1 /* libFLAC - Free Lossless Audio Codec library
2 * Copyright (C) 2000-2009 Josh Coalson
3 * Copyright (C) 2011-2014 Xiph.Org Foundation
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 *
9 * - Redistributions of source code must retain the above copyright
10 * notice, this list of conditions and the following disclaimer.
11 *
12 * - Redistributions in binary form must reproduce the above copyright
13 * notice, this list of conditions and the following disclaimer in the
14 * documentation and/or other materials provided with the distribution.
15 *
16 * - Neither the name of the Xiph.org Foundation nor the names of its
17 * contributors may be used to endorse or promote products derived from
18 * this software without specific prior written permission.
19 *
20 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
21 * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
22 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
23 * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR
24 * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
25 * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
26 * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
27 * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
28 * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
29 * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
30 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
31 */
32
33 #ifdef HAVE_CONFIG_H
34 # include <config.h>
35 #endif
36
37 #include <math.h>
38 #include <string.h>
39 #include "share/compat.h"
40 #include "private/bitmath.h"
41 #include "private/fixed.h"
42 #include "private/macros.h"
43 #include "FLAC/assert.h"
44
45 #ifdef local_abs
46 #undef local_abs
47 #endif
48 #define local_abs(x) ((unsigned)((x)<0? -(x) : (x)))
49
50 #ifdef FLAC__INTEGER_ONLY_LIBRARY
51 /* rbps stands for residual bits per sample
52 *
53 * (ln(2) * err)
54 * rbps = log (-----------)
55 * 2 ( n )
56 */
local__compute_rbps_integerized(FLAC__uint32 err,FLAC__uint32 n)57 static FLAC__fixedpoint local__compute_rbps_integerized(FLAC__uint32 err, FLAC__uint32 n)
58 {
59 FLAC__uint32 rbps;
60 unsigned bits; /* the number of bits required to represent a number */
61 int fracbits; /* the number of bits of rbps that comprise the fractional part */
62
63 FLAC__ASSERT(sizeof(rbps) == sizeof(FLAC__fixedpoint));
64 FLAC__ASSERT(err > 0);
65 FLAC__ASSERT(n > 0);
66
67 FLAC__ASSERT(n <= FLAC__MAX_BLOCK_SIZE);
68 if(err <= n)
69 return 0;
70 /*
71 * The above two things tell us 1) n fits in 16 bits; 2) err/n > 1.
72 * These allow us later to know we won't lose too much precision in the
73 * fixed-point division (err<<fracbits)/n.
74 */
75
76 fracbits = (8*sizeof(err)) - (FLAC__bitmath_ilog2(err)+1);
77
78 err <<= fracbits;
79 err /= n;
80 /* err now holds err/n with fracbits fractional bits */
81
82 /*
83 * Whittle err down to 16 bits max. 16 significant bits is enough for
84 * our purposes.
85 */
86 FLAC__ASSERT(err > 0);
87 bits = FLAC__bitmath_ilog2(err)+1;
88 if(bits > 16) {
89 err >>= (bits-16);
90 fracbits -= (bits-16);
91 }
92 rbps = (FLAC__uint32)err;
93
94 /* Multiply by fixed-point version of ln(2), with 16 fractional bits */
95 rbps *= FLAC__FP_LN2;
96 fracbits += 16;
97 FLAC__ASSERT(fracbits >= 0);
98
99 /* FLAC__fixedpoint_log2 requires fracbits%4 to be 0 */
100 {
101 const int f = fracbits & 3;
102 if(f) {
103 rbps >>= f;
104 fracbits -= f;
105 }
106 }
107
108 rbps = FLAC__fixedpoint_log2(rbps, fracbits, (unsigned)(-1));
109
110 if(rbps == 0)
111 return 0;
112
113 /*
114 * The return value must have 16 fractional bits. Since the whole part
115 * of the base-2 log of a 32 bit number must fit in 5 bits, and fracbits
116 * must be >= -3, these assertion allows us to be able to shift rbps
117 * left if necessary to get 16 fracbits without losing any bits of the
118 * whole part of rbps.
119 *
120 * There is a slight chance due to accumulated error that the whole part
121 * will require 6 bits, so we use 6 in the assertion. Really though as
122 * long as it fits in 13 bits (32 - (16 - (-3))) we are fine.
123 */
124 FLAC__ASSERT((int)FLAC__bitmath_ilog2(rbps)+1 <= fracbits + 6);
125 FLAC__ASSERT(fracbits >= -3);
126
127 /* now shift the decimal point into place */
128 if(fracbits < 16)
129 return rbps << (16-fracbits);
130 else if(fracbits > 16)
131 return rbps >> (fracbits-16);
132 else
133 return rbps;
134 }
135
local__compute_rbps_wide_integerized(FLAC__uint64 err,FLAC__uint32 n)136 static FLAC__fixedpoint local__compute_rbps_wide_integerized(FLAC__uint64 err, FLAC__uint32 n)
137 {
138 FLAC__uint32 rbps;
139 unsigned bits; /* the number of bits required to represent a number */
140 int fracbits; /* the number of bits of rbps that comprise the fractional part */
141
142 FLAC__ASSERT(sizeof(rbps) == sizeof(FLAC__fixedpoint));
143 FLAC__ASSERT(err > 0);
144 FLAC__ASSERT(n > 0);
145
146 FLAC__ASSERT(n <= FLAC__MAX_BLOCK_SIZE);
147 if(err <= n)
148 return 0;
149 /*
150 * The above two things tell us 1) n fits in 16 bits; 2) err/n > 1.
151 * These allow us later to know we won't lose too much precision in the
152 * fixed-point division (err<<fracbits)/n.
153 */
154
155 fracbits = (8*sizeof(err)) - (FLAC__bitmath_ilog2_wide(err)+1);
156
157 err <<= fracbits;
158 err /= n;
159 /* err now holds err/n with fracbits fractional bits */
160
161 /*
162 * Whittle err down to 16 bits max. 16 significant bits is enough for
163 * our purposes.
164 */
165 FLAC__ASSERT(err > 0);
166 bits = FLAC__bitmath_ilog2_wide(err)+1;
167 if(bits > 16) {
168 err >>= (bits-16);
169 fracbits -= (bits-16);
170 }
171 rbps = (FLAC__uint32)err;
172
173 /* Multiply by fixed-point version of ln(2), with 16 fractional bits */
174 rbps *= FLAC__FP_LN2;
175 fracbits += 16;
176 FLAC__ASSERT(fracbits >= 0);
177
178 /* FLAC__fixedpoint_log2 requires fracbits%4 to be 0 */
179 {
180 const int f = fracbits & 3;
181 if(f) {
182 rbps >>= f;
183 fracbits -= f;
184 }
185 }
186
187 rbps = FLAC__fixedpoint_log2(rbps, fracbits, (unsigned)(-1));
188
189 if(rbps == 0)
190 return 0;
191
192 /*
193 * The return value must have 16 fractional bits. Since the whole part
194 * of the base-2 log of a 32 bit number must fit in 5 bits, and fracbits
195 * must be >= -3, these assertion allows us to be able to shift rbps
196 * left if necessary to get 16 fracbits without losing any bits of the
197 * whole part of rbps.
198 *
199 * There is a slight chance due to accumulated error that the whole part
200 * will require 6 bits, so we use 6 in the assertion. Really though as
201 * long as it fits in 13 bits (32 - (16 - (-3))) we are fine.
202 */
203 FLAC__ASSERT((int)FLAC__bitmath_ilog2(rbps)+1 <= fracbits + 6);
204 FLAC__ASSERT(fracbits >= -3);
205
206 /* now shift the decimal point into place */
207 if(fracbits < 16)
208 return rbps << (16-fracbits);
209 else if(fracbits > 16)
210 return rbps >> (fracbits-16);
211 else
212 return rbps;
213 }
214 #endif
215
216 #ifndef FLAC__INTEGER_ONLY_LIBRARY
FLAC__fixed_compute_best_predictor(const FLAC__int32 data[],unsigned data_len,FLAC__float residual_bits_per_sample[FLAC__MAX_FIXED_ORDER+1])217 unsigned FLAC__fixed_compute_best_predictor(const FLAC__int32 data[], unsigned data_len, FLAC__float residual_bits_per_sample[FLAC__MAX_FIXED_ORDER+1])
218 #else
219 unsigned FLAC__fixed_compute_best_predictor(const FLAC__int32 data[], unsigned data_len, FLAC__fixedpoint residual_bits_per_sample[FLAC__MAX_FIXED_ORDER+1])
220 #endif
221 {
222 FLAC__int32 last_error_0 = data[-1];
223 FLAC__int32 last_error_1 = data[-1] - data[-2];
224 FLAC__int32 last_error_2 = last_error_1 - (data[-2] - data[-3]);
225 FLAC__int32 last_error_3 = last_error_2 - (data[-2] - 2*data[-3] + data[-4]);
226 FLAC__int32 error, save;
227 FLAC__uint32 total_error_0 = 0, total_error_1 = 0, total_error_2 = 0, total_error_3 = 0, total_error_4 = 0;
228 unsigned i, order;
229
230 for(i = 0; i < data_len; i++) {
231 error = data[i] ; total_error_0 += local_abs(error); save = error;
232 error -= last_error_0; total_error_1 += local_abs(error); last_error_0 = save; save = error;
233 error -= last_error_1; total_error_2 += local_abs(error); last_error_1 = save; save = error;
234 error -= last_error_2; total_error_3 += local_abs(error); last_error_2 = save; save = error;
235 error -= last_error_3; total_error_4 += local_abs(error); last_error_3 = save;
236 }
237
238 if(total_error_0 < flac_min(flac_min(flac_min(total_error_1, total_error_2), total_error_3), total_error_4))
239 order = 0;
240 else if(total_error_1 < flac_min(flac_min(total_error_2, total_error_3), total_error_4))
241 order = 1;
242 else if(total_error_2 < flac_min(total_error_3, total_error_4))
243 order = 2;
244 else if(total_error_3 < total_error_4)
245 order = 3;
246 else
247 order = 4;
248
249 /* Estimate the expected number of bits per residual signal sample. */
250 /* 'total_error*' is linearly related to the variance of the residual */
251 /* signal, so we use it directly to compute E(|x|) */
252 FLAC__ASSERT(data_len > 0 || total_error_0 == 0);
253 FLAC__ASSERT(data_len > 0 || total_error_1 == 0);
254 FLAC__ASSERT(data_len > 0 || total_error_2 == 0);
255 FLAC__ASSERT(data_len > 0 || total_error_3 == 0);
256 FLAC__ASSERT(data_len > 0 || total_error_4 == 0);
257 #ifndef FLAC__INTEGER_ONLY_LIBRARY
258 residual_bits_per_sample[0] = (FLAC__float)((total_error_0 > 0) ? log(M_LN2 * (FLAC__double)total_error_0 / (FLAC__double)data_len) / M_LN2 : 0.0);
259 residual_bits_per_sample[1] = (FLAC__float)((total_error_1 > 0) ? log(M_LN2 * (FLAC__double)total_error_1 / (FLAC__double)data_len) / M_LN2 : 0.0);
260 residual_bits_per_sample[2] = (FLAC__float)((total_error_2 > 0) ? log(M_LN2 * (FLAC__double)total_error_2 / (FLAC__double)data_len) / M_LN2 : 0.0);
261 residual_bits_per_sample[3] = (FLAC__float)((total_error_3 > 0) ? log(M_LN2 * (FLAC__double)total_error_3 / (FLAC__double)data_len) / M_LN2 : 0.0);
262 residual_bits_per_sample[4] = (FLAC__float)((total_error_4 > 0) ? log(M_LN2 * (FLAC__double)total_error_4 / (FLAC__double)data_len) / M_LN2 : 0.0);
263 #else
264 residual_bits_per_sample[0] = (total_error_0 > 0) ? local__compute_rbps_integerized(total_error_0, data_len) : 0;
265 residual_bits_per_sample[1] = (total_error_1 > 0) ? local__compute_rbps_integerized(total_error_1, data_len) : 0;
266 residual_bits_per_sample[2] = (total_error_2 > 0) ? local__compute_rbps_integerized(total_error_2, data_len) : 0;
267 residual_bits_per_sample[3] = (total_error_3 > 0) ? local__compute_rbps_integerized(total_error_3, data_len) : 0;
268 residual_bits_per_sample[4] = (total_error_4 > 0) ? local__compute_rbps_integerized(total_error_4, data_len) : 0;
269 #endif
270
271 return order;
272 }
273
274 #ifndef FLAC__INTEGER_ONLY_LIBRARY
FLAC__fixed_compute_best_predictor_wide(const FLAC__int32 data[],unsigned data_len,FLAC__float residual_bits_per_sample[FLAC__MAX_FIXED_ORDER+1])275 unsigned FLAC__fixed_compute_best_predictor_wide(const FLAC__int32 data[], unsigned data_len, FLAC__float residual_bits_per_sample[FLAC__MAX_FIXED_ORDER+1])
276 #else
277 unsigned FLAC__fixed_compute_best_predictor_wide(const FLAC__int32 data[], unsigned data_len, FLAC__fixedpoint residual_bits_per_sample[FLAC__MAX_FIXED_ORDER+1])
278 #endif
279 {
280 FLAC__int32 last_error_0 = data[-1];
281 FLAC__int32 last_error_1 = data[-1] - data[-2];
282 FLAC__int32 last_error_2 = last_error_1 - (data[-2] - data[-3]);
283 FLAC__int32 last_error_3 = last_error_2 - (data[-2] - 2*data[-3] + data[-4]);
284 FLAC__int32 error, save;
285 /* total_error_* are 64-bits to avoid overflow when encoding
286 * erratic signals when the bits-per-sample and blocksize are
287 * large.
288 */
289 FLAC__uint64 total_error_0 = 0, total_error_1 = 0, total_error_2 = 0, total_error_3 = 0, total_error_4 = 0;
290 unsigned i, order;
291
292 for(i = 0; i < data_len; i++) {
293 error = data[i] ; total_error_0 += local_abs(error); save = error;
294 error -= last_error_0; total_error_1 += local_abs(error); last_error_0 = save; save = error;
295 error -= last_error_1; total_error_2 += local_abs(error); last_error_1 = save; save = error;
296 error -= last_error_2; total_error_3 += local_abs(error); last_error_2 = save; save = error;
297 error -= last_error_3; total_error_4 += local_abs(error); last_error_3 = save;
298 }
299
300 if(total_error_0 < flac_min(flac_min(flac_min(total_error_1, total_error_2), total_error_3), total_error_4))
301 order = 0;
302 else if(total_error_1 < flac_min(flac_min(total_error_2, total_error_3), total_error_4))
303 order = 1;
304 else if(total_error_2 < flac_min(total_error_3, total_error_4))
305 order = 2;
306 else if(total_error_3 < total_error_4)
307 order = 3;
308 else
309 order = 4;
310
311 /* Estimate the expected number of bits per residual signal sample. */
312 /* 'total_error*' is linearly related to the variance of the residual */
313 /* signal, so we use it directly to compute E(|x|) */
314 FLAC__ASSERT(data_len > 0 || total_error_0 == 0);
315 FLAC__ASSERT(data_len > 0 || total_error_1 == 0);
316 FLAC__ASSERT(data_len > 0 || total_error_2 == 0);
317 FLAC__ASSERT(data_len > 0 || total_error_3 == 0);
318 FLAC__ASSERT(data_len > 0 || total_error_4 == 0);
319 #ifndef FLAC__INTEGER_ONLY_LIBRARY
320 residual_bits_per_sample[0] = (FLAC__float)((total_error_0 > 0) ? log(M_LN2 * (FLAC__double)total_error_0 / (FLAC__double)data_len) / M_LN2 : 0.0);
321 residual_bits_per_sample[1] = (FLAC__float)((total_error_1 > 0) ? log(M_LN2 * (FLAC__double)total_error_1 / (FLAC__double)data_len) / M_LN2 : 0.0);
322 residual_bits_per_sample[2] = (FLAC__float)((total_error_2 > 0) ? log(M_LN2 * (FLAC__double)total_error_2 / (FLAC__double)data_len) / M_LN2 : 0.0);
323 residual_bits_per_sample[3] = (FLAC__float)((total_error_3 > 0) ? log(M_LN2 * (FLAC__double)total_error_3 / (FLAC__double)data_len) / M_LN2 : 0.0);
324 residual_bits_per_sample[4] = (FLAC__float)((total_error_4 > 0) ? log(M_LN2 * (FLAC__double)total_error_4 / (FLAC__double)data_len) / M_LN2 : 0.0);
325 #else
326 residual_bits_per_sample[0] = (total_error_0 > 0) ? local__compute_rbps_wide_integerized(total_error_0, data_len) : 0;
327 residual_bits_per_sample[1] = (total_error_1 > 0) ? local__compute_rbps_wide_integerized(total_error_1, data_len) : 0;
328 residual_bits_per_sample[2] = (total_error_2 > 0) ? local__compute_rbps_wide_integerized(total_error_2, data_len) : 0;
329 residual_bits_per_sample[3] = (total_error_3 > 0) ? local__compute_rbps_wide_integerized(total_error_3, data_len) : 0;
330 residual_bits_per_sample[4] = (total_error_4 > 0) ? local__compute_rbps_wide_integerized(total_error_4, data_len) : 0;
331 #endif
332
333 return order;
334 }
335
FLAC__fixed_compute_residual(const FLAC__int32 data[],unsigned data_len,unsigned order,FLAC__int32 residual[])336 void FLAC__fixed_compute_residual(const FLAC__int32 data[], unsigned data_len, unsigned order, FLAC__int32 residual[])
337 {
338 const int idata_len = (int)data_len;
339 int i;
340
341 switch(order) {
342 case 0:
343 FLAC__ASSERT(sizeof(residual[0]) == sizeof(data[0]));
344 memcpy(residual, data, sizeof(residual[0])*data_len);
345 break;
346 case 1:
347 for(i = 0; i < idata_len; i++)
348 residual[i] = data[i] - data[i-1];
349 break;
350 case 2:
351 for(i = 0; i < idata_len; i++)
352 #if 1 /* OPT: may be faster with some compilers on some systems */
353 residual[i] = data[i] - (data[i-1] << 1) + data[i-2];
354 #else
355 residual[i] = data[i] - 2*data[i-1] + data[i-2];
356 #endif
357 break;
358 case 3:
359 for(i = 0; i < idata_len; i++)
360 #if 1 /* OPT: may be faster with some compilers on some systems */
361 residual[i] = data[i] - (((data[i-1]-data[i-2])<<1) + (data[i-1]-data[i-2])) - data[i-3];
362 #else
363 residual[i] = data[i] - 3*data[i-1] + 3*data[i-2] - data[i-3];
364 #endif
365 break;
366 case 4:
367 for(i = 0; i < idata_len; i++)
368 #if 1 /* OPT: may be faster with some compilers on some systems */
369 residual[i] = data[i] - ((data[i-1]+data[i-3])<<2) + ((data[i-2]<<2) + (data[i-2]<<1)) + data[i-4];
370 #else
371 residual[i] = data[i] - 4*data[i-1] + 6*data[i-2] - 4*data[i-3] + data[i-4];
372 #endif
373 break;
374 default:
375 FLAC__ASSERT(0);
376 }
377 }
378
FLAC__fixed_restore_signal(const FLAC__int32 residual[],unsigned data_len,unsigned order,FLAC__int32 data[])379 void FLAC__fixed_restore_signal(const FLAC__int32 residual[], unsigned data_len, unsigned order, FLAC__int32 data[])
380 {
381 int i, idata_len = (int)data_len;
382
383 switch(order) {
384 case 0:
385 FLAC__ASSERT(sizeof(residual[0]) == sizeof(data[0]));
386 memcpy(data, residual, sizeof(residual[0])*data_len);
387 break;
388 case 1:
389 for(i = 0; i < idata_len; i++)
390 data[i] = residual[i] + data[i-1];
391 break;
392 case 2:
393 for(i = 0; i < idata_len; i++)
394 #if 1 /* OPT: may be faster with some compilers on some systems */
395 data[i] = residual[i] + (data[i-1]<<1) - data[i-2];
396 #else
397 data[i] = residual[i] + 2*data[i-1] - data[i-2];
398 #endif
399 break;
400 case 3:
401 for(i = 0; i < idata_len; i++)
402 #if 1 /* OPT: may be faster with some compilers on some systems */
403 data[i] = residual[i] + (((data[i-1]-data[i-2])<<1) + (data[i-1]-data[i-2])) + data[i-3];
404 #else
405 data[i] = residual[i] + 3*data[i-1] - 3*data[i-2] + data[i-3];
406 #endif
407 break;
408 case 4:
409 for(i = 0; i < idata_len; i++)
410 #if 1 /* OPT: may be faster with some compilers on some systems */
411 data[i] = residual[i] + ((data[i-1]+data[i-3])<<2) - ((data[i-2]<<2) + (data[i-2]<<1)) - data[i-4];
412 #else
413 data[i] = residual[i] + 4*data[i-1] - 6*data[i-2] + 4*data[i-3] - data[i-4];
414 #endif
415 break;
416 default:
417 FLAC__ASSERT(0);
418 }
419 }
420