1 /* libFLAC - Free Lossless Audio Codec library
2 * Copyright (C) 2000,2001,2002,2003,2004,2005,2006,2007 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 #ifdef HAVE_CONFIG_H
33 # include <config.h>
34 #endif
35
36 #include <math.h>
37 #include <string.h>
38 #include "private/bitmath.h"
39 #include "private/fixed.h"
40 #include "FLAC/assert.h"
41
42 #ifndef M_LN2
43 /* math.h in VC++ doesn't seem to have this (how Microsoft is that?) */
44 #define M_LN2 0.69314718055994530942
45 #endif
46
47 #ifdef min
48 #undef min
49 #endif
50 #define min(x,y) ((x) < (y)? (x) : (y))
51
52 #ifdef local_abs
53 #undef local_abs
54 #endif
55 #define local_abs(x) ((unsigned)((x)<0? -(x) : (x)))
56
57 #ifdef FLAC__INTEGER_ONLY_LIBRARY
58 /* rbps stands for residual bits per sample
59 *
60 * (ln(2) * err)
61 * rbps = log (-----------)
62 * 2 ( n )
63 */
local__compute_rbps_integerized(FLAC__uint32 err,FLAC__uint32 n)64 static FLAC__fixedpoint local__compute_rbps_integerized(FLAC__uint32 err, FLAC__uint32 n)
65 {
66 FLAC__uint32 rbps;
67 unsigned bits; /* the number of bits required to represent a number */
68 int fracbits; /* the number of bits of rbps that comprise the fractional part */
69
70 FLAC__ASSERT(sizeof(rbps) == sizeof(FLAC__fixedpoint));
71 FLAC__ASSERT(err > 0);
72 FLAC__ASSERT(n > 0);
73
74 FLAC__ASSERT(n <= FLAC__MAX_BLOCK_SIZE);
75 if(err <= n)
76 return 0;
77 /*
78 * The above two things tell us 1) n fits in 16 bits; 2) err/n > 1.
79 * These allow us later to know we won't lose too much precision in the
80 * fixed-point division (err<<fracbits)/n.
81 */
82
83 fracbits = (8*sizeof(err)) - (FLAC__bitmath_ilog2(err)+1);
84
85 err <<= fracbits;
86 err /= n;
87 /* err now holds err/n with fracbits fractional bits */
88
89 /*
90 * Whittle err down to 16 bits max. 16 significant bits is enough for
91 * our purposes.
92 */
93 FLAC__ASSERT(err > 0);
94 bits = FLAC__bitmath_ilog2(err)+1;
95 if(bits > 16) {
96 err >>= (bits-16);
97 fracbits -= (bits-16);
98 }
99 rbps = (FLAC__uint32)err;
100
101 /* Multiply by fixed-point version of ln(2), with 16 fractional bits */
102 rbps *= FLAC__FP_LN2;
103 fracbits += 16;
104 FLAC__ASSERT(fracbits >= 0);
105
106 /* FLAC__fixedpoint_log2 requires fracbits%4 to be 0 */
107 {
108 const int f = fracbits & 3;
109 if(f) {
110 rbps >>= f;
111 fracbits -= f;
112 }
113 }
114
115 rbps = FLAC__fixedpoint_log2(rbps, fracbits, (unsigned)(-1));
116
117 if(rbps == 0)
118 return 0;
119
120 /*
121 * The return value must have 16 fractional bits. Since the whole part
122 * of the base-2 log of a 32 bit number must fit in 5 bits, and fracbits
123 * must be >= -3, these assertion allows us to be able to shift rbps
124 * left if necessary to get 16 fracbits without losing any bits of the
125 * whole part of rbps.
126 *
127 * There is a slight chance due to accumulated error that the whole part
128 * will require 6 bits, so we use 6 in the assertion. Really though as
129 * long as it fits in 13 bits (32 - (16 - (-3))) we are fine.
130 */
131 FLAC__ASSERT((int)FLAC__bitmath_ilog2(rbps)+1 <= fracbits + 6);
132 FLAC__ASSERT(fracbits >= -3);
133
134 /* now shift the decimal point into place */
135 if(fracbits < 16)
136 return rbps << (16-fracbits);
137 else if(fracbits > 16)
138 return rbps >> (fracbits-16);
139 else
140 return rbps;
141 }
142
local__compute_rbps_wide_integerized(FLAC__uint64 err,FLAC__uint32 n)143 static FLAC__fixedpoint local__compute_rbps_wide_integerized(FLAC__uint64 err, FLAC__uint32 n)
144 {
145 FLAC__uint32 rbps;
146 unsigned bits; /* the number of bits required to represent a number */
147 int fracbits; /* the number of bits of rbps that comprise the fractional part */
148
149 FLAC__ASSERT(sizeof(rbps) == sizeof(FLAC__fixedpoint));
150 FLAC__ASSERT(err > 0);
151 FLAC__ASSERT(n > 0);
152
153 FLAC__ASSERT(n <= FLAC__MAX_BLOCK_SIZE);
154 if(err <= n)
155 return 0;
156 /*
157 * The above two things tell us 1) n fits in 16 bits; 2) err/n > 1.
158 * These allow us later to know we won't lose too much precision in the
159 * fixed-point division (err<<fracbits)/n.
160 */
161
162 fracbits = (8*sizeof(err)) - (FLAC__bitmath_ilog2_wide(err)+1);
163
164 err <<= fracbits;
165 err /= n;
166 /* err now holds err/n with fracbits fractional bits */
167
168 /*
169 * Whittle err down to 16 bits max. 16 significant bits is enough for
170 * our purposes.
171 */
172 FLAC__ASSERT(err > 0);
173 bits = FLAC__bitmath_ilog2_wide(err)+1;
174 if(bits > 16) {
175 err >>= (bits-16);
176 fracbits -= (bits-16);
177 }
178 rbps = (FLAC__uint32)err;
179
180 /* Multiply by fixed-point version of ln(2), with 16 fractional bits */
181 rbps *= FLAC__FP_LN2;
182 fracbits += 16;
183 FLAC__ASSERT(fracbits >= 0);
184
185 /* FLAC__fixedpoint_log2 requires fracbits%4 to be 0 */
186 {
187 const int f = fracbits & 3;
188 if(f) {
189 rbps >>= f;
190 fracbits -= f;
191 }
192 }
193
194 rbps = FLAC__fixedpoint_log2(rbps, fracbits, (unsigned)(-1));
195
196 if(rbps == 0)
197 return 0;
198
199 /*
200 * The return value must have 16 fractional bits. Since the whole part
201 * of the base-2 log of a 32 bit number must fit in 5 bits, and fracbits
202 * must be >= -3, these assertion allows us to be able to shift rbps
203 * left if necessary to get 16 fracbits without losing any bits of the
204 * whole part of rbps.
205 *
206 * There is a slight chance due to accumulated error that the whole part
207 * will require 6 bits, so we use 6 in the assertion. Really though as
208 * long as it fits in 13 bits (32 - (16 - (-3))) we are fine.
209 */
210 FLAC__ASSERT((int)FLAC__bitmath_ilog2(rbps)+1 <= fracbits + 6);
211 FLAC__ASSERT(fracbits >= -3);
212
213 /* now shift the decimal point into place */
214 if(fracbits < 16)
215 return rbps << (16-fracbits);
216 else if(fracbits > 16)
217 return rbps >> (fracbits-16);
218 else
219 return rbps;
220 }
221 #endif
222
223 #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])224 unsigned FLAC__fixed_compute_best_predictor(const FLAC__int32 data[], unsigned data_len, FLAC__float residual_bits_per_sample[FLAC__MAX_FIXED_ORDER+1])
225 #else
226 unsigned FLAC__fixed_compute_best_predictor(const FLAC__int32 data[], unsigned data_len, FLAC__fixedpoint residual_bits_per_sample[FLAC__MAX_FIXED_ORDER+1])
227 #endif
228 {
229 FLAC__int32 last_error_0 = data[-1];
230 FLAC__int32 last_error_1 = data[-1] - data[-2];
231 FLAC__int32 last_error_2 = last_error_1 - (data[-2] - data[-3]);
232 FLAC__int32 last_error_3 = last_error_2 - (data[-2] - 2*data[-3] + data[-4]);
233 FLAC__int32 error, save;
234 FLAC__uint32 total_error_0 = 0, total_error_1 = 0, total_error_2 = 0, total_error_3 = 0, total_error_4 = 0;
235 unsigned i, order;
236
237 for(i = 0; i < data_len; i++) {
238 error = data[i] ; total_error_0 += local_abs(error); save = error;
239 error -= last_error_0; total_error_1 += local_abs(error); last_error_0 = save; save = error;
240 error -= last_error_1; total_error_2 += local_abs(error); last_error_1 = save; save = error;
241 error -= last_error_2; total_error_3 += local_abs(error); last_error_2 = save; save = error;
242 error -= last_error_3; total_error_4 += local_abs(error); last_error_3 = save;
243 }
244
245 if(total_error_0 < min(min(min(total_error_1, total_error_2), total_error_3), total_error_4))
246 order = 0;
247 else if(total_error_1 < min(min(total_error_2, total_error_3), total_error_4))
248 order = 1;
249 else if(total_error_2 < min(total_error_3, total_error_4))
250 order = 2;
251 else if(total_error_3 < total_error_4)
252 order = 3;
253 else
254 order = 4;
255
256 /* Estimate the expected number of bits per residual signal sample. */
257 /* 'total_error*' is linearly related to the variance of the residual */
258 /* signal, so we use it directly to compute E(|x|) */
259 FLAC__ASSERT(data_len > 0 || total_error_0 == 0);
260 FLAC__ASSERT(data_len > 0 || total_error_1 == 0);
261 FLAC__ASSERT(data_len > 0 || total_error_2 == 0);
262 FLAC__ASSERT(data_len > 0 || total_error_3 == 0);
263 FLAC__ASSERT(data_len > 0 || total_error_4 == 0);
264 #ifndef FLAC__INTEGER_ONLY_LIBRARY
265 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);
266 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);
267 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);
268 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);
269 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);
270 #else
271 residual_bits_per_sample[0] = (total_error_0 > 0) ? local__compute_rbps_integerized(total_error_0, data_len) : 0;
272 residual_bits_per_sample[1] = (total_error_1 > 0) ? local__compute_rbps_integerized(total_error_1, data_len) : 0;
273 residual_bits_per_sample[2] = (total_error_2 > 0) ? local__compute_rbps_integerized(total_error_2, data_len) : 0;
274 residual_bits_per_sample[3] = (total_error_3 > 0) ? local__compute_rbps_integerized(total_error_3, data_len) : 0;
275 residual_bits_per_sample[4] = (total_error_4 > 0) ? local__compute_rbps_integerized(total_error_4, data_len) : 0;
276 #endif
277
278 return order;
279 }
280
281 #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])282 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])
283 #else
284 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])
285 #endif
286 {
287 FLAC__int32 last_error_0 = data[-1];
288 FLAC__int32 last_error_1 = data[-1] - data[-2];
289 FLAC__int32 last_error_2 = last_error_1 - (data[-2] - data[-3]);
290 FLAC__int32 last_error_3 = last_error_2 - (data[-2] - 2*data[-3] + data[-4]);
291 FLAC__int32 error, save;
292 /* total_error_* are 64-bits to avoid overflow when encoding
293 * erratic signals when the bits-per-sample and blocksize are
294 * large.
295 */
296 FLAC__uint64 total_error_0 = 0, total_error_1 = 0, total_error_2 = 0, total_error_3 = 0, total_error_4 = 0;
297 unsigned i, order;
298
299 for(i = 0; i < data_len; i++) {
300 error = data[i] ; total_error_0 += local_abs(error); save = error;
301 error -= last_error_0; total_error_1 += local_abs(error); last_error_0 = save; save = error;
302 error -= last_error_1; total_error_2 += local_abs(error); last_error_1 = save; save = error;
303 error -= last_error_2; total_error_3 += local_abs(error); last_error_2 = save; save = error;
304 error -= last_error_3; total_error_4 += local_abs(error); last_error_3 = save;
305 }
306
307 if(total_error_0 < min(min(min(total_error_1, total_error_2), total_error_3), total_error_4))
308 order = 0;
309 else if(total_error_1 < min(min(total_error_2, total_error_3), total_error_4))
310 order = 1;
311 else if(total_error_2 < min(total_error_3, total_error_4))
312 order = 2;
313 else if(total_error_3 < total_error_4)
314 order = 3;
315 else
316 order = 4;
317
318 /* Estimate the expected number of bits per residual signal sample. */
319 /* 'total_error*' is linearly related to the variance of the residual */
320 /* signal, so we use it directly to compute E(|x|) */
321 FLAC__ASSERT(data_len > 0 || total_error_0 == 0);
322 FLAC__ASSERT(data_len > 0 || total_error_1 == 0);
323 FLAC__ASSERT(data_len > 0 || total_error_2 == 0);
324 FLAC__ASSERT(data_len > 0 || total_error_3 == 0);
325 FLAC__ASSERT(data_len > 0 || total_error_4 == 0);
326 #ifndef FLAC__INTEGER_ONLY_LIBRARY
327 #if defined _MSC_VER || defined __MINGW32__
328 /* with MSVC you have to spoon feed it the casting */
329 residual_bits_per_sample[0] = (FLAC__float)((total_error_0 > 0) ? log(M_LN2 * (FLAC__double)(FLAC__int64)total_error_0 / (FLAC__double)data_len) / M_LN2 : 0.0);
330 residual_bits_per_sample[1] = (FLAC__float)((total_error_1 > 0) ? log(M_LN2 * (FLAC__double)(FLAC__int64)total_error_1 / (FLAC__double)data_len) / M_LN2 : 0.0);
331 residual_bits_per_sample[2] = (FLAC__float)((total_error_2 > 0) ? log(M_LN2 * (FLAC__double)(FLAC__int64)total_error_2 / (FLAC__double)data_len) / M_LN2 : 0.0);
332 residual_bits_per_sample[3] = (FLAC__float)((total_error_3 > 0) ? log(M_LN2 * (FLAC__double)(FLAC__int64)total_error_3 / (FLAC__double)data_len) / M_LN2 : 0.0);
333 residual_bits_per_sample[4] = (FLAC__float)((total_error_4 > 0) ? log(M_LN2 * (FLAC__double)(FLAC__int64)total_error_4 / (FLAC__double)data_len) / M_LN2 : 0.0);
334 #else
335 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);
336 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);
337 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);
338 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);
339 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);
340 #endif
341 #else
342 residual_bits_per_sample[0] = (total_error_0 > 0) ? local__compute_rbps_wide_integerized(total_error_0, data_len) : 0;
343 residual_bits_per_sample[1] = (total_error_1 > 0) ? local__compute_rbps_wide_integerized(total_error_1, data_len) : 0;
344 residual_bits_per_sample[2] = (total_error_2 > 0) ? local__compute_rbps_wide_integerized(total_error_2, data_len) : 0;
345 residual_bits_per_sample[3] = (total_error_3 > 0) ? local__compute_rbps_wide_integerized(total_error_3, data_len) : 0;
346 residual_bits_per_sample[4] = (total_error_4 > 0) ? local__compute_rbps_wide_integerized(total_error_4, data_len) : 0;
347 #endif
348
349 return order;
350 }
351
FLAC__fixed_compute_residual(const FLAC__int32 data[],unsigned data_len,unsigned order,FLAC__int32 residual[])352 void FLAC__fixed_compute_residual(const FLAC__int32 data[], unsigned data_len, unsigned order, FLAC__int32 residual[])
353 {
354 const int idata_len = (int)data_len;
355 int i;
356
357 switch(order) {
358 case 0:
359 FLAC__ASSERT(sizeof(residual[0]) == sizeof(data[0]));
360 memcpy(residual, data, sizeof(residual[0])*data_len);
361 break;
362 case 1:
363 for(i = 0; i < idata_len; i++)
364 residual[i] = data[i] - data[i-1];
365 break;
366 case 2:
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] << 1) + data[i-2];
370 #else
371 residual[i] = data[i] - 2*data[i-1] + data[i-2];
372 #endif
373 break;
374 case 3:
375 for(i = 0; i < idata_len; i++)
376 #if 1 /* OPT: may be faster with some compilers on some systems */
377 residual[i] = data[i] - (((data[i-1]-data[i-2])<<1) + (data[i-1]-data[i-2])) - data[i-3];
378 #else
379 residual[i] = data[i] - 3*data[i-1] + 3*data[i-2] - data[i-3];
380 #endif
381 break;
382 case 4:
383 for(i = 0; i < idata_len; i++)
384 #if 1 /* OPT: may be faster with some compilers on some systems */
385 residual[i] = data[i] - ((data[i-1]+data[i-3])<<2) + ((data[i-2]<<2) + (data[i-2]<<1)) + data[i-4];
386 #else
387 residual[i] = data[i] - 4*data[i-1] + 6*data[i-2] - 4*data[i-3] + data[i-4];
388 #endif
389 break;
390 default:
391 FLAC__ASSERT(0);
392 }
393 }
394
FLAC__fixed_restore_signal(const FLAC__int32 residual[],unsigned data_len,unsigned order,FLAC__int32 data[])395 void FLAC__fixed_restore_signal(const FLAC__int32 residual[], unsigned data_len, unsigned order, FLAC__int32 data[])
396 {
397 int i, idata_len = (int)data_len;
398
399 switch(order) {
400 case 0:
401 FLAC__ASSERT(sizeof(residual[0]) == sizeof(data[0]));
402 memcpy(data, residual, sizeof(residual[0])*data_len);
403 break;
404 case 1:
405 for(i = 0; i < idata_len; i++)
406 data[i] = residual[i] + data[i-1];
407 break;
408 case 2:
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]<<1) - data[i-2];
412 #else
413 data[i] = residual[i] + 2*data[i-1] - data[i-2];
414 #endif
415 break;
416 case 3:
417 for(i = 0; i < idata_len; i++)
418 #if 1 /* OPT: may be faster with some compilers on some systems */
419 data[i] = residual[i] + (((data[i-1]-data[i-2])<<1) + (data[i-1]-data[i-2])) + data[i-3];
420 #else
421 data[i] = residual[i] + 3*data[i-1] - 3*data[i-2] + data[i-3];
422 #endif
423 break;
424 case 4:
425 for(i = 0; i < idata_len; i++)
426 #if 1 /* OPT: may be faster with some compilers on some systems */
427 data[i] = residual[i] + ((data[i-1]+data[i-3])<<2) - ((data[i-2]<<2) + (data[i-2]<<1)) - data[i-4];
428 #else
429 data[i] = residual[i] + 4*data[i-1] - 6*data[i-2] + 4*data[i-3] - data[i-4];
430 #endif
431 break;
432 default:
433 FLAC__ASSERT(0);
434 }
435 }
436