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+/*
+ * copyright (c) 2005-2012 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
+ * @addtogroup lavu_math
+ * Mathematical utilities for working with timestamp and time base.
+ */
+
+#ifndef AVUTIL_MATHEMATICS_H
+#define AVUTIL_MATHEMATICS_H
+
+#include <stdint.h>
+#include <math.h>
+#include "attributes.h"
+#include "rational.h"
+#include "intfloat.h"
+
+#ifndef M_E
+#define M_E 2.7182818284590452354 /* e */
+#endif
+#ifndef M_LN2
+#define M_LN2 0.69314718055994530942 /* log_e 2 */
+#endif
+#ifndef M_LN10
+#define M_LN10 2.30258509299404568402 /* log_e 10 */
+#endif
+#ifndef M_LOG2_10
+#define M_LOG2_10 3.32192809488736234787 /* log_2 10 */
+#endif
+#ifndef M_PHI
+#define M_PHI 1.61803398874989484820 /* phi / golden ratio */
+#endif
+#ifndef M_PI
+#define M_PI 3.14159265358979323846 /* pi */
+#endif
+#ifndef M_PI_2
+#define M_PI_2 1.57079632679489661923 /* pi/2 */
+#endif
+#ifndef M_SQRT1_2
+#define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
+#endif
+#ifndef M_SQRT2
+#define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
+#endif
+#ifndef NAN
+#define NAN av_int2float(0x7fc00000)
+#endif
+#ifndef INFINITY
+#define INFINITY av_int2float(0x7f800000)
+#endif
+
+/**
+ * @addtogroup lavu_math
+ *
+ * @{
+ */
+
+/**
+ * Rounding methods.
+ */
+enum AVRounding {
+ AV_ROUND_ZERO = 0, ///< Round toward zero.
+ AV_ROUND_INF = 1, ///< Round away from zero.
+ AV_ROUND_DOWN = 2, ///< Round toward -infinity.
+ AV_ROUND_UP = 3, ///< Round toward +infinity.
+ AV_ROUND_NEAR_INF = 5, ///< Round to nearest and halfway cases away from zero.
+ /**
+ * Flag telling rescaling functions to pass `INT64_MIN`/`MAX` through
+ * unchanged, avoiding special cases for #AV_NOPTS_VALUE.
+ *
+ * Unlike other values of the enumeration AVRounding, this value is a
+ * bitmask that must be used in conjunction with another value of the
+ * enumeration through a bitwise OR, in order to set behavior for normal
+ * cases.
+ *
+ * @code{.c}
+ * av_rescale_rnd(3, 1, 2, AV_ROUND_UP | AV_ROUND_PASS_MINMAX);
+ * // Rescaling 3:
+ * // Calculating 3 * 1 / 2
+ * // 3 / 2 is rounded up to 2
+ * // => 2
+ *
+ * av_rescale_rnd(AV_NOPTS_VALUE, 1, 2, AV_ROUND_UP | AV_ROUND_PASS_MINMAX);
+ * // Rescaling AV_NOPTS_VALUE:
+ * // AV_NOPTS_VALUE == INT64_MIN
+ * // AV_NOPTS_VALUE is passed through
+ * // => AV_NOPTS_VALUE
+ * @endcode
+ */
+ AV_ROUND_PASS_MINMAX = 8192,
+};
+
+/**
+ * Compute the greatest common divisor of two integer operands.
+ *
+ * @param a Operand
+ * @param b Operand
+ * @return GCD of a and b up to sign; if a >= 0 and b >= 0, return value is >= 0;
+ * if a == 0 and b == 0, returns 0.
+ */
+int64_t av_const av_gcd(int64_t a, int64_t b);
+
+/**
+ * Rescale a 64-bit integer with rounding to nearest.
+ *
+ * The operation is mathematically equivalent to `a * b / c`, but writing that
+ * directly can overflow.
+ *
+ * This function is equivalent to av_rescale_rnd() with #AV_ROUND_NEAR_INF.
+ *
+ * @see av_rescale_rnd(), av_rescale_q(), av_rescale_q_rnd()
+ */
+int64_t av_rescale(int64_t a, int64_t b, int64_t c) av_const;
+
+/**
+ * Rescale a 64-bit integer with specified rounding.
+ *
+ * The operation is mathematically equivalent to `a * b / c`, but writing that
+ * directly can overflow, and does not support different rounding methods.
+ * If the result is not representable then INT64_MIN is returned.
+ *
+ * @see av_rescale(), av_rescale_q(), av_rescale_q_rnd()
+ */
+int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd) av_const;
+
+/**
+ * Rescale a 64-bit integer by 2 rational numbers.
+ *
+ * The operation is mathematically equivalent to `a * bq / cq`.
+ *
+ * This function is equivalent to av_rescale_q_rnd() with #AV_ROUND_NEAR_INF.
+ *
+ * @see av_rescale(), av_rescale_rnd(), av_rescale_q_rnd()
+ */
+int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq) av_const;
+
+/**
+ * Rescale a 64-bit integer by 2 rational numbers with specified rounding.
+ *
+ * The operation is mathematically equivalent to `a * bq / cq`.
+ *
+ * @see av_rescale(), av_rescale_rnd(), av_rescale_q()
+ */
+int64_t av_rescale_q_rnd(int64_t a, AVRational bq, AVRational cq,
+ enum AVRounding rnd) av_const;
+
+/**
+ * Compare two timestamps each in its own time base.
+ *
+ * @return One of the following values:
+ * - -1 if `ts_a` is before `ts_b`
+ * - 1 if `ts_a` is after `ts_b`
+ * - 0 if they represent the same position
+ *
+ * @warning
+ * The result of the function is undefined if one of the timestamps is outside
+ * the `int64_t` range when represented in the other's timebase.
+ */
+int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b);
+
+/**
+ * Compare the remainders of two integer operands divided by a common divisor.
+ *
+ * In other words, compare the least significant `log2(mod)` bits of integers
+ * `a` and `b`.
+ *
+ * @code{.c}
+ * av_compare_mod(0x11, 0x02, 0x10) < 0 // since 0x11 % 0x10 (0x1) < 0x02 % 0x10 (0x2)
+ * av_compare_mod(0x11, 0x02, 0x20) > 0 // since 0x11 % 0x20 (0x11) > 0x02 % 0x20 (0x02)
+ * @endcode
+ *
+ * @param a Operand
+ * @param b Operand
+ * @param mod Divisor; must be a power of 2
+ * @return
+ * - a negative value if `a % mod < b % mod`
+ * - a positive value if `a % mod > b % mod`
+ * - zero if `a % mod == b % mod`
+ */
+int64_t av_compare_mod(uint64_t a, uint64_t b, uint64_t mod);
+
+/**
+ * Rescale a timestamp while preserving known durations.
+ *
+ * This function is designed to be called per audio packet to scale the input
+ * timestamp to a different time base. Compared to a simple av_rescale_q()
+ * call, this function is robust against possible inconsistent frame durations.
+ *
+ * The `last` parameter is a state variable that must be preserved for all
+ * subsequent calls for the same stream. For the first call, `*last` should be
+ * initialized to #AV_NOPTS_VALUE.
+ *
+ * @param[in] in_tb Input time base
+ * @param[in] in_ts Input timestamp
+ * @param[in] fs_tb Duration time base; typically this is finer-grained
+ * (greater) than `in_tb` and `out_tb`
+ * @param[in] duration Duration till the next call to this function (i.e.
+ * duration of the current packet/frame)
+ * @param[in,out] last Pointer to a timestamp expressed in terms of
+ * `fs_tb`, acting as a state variable
+ * @param[in] out_tb Output timebase
+ * @return Timestamp expressed in terms of `out_tb`
+ *
+ * @note In the context of this function, "duration" is in term of samples, not
+ * seconds.
+ */
+int64_t av_rescale_delta(AVRational in_tb, int64_t in_ts, AVRational fs_tb, int duration, int64_t *last, AVRational out_tb);
+
+/**
+ * Add a value to a timestamp.
+ *
+ * This function guarantees that when the same value is repeatly added that
+ * no accumulation of rounding errors occurs.
+ *
+ * @param[in] ts Input timestamp
+ * @param[in] ts_tb Input timestamp time base
+ * @param[in] inc Value to be added
+ * @param[in] inc_tb Time base of `inc`
+ */
+int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, int64_t inc);
+
+
+/**
+ * @}
+ */
+
+#endif /* AVUTIL_MATHEMATICS_H */