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Move bessel_i0() from swresample/resample to avutil/mathematics

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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>
pull/389/head
Michael Niedermayer 2 years ago
parent 0c78b0dd3b
commit 75918016ab
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5 changed files with 113 additions and 106 deletions
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  1. 3
      doc/APIchanges
  2. 104
      libavutil/mathematics.c
  3. 4
      libavutil/mathematics.h
  4. 2
      libavutil/version.h
  5. 106
      libswresample/resample.c

3
doc/APIchanges
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@ -2,6 +2,9 @@ The last version increases of all libraries were on 2023-02-09
API changes, most recent first:
2023-05-29 - xxxxxxxxxx - lavu 58.12.100 - mathematics.h
Add av_bessel_i0()
2023-05-xx - xxxxxxxxxx - lavc 60.15.100 - avcodec.h
Add AVHWAccel.update_thread_context, AVHWAccel.free_frame_priv,
AVHWAccel.flush.

104
libavutil/mathematics.c
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@ -213,3 +213,107 @@ int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, int64_t i
return av_sat_add64(av_rescale_q(old + 1, inc_tb, ts_tb), ts - old_ts);
}
}
static inline double eval_poly(const double *coeff, int size, double x) {
double sum = coeff[size-1];
int i;
for (i = size-2; i >= 0; --i) {
sum *= x;
sum += coeff[i];
}
return sum;
}
/**
* 0th order modified bessel function of the first kind.
* Algorithm taken from the Boost project, source:
* https://searchcode.com/codesearch/view/14918379/
* Use, modification and distribution are subject to the
* Boost Software License, Version 1.0 (see notice below).
* Boost Software License - Version 1.0 - August 17th, 2003
Permission is hereby granted, free of charge, to any person or organization
obtaining a copy of the software and accompanying documentation covered by
this license (the "Software") to use, reproduce, display, distribute,
execute, and transmit the Software, and to prepare derivative works of the
Software, and to permit third-parties to whom the Software is furnished to
do so, all subject to the following:
The copyright notices in the Software and this entire statement, including
the above license grant, this restriction and the following disclaimer,
must be included in all copies of the Software, in whole or in part, and
all derivative works of the Software, unless such copies or derivative
works are solely in the form of machine-executable object code generated by
a source language processor.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
DEALINGS IN THE SOFTWARE.
*/
double av_bessel_i0(double x) {
// Modified Bessel function of the first kind of order zero
// minimax rational approximations on intervals, see
// Blair and Edwards, Chalk River Report AECL-4928, 1974
static const double p1[] = {
-2.2335582639474375249e+15,
-5.5050369673018427753e+14,
-3.2940087627407749166e+13,
-8.4925101247114157499e+11,
-1.1912746104985237192e+10,
-1.0313066708737980747e+08,
-5.9545626019847898221e+05,
-2.4125195876041896775e+03,
-7.0935347449210549190e+00,
-1.5453977791786851041e-02,
-2.5172644670688975051e-05,
-3.0517226450451067446e-08,
-2.6843448573468483278e-11,
-1.5982226675653184646e-14,
-5.2487866627945699800e-18,
};
static const double q1[] = {
-2.2335582639474375245e+15,
7.8858692566751002988e+12,
-1.2207067397808979846e+10,
1.0377081058062166144e+07,
-4.8527560179962773045e+03,
1.0,
};
static const double p2[] = {
-2.2210262233306573296e-04,
1.3067392038106924055e-02,
-4.4700805721174453923e-01,
5.5674518371240761397e+00,
-2.3517945679239481621e+01,
3.1611322818701131207e+01,
-9.6090021968656180000e+00,
};
static const double q2[] = {
-5.5194330231005480228e-04,
3.2547697594819615062e-02,
-1.1151759188741312645e+00,
1.3982595353892851542e+01,
-6.0228002066743340583e+01,
8.5539563258012929600e+01,
-3.1446690275135491500e+01,
1.0,
};
double y, r, factor;
if (x == 0)
return 1.0;
x = fabs(x);
if (x <= 15) {
y = x * x;
return eval_poly(p1, FF_ARRAY_ELEMS(p1), y) / eval_poly(q1, FF_ARRAY_ELEMS(q1), y);
}
else {
y = 1 / x - 1.0 / 15;
r = eval_poly(p2, FF_ARRAY_ELEMS(p2), y) / eval_poly(q2, FF_ARRAY_ELEMS(q2), y);
factor = exp(x) / sqrt(x);
return factor * r;
}
}

4
libavutil/mathematics.h
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@ -288,6 +288,10 @@ int64_t av_rescale_delta(AVRational in_tb, int64_t in_ts, AVRational fs_tb, int
*/
int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, int64_t inc);
/**
* 0th order modified bessel function of the first kind.
*/
double av_bessel_i0(double x);
/**
* @}

2
libavutil/version.h
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@ -79,7 +79,7 @@
*/
#define LIBAVUTIL_VERSION_MAJOR 58
#define LIBAVUTIL_VERSION_MINOR 11
#define LIBAVUTIL_VERSION_MINOR 12
#define LIBAVUTIL_VERSION_MICRO 100
#define LIBAVUTIL_VERSION_INT AV_VERSION_INT(LIBAVUTIL_VERSION_MAJOR, \

106
libswresample/resample.c
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@ -30,110 +30,6 @@
#include "libavutil/cpu.h"
#include "resample.h"
static inline double eval_poly(const double *coeff, int size, double x) {
double sum = coeff[size-1];
int i;
for (i = size-2; i >= 0; --i) {
sum *= x;
sum += coeff[i];
}
return sum;
}
/**
* 0th order modified bessel function of the first kind.
* Algorithm taken from the Boost project, source:
* https://searchcode.com/codesearch/view/14918379/
* Use, modification and distribution are subject to the
* Boost Software License, Version 1.0 (see notice below).
* Boost Software License - Version 1.0 - August 17th, 2003
Permission is hereby granted, free of charge, to any person or organization
obtaining a copy of the software and accompanying documentation covered by
this license (the "Software") to use, reproduce, display, distribute,
execute, and transmit the Software, and to prepare derivative works of the
Software, and to permit third-parties to whom the Software is furnished to
do so, all subject to the following:
The copyright notices in the Software and this entire statement, including
the above license grant, this restriction and the following disclaimer,
must be included in all copies of the Software, in whole or in part, and
all derivative works of the Software, unless such copies or derivative
works are solely in the form of machine-executable object code generated by
a source language processor.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
DEALINGS IN THE SOFTWARE.
*/
static double bessel(double x) {
// Modified Bessel function of the first kind of order zero
// minimax rational approximations on intervals, see
// Blair and Edwards, Chalk River Report AECL-4928, 1974
static const double p1[] = {
-2.2335582639474375249e+15,
-5.5050369673018427753e+14,
-3.2940087627407749166e+13,
-8.4925101247114157499e+11,
-1.1912746104985237192e+10,
-1.0313066708737980747e+08,
-5.9545626019847898221e+05,
-2.4125195876041896775e+03,
-7.0935347449210549190e+00,
-1.5453977791786851041e-02,
-2.5172644670688975051e-05,
-3.0517226450451067446e-08,
-2.6843448573468483278e-11,
-1.5982226675653184646e-14,
-5.2487866627945699800e-18,
};
static const double q1[] = {
-2.2335582639474375245e+15,
7.8858692566751002988e+12,
-1.2207067397808979846e+10,
1.0377081058062166144e+07,
-4.8527560179962773045e+03,
1.0,
};
static const double p2[] = {
-2.2210262233306573296e-04,
1.3067392038106924055e-02,
-4.4700805721174453923e-01,
5.5674518371240761397e+00,
-2.3517945679239481621e+01,
3.1611322818701131207e+01,
-9.6090021968656180000e+00,
};
static const double q2[] = {
-5.5194330231005480228e-04,
3.2547697594819615062e-02,
-1.1151759188741312645e+00,
1.3982595353892851542e+01,
-6.0228002066743340583e+01,
8.5539563258012929600e+01,
-3.1446690275135491500e+01,
1.0,
};
double y, r, factor;
if (x == 0)
return 1.0;
x = fabs(x);
if (x <= 15) {
y = x * x;
return eval_poly(p1, FF_ARRAY_ELEMS(p1), y) / eval_poly(q1, FF_ARRAY_ELEMS(q1), y);
}
else {
y = 1 / x - 1.0 / 15;
r = eval_poly(p2, FF_ARRAY_ELEMS(p2), y) / eval_poly(q2, FF_ARRAY_ELEMS(q2), y);
factor = exp(x) / sqrt(x);
return factor * r;
}
}
/**
* builds a polyphase filterbank.
* @param factor resampling factor
@ -189,7 +85,7 @@ static int build_filter(ResampleContext *c, void *filter, double factor, int tap
break;
case SWR_FILTER_TYPE_KAISER:
w = 2.0*x / (factor*tap_count*M_PI);
y *= bessel(kaiser_beta*sqrt(FFMAX(1-w*w, 0)));
y *= av_bessel_i0(kaiser_beta*sqrt(FFMAX(1-w*w, 0)));
break;
default:
av_assert0(0);

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