75918016ab
0th order modified bessel function of the first kind are used in multiple places, lets avoid having 3+ different implementations I picked this one as its accurate and quite fast, it can be replaced if a better one is found Signed-off-by: Michael Niedermayer <michael@niedermayer.cc>
301 lines
9.3 KiB
C
301 lines
9.3 KiB
C
/*
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* copyright (c) 2005-2012 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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* @addtogroup lavu_math
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* Mathematical utilities for working with timestamp and time base.
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*/
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#ifndef AVUTIL_MATHEMATICS_H
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#define AVUTIL_MATHEMATICS_H
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#include <stdint.h>
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#include <math.h>
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#include "attributes.h"
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#include "rational.h"
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#include "intfloat.h"
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#ifndef M_E
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#define M_E 2.7182818284590452354 /* e */
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#endif
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#ifndef M_Ef
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#define M_Ef 2.7182818284590452354f /* e */
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#endif
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#ifndef M_LN2
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#define M_LN2 0.69314718055994530942 /* log_e 2 */
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#endif
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#ifndef M_LN2f
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#define M_LN2f 0.69314718055994530942f /* log_e 2 */
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#endif
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#ifndef M_LN10
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#define M_LN10 2.30258509299404568402 /* log_e 10 */
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#endif
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#ifndef M_LN10f
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#define M_LN10f 2.30258509299404568402f /* log_e 10 */
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#endif
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#ifndef M_LOG2_10
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#define M_LOG2_10 3.32192809488736234787 /* log_2 10 */
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#endif
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#ifndef M_LOG2_10f
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#define M_LOG2_10f 3.32192809488736234787f /* log_2 10 */
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#endif
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#ifndef M_PHI
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#define M_PHI 1.61803398874989484820 /* phi / golden ratio */
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#endif
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#ifndef M_PHIf
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#define M_PHIf 1.61803398874989484820f /* phi / golden ratio */
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#endif
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#ifndef M_PI
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#define M_PI 3.14159265358979323846 /* pi */
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#endif
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#ifndef M_PIf
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#define M_PIf 3.14159265358979323846f /* pi */
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#endif
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#ifndef M_PI_2
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#define M_PI_2 1.57079632679489661923 /* pi/2 */
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#endif
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#ifndef M_PI_2f
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#define M_PI_2f 1.57079632679489661923f /* pi/2 */
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#endif
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#ifndef M_PI_4
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#define M_PI_4 0.78539816339744830962 /* pi/4 */
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#endif
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#ifndef M_PI_4f
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#define M_PI_4f 0.78539816339744830962f /* pi/4 */
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#endif
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#ifndef M_1_PI
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#define M_1_PI 0.31830988618379067154 /* 1/pi */
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#endif
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#ifndef M_1_PIf
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#define M_1_PIf 0.31830988618379067154f /* 1/pi */
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#endif
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#ifndef M_2_PI
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#define M_2_PI 0.63661977236758134308 /* 2/pi */
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#endif
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#ifndef M_2_PIf
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#define M_2_PIf 0.63661977236758134308f /* 2/pi */
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#endif
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#ifndef M_2_SQRTPI
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#define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */
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#endif
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#ifndef M_2_SQRTPIf
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#define M_2_SQRTPIf 1.12837916709551257390f /* 2/sqrt(pi) */
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#endif
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#ifndef M_SQRT1_2
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#define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
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#endif
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#ifndef M_SQRT1_2f
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#define M_SQRT1_2f 0.70710678118654752440f /* 1/sqrt(2) */
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#endif
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#ifndef M_SQRT2
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#define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
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#endif
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#ifndef M_SQRT2f
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#define M_SQRT2f 1.41421356237309504880f /* sqrt(2) */
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#endif
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#ifndef NAN
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#define NAN av_int2float(0x7fc00000)
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#endif
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#ifndef INFINITY
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#define INFINITY av_int2float(0x7f800000)
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#endif
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/**
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* @addtogroup lavu_math
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*
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* @{
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*/
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/**
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* Rounding methods.
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*/
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enum AVRounding {
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AV_ROUND_ZERO = 0, ///< Round toward zero.
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AV_ROUND_INF = 1, ///< Round away from zero.
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AV_ROUND_DOWN = 2, ///< Round toward -infinity.
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AV_ROUND_UP = 3, ///< Round toward +infinity.
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AV_ROUND_NEAR_INF = 5, ///< Round to nearest and halfway cases away from zero.
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/**
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* Flag telling rescaling functions to pass `INT64_MIN`/`MAX` through
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* unchanged, avoiding special cases for #AV_NOPTS_VALUE.
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*
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* Unlike other values of the enumeration AVRounding, this value is a
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* bitmask that must be used in conjunction with another value of the
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* enumeration through a bitwise OR, in order to set behavior for normal
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* cases.
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*
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* @code{.c}
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* av_rescale_rnd(3, 1, 2, AV_ROUND_UP | AV_ROUND_PASS_MINMAX);
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* // Rescaling 3:
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* // Calculating 3 * 1 / 2
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* // 3 / 2 is rounded up to 2
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* // => 2
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*
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* av_rescale_rnd(AV_NOPTS_VALUE, 1, 2, AV_ROUND_UP | AV_ROUND_PASS_MINMAX);
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* // Rescaling AV_NOPTS_VALUE:
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* // AV_NOPTS_VALUE == INT64_MIN
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* // AV_NOPTS_VALUE is passed through
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* // => AV_NOPTS_VALUE
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* @endcode
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*/
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AV_ROUND_PASS_MINMAX = 8192,
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};
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/**
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* Compute the greatest common divisor of two integer operands.
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*
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* @param a Operand
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* @param b Operand
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* @return GCD of a and b up to sign; if a >= 0 and b >= 0, return value is >= 0;
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* if a == 0 and b == 0, returns 0.
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*/
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int64_t av_const av_gcd(int64_t a, int64_t b);
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/**
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* Rescale a 64-bit integer with rounding to nearest.
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*
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* The operation is mathematically equivalent to `a * b / c`, but writing that
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* directly can overflow.
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*
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* This function is equivalent to av_rescale_rnd() with #AV_ROUND_NEAR_INF.
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*
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* @see av_rescale_rnd(), av_rescale_q(), av_rescale_q_rnd()
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*/
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int64_t av_rescale(int64_t a, int64_t b, int64_t c) av_const;
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/**
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* Rescale a 64-bit integer with specified rounding.
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*
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* The operation is mathematically equivalent to `a * b / c`, but writing that
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* directly can overflow, and does not support different rounding methods.
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* If the result is not representable then INT64_MIN is returned.
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*
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* @see av_rescale(), av_rescale_q(), av_rescale_q_rnd()
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*/
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int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd) av_const;
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/**
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* Rescale a 64-bit integer by 2 rational numbers.
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*
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* The operation is mathematically equivalent to `a * bq / cq`.
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*
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* This function is equivalent to av_rescale_q_rnd() with #AV_ROUND_NEAR_INF.
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*
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* @see av_rescale(), av_rescale_rnd(), av_rescale_q_rnd()
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*/
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int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq) av_const;
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/**
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* Rescale a 64-bit integer by 2 rational numbers with specified rounding.
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*
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* The operation is mathematically equivalent to `a * bq / cq`.
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*
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* @see av_rescale(), av_rescale_rnd(), av_rescale_q()
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*/
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int64_t av_rescale_q_rnd(int64_t a, AVRational bq, AVRational cq,
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enum AVRounding rnd) av_const;
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/**
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* Compare two timestamps each in its own time base.
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*
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* @return One of the following values:
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* - -1 if `ts_a` is before `ts_b`
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* - 1 if `ts_a` is after `ts_b`
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* - 0 if they represent the same position
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*
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* @warning
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* The result of the function is undefined if one of the timestamps is outside
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* the `int64_t` range when represented in the other's timebase.
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*/
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int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b);
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/**
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* Compare the remainders of two integer operands divided by a common divisor.
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*
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* In other words, compare the least significant `log2(mod)` bits of integers
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* `a` and `b`.
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*
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* @code{.c}
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* av_compare_mod(0x11, 0x02, 0x10) < 0 // since 0x11 % 0x10 (0x1) < 0x02 % 0x10 (0x2)
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* av_compare_mod(0x11, 0x02, 0x20) > 0 // since 0x11 % 0x20 (0x11) > 0x02 % 0x20 (0x02)
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* @endcode
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*
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* @param a Operand
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* @param b Operand
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* @param mod Divisor; must be a power of 2
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* @return
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* - a negative value if `a % mod < b % mod`
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* - a positive value if `a % mod > b % mod`
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* - zero if `a % mod == b % mod`
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*/
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int64_t av_compare_mod(uint64_t a, uint64_t b, uint64_t mod);
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/**
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* Rescale a timestamp while preserving known durations.
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*
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* This function is designed to be called per audio packet to scale the input
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* timestamp to a different time base. Compared to a simple av_rescale_q()
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* call, this function is robust against possible inconsistent frame durations.
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*
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* The `last` parameter is a state variable that must be preserved for all
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* subsequent calls for the same stream. For the first call, `*last` should be
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* initialized to #AV_NOPTS_VALUE.
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*
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* @param[in] in_tb Input time base
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* @param[in] in_ts Input timestamp
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* @param[in] fs_tb Duration time base; typically this is finer-grained
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* (greater) than `in_tb` and `out_tb`
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* @param[in] duration Duration till the next call to this function (i.e.
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* duration of the current packet/frame)
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* @param[in,out] last Pointer to a timestamp expressed in terms of
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* `fs_tb`, acting as a state variable
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* @param[in] out_tb Output timebase
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* @return Timestamp expressed in terms of `out_tb`
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*
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* @note In the context of this function, "duration" is in term of samples, not
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* seconds.
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*/
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int64_t av_rescale_delta(AVRational in_tb, int64_t in_ts, AVRational fs_tb, int duration, int64_t *last, AVRational out_tb);
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/**
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* Add a value to a timestamp.
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*
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* This function guarantees that when the same value is repeatly added that
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* no accumulation of rounding errors occurs.
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*
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* @param[in] ts Input timestamp
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* @param[in] ts_tb Input timestamp time base
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* @param[in] inc Value to be added
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* @param[in] inc_tb Time base of `inc`
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*/
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int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, int64_t inc);
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/**
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* 0th order modified bessel function of the first kind.
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*/
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double av_bessel_i0(double x);
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/**
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* @}
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*/
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#endif /* AVUTIL_MATHEMATICS_H */
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