src/libFLAC/lpc.c

   1 /* libFLAC - Free Lossless Audio Codec library
   2  * Copyright (C) 2000,2001,2002  Josh Coalson
   3  *
   4  * This library is free software; you can redistribute it and/or
   5  * modify it under the terms of the GNU Library General Public
   6  * License as published by the Free Software Foundation; either
   7  * version 2 of the License, or (at your option) any later version.
   8  *
   9  * This library is distributed in the hope that it will be useful,
  10  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  11  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  12  * Library General Public License for more details.
  13  *
  14  * You should have received a copy of the GNU Library General Public
  15  * License along with this library; if not, write to the
  16  * Free Software Foundation, Inc., 59 Temple Place - Suite 330,
  17  * Boston, MA  02111-1307, USA.
  18  */
  19
  20 #include <math.h>
  21 #include "FLAC/assert.h"
  22 #include "FLAC/format.h"
  23 #include "private/lpc.h"
  24 #if defined DEBUG || defined FLAC__OVERFLOW_DETECT || defined FLAC__OVERFLOW_DETECT_VERBOSE
  25 #include <stdio.h>
  26 #endif
  27
  28 #ifndef M_LN2
  29 /* math.h in VC++ doesn't seem to have this (how Microsoft is that?) */
  30 #define M_LN2 0.69314718055994530942
  31 #endif
  32
  33 void FLAC__lpc_compute_autocorrelation(const FLAC__real data[], unsigned data_len, unsigned lag, FLAC__real autoc[])
  34 {
  35         /* a readable, but slower, version */
  36 #if 0
  37         FLAC__real d;
  38         unsigned i;
  39
  40         FLAC__ASSERT(lag > 0);
  41         FLAC__ASSERT(lag <= data_len);
  42
  43         while(lag--) {
  44                 for(i = lag, d = 0.0; i < data_len; i++)
  45                         d += data[i] * data[i - lag];
  46                 autoc[lag] = d;
  47         }
  48 #endif
  49
  50         /*
  51          * this version tends to run faster because of better data locality
  52          * ('data_len' is usually much larger than 'lag')
  53          */
  54         FLAC__real d;
  55         unsigned sample, coeff;
  56         const unsigned limit = data_len - lag;
  57
  58         FLAC__ASSERT(lag > 0);
  59         FLAC__ASSERT(lag <= data_len);
  60
  61         for(coeff = 0; coeff < lag; coeff++)
  62                 autoc[coeff] = 0.0;
  63         for(sample = 0; sample <= limit; sample++) {
  64                 d = data[sample];
  65                 for(coeff = 0; coeff < lag; coeff++)
  66                         autoc[coeff] += d * data[sample+coeff];
  67         }
  68         for(; sample < data_len; sample++) {
  69                 d = data[sample];
  70                 for(coeff = 0; coeff < data_len - sample; coeff++)
  71                         autoc[coeff] += d * data[sample+coeff];
  72         }
  73 }
  74
  75 void FLAC__lpc_compute_lp_coefficients(const FLAC__real autoc[], unsigned max_order, FLAC__real lp_coeff[][FLAC__MAX_LPC_ORDER], FLAC__real error[])
  76 {
  77         unsigned i, j;
  78         double r, err, ref[FLAC__MAX_LPC_ORDER], lpc[FLAC__MAX_LPC_ORDER];
  79
  80         FLAC__ASSERT(0 < max_order);
  81         FLAC__ASSERT(max_order <= FLAC__MAX_LPC_ORDER);
  82         FLAC__ASSERT(autoc[0] != 0.0);
  83
  84         err = autoc[0];
  85
  86         for(i = 0; i < max_order; i++) {
  87                 /* Sum up this iteration's reflection coefficient. */
  88                 r = -autoc[i+1];
  89                 for(j = 0; j < i; j++)
  90                         r -= lpc[j] * autoc[i-j];
  91                 ref[i] = (r/=err);
  92
  93                 /* Update LPC coefficients and total error. */
  94                 lpc[i]=r;
  95                 for(j = 0; j < (i>>1); j++) {
  96                         double tmp = lpc[j];
  97                         lpc[j] += r * lpc[i-1-j];
  98                         lpc[i-1-j] += r * tmp;
  99                 }
 100                 if(i & 1)
 101                         lpc[j] += lpc[j] * r;
 102
 103                 err *= (1.0 - r * r);
 104
 105                 /* save this order */
 106                 for(j = 0; j <= i; j++)
 107                         lp_coeff[i][j] = (FLAC__real)(-lpc[j]); /* negate FIR filter coeff to get predictor coeff */
 108                 error[i] = (FLAC__real)err;
 109         }
 110 }
 111
 112 int FLAC__lpc_quantize_coefficients(const FLAC__real lp_coeff[], unsigned order, unsigned precision, unsigned bits_per_sample, FLAC__int32 qlp_coeff[], int *shift)
 113 {
 114         unsigned i;
 115         double d, cmax = -1e32;
 116         FLAC__int32 qmax, qmin;
 117         const int max_shiftlimit = (1 << (FLAC__SUBFRAME_LPC_QLP_SHIFT_LEN-1)) - 1;
 118         const int min_shiftlimit = -max_shiftlimit - 1;
 119
 120         FLAC__ASSERT(bits_per_sample > 0);
 121         FLAC__ASSERT(bits_per_sample <= sizeof(FLAC__int32)*8);
 122         FLAC__ASSERT(precision > 0);
 123         FLAC__ASSERT(precision >= FLAC__MIN_QLP_COEFF_PRECISION);
 124         FLAC__ASSERT(precision + bits_per_sample < sizeof(FLAC__int32)*8);
 125 #ifdef NDEBUG
 126         (void)bits_per_sample; /* silence compiler warning about unused parameter */
 127 #endif
 128
 129         /* drop one bit for the sign; from here on out we consider only |lp_coeff[i]| */
 130         precision--;
 131         qmax = 1 << precision;
 132         qmin = -qmax;
 133         qmax--;
 134
 135         for(i = 0; i < order; i++) {
 136                 if(lp_coeff[i] == 0.0)
 137                         continue;
 138                 d = fabs(lp_coeff[i]);
 139                 if(d > cmax)
 140                         cmax = d;
 141         }
 142 redo_it:
 143         if(cmax <= 0.0) {
 144                 /* => coefficients are all 0, which means our constant-detect didn't work */
 145                 return 2;
 146         }
 147         else {
 148                 int log2cmax;
 149
 150                 (void)frexp(cmax, &log2cmax);
 151                 log2cmax--;
 152                 *shift = (int)precision - log2cmax - 1;
 153
 154                 if(*shift < min_shiftlimit || *shift > max_shiftlimit) {
 155                         return 1;
 156                 }
 157         }
 158
 159         if(*shift >= 0) {
 160                 for(i = 0; i < order; i++) {
 161                         qlp_coeff[i] = (FLAC__int32)floor((double)lp_coeff[i] * (double)(1 << *shift));
 162
 163                         /* double-check the result */
 164                         if(qlp_coeff[i] > qmax || qlp_coeff[i] < qmin) {
 165 #ifdef FLAC__OVERFLOW_DETECT
 166                                 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)));
 167 #endif
 168                                 cmax *= 2.0;
 169                                 goto redo_it;
 170                         }
 171                 }
 172         }
 173         else { /* (*shift < 0) */
 174                 const int nshift = -(*shift);
 175 #ifdef DEBUG
 176                 fprintf(stderr,"FLAC__lpc_quantize_coefficients: negative shift = %d\n", *shift);
 177 #endif
 178                 for(i = 0; i < order; i++) {
 179                         qlp_coeff[i] = (FLAC__int32)floor((double)lp_coeff[i] / (double)(1 << nshift));
 180
 181                         /* double-check the result */
 182                         if(qlp_coeff[i] > qmax || qlp_coeff[i] < qmin) {
 183 #ifdef FLAC__OVERFLOW_DETECT
 184                                 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)));
 185 #endif
 186                                 cmax *= 2.0;
 187                                 goto redo_it;
 188                         }
 189                 }
 190         }
 191
 192         return 0;
 193 }
 194
 195 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[])
 196 {
 197 #ifdef FLAC__OVERFLOW_DETECT
 198         FLAC__int64 sumo;
 199 #endif
 200         unsigned i, j;
 201         FLAC__int32 sum;
 202         const FLAC__int32 *history;
 203
 204 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 205         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 206         for(i=0;i<order;i++)
 207                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 208         fprintf(stderr,"\n");
 209 #endif
 210         FLAC__ASSERT(order > 0);
 211
 212         for(i = 0; i < data_len; i++) {
 213 #ifdef FLAC__OVERFLOW_DETECT
 214                 sumo = 0;
 215 #endif
 216                 sum = 0;
 217                 history = data;
 218                 for(j = 0; j < order; j++) {
 219                         sum += qlp_coeff[j] * (*(--history));
 220 #ifdef FLAC__OVERFLOW_DETECT
 221                         sumo += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*history);
 222 #if defined _MSC_VER || defined __MINGW32__ /* don't know how to do 64-bit literals in VC++ */
 223                         if(sumo < 0) sumo = -sumo;
 224                         if(sumo > 2147483647)
 225 #else
 226                         if(sumo > 2147483647ll || sumo < -2147483648ll)
 227 #endif
 228                         {
 229                                 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);
 230                         }
 231 #endif
 232                 }
 233                 *(residual++) = *(data++) - (sum >> lp_quantization);
 234         }
 235
 236         /* Here's a slower but clearer version:
 237         for(i = 0; i < data_len; i++) {
 238                 sum = 0;
 239                 for(j = 0; j < order; j++)
 240                         sum += qlp_coeff[j] * data[i-j-1];
 241                 residual[i] = data[i] - (sum >> lp_quantization);
 242         }
 243         */
 244 }
 245
 246 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[])
 247 {
 248 #ifdef FLAC__OVERFLOW_DETECT
 249         FLAC__int64 sumo;
 250 #endif
 251         unsigned i, j;
 252         FLAC__int32 sum;
 253         const FLAC__int32 *history;
 254
 255 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 256         fprintf(stderr,"FLAC__lpc_restore_signal: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 257         for(i=0;i<order;i++)
 258                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 259         fprintf(stderr,"\n");
 260 #endif
 261         FLAC__ASSERT(order > 0);
 262
 263         for(i = 0; i < data_len; i++) {
 264 #ifdef FLAC__OVERFLOW_DETECT
 265                 sumo = 0;
 266 #endif
 267                 sum = 0;
 268                 history = data;
 269                 for(j = 0; j < order; j++) {
 270                         sum += qlp_coeff[j] * (*(--history));
 271 #ifdef FLAC__OVERFLOW_DETECT
 272                         sumo += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*history);
 273 #if defined _MSC_VER || defined __MINGW32__ /* don't know how to do 64-bit literals in VC++ */
 274                         if(sumo < 0) sumo = -sumo;
 275                         if(sumo > 2147483647)
 276 #else
 277                         if(sumo > 2147483647ll || sumo < -2147483648ll)
 278 #endif
 279                         {
 280                                 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);
 281                         }
 282 #endif
 283                 }
 284                 *(data++) = *(residual++) + (sum >> lp_quantization);
 285         }
 286
 287         /* Here's a slower but clearer version:
 288         for(i = 0; i < data_len; i++) {
 289                 sum = 0;
 290                 for(j = 0; j < order; j++)
 291                         sum += qlp_coeff[j] * data[i-j-1];
 292                 data[i] = residual[i] + (sum >> lp_quantization);
 293         }
 294         */
 295 }
 296
 297 FLAC__real FLAC__lpc_compute_expected_bits_per_residual_sample(FLAC__real lpc_error, unsigned total_samples)
 298 {
 299         double error_scale;
 300
 301         FLAC__ASSERT(total_samples > 0);
 302
 303         error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__real)total_samples;
 304
 305         return FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error, error_scale);
 306 }
 307
 308 FLAC__real FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(FLAC__real lpc_error, double error_scale)
 309 {
 310         if(lpc_error > 0.0) {
 311                 FLAC__real bps = (FLAC__real)((double)0.5 * log(error_scale * lpc_error) / M_LN2);
 312                 if(bps >= 0.0)
 313                         return bps;
 314                 else
 315                         return 0.0;
 316         }
 317         else if(lpc_error < 0.0) { /* error should not be negative but can happen due to inadequate float resolution */
 318                 return (FLAC__real)1e32;
 319         }
 320         else {
 321                 return 0.0;
 322         }
 323 }
 324
 325 unsigned FLAC__lpc_compute_best_order(const FLAC__real lpc_error[], unsigned max_order, unsigned total_samples, unsigned bits_per_signal_sample)
 326 {
 327         unsigned order, best_order;
 328         FLAC__real best_bits, tmp_bits;
 329         double error_scale;
 330
 331         FLAC__ASSERT(max_order > 0);
 332         FLAC__ASSERT(total_samples > 0);
 333
 334         error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__real)total_samples;
 335
 336         best_order = 0;
 337         best_bits = FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error[0], error_scale) * (FLAC__real)total_samples;
 338
 339         for(order = 1; order < max_order; order++) {
 340                 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);
 341                 if(tmp_bits < best_bits) {
 342                         best_order = order;
 343                         best_bits = tmp_bits;
 344                 }
 345         }
 346
 347         return best_order+1; /* +1 since index of lpc_error[] is order-1 */
 348 }