ref: 985b2457cda207c2c65edeb647aedbb6e92dac46
dir: /sys/src/cmd/audio/libFLAC/lpc.c/
/* libFLAC - Free Lossless Audio Codec library
* Copyright (C) 2000,2001,2002,2003,2004 Josh Coalson
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* - Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* - Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* - Neither the name of the Xiph.org Foundation nor the names of its
* contributors may be used to endorse or promote products derived from
* this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR
* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
* LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#include <math.h>
#include "FLAC/assert.h"
#include "FLAC/format.h"
#include "private/bitmath.h"
#include "private/lpc.h"
#if defined DEBUG || defined FLAC__OVERFLOW_DETECT || defined FLAC__OVERFLOW_DETECT_VERBOSE
#include <stdio.h>
#endif
#ifndef M_LN2
/* math.h in VC++ doesn't seem to have this (how Microsoft is that?) */
#define M_LN2 0.69314718055994530942
#endif
void FLAC__lpc_compute_autocorrelation(const FLAC__real data[], unsigned data_len, unsigned lag, FLAC__real autoc[])
{
/* a readable, but slower, version */
#if 0
FLAC__real d;
unsigned i;
FLAC__ASSERT(lag > 0);
FLAC__ASSERT(lag <= data_len);
while(lag--) {
for(i = lag, d = 0.0; i < data_len; i++)
d += data[i] * data[i - lag];
autoc[lag] = d;
}
#endif
/*
* this version tends to run faster because of better data locality
* ('data_len' is usually much larger than 'lag')
*/
FLAC__real d;
unsigned sample, coeff;
const unsigned limit = data_len - lag;
FLAC__ASSERT(lag > 0);
FLAC__ASSERT(lag <= data_len);
for(coeff = 0; coeff < lag; coeff++)
autoc[coeff] = 0.0;
for(sample = 0; sample <= limit; sample++) {
d = data[sample];
for(coeff = 0; coeff < lag; coeff++)
autoc[coeff] += d * data[sample+coeff];
}
for(; sample < data_len; sample++) {
d = data[sample];
for(coeff = 0; coeff < data_len - sample; coeff++)
autoc[coeff] += d * data[sample+coeff];
}
}
void FLAC__lpc_compute_lp_coefficients(const FLAC__real autoc[], unsigned max_order, FLAC__real lp_coeff[][FLAC__MAX_LPC_ORDER], FLAC__real error[])
{
unsigned i, j;
double r, err, ref[FLAC__MAX_LPC_ORDER], lpc[FLAC__MAX_LPC_ORDER];
FLAC__ASSERT(0 < max_order);
FLAC__ASSERT(max_order <= FLAC__MAX_LPC_ORDER);
FLAC__ASSERT(autoc[0] != 0.0);
err = autoc[0];
for(i = 0; i < max_order; i++) {
/* Sum up this iteration's reflection coefficient. */
r = -autoc[i+1];
for(j = 0; j < i; j++)
r -= lpc[j] * autoc[i-j];
ref[i] = (r/=err);
/* Update LPC coefficients and total error. */
lpc[i]=r;
for(j = 0; j < (i>>1); j++) {
double tmp = lpc[j];
lpc[j] += r * lpc[i-1-j];
lpc[i-1-j] += r * tmp;
}
if(i & 1)
lpc[j] += lpc[j] * r;
err *= (1.0 - r * r);
/* save this order */
for(j = 0; j <= i; j++)
lp_coeff[i][j] = (FLAC__real)(-lpc[j]); /* negate FIR filter coeff to get predictor coeff */
error[i] = (FLAC__real)err;
}
}
int FLAC__lpc_quantize_coefficients(const FLAC__real lp_coeff[], unsigned order, unsigned precision, FLAC__int32 qlp_coeff[], int *shift)
{
unsigned i;
double d, cmax = -1e32;
FLAC__int32 qmax, qmin;
const int max_shiftlimit = (1 << (FLAC__SUBFRAME_LPC_QLP_SHIFT_LEN-1)) - 1;
const int min_shiftlimit = -max_shiftlimit - 1;
FLAC__ASSERT(precision > 0);
FLAC__ASSERT(precision >= FLAC__MIN_QLP_COEFF_PRECISION);
/* drop one bit for the sign; from here on out we consider only |lp_coeff[i]| */
precision--;
qmax = 1 << precision;
qmin = -qmax;
qmax--;
for(i = 0; i < order; i++) {
if(lp_coeff[i] == 0.0)
continue;
d = fabs(lp_coeff[i]);
if(d > cmax)
cmax = d;
}
redo_it:
if(cmax <= 0.0) {
/* => coefficients are all 0, which means our constant-detect didn't work */
return 2;
}
else {
int log2cmax;
(void)frexp(cmax, &log2cmax);
log2cmax--;
*shift = (int)precision - log2cmax - 1;
if(*shift < min_shiftlimit || *shift > max_shiftlimit) {
#if 0
/*@@@ this does not seem to help at all, but was not extensively tested either: */
if(*shift > max_shiftlimit)
*shift = max_shiftlimit;
else
#endif
return 1;
}
}
if(*shift >= 0) {
for(i = 0; i < order; i++) {
qlp_coeff[i] = (FLAC__int32)floor((double)lp_coeff[i] * (double)(1 << *shift));
/* double-check the result */
if(qlp_coeff[i] > qmax || qlp_coeff[i] < qmin) {
#ifdef FLAC__OVERFLOW_DETECT
fprintf(stderr,"FLAC__lpc_quantize_coefficients: compensating for overflow, qlp_coeff[%u]=%d, lp_coeff[%u]=%f, cmax=%f, precision=%u, shift=%d, q=%f, f(q)=%f\n", i, qlp_coeff[i], i, lp_coeff[i], cmax, precision, *shift, (double)lp_coeff[i] * (double)(1 << *shift), floor((double)lp_coeff[i] * (double)(1 << *shift)));
#endif
cmax *= 2.0;
goto redo_it;
}
}
}
else { /* (*shift < 0) */
const int nshift = -(*shift);
#ifdef DEBUG
fprintf(stderr,"FLAC__lpc_quantize_coefficients: negative shift = %d\n", *shift);
#endif
for(i = 0; i < order; i++) {
qlp_coeff[i] = (FLAC__int32)floor((double)lp_coeff[i] / (double)(1 << nshift));
/* double-check the result */
if(qlp_coeff[i] > qmax || qlp_coeff[i] < qmin) {
#ifdef FLAC__OVERFLOW_DETECT
fprintf(stderr,"FLAC__lpc_quantize_coefficients: compensating for overflow, qlp_coeff[%u]=%d, lp_coeff[%u]=%f, cmax=%f, precision=%u, shift=%d, q=%f, f(q)=%f\n", i, qlp_coeff[i], i, lp_coeff[i], cmax, precision, *shift, (double)lp_coeff[i] / (double)(1 << nshift), floor((double)lp_coeff[i] / (double)(1 << nshift)));
#endif
cmax *= 2.0;
goto redo_it;
}
}
}
return 0;
}
void FLAC__lpc_compute_residual_from_qlp_coefficients(const FLAC__int32 data[], unsigned data_len, const FLAC__int32 qlp_coeff[], unsigned order, int lp_quantization, FLAC__int32 residual[])
{
#ifdef FLAC__OVERFLOW_DETECT
FLAC__int64 sumo;
#endif
unsigned i, j;
FLAC__int32 sum;
const FLAC__int32 *history;
#ifdef FLAC__OVERFLOW_DETECT_VERBOSE
fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
for(i=0;i<order;i++)
fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
fprintf(stderr,"\n");
#endif
FLAC__ASSERT(order > 0);
for(i = 0; i < data_len; i++) {
#ifdef FLAC__OVERFLOW_DETECT
sumo = 0;
#endif
sum = 0;
history = data;
for(j = 0; j < order; j++) {
sum += qlp_coeff[j] * (*(--history));
#ifdef FLAC__OVERFLOW_DETECT
sumo += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*history);
#if defined _MSC_VER
if(sumo > 2147483647I64 || sumo < -2147483648I64)
fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients: OVERFLOW, i=%u, j=%u, c=%d, d=%d, sumo=%I64d\n",i,j,qlp_coeff[j],*history,sumo);
#else
if(sumo > 2147483647ll || sumo < -2147483648ll)
fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients: OVERFLOW, i=%u, j=%u, c=%d, d=%d, sumo=%lld\n",i,j,qlp_coeff[j],*history,sumo);
#endif
#endif
}
*(residual++) = *(data++) - (sum >> lp_quantization);
}
/* Here's a slower but clearer version:
for(i = 0; i < data_len; i++) {
sum = 0;
for(j = 0; j < order; j++)
sum += qlp_coeff[j] * data[i-j-1];
residual[i] = data[i] - (sum >> lp_quantization);
}
*/
}
void FLAC__lpc_compute_residual_from_qlp_coefficients_wide(const FLAC__int32 data[], unsigned data_len, const FLAC__int32 qlp_coeff[], unsigned order, int lp_quantization, FLAC__int32 residual[])
{
unsigned i, j;
FLAC__int64 sum;
const FLAC__int32 *history;
#ifdef FLAC__OVERFLOW_DETECT_VERBOSE
fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
for(i=0;i<order;i++)
fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
fprintf(stderr,"\n");
#endif
FLAC__ASSERT(order > 0);
for(i = 0; i < data_len; i++) {
sum = 0;
history = data;
for(j = 0; j < order; j++)
sum += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*(--history));
#ifdef FLAC__OVERFLOW_DETECT
if(FLAC__bitmath_silog2_wide(sum >> lp_quantization) > 32) {
fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: OVERFLOW, i=%u, sum=%lld\n", i, sum >> lp_quantization);
break;
}
if(FLAC__bitmath_silog2_wide((FLAC__int64)(*data) - (sum >> lp_quantization)) > 32) {
fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: OVERFLOW, i=%u, data=%d, sum=%lld, residual=%lld\n", i, *data, sum >> lp_quantization, (FLAC__int64)(*data) - (sum >> lp_quantization));
break;
}
#endif
*(residual++) = *(data++) - (FLAC__int32)(sum >> lp_quantization);
}
}
void FLAC__lpc_restore_signal(const FLAC__int32 residual[], unsigned data_len, const FLAC__int32 qlp_coeff[], unsigned order, int lp_quantization, FLAC__int32 data[])
{
#ifdef FLAC__OVERFLOW_DETECT
FLAC__int64 sumo;
#endif
unsigned i, j;
FLAC__int32 sum;
const FLAC__int32 *history;
#ifdef FLAC__OVERFLOW_DETECT_VERBOSE
fprintf(stderr,"FLAC__lpc_restore_signal: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
for(i=0;i<order;i++)
fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
fprintf(stderr,"\n");
#endif
FLAC__ASSERT(order > 0);
for(i = 0; i < data_len; i++) {
#ifdef FLAC__OVERFLOW_DETECT
sumo = 0;
#endif
sum = 0;
history = data;
for(j = 0; j < order; j++) {
sum += qlp_coeff[j] * (*(--history));
#ifdef FLAC__OVERFLOW_DETECT
sumo += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*history);
#if defined _MSC_VER
if(sumo > 2147483647I64 || sumo < -2147483648I64)
fprintf(stderr,"FLAC__lpc_restore_signal: OVERFLOW, i=%u, j=%u, c=%d, d=%d, sumo=%I64d\n",i,j,qlp_coeff[j],*history,sumo);
#else
if(sumo > 2147483647ll || sumo < -2147483648ll)
fprintf(stderr,"FLAC__lpc_restore_signal: OVERFLOW, i=%u, j=%u, c=%d, d=%d, sumo=%lld\n",i,j,qlp_coeff[j],*history,sumo);
#endif
#endif
}
*(data++) = *(residual++) + (sum >> lp_quantization);
}
/* Here's a slower but clearer version:
for(i = 0; i < data_len; i++) {
sum = 0;
for(j = 0; j < order; j++)
sum += qlp_coeff[j] * data[i-j-1];
data[i] = residual[i] + (sum >> lp_quantization);
}
*/
}
void FLAC__lpc_restore_signal_wide(const FLAC__int32 residual[], unsigned data_len, const FLAC__int32 qlp_coeff[], unsigned order, int lp_quantization, FLAC__int32 data[])
{
unsigned i, j;
FLAC__int64 sum;
const FLAC__int32 *history;
#ifdef FLAC__OVERFLOW_DETECT_VERBOSE
fprintf(stderr,"FLAC__lpc_restore_signal_wide: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
for(i=0;i<order;i++)
fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
fprintf(stderr,"\n");
#endif
FLAC__ASSERT(order > 0);
for(i = 0; i < data_len; i++) {
sum = 0;
history = data;
for(j = 0; j < order; j++)
sum += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*(--history));
#ifdef FLAC__OVERFLOW_DETECT
if(FLAC__bitmath_silog2_wide(sum >> lp_quantization) > 32) {
fprintf(stderr,"FLAC__lpc_restore_signal_wide: OVERFLOW, i=%u, sum=%lld\n", i, sum >> lp_quantization);
break;
}
if(FLAC__bitmath_silog2_wide((FLAC__int64)(*residual) + (sum >> lp_quantization)) > 32) {
fprintf(stderr,"FLAC__lpc_restore_signal_wide: OVERFLOW, i=%u, residual=%d, sum=%lld, data=%lld\n", i, *residual, sum >> lp_quantization, (FLAC__int64)(*residual) + (sum >> lp_quantization));
break;
}
#endif
*(data++) = *(residual++) + (FLAC__int32)(sum >> lp_quantization);
}
}
FLAC__real FLAC__lpc_compute_expected_bits_per_residual_sample(FLAC__real lpc_error, unsigned total_samples)
{
double error_scale;
FLAC__ASSERT(total_samples > 0);
error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__real)total_samples;
return FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error, error_scale);
}
FLAC__real FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(FLAC__real lpc_error, double error_scale)
{
if(lpc_error > 0.0) {
FLAC__real bps = (FLAC__real)((double)0.5 * log(error_scale * lpc_error) / M_LN2);
if(bps >= 0.0)
return bps;
else
return 0.0;
}
else if(lpc_error < 0.0) { /* error should not be negative but can happen due to inadequate float resolution */
return (FLAC__real)1e32;
}
else {
return 0.0;
}
}
unsigned FLAC__lpc_compute_best_order(const FLAC__real lpc_error[], unsigned max_order, unsigned total_samples, unsigned bits_per_signal_sample)
{
unsigned order, best_order;
FLAC__real best_bits, tmp_bits;
double error_scale;
FLAC__ASSERT(max_order > 0);
FLAC__ASSERT(total_samples > 0);
error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__real)total_samples;
best_order = 0;
best_bits = FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error[0], error_scale) * (FLAC__real)total_samples;
for(order = 1; order < max_order; order++) {
tmp_bits = FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error[order], error_scale) * (FLAC__real)(total_samples - order) + (FLAC__real)(order * bits_per_signal_sample);
if(tmp_bits < best_bits) {
best_order = order;
best_bits = tmp_bits;
}
}
return best_order+1; /* +1 since index of lpc_error[] is order-1 */
}