src/libFLAC/lpc.c

   1 /* libFLAC - Free Lossless Audio Codec library
   2  * Copyright (C) 2000,2001  Josh Coalson
   3  *
   4  * This library is free software; you can redistribute it and/or
   5  * modify it under the terms of the GNU Library General Public
   6  * License as published by the Free Software Foundation; either
   7  * version 2 of the License, or (at your option) any later version.
   8  *
   9  * This library is distributed in the hope that it will be useful,
  10  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  11  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  12  * Library General Public License for more details.
  13  *
  14  * You should have received a copy of the GNU Library General Public
  15  * License along with this library; if not, write to the
  16  * Free Software Foundation, Inc., 59 Temple Place - Suite 330,
  17  * Boston, MA  02111-1307, USA.
  18  */
  19
  20 #include <math.h>
  21 #include <stdio.h>
  22 #include "FLAC/assert.h"
  23 #include "FLAC/format.h"
  24 #include "private/lpc.h"
  25
  26 #ifndef M_LN2
  27 /* math.h in VC++ doesn't seem to have this (how Microsoft is that?) */
  28 #define M_LN2 0.69314718055994530942
  29 #endif
  30
  31 #define LOCAL_FABS(x) ((x)<0.0? -(x):(x))
  32
  33 void FLAC__lpc_compute_autocorrelation(const real data[], unsigned data_len, unsigned lag, real autoc[])
  34 {
  35         /* a readable, but slower, version */
  36 #if 0
  37         real d;
  38         unsigned i;
  39
  40         FLAC__ASSERT(lag > 0);
  41         FLAC__ASSERT(lag <= data_len);
  42
  43         while(lag--) {
  44                 for(i = lag, d = 0.0; i < data_len; i++)
  45                         d += data[i] * data[i - lag];
  46                 autoc[lag] = d;
  47         }
  48 #endif
  49
  50         /*
  51          * this version tends to run faster because of better data locality
  52          * ('data_len' is usually much larger than 'lag')
  53          */
  54         real d;
  55         unsigned sample, coeff;
  56         const unsigned limit = data_len - lag;
  57
  58         FLAC__ASSERT(lag > 0);
  59         FLAC__ASSERT(lag <= data_len);
  60
  61         for(coeff = 0; coeff < lag; coeff++)
  62                 autoc[coeff] = 0.0;
  63         for(sample = 0; sample <= limit; sample++) {
  64                 d = data[sample];
  65                 for(coeff = 0; coeff < lag; coeff++)
  66                         autoc[coeff] += d * data[sample+coeff];
  67         }
  68         for(; sample < data_len; sample++) {
  69                 d = data[sample];
  70                 for(coeff = 0; coeff < data_len - sample; coeff++)
  71                         autoc[coeff] += d * data[sample+coeff];
  72         }
  73 }
  74
  75 void FLAC__lpc_compute_lp_coefficients(const real autoc[], unsigned max_order, real lp_coeff[][FLAC__MAX_LPC_ORDER], real error[])
  76 {
  77         unsigned i, j;
  78         real r, err, ref[FLAC__MAX_LPC_ORDER], lpc[FLAC__MAX_LPC_ORDER];
  79
  80         FLAC__ASSERT(0 < max_order);
  81         FLAC__ASSERT(max_order <= FLAC__MAX_LPC_ORDER);
  82         FLAC__ASSERT(autoc[0] != 0.0);
  83
  84         err = autoc[0];
  85
  86         for(i = 0; i < max_order; i++) {
  87                 /* Sum up this iteration's reflection coefficient. */
  88                 r = -autoc[i+1];
  89                 for(j = 0; j < i; j++)
  90                         r -= lpc[j] * autoc[i-j];
  91                 ref[i] = (r/=err);
  92
  93                 /* Update LPC coefficients and total error. */
  94                 lpc[i]=r;
  95                 for(j = 0; j < (i>>1); j++) {
  96                         real tmp = lpc[j];
  97                         lpc[j] += r * lpc[i-1-j];
  98                         lpc[i-1-j] += r * tmp;
  99                 }
 100                 if(i & 1)
 101                         lpc[j] += lpc[j] * r;
 102
 103                 err *= (1.0 - r * r);
 104
 105                 /* save this order */
 106                 for(j = 0; j <= i; j++)
 107                         lp_coeff[i][j] = -lpc[j]; /* negate FIR filter coeff to get predictor coeff */
 108                 error[i] = err;
 109         }
 110 }
 111
 112 int FLAC__lpc_quantize_coefficients(const real lp_coeff[], unsigned order, unsigned precision, unsigned bits_per_sample, int32 qlp_coeff[], int *shift)
 113 {
 114         unsigned i;
 115         real d, cmax = -1e32;
 116
 117         FLAC__ASSERT(bits_per_sample > 0);
 118         FLAC__ASSERT(bits_per_sample <= sizeof(int32)*8);
 119         FLAC__ASSERT(precision > 0);
 120         FLAC__ASSERT(precision >= FLAC__MIN_QLP_COEFF_PRECISION);
 121         FLAC__ASSERT(precision + bits_per_sample < sizeof(int32)*8);
 122 #ifdef NDEBUG
 123         (void)bits_per_sample; /* silence compiler warning about unused parameter */
 124 #endif
 125
 126         /* drop one bit for the sign; from here on out we consider only |lp_coeff[i]| */
 127         precision--;
 128
 129         for(i = 0; i < order; i++) {
 130                 if(lp_coeff[i] == 0.0)
 131                         continue;
 132                 d = LOCAL_FABS(lp_coeff[i]);
 133                 if(d > cmax)
 134                         cmax = d;
 135         }
 136         if(cmax < 0.0) {
 137                 /* => coefficients are all 0, which means our constant-detect didn't work */
 138                 return 2;
 139         }
 140         else {
 141                 const int maxshift = (int)precision - (int)floor(log(cmax) / M_LN2) - 1;
 142                 const int max_shiftlimit = (1 << (FLAC__SUBFRAME_LPC_QLP_SHIFT_LEN-1)) - 1;
 143                 const int min_shiftlimit = -max_shiftlimit - 1;
 144
 145                 *shift = maxshift;
 146
 147                 if(*shift < min_shiftlimit || *shift > max_shiftlimit) {
 148                         return 1;
 149                 }
 150         }
 151
 152         if(*shift != 0) { /* just to avoid wasting time... */
 153                 for(i = 0; i < order; i++)
 154                         qlp_coeff[i] = (int32)floor(lp_coeff[i] * (real)(1 << *shift));
 155         }
 156         return 0;
 157 }
 158
 159 void FLAC__lpc_compute_residual_from_qlp_coefficients(const int32 data[], unsigned data_len, const int32 qlp_coeff[], unsigned order, int lp_quantization, int32 residual[])
 160 {
 161 #ifdef FLAC__OVERFLOW_DETECT
 162         int64 sumo;
 163 #endif
 164         unsigned i, j;
 165         int32 sum;
 166         const int32 *history;
 167
 168 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 169         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 170         for(i=0;i<order;i++)
 171                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 172         fprintf(stderr,"\n");
 173 #endif
 174         FLAC__ASSERT(order > 0);
 175
 176         for(i = 0; i < data_len; i++) {
 177 #ifdef FLAC__OVERFLOW_DETECT
 178                 sumo = 0;
 179 #endif
 180                 sum = 0;
 181                 history = data;
 182                 for(j = 0; j < order; j++) {
 183                         sum += qlp_coeff[j] * (*(--history));
 184 #ifdef FLAC__OVERFLOW_DETECT
 185                         sumo += (int64)qlp_coeff[j] * (int64)(*history);
 186                         if(sumo > 2147483647ll || sumo < -2147483648ll) {
 187                                 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);
 188                         }
 189 #endif
 190                 }
 191                 *(residual++) = *(data++) - (sum >> lp_quantization);
 192         }
 193
 194         /* Here's a slower but clearer version:
 195         for(i = 0; i < data_len; i++) {
 196                 sum = 0;
 197                 for(j = 0; j < order; j++)
 198                         sum += qlp_coeff[j] * data[i-j-1];
 199                 residual[i] = data[i] - (sum >> lp_quantization);
 200         }
 201         */
 202 }
 203
 204 void FLAC__lpc_restore_signal(const int32 residual[], unsigned data_len, const int32 qlp_coeff[], unsigned order, int lp_quantization, int32 data[])
 205 {
 206 #ifdef FLAC__OVERFLOW_DETECT
 207         int64 sumo;
 208 #endif
 209         unsigned i, j;
 210         int32 sum;
 211         const int32 *history;
 212
 213 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
 214         fprintf(stderr,"FLAC__lpc_restore_signal: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
 215         for(i=0;i<order;i++)
 216                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
 217         fprintf(stderr,"\n");
 218 #endif
 219         FLAC__ASSERT(order > 0);
 220
 221         for(i = 0; i < data_len; i++) {
 222 #ifdef FLAC__OVERFLOW_DETECT
 223                 sumo = 0;
 224 #endif
 225                 sum = 0;
 226                 history = data;
 227                 for(j = 0; j < order; j++) {
 228                         sum += qlp_coeff[j] * (*(--history));
 229 #ifdef FLAC__OVERFLOW_DETECT
 230                         sumo += (int64)qlp_coeff[j] * (int64)(*history);
 231                         if(sumo > 2147483647ll || sumo < -2147483648ll) {
 232                                 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);
 233                         }
 234 #endif
 235                 }
 236                 *(data++) = *(residual++) + (sum >> lp_quantization);
 237         }
 238
 239         /* Here's a slower but clearer version:
 240         for(i = 0; i < data_len; i++) {
 241                 sum = 0;
 242                 for(j = 0; j < order; j++)
 243                         sum += qlp_coeff[j] * data[i-j-1];
 244                 data[i] = residual[i] + (sum >> lp_quantization);
 245         }
 246         */
 247 }
 248
 249 real FLAC__lpc_compute_expected_bits_per_residual_sample(real lpc_error, unsigned total_samples)
 250 {
 251         real error_scale;
 252
 253         FLAC__ASSERT(total_samples > 0);
 254
 255         error_scale = 0.5 * M_LN2 * M_LN2 / (real)total_samples;
 256
 257         if(lpc_error > 0.0) {
 258                 real bps = 0.5 * log(error_scale * lpc_error) / M_LN2;
 259                 if(bps >= 0.0)
 260                         return bps;
 261                 else
 262                         return 0.0;
 263         }
 264         else if(lpc_error < 0.0) { /* error should not be negative but can happen due to inadequate float resolution */
 265                 return 1e32;
 266         }
 267         else {
 268                 return 0.0;
 269         }
 270 }
 271
 272 real FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(real lpc_error, real error_scale)
 273 {
 274         if(lpc_error > 0.0) {
 275                 real bps = 0.5 * log(error_scale * lpc_error) / M_LN2;
 276                 if(bps >= 0.0)
 277                         return bps;
 278                 else
 279                         return 0.0;
 280         }
 281         else if(lpc_error < 0.0) { /* error should not be negative but can happen due to inadequate float resolution */
 282                 return 1e32;
 283         }
 284         else {
 285                 return 0.0;
 286         }
 287 }
 288
 289 unsigned FLAC__lpc_compute_best_order(const real lpc_error[], unsigned max_order, unsigned total_samples, unsigned bits_per_signal_sample)
 290 {
 291         unsigned order, best_order;
 292         real best_bits, tmp_bits, error_scale;
 293
 294         FLAC__ASSERT(max_order > 0);
 295         FLAC__ASSERT(total_samples > 0);
 296
 297         error_scale = 0.5 * M_LN2 * M_LN2 / (real)total_samples;
 298
 299         best_order = 0;
 300         best_bits = FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error[0], error_scale) * (real)total_samples;
 301
 302         for(order = 1; order < max_order; order++) {
 303                 tmp_bits = FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error[order], error_scale) * (real)(total_samples - order) + (real)(order * bits_per_signal_sample);
 304                 if(tmp_bits < best_bits) {
 305                         best_order = order;
 306                         best_bits = tmp_bits;
 307                 }
 308         }
 309
 310         return best_order+1; /* +1 since index of lpc_error[] is order-1 */
 311 }