src/libFLAC/lpc.c

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