1 /* libFLAC - Free Lossless Audio Codec library
2 * Copyright (C) 2000,2001,2002,2003,2004,2005,2006,2007,2008,2009 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.
38 #include "private/bitmath.h"
39 #include "private/fixed.h"
40 #include "private/macros.h"
41 #include "FLAC/assert.h"
44 /* math.h in VC++ doesn't seem to have this (how Microsoft is that?) */
45 #define M_LN2 0.69314718055994530942
51 #define local_abs(x) ((unsigned)((x)<0? -(x) : (x)))
53 #ifdef FLAC__INTEGER_ONLY_LIBRARY
54 /* rbps stands for residual bits per sample
57 * rbps = log (-----------)
60 static FLAC__fixedpoint local__compute_rbps_integerized(FLAC__uint32 err, FLAC__uint32 n)
63 unsigned bits; /* the number of bits required to represent a number */
64 int fracbits; /* the number of bits of rbps that comprise the fractional part */
66 FLAC__ASSERT(sizeof(rbps) == sizeof(FLAC__fixedpoint));
67 FLAC__ASSERT(err > 0);
70 FLAC__ASSERT(n <= FLAC__MAX_BLOCK_SIZE);
74 * The above two things tell us 1) n fits in 16 bits; 2) err/n > 1.
75 * These allow us later to know we won't lose too much precision in the
76 * fixed-point division (err<<fracbits)/n.
79 fracbits = (8*sizeof(err)) - (FLAC__bitmath_ilog2(err)+1);
83 /* err now holds err/n with fracbits fractional bits */
86 * Whittle err down to 16 bits max. 16 significant bits is enough for
89 FLAC__ASSERT(err > 0);
90 bits = FLAC__bitmath_ilog2(err)+1;
93 fracbits -= (bits-16);
95 rbps = (FLAC__uint32)err;
97 /* Multiply by fixed-point version of ln(2), with 16 fractional bits */
100 FLAC__ASSERT(fracbits >= 0);
102 /* FLAC__fixedpoint_log2 requires fracbits%4 to be 0 */
104 const int f = fracbits & 3;
111 rbps = FLAC__fixedpoint_log2(rbps, fracbits, (unsigned)(-1));
117 * The return value must have 16 fractional bits. Since the whole part
118 * of the base-2 log of a 32 bit number must fit in 5 bits, and fracbits
119 * must be >= -3, these assertion allows us to be able to shift rbps
120 * left if necessary to get 16 fracbits without losing any bits of the
121 * whole part of rbps.
123 * There is a slight chance due to accumulated error that the whole part
124 * will require 6 bits, so we use 6 in the assertion. Really though as
125 * long as it fits in 13 bits (32 - (16 - (-3))) we are fine.
127 FLAC__ASSERT((int)FLAC__bitmath_ilog2(rbps)+1 <= fracbits + 6);
128 FLAC__ASSERT(fracbits >= -3);
130 /* now shift the decimal point into place */
132 return rbps << (16-fracbits);
133 else if(fracbits > 16)
134 return rbps >> (fracbits-16);
139 static FLAC__fixedpoint local__compute_rbps_wide_integerized(FLAC__uint64 err, FLAC__uint32 n)
142 unsigned bits; /* the number of bits required to represent a number */
143 int fracbits; /* the number of bits of rbps that comprise the fractional part */
145 FLAC__ASSERT(sizeof(rbps) == sizeof(FLAC__fixedpoint));
146 FLAC__ASSERT(err > 0);
149 FLAC__ASSERT(n <= FLAC__MAX_BLOCK_SIZE);
153 * The above two things tell us 1) n fits in 16 bits; 2) err/n > 1.
154 * These allow us later to know we won't lose too much precision in the
155 * fixed-point division (err<<fracbits)/n.
158 fracbits = (8*sizeof(err)) - (FLAC__bitmath_ilog2_wide(err)+1);
162 /* err now holds err/n with fracbits fractional bits */
165 * Whittle err down to 16 bits max. 16 significant bits is enough for
168 FLAC__ASSERT(err > 0);
169 bits = FLAC__bitmath_ilog2_wide(err)+1;
172 fracbits -= (bits-16);
174 rbps = (FLAC__uint32)err;
176 /* Multiply by fixed-point version of ln(2), with 16 fractional bits */
177 rbps *= FLAC__FP_LN2;
179 FLAC__ASSERT(fracbits >= 0);
181 /* FLAC__fixedpoint_log2 requires fracbits%4 to be 0 */
183 const int f = fracbits & 3;
190 rbps = FLAC__fixedpoint_log2(rbps, fracbits, (unsigned)(-1));
196 * The return value must have 16 fractional bits. Since the whole part
197 * of the base-2 log of a 32 bit number must fit in 5 bits, and fracbits
198 * must be >= -3, these assertion allows us to be able to shift rbps
199 * left if necessary to get 16 fracbits without losing any bits of the
200 * whole part of rbps.
202 * There is a slight chance due to accumulated error that the whole part
203 * will require 6 bits, so we use 6 in the assertion. Really though as
204 * long as it fits in 13 bits (32 - (16 - (-3))) we are fine.
206 FLAC__ASSERT((int)FLAC__bitmath_ilog2(rbps)+1 <= fracbits + 6);
207 FLAC__ASSERT(fracbits >= -3);
209 /* now shift the decimal point into place */
211 return rbps << (16-fracbits);
212 else if(fracbits > 16)
213 return rbps >> (fracbits-16);
219 #ifndef FLAC__INTEGER_ONLY_LIBRARY
220 unsigned FLAC__fixed_compute_best_predictor(const FLAC__int32 data[], unsigned data_len, FLAC__float residual_bits_per_sample[FLAC__MAX_FIXED_ORDER+1])
222 unsigned FLAC__fixed_compute_best_predictor(const FLAC__int32 data[], unsigned data_len, FLAC__fixedpoint residual_bits_per_sample[FLAC__MAX_FIXED_ORDER+1])
225 FLAC__int32 last_error_0 = data[-1];
226 FLAC__int32 last_error_1 = data[-1] - data[-2];
227 FLAC__int32 last_error_2 = last_error_1 - (data[-2] - data[-3]);
228 FLAC__int32 last_error_3 = last_error_2 - (data[-2] - 2*data[-3] + data[-4]);
229 FLAC__int32 error, save;
230 FLAC__uint32 total_error_0 = 0, total_error_1 = 0, total_error_2 = 0, total_error_3 = 0, total_error_4 = 0;
233 for(i = 0; i < data_len; i++) {
234 error = data[i] ; total_error_0 += local_abs(error); save = error;
235 error -= last_error_0; total_error_1 += local_abs(error); last_error_0 = save; save = error;
236 error -= last_error_1; total_error_2 += local_abs(error); last_error_1 = save; save = error;
237 error -= last_error_2; total_error_3 += local_abs(error); last_error_2 = save; save = error;
238 error -= last_error_3; total_error_4 += local_abs(error); last_error_3 = save;
241 if(total_error_0 < flac_min(flac_min(flac_min(total_error_1, total_error_2), total_error_3), total_error_4))
243 else if(total_error_1 < flac_min(flac_min(total_error_2, total_error_3), total_error_4))
245 else if(total_error_2 < flac_min(total_error_3, total_error_4))
247 else if(total_error_3 < total_error_4)
252 /* Estimate the expected number of bits per residual signal sample. */
253 /* 'total_error*' is linearly related to the variance of the residual */
254 /* signal, so we use it directly to compute E(|x|) */
255 FLAC__ASSERT(data_len > 0 || total_error_0 == 0);
256 FLAC__ASSERT(data_len > 0 || total_error_1 == 0);
257 FLAC__ASSERT(data_len > 0 || total_error_2 == 0);
258 FLAC__ASSERT(data_len > 0 || total_error_3 == 0);
259 FLAC__ASSERT(data_len > 0 || total_error_4 == 0);
260 #ifndef FLAC__INTEGER_ONLY_LIBRARY
261 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);
262 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);
263 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);
264 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);
265 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);
267 residual_bits_per_sample[0] = (total_error_0 > 0) ? local__compute_rbps_integerized(total_error_0, data_len) : 0;
268 residual_bits_per_sample[1] = (total_error_1 > 0) ? local__compute_rbps_integerized(total_error_1, data_len) : 0;
269 residual_bits_per_sample[2] = (total_error_2 > 0) ? local__compute_rbps_integerized(total_error_2, data_len) : 0;
270 residual_bits_per_sample[3] = (total_error_3 > 0) ? local__compute_rbps_integerized(total_error_3, data_len) : 0;
271 residual_bits_per_sample[4] = (total_error_4 > 0) ? local__compute_rbps_integerized(total_error_4, data_len) : 0;
277 #ifndef FLAC__INTEGER_ONLY_LIBRARY
278 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])
280 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])
283 FLAC__int32 last_error_0 = data[-1];
284 FLAC__int32 last_error_1 = data[-1] - data[-2];
285 FLAC__int32 last_error_2 = last_error_1 - (data[-2] - data[-3]);
286 FLAC__int32 last_error_3 = last_error_2 - (data[-2] - 2*data[-3] + data[-4]);
287 FLAC__int32 error, save;
288 /* total_error_* are 64-bits to avoid overflow when encoding
289 * erratic signals when the bits-per-sample and blocksize are
292 FLAC__uint64 total_error_0 = 0, total_error_1 = 0, total_error_2 = 0, total_error_3 = 0, total_error_4 = 0;
295 for(i = 0; i < data_len; i++) {
296 error = data[i] ; total_error_0 += local_abs(error); save = error;
297 error -= last_error_0; total_error_1 += local_abs(error); last_error_0 = save; save = error;
298 error -= last_error_1; total_error_2 += local_abs(error); last_error_1 = save; save = error;
299 error -= last_error_2; total_error_3 += local_abs(error); last_error_2 = save; save = error;
300 error -= last_error_3; total_error_4 += local_abs(error); last_error_3 = save;
303 if(total_error_0 < flac_min(flac_min(flac_min(total_error_1, total_error_2), total_error_3), total_error_4))
305 else if(total_error_1 < flac_min(flac_min(total_error_2, total_error_3), total_error_4))
307 else if(total_error_2 < flac_min(total_error_3, total_error_4))
309 else if(total_error_3 < total_error_4)
314 /* Estimate the expected number of bits per residual signal sample. */
315 /* 'total_error*' is linearly related to the variance of the residual */
316 /* signal, so we use it directly to compute E(|x|) */
317 FLAC__ASSERT(data_len > 0 || total_error_0 == 0);
318 FLAC__ASSERT(data_len > 0 || total_error_1 == 0);
319 FLAC__ASSERT(data_len > 0 || total_error_2 == 0);
320 FLAC__ASSERT(data_len > 0 || total_error_3 == 0);
321 FLAC__ASSERT(data_len > 0 || total_error_4 == 0);
322 #ifndef FLAC__INTEGER_ONLY_LIBRARY
323 #if defined _MSC_VER || defined __MINGW32__
324 /* with MSVC you have to spoon feed it the casting */
325 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);
326 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);
327 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);
328 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);
329 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);
331 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);
332 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);
333 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);
334 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);
335 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);
338 residual_bits_per_sample[0] = (total_error_0 > 0) ? local__compute_rbps_wide_integerized(total_error_0, data_len) : 0;
339 residual_bits_per_sample[1] = (total_error_1 > 0) ? local__compute_rbps_wide_integerized(total_error_1, data_len) : 0;
340 residual_bits_per_sample[2] = (total_error_2 > 0) ? local__compute_rbps_wide_integerized(total_error_2, data_len) : 0;
341 residual_bits_per_sample[3] = (total_error_3 > 0) ? local__compute_rbps_wide_integerized(total_error_3, data_len) : 0;
342 residual_bits_per_sample[4] = (total_error_4 > 0) ? local__compute_rbps_wide_integerized(total_error_4, data_len) : 0;
348 void FLAC__fixed_compute_residual(const FLAC__int32 data[], unsigned data_len, unsigned order, FLAC__int32 residual[])
350 const int idata_len = (int)data_len;
355 FLAC__ASSERT(sizeof(residual[0]) == sizeof(data[0]));
356 memcpy(residual, data, sizeof(residual[0])*data_len);
359 for(i = 0; i < idata_len; i++)
360 residual[i] = data[i] - data[i-1];
363 for(i = 0; i < idata_len; i++)
364 #if 1 /* OPT: may be faster with some compilers on some systems */
365 residual[i] = data[i] - (data[i-1] << 1) + data[i-2];
367 residual[i] = data[i] - 2*data[i-1] + data[i-2];
371 for(i = 0; i < idata_len; i++)
372 #if 1 /* OPT: may be faster with some compilers on some systems */
373 residual[i] = data[i] - (((data[i-1]-data[i-2])<<1) + (data[i-1]-data[i-2])) - data[i-3];
375 residual[i] = data[i] - 3*data[i-1] + 3*data[i-2] - data[i-3];
379 for(i = 0; i < idata_len; i++)
380 #if 1 /* OPT: may be faster with some compilers on some systems */
381 residual[i] = data[i] - ((data[i-1]+data[i-3])<<2) + ((data[i-2]<<2) + (data[i-2]<<1)) + data[i-4];
383 residual[i] = data[i] - 4*data[i-1] + 6*data[i-2] - 4*data[i-3] + data[i-4];
391 void FLAC__fixed_restore_signal(const FLAC__int32 residual[], unsigned data_len, unsigned order, FLAC__int32 data[])
393 int i, idata_len = (int)data_len;
397 FLAC__ASSERT(sizeof(residual[0]) == sizeof(data[0]));
398 memcpy(data, residual, sizeof(residual[0])*data_len);
401 for(i = 0; i < idata_len; i++)
402 data[i] = residual[i] + data[i-1];
405 for(i = 0; i < idata_len; i++)
406 #if 1 /* OPT: may be faster with some compilers on some systems */
407 data[i] = residual[i] + (data[i-1]<<1) - data[i-2];
409 data[i] = residual[i] + 2*data[i-1] - data[i-2];
413 for(i = 0; i < idata_len; i++)
414 #if 1 /* OPT: may be faster with some compilers on some systems */
415 data[i] = residual[i] + (((data[i-1]-data[i-2])<<1) + (data[i-1]-data[i-2])) + data[i-3];
417 data[i] = residual[i] + 3*data[i-1] - 3*data[i-2] + data[i-3];
421 for(i = 0; i < idata_len; i++)
422 #if 1 /* OPT: may be faster with some compilers on some systems */
423 data[i] = residual[i] + ((data[i-1]+data[i-3])<<2) - ((data[i-2]<<2) + (data[i-2]<<1)) - data[i-4];
425 data[i] = residual[i] + 4*data[i-1] - 6*data[i-2] + 4*data[i-3] - data[i-4];