minor comments
[flac.git] / 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 #if HAVE_CONFIG_H
33 #  include <config.h>
34 #endif
35
36 #include <math.h>
37 #include "FLAC/assert.h"
38 #include "FLAC/format.h"
39 #include "private/bitmath.h"
40 #include "private/lpc.h"
41 #if defined DEBUG || defined FLAC__OVERFLOW_DETECT || defined FLAC__OVERFLOW_DETECT_VERBOSE
42 #include <stdio.h>
43 #endif
44
45 #ifndef FLAC__INTEGER_ONLY_LIBRARY
46
47 #ifndef M_LN2
48 /* math.h in VC++ doesn't seem to have this (how Microsoft is that?) */
49 #define M_LN2 0.69314718055994530942
50 #endif
51
52 void FLAC__lpc_window_data(const FLAC__real in[], const FLAC__real window[], FLAC__real out[], unsigned data_len)
53 {
54         unsigned i;
55         for(i = 0; i < data_len; i++)
56                 out[i] = in[i] * window[i];
57 }
58
59 void FLAC__lpc_compute_autocorrelation(const FLAC__real data[], unsigned data_len, unsigned lag, FLAC__real autoc[])
60 {
61         /* a readable, but slower, version */
62 #if 0
63         FLAC__real d;
64         unsigned i;
65
66         FLAC__ASSERT(lag > 0);
67         FLAC__ASSERT(lag <= data_len);
68
69         /*
70          * Technically we should subtract the mean first like so:
71          *   for(i = 0; i < data_len; i++)
72          *     data[i] -= mean;
73          * but it appears not to make enough of a difference to matter, and
74          * most signals are already closely centered around zero
75          */
76         while(lag--) {
77                 for(i = lag, d = 0.0; i < data_len; i++)
78                         d += data[i] * data[i - lag];
79                 autoc[lag] = d;
80         }
81 #endif
82
83         /*
84          * this version tends to run faster because of better data locality
85          * ('data_len' is usually much larger than 'lag')
86          */
87         FLAC__real d;
88         unsigned sample, coeff;
89         const unsigned limit = data_len - lag;
90
91         FLAC__ASSERT(lag > 0);
92         FLAC__ASSERT(lag <= data_len);
93
94         for(coeff = 0; coeff < lag; coeff++)
95                 autoc[coeff] = 0.0;
96         for(sample = 0; sample <= limit; sample++) {
97                 d = data[sample];
98                 for(coeff = 0; coeff < lag; coeff++)
99                         autoc[coeff] += d * data[sample+coeff];
100         }
101         for(; sample < data_len; sample++) {
102                 d = data[sample];
103                 for(coeff = 0; coeff < data_len - sample; coeff++)
104                         autoc[coeff] += d * data[sample+coeff];
105         }
106 }
107
108 void FLAC__lpc_compute_lp_coefficients(const FLAC__real autoc[], unsigned max_order, FLAC__real lp_coeff[][FLAC__MAX_LPC_ORDER], FLAC__double error[])
109 {
110         unsigned i, j;
111         FLAC__double r, err, ref[FLAC__MAX_LPC_ORDER], lpc[FLAC__MAX_LPC_ORDER];
112
113         FLAC__ASSERT(0 < max_order);
114         FLAC__ASSERT(max_order <= FLAC__MAX_LPC_ORDER);
115         FLAC__ASSERT(autoc[0] != 0.0);
116
117         err = autoc[0];
118
119         for(i = 0; i < max_order; i++) {
120                 /* Sum up this iteration's reflection coefficient. */
121                 r = -autoc[i+1];
122                 for(j = 0; j < i; j++)
123                         r -= lpc[j] * autoc[i-j];
124                 ref[i] = (r/=err);
125
126                 /* Update LPC coefficients and total error. */
127                 lpc[i]=r;
128                 for(j = 0; j < (i>>1); j++) {
129                         FLAC__double tmp = lpc[j];
130                         lpc[j] += r * lpc[i-1-j];
131                         lpc[i-1-j] += r * tmp;
132                 }
133                 if(i & 1)
134                         lpc[j] += lpc[j] * r;
135
136                 err *= (1.0 - r * r);
137
138                 /* save this order */
139                 for(j = 0; j <= i; j++)
140                         lp_coeff[i][j] = (FLAC__real)(-lpc[j]); /* negate FIR filter coeff to get predictor coeff */
141                 error[i] = err;
142         }
143 }
144
145 int FLAC__lpc_quantize_coefficients(const FLAC__real lp_coeff[], unsigned order, unsigned precision, FLAC__int32 qlp_coeff[], int *shift)
146 {
147         unsigned i;
148         FLAC__double d, cmax = -1e32;
149         FLAC__int32 qmax, qmin;
150         const int max_shiftlimit = (1 << (FLAC__SUBFRAME_LPC_QLP_SHIFT_LEN-1)) - 1;
151         const int min_shiftlimit = -max_shiftlimit - 1;
152
153         FLAC__ASSERT(precision > 0);
154         FLAC__ASSERT(precision >= FLAC__MIN_QLP_COEFF_PRECISION);
155
156         /* drop one bit for the sign; from here on out we consider only |lp_coeff[i]| */
157         precision--;
158         qmax = 1 << precision;
159         qmin = -qmax;
160         qmax--;
161
162         for(i = 0; i < order; i++) {
163                 if(lp_coeff[i] == 0.0)
164                         continue;
165                 d = fabs(lp_coeff[i]);
166                 if(d > cmax)
167                         cmax = d;
168         }
169 redo_it:
170         if(cmax <= 0.0) {
171                 /* => coefficients are all 0, which means our constant-detect didn't work */
172                 return 2;
173         }
174         else {
175                 int log2cmax;
176
177                 (void)frexp(cmax, &log2cmax);
178                 log2cmax--;
179                 *shift = (int)precision - log2cmax - 1;
180
181                 if(*shift < min_shiftlimit || *shift > max_shiftlimit) {
182 #if 0
183                         /*@@@ this does not seem to help at all, but was not extensively tested either: */
184                         if(*shift > max_shiftlimit)
185                                 *shift = max_shiftlimit;
186                         else
187 #endif
188                                 return 1;
189                 }
190         }
191
192         if(*shift >= 0) {
193                 for(i = 0; i < order; i++) {
194                         qlp_coeff[i] = (FLAC__int32)floor((FLAC__double)lp_coeff[i] * (FLAC__double)(1 << *shift));
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 << *shift), floor((FLAC__double)lp_coeff[i] * (FLAC__double)(1 << *shift)));
200 #endif
201                                 cmax *= 2.0;
202                                 goto redo_it;
203                         }
204                 }
205         }
206         else { /* (*shift < 0) */
207                 const int nshift = -(*shift);
208 #ifdef DEBUG
209                 fprintf(stderr,"FLAC__lpc_quantize_coefficients: negative shift = %d\n", *shift);
210 #endif
211                 for(i = 0; i < order; i++) {
212                         qlp_coeff[i] = (FLAC__int32)floor((FLAC__double)lp_coeff[i] / (FLAC__double)(1 << nshift));
213
214                         /* double-check the result */
215                         if(qlp_coeff[i] > qmax || qlp_coeff[i] < qmin) {
216 #ifdef FLAC__OVERFLOW_DETECT
217                                 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)));
218 #endif
219                                 cmax *= 2.0;
220                                 goto redo_it;
221                         }
222                 }
223         }
224
225         return 0;
226 }
227
228 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[])
229 {
230 #ifdef FLAC__OVERFLOW_DETECT
231         FLAC__int64 sumo;
232 #endif
233         unsigned i, j;
234         FLAC__int32 sum;
235         const FLAC__int32 *history;
236
237 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
238         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
239         for(i=0;i<order;i++)
240                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
241         fprintf(stderr,"\n");
242 #endif
243         FLAC__ASSERT(order > 0);
244
245         for(i = 0; i < data_len; i++) {
246 #ifdef FLAC__OVERFLOW_DETECT
247                 sumo = 0;
248 #endif
249                 sum = 0;
250                 history = data;
251                 for(j = 0; j < order; j++) {
252                         sum += qlp_coeff[j] * (*(--history));
253 #ifdef FLAC__OVERFLOW_DETECT
254                         sumo += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*history);
255 #if defined _MSC_VER
256                         if(sumo > 2147483647I64 || sumo < -2147483648I64)
257                                 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);
258 #else
259                         if(sumo > 2147483647ll || sumo < -2147483648ll)
260                                 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);
261 #endif
262 #endif
263                 }
264                 *(residual++) = *(data++) - (sum >> lp_quantization);
265         }
266
267         /* Here's a slower but clearer version:
268         for(i = 0; i < data_len; i++) {
269                 sum = 0;
270                 for(j = 0; j < order; j++)
271                         sum += qlp_coeff[j] * data[i-j-1];
272                 residual[i] = data[i] - (sum >> lp_quantization);
273         }
274         */
275 }
276
277 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[])
278 {
279         unsigned i, j;
280         FLAC__int64 sum;
281         const FLAC__int32 *history;
282
283 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
284         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
285         for(i=0;i<order;i++)
286                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
287         fprintf(stderr,"\n");
288 #endif
289         FLAC__ASSERT(order > 0);
290
291         for(i = 0; i < data_len; i++) {
292                 sum = 0;
293                 history = data;
294                 for(j = 0; j < order; j++)
295                         sum += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*(--history));
296 #ifdef FLAC__OVERFLOW_DETECT
297                 if(FLAC__bitmath_silog2_wide(sum >> lp_quantization) > 32) {
298                         fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: OVERFLOW, i=%u, sum=%lld\n", i, sum >> lp_quantization);
299                         break;
300                 }
301                 if(FLAC__bitmath_silog2_wide((FLAC__int64)(*data) - (sum >> lp_quantization)) > 32) {
302                         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));
303                         break;
304                 }
305 #endif
306                 *(residual++) = *(data++) - (FLAC__int32)(sum >> lp_quantization);
307         }
308 }
309
310 #endif /* !defined FLAC__INTEGER_ONLY_LIBRARY */
311
312 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[])
313 {
314 #ifdef FLAC__OVERFLOW_DETECT
315         FLAC__int64 sumo;
316 #endif
317         unsigned i, j;
318         FLAC__int32 sum;
319         const FLAC__int32 *history;
320
321 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
322         fprintf(stderr,"FLAC__lpc_restore_signal: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
323         for(i=0;i<order;i++)
324                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
325         fprintf(stderr,"\n");
326 #endif
327         FLAC__ASSERT(order > 0);
328
329         for(i = 0; i < data_len; i++) {
330 #ifdef FLAC__OVERFLOW_DETECT
331                 sumo = 0;
332 #endif
333                 sum = 0;
334                 history = data;
335                 for(j = 0; j < order; j++) {
336                         sum += qlp_coeff[j] * (*(--history));
337 #ifdef FLAC__OVERFLOW_DETECT
338                         sumo += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*history);
339 #if defined _MSC_VER
340                         if(sumo > 2147483647I64 || sumo < -2147483648I64)
341                                 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);
342 #else
343                         if(sumo > 2147483647ll || sumo < -2147483648ll)
344                                 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);
345 #endif
346 #endif
347                 }
348                 *(data++) = *(residual++) + (sum >> lp_quantization);
349         }
350
351         /* Here's a slower but clearer version:
352         for(i = 0; i < data_len; i++) {
353                 sum = 0;
354                 for(j = 0; j < order; j++)
355                         sum += qlp_coeff[j] * data[i-j-1];
356                 data[i] = residual[i] + (sum >> lp_quantization);
357         }
358         */
359 }
360
361 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[])
362 {
363         unsigned i, j;
364         FLAC__int64 sum;
365         const FLAC__int32 *history;
366
367 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
368         fprintf(stderr,"FLAC__lpc_restore_signal_wide: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
369         for(i=0;i<order;i++)
370                 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
371         fprintf(stderr,"\n");
372 #endif
373         FLAC__ASSERT(order > 0);
374
375         for(i = 0; i < data_len; i++) {
376                 sum = 0;
377                 history = data;
378                 for(j = 0; j < order; j++)
379                         sum += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*(--history));
380 #ifdef FLAC__OVERFLOW_DETECT
381                 if(FLAC__bitmath_silog2_wide(sum >> lp_quantization) > 32) {
382                         fprintf(stderr,"FLAC__lpc_restore_signal_wide: OVERFLOW, i=%u, sum=%lld\n", i, sum >> lp_quantization);
383                         break;
384                 }
385                 if(FLAC__bitmath_silog2_wide((FLAC__int64)(*residual) + (sum >> lp_quantization)) > 32) {
386                         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));
387                         break;
388                 }
389 #endif
390                 *(data++) = *(residual++) + (FLAC__int32)(sum >> lp_quantization);
391         }
392 }
393
394 #ifndef FLAC__INTEGER_ONLY_LIBRARY
395
396 FLAC__double FLAC__lpc_compute_expected_bits_per_residual_sample(FLAC__double lpc_error, unsigned total_samples)
397 {
398         FLAC__double error_scale;
399
400         FLAC__ASSERT(total_samples > 0);
401
402         error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__double)total_samples;
403
404         return FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error, error_scale);
405 }
406
407 FLAC__double FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(FLAC__double lpc_error, FLAC__double error_scale)
408 {
409         if(lpc_error > 0.0) {
410                 FLAC__double bps = (FLAC__double)0.5 * log(error_scale * lpc_error) / M_LN2;
411                 if(bps >= 0.0)
412                         return bps;
413                 else
414                         return 0.0;
415         }
416         else if(lpc_error < 0.0) { /* error should not be negative but can happen due to inadequate floating-point resolution */
417                 return 1e32;
418         }
419         else {
420                 return 0.0;
421         }
422 }
423
424 unsigned FLAC__lpc_compute_best_order(const FLAC__double lpc_error[], unsigned max_order, unsigned total_samples, unsigned overhead_bits_per_order)
425 {
426         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 */
427         FLAC__double bits, best_bits, error_scale;
428
429         FLAC__ASSERT(max_order > 0);
430         FLAC__ASSERT(total_samples > 0);
431
432         error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__double)total_samples;
433
434         best_index = 0;
435         best_bits = (unsigned)(-1);
436
437         for(index = 0, order = 1; index < max_order; index++, order++) {
438                 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);
439                 if(bits < best_bits) {
440                         best_index = index;
441                         best_bits = bits;
442                 }
443         }
444
445         return best_index+1; /* +1 since index of lpc_error[] is order-1 */
446 }
447
448 #endif /* !defined FLAC__INTEGER_ONLY_LIBRARY */