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(max_order <= FLAC__MAX_LPC_ORDER);
 115         FLAC__ASSERT(autoc[0] != 0.0);
 116
 117         err = autoc[0];
 118
 119         for(i = 0; i < max_order; i++) {
 120                 /* Sum up this iteration's reflection coefficient. */
 121                 r = -autoc[i+1];
 122                 for(j = 0; j < i; j++)
 123                         r -= lpc[j] * autoc[i-j];
 124                 ref[i] = (r/=err);
 125
 126                 /* Update LPC coefficients and total error. */
 127                 lpc[i]=r;
 128                 for(j = 0; j < (i>>1); j++) {
 129                         FLAC__double tmp = lpc[j];
 130                         lpc[j] += r * lpc[i-1-j];
 131                         lpc[i-1-j] += r * tmp;
 132                 }
 133                 if(i & 1)
 134                         lpc[j] += lpc[j] * r;
 135
 136                 err *= (1.0 - r * r);
 137
 138                 /* save this order */
 139                 for(j = 0; j <= i; j++)
 140                         lp_coeff[i][j] = (FLAC__real)(-lpc[j]); /* negate FIR filter coeff to get predictor coeff */
 141                 error[i] = err;
 142         }
 143 }
 144
 145 int FLAC__lpc_quantize_coefficients(const FLAC__real lp_coeff[], unsigned order, unsigned precision, FLAC__int32 qlp_coeff[], int *shift)
 146 {
 147         unsigned i;
 148         FLAC__double d, cmax = -1e32;
 149         FLAC__int32 qmax, qmin;
 150         const int max_shiftlimit = (1 << (FLAC__SUBFRAME_LPC_QLP_SHIFT_LEN-1)) - 1;
 151         const int min_shiftlimit = -max_shiftlimit - 1;
 152
 153         FLAC__ASSERT(precision > 0);
 154         FLAC__ASSERT(precision >= FLAC__MIN_QLP_COEFF_PRECISION);
 155
 156         /* drop one bit for the sign; from here on out we consider only |lp_coeff[i]| */
 157         precision--;
 158         qmax = 1 << precision;
 159         qmin = -qmax;
 160         qmax--;
 161
 162         for(i = 0; i < order; i++) {
 163                 if(lp_coeff[i] == 0.0)
 164                         continue;
 165                 d = fabs(lp_coeff[i]);
 166                 if(d > cmax)
 167                         cmax = d;
 168         }
 169 redo_it:
 170         if(cmax <= 0.0) {
 171                 /* => coefficients are all 0, which means our constant-detect didn't work */
 172                 return 2;
 173         }
 174         else {
 175                 int log2cmax;
 176
 177                 (void)frexp(cmax, &log2cmax);
 178                 log2cmax--;
 179                 *shift = (int)precision - log2cmax - 1;
 180
 181                 if(*shift < min_shiftlimit || *shift > max_shiftlimit) {
 182 #if 0
 183                         /*@@@ this does not seem to help at all, but was not extensively tested either: */
 184                         if(*shift > max_shiftlimit)
 185                                 *shift = max_shiftlimit;
 186                         else
 187 #endif
 188                                 return 1;
 189                 }
 190         }
 191
 192         if(*shift >= 0) {
 193                 for(i = 0; i < order; i++) {
 194                         qlp_coeff[i] = (FLAC__int32)floor((FLAC__double)lp_coeff[i] * (FLAC__double)(1 << *shift));
 195
 196                         /* double-check the result */
 197                         if(qlp_coeff[i] > qmax || qlp_coeff[i] < qmin) {
 198 #ifdef FLAC__OVERFLOW_DETECT
 199                                 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)));
 200 #endif
 201                                 cmax *= 2.0;
 202                                 goto redo_it;
 203                         }
 204                 }
 205         }
 206         else { /* (*shift < 0) */
 207                 const int nshift = -(*shift);
 208 #ifdef DEBUG
 209                 fprintf(stderr,"FLAC__lpc_quantize_coefficients: negative shift = %d\n", *shift);
 210 #endif
 211                 for(i = 0; i < order; i++) {
 212                         qlp_coeff[i] = (FLAC__int32)floor((FLAC__double)lp_coeff[i] / (FLAC__double)(1 << nshift));
 213
 214                         /* double-check the result */
 215                         if(qlp_coeff[i] > qmax || qlp_coeff[i] < qmin) {
 216 #ifdef FLAC__OVERFLOW_DETECT
 217                                 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)));
 218 #endif
 219                                 cmax *= 2.0;
 220                                 goto redo_it;
 221                         }
 222                 }
 223         }
 224
 225         return 0;
 226 }
 227
 228 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[])
 229 {
 230 #ifdef FLAC__OVERFLOW_DETECT
 231         FLAC__int64 sumo;
 232 #endif
 233         unsigned i, j;
 234         FLAC__int32 sum;
 235         const FLAC__int32 *history;
 236
 237 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 238         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 239         for(i=0;i<order;i++)
 240                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 241         fprintf(stderr,"\n");
 242 #endif
 243         FLAC__ASSERT(order > 0);
 244
 245         for(i = 0; i < data_len; i++) {
 246 #ifdef FLAC__OVERFLOW_DETECT
 247                 sumo = 0;
 248 #endif
 249                 sum = 0;
 250                 history = data;
 251                 for(j = 0; j < order; j++) {
 252                         sum += qlp_coeff[j] * (*(--history));
 253 #ifdef FLAC__OVERFLOW_DETECT
 254                         sumo += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*history);
 255 #if defined _MSC_VER
 256                         if(sumo > 2147483647I64 || sumo < -2147483648I64)
 257                                 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);
 258 #else
 259                         if(sumo > 2147483647ll || sumo < -2147483648ll)
 260                                 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);
 261 #endif
 262 #endif
 263                 }
 264                 *(residual++) = *(data++) - (sum >> lp_quantization);
 265         }
 266
 267         /* Here's a slower but clearer version:
 268         for(i = 0; i < data_len; i++) {
 269                 sum = 0;
 270                 for(j = 0; j < order; j++)
 271                         sum += qlp_coeff[j] * data[i-j-1];
 272                 residual[i] = data[i] - (sum >> lp_quantization);
 273         }
 274         */
 275 }
 276
 277 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[])
 278 {
 279         unsigned i, j;
 280         FLAC__int64 sum;
 281         const FLAC__int32 *history;
 282
 283 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 284         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 285         for(i=0;i<order;i++)
 286                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 287         fprintf(stderr,"\n");
 288 #endif
 289         FLAC__ASSERT(order > 0);
 290
 291         for(i = 0; i < data_len; i++) {
 292                 sum = 0;
 293                 history = data;
 294                 for(j = 0; j < order; j++)
 295                         sum += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*(--history));
 296 #ifdef FLAC__OVERFLOW_DETECT
 297                 if(FLAC__bitmath_silog2_wide(sum >> lp_quantization) > 32) {
 298                         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: OVERFLOW, i=%u, sum=%lld\n", i, (long long)(sum >> lp_quantization));
 299                         break;
 300                 }
 301                 if(FLAC__bitmath_silog2_wide((FLAC__int64)(*data) - (sum >> lp_quantization)) > 32) {
 302                         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)));
 303                         break;
 304                 }
 305 #endif
 306                 *(residual++) = *(data++) - (FLAC__int32)(sum >> lp_quantization);
 307         }
 308 }
 309
 310 #endif /* !defined FLAC__INTEGER_ONLY_LIBRARY */
 311
 312 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[])
 313 {
 314 #ifdef FLAC__OVERFLOW_DETECT
 315         FLAC__int64 sumo;
 316 #endif
 317         unsigned i, j;
 318         FLAC__int32 sum;
 319         const FLAC__int32 *history;
 320
 321 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 322         fprintf(stderr,"FLAC__lpc_restore_signal: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 323         for(i=0;i<order;i++)
 324                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 325         fprintf(stderr,"\n");
 326 #endif
 327         FLAC__ASSERT(order > 0);
 328
 329         for(i = 0; i < data_len; i++) {
 330 #ifdef FLAC__OVERFLOW_DETECT
 331                 sumo = 0;
 332 #endif
 333                 sum = 0;
 334                 history = data;
 335                 for(j = 0; j < order; j++) {
 336                         sum += qlp_coeff[j] * (*(--history));
 337 #ifdef FLAC__OVERFLOW_DETECT
 338                         sumo += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*history);
 339 #if defined _MSC_VER
 340                         if(sumo > 2147483647I64 || sumo < -2147483648I64)
 341                                 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);
 342 #else
 343                         if(sumo > 2147483647ll || sumo < -2147483648ll)
 344                                 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);
 345 #endif
 346 #endif
 347                 }
 348                 *(data++) = *(residual++) + (sum >> lp_quantization);
 349         }
 350
 351         /* Here's a slower but clearer version:
 352         for(i = 0; i < data_len; i++) {
 353                 sum = 0;
 354                 for(j = 0; j < order; j++)
 355                         sum += qlp_coeff[j] * data[i-j-1];
 356                 data[i] = residual[i] + (sum >> lp_quantization);
 357         }
 358         */
 359 }
 360
 361 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[])
 362 {
 363         unsigned i, j;
 364         FLAC__int64 sum;
 365         const FLAC__int32 *history;
 366
 367 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 368         fprintf(stderr,"FLAC__lpc_restore_signal_wide: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 369         for(i=0;i<order;i++)
 370                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 371         fprintf(stderr,"\n");
 372 #endif
 373         FLAC__ASSERT(order > 0);
 374
 375         for(i = 0; i < data_len; i++) {
 376                 sum = 0;
 377                 history = data;
 378                 for(j = 0; j < order; j++)
 379                         sum += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*(--history));
 380 #ifdef FLAC__OVERFLOW_DETECT
 381                 if(FLAC__bitmath_silog2_wide(sum >> lp_quantization) > 32) {
 382                         fprintf(stderr,"FLAC__lpc_restore_signal_wide: OVERFLOW, i=%u, sum=%lld\n", i, (long long)(sum >> lp_quantization));
 383                         break;
 384                 }
 385                 if(FLAC__bitmath_silog2_wide((FLAC__int64)(*residual) + (sum >> lp_quantization)) > 32) {
 386                         fprintf(stderr,"FLAC__lpc_restore_signal_wide: OVERFLOW, i=%u, residual=%d, sum=%lld, data=%lld\n", i, *residual, (long long)(sum >> lp_quantization), (long long)((FLAC__int64)(*residual) + (sum >> lp_quantization)));
 387                         break;
 388                 }
 389 #endif
 390                 *(data++) = *(residual++) + (FLAC__int32)(sum >> lp_quantization);
 391         }
 392 }
 393
 394 #ifndef FLAC__INTEGER_ONLY_LIBRARY
 395
 396 FLAC__double FLAC__lpc_compute_expected_bits_per_residual_sample(FLAC__double lpc_error, unsigned total_samples)
 397 {
 398         FLAC__double error_scale;
 399
 400         FLAC__ASSERT(total_samples > 0);
 401
 402         error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__double)total_samples;
 403
 404         return FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error, error_scale);
 405 }
 406
 407 FLAC__double FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(FLAC__double lpc_error, FLAC__double error_scale)
 408 {
 409         if(lpc_error > 0.0) {
 410                 FLAC__double bps = (FLAC__double)0.5 * log(error_scale * lpc_error) / M_LN2;
 411                 if(bps >= 0.0)
 412                         return bps;
 413                 else
 414                         return 0.0;
 415         }
 416         else if(lpc_error < 0.0) { /* error should not be negative but can happen due to inadequate floating-point resolution */
 417                 return 1e32;
 418         }
 419         else {
 420                 return 0.0;
 421         }
 422 }
 423
 424 unsigned FLAC__lpc_compute_best_order(const FLAC__double lpc_error[], unsigned max_order, unsigned total_samples, unsigned overhead_bits_per_order)
 425 {
 426         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 */
 427         FLAC__double bits, best_bits, error_scale;
 428
 429         FLAC__ASSERT(max_order > 0);
 430         FLAC__ASSERT(total_samples > 0);
 431
 432         error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__double)total_samples;
 433
 434         best_index = 0;
 435         best_bits = (unsigned)(-1);
 436
 437         for(index = 0, order = 1; index < max_order; index++, order++) {
 438                 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);
 439                 if(bits < best_bits) {
 440                         best_index = index;
 441                         best_bits = bits;
 442                 }
 443         }
 444
 445         return best_index+1; /* +1 since index of lpc_error[] is order-1 */
 446 }
 447
 448 #endif /* !defined FLAC__INTEGER_ONLY_LIBRARY */