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+/*
+ * 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    Rational to be tested
+ * @param q2    Rational 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 */