src/libFLAC/lpc.c

   1 /* libFLAC - Free Lossless Audio Codec library
   2  * Copyright (C) 2000,2001,2002,2003,2004,2005,2006  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 d, cmax = -1e32;
 156         FLAC__int32 qmax, qmin;
 157         const int max_shiftlimit = (1 << (FLAC__SUBFRAME_LPC_QLP_SHIFT_LEN-1)) - 1;
 158         const int min_shiftlimit = -max_shiftlimit - 1;
 159
 160         FLAC__ASSERT(precision > 0);
 161         FLAC__ASSERT(precision >= FLAC__MIN_QLP_COEFF_PRECISION);
 162
 163         /* drop one bit for the sign; from here on out we consider only |lp_coeff[i]| */
 164         precision--;
 165         qmax = 1 << precision;
 166         qmin = -qmax;
 167         qmax--;
 168
 169         for(i = 0; i < order; i++) {
 170                 if(lp_coeff[i] == 0.0)
 171                         continue;
 172                 d = fabs(lp_coeff[i]);
 173                 if(d > cmax)
 174                         cmax = d;
 175         }
 176 redo_it:
 177         if(cmax <= 0.0) {
 178                 /* => coefficients are all 0, which means our constant-detect didn't work */
 179                 return 2;
 180         }
 181         else {
 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 #if 0
 190                         /*@@@ this does not seem to help at all, but was not extensively tested either: */
 191                         if(*shift > max_shiftlimit)
 192                                 *shift = max_shiftlimit;
 193                         else
 194 #endif
 195                                 return 1;
 196                 }
 197         }
 198
 199         if(*shift >= 0) {
 200                 for(i = 0; i < order; i++) {
 201                         qlp_coeff[i] = (FLAC__int32)floor((FLAC__double)lp_coeff[i] * (FLAC__double)(1 << *shift));
 202
 203                         /* double-check the result */
 204                         if(qlp_coeff[i] > qmax || qlp_coeff[i] < qmin) {
 205 #ifdef FLAC__OVERFLOW_DETECT
 206                                 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, (FLAC__double)lp_coeff[i] * (FLAC__double)(1 << *shift), floor((FLAC__double)lp_coeff[i] * (FLAC__double)(1 << *shift)));
 207 #endif
 208                                 cmax *= 2.0;
 209                                 goto redo_it;
 210                         }
 211                 }
 212         }
 213         else { /* (*shift < 0) */
 214                 const int nshift = -(*shift);
 215 #ifdef DEBUG
 216                 fprintf(stderr,"FLAC__lpc_quantize_coefficients: negative shift = %d\n", *shift);
 217 #endif
 218                 for(i = 0; i < order; i++) {
 219                         qlp_coeff[i] = (FLAC__int32)floor((FLAC__double)lp_coeff[i] / (FLAC__double)(1 << nshift));
 220
 221                         /* double-check the result */
 222                         if(qlp_coeff[i] > qmax || qlp_coeff[i] < qmin) {
 223 #ifdef FLAC__OVERFLOW_DETECT
 224                                 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, (FLAC__double)lp_coeff[i] / (FLAC__double)(1 << nshift), floor((FLAC__double)lp_coeff[i] / (FLAC__double)(1 << nshift)));
 225 #endif
 226                                 cmax *= 2.0;
 227                                 goto redo_it;
 228                         }
 229                 }
 230         }
 231
 232         return 0;
 233 }
 234
 235 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[])
 236 {
 237 #ifdef FLAC__OVERFLOW_DETECT
 238         FLAC__int64 sumo;
 239 #endif
 240         unsigned i, j;
 241         FLAC__int32 sum;
 242         const FLAC__int32 *history;
 243
 244 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 245         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 246         for(i=0;i<order;i++)
 247                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 248         fprintf(stderr,"\n");
 249 #endif
 250         FLAC__ASSERT(order > 0);
 251
 252         for(i = 0; i < data_len; i++) {
 253 #ifdef FLAC__OVERFLOW_DETECT
 254                 sumo = 0;
 255 #endif
 256                 sum = 0;
 257                 history = data;
 258                 for(j = 0; j < order; j++) {
 259                         sum += qlp_coeff[j] * (*(--history));
 260 #ifdef FLAC__OVERFLOW_DETECT
 261                         sumo += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*history);
 262 #if defined _MSC_VER
 263                         if(sumo > 2147483647I64 || sumo < -2147483648I64)
 264                                 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);
 265 #else
 266                         if(sumo > 2147483647ll || sumo < -2147483648ll)
 267                                 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);
 268 #endif
 269 #endif
 270                 }
 271                 *(residual++) = *(data++) - (sum >> lp_quantization);
 272         }
 273
 274         /* Here's a slower but clearer version:
 275         for(i = 0; i < data_len; i++) {
 276                 sum = 0;
 277                 for(j = 0; j < order; j++)
 278                         sum += qlp_coeff[j] * data[i-j-1];
 279                 residual[i] = data[i] - (sum >> lp_quantization);
 280         }
 281         */
 282 }
 283
 284 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[])
 285 {
 286         unsigned i, j;
 287         FLAC__int64 sum;
 288         const FLAC__int32 *history;
 289
 290 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 291         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 292         for(i=0;i<order;i++)
 293                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 294         fprintf(stderr,"\n");
 295 #endif
 296         FLAC__ASSERT(order > 0);
 297
 298         for(i = 0; i < data_len; i++) {
 299                 sum = 0;
 300                 history = data;
 301                 for(j = 0; j < order; j++)
 302                         sum += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*(--history));
 303 #ifdef FLAC__OVERFLOW_DETECT
 304                 if(FLAC__bitmath_silog2_wide(sum >> lp_quantization) > 32) {
 305                         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: OVERFLOW, i=%u, sum=%lld\n", i, (long long)(sum >> lp_quantization));
 306                         break;
 307                 }
 308                 if(FLAC__bitmath_silog2_wide((FLAC__int64)(*data) - (sum >> lp_quantization)) > 32) {
 309                         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)));
 310                         break;
 311                 }
 312 #endif
 313                 *(residual++) = *(data++) - (FLAC__int32)(sum >> lp_quantization);
 314         }
 315 }
 316
 317 #endif /* !defined FLAC__INTEGER_ONLY_LIBRARY */
 318
 319 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[])
 320 {
 321 #ifdef FLAC__OVERFLOW_DETECT
 322         FLAC__int64 sumo;
 323 #endif
 324         unsigned i, j;
 325         FLAC__int32 sum;
 326         const FLAC__int32 *r = residual, *history;
 327
 328 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 329         fprintf(stderr,"FLAC__lpc_restore_signal: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 330         for(i=0;i<order;i++)
 331                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 332         fprintf(stderr,"\n");
 333 #endif
 334         FLAC__ASSERT(order > 0);
 335
 336         for(i = 0; i < data_len; i++) {
 337 #ifdef FLAC__OVERFLOW_DETECT
 338                 sumo = 0;
 339 #endif
 340                 sum = 0;
 341                 history = data;
 342                 for(j = 0; j < order; j++) {
 343                         sum += qlp_coeff[j] * (*(--history));
 344 #ifdef FLAC__OVERFLOW_DETECT
 345                         sumo += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*history);
 346 #if defined _MSC_VER
 347                         if(sumo > 2147483647I64 || sumo < -2147483648I64)
 348                                 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);
 349 #else
 350                         if(sumo > 2147483647ll || sumo < -2147483648ll)
 351                                 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);
 352 #endif
 353 #endif
 354                 }
 355                 *(data++) = *(r++) + (sum >> lp_quantization);
 356         }
 357
 358         /* Here's a slower but clearer version:
 359         for(i = 0; i < data_len; i++) {
 360                 sum = 0;
 361                 for(j = 0; j < order; j++)
 362                         sum += qlp_coeff[j] * data[i-j-1];
 363                 data[i] = residual[i] + (sum >> lp_quantization);
 364         }
 365         */
 366 }
 367
 368 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[])
 369 {
 370         unsigned i, j;
 371         FLAC__int64 sum;
 372         const FLAC__int32 *r = residual, *history;
 373
 374 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 375         fprintf(stderr,"FLAC__lpc_restore_signal_wide: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 376         for(i=0;i<order;i++)
 377                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 378         fprintf(stderr,"\n");
 379 #endif
 380         FLAC__ASSERT(order > 0);
 381
 382         for(i = 0; i < data_len; i++) {
 383                 sum = 0;
 384                 history = data;
 385                 for(j = 0; j < order; j++)
 386                         sum += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*(--history));
 387 #ifdef FLAC__OVERFLOW_DETECT
 388                 if(FLAC__bitmath_silog2_wide(sum >> lp_quantization) > 32) {
 389                         fprintf(stderr,"FLAC__lpc_restore_signal_wide: OVERFLOW, i=%u, sum=%lld\n", i, (long long)(sum >> lp_quantization));
 390                         break;
 391                 }
 392                 if(FLAC__bitmath_silog2_wide((FLAC__int64)(*r) + (sum >> lp_quantization)) > 32) {
 393                         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)));
 394                         break;
 395                 }
 396 #endif
 397                 *(data++) = *(r++) + (FLAC__int32)(sum >> lp_quantization);
 398         }
 399 }
 400
 401 #ifndef FLAC__INTEGER_ONLY_LIBRARY
 402
 403 FLAC__double FLAC__lpc_compute_expected_bits_per_residual_sample(FLAC__double lpc_error, unsigned total_samples)
 404 {
 405         FLAC__double error_scale;
 406
 407         FLAC__ASSERT(total_samples > 0);
 408
 409         error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__double)total_samples;
 410
 411         return FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error, error_scale);
 412 }
 413
 414 FLAC__double FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(FLAC__double lpc_error, FLAC__double error_scale)
 415 {
 416         if(lpc_error > 0.0) {
 417                 FLAC__double bps = (FLAC__double)0.5 * log(error_scale * lpc_error) / M_LN2;
 418                 if(bps >= 0.0)
 419                         return bps;
 420                 else
 421                         return 0.0;
 422         }
 423         else if(lpc_error < 0.0) { /* error should not be negative but can happen due to inadequate floating-point resolution */
 424                 return 1e32;
 425         }
 426         else {
 427                 return 0.0;
 428         }
 429 }
 430
 431 unsigned FLAC__lpc_compute_best_order(const FLAC__double lpc_error[], unsigned max_order, unsigned total_samples, unsigned overhead_bits_per_order)
 432 {
 433         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 */
 434         FLAC__double bits, best_bits, error_scale;
 435
 436         FLAC__ASSERT(max_order > 0);
 437         FLAC__ASSERT(total_samples > 0);
 438
 439         error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__double)total_samples;
 440
 441         best_index = 0;
 442         best_bits = (unsigned)(-1);
 443
 444         for(index = 0, order = 1; index < max_order; index++, order++) {
 445                 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);
 446                 if(bits < best_bits) {
 447                         best_index = index;
 448                         best_bits = bits;
 449                 }
 450         }
 451
 452         return best_index+1; /* +1 since index of lpc_error[] is order-1 */
 453 }
 454
 455 #endif /* !defined FLAC__INTEGER_ONLY_LIBRARY */