src/libFLAC/lpc.c - platform/external/flac - Gitiles

 /* libFLAC - Free Lossless Audio Codec library
  * Copyright (C) 2000,2001,2002,2003,2004,2005,2006  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 FLAC__INTEGER_ONLY_LIBRARY

 #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_window_data(const FLAC__real in[], const FLAC__real window[], FLAC__real out[], unsigned data_len)
 {
 	unsigned i;
 	for(i = 0; i < data_len; i++)
 		out[i] = in[i] * window[i];
 }

 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__double error[])
 {
 	unsigned i, j;
 	FLAC__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++) {
 			FLAC__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] = err;
 	}
 }

 int FLAC__lpc_quantize_coefficients(const FLAC__real lp_coeff[], unsigned order, unsigned precision, FLAC__int32 qlp_coeff[], int *shift)
 {
 	unsigned i;
 	FLAC__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((FLAC__double)lp_coeff[i] * (FLAC__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, (FLAC__double)lp_coeff[i] * (FLAC__double)(1 << *shift), floor((FLAC__double)lp_coeff[i] * (FLAC__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((FLAC__double)lp_coeff[i] / (FLAC__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, (FLAC__double)lp_coeff[i] / (FLAC__double)(1 << nshift), floor((FLAC__double)lp_coeff[i] / (FLAC__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);
 	}
 }

 #endif /* !defined FLAC__INTEGER_ONLY_LIBRARY */

 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);
 	}
 }

 #ifndef FLAC__INTEGER_ONLY_LIBRARY

 FLAC__double FLAC__lpc_compute_expected_bits_per_residual_sample(FLAC__double lpc_error, unsigned total_samples)
 {
 	FLAC__double error_scale;

 	FLAC__ASSERT(total_samples > 0);

 	error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__double)total_samples;

 	return FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error, error_scale);
 }

 FLAC__double FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(FLAC__double lpc_error, FLAC__double error_scale)
 {
 	if(lpc_error > 0.0) {
 		FLAC__double bps = (FLAC__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 floating-point resolution */
 		return 1e32;
 	}
 	else {
 		return 0.0;
 	}
 }

 unsigned FLAC__lpc_compute_best_order(const FLAC__double lpc_error[], unsigned max_order, unsigned total_samples, unsigned bits_per_signal_sample)
 {
 	unsigned order, best_order;
 	FLAC__double best_bits, tmp_bits, error_scale;

 	FLAC__ASSERT(max_order > 0);
 	FLAC__ASSERT(total_samples > 0);

 	error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__double)total_samples;

 	best_order = 0;
 	best_bits = FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error[0], error_scale) * (FLAC__double)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__double)(total_samples - order) + (FLAC__double)(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 */
 }

 #endif /* !defined FLAC__INTEGER_ONLY_LIBRARY */
	/* libFLAC - Free Lossless Audio Codec library
	* Copyright (C) 2000,2001,2002,2003,2004,2005,2006 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 FLAC__INTEGER_ONLY_LIBRARY

	#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_window_data(const FLAC__real in[], const FLAC__real window[], FLAC__real out[], unsigned data_len)
	{
	unsigned i;
	for(i = 0; i < data_len; i++)
	out[i] = in[i] * window[i];
	}

	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__double error[])
	{
	unsigned i, j;
	FLAC__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++) {
	FLAC__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] = err;
	}
	}

	int FLAC__lpc_quantize_coefficients(const FLAC__real lp_coeff[], unsigned order, unsigned precision, FLAC__int32 qlp_coeff[], int *shift)
	{
	unsigned i;
	FLAC__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((FLAC__double)lp_coeff[i] * (FLAC__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, (FLAC__double)lp_coeff[i] (FLAC__double)(1 << shift), floor((FLAC__double)lp_coeff[i] (FLAC__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((FLAC__double)lp_coeff[i] / (FLAC__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, (FLAC__double)lp_coeff[i] / (FLAC__double)(1 << nshift), floor((FLAC__double)lp_coeff[i] / (FLAC__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);
	}
	}

	#endif /* !defined FLAC__INTEGER_ONLY_LIBRARY */

	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);
	}
	}

	#ifndef FLAC__INTEGER_ONLY_LIBRARY

	FLAC__double FLAC__lpc_compute_expected_bits_per_residual_sample(FLAC__double lpc_error, unsigned total_samples)
	{
	FLAC__double error_scale;

	FLAC__ASSERT(total_samples > 0);

	error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__double)total_samples;

	return FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error, error_scale);
	}

	FLAC__double FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(FLAC__double lpc_error, FLAC__double error_scale)
	{
	if(lpc_error > 0.0) {
	FLAC__double bps = (FLAC__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 floating-point resolution */
	return 1e32;
	}
	else {
	return 0.0;
	}
	}

	unsigned FLAC__lpc_compute_best_order(const FLAC__double lpc_error[], unsigned max_order, unsigned total_samples, unsigned bits_per_signal_sample)
	{
	unsigned order, best_order;
	FLAC__double best_bits, tmp_bits, error_scale;

	FLAC__ASSERT(max_order > 0);
	FLAC__ASSERT(total_samples > 0);

	error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__double)total_samples;

	best_order = 0;
	best_bits = FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error[0], error_scale) * (FLAC__double)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__double)(total_samples - order) + (FLAC__double)(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 */
	}

	#endif /* !defined FLAC__INTEGER_ONLY_LIBRARY */