src/libFLAC/lpc.c

   1 /* libFLAC - Free Lossless Audio Codec library
   2  * Copyright (C) 2000,2001,2002,2003,2004,2005,2006,2007  Josh Coalson
   3  *
   4  * Redistribution and use in source and binary forms, with or without
   5  * modification, are permitted provided that the following conditions
   6  * are met:
   7  *
   8  * - Redistributions of source code must retain the above copyright
   9  * notice, this list of conditions and the following disclaimer.
  10  *
  11  * - Redistributions in binary form must reproduce the above copyright
  12  * notice, this list of conditions and the following disclaimer in the
  13  * documentation and/or other materials provided with the distribution.
  14  *
  15  * - Neither the name of the Xiph.org Foundation nor the names of its
  16  * contributors may be used to endorse or promote products derived from
  17  * this software without specific prior written permission.
  18  *
  19  * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
  20  * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
  21  * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
  22  * A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR
  23  * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
  24  * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
  25  * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
  26  * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
  27  * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
  28  * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
  29  * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  30  */
  31
  32 #if HAVE_CONFIG_H
  33 #  include <config.h>
  34 #endif
  35
  36 #include <math.h>
  37 #include "FLAC/assert.h"
  38 #include "FLAC/format.h"
  39 #include "private/bitmath.h"
  40 #include "private/lpc.h"
  41 #if defined DEBUG || defined FLAC__OVERFLOW_DETECT || defined FLAC__OVERFLOW_DETECT_VERBOSE
  42 #include <stdio.h>
  43 #endif
  44
  45 #ifndef FLAC__INTEGER_ONLY_LIBRARY
  46
  47 #ifndef M_LN2
  48 /* math.h in VC++ doesn't seem to have this (how Microsoft is that?) */
  49 #define M_LN2 0.69314718055994530942
  50 #endif
  51
  52 void FLAC__lpc_window_data(const FLAC__real in[], const FLAC__real window[], FLAC__real out[], unsigned data_len)
  53 {
  54         unsigned i;
  55         for(i = 0; i < data_len; i++)
  56                 out[i] = in[i] * window[i];
  57 }
  58
  59 void FLAC__lpc_compute_autocorrelation(const FLAC__real data[], unsigned data_len, unsigned lag, FLAC__real autoc[])
  60 {
  61         /* a readable, but slower, version */
  62 #if 0
  63         FLAC__real d;
  64         unsigned i;
  65
  66         FLAC__ASSERT(lag > 0);
  67         FLAC__ASSERT(lag <= data_len);
  68
  69         /*
  70          * Technically we should subtract the mean first like so:
  71          *   for(i = 0; i < data_len; i++)
  72          *     data[i] -= mean;
  73          * but it appears not to make enough of a difference to matter, and
  74          * most signals are already closely centered around zero
  75          */
  76         while(lag--) {
  77                 for(i = lag, d = 0.0; i < data_len; i++)
  78                         d += data[i] * data[i - lag];
  79                 autoc[lag] = d;
  80         }
  81 #endif
  82
  83         /*
  84          * this version tends to run faster because of better data locality
  85          * ('data_len' is usually much larger than 'lag')
  86          */
  87         FLAC__real d;
  88         unsigned sample, coeff;
  89         const unsigned limit = data_len - lag;
  90
  91         FLAC__ASSERT(lag > 0);
  92         FLAC__ASSERT(lag <= data_len);
  93
  94         for(coeff = 0; coeff < lag; coeff++)
  95                 autoc[coeff] = 0.0;
  96         for(sample = 0; sample <= limit; sample++) {
  97                 d = data[sample];
  98                 for(coeff = 0; coeff < lag; coeff++)
  99                         autoc[coeff] += d * data[sample+coeff];
 100         }
 101         for(; sample < data_len; sample++) {
 102                 d = data[sample];
 103                 for(coeff = 0; coeff < data_len - sample; coeff++)
 104                         autoc[coeff] += d * data[sample+coeff];
 105         }
 106 }
 107
 108 void FLAC__lpc_compute_lp_coefficients(const FLAC__real autoc[], unsigned *max_order, FLAC__real lp_coeff[][FLAC__MAX_LPC_ORDER], FLAC__double error[])
 109 {
 110         unsigned i, j;
 111         FLAC__double r, err, ref[FLAC__MAX_LPC_ORDER], lpc[FLAC__MAX_LPC_ORDER];
 112
 113         FLAC__ASSERT(0 != max_order);
 114         FLAC__ASSERT(0 < *max_order);
 115         FLAC__ASSERT(*max_order <= FLAC__MAX_LPC_ORDER);
 116         FLAC__ASSERT(autoc[0] != 0.0);
 117
 118         err = autoc[0];
 119
 120         for(i = 0; i < *max_order; i++) {
 121                 /* Sum up this iteration's reflection coefficient. */
 122                 r = -autoc[i+1];
 123                 for(j = 0; j < i; j++)
 124                         r -= lpc[j] * autoc[i-j];
 125                 ref[i] = (r/=err);
 126
 127                 /* Update LPC coefficients and total error. */
 128                 lpc[i]=r;
 129                 for(j = 0; j < (i>>1); j++) {
 130                         FLAC__double tmp = lpc[j];
 131                         lpc[j] += r * lpc[i-1-j];
 132                         lpc[i-1-j] += r * tmp;
 133                 }
 134                 if(i & 1)
 135                         lpc[j] += lpc[j] * r;
 136
 137                 err *= (1.0 - r * r);
 138
 139                 /* save this order */
 140                 for(j = 0; j <= i; j++)
 141                         lp_coeff[i][j] = (FLAC__real)(-lpc[j]); /* negate FIR filter coeff to get predictor coeff */
 142                 error[i] = err;
 143
 144                 /* see SF bug #1601812 http://sourceforge.net/tracker/index.php?func=detail&aid=1601812&group_id=13478&atid=113478 */
 145                 if(err == 0.0) {
 146                         *max_order = i+1;
 147                         return;
 148                 }
 149         }
 150 }
 151
 152 int FLAC__lpc_quantize_coefficients(const FLAC__real lp_coeff[], unsigned order, unsigned precision, FLAC__int32 qlp_coeff[], int *shift)
 153 {
 154         unsigned i;
 155         FLAC__double cmax;
 156         FLAC__int32 qmax, qmin;
 157
 158         FLAC__ASSERT(precision > 0);
 159         FLAC__ASSERT(precision >= FLAC__MIN_QLP_COEFF_PRECISION);
 160
 161         /* drop one bit for the sign; from here on out we consider only |lp_coeff[i]| */
 162         precision--;
 163         qmax = 1 << precision;
 164         qmin = -qmax;
 165         qmax--;
 166
 167         /* calc cmax = max( |lp_coeff[i]| ) */
 168         cmax = 0.0;
 169         for(i = 0; i < order; i++) {
 170                 const FLAC__double d = fabs(lp_coeff[i]);
 171                 if(d > cmax)
 172                         cmax = d;
 173         }
 174
 175         if(cmax <= 0.0) {
 176                 /* => coefficients are all 0, which means our constant-detect didn't work */
 177                 return 2;
 178         }
 179         else {
 180                 const int max_shiftlimit = (1 << (FLAC__SUBFRAME_LPC_QLP_SHIFT_LEN-1)) - 1;
 181                 const int min_shiftlimit = -max_shiftlimit - 1;
 182                 int log2cmax;
 183
 184                 (void)frexp(cmax, &log2cmax);
 185                 log2cmax--;
 186                 *shift = (int)precision - log2cmax - 1;
 187
 188                 if(*shift > max_shiftlimit)
 189                         *shift = max_shiftlimit;
 190                 else if(*shift < min_shiftlimit)
 191                         return 1;
 192         }
 193
 194         if(*shift >= 0) {
 195                 FLAC__double error = 0.0;
 196                 FLAC__int32 q;
 197                 for(i = 0; i < order; i++) {
 198                         error += lp_coeff[i] * (1 << *shift);
 199 #if defined _MSC_VER
 200                         if(error >= 0.0)
 201                                 q = (FLAC__int32)(error + 0.5);
 202                         else
 203                                 q = (FLAC__int32)(error - 0.5);
 204 #else
 205                         q = lround(error); /* round() is also suitable */
 206 #endif
 207 #ifdef FLAC__OVERFLOW_DETECT
 208                         if(q > qmax+1) /* we expect q==qmax+1 occasionally due to lround() */
 209                                 fprintf(stderr,"FLAC__lpc_quantize_coefficients: quantizer overflow: q>qmax %d>%d shift=%d cmax=%f precision=%u lpc[%u]=%f\n",q,qmax,*shift,cmax,precision+1,i,lp_coeff[i]);
 210                         else if(q < qmin)
 211                                 fprintf(stderr,"FLAC__lpc_quantize_coefficients: quantizer overflow: q<qmin %d<%d shift=%d cmax=%f precision=%u lpc[%u]=%f\n",q,qmin,*shift,cmax,precision+1,i,lp_coeff[i]);
 212 #endif
 213                         if(q > qmax)
 214                                 q = qmax;
 215                         else if(q < qmin)
 216                                 q = qmin;
 217                         error -= q;
 218                         qlp_coeff[i] = q;
 219                 }
 220         }
 221         /* negative shift is very rare but due to design flaw, negative shift is
 222          * a NOP in the decoder, so it must be handled specially by scaling down
 223          * coeffs
 224          */
 225         else {
 226                 const int nshift = -(*shift);
 227                 FLAC__double error = 0.0;
 228                 FLAC__int32 q;
 229 #ifdef DEBUG
 230                 fprintf(stderr,"FLAC__lpc_quantize_coefficients: negative shift=%d order=%u cmax=%f\n", *shift, order, cmax);
 231 #endif
 232                 for(i = 0; i < order; i++) {
 233                         error += lp_coeff[i] / (1 << nshift);
 234 #if defined _MSC_VER
 235                         if(error >= 0.0)
 236                                 q = (FLAC__int32)(error + 0.5);
 237                         else
 238                                 q = (FLAC__int32)(error - 0.5);
 239 #else
 240                         q = lround(error); /* round() is also suitable */
 241 #endif
 242 #ifdef FLAC__OVERFLOW_DETECT
 243                         if(q > qmax+1) /* we expect q==qmax+1 occasionally due to lround() */
 244                                 fprintf(stderr,"FLAC__lpc_quantize_coefficients: quantizer overflow: q>qmax %d>%d shift=%d cmax=%f precision=%u lpc[%u]=%f\n",q,qmax,*shift,cmax,precision+1,i,lp_coeff[i]);
 245                         else if(q < qmin)
 246                                 fprintf(stderr,"FLAC__lpc_quantize_coefficients: quantizer overflow: q<qmin %d<%d shift=%d cmax=%f precision=%u lpc[%u]=%f\n",q,qmin,*shift,cmax,precision+1,i,lp_coeff[i]);
 247 #endif
 248                         if(q > qmax)
 249                                 q = qmax;
 250                         else if(q < qmin)
 251                                 q = qmin;
 252                         error -= q;
 253                         qlp_coeff[i] = q;
 254                 }
 255                 *shift = 0;
 256         }
 257
 258         return 0;
 259 }
 260
 261 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[])
 262 {
 263 #ifdef FLAC__OVERFLOW_DETECT
 264         FLAC__int64 sumo;
 265 #endif
 266         unsigned i, j;
 267         FLAC__int32 sum;
 268         const FLAC__int32 *history;
 269
 270 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 271         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 272         for(i=0;i<order;i++)
 273                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 274         fprintf(stderr,"\n");
 275 #endif
 276         FLAC__ASSERT(order > 0);
 277
 278         for(i = 0; i < data_len; i++) {
 279 #ifdef FLAC__OVERFLOW_DETECT
 280                 sumo = 0;
 281 #endif
 282                 sum = 0;
 283                 history = data;
 284                 for(j = 0; j < order; j++) {
 285                         sum += qlp_coeff[j] * (*(--history));
 286 #ifdef FLAC__OVERFLOW_DETECT
 287                         sumo += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*history);
 288 #if defined _MSC_VER
 289                         if(sumo > 2147483647I64 || sumo < -2147483648I64)
 290                                 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);
 291 #else
 292                         if(sumo > 2147483647ll || sumo < -2147483648ll)
 293                                 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,(long long)sumo);
 294 #endif
 295 #endif
 296                 }
 297                 *(residual++) = *(data++) - (sum >> lp_quantization);
 298         }
 299
 300         /* Here's a slower but clearer version:
 301         for(i = 0; i < data_len; i++) {
 302                 sum = 0;
 303                 for(j = 0; j < order; j++)
 304                         sum += qlp_coeff[j] * data[i-j-1];
 305                 residual[i] = data[i] - (sum >> lp_quantization);
 306         }
 307         */
 308 }
 309
 310 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[])
 311 {
 312         unsigned i, j;
 313         FLAC__int64 sum;
 314         const FLAC__int32 *history;
 315
 316 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 317         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 318         for(i=0;i<order;i++)
 319                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 320         fprintf(stderr,"\n");
 321 #endif
 322         FLAC__ASSERT(order > 0);
 323
 324         for(i = 0; i < data_len; i++) {
 325                 sum = 0;
 326                 history = data;
 327                 for(j = 0; j < order; j++)
 328                         sum += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*(--history));
 329 #ifdef FLAC__OVERFLOW_DETECT
 330                 if(FLAC__bitmath_silog2_wide(sum >> lp_quantization) > 32) {
 331                         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: OVERFLOW, i=%u, sum=%lld\n", i, (long long)(sum >> lp_quantization));
 332                         break;
 333                 }
 334                 if(FLAC__bitmath_silog2_wide((FLAC__int64)(*data) - (sum >> lp_quantization)) > 32) {
 335                         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: OVERFLOW, i=%u, data=%d, sum=%lld, residual=%lld\n", i, *data, (long long)(sum >> lp_quantization), (long long)((FLAC__int64)(*data) - (sum >> lp_quantization)));
 336                         break;
 337                 }
 338 #endif
 339                 *(residual++) = *(data++) - (FLAC__int32)(sum >> lp_quantization);
 340         }
 341 }
 342
 343 #endif /* !defined FLAC__INTEGER_ONLY_LIBRARY */
 344
 345 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[])
 346 {
 347 #ifdef FLAC__OVERFLOW_DETECT
 348         FLAC__int64 sumo;
 349 #endif
 350         unsigned i, j;
 351         FLAC__int32 sum;
 352         const FLAC__int32 *r = residual, *history;
 353
 354 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 355         fprintf(stderr,"FLAC__lpc_restore_signal: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 356         for(i=0;i<order;i++)
 357                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 358         fprintf(stderr,"\n");
 359 #endif
 360         FLAC__ASSERT(order > 0);
 361
 362         for(i = 0; i < data_len; i++) {
 363 #ifdef FLAC__OVERFLOW_DETECT
 364                 sumo = 0;
 365 #endif
 366                 sum = 0;
 367                 history = data;
 368                 for(j = 0; j < order; j++) {
 369                         sum += qlp_coeff[j] * (*(--history));
 370 #ifdef FLAC__OVERFLOW_DETECT
 371                         sumo += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*history);
 372 #if defined _MSC_VER
 373                         if(sumo > 2147483647I64 || sumo < -2147483648I64)
 374                                 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);
 375 #else
 376                         if(sumo > 2147483647ll || sumo < -2147483648ll)
 377                                 fprintf(stderr,"FLAC__lpc_restore_signal: OVERFLOW, i=%u, j=%u, c=%d, d=%d, sumo=%lld\n",i,j,qlp_coeff[j],*history,(long long)sumo);
 378 #endif
 379 #endif
 380                 }
 381                 *(data++) = *(r++) + (sum >> lp_quantization);
 382         }
 383
 384         /* Here's a slower but clearer version:
 385         for(i = 0; i < data_len; i++) {
 386                 sum = 0;
 387                 for(j = 0; j < order; j++)
 388                         sum += qlp_coeff[j] * data[i-j-1];
 389                 data[i] = residual[i] + (sum >> lp_quantization);
 390         }
 391         */
 392 }
 393
 394 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[])
 395 {
 396         unsigned i, j;
 397         FLAC__int64 sum;
 398         const FLAC__int32 *r = residual, *history;
 399
 400 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 401         fprintf(stderr,"FLAC__lpc_restore_signal_wide: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 402         for(i=0;i<order;i++)
 403                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 404         fprintf(stderr,"\n");
 405 #endif
 406         FLAC__ASSERT(order > 0);
 407
 408         for(i = 0; i < data_len; i++) {
 409                 sum = 0;
 410                 history = data;
 411                 for(j = 0; j < order; j++)
 412                         sum += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*(--history));
 413 #ifdef FLAC__OVERFLOW_DETECT
 414                 if(FLAC__bitmath_silog2_wide(sum >> lp_quantization) > 32) {
 415                         fprintf(stderr,"FLAC__lpc_restore_signal_wide: OVERFLOW, i=%u, sum=%lld\n", i, (long long)(sum >> lp_quantization));
 416                         break;
 417                 }
 418                 if(FLAC__bitmath_silog2_wide((FLAC__int64)(*r) + (sum >> lp_quantization)) > 32) {
 419                         fprintf(stderr,"FLAC__lpc_restore_signal_wide: OVERFLOW, i=%u, residual=%d, sum=%lld, data=%lld\n", i, *r, (long long)(sum >> lp_quantization), (long long)((FLAC__int64)(*r) + (sum >> lp_quantization)));
 420                         break;
 421                 }
 422 #endif
 423                 *(data++) = *(r++) + (FLAC__int32)(sum >> lp_quantization);
 424         }
 425 }
 426
 427 #ifndef FLAC__INTEGER_ONLY_LIBRARY
 428
 429 FLAC__double FLAC__lpc_compute_expected_bits_per_residual_sample(FLAC__double lpc_error, unsigned total_samples)
 430 {
 431         FLAC__double error_scale;
 432
 433         FLAC__ASSERT(total_samples > 0);
 434
 435         error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__double)total_samples;
 436
 437         return FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error, error_scale);
 438 }
 439
 440 FLAC__double FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(FLAC__double lpc_error, FLAC__double error_scale)
 441 {
 442         if(lpc_error > 0.0) {
 443                 FLAC__double bps = (FLAC__double)0.5 * log(error_scale * lpc_error) / M_LN2;
 444                 if(bps >= 0.0)
 445                         return bps;
 446                 else
 447                         return 0.0;
 448         }
 449         else if(lpc_error < 0.0) { /* error should not be negative but can happen due to inadequate floating-point resolution */
 450                 return 1e32;
 451         }
 452         else {
 453                 return 0.0;
 454         }
 455 }
 456
 457 unsigned FLAC__lpc_compute_best_order(const FLAC__double lpc_error[], unsigned max_order, unsigned total_samples, unsigned overhead_bits_per_order)
 458 {
 459         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 */
 460         FLAC__double bits, best_bits, error_scale;
 461
 462         FLAC__ASSERT(max_order > 0);
 463         FLAC__ASSERT(total_samples > 0);
 464
 465         error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__double)total_samples;
 466
 467         best_index = 0;
 468         best_bits = (unsigned)(-1);
 469
 470         for(index = 0, order = 1; index < max_order; index++, order++) {
 471                 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);
 472                 if(bits < best_bits) {
 473                         best_index = index;
 474                         best_bits = bits;
 475                 }
 476         }
 477
 478         return best_index+1; /* +1 since index of lpc_error[] is order-1 */
 479 }
 480
 481 #endif /* !defined FLAC__INTEGER_ONLY_LIBRARY */