src/libFLAC/lpc.c

   1 /* libFLAC - Free Lossless Audio Codec library
   2  * Copyright (C) 2000,2001,2002,2003,2004,2005  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 #include <math.h>
  33 #include "FLAC/assert.h"
  34 #include "FLAC/format.h"
  35 #include "private/bitmath.h"
  36 #include "private/lpc.h"
  37 #if defined DEBUG || defined FLAC__OVERFLOW_DETECT || defined FLAC__OVERFLOW_DETECT_VERBOSE
  38 #include <stdio.h>
  39 #endif
  40
  41 #ifndef FLAC__INTEGER_ONLY_LIBRARY
  42
  43 #ifndef M_LN2
  44 /* math.h in VC++ doesn't seem to have this (how Microsoft is that?) */
  45 #define M_LN2 0.69314718055994530942
  46 #endif
  47
  48 void FLAC__lpc_compute_autocorrelation(const FLAC__real data[], unsigned data_len, unsigned lag, FLAC__real autoc[])
  49 {
  50         /* a readable, but slower, version */
  51 #if 0
  52         FLAC__real d;
  53         unsigned i;
  54
  55         FLAC__ASSERT(lag > 0);
  56         FLAC__ASSERT(lag <= data_len);
  57
  58         while(lag--) {
  59                 for(i = lag, d = 0.0; i < data_len; i++)
  60                         d += data[i] * data[i - lag];
  61                 autoc[lag] = d;
  62         }
  63 #endif
  64
  65         /*
  66          * this version tends to run faster because of better data locality
  67          * ('data_len' is usually much larger than 'lag')
  68          */
  69         FLAC__real d;
  70         unsigned sample, coeff;
  71         const unsigned limit = data_len - lag;
  72
  73         FLAC__ASSERT(lag > 0);
  74         FLAC__ASSERT(lag <= data_len);
  75
  76         for(coeff = 0; coeff < lag; coeff++)
  77                 autoc[coeff] = 0.0;
  78         for(sample = 0; sample <= limit; sample++) {
  79                 d = data[sample];
  80                 for(coeff = 0; coeff < lag; coeff++)
  81                         autoc[coeff] += d * data[sample+coeff];
  82         }
  83         for(; sample < data_len; sample++) {
  84                 d = data[sample];
  85                 for(coeff = 0; coeff < data_len - sample; coeff++)
  86                         autoc[coeff] += d * data[sample+coeff];
  87         }
  88 }
  89
  90 void FLAC__lpc_compute_lp_coefficients(const FLAC__real autoc[], unsigned max_order, FLAC__real lp_coeff[][FLAC__MAX_LPC_ORDER], FLAC__double error[])
  91 {
  92         unsigned i, j;
  93         FLAC__double r, err, ref[FLAC__MAX_LPC_ORDER], lpc[FLAC__MAX_LPC_ORDER];
  94
  95         FLAC__ASSERT(0 < max_order);
  96         FLAC__ASSERT(max_order <= FLAC__MAX_LPC_ORDER);
  97         FLAC__ASSERT(autoc[0] != 0.0);
  98
  99         err = autoc[0];
 100
 101         for(i = 0; i < max_order; i++) {
 102                 /* Sum up this iteration's reflection coefficient. */
 103                 r = -autoc[i+1];
 104                 for(j = 0; j < i; j++)
 105                         r -= lpc[j] * autoc[i-j];
 106                 ref[i] = (r/=err);
 107
 108                 /* Update LPC coefficients and total error. */
 109                 lpc[i]=r;
 110                 for(j = 0; j < (i>>1); j++) {
 111                         FLAC__double tmp = lpc[j];
 112                         lpc[j] += r * lpc[i-1-j];
 113                         lpc[i-1-j] += r * tmp;
 114                 }
 115                 if(i & 1)
 116                         lpc[j] += lpc[j] * r;
 117
 118                 err *= (1.0 - r * r);
 119
 120                 /* save this order */
 121                 for(j = 0; j <= i; j++)
 122                         lp_coeff[i][j] = (FLAC__real)(-lpc[j]); /* negate FIR filter coeff to get predictor coeff */
 123                 error[i] = err;
 124         }
 125 }
 126
 127 int FLAC__lpc_quantize_coefficients(const FLAC__real lp_coeff[], unsigned order, unsigned precision, FLAC__int32 qlp_coeff[], int *shift)
 128 {
 129         unsigned i;
 130         FLAC__double d, cmax = -1e32;
 131         FLAC__int32 qmax, qmin;
 132         const int max_shiftlimit = (1 << (FLAC__SUBFRAME_LPC_QLP_SHIFT_LEN-1)) - 1;
 133         const int min_shiftlimit = -max_shiftlimit - 1;
 134
 135         FLAC__ASSERT(precision > 0);
 136         FLAC__ASSERT(precision >= FLAC__MIN_QLP_COEFF_PRECISION);
 137
 138         /* drop one bit for the sign; from here on out we consider only |lp_coeff[i]| */
 139         precision--;
 140         qmax = 1 << precision;
 141         qmin = -qmax;
 142         qmax--;
 143
 144         for(i = 0; i < order; i++) {
 145                 if(lp_coeff[i] == 0.0)
 146                         continue;
 147                 d = fabs(lp_coeff[i]);
 148                 if(d > cmax)
 149                         cmax = d;
 150         }
 151 redo_it:
 152         if(cmax <= 0.0) {
 153                 /* => coefficients are all 0, which means our constant-detect didn't work */
 154                 return 2;
 155         }
 156         else {
 157                 int log2cmax;
 158
 159                 (void)frexp(cmax, &log2cmax);
 160                 log2cmax--;
 161                 *shift = (int)precision - log2cmax - 1;
 162
 163                 if(*shift < min_shiftlimit || *shift > max_shiftlimit) {
 164 #if 0
 165                         /*@@@ this does not seem to help at all, but was not extensively tested either: */
 166                         if(*shift > max_shiftlimit)
 167                                 *shift = max_shiftlimit;
 168                         else
 169 #endif
 170                                 return 1;
 171                 }
 172         }
 173
 174         if(*shift >= 0) {
 175                 for(i = 0; i < order; i++) {
 176                         qlp_coeff[i] = (FLAC__int32)floor((FLAC__double)lp_coeff[i] * (FLAC__double)(1 << *shift));
 177
 178                         /* double-check the result */
 179                         if(qlp_coeff[i] > qmax || qlp_coeff[i] < qmin) {
 180 #ifdef FLAC__OVERFLOW_DETECT
 181                                 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)));
 182 #endif
 183                                 cmax *= 2.0;
 184                                 goto redo_it;
 185                         }
 186                 }
 187         }
 188         else { /* (*shift < 0) */
 189                 const int nshift = -(*shift);
 190 #ifdef DEBUG
 191                 fprintf(stderr,"FLAC__lpc_quantize_coefficients: negative shift = %d\n", *shift);
 192 #endif
 193                 for(i = 0; i < order; i++) {
 194                         qlp_coeff[i] = (FLAC__int32)floor((FLAC__double)lp_coeff[i] / (FLAC__double)(1 << nshift));
 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 << nshift), floor((FLAC__double)lp_coeff[i] / (FLAC__double)(1 << nshift)));
 200 #endif
 201                                 cmax *= 2.0;
 202                                 goto redo_it;
 203                         }
 204                 }
 205         }
 206
 207         return 0;
 208 }
 209
 210 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[])
 211 {
 212 #ifdef FLAC__OVERFLOW_DETECT
 213         FLAC__int64 sumo;
 214 #endif
 215         unsigned i, j;
 216         FLAC__int32 sum;
 217         const FLAC__int32 *history;
 218
 219 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 220         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 221         for(i=0;i<order;i++)
 222                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 223         fprintf(stderr,"\n");
 224 #endif
 225         FLAC__ASSERT(order > 0);
 226
 227         for(i = 0; i < data_len; i++) {
 228 #ifdef FLAC__OVERFLOW_DETECT
 229                 sumo = 0;
 230 #endif
 231                 sum = 0;
 232                 history = data;
 233                 for(j = 0; j < order; j++) {
 234                         sum += qlp_coeff[j] * (*(--history));
 235 #ifdef FLAC__OVERFLOW_DETECT
 236                         sumo += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*history);
 237 #if defined _MSC_VER
 238                         if(sumo > 2147483647I64 || sumo < -2147483648I64)
 239                                 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);
 240 #else
 241                         if(sumo > 2147483647ll || sumo < -2147483648ll)
 242                                 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,sumo);
 243 #endif
 244 #endif
 245                 }
 246                 *(residual++) = *(data++) - (sum >> lp_quantization);
 247         }
 248
 249         /* Here's a slower but clearer version:
 250         for(i = 0; i < data_len; i++) {
 251                 sum = 0;
 252                 for(j = 0; j < order; j++)
 253                         sum += qlp_coeff[j] * data[i-j-1];
 254                 residual[i] = data[i] - (sum >> lp_quantization);
 255         }
 256         */
 257 }
 258
 259 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[])
 260 {
 261         unsigned i, j;
 262         FLAC__int64 sum;
 263         const FLAC__int32 *history;
 264
 265 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 266         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 267         for(i=0;i<order;i++)
 268                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 269         fprintf(stderr,"\n");
 270 #endif
 271         FLAC__ASSERT(order > 0);
 272
 273         for(i = 0; i < data_len; i++) {
 274                 sum = 0;
 275                 history = data;
 276                 for(j = 0; j < order; j++)
 277                         sum += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*(--history));
 278 #ifdef FLAC__OVERFLOW_DETECT
 279                 if(FLAC__bitmath_silog2_wide(sum >> lp_quantization) > 32) {
 280                         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: OVERFLOW, i=%u, sum=%lld\n", i, sum >> lp_quantization);
 281                         break;
 282                 }
 283                 if(FLAC__bitmath_silog2_wide((FLAC__int64)(*data) - (sum >> lp_quantization)) > 32) {
 284                         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: OVERFLOW, i=%u, data=%d, sum=%lld, residual=%lld\n", i, *data, sum >> lp_quantization, (FLAC__int64)(*data) - (sum >> lp_quantization));
 285                         break;
 286                 }
 287 #endif
 288                 *(residual++) = *(data++) - (FLAC__int32)(sum >> lp_quantization);
 289         }
 290 }
 291
 292 #endif /* !defined FLAC__INTEGER_ONLY_LIBRARY */
 293
 294 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[])
 295 {
 296 #ifdef FLAC__OVERFLOW_DETECT
 297         FLAC__int64 sumo;
 298 #endif
 299         unsigned i, j;
 300         FLAC__int32 sum;
 301         const FLAC__int32 *history;
 302
 303 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 304         fprintf(stderr,"FLAC__lpc_restore_signal: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 305         for(i=0;i<order;i++)
 306                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 307         fprintf(stderr,"\n");
 308 #endif
 309         FLAC__ASSERT(order > 0);
 310
 311         for(i = 0; i < data_len; i++) {
 312 #ifdef FLAC__OVERFLOW_DETECT
 313                 sumo = 0;
 314 #endif
 315                 sum = 0;
 316                 history = data;
 317                 for(j = 0; j < order; j++) {
 318                         sum += qlp_coeff[j] * (*(--history));
 319 #ifdef FLAC__OVERFLOW_DETECT
 320                         sumo += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*history);
 321 #if defined _MSC_VER
 322                         if(sumo > 2147483647I64 || sumo < -2147483648I64)
 323                                 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);
 324 #else
 325                         if(sumo > 2147483647ll || sumo < -2147483648ll)
 326                                 fprintf(stderr,"FLAC__lpc_restore_signal: OVERFLOW, i=%u, j=%u, c=%d, d=%d, sumo=%lld\n",i,j,qlp_coeff[j],*history,sumo);
 327 #endif
 328 #endif
 329                 }
 330                 *(data++) = *(residual++) + (sum >> lp_quantization);
 331         }
 332
 333         /* Here's a slower but clearer version:
 334         for(i = 0; i < data_len; i++) {
 335                 sum = 0;
 336                 for(j = 0; j < order; j++)
 337                         sum += qlp_coeff[j] * data[i-j-1];
 338                 data[i] = residual[i] + (sum >> lp_quantization);
 339         }
 340         */
 341 }
 342
 343 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[])
 344 {
 345         unsigned i, j;
 346         FLAC__int64 sum;
 347         const FLAC__int32 *history;
 348
 349 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 350         fprintf(stderr,"FLAC__lpc_restore_signal_wide: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 351         for(i=0;i<order;i++)
 352                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 353         fprintf(stderr,"\n");
 354 #endif
 355         FLAC__ASSERT(order > 0);
 356
 357         for(i = 0; i < data_len; i++) {
 358                 sum = 0;
 359                 history = data;
 360                 for(j = 0; j < order; j++)
 361                         sum += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*(--history));
 362 #ifdef FLAC__OVERFLOW_DETECT
 363                 if(FLAC__bitmath_silog2_wide(sum >> lp_quantization) > 32) {
 364                         fprintf(stderr,"FLAC__lpc_restore_signal_wide: OVERFLOW, i=%u, sum=%lld\n", i, sum >> lp_quantization);
 365                         break;
 366                 }
 367                 if(FLAC__bitmath_silog2_wide((FLAC__int64)(*residual) + (sum >> lp_quantization)) > 32) {
 368                         fprintf(stderr,"FLAC__lpc_restore_signal_wide: OVERFLOW, i=%u, residual=%d, sum=%lld, data=%lld\n", i, *residual, sum >> lp_quantization, (FLAC__int64)(*residual) + (sum >> lp_quantization));
 369                         break;
 370                 }
 371 #endif
 372                 *(data++) = *(residual++) + (FLAC__int32)(sum >> lp_quantization);
 373         }
 374 }
 375
 376 #ifndef FLAC__INTEGER_ONLY_LIBRARY
 377
 378 FLAC__double FLAC__lpc_compute_expected_bits_per_residual_sample(FLAC__double lpc_error, unsigned total_samples)
 379 {
 380         FLAC__double error_scale;
 381
 382         FLAC__ASSERT(total_samples > 0);
 383
 384         error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__double)total_samples;
 385
 386         return FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error, error_scale);
 387 }
 388
 389 FLAC__double FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(FLAC__double lpc_error, FLAC__double error_scale)
 390 {
 391         if(lpc_error > 0.0) {
 392                 FLAC__double bps = (FLAC__double)0.5 * log(error_scale * lpc_error) / M_LN2;
 393                 if(bps >= 0.0)
 394                         return bps;
 395                 else
 396                         return 0.0;
 397         }
 398         else if(lpc_error < 0.0) { /* error should not be negative but can happen due to inadequate floating-point resolution */
 399                 return 1e32;
 400         }
 401         else {
 402                 return 0.0;
 403         }
 404 }
 405
 406 unsigned FLAC__lpc_compute_best_order(const FLAC__double lpc_error[], unsigned max_order, unsigned total_samples, unsigned bits_per_signal_sample)
 407 {
 408         unsigned order, best_order;
 409         FLAC__double best_bits, tmp_bits, error_scale;
 410
 411         FLAC__ASSERT(max_order > 0);
 412         FLAC__ASSERT(total_samples > 0);
 413
 414         error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__double)total_samples;
 415
 416         best_order = 0;
 417         best_bits = FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error[0], error_scale) * (FLAC__double)total_samples;
 418
 419         for(order = 1; order < max_order; order++) {
 420                 tmp_bits = FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error[order], error_scale) * (FLAC__double)(total_samples - order) + (FLAC__double)(order * bits_per_signal_sample);
 421                 if(tmp_bits < best_bits) {
 422                         best_order = order;
 423                         best_bits = tmp_bits;
 424                 }
 425         }
 426
 427         return best_order+1; /* +1 since index of lpc_error[] is order-1 */
 428 }
 429
 430 #endif /* !defined FLAC__INTEGER_ONLY_LIBRARY */