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 < min_shiftlimit || *shift > max_shiftlimit) {
 189 #ifdef FLAC__OVERFLOW_DETECT
 190                         fprintf(stderr,"FLAC__lpc_quantize_coefficients: shift out of limit: shift=%d cmax=%f precision=%u\n",*shift,cmax,precision+1);
 191 #endif
 192 #if 0
 193                         /*@@@ this does not seem to help at all, but was not extensively tested either: */
 194                         if(*shift > max_shiftlimit)
 195                                 *shift = max_shiftlimit;
 196                         else
 197 #endif
 198                                 return 1;
 199                 }
 200         }
 201
 202         if(*shift >= 0) {
 203                 FLAC__double error = 0.0;
 204                 FLAC__int32 q;
 205                 for(i = 0; i < order; i++) {
 206                         error += lp_coeff[i] * (1 << *shift);
 207 #if defined _MSC_VER
 208                         if(error >= 0.0)
 209                                 q = (FLAC__int32)(error + 0.5);
 210                         else
 211                                 q = (FLAC__int32)(error - 0.5);
 212 #else
 213                         q = lround(error); /* round() is also suitable */
 214 #endif
 215 #ifdef FLAC__OVERFLOW_DETECT
 216                         if(q > qmax+1) /* we expect q==qmax+1 occasionally due to lround() */
 217                                 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]);
 218                         else if(q < qmin)
 219                                 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]);
 220 #endif
 221                         if(q > qmax)
 222                                 q = qmax;
 223                         else if(q < qmin)
 224                                 q = qmin;
 225                         error -= q;
 226                         qlp_coeff[i] = q;
 227                 }
 228         }
 229         /* negative shift is very rare but due to design flaw, negative shift is
 230          * a NOP in the decoder, so it must be handled specially by scaling down
 231          * coeffs
 232          */
 233         else {
 234                 const int nshift = -(*shift);
 235                 FLAC__double error = 0.0;
 236                 FLAC__int32 q;
 237 #ifdef DEBUG
 238                 fprintf(stderr,"FLAC__lpc_quantize_coefficients: negative shift=%d order=%u cmax=%f\n", *shift, order, cmax);
 239 #endif
 240                 for(i = 0; i < order; i++) {
 241                         error += lp_coeff[i] / (1 << nshift);
 242 #if defined _MSC_VER
 243                         if(error >= 0.0)
 244                                 q = (FLAC__int32)(error + 0.5);
 245                         else
 246                                 q = (FLAC__int32)(error - 0.5);
 247 #else
 248                         q = lround(error); /* round() is also suitable */
 249 #endif
 250 #ifdef FLAC__OVERFLOW_DETECT
 251                         if(q > qmax+1) /* we expect q==qmax+1 occasionally due to lround() */
 252                                 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]);
 253                         else if(q < qmin)
 254                                 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]);
 255 #endif
 256                         if(q > qmax)
 257                                 q = qmax;
 258                         else if(q < qmin)
 259                                 q = qmin;
 260                         error -= q;
 261                         qlp_coeff[i] = q;
 262                 }
 263                 *shift = 0;
 264         }
 265
 266         return 0;
 267 }
 268
 269 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[])
 270 {
 271 #ifdef FLAC__OVERFLOW_DETECT
 272         FLAC__int64 sumo;
 273 #endif
 274         unsigned i, j;
 275         FLAC__int32 sum;
 276         const FLAC__int32 *history;
 277
 278 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 279         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 280         for(i=0;i<order;i++)
 281                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 282         fprintf(stderr,"\n");
 283 #endif
 284         FLAC__ASSERT(order > 0);
 285
 286         for(i = 0; i < data_len; i++) {
 287 #ifdef FLAC__OVERFLOW_DETECT
 288                 sumo = 0;
 289 #endif
 290                 sum = 0;
 291                 history = data;
 292                 for(j = 0; j < order; j++) {
 293                         sum += qlp_coeff[j] * (*(--history));
 294 #ifdef FLAC__OVERFLOW_DETECT
 295                         sumo += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*history);
 296 #if defined _MSC_VER
 297                         if(sumo > 2147483647I64 || sumo < -2147483648I64)
 298                                 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);
 299 #else
 300                         if(sumo > 2147483647ll || sumo < -2147483648ll)
 301                                 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);
 302 #endif
 303 #endif
 304                 }
 305                 *(residual++) = *(data++) - (sum >> lp_quantization);
 306         }
 307
 308         /* Here's a slower but clearer version:
 309         for(i = 0; i < data_len; i++) {
 310                 sum = 0;
 311                 for(j = 0; j < order; j++)
 312                         sum += qlp_coeff[j] * data[i-j-1];
 313                 residual[i] = data[i] - (sum >> lp_quantization);
 314         }
 315         */
 316 }
 317
 318 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[])
 319 {
 320         unsigned i, j;
 321         FLAC__int64 sum;
 322         const FLAC__int32 *history;
 323
 324 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 325         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 326         for(i=0;i<order;i++)
 327                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 328         fprintf(stderr,"\n");
 329 #endif
 330         FLAC__ASSERT(order > 0);
 331
 332         for(i = 0; i < data_len; i++) {
 333                 sum = 0;
 334                 history = data;
 335                 for(j = 0; j < order; j++)
 336                         sum += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*(--history));
 337 #ifdef FLAC__OVERFLOW_DETECT
 338                 if(FLAC__bitmath_silog2_wide(sum >> lp_quantization) > 32) {
 339                         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: OVERFLOW, i=%u, sum=%lld\n", i, (long long)(sum >> lp_quantization));
 340                         break;
 341                 }
 342                 if(FLAC__bitmath_silog2_wide((FLAC__int64)(*data) - (sum >> lp_quantization)) > 32) {
 343                         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)));
 344                         break;
 345                 }
 346 #endif
 347                 *(residual++) = *(data++) - (FLAC__int32)(sum >> lp_quantization);
 348         }
 349 }
 350
 351 #endif /* !defined FLAC__INTEGER_ONLY_LIBRARY */
 352
 353 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[])
 354 {
 355 #ifdef FLAC__OVERFLOW_DETECT
 356         FLAC__int64 sumo;
 357 #endif
 358         unsigned i, j;
 359         FLAC__int32 sum;
 360         const FLAC__int32 *r = residual, *history;
 361
 362 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 363         fprintf(stderr,"FLAC__lpc_restore_signal: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 364         for(i=0;i<order;i++)
 365                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 366         fprintf(stderr,"\n");
 367 #endif
 368         FLAC__ASSERT(order > 0);
 369
 370         for(i = 0; i < data_len; i++) {
 371 #ifdef FLAC__OVERFLOW_DETECT
 372                 sumo = 0;
 373 #endif
 374                 sum = 0;
 375                 history = data;
 376                 for(j = 0; j < order; j++) {
 377                         sum += qlp_coeff[j] * (*(--history));
 378 #ifdef FLAC__OVERFLOW_DETECT
 379                         sumo += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*history);
 380 #if defined _MSC_VER
 381                         if(sumo > 2147483647I64 || sumo < -2147483648I64)
 382                                 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);
 383 #else
 384                         if(sumo > 2147483647ll || sumo < -2147483648ll)
 385                                 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);
 386 #endif
 387 #endif
 388                 }
 389                 *(data++) = *(r++) + (sum >> lp_quantization);
 390         }
 391
 392         /* Here's a slower but clearer version:
 393         for(i = 0; i < data_len; i++) {
 394                 sum = 0;
 395                 for(j = 0; j < order; j++)
 396                         sum += qlp_coeff[j] * data[i-j-1];
 397                 data[i] = residual[i] + (sum >> lp_quantization);
 398         }
 399         */
 400 }
 401
 402 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[])
 403 {
 404         unsigned i, j;
 405         FLAC__int64 sum;
 406         const FLAC__int32 *r = residual, *history;
 407
 408 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 409         fprintf(stderr,"FLAC__lpc_restore_signal_wide: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 410         for(i=0;i<order;i++)
 411                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 412         fprintf(stderr,"\n");
 413 #endif
 414         FLAC__ASSERT(order > 0);
 415
 416         for(i = 0; i < data_len; i++) {
 417                 sum = 0;
 418                 history = data;
 419                 for(j = 0; j < order; j++)
 420                         sum += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*(--history));
 421 #ifdef FLAC__OVERFLOW_DETECT
 422                 if(FLAC__bitmath_silog2_wide(sum >> lp_quantization) > 32) {
 423                         fprintf(stderr,"FLAC__lpc_restore_signal_wide: OVERFLOW, i=%u, sum=%lld\n", i, (long long)(sum >> lp_quantization));
 424                         break;
 425                 }
 426                 if(FLAC__bitmath_silog2_wide((FLAC__int64)(*r) + (sum >> lp_quantization)) > 32) {
 427                         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)));
 428                         break;
 429                 }
 430 #endif
 431                 *(data++) = *(r++) + (FLAC__int32)(sum >> lp_quantization);
 432         }
 433 }
 434
 435 #ifndef FLAC__INTEGER_ONLY_LIBRARY
 436
 437 FLAC__double FLAC__lpc_compute_expected_bits_per_residual_sample(FLAC__double lpc_error, unsigned total_samples)
 438 {
 439         FLAC__double error_scale;
 440
 441         FLAC__ASSERT(total_samples > 0);
 442
 443         error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__double)total_samples;
 444
 445         return FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error, error_scale);
 446 }
 447
 448 FLAC__double FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(FLAC__double lpc_error, FLAC__double error_scale)
 449 {
 450         if(lpc_error > 0.0) {
 451                 FLAC__double bps = (FLAC__double)0.5 * log(error_scale * lpc_error) / M_LN2;
 452                 if(bps >= 0.0)
 453                         return bps;
 454                 else
 455                         return 0.0;
 456         }
 457         else if(lpc_error < 0.0) { /* error should not be negative but can happen due to inadequate floating-point resolution */
 458                 return 1e32;
 459         }
 460         else {
 461                 return 0.0;
 462         }
 463 }
 464
 465 unsigned FLAC__lpc_compute_best_order(const FLAC__double lpc_error[], unsigned max_order, unsigned total_samples, unsigned overhead_bits_per_order)
 466 {
 467         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 */
 468         FLAC__double bits, best_bits, error_scale;
 469
 470         FLAC__ASSERT(max_order > 0);
 471         FLAC__ASSERT(total_samples > 0);
 472
 473         error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__double)total_samples;
 474
 475         best_index = 0;
 476         best_bits = (unsigned)(-1);
 477
 478         for(index = 0, order = 1; index < max_order; index++, order++) {
 479                 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);
 480                 if(bits < best_bits) {
 481                         best_index = index;
 482                         best_bits = bits;
 483                 }
 484         }
 485
 486         return best_index+1; /* +1 since index of lpc_error[] is order-1 */
 487 }
 488
 489 #endif /* !defined FLAC__INTEGER_ONLY_LIBRARY */