1 /* libFLAC - Free Lossless Audio Codec library
2 * Copyright (C) 2000,2001,2002,2003,2004,2005,2006,2007 Josh Coalson
4 * Redistribution and use in source and binary forms, with or without
5 * modification, are permitted provided that the following conditions
8 * - Redistributions of source code must retain the above copyright
9 * notice, this list of conditions and the following disclaimer.
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.
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.
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.
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
45 #ifndef FLAC__INTEGER_ONLY_LIBRARY
48 /* math.h in VC++ doesn't seem to have this (how Microsoft is that?) */
49 #define M_LN2 0.69314718055994530942
52 void FLAC__lpc_window_data(const FLAC__real in[], const FLAC__real window[], FLAC__real out[], unsigned data_len)
55 for(i = 0; i < data_len; i++)
56 out[i] = in[i] * window[i];
59 void FLAC__lpc_compute_autocorrelation(const FLAC__real data[], unsigned data_len, unsigned lag, FLAC__real autoc[])
61 /* a readable, but slower, version */
66 FLAC__ASSERT(lag > 0);
67 FLAC__ASSERT(lag <= data_len);
70 * Technically we should subtract the mean first like so:
71 * for(i = 0; i < data_len; i++)
73 * but it appears not to make enough of a difference to matter, and
74 * most signals are already closely centered around zero
77 for(i = lag, d = 0.0; i < data_len; i++)
78 d += data[i] * data[i - lag];
84 * this version tends to run faster because of better data locality
85 * ('data_len' is usually much larger than 'lag')
88 unsigned sample, coeff;
89 const unsigned limit = data_len - lag;
91 FLAC__ASSERT(lag > 0);
92 FLAC__ASSERT(lag <= data_len);
94 for(coeff = 0; coeff < lag; coeff++)
96 for(sample = 0; sample <= limit; sample++) {
98 for(coeff = 0; coeff < lag; coeff++)
99 autoc[coeff] += d * data[sample+coeff];
101 for(; sample < data_len; sample++) {
103 for(coeff = 0; coeff < data_len - sample; coeff++)
104 autoc[coeff] += d * data[sample+coeff];
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[])
111 FLAC__double r, err, ref[FLAC__MAX_LPC_ORDER], lpc[FLAC__MAX_LPC_ORDER];
113 FLAC__ASSERT(0 != max_order);
114 FLAC__ASSERT(0 < *max_order);
115 FLAC__ASSERT(*max_order <= FLAC__MAX_LPC_ORDER);
116 FLAC__ASSERT(autoc[0] != 0.0);
120 for(i = 0; i < *max_order; i++) {
121 /* Sum up this iteration's reflection coefficient. */
123 for(j = 0; j < i; j++)
124 r -= lpc[j] * autoc[i-j];
127 /* Update LPC coefficients and total error. */
129 for(j = 0; j < (i>>1); j++) {
130 FLAC__double tmp = lpc[j];
131 lpc[j] += r * lpc[i-1-j];
132 lpc[i-1-j] += r * tmp;
135 lpc[j] += lpc[j] * r;
137 err *= (1.0 - r * r);
139 /* save this order */
140 for(j = 0; j <= i; j++)
141 lp_coeff[i][j] = (FLAC__real)(-lpc[j]); /* negate FIR filter coeff to get predictor coeff */
144 /* see SF bug #1601812 http://sourceforge.net/tracker/index.php?func=detail&aid=1601812&group_id=13478&atid=113478 */
152 int FLAC__lpc_quantize_coefficients(const FLAC__real lp_coeff[], unsigned order, unsigned precision, FLAC__int32 qlp_coeff[], int *shift)
156 FLAC__int32 qmax, qmin;
158 FLAC__ASSERT(precision > 0);
159 FLAC__ASSERT(precision >= FLAC__MIN_QLP_COEFF_PRECISION);
161 /* drop one bit for the sign; from here on out we consider only |lp_coeff[i]| */
163 qmax = 1 << precision;
167 /* calc cmax = max( |lp_coeff[i]| ) */
169 for(i = 0; i < order; i++) {
170 const FLAC__double d = fabs(lp_coeff[i]);
176 /* => coefficients are all 0, which means our constant-detect didn't work */
180 const int max_shiftlimit = (1 << (FLAC__SUBFRAME_LPC_QLP_SHIFT_LEN-1)) - 1;
181 const int min_shiftlimit = -max_shiftlimit - 1;
184 (void)frexp(cmax, &log2cmax);
186 *shift = (int)precision - log2cmax - 1;
188 if(*shift > max_shiftlimit)
189 *shift = max_shiftlimit;
190 else if(*shift < min_shiftlimit)
195 FLAC__double error = 0.0;
197 for(i = 0; i < order; i++) {
198 error += lp_coeff[i] * (1 << *shift);
201 q = (FLAC__int32)(error + 0.5);
203 q = (FLAC__int32)(error - 0.5);
205 q = lround(error); /* round() is also suitable */
207 #ifdef FLAC__OVERFLOW_DETECT
208 if(q > qmax+1) /* we expect q==qmax+1 occasionally due to lround() */
209 fprintf(stderr,"FLAC__lpc_quantize_coefficients: quantizer overflow: q>qmax %d>%d shift=%d cmax=%f precision=%u lpc[%u]=%f\n",q,qmax,*shift,cmax,precision+1,i,lp_coeff[i]);
211 fprintf(stderr,"FLAC__lpc_quantize_coefficients: quantizer overflow: q<qmin %d<%d shift=%d cmax=%f precision=%u lpc[%u]=%f\n",q,qmin,*shift,cmax,precision+1,i,lp_coeff[i]);
221 /* negative shift is very rare but due to design flaw, negative shift is
222 * a NOP in the decoder, so it must be handled specially by scaling down
226 const int nshift = -(*shift);
227 FLAC__double error = 0.0;
230 fprintf(stderr,"FLAC__lpc_quantize_coefficients: negative shift=%d order=%u cmax=%f\n", *shift, order, cmax);
232 for(i = 0; i < order; i++) {
233 error += lp_coeff[i] / (1 << nshift);
236 q = (FLAC__int32)(error + 0.5);
238 q = (FLAC__int32)(error - 0.5);
240 q = lround(error); /* round() is also suitable */
242 #ifdef FLAC__OVERFLOW_DETECT
243 if(q > qmax+1) /* we expect q==qmax+1 occasionally due to lround() */
244 fprintf(stderr,"FLAC__lpc_quantize_coefficients: quantizer overflow: q>qmax %d>%d shift=%d cmax=%f precision=%u lpc[%u]=%f\n",q,qmax,*shift,cmax,precision+1,i,lp_coeff[i]);
246 fprintf(stderr,"FLAC__lpc_quantize_coefficients: quantizer overflow: q<qmin %d<%d shift=%d cmax=%f precision=%u lpc[%u]=%f\n",q,qmin,*shift,cmax,precision+1,i,lp_coeff[i]);
261 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[])
263 #ifdef FLAC__OVERFLOW_DETECT
268 const FLAC__int32 *history;
270 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
271 fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
273 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
274 fprintf(stderr,"\n");
276 FLAC__ASSERT(order > 0);
278 for(i = 0; i < data_len; i++) {
279 #ifdef FLAC__OVERFLOW_DETECT
284 for(j = 0; j < order; j++) {
285 sum += qlp_coeff[j] * (*(--history));
286 #ifdef FLAC__OVERFLOW_DETECT
287 sumo += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*history);
289 if(sumo > 2147483647I64 || sumo < -2147483648I64)
290 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);
292 if(sumo > 2147483647ll || sumo < -2147483648ll)
293 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,(long long)sumo);
297 *(residual++) = *(data++) - (sum >> lp_quantization);
300 /* Here's a slower but clearer version:
301 for(i = 0; i < data_len; i++) {
303 for(j = 0; j < order; j++)
304 sum += qlp_coeff[j] * data[i-j-1];
305 residual[i] = data[i] - (sum >> lp_quantization);
310 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[])
314 const FLAC__int32 *history;
316 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
317 fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
319 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
320 fprintf(stderr,"\n");
322 FLAC__ASSERT(order > 0);
324 for(i = 0; i < data_len; i++) {
327 for(j = 0; j < order; j++)
328 sum += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*(--history));
329 #ifdef FLAC__OVERFLOW_DETECT
330 if(FLAC__bitmath_silog2_wide(sum >> lp_quantization) > 32) {
332 fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: OVERFLOW, i=%u, sum=%I64d\n", i, sum >> lp_quantization);
334 fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: OVERFLOW, i=%u, sum=%lld\n", i, (long long)(sum >> lp_quantization));
338 if(FLAC__bitmath_silog2_wide((FLAC__int64)(*data) - (sum >> lp_quantization)) > 32) {
340 fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: OVERFLOW, i=%u, data=%d, sum=%I64d, residual=%I64d\n", i, *data, sum >> lp_quantization, (FLAC__int64)(*data) - (sum >> lp_quantization));
342 fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: OVERFLOW, i=%u, data=%d, sum=%lld, residual=%lld\n", i, *data, (long long)(sum >> lp_quantization), (long long)((FLAC__int64)(*data) - (sum >> lp_quantization)));
347 *(residual++) = *(data++) - (FLAC__int32)(sum >> lp_quantization);
351 #endif /* !defined FLAC__INTEGER_ONLY_LIBRARY */
353 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[])
355 #ifdef FLAC__OVERFLOW_DETECT
360 const FLAC__int32 *r = residual, *history;
362 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
363 fprintf(stderr,"FLAC__lpc_restore_signal: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
365 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
366 fprintf(stderr,"\n");
368 FLAC__ASSERT(order > 0);
370 for(i = 0; i < data_len; i++) {
371 #ifdef FLAC__OVERFLOW_DETECT
376 for(j = 0; j < order; j++) {
377 sum += qlp_coeff[j] * (*(--history));
378 #ifdef FLAC__OVERFLOW_DETECT
379 sumo += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*history);
381 if(sumo > 2147483647I64 || sumo < -2147483648I64)
382 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);
384 if(sumo > 2147483647ll || sumo < -2147483648ll)
385 fprintf(stderr,"FLAC__lpc_restore_signal: OVERFLOW, i=%u, j=%u, c=%d, d=%d, sumo=%lld\n",i,j,qlp_coeff[j],*history,(long long)sumo);
389 *(data++) = *(r++) + (sum >> lp_quantization);
392 /* Here's a slower but clearer version:
393 for(i = 0; i < data_len; i++) {
395 for(j = 0; j < order; j++)
396 sum += qlp_coeff[j] * data[i-j-1];
397 data[i] = residual[i] + (sum >> lp_quantization);
402 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[])
406 const FLAC__int32 *r = residual, *history;
408 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
409 fprintf(stderr,"FLAC__lpc_restore_signal_wide: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
411 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
412 fprintf(stderr,"\n");
414 FLAC__ASSERT(order > 0);
416 for(i = 0; i < data_len; i++) {
419 for(j = 0; j < order; j++)
420 sum += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*(--history));
421 #ifdef FLAC__OVERFLOW_DETECT
422 if(FLAC__bitmath_silog2_wide(sum >> lp_quantization) > 32) {
424 fprintf(stderr,"FLAC__lpc_restore_signal_wide: OVERFLOW, i=%u, sum=%I64d\n", i, sum >> lp_quantization);
426 fprintf(stderr,"FLAC__lpc_restore_signal_wide: OVERFLOW, i=%u, sum=%lld\n", i, (long long)(sum >> lp_quantization));
430 if(FLAC__bitmath_silog2_wide((FLAC__int64)(*r) + (sum >> lp_quantization)) > 32) {
432 fprintf(stderr,"FLAC__lpc_restore_signal_wide: OVERFLOW, i=%u, residual=%d, sum=%I64d, data=%I64d\n", i, *r, sum >> lp_quantization, (FLAC__int64)(*r) + (sum >> lp_quantization));
434 fprintf(stderr,"FLAC__lpc_restore_signal_wide: OVERFLOW, i=%u, residual=%d, sum=%lld, data=%lld\n", i, *r, (long long)(sum >> lp_quantization), (long long)((FLAC__int64)(*r) + (sum >> lp_quantization)));
439 *(data++) = *(r++) + (FLAC__int32)(sum >> lp_quantization);
443 #ifndef FLAC__INTEGER_ONLY_LIBRARY
445 FLAC__double FLAC__lpc_compute_expected_bits_per_residual_sample(FLAC__double lpc_error, unsigned total_samples)
447 FLAC__double error_scale;
449 FLAC__ASSERT(total_samples > 0);
451 error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__double)total_samples;
453 return FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error, error_scale);
456 FLAC__double FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(FLAC__double lpc_error, FLAC__double error_scale)
458 if(lpc_error > 0.0) {
459 FLAC__double bps = (FLAC__double)0.5 * log(error_scale * lpc_error) / M_LN2;
465 else if(lpc_error < 0.0) { /* error should not be negative but can happen due to inadequate floating-point resolution */
473 unsigned FLAC__lpc_compute_best_order(const FLAC__double lpc_error[], unsigned max_order, unsigned total_samples, unsigned overhead_bits_per_order)
475 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 */
476 FLAC__double bits, best_bits, error_scale;
478 FLAC__ASSERT(max_order > 0);
479 FLAC__ASSERT(total_samples > 0);
481 error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__double)total_samples;
484 best_bits = (unsigned)(-1);
486 for(index = 0, order = 1; index < max_order; index++, order++) {
487 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);
488 if(bits < best_bits) {
494 return best_index+1; /* +1 since index of lpc_error[] is order-1 */
497 #endif /* !defined FLAC__INTEGER_ONLY_LIBRARY */