src/libFLAC/lpc.c

   1 /* libFLAC - Free Lossless Audio Codec library
   2  * Copyright (C) 2000,2001,2002,2003  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/bitmath.h"
  24 #include "private/lpc.h"
  25 #if defined DEBUG || defined FLAC__OVERFLOW_DETECT || defined FLAC__OVERFLOW_DETECT_VERBOSE
  26 #include <stdio.h>
  27 #endif
  28
  29 #ifndef M_LN2
  30 /* math.h in VC++ doesn't seem to have this (how Microsoft is that?) */
  31 #define M_LN2 0.69314718055994530942
  32 #endif
  33
  34 void FLAC__lpc_compute_autocorrelation(const FLAC__real data[], unsigned data_len, unsigned lag, FLAC__real autoc[])
  35 {
  36         /* a readable, but slower, version */
  37 #if 0
  38         FLAC__real d;
  39         unsigned i;
  40
  41         FLAC__ASSERT(lag > 0);
  42         FLAC__ASSERT(lag <= data_len);
  43
  44         while(lag--) {
  45                 for(i = lag, d = 0.0; i < data_len; i++)
  46                         d += data[i] * data[i - lag];
  47                 autoc[lag] = d;
  48         }
  49 #endif
  50
  51         /*
  52          * this version tends to run faster because of better data locality
  53          * ('data_len' is usually much larger than 'lag')
  54          */
  55         FLAC__real d;
  56         unsigned sample, coeff;
  57         const unsigned limit = data_len - lag;
  58
  59         FLAC__ASSERT(lag > 0);
  60         FLAC__ASSERT(lag <= data_len);
  61
  62         for(coeff = 0; coeff < lag; coeff++)
  63                 autoc[coeff] = 0.0;
  64         for(sample = 0; sample <= limit; sample++) {
  65                 d = data[sample];
  66                 for(coeff = 0; coeff < lag; coeff++)
  67                         autoc[coeff] += d * data[sample+coeff];
  68         }
  69         for(; sample < data_len; sample++) {
  70                 d = data[sample];
  71                 for(coeff = 0; coeff < data_len - sample; coeff++)
  72                         autoc[coeff] += d * data[sample+coeff];
  73         }
  74 }
  75
  76 void FLAC__lpc_compute_lp_coefficients(const FLAC__real autoc[], unsigned max_order, FLAC__real lp_coeff[][FLAC__MAX_LPC_ORDER], FLAC__real error[])
  77 {
  78         unsigned i, j;
  79         double r, err, ref[FLAC__MAX_LPC_ORDER], lpc[FLAC__MAX_LPC_ORDER];
  80
  81         FLAC__ASSERT(0 < max_order);
  82         FLAC__ASSERT(max_order <= FLAC__MAX_LPC_ORDER);
  83         FLAC__ASSERT(autoc[0] != 0.0);
  84
  85         err = autoc[0];
  86
  87         for(i = 0; i < max_order; i++) {
  88                 /* Sum up this iteration's reflection coefficient. */
  89                 r = -autoc[i+1];
  90                 for(j = 0; j < i; j++)
  91                         r -= lpc[j] * autoc[i-j];
  92                 ref[i] = (r/=err);
  93
  94                 /* Update LPC coefficients and total error. */
  95                 lpc[i]=r;
  96                 for(j = 0; j < (i>>1); j++) {
  97                         double tmp = lpc[j];
  98                         lpc[j] += r * lpc[i-1-j];
  99                         lpc[i-1-j] += r * tmp;
 100                 }
 101                 if(i & 1)
 102                         lpc[j] += lpc[j] * r;
 103
 104                 err *= (1.0 - r * r);
 105
 106                 /* save this order */
 107                 for(j = 0; j <= i; j++)
 108                         lp_coeff[i][j] = (FLAC__real)(-lpc[j]); /* negate FIR filter coeff to get predictor coeff */
 109                 error[i] = (FLAC__real)err;
 110         }
 111 }
 112
 113 int FLAC__lpc_quantize_coefficients(const FLAC__real lp_coeff[], unsigned order, unsigned precision, FLAC__int32 qlp_coeff[], int *shift)
 114 {
 115         unsigned i;
 116         double d, cmax = -1e32;
 117         FLAC__int32 qmax, qmin;
 118         const int max_shiftlimit = (1 << (FLAC__SUBFRAME_LPC_QLP_SHIFT_LEN-1)) - 1;
 119         const int min_shiftlimit = -max_shiftlimit - 1;
 120
 121         FLAC__ASSERT(precision > 0);
 122         FLAC__ASSERT(precision >= FLAC__MIN_QLP_COEFF_PRECISION);
 123
 124         /* drop one bit for the sign; from here on out we consider only |lp_coeff[i]| */
 125         precision--;
 126         qmax = 1 << precision;
 127         qmin = -qmax;
 128         qmax--;
 129
 130         for(i = 0; i < order; i++) {
 131                 if(lp_coeff[i] == 0.0)
 132                         continue;
 133                 d = fabs(lp_coeff[i]);
 134                 if(d > cmax)
 135                         cmax = d;
 136         }
 137 redo_it:
 138         if(cmax <= 0.0) {
 139                 /* => coefficients are all 0, which means our constant-detect didn't work */
 140                 return 2;
 141         }
 142         else {
 143                 int log2cmax;
 144
 145                 (void)frexp(cmax, &log2cmax);
 146                 log2cmax--;
 147                 *shift = (int)precision - log2cmax - 1;
 148
 149                 if(*shift < min_shiftlimit || *shift > max_shiftlimit) {
 150 #if 0
 151                         /*@@@ this does not seem to help at all, but was not extensively tested either: */
 152                         if(*shift > max_shiftlimit)
 153                                 *shift = max_shiftlimit;
 154                         else
 155 #endif
 156                                 return 1;
 157                 }
 158         }
 159
 160         if(*shift >= 0) {
 161                 for(i = 0; i < order; i++) {
 162                         qlp_coeff[i] = (FLAC__int32)floor((double)lp_coeff[i] * (double)(1 << *shift));
 163
 164                         /* double-check the result */
 165                         if(qlp_coeff[i] > qmax || qlp_coeff[i] < qmin) {
 166 #ifdef FLAC__OVERFLOW_DETECT
 167                                 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)));
 168 #endif
 169                                 cmax *= 2.0;
 170                                 goto redo_it;
 171                         }
 172                 }
 173         }
 174         else { /* (*shift < 0) */
 175                 const int nshift = -(*shift);
 176 #ifdef DEBUG
 177                 fprintf(stderr,"FLAC__lpc_quantize_coefficients: negative shift = %d\n", *shift);
 178 #endif
 179                 for(i = 0; i < order; i++) {
 180                         qlp_coeff[i] = (FLAC__int32)floor((double)lp_coeff[i] / (double)(1 << nshift));
 181
 182                         /* double-check the result */
 183                         if(qlp_coeff[i] > qmax || qlp_coeff[i] < qmin) {
 184 #ifdef FLAC__OVERFLOW_DETECT
 185                                 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)));
 186 #endif
 187                                 cmax *= 2.0;
 188                                 goto redo_it;
 189                         }
 190                 }
 191         }
 192
 193         return 0;
 194 }
 195
 196 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[])
 197 {
 198 #ifdef FLAC__OVERFLOW_DETECT
 199         FLAC__int64 sumo;
 200 #endif
 201         unsigned i, j;
 202         FLAC__int32 sum;
 203         const FLAC__int32 *history;
 204
 205 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 206         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 207         for(i=0;i<order;i++)
 208                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 209         fprintf(stderr,"\n");
 210 #endif
 211         FLAC__ASSERT(order > 0);
 212
 213         for(i = 0; i < data_len; i++) {
 214 #ifdef FLAC__OVERFLOW_DETECT
 215                 sumo = 0;
 216 #endif
 217                 sum = 0;
 218                 history = data;
 219                 for(j = 0; j < order; j++) {
 220                         sum += qlp_coeff[j] * (*(--history));
 221 #ifdef FLAC__OVERFLOW_DETECT
 222                         sumo += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*history);
 223 #if defined _MSC_VER
 224                         if(sumo > 2147483647I64 || sumo < -2147483648I64)
 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_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[])
 247 {
 248         unsigned i, j;
 249         FLAC__int64 sum;
 250         const FLAC__int32 *history;
 251
 252 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 253         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 254         for(i=0;i<order;i++)
 255                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 256         fprintf(stderr,"\n");
 257 #endif
 258         FLAC__ASSERT(order > 0);
 259
 260         for(i = 0; i < data_len; i++) {
 261                 sum = 0;
 262                 history = data;
 263                 for(j = 0; j < order; j++)
 264                         sum += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*(--history));
 265 #ifdef FLAC__OVERFLOW_DETECT
 266                 if(FLAC__bitmath_silog2_wide(sum >> lp_quantization) > 32) {
 267                         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: OVERFLOW, i=%u, sum=%lld\n", i, sum >> lp_quantization);
 268                         break;
 269                 }
 270                 if(FLAC__bitmath_silog2_wide((FLAC__int64)(*data) - (sum >> lp_quantization)) > 32) {
 271                         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));
 272                         break;
 273                 }
 274 #endif
 275                 *(residual++) = *(data++) - (FLAC__int32)(sum >> lp_quantization);
 276         }
 277 }
 278
 279 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[])
 280 {
 281 #ifdef FLAC__OVERFLOW_DETECT
 282         FLAC__int64 sumo;
 283 #endif
 284         unsigned i, j;
 285         FLAC__int32 sum;
 286         const FLAC__int32 *history;
 287
 288 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 289         fprintf(stderr,"FLAC__lpc_restore_signal: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 290         for(i=0;i<order;i++)
 291                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 292         fprintf(stderr,"\n");
 293 #endif
 294         FLAC__ASSERT(order > 0);
 295
 296         for(i = 0; i < data_len; i++) {
 297 #ifdef FLAC__OVERFLOW_DETECT
 298                 sumo = 0;
 299 #endif
 300                 sum = 0;
 301                 history = data;
 302                 for(j = 0; j < order; j++) {
 303                         sum += qlp_coeff[j] * (*(--history));
 304 #ifdef FLAC__OVERFLOW_DETECT
 305                         sumo += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*history);
 306 #if defined _MSC_VER
 307                         if(sumo > 2147483647I64 || sumo < -2147483648I64)
 308 #else
 309                         if(sumo > 2147483647ll || sumo < -2147483648ll)
 310 #endif
 311                         {
 312                                 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);
 313                         }
 314 #endif
 315                 }
 316                 *(data++) = *(residual++) + (sum >> lp_quantization);
 317         }
 318
 319         /* Here's a slower but clearer version:
 320         for(i = 0; i < data_len; i++) {
 321                 sum = 0;
 322                 for(j = 0; j < order; j++)
 323                         sum += qlp_coeff[j] * data[i-j-1];
 324                 data[i] = residual[i] + (sum >> lp_quantization);
 325         }
 326         */
 327 }
 328
 329 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[])
 330 {
 331         unsigned i, j;
 332         FLAC__int64 sum;
 333         const FLAC__int32 *history;
 334
 335 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 336         fprintf(stderr,"FLAC__lpc_restore_signal_wide: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 337         for(i=0;i<order;i++)
 338                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 339         fprintf(stderr,"\n");
 340 #endif
 341         FLAC__ASSERT(order > 0);
 342
 343         for(i = 0; i < data_len; i++) {
 344                 sum = 0;
 345                 history = data;
 346                 for(j = 0; j < order; j++)
 347                         sum += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*(--history));
 348 #ifdef FLAC__OVERFLOW_DETECT
 349                 if(FLAC__bitmath_silog2_wide(sum >> lp_quantization) > 32) {
 350                         fprintf(stderr,"FLAC__lpc_restore_signal_wide: OVERFLOW, i=%u, sum=%lld\n", i, sum >> lp_quantization);
 351                         break;
 352                 }
 353                 if(FLAC__bitmath_silog2_wide((FLAC__int64)(*residual) + (sum >> lp_quantization)) > 32) {
 354                         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));
 355                         break;
 356                 }
 357 #endif
 358                 *(data++) = *(residual++) + (FLAC__int32)(sum >> lp_quantization);
 359         }
 360 }
 361
 362 FLAC__real FLAC__lpc_compute_expected_bits_per_residual_sample(FLAC__real lpc_error, unsigned total_samples)
 363 {
 364         double error_scale;
 365
 366         FLAC__ASSERT(total_samples > 0);
 367
 368         error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__real)total_samples;
 369
 370         return FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error, error_scale);
 371 }
 372
 373 FLAC__real FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(FLAC__real lpc_error, double error_scale)
 374 {
 375         if(lpc_error > 0.0) {
 376                 FLAC__real bps = (FLAC__real)((double)0.5 * log(error_scale * lpc_error) / M_LN2);
 377                 if(bps >= 0.0)
 378                         return bps;
 379                 else
 380                         return 0.0;
 381         }
 382         else if(lpc_error < 0.0) { /* error should not be negative but can happen due to inadequate float resolution */
 383                 return (FLAC__real)1e32;
 384         }
 385         else {
 386                 return 0.0;
 387         }
 388 }
 389
 390 unsigned FLAC__lpc_compute_best_order(const FLAC__real lpc_error[], unsigned max_order, unsigned total_samples, unsigned bits_per_signal_sample)
 391 {
 392         unsigned order, best_order;
 393         FLAC__real best_bits, tmp_bits;
 394         double error_scale;
 395
 396         FLAC__ASSERT(max_order > 0);
 397         FLAC__ASSERT(total_samples > 0);
 398
 399         error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__real)total_samples;
 400
 401         best_order = 0;
 402         best_bits = FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error[0], error_scale) * (FLAC__real)total_samples;
 403
 404         for(order = 1; order < max_order; order++) {
 405                 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);
 406                 if(tmp_bits < best_bits) {
 407                         best_order = order;
 408                         best_bits = tmp_bits;
 409                 }
 410         }
 411
 412         return best_order+1; /* +1 since index of lpc_error[] is order-1 */
 413 }