* @param q_list Array of rationals terminated by `{0, 0}`
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* @return Index of the nearest value found in the array
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*/
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int av_find_nearest_q_idx(AVRational q, const AVRational* q_list);
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/**
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* Convert an AVRational to a IEEE 32-bit `float` expressed in fixed-point
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* format.
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*
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* @param q Rational to be converted
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* @return Equivalent floating-point value, expressed as an unsigned 32-bit
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* integer.
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* @note The returned value is platform-indepedant.
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*/
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uint32_t av_q2intfloat(AVRational q);
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/**
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* Return the best rational so that a and b are multiple of it.
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* If the resulting denominator is larger than max_den, return def.
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*/
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AVRational av_gcd_q(AVRational a, AVRational b, int max_den, AVRational def);
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/**
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* @}
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*/
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#endif /* AVUTIL_RATIONAL_H */
```