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ffmpeg/libswresample/resample.c
Ganesh Ajjanagadde cf491a925e swresample/resample: speed up Blackman Nuttall filter 
This may be a slightly surprising optimization, but is actually based on
an understanding of how math libraries compute trigonometric functions.
Explanation is given here so that future development uses libm more effectively
across the codebase.

All libm's essentially compute transcendental functions via some kind of
polynomial approximation, be it Taylor-Maclaurin or Chebyshev.
Correction terms are added via polynomial correction factors when needed
to squeeze out the last bits of accuracy. Lookup tables are also
inserted strategically.

In the case of trigonometric functions, periodicity is exploited via
first doing a range reduction to an interval around zero, and then using
some polynomial approximation.

This range reduction is the most natural way of doing things - else one
would need polynomials for ranges in different periods which makes no
sense whatsoever.

To avoid the need for the range reduction, it is helpful to feed in
arguments as close to the origin as possible for the trigonometric
functions. In fact, this also makes sense from an accuracy point of view:
IEEE floating point has far more resolution for small numbers than big ones.

This patch does this for the Blackman-Nuttall filter, and yields a
non-negligible speedup.

Sample benchmark (x86-64, Haswell, GNU/Linux)
test: fate-swr-resample-dblp-2626-44100
old:
18893514 decicycles in build_filter (loop 1000),     256 runs,      0 skips
18599863 decicycles in build_filter (loop 1000),     512 runs,      0 skips
18445574 decicycles in build_filter (loop 1000),    1000 runs,     24 skips

new:
16290697 decicycles in build_filter (loop 1000),     256 runs,      0 skips
16267172 decicycles in build_filter (loop 1000),     512 runs,      0 skips
16251105 decicycles in build_filter (loop 1000),    1000 runs,     24 skips

Reviewed-by: Michael Niedermayer <michael@niedermayer.cc>
Signed-off-by: Ganesh Ajjanagadde <gajjanagadde@gmail.com>
2015-11-09 18:41:32 -05:00

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/*
* audio resampling
* Copyright (c) 2004-2012 Michael Niedermayer <michaelni@gmx.at>
* bessel function: Copyright (c) 2006 Xiaogang Zhang
*
* 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
* audio resampling
* @author Michael Niedermayer <michaelni@gmx.at>
*/
#include "libavutil/avassert.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,
1.0L,
};
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,
1.0L,
};
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
* @param scale wanted sum of coefficients for each filter
* @param filter_type filter type
* @param kaiser_beta kaiser window beta
* @return 0 on success, negative on error
*/
static int build_filter(ResampleContext *c, void *filter, double factor, int tap_count, int alloc, int phase_count, int scale,
int filter_type, double kaiser_beta){
int ph, i;
double x, y, w, t, s;
double *tab = av_malloc_array(tap_count+1, sizeof(*tab));
double *sin_lut = av_malloc_array(phase_count / 2 + 1, sizeof(*sin_lut));
const int center= (tap_count-1)/2;
if (!tab || !sin_lut)
goto fail;
/* if upsampling, only need to interpolate, no filter */
if (factor > 1.0)
factor = 1.0;
av_assert0(phase_count == 1 || phase_count % 2 == 0);
if (factor == 1.0) {
for (ph = 0; ph <= phase_count / 2; ph++)
sin_lut[ph] = sin(M_PI * ph / phase_count);
}
for(ph = 0; ph <= phase_count / 2; ph++) {
double norm = 0;
s = sin_lut[ph];
for(i=0;i<=tap_count;i++) {
x = M_PI * ((double)(i - center) - (double)ph / phase_count) * factor;
if (x == 0) y = 1.0;
else if (factor == 1.0)
y = s / x;
else
y = sin(x) / x;
switch(filter_type){
case SWR_FILTER_TYPE_CUBIC:{
const float d= -0.5; //first order derivative = -0.5
x = fabs(((double)(i - center) - (double)ph / phase_count) * factor);
if(x<1.0) y= 1 - 3*x*x + 2*x*x*x + d*( -x*x + x*x*x);
else y= d*(-4 + 8*x - 5*x*x + x*x*x);
break;}
case SWR_FILTER_TYPE_BLACKMAN_NUTTALL:
w = 2.0*x / (factor*tap_count);
t = -cos(w);
y *= 0.3635819 - 0.4891775 * t + 0.1365995 * (2*t*t-1) - 0.0106411 * (4*t*t*t - 3*t);
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)));
break;
default:
av_assert0(0);
}
tab[i] = y;
s = -s;
if (i < tap_count)
norm += y;
}
/* normalize so that an uniform color remains the same */
switch(c->format){
case AV_SAMPLE_FMT_S16P:
for(i=0;i<tap_count;i++)
((int16_t*)filter)[ph * alloc + i] = av_clip(lrintf(tab[i] * scale / norm), INT16_MIN, INT16_MAX);
if (tap_count % 2 == 0) {
for (i = 0; i < tap_count; i++)
((int16_t*)filter)[(phase_count-ph) * alloc + tap_count-1-i] = ((int16_t*)filter)[ph * alloc + i];
}
else {
for (i = 1; i <= tap_count; i++)
((int16_t*)filter)[(phase_count-ph) * alloc + tap_count-i] =
av_clip(lrintf(tab[i] * scale / (norm - tab[0] + tab[tap_count])), INT16_MIN, INT16_MAX);
}
break;
case AV_SAMPLE_FMT_S32P:
for(i=0;i<tap_count;i++)
((int32_t*)filter)[ph * alloc + i] = av_clipl_int32(llrint(tab[i] * scale / norm));
if (tap_count % 2 == 0) {
for (i = 0; i < tap_count; i++)
((int32_t*)filter)[(phase_count-ph) * alloc + tap_count-1-i] = ((int32_t*)filter)[ph * alloc + i];
}
else {
for (i = 1; i <= tap_count; i++)
((int32_t*)filter)[(phase_count-ph) * alloc + tap_count-i] =
av_clipl_int32(llrint(tab[i] * scale / (norm - tab[0] + tab[tap_count])));
}
break;
case AV_SAMPLE_FMT_FLTP:
for(i=0;i<tap_count;i++)
((float*)filter)[ph * alloc + i] = tab[i] * scale / norm;
if (tap_count % 2 == 0) {
for (i = 0; i < tap_count; i++)
((float*)filter)[(phase_count-ph) * alloc + tap_count-1-i] = ((float*)filter)[ph * alloc + i];
}
else {
for (i = 1; i <= tap_count; i++)
((float*)filter)[(phase_count-ph) * alloc + tap_count-i] = tab[i] * scale / (norm - tab[0] + tab[tap_count]);
}
break;
case AV_SAMPLE_FMT_DBLP:
for(i=0;i<tap_count;i++)
((double*)filter)[ph * alloc + i] = tab[i] * scale / norm;
if (tap_count % 2 == 0) {
for (i = 0; i < tap_count; i++)
((double*)filter)[(phase_count-ph) * alloc + tap_count-1-i] = ((double*)filter)[ph * alloc + i];
}
else {
for (i = 1; i <= tap_count; i++)
((double*)filter)[(phase_count-ph) * alloc + tap_count-i] = tab[i] * scale / (norm - tab[0] + tab[tap_count]);
}
break;
}
}
#if 0
{
#define LEN 1024
int j,k;
double sine[LEN + tap_count];
double filtered[LEN];
double maxff=-2, minff=2, maxsf=-2, minsf=2;
for(i=0; i<LEN; i++){
double ss=0, sf=0, ff=0;
for(j=0; j<LEN+tap_count; j++)
sine[j]= cos(i*j*M_PI/LEN);
for(j=0; j<LEN; j++){
double sum=0;
ph=0;
for(k=0; k<tap_count; k++)
sum += filter[ph * tap_count + k] * sine[k+j];
filtered[j]= sum / (1<<FILTER_SHIFT);
ss+= sine[j + center] * sine[j + center];
ff+= filtered[j] * filtered[j];
sf+= sine[j + center] * filtered[j];
}
ss= sqrt(2*ss/LEN);
ff= sqrt(2*ff/LEN);
sf= 2*sf/LEN;
maxff= FFMAX(maxff, ff);
minff= FFMIN(minff, ff);
maxsf= FFMAX(maxsf, sf);
minsf= FFMIN(minsf, sf);
if(i%11==0){
av_log(NULL, AV_LOG_ERROR, "i:%4d ss:%f ff:%13.6e-%13.6e sf:%13.6e-%13.6e\n", i, ss, maxff, minff, maxsf, minsf);
minff=minsf= 2;
maxff=maxsf= -2;
}
}
}
#endif
fail:
av_free(tab);
av_free(sin_lut);
return 0;
}
static ResampleContext *resample_init(ResampleContext *c, int out_rate, int in_rate, int filter_size, int phase_shift, int linear,
double cutoff0, enum AVSampleFormat format, enum SwrFilterType filter_type, double kaiser_beta,
double precision, int cheby)
{
double cutoff = cutoff0? cutoff0 : 0.97;
double factor= FFMIN(out_rate * cutoff / in_rate, 1.0);
int phase_count= 1<<phase_shift;
if (!c || c->phase_shift != phase_shift || c->linear!=linear || c->factor != factor
|| c->filter_length != FFMAX((int)ceil(filter_size/factor), 1) || c->format != format
|| c->filter_type != filter_type || c->kaiser_beta != kaiser_beta) {
c = av_mallocz(sizeof(*c));
if (!c)
return NULL;
c->format= format;
c->felem_size= av_get_bytes_per_sample(c->format);
switch(c->format){
case AV_SAMPLE_FMT_S16P:
c->filter_shift = 15;
break;
case AV_SAMPLE_FMT_S32P:
c->filter_shift = 30;
break;
case AV_SAMPLE_FMT_FLTP:
case AV_SAMPLE_FMT_DBLP:
c->filter_shift = 0;
break;
default:
av_log(NULL, AV_LOG_ERROR, "Unsupported sample format\n");
av_assert0(0);
}
if (filter_size/factor > INT32_MAX/256) {
av_log(NULL, AV_LOG_ERROR, "Filter length too large\n");
goto error;
}
c->phase_shift = phase_shift;
c->phase_mask = phase_count - 1;
c->linear = linear;
c->factor = factor;
c->filter_length = FFMAX((int)ceil(filter_size/factor), 1);
c->filter_alloc = FFALIGN(c->filter_length, 8);
c->filter_bank = av_calloc(c->filter_alloc, (phase_count+1)*c->felem_size);
c->filter_type = filter_type;
c->kaiser_beta = kaiser_beta;
if (!c->filter_bank)
goto error;
if (build_filter(c, (void*)c->filter_bank, factor, c->filter_length, c->filter_alloc, phase_count, 1<<c->filter_shift, filter_type, kaiser_beta))
goto error;
memcpy(c->filter_bank + (c->filter_alloc*phase_count+1)*c->felem_size, c->filter_bank, (c->filter_alloc-1)*c->felem_size);
memcpy(c->filter_bank + (c->filter_alloc*phase_count )*c->felem_size, c->filter_bank + (c->filter_alloc - 1)*c->felem_size, c->felem_size);
}
c->compensation_distance= 0;
if(!av_reduce(&c->src_incr, &c->dst_incr, out_rate, in_rate * (int64_t)phase_count, INT32_MAX/2))
goto error;
c->ideal_dst_incr = c->dst_incr;
c->dst_incr_div = c->dst_incr / c->src_incr;
c->dst_incr_mod = c->dst_incr % c->src_incr;
c->index= -phase_count*((c->filter_length-1)/2);
c->frac= 0;
swri_resample_dsp_init(c);
return c;
error:
av_freep(&c->filter_bank);
av_free(c);
return NULL;
}
static void resample_free(ResampleContext **c){
if(!*c)
return;
av_freep(&(*c)->filter_bank);
av_freep(c);
}
static int set_compensation(ResampleContext *c, int sample_delta, int compensation_distance){
c->compensation_distance= compensation_distance;
if (compensation_distance)
c->dst_incr = c->ideal_dst_incr - c->ideal_dst_incr * (int64_t)sample_delta / compensation_distance;
else
c->dst_incr = c->ideal_dst_incr;
c->dst_incr_div = c->dst_incr / c->src_incr;
c->dst_incr_mod = c->dst_incr % c->src_incr;
return 0;
}
static int swri_resample(ResampleContext *c,
uint8_t *dst, const uint8_t *src, int *consumed,
int src_size, int dst_size, int update_ctx)
{
if (c->filter_length == 1 && c->phase_shift == 0) {
int index= c->index;
int frac= c->frac;
int64_t index2= (1LL<<32)*c->frac/c->src_incr + (1LL<<32)*index;
int64_t incr= (1LL<<32) * c->dst_incr / c->src_incr;
int new_size = (src_size * (int64_t)c->src_incr - frac + c->dst_incr - 1) / c->dst_incr;
dst_size= FFMIN(dst_size, new_size);
c->dsp.resample_one(dst, src, dst_size, index2, incr);
index += dst_size * c->dst_incr_div;
index += (frac + dst_size * (int64_t)c->dst_incr_mod) / c->src_incr;
av_assert2(index >= 0);
*consumed= index;
if (update_ctx) {
c->frac = (frac + dst_size * (int64_t)c->dst_incr_mod) % c->src_incr;
c->index = 0;
}
} else {
int64_t end_index = (1LL + src_size - c->filter_length) << c->phase_shift;
int64_t delta_frac = (end_index - c->index) * c->src_incr - c->frac;
int delta_n = (delta_frac + c->dst_incr - 1) / c->dst_incr;
dst_size = FFMIN(dst_size, delta_n);
if (dst_size > 0) {
*consumed = c->dsp.resample(c, dst, src, dst_size, update_ctx);
} else {
*consumed = 0;
}
}
return dst_size;
}
static int multiple_resample(ResampleContext *c, AudioData *dst, int dst_size, AudioData *src, int src_size, int *consumed){
int i, ret= -1;
int av_unused mm_flags = av_get_cpu_flags();
int need_emms = c->format == AV_SAMPLE_FMT_S16P && ARCH_X86_32 &&
(mm_flags & (AV_CPU_FLAG_MMX2 | AV_CPU_FLAG_SSE2)) == AV_CPU_FLAG_MMX2;
int64_t max_src_size = (INT64_MAX >> (c->phase_shift+1)) / c->src_incr;
if (c->compensation_distance)
dst_size = FFMIN(dst_size, c->compensation_distance);
src_size = FFMIN(src_size, max_src_size);
for(i=0; i<dst->ch_count; i++){
ret= swri_resample(c, dst->ch[i], src->ch[i],
consumed, src_size, dst_size, i+1==dst->ch_count);
}
if(need_emms)
emms_c();
if (c->compensation_distance) {
c->compensation_distance -= ret;
if (!c->compensation_distance) {
c->dst_incr = c->ideal_dst_incr;
c->dst_incr_div = c->dst_incr / c->src_incr;
c->dst_incr_mod = c->dst_incr % c->src_incr;
}
}
return ret;
}
static int64_t get_delay(struct SwrContext *s, int64_t base){
ResampleContext *c = s->resample;
int64_t num = s->in_buffer_count - (c->filter_length-1)/2;
num *= 1 << c->phase_shift;
num -= c->index;
num *= c->src_incr;
num -= c->frac;
return av_rescale(num, base, s->in_sample_rate*(int64_t)c->src_incr << c->phase_shift);
}
static int64_t get_out_samples(struct SwrContext *s, int in_samples) {
ResampleContext *c = s->resample;
// The + 2 are added to allow implementations to be slightly inaccurate, they should not be needed currently.
// They also make it easier to proof that changes and optimizations do not
// break the upper bound.
int64_t num = s->in_buffer_count + 2LL + in_samples;
num *= 1 << c->phase_shift;
num -= c->index;
num = av_rescale_rnd(num, s->out_sample_rate, ((int64_t)s->in_sample_rate) << c->phase_shift, AV_ROUND_UP) + 2;
if (c->compensation_distance) {
if (num > INT_MAX)
return AVERROR(EINVAL);
num = FFMAX(num, (num * c->ideal_dst_incr - 1) / c->dst_incr + 1);
}
return num;
}
static int resample_flush(struct SwrContext *s) {
AudioData *a= &s->in_buffer;
int i, j, ret;
if((ret = swri_realloc_audio(a, s->in_buffer_index + 2*s->in_buffer_count)) < 0)
return ret;
av_assert0(a->planar);
for(i=0; i<a->ch_count; i++){
for(j=0; j<s->in_buffer_count; j++){
memcpy(a->ch[i] + (s->in_buffer_index+s->in_buffer_count+j )*a->bps,
a->ch[i] + (s->in_buffer_index+s->in_buffer_count-j-1)*a->bps, a->bps);
}
}
s->in_buffer_count += (s->in_buffer_count+1)/2;
return 0;
}
// in fact the whole handle multiple ridiculously small buffers might need more thinking...
static int invert_initial_buffer(ResampleContext *c, AudioData *dst, const AudioData *src,
int in_count, int *out_idx, int *out_sz)
{
int n, ch, num = FFMIN(in_count + *out_sz, c->filter_length + 1), res;
if (c->index >= 0)
return 0;
if ((res = swri_realloc_audio(dst, c->filter_length * 2 + 1)) < 0)
return res;
// copy
for (n = *out_sz; n < num; n++) {
for (ch = 0; ch < src->ch_count; ch++) {
memcpy(dst->ch[ch] + ((c->filter_length + n) * c->felem_size),
src->ch[ch] + ((n - *out_sz) * c->felem_size), c->felem_size);
}
}
// if not enough data is in, return and wait for more
if (num < c->filter_length + 1) {
*out_sz = num;
*out_idx = c->filter_length;
return INT_MAX;
}
// else invert
for (n = 1; n <= c->filter_length; n++) {
for (ch = 0; ch < src->ch_count; ch++) {
memcpy(dst->ch[ch] + ((c->filter_length - n) * c->felem_size),
dst->ch[ch] + ((c->filter_length + n) * c->felem_size),
c->felem_size);
}
}
res = num - *out_sz;
*out_idx = c->filter_length + (c->index >> c->phase_shift);
*out_sz = FFMAX(*out_sz + c->filter_length,
1 + c->filter_length * 2) - *out_idx;
c->index &= c->phase_mask;
return FFMAX(res, 0);
}
struct Resampler const swri_resampler={
resample_init,
resample_free,
multiple_resample,
resample_flush,
set_compensation,
get_delay,
invert_initial_buffer,
get_out_samples,
};
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