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