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 #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         /*
  66          * Technically we should subtract the mean first like so:
  67          *   for(i = 0; i < data_len; i++)
  68          *     data[i] -= mean;
  69          * but it appears not to make enough of a difference to matter, and
  70          * most signals are already closely centered around zero
  71          */
  72         while(lag--) {
  73                 for(i = lag, d = 0.0; i < data_len; i++)
  74                         d += data[i] * data[i - lag];
  75                 autoc[lag] = d;
  76         }
  77 #endif
  78
  79         /*
  80          * this version tends to run faster because of better data locality
  81          * ('data_len' is usually much larger than 'lag')
  82          */
  83         FLAC__real d;
  84         unsigned sample, coeff;
  85         const unsigned limit = data_len - lag;
  86
  87         FLAC__ASSERT(lag > 0);
  88         FLAC__ASSERT(lag <= data_len);
  89
  90         for(coeff = 0; coeff < lag; coeff++)
  91                 autoc[coeff] = 0.0;
  92         for(sample = 0; sample <= limit; sample++) {
  93                 d = data[sample];
  94                 for(coeff = 0; coeff < lag; coeff++)
  95                         autoc[coeff] += d * data[sample+coeff];
  96         }
  97         for(; sample < data_len; sample++) {
  98                 d = data[sample];
  99                 for(coeff = 0; coeff < data_len - sample; coeff++)
 100                         autoc[coeff] += d * data[sample+coeff];
 101         }
 102 }
 103
 104 void FLAC__lpc_compute_lp_coefficients(const FLAC__real autoc[], unsigned max_order, FLAC__real lp_coeff[][FLAC__MAX_LPC_ORDER], FLAC__double error[])
 105 {
 106         unsigned i, j;
 107         FLAC__double r, err, ref[FLAC__MAX_LPC_ORDER], lpc[FLAC__MAX_LPC_ORDER];
 108
 109         FLAC__ASSERT(0 < max_order);
 110         FLAC__ASSERT(max_order <= FLAC__MAX_LPC_ORDER);
 111         FLAC__ASSERT(autoc[0] != 0.0);
 112
 113         err = autoc[0];
 114
 115         for(i = 0; i < max_order; i++) {
 116                 /* Sum up this iteration's reflection coefficient. */
 117                 r = -autoc[i+1];
 118                 for(j = 0; j < i; j++)
 119                         r -= lpc[j] * autoc[i-j];
 120                 ref[i] = (r/=err);
 121
 122                 /* Update LPC coefficients and total error. */
 123                 lpc[i]=r;
 124                 for(j = 0; j < (i>>1); j++) {
 125                         FLAC__double tmp = lpc[j];
 126                         lpc[j] += r * lpc[i-1-j];
 127                         lpc[i-1-j] += r * tmp;
 128                 }
 129                 if(i & 1)
 130                         lpc[j] += lpc[j] * r;
 131
 132                 err *= (1.0 - r * r);
 133
 134                 /* save this order */
 135                 for(j = 0; j <= i; j++)
 136                         lp_coeff[i][j] = (FLAC__real)(-lpc[j]); /* negate FIR filter coeff to get predictor coeff */
 137                 error[i] = err;
 138         }
 139 }
 140
 141 int FLAC__lpc_quantize_coefficients(const FLAC__real lp_coeff[], unsigned order, unsigned precision, FLAC__int32 qlp_coeff[], int *shift)
 142 {
 143         unsigned i;
 144         FLAC__double d, cmax = -1e32;
 145         FLAC__int32 qmax, qmin;
 146         const int max_shiftlimit = (1 << (FLAC__SUBFRAME_LPC_QLP_SHIFT_LEN-1)) - 1;
 147         const int min_shiftlimit = -max_shiftlimit - 1;
 148
 149         FLAC__ASSERT(precision > 0);
 150         FLAC__ASSERT(precision >= FLAC__MIN_QLP_COEFF_PRECISION);
 151
 152         /* drop one bit for the sign; from here on out we consider only |lp_coeff[i]| */
 153         precision--;
 154         qmax = 1 << precision;
 155         qmin = -qmax;
 156         qmax--;
 157
 158         for(i = 0; i < order; i++) {
 159                 if(lp_coeff[i] == 0.0)
 160                         continue;
 161                 d = fabs(lp_coeff[i]);
 162                 if(d > cmax)
 163                         cmax = d;
 164         }
 165 redo_it:
 166         if(cmax <= 0.0) {
 167                 /* => coefficients are all 0, which means our constant-detect didn't work */
 168                 return 2;
 169         }
 170         else {
 171                 int log2cmax;
 172
 173                 (void)frexp(cmax, &log2cmax);
 174                 log2cmax--;
 175                 *shift = (int)precision - log2cmax - 1;
 176
 177                 if(*shift < min_shiftlimit || *shift > max_shiftlimit) {
 178 #if 0
 179                         /*@@@ this does not seem to help at all, but was not extensively tested either: */
 180                         if(*shift > max_shiftlimit)
 181                                 *shift = max_shiftlimit;
 182                         else
 183 #endif
 184                                 return 1;
 185                 }
 186         }
 187
 188         if(*shift >= 0) {
 189                 for(i = 0; i < order; i++) {
 190                         qlp_coeff[i] = (FLAC__int32)floor((FLAC__double)lp_coeff[i] * (FLAC__double)(1 << *shift));
 191
 192                         /* double-check the result */
 193                         if(qlp_coeff[i] > qmax || qlp_coeff[i] < qmin) {
 194 #ifdef FLAC__OVERFLOW_DETECT
 195                                 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)));
 196 #endif
 197                                 cmax *= 2.0;
 198                                 goto redo_it;
 199                         }
 200                 }
 201         }
 202         else { /* (*shift < 0) */
 203                 const int nshift = -(*shift);
 204 #ifdef DEBUG
 205                 fprintf(stderr,"FLAC__lpc_quantize_coefficients: negative shift = %d\n", *shift);
 206 #endif
 207                 for(i = 0; i < order; i++) {
 208                         qlp_coeff[i] = (FLAC__int32)floor((FLAC__double)lp_coeff[i] / (FLAC__double)(1 << nshift));
 209
 210                         /* double-check the result */
 211                         if(qlp_coeff[i] > qmax || qlp_coeff[i] < qmin) {
 212 #ifdef FLAC__OVERFLOW_DETECT
 213                                 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)));
 214 #endif
 215                                 cmax *= 2.0;
 216                                 goto redo_it;
 217                         }
 218                 }
 219         }
 220
 221         return 0;
 222 }
 223
 224 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[])
 225 {
 226 #ifdef FLAC__OVERFLOW_DETECT
 227         FLAC__int64 sumo;
 228 #endif
 229         unsigned i, j;
 230         FLAC__int32 sum;
 231         const FLAC__int32 *history;
 232
 233 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 234         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 235         for(i=0;i<order;i++)
 236                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 237         fprintf(stderr,"\n");
 238 #endif
 239         FLAC__ASSERT(order > 0);
 240
 241         for(i = 0; i < data_len; i++) {
 242 #ifdef FLAC__OVERFLOW_DETECT
 243                 sumo = 0;
 244 #endif
 245                 sum = 0;
 246                 history = data;
 247                 for(j = 0; j < order; j++) {
 248                         sum += qlp_coeff[j] * (*(--history));
 249 #ifdef FLAC__OVERFLOW_DETECT
 250                         sumo += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*history);
 251 #if defined _MSC_VER
 252                         if(sumo > 2147483647I64 || sumo < -2147483648I64)
 253                                 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);
 254 #else
 255                         if(sumo > 2147483647ll || sumo < -2147483648ll)
 256                                 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);
 257 #endif
 258 #endif
 259                 }
 260                 *(residual++) = *(data++) - (sum >> lp_quantization);
 261         }
 262
 263         /* Here's a slower but clearer version:
 264         for(i = 0; i < data_len; i++) {
 265                 sum = 0;
 266                 for(j = 0; j < order; j++)
 267                         sum += qlp_coeff[j] * data[i-j-1];
 268                 residual[i] = data[i] - (sum >> lp_quantization);
 269         }
 270         */
 271 }
 272
 273 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[])
 274 {
 275         unsigned i, j;
 276         FLAC__int64 sum;
 277         const FLAC__int32 *history;
 278
 279 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 280         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 281         for(i=0;i<order;i++)
 282                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 283         fprintf(stderr,"\n");
 284 #endif
 285         FLAC__ASSERT(order > 0);
 286
 287         for(i = 0; i < data_len; i++) {
 288                 sum = 0;
 289                 history = data;
 290                 for(j = 0; j < order; j++)
 291                         sum += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*(--history));
 292 #ifdef FLAC__OVERFLOW_DETECT
 293                 if(FLAC__bitmath_silog2_wide(sum >> lp_quantization) > 32) {
 294                         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: OVERFLOW, i=%u, sum=%lld\n", i, sum >> lp_quantization);
 295                         break;
 296                 }
 297                 if(FLAC__bitmath_silog2_wide((FLAC__int64)(*data) - (sum >> lp_quantization)) > 32) {
 298                         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));
 299                         break;
 300                 }
 301 #endif
 302                 *(residual++) = *(data++) - (FLAC__int32)(sum >> lp_quantization);
 303         }
 304 }
 305
 306 #endif /* !defined FLAC__INTEGER_ONLY_LIBRARY */
 307
 308 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[])
 309 {
 310 #ifdef FLAC__OVERFLOW_DETECT
 311         FLAC__int64 sumo;
 312 #endif
 313         unsigned i, j;
 314         FLAC__int32 sum;
 315         const FLAC__int32 *history;
 316
 317 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 318         fprintf(stderr,"FLAC__lpc_restore_signal: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 319         for(i=0;i<order;i++)
 320                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 321         fprintf(stderr,"\n");
 322 #endif
 323         FLAC__ASSERT(order > 0);
 324
 325         for(i = 0; i < data_len; i++) {
 326 #ifdef FLAC__OVERFLOW_DETECT
 327                 sumo = 0;
 328 #endif
 329                 sum = 0;
 330                 history = data;
 331                 for(j = 0; j < order; j++) {
 332                         sum += qlp_coeff[j] * (*(--history));
 333 #ifdef FLAC__OVERFLOW_DETECT
 334                         sumo += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*history);
 335 #if defined _MSC_VER
 336                         if(sumo > 2147483647I64 || sumo < -2147483648I64)
 337                                 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);
 338 #else
 339                         if(sumo > 2147483647ll || sumo < -2147483648ll)
 340                                 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);
 341 #endif
 342 #endif
 343                 }
 344                 *(data++) = *(residual++) + (sum >> lp_quantization);
 345         }
 346
 347         /* Here's a slower but clearer version:
 348         for(i = 0; i < data_len; i++) {
 349                 sum = 0;
 350                 for(j = 0; j < order; j++)
 351                         sum += qlp_coeff[j] * data[i-j-1];
 352                 data[i] = residual[i] + (sum >> lp_quantization);
 353         }
 354         */
 355 }
 356
 357 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[])
 358 {
 359         unsigned i, j;
 360         FLAC__int64 sum;
 361         const FLAC__int32 *history;
 362
 363 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 364         fprintf(stderr,"FLAC__lpc_restore_signal_wide: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 365         for(i=0;i<order;i++)
 366                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 367         fprintf(stderr,"\n");
 368 #endif
 369         FLAC__ASSERT(order > 0);
 370
 371         for(i = 0; i < data_len; i++) {
 372                 sum = 0;
 373                 history = data;
 374                 for(j = 0; j < order; j++)
 375                         sum += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*(--history));
 376 #ifdef FLAC__OVERFLOW_DETECT
 377                 if(FLAC__bitmath_silog2_wide(sum >> lp_quantization) > 32) {
 378                         fprintf(stderr,"FLAC__lpc_restore_signal_wide: OVERFLOW, i=%u, sum=%lld\n", i, sum >> lp_quantization);
 379                         break;
 380                 }
 381                 if(FLAC__bitmath_silog2_wide((FLAC__int64)(*residual) + (sum >> lp_quantization)) > 32) {
 382                         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));
 383                         break;
 384                 }
 385 #endif
 386                 *(data++) = *(residual++) + (FLAC__int32)(sum >> lp_quantization);
 387         }
 388 }
 389
 390 #ifndef FLAC__INTEGER_ONLY_LIBRARY
 391
 392 FLAC__double FLAC__lpc_compute_expected_bits_per_residual_sample(FLAC__double lpc_error, unsigned total_samples)
 393 {
 394         FLAC__double error_scale;
 395
 396         FLAC__ASSERT(total_samples > 0);
 397
 398         error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__double)total_samples;
 399
 400         return FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error, error_scale);
 401 }
 402
 403 FLAC__double FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(FLAC__double lpc_error, FLAC__double error_scale)
 404 {
 405         if(lpc_error > 0.0) {
 406                 FLAC__double bps = (FLAC__double)0.5 * log(error_scale * lpc_error) / M_LN2;
 407                 if(bps >= 0.0)
 408                         return bps;
 409                 else
 410                         return 0.0;
 411         }
 412         else if(lpc_error < 0.0) { /* error should not be negative but can happen due to inadequate floating-point resolution */
 413                 return 1e32;
 414         }
 415         else {
 416                 return 0.0;
 417         }
 418 }
 419
 420 unsigned FLAC__lpc_compute_best_order(const FLAC__double lpc_error[], unsigned max_order, unsigned total_samples, unsigned overhead_bits_per_order)
 421 {
 422         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 */
 423         FLAC__double bits, best_bits, error_scale;
 424
 425         FLAC__ASSERT(max_order > 0);
 426         FLAC__ASSERT(total_samples > 0);
 427
 428         error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__double)total_samples;
 429
 430         best_index = 0;
 431         best_bits = (unsigned)(-1);
 432
 433         for(index = 0, order = 1; index < max_order; index++, order++) {
 434                 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);
 435                 if(bits < best_bits) {
 436                         best_index = index;
 437                         best_bits = bits;
 438                 }
 439         }
 440
 441         return best_index+1; /* +1 since index of lpc_error[] is order-1 */
 442 }
 443
 444 #endif /* !defined FLAC__INTEGER_ONLY_LIBRARY */