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_window_data(const FLAC__real in[], const FLAC__real window[], FLAC__real out[], unsigned data_len)
  49 {
  50         unsigned i;
  51         for(i = 0; i < data_len; i++)
  52                 out[i] = in[i] * window[i];
  53 }
  54
  55 void FLAC__lpc_compute_autocorrelation(const FLAC__real data[], unsigned data_len, unsigned lag, FLAC__real autoc[])
  56 {
  57         /* a readable, but slower, version */
  58 #if 0
  59         FLAC__real d;
  60         unsigned i;
  61
  62         FLAC__ASSERT(lag > 0);
  63         FLAC__ASSERT(lag <= data_len);
  64
  65         while(lag--) {
  66                 for(i = lag, d = 0.0; i < data_len; i++)
  67                         d += data[i] * data[i - lag];
  68                 autoc[lag] = d;
  69         }
  70 #endif
  71
  72         /*
  73          * this version tends to run faster because of better data locality
  74          * ('data_len' is usually much larger than 'lag')
  75          */
  76         FLAC__real d;
  77         unsigned sample, coeff;
  78         const unsigned limit = data_len - lag;
  79
  80         FLAC__ASSERT(lag > 0);
  81         FLAC__ASSERT(lag <= data_len);
  82
  83         for(coeff = 0; coeff < lag; coeff++)
  84                 autoc[coeff] = 0.0;
  85         for(sample = 0; sample <= limit; sample++) {
  86                 d = data[sample];
  87                 for(coeff = 0; coeff < lag; coeff++)
  88                         autoc[coeff] += d * data[sample+coeff];
  89         }
  90         for(; sample < data_len; sample++) {
  91                 d = data[sample];
  92                 for(coeff = 0; coeff < data_len - sample; coeff++)
  93                         autoc[coeff] += d * data[sample+coeff];
  94         }
  95 }
  96
  97 void FLAC__lpc_compute_lp_coefficients(const FLAC__real autoc[], unsigned max_order, FLAC__real lp_coeff[][FLAC__MAX_LPC_ORDER], FLAC__double error[])
  98 {
  99         unsigned i, j;
 100         FLAC__double r, err, ref[FLAC__MAX_LPC_ORDER], lpc[FLAC__MAX_LPC_ORDER];
 101
 102         FLAC__ASSERT(0 < max_order);
 103         FLAC__ASSERT(max_order <= FLAC__MAX_LPC_ORDER);
 104         FLAC__ASSERT(autoc[0] != 0.0);
 105
 106         err = autoc[0];
 107
 108         for(i = 0; i < max_order; i++) {
 109                 /* Sum up this iteration's reflection coefficient. */
 110                 r = -autoc[i+1];
 111                 for(j = 0; j < i; j++)
 112                         r -= lpc[j] * autoc[i-j];
 113                 ref[i] = (r/=err);
 114
 115                 /* Update LPC coefficients and total error. */
 116                 lpc[i]=r;
 117                 for(j = 0; j < (i>>1); j++) {
 118                         FLAC__double tmp = lpc[j];
 119                         lpc[j] += r * lpc[i-1-j];
 120                         lpc[i-1-j] += r * tmp;
 121                 }
 122                 if(i & 1)
 123                         lpc[j] += lpc[j] * r;
 124
 125                 err *= (1.0 - r * r);
 126
 127                 /* save this order */
 128                 for(j = 0; j <= i; j++)
 129                         lp_coeff[i][j] = (FLAC__real)(-lpc[j]); /* negate FIR filter coeff to get predictor coeff */
 130                 error[i] = err;
 131         }
 132 }
 133
 134 int FLAC__lpc_quantize_coefficients(const FLAC__real lp_coeff[], unsigned order, unsigned precision, FLAC__int32 qlp_coeff[], int *shift)
 135 {
 136         unsigned i;
 137         FLAC__double d, cmax = -1e32;
 138         FLAC__int32 qmax, qmin;
 139         const int max_shiftlimit = (1 << (FLAC__SUBFRAME_LPC_QLP_SHIFT_LEN-1)) - 1;
 140         const int min_shiftlimit = -max_shiftlimit - 1;
 141
 142         FLAC__ASSERT(precision > 0);
 143         FLAC__ASSERT(precision >= FLAC__MIN_QLP_COEFF_PRECISION);
 144
 145         /* drop one bit for the sign; from here on out we consider only |lp_coeff[i]| */
 146         precision--;
 147         qmax = 1 << precision;
 148         qmin = -qmax;
 149         qmax--;
 150
 151         for(i = 0; i < order; i++) {
 152                 if(lp_coeff[i] == 0.0)
 153                         continue;
 154                 d = fabs(lp_coeff[i]);
 155                 if(d > cmax)
 156                         cmax = d;
 157         }
 158 redo_it:
 159         if(cmax <= 0.0) {
 160                 /* => coefficients are all 0, which means our constant-detect didn't work */
 161                 return 2;
 162         }
 163         else {
 164                 int log2cmax;
 165
 166                 (void)frexp(cmax, &log2cmax);
 167                 log2cmax--;
 168                 *shift = (int)precision - log2cmax - 1;
 169
 170                 if(*shift < min_shiftlimit || *shift > max_shiftlimit) {
 171 #if 0
 172                         /*@@@ this does not seem to help at all, but was not extensively tested either: */
 173                         if(*shift > max_shiftlimit)
 174                                 *shift = max_shiftlimit;
 175                         else
 176 #endif
 177                                 return 1;
 178                 }
 179         }
 180
 181         if(*shift >= 0) {
 182                 for(i = 0; i < order; i++) {
 183                         qlp_coeff[i] = (FLAC__int32)floor((FLAC__double)lp_coeff[i] * (FLAC__double)(1 << *shift));
 184
 185                         /* double-check the result */
 186                         if(qlp_coeff[i] > qmax || qlp_coeff[i] < qmin) {
 187 #ifdef FLAC__OVERFLOW_DETECT
 188                                 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)));
 189 #endif
 190                                 cmax *= 2.0;
 191                                 goto redo_it;
 192                         }
 193                 }
 194         }
 195         else { /* (*shift < 0) */
 196                 const int nshift = -(*shift);
 197 #ifdef DEBUG
 198                 fprintf(stderr,"FLAC__lpc_quantize_coefficients: negative shift = %d\n", *shift);
 199 #endif
 200                 for(i = 0; i < order; i++) {
 201                         qlp_coeff[i] = (FLAC__int32)floor((FLAC__double)lp_coeff[i] / (FLAC__double)(1 << nshift));
 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 << nshift), floor((FLAC__double)lp_coeff[i] / (FLAC__double)(1 << nshift)));
 207 #endif
 208                                 cmax *= 2.0;
 209                                 goto redo_it;
 210                         }
 211                 }
 212         }
 213
 214         return 0;
 215 }
 216
 217 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[])
 218 {
 219 #ifdef FLAC__OVERFLOW_DETECT
 220         FLAC__int64 sumo;
 221 #endif
 222         unsigned i, j;
 223         FLAC__int32 sum;
 224         const FLAC__int32 *history;
 225
 226 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 227         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 228         for(i=0;i<order;i++)
 229                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 230         fprintf(stderr,"\n");
 231 #endif
 232         FLAC__ASSERT(order > 0);
 233
 234         for(i = 0; i < data_len; i++) {
 235 #ifdef FLAC__OVERFLOW_DETECT
 236                 sumo = 0;
 237 #endif
 238                 sum = 0;
 239                 history = data;
 240                 for(j = 0; j < order; j++) {
 241                         sum += qlp_coeff[j] * (*(--history));
 242 #ifdef FLAC__OVERFLOW_DETECT
 243                         sumo += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*history);
 244 #if defined _MSC_VER
 245                         if(sumo > 2147483647I64 || sumo < -2147483648I64)
 246                                 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);
 247 #else
 248                         if(sumo > 2147483647ll || sumo < -2147483648ll)
 249                                 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);
 250 #endif
 251 #endif
 252                 }
 253                 *(residual++) = *(data++) - (sum >> lp_quantization);
 254         }
 255
 256         /* Here's a slower but clearer version:
 257         for(i = 0; i < data_len; i++) {
 258                 sum = 0;
 259                 for(j = 0; j < order; j++)
 260                         sum += qlp_coeff[j] * data[i-j-1];
 261                 residual[i] = data[i] - (sum >> lp_quantization);
 262         }
 263         */
 264 }
 265
 266 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[])
 267 {
 268         unsigned i, j;
 269         FLAC__int64 sum;
 270         const FLAC__int32 *history;
 271
 272 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 273         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 274         for(i=0;i<order;i++)
 275                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 276         fprintf(stderr,"\n");
 277 #endif
 278         FLAC__ASSERT(order > 0);
 279
 280         for(i = 0; i < data_len; i++) {
 281                 sum = 0;
 282                 history = data;
 283                 for(j = 0; j < order; j++)
 284                         sum += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*(--history));
 285 #ifdef FLAC__OVERFLOW_DETECT
 286                 if(FLAC__bitmath_silog2_wide(sum >> lp_quantization) > 32) {
 287                         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: OVERFLOW, i=%u, sum=%lld\n", i, sum >> lp_quantization);
 288                         break;
 289                 }
 290                 if(FLAC__bitmath_silog2_wide((FLAC__int64)(*data) - (sum >> lp_quantization)) > 32) {
 291                         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));
 292                         break;
 293                 }
 294 #endif
 295                 *(residual++) = *(data++) - (FLAC__int32)(sum >> lp_quantization);
 296         }
 297 }
 298
 299 #endif /* !defined FLAC__INTEGER_ONLY_LIBRARY */
 300
 301 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[])
 302 {
 303 #ifdef FLAC__OVERFLOW_DETECT
 304         FLAC__int64 sumo;
 305 #endif
 306         unsigned i, j;
 307         FLAC__int32 sum;
 308         const FLAC__int32 *history;
 309
 310 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 311         fprintf(stderr,"FLAC__lpc_restore_signal: 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 #ifdef FLAC__OVERFLOW_DETECT
 320                 sumo = 0;
 321 #endif
 322                 sum = 0;
 323                 history = data;
 324                 for(j = 0; j < order; j++) {
 325                         sum += qlp_coeff[j] * (*(--history));
 326 #ifdef FLAC__OVERFLOW_DETECT
 327                         sumo += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*history);
 328 #if defined _MSC_VER
 329                         if(sumo > 2147483647I64 || sumo < -2147483648I64)
 330                                 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);
 331 #else
 332                         if(sumo > 2147483647ll || sumo < -2147483648ll)
 333                                 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);
 334 #endif
 335 #endif
 336                 }
 337                 *(data++) = *(residual++) + (sum >> lp_quantization);
 338         }
 339
 340         /* Here's a slower but clearer version:
 341         for(i = 0; i < data_len; i++) {
 342                 sum = 0;
 343                 for(j = 0; j < order; j++)
 344                         sum += qlp_coeff[j] * data[i-j-1];
 345                 data[i] = residual[i] + (sum >> lp_quantization);
 346         }
 347         */
 348 }
 349
 350 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[])
 351 {
 352         unsigned i, j;
 353         FLAC__int64 sum;
 354         const FLAC__int32 *history;
 355
 356 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 357         fprintf(stderr,"FLAC__lpc_restore_signal_wide: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 358         for(i=0;i<order;i++)
 359                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 360         fprintf(stderr,"\n");
 361 #endif
 362         FLAC__ASSERT(order > 0);
 363
 364         for(i = 0; i < data_len; i++) {
 365                 sum = 0;
 366                 history = data;
 367                 for(j = 0; j < order; j++)
 368                         sum += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*(--history));
 369 #ifdef FLAC__OVERFLOW_DETECT
 370                 if(FLAC__bitmath_silog2_wide(sum >> lp_quantization) > 32) {
 371                         fprintf(stderr,"FLAC__lpc_restore_signal_wide: OVERFLOW, i=%u, sum=%lld\n", i, sum >> lp_quantization);
 372                         break;
 373                 }
 374                 if(FLAC__bitmath_silog2_wide((FLAC__int64)(*residual) + (sum >> lp_quantization)) > 32) {
 375                         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));
 376                         break;
 377                 }
 378 #endif
 379                 *(data++) = *(residual++) + (FLAC__int32)(sum >> lp_quantization);
 380         }
 381 }
 382
 383 #ifndef FLAC__INTEGER_ONLY_LIBRARY
 384
 385 FLAC__double FLAC__lpc_compute_expected_bits_per_residual_sample(FLAC__double lpc_error, unsigned total_samples)
 386 {
 387         FLAC__double error_scale;
 388
 389         FLAC__ASSERT(total_samples > 0);
 390
 391         error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__double)total_samples;
 392
 393         return FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error, error_scale);
 394 }
 395
 396 FLAC__double FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(FLAC__double lpc_error, FLAC__double error_scale)
 397 {
 398         if(lpc_error > 0.0) {
 399                 FLAC__double bps = (FLAC__double)0.5 * log(error_scale * lpc_error) / M_LN2;
 400                 if(bps >= 0.0)
 401                         return bps;
 402                 else
 403                         return 0.0;
 404         }
 405         else if(lpc_error < 0.0) { /* error should not be negative but can happen due to inadequate floating-point resolution */
 406                 return 1e32;
 407         }
 408         else {
 409                 return 0.0;
 410         }
 411 }
 412
 413 unsigned FLAC__lpc_compute_best_order(const FLAC__double lpc_error[], unsigned max_order, unsigned total_samples, unsigned bits_per_signal_sample)
 414 {
 415         unsigned order, best_order;
 416         FLAC__double best_bits, tmp_bits, error_scale;
 417
 418         FLAC__ASSERT(max_order > 0);
 419         FLAC__ASSERT(total_samples > 0);
 420
 421         error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__double)total_samples;
 422
 423         best_order = 0;
 424         best_bits = FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error[0], error_scale) * (FLAC__double)total_samples;
 425
 426         for(order = 1; order < max_order; order++) {
 427                 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);
 428                 if(tmp_bits < best_bits) {
 429                         best_order = order;
 430                         best_bits = tmp_bits;
 431                 }
 432         }
 433
 434         return best_order+1; /* +1 since index of lpc_error[] is order-1 */
 435 }
 436
 437 #endif /* !defined FLAC__INTEGER_ONLY_LIBRARY */