1 /* libFLAC - Free Lossless Audio Codec library
2 * Copyright (C) 2000,2001,2002,2003,2004,2005,2006 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(max_order <= FLAC__MAX_LPC_ORDER);
115 FLAC__ASSERT(autoc[0] != 0.0);
119 for(i = 0; i < max_order; i++) {
120 /* Sum up this iteration's reflection coefficient. */
122 for(j = 0; j < i; j++)
123 r -= lpc[j] * autoc[i-j];
126 /* Update LPC coefficients and total error. */
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;
134 lpc[j] += lpc[j] * r;
136 err *= (1.0 - r * r);
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 */
145 int FLAC__lpc_quantize_coefficients(const FLAC__real lp_coeff[], unsigned order, unsigned precision, FLAC__int32 qlp_coeff[], int *shift)
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;
153 FLAC__ASSERT(precision > 0);
154 FLAC__ASSERT(precision >= FLAC__MIN_QLP_COEFF_PRECISION);
156 /* drop one bit for the sign; from here on out we consider only |lp_coeff[i]| */
158 qmax = 1 << precision;
162 for(i = 0; i < order; i++) {
163 if(lp_coeff[i] == 0.0)
165 d = fabs(lp_coeff[i]);
171 /* => coefficients are all 0, which means our constant-detect didn't work */
177 (void)frexp(cmax, &log2cmax);
179 *shift = (int)precision - log2cmax - 1;
181 if(*shift < min_shiftlimit || *shift > max_shiftlimit) {
183 /*@@@ this does not seem to help at all, but was not extensively tested either: */
184 if(*shift > max_shiftlimit)
185 *shift = max_shiftlimit;
193 for(i = 0; i < order; i++) {
194 qlp_coeff[i] = (FLAC__int32)floor((FLAC__double)lp_coeff[i] * (FLAC__double)(1 << *shift));
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)));
206 else { /* (*shift < 0) */
207 const int nshift = -(*shift);
209 fprintf(stderr,"FLAC__lpc_quantize_coefficients: negative shift = %d\n", *shift);
211 for(i = 0; i < order; i++) {
212 qlp_coeff[i] = (FLAC__int32)floor((FLAC__double)lp_coeff[i] / (FLAC__double)(1 << nshift));
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)));
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[])
230 #ifdef FLAC__OVERFLOW_DETECT
235 const FLAC__int32 *history;
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);
240 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
241 fprintf(stderr,"\n");
243 FLAC__ASSERT(order > 0);
245 for(i = 0; i < data_len; i++) {
246 #ifdef FLAC__OVERFLOW_DETECT
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);
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);
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);
264 *(residual++) = *(data++) - (sum >> lp_quantization);
267 /* Here's a slower but clearer version:
268 for(i = 0; i < data_len; i++) {
270 for(j = 0; j < order; j++)
271 sum += qlp_coeff[j] * data[i-j-1];
272 residual[i] = data[i] - (sum >> lp_quantization);
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[])
281 const FLAC__int32 *history;
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);
286 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
287 fprintf(stderr,"\n");
289 FLAC__ASSERT(order > 0);
291 for(i = 0; i < data_len; i++) {
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);
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));
306 *(residual++) = *(data++) - (FLAC__int32)(sum >> lp_quantization);
310 #endif /* !defined FLAC__INTEGER_ONLY_LIBRARY */
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[])
314 #ifdef FLAC__OVERFLOW_DETECT
319 const FLAC__int32 *history;
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);
324 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
325 fprintf(stderr,"\n");
327 FLAC__ASSERT(order > 0);
329 for(i = 0; i < data_len; i++) {
330 #ifdef FLAC__OVERFLOW_DETECT
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);
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);
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);
348 *(data++) = *(residual++) + (sum >> lp_quantization);
351 /* Here's a slower but clearer version:
352 for(i = 0; i < data_len; i++) {
354 for(j = 0; j < order; j++)
355 sum += qlp_coeff[j] * data[i-j-1];
356 data[i] = residual[i] + (sum >> lp_quantization);
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[])
365 const FLAC__int32 *history;
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);
370 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
371 fprintf(stderr,"\n");
373 FLAC__ASSERT(order > 0);
375 for(i = 0; i < data_len; i++) {
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);
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));
390 *(data++) = *(residual++) + (FLAC__int32)(sum >> lp_quantization);
394 #ifndef FLAC__INTEGER_ONLY_LIBRARY
396 FLAC__double FLAC__lpc_compute_expected_bits_per_residual_sample(FLAC__double lpc_error, unsigned total_samples)
398 FLAC__double error_scale;
400 FLAC__ASSERT(total_samples > 0);
402 error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__double)total_samples;
404 return FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error, error_scale);
407 FLAC__double FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(FLAC__double lpc_error, FLAC__double error_scale)
409 if(lpc_error > 0.0) {
410 FLAC__double bps = (FLAC__double)0.5 * log(error_scale * lpc_error) / M_LN2;
416 else if(lpc_error < 0.0) { /* error should not be negative but can happen due to inadequate floating-point resolution */
424 unsigned FLAC__lpc_compute_best_order(const FLAC__double lpc_error[], unsigned max_order, unsigned total_samples, unsigned overhead_bits_per_order)
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;
429 FLAC__ASSERT(max_order > 0);
430 FLAC__ASSERT(total_samples > 0);
432 error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__double)total_samples;
435 best_bits = (unsigned)(-1);
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) {
445 return best_index+1; /* +1 since index of lpc_error[] is order-1 */
448 #endif /* !defined FLAC__INTEGER_ONLY_LIBRARY */