1 /* libFLAC - Free Lossless Audio Codec library
2 * Copyright (C) 2000,2001,2002,2003,2004 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.
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
41 #ifndef FLAC__INTEGER_ONLY_LIBRARY
44 /* math.h in VC++ doesn't seem to have this (how Microsoft is that?) */
45 #define M_LN2 0.69314718055994530942
48 void FLAC__lpc_compute_autocorrelation(const FLAC__real data[], unsigned data_len, unsigned lag, FLAC__real autoc[])
50 /* a readable, but slower, version */
55 FLAC__ASSERT(lag > 0);
56 FLAC__ASSERT(lag <= data_len);
59 for(i = lag, d = 0.0; i < data_len; i++)
60 d += data[i] * data[i - lag];
66 * this version tends to run faster because of better data locality
67 * ('data_len' is usually much larger than 'lag')
70 unsigned sample, coeff;
71 const unsigned limit = data_len - lag;
73 FLAC__ASSERT(lag > 0);
74 FLAC__ASSERT(lag <= data_len);
76 for(coeff = 0; coeff < lag; coeff++)
78 for(sample = 0; sample <= limit; sample++) {
80 for(coeff = 0; coeff < lag; coeff++)
81 autoc[coeff] += d * data[sample+coeff];
83 for(; sample < data_len; sample++) {
85 for(coeff = 0; coeff < data_len - sample; coeff++)
86 autoc[coeff] += d * data[sample+coeff];
90 void FLAC__lpc_compute_lp_coefficients(const FLAC__real autoc[], unsigned max_order, FLAC__real lp_coeff[][FLAC__MAX_LPC_ORDER], FLAC__double error[])
93 FLAC__double r, err, ref[FLAC__MAX_LPC_ORDER], lpc[FLAC__MAX_LPC_ORDER];
95 FLAC__ASSERT(0 < max_order);
96 FLAC__ASSERT(max_order <= FLAC__MAX_LPC_ORDER);
97 FLAC__ASSERT(autoc[0] != 0.0);
101 for(i = 0; i < max_order; i++) {
102 /* Sum up this iteration's reflection coefficient. */
104 for(j = 0; j < i; j++)
105 r -= lpc[j] * autoc[i-j];
108 /* Update LPC coefficients and total error. */
110 for(j = 0; j < (i>>1); j++) {
111 FLAC__double tmp = lpc[j];
112 lpc[j] += r * lpc[i-1-j];
113 lpc[i-1-j] += r * tmp;
116 lpc[j] += lpc[j] * r;
118 err *= (1.0 - r * r);
120 /* save this order */
121 for(j = 0; j <= i; j++)
122 lp_coeff[i][j] = (FLAC__real)(-lpc[j]); /* negate FIR filter coeff to get predictor coeff */
127 int FLAC__lpc_quantize_coefficients(const FLAC__real lp_coeff[], unsigned order, unsigned precision, FLAC__int32 qlp_coeff[], int *shift)
130 FLAC__double d, cmax = -1e32;
131 FLAC__int32 qmax, qmin;
132 const int max_shiftlimit = (1 << (FLAC__SUBFRAME_LPC_QLP_SHIFT_LEN-1)) - 1;
133 const int min_shiftlimit = -max_shiftlimit - 1;
135 FLAC__ASSERT(precision > 0);
136 FLAC__ASSERT(precision >= FLAC__MIN_QLP_COEFF_PRECISION);
138 /* drop one bit for the sign; from here on out we consider only |lp_coeff[i]| */
140 qmax = 1 << precision;
144 for(i = 0; i < order; i++) {
145 if(lp_coeff[i] == 0.0)
147 d = fabs(lp_coeff[i]);
153 /* => coefficients are all 0, which means our constant-detect didn't work */
159 (void)frexp(cmax, &log2cmax);
161 *shift = (int)precision - log2cmax - 1;
163 if(*shift < min_shiftlimit || *shift > max_shiftlimit) {
165 /*@@@ this does not seem to help at all, but was not extensively tested either: */
166 if(*shift > max_shiftlimit)
167 *shift = max_shiftlimit;
175 for(i = 0; i < order; i++) {
176 qlp_coeff[i] = (FLAC__int32)floor((FLAC__double)lp_coeff[i] * (FLAC__double)(1 << *shift));
178 /* double-check the result */
179 if(qlp_coeff[i] > qmax || qlp_coeff[i] < qmin) {
180 #ifdef FLAC__OVERFLOW_DETECT
181 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)));
188 else { /* (*shift < 0) */
189 const int nshift = -(*shift);
191 fprintf(stderr,"FLAC__lpc_quantize_coefficients: negative shift = %d\n", *shift);
193 for(i = 0; i < order; i++) {
194 qlp_coeff[i] = (FLAC__int32)floor((FLAC__double)lp_coeff[i] / (FLAC__double)(1 << nshift));
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 << nshift), floor((FLAC__double)lp_coeff[i] / (FLAC__double)(1 << nshift)));
210 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[])
212 #ifdef FLAC__OVERFLOW_DETECT
217 const FLAC__int32 *history;
219 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
220 fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
222 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
223 fprintf(stderr,"\n");
225 FLAC__ASSERT(order > 0);
227 for(i = 0; i < data_len; i++) {
228 #ifdef FLAC__OVERFLOW_DETECT
233 for(j = 0; j < order; j++) {
234 sum += qlp_coeff[j] * (*(--history));
235 #ifdef FLAC__OVERFLOW_DETECT
236 sumo += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*history);
238 if(sumo > 2147483647I64 || sumo < -2147483648I64)
239 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);
241 if(sumo > 2147483647ll || sumo < -2147483648ll)
242 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);
246 *(residual++) = *(data++) - (sum >> lp_quantization);
249 /* Here's a slower but clearer version:
250 for(i = 0; i < data_len; i++) {
252 for(j = 0; j < order; j++)
253 sum += qlp_coeff[j] * data[i-j-1];
254 residual[i] = data[i] - (sum >> lp_quantization);
259 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[])
263 const FLAC__int32 *history;
265 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
266 fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
268 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
269 fprintf(stderr,"\n");
271 FLAC__ASSERT(order > 0);
273 for(i = 0; i < data_len; i++) {
276 for(j = 0; j < order; j++)
277 sum += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*(--history));
278 #ifdef FLAC__OVERFLOW_DETECT
279 if(FLAC__bitmath_silog2_wide(sum >> lp_quantization) > 32) {
280 fprintf(stderr,"FLAC__lpc_compute_residual_from_qlp_coefficients_wide: OVERFLOW, i=%u, sum=%lld\n", i, sum >> lp_quantization);
283 if(FLAC__bitmath_silog2_wide((FLAC__int64)(*data) - (sum >> lp_quantization)) > 32) {
284 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));
288 *(residual++) = *(data++) - (FLAC__int32)(sum >> lp_quantization);
292 #endif /* !defined FLAC__INTEGER_ONLY_LIBRARY */
294 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[])
296 #ifdef FLAC__OVERFLOW_DETECT
301 const FLAC__int32 *history;
303 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
304 fprintf(stderr,"FLAC__lpc_restore_signal: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
306 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
307 fprintf(stderr,"\n");
309 FLAC__ASSERT(order > 0);
311 for(i = 0; i < data_len; i++) {
312 #ifdef FLAC__OVERFLOW_DETECT
317 for(j = 0; j < order; j++) {
318 sum += qlp_coeff[j] * (*(--history));
319 #ifdef FLAC__OVERFLOW_DETECT
320 sumo += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*history);
322 if(sumo > 2147483647I64 || sumo < -2147483648I64)
323 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);
325 if(sumo > 2147483647ll || sumo < -2147483648ll)
326 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);
330 *(data++) = *(residual++) + (sum >> lp_quantization);
333 /* Here's a slower but clearer version:
334 for(i = 0; i < data_len; i++) {
336 for(j = 0; j < order; j++)
337 sum += qlp_coeff[j] * data[i-j-1];
338 data[i] = residual[i] + (sum >> lp_quantization);
343 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[])
347 const FLAC__int32 *history;
349 #ifdef FLAC__OVERFLOW_DETECT_VERBOSE
350 fprintf(stderr,"FLAC__lpc_restore_signal_wide: data_len=%d, order=%u, lpq=%d",data_len,order,lp_quantization);
352 fprintf(stderr,", q[%u]=%d",i,qlp_coeff[i]);
353 fprintf(stderr,"\n");
355 FLAC__ASSERT(order > 0);
357 for(i = 0; i < data_len; i++) {
360 for(j = 0; j < order; j++)
361 sum += (FLAC__int64)qlp_coeff[j] * (FLAC__int64)(*(--history));
362 #ifdef FLAC__OVERFLOW_DETECT
363 if(FLAC__bitmath_silog2_wide(sum >> lp_quantization) > 32) {
364 fprintf(stderr,"FLAC__lpc_restore_signal_wide: OVERFLOW, i=%u, sum=%lld\n", i, sum >> lp_quantization);
367 if(FLAC__bitmath_silog2_wide((FLAC__int64)(*residual) + (sum >> lp_quantization)) > 32) {
368 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));
372 *(data++) = *(residual++) + (FLAC__int32)(sum >> lp_quantization);
376 #ifndef FLAC__INTEGER_ONLY_LIBRARY
378 FLAC__double FLAC__lpc_compute_expected_bits_per_residual_sample(FLAC__double lpc_error, unsigned total_samples)
380 FLAC__double error_scale;
382 FLAC__ASSERT(total_samples > 0);
384 error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__double)total_samples;
386 return FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error, error_scale);
389 FLAC__double FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(FLAC__double lpc_error, FLAC__double error_scale)
391 if(lpc_error > 0.0) {
392 FLAC__double bps = (FLAC__double)0.5 * log(error_scale * lpc_error) / M_LN2;
398 else if(lpc_error < 0.0) { /* error should not be negative but can happen due to inadequate floating-point resolution */
406 unsigned FLAC__lpc_compute_best_order(const FLAC__double lpc_error[], unsigned max_order, unsigned total_samples, unsigned bits_per_signal_sample)
408 unsigned order, best_order;
409 FLAC__double best_bits, tmp_bits, error_scale;
411 FLAC__ASSERT(max_order > 0);
412 FLAC__ASSERT(total_samples > 0);
414 error_scale = 0.5 * M_LN2 * M_LN2 / (FLAC__double)total_samples;
417 best_bits = FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error[0], error_scale) * (FLAC__double)total_samples;
419 for(order = 1; order < max_order; order++) {
420 tmp_bits = FLAC__lpc_compute_expected_bits_per_residual_sample_with_error_scale(lpc_error[order], error_scale) * (FLAC__double)(total_samples - order) + (FLAC__double)(order * bits_per_signal_sample);
421 if(tmp_bits < best_bits) {
423 best_bits = tmp_bits;
427 return best_order+1; /* +1 since index of lpc_error[] is order-1 */
430 #endif /* !defined FLAC__INTEGER_ONLY_LIBRARY */