| /* libFLAC - Free Lossless Audio Codec library |
| * Copyright (C) 2000,2001,2002 Josh Coalson |
| * |
| * This library is free software; you can redistribute it and/or |
| * modify it under the terms of the GNU Library General Public |
| * License as published by the Free Software Foundation; either |
| * version 2 of the License, or (at your option) any later version. |
| * |
| * This library 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 |
| * Library General Public License for more details. |
| * |
| * You should have received a copy of the GNU Library General Public |
| * License along with this library; if not, write to the |
| * Free Software Foundation, Inc., 59 Temple Place - Suite 330, |
| * Boston, MA 02111-1307, USA. |
| */ |
| |
| #include <math.h> |
| #include "FLAC/assert.h" |
| #include "FLAC/format.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, unsigned bits_per_sample, 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(bits_per_sample > 0); |
| FLAC__ASSERT(bits_per_sample <= sizeof(FLAC__int32)*8); |
| FLAC__ASSERT(precision > 0); |
| FLAC__ASSERT(precision >= FLAC__MIN_QLP_COEFF_PRECISION); |
| FLAC__ASSERT(precision + bits_per_sample < sizeof(FLAC__int32)*8); |
| #ifdef NDEBUG |
| (void)bits_per_sample; /* silence compiler warning about unused parameter */ |
| #endif |
| |
| /* 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) { |
| 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 || defined __MINGW32__ /* don't know how to do 64-bit literals in VC++ */ |
| if(sumo < 0) sumo = -sumo; |
| if(sumo > 2147483647) |
| #else |
| if(sumo > 2147483647ll || sumo < -2147483648ll) |
| #endif |
| { |
| 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 |
| } |
| *(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_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 || defined __MINGW32__ /* don't know how to do 64-bit literals in VC++ */ |
| if(sumo < 0) sumo = -sumo; |
| if(sumo > 2147483647) |
| #else |
| if(sumo > 2147483647ll || sumo < -2147483648ll) |
| #endif |
| { |
| 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 |
| } |
| *(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); |
| } |
| */ |
| } |
| |
| 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 */ |
| } |