| /* 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. |
| */ |
| |
| #if HAVE_CONFIG_H |
| # include <config.h> |
| #endif |
| |
| #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); |
| |
| /* |
| * Technically we should subtract the mean first like so: |
| * for(i = 0; i < data_len; i++) |
| * data[i] -= mean; |
| * but it appears not to make enough of a difference to matter, and |
| * most signals are already closely centered around zero |
| */ |
| 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 overhead_bits_per_order) |
| { |
| unsigned order, index, best_index; /* 'index' the index into lpc_error; index==order-1 since lpc_error[0] is for order==1, lpc_error[1] is for order==2, etc */ |
| FLAC__double bits, best_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_index = 0; |
| best_bits = (unsigned)(-1); |
| |
| for(index = 0, order = 1; index < max_order; index++, order++) { |
| bits = FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error[index], error_scale) * (FLAC__double)(total_samples - order) + (FLAC__double)(order * overhead_bits_per_order); |
| if(bits < best_bits) { |
| best_index = index; |
| best_bits = bits; |
| } |
| } |
| |
| return best_index+1; /* +1 since index of lpc_error[] is order-1 */ |
| } |
| |
| #endif /* !defined FLAC__INTEGER_ONLY_LIBRARY */ |