1 /* libFLAC - Free Lossless Audio Codec library
2 * Copyright (C) 2000-2009 Josh Coalson
3 * Copyright (C) 2011-2013 Xiph.Org Foundation
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
9 * - Redistributions of source code must retain the above copyright
10 * notice, this list of conditions and the following disclaimer.
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.
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.
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.
39 #include "private/bitmath.h"
40 #include "private/fixed.h"
41 #include "private/macros.h"
42 #include "FLAC/assert.h"
45 /* math.h in VC++ doesn't seem to have this (how Microsoft is that?) */
46 #define M_LN2 0.69314718055994530942
52 #define local_abs(x) ((unsigned)((x)<0? -(x) : (x)))
54 #ifdef FLAC__INTEGER_ONLY_LIBRARY
55 /* rbps stands for residual bits per sample
58 * rbps = log (-----------)
61 static FLAC__fixedpoint local__compute_rbps_integerized(FLAC__uint32 err, FLAC__uint32 n)
64 unsigned bits; /* the number of bits required to represent a number */
65 int fracbits; /* the number of bits of rbps that comprise the fractional part */
67 FLAC__ASSERT(sizeof(rbps) == sizeof(FLAC__fixedpoint));
68 FLAC__ASSERT(err > 0);
71 FLAC__ASSERT(n <= FLAC__MAX_BLOCK_SIZE);
75 * The above two things tell us 1) n fits in 16 bits; 2) err/n > 1.
76 * These allow us later to know we won't lose too much precision in the
77 * fixed-point division (err<<fracbits)/n.
80 fracbits = (8*sizeof(err)) - (FLAC__bitmath_ilog2(err)+1);
84 /* err now holds err/n with fracbits fractional bits */
87 * Whittle err down to 16 bits max. 16 significant bits is enough for
90 FLAC__ASSERT(err > 0);
91 bits = FLAC__bitmath_ilog2(err)+1;
94 fracbits -= (bits-16);
96 rbps = (FLAC__uint32)err;
98 /* Multiply by fixed-point version of ln(2), with 16 fractional bits */
101 FLAC__ASSERT(fracbits >= 0);
103 /* FLAC__fixedpoint_log2 requires fracbits%4 to be 0 */
105 const int f = fracbits & 3;
112 rbps = FLAC__fixedpoint_log2(rbps, fracbits, (unsigned)(-1));
118 * The return value must have 16 fractional bits. Since the whole part
119 * of the base-2 log of a 32 bit number must fit in 5 bits, and fracbits
120 * must be >= -3, these assertion allows us to be able to shift rbps
121 * left if necessary to get 16 fracbits without losing any bits of the
122 * whole part of rbps.
124 * There is a slight chance due to accumulated error that the whole part
125 * will require 6 bits, so we use 6 in the assertion. Really though as
126 * long as it fits in 13 bits (32 - (16 - (-3))) we are fine.
128 FLAC__ASSERT((int)FLAC__bitmath_ilog2(rbps)+1 <= fracbits + 6);
129 FLAC__ASSERT(fracbits >= -3);
131 /* now shift the decimal point into place */
133 return rbps << (16-fracbits);
134 else if(fracbits > 16)
135 return rbps >> (fracbits-16);
140 static FLAC__fixedpoint local__compute_rbps_wide_integerized(FLAC__uint64 err, FLAC__uint32 n)
143 unsigned bits; /* the number of bits required to represent a number */
144 int fracbits; /* the number of bits of rbps that comprise the fractional part */
146 FLAC__ASSERT(sizeof(rbps) == sizeof(FLAC__fixedpoint));
147 FLAC__ASSERT(err > 0);
150 FLAC__ASSERT(n <= FLAC__MAX_BLOCK_SIZE);
154 * The above two things tell us 1) n fits in 16 bits; 2) err/n > 1.
155 * These allow us later to know we won't lose too much precision in the
156 * fixed-point division (err<<fracbits)/n.
159 fracbits = (8*sizeof(err)) - (FLAC__bitmath_ilog2_wide(err)+1);
163 /* err now holds err/n with fracbits fractional bits */
166 * Whittle err down to 16 bits max. 16 significant bits is enough for
169 FLAC__ASSERT(err > 0);
170 bits = FLAC__bitmath_ilog2_wide(err)+1;
173 fracbits -= (bits-16);
175 rbps = (FLAC__uint32)err;
177 /* Multiply by fixed-point version of ln(2), with 16 fractional bits */
178 rbps *= FLAC__FP_LN2;
180 FLAC__ASSERT(fracbits >= 0);
182 /* FLAC__fixedpoint_log2 requires fracbits%4 to be 0 */
184 const int f = fracbits & 3;
191 rbps = FLAC__fixedpoint_log2(rbps, fracbits, (unsigned)(-1));
197 * The return value must have 16 fractional bits. Since the whole part
198 * of the base-2 log of a 32 bit number must fit in 5 bits, and fracbits
199 * must be >= -3, these assertion allows us to be able to shift rbps
200 * left if necessary to get 16 fracbits without losing any bits of the
201 * whole part of rbps.
203 * There is a slight chance due to accumulated error that the whole part
204 * will require 6 bits, so we use 6 in the assertion. Really though as
205 * long as it fits in 13 bits (32 - (16 - (-3))) we are fine.
207 FLAC__ASSERT((int)FLAC__bitmath_ilog2(rbps)+1 <= fracbits + 6);
208 FLAC__ASSERT(fracbits >= -3);
210 /* now shift the decimal point into place */
212 return rbps << (16-fracbits);
213 else if(fracbits > 16)
214 return rbps >> (fracbits-16);
220 #ifndef FLAC__INTEGER_ONLY_LIBRARY
221 unsigned FLAC__fixed_compute_best_predictor(const FLAC__int32 data[], unsigned data_len, FLAC__float residual_bits_per_sample[FLAC__MAX_FIXED_ORDER+1])
223 unsigned FLAC__fixed_compute_best_predictor(const FLAC__int32 data[], unsigned data_len, FLAC__fixedpoint residual_bits_per_sample[FLAC__MAX_FIXED_ORDER+1])
226 FLAC__int32 last_error_0 = data[-1];
227 FLAC__int32 last_error_1 = data[-1] - data[-2];
228 FLAC__int32 last_error_2 = last_error_1 - (data[-2] - data[-3]);
229 FLAC__int32 last_error_3 = last_error_2 - (data[-2] - 2*data[-3] + data[-4]);
230 FLAC__int32 error, save;
231 FLAC__uint32 total_error_0 = 0, total_error_1 = 0, total_error_2 = 0, total_error_3 = 0, total_error_4 = 0;
234 for(i = 0; i < data_len; i++) {
235 error = data[i] ; total_error_0 += local_abs(error); save = error;
236 error -= last_error_0; total_error_1 += local_abs(error); last_error_0 = save; save = error;
237 error -= last_error_1; total_error_2 += local_abs(error); last_error_1 = save; save = error;
238 error -= last_error_2; total_error_3 += local_abs(error); last_error_2 = save; save = error;
239 error -= last_error_3; total_error_4 += local_abs(error); last_error_3 = save;
242 if(total_error_0 < flac_min(flac_min(flac_min(total_error_1, total_error_2), total_error_3), total_error_4))
244 else if(total_error_1 < flac_min(flac_min(total_error_2, total_error_3), total_error_4))
246 else if(total_error_2 < flac_min(total_error_3, total_error_4))
248 else if(total_error_3 < total_error_4)
253 /* Estimate the expected number of bits per residual signal sample. */
254 /* 'total_error*' is linearly related to the variance of the residual */
255 /* signal, so we use it directly to compute E(|x|) */
256 FLAC__ASSERT(data_len > 0 || total_error_0 == 0);
257 FLAC__ASSERT(data_len > 0 || total_error_1 == 0);
258 FLAC__ASSERT(data_len > 0 || total_error_2 == 0);
259 FLAC__ASSERT(data_len > 0 || total_error_3 == 0);
260 FLAC__ASSERT(data_len > 0 || total_error_4 == 0);
261 #ifndef FLAC__INTEGER_ONLY_LIBRARY
262 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);
263 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);
264 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);
265 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);
266 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);
268 residual_bits_per_sample[0] = (total_error_0 > 0) ? local__compute_rbps_integerized(total_error_0, data_len) : 0;
269 residual_bits_per_sample[1] = (total_error_1 > 0) ? local__compute_rbps_integerized(total_error_1, data_len) : 0;
270 residual_bits_per_sample[2] = (total_error_2 > 0) ? local__compute_rbps_integerized(total_error_2, data_len) : 0;
271 residual_bits_per_sample[3] = (total_error_3 > 0) ? local__compute_rbps_integerized(total_error_3, data_len) : 0;
272 residual_bits_per_sample[4] = (total_error_4 > 0) ? local__compute_rbps_integerized(total_error_4, data_len) : 0;
278 #ifndef FLAC__INTEGER_ONLY_LIBRARY
279 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])
281 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])
284 FLAC__int32 last_error_0 = data[-1];
285 FLAC__int32 last_error_1 = data[-1] - data[-2];
286 FLAC__int32 last_error_2 = last_error_1 - (data[-2] - data[-3]);
287 FLAC__int32 last_error_3 = last_error_2 - (data[-2] - 2*data[-3] + data[-4]);
288 FLAC__int32 error, save;
289 /* total_error_* are 64-bits to avoid overflow when encoding
290 * erratic signals when the bits-per-sample and blocksize are
293 FLAC__uint64 total_error_0 = 0, total_error_1 = 0, total_error_2 = 0, total_error_3 = 0, total_error_4 = 0;
296 for(i = 0; i < data_len; i++) {
297 error = data[i] ; total_error_0 += local_abs(error); save = error;
298 error -= last_error_0; total_error_1 += local_abs(error); last_error_0 = save; save = error;
299 error -= last_error_1; total_error_2 += local_abs(error); last_error_1 = save; save = error;
300 error -= last_error_2; total_error_3 += local_abs(error); last_error_2 = save; save = error;
301 error -= last_error_3; total_error_4 += local_abs(error); last_error_3 = save;
304 if(total_error_0 < flac_min(flac_min(flac_min(total_error_1, total_error_2), total_error_3), total_error_4))
306 else if(total_error_1 < flac_min(flac_min(total_error_2, total_error_3), total_error_4))
308 else if(total_error_2 < flac_min(total_error_3, total_error_4))
310 else if(total_error_3 < total_error_4)
315 /* Estimate the expected number of bits per residual signal sample. */
316 /* 'total_error*' is linearly related to the variance of the residual */
317 /* signal, so we use it directly to compute E(|x|) */
318 FLAC__ASSERT(data_len > 0 || total_error_0 == 0);
319 FLAC__ASSERT(data_len > 0 || total_error_1 == 0);
320 FLAC__ASSERT(data_len > 0 || total_error_2 == 0);
321 FLAC__ASSERT(data_len > 0 || total_error_3 == 0);
322 FLAC__ASSERT(data_len > 0 || total_error_4 == 0);
323 #ifndef FLAC__INTEGER_ONLY_LIBRARY
324 #if defined _MSC_VER || defined __MINGW32__
325 /* with MSVC you have to spoon feed it the casting */
326 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);
327 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);
328 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);
329 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);
330 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);
332 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);
333 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);
334 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);
335 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);
336 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);
339 residual_bits_per_sample[0] = (total_error_0 > 0) ? local__compute_rbps_wide_integerized(total_error_0, data_len) : 0;
340 residual_bits_per_sample[1] = (total_error_1 > 0) ? local__compute_rbps_wide_integerized(total_error_1, data_len) : 0;
341 residual_bits_per_sample[2] = (total_error_2 > 0) ? local__compute_rbps_wide_integerized(total_error_2, data_len) : 0;
342 residual_bits_per_sample[3] = (total_error_3 > 0) ? local__compute_rbps_wide_integerized(total_error_3, data_len) : 0;
343 residual_bits_per_sample[4] = (total_error_4 > 0) ? local__compute_rbps_wide_integerized(total_error_4, data_len) : 0;
349 void FLAC__fixed_compute_residual(const FLAC__int32 data[], unsigned data_len, unsigned order, FLAC__int32 residual[])
351 const int idata_len = (int)data_len;
356 FLAC__ASSERT(sizeof(residual[0]) == sizeof(data[0]));
357 memcpy(residual, data, sizeof(residual[0])*data_len);
360 for(i = 0; i < idata_len; i++)
361 residual[i] = data[i] - data[i-1];
364 for(i = 0; i < idata_len; i++)
365 #if 1 /* OPT: may be faster with some compilers on some systems */
366 residual[i] = data[i] - (data[i-1] << 1) + data[i-2];
368 residual[i] = data[i] - 2*data[i-1] + data[i-2];
372 for(i = 0; i < idata_len; i++)
373 #if 1 /* OPT: may be faster with some compilers on some systems */
374 residual[i] = data[i] - (((data[i-1]-data[i-2])<<1) + (data[i-1]-data[i-2])) - data[i-3];
376 residual[i] = data[i] - 3*data[i-1] + 3*data[i-2] - data[i-3];
380 for(i = 0; i < idata_len; i++)
381 #if 1 /* OPT: may be faster with some compilers on some systems */
382 residual[i] = data[i] - ((data[i-1]+data[i-3])<<2) + ((data[i-2]<<2) + (data[i-2]<<1)) + data[i-4];
384 residual[i] = data[i] - 4*data[i-1] + 6*data[i-2] - 4*data[i-3] + data[i-4];
392 void FLAC__fixed_restore_signal(const FLAC__int32 residual[], unsigned data_len, unsigned order, FLAC__int32 data[])
394 int i, idata_len = (int)data_len;
398 FLAC__ASSERT(sizeof(residual[0]) == sizeof(data[0]));
399 memcpy(data, residual, sizeof(residual[0])*data_len);
402 for(i = 0; i < idata_len; i++)
403 data[i] = residual[i] + data[i-1];
406 for(i = 0; i < idata_len; i++)
407 #if 1 /* OPT: may be faster with some compilers on some systems */
408 data[i] = residual[i] + (data[i-1]<<1) - data[i-2];
410 data[i] = residual[i] + 2*data[i-1] - data[i-2];
414 for(i = 0; i < idata_len; i++)
415 #if 1 /* OPT: may be faster with some compilers on some systems */
416 data[i] = residual[i] + (((data[i-1]-data[i-2])<<1) + (data[i-1]-data[i-2])) + data[i-3];
418 data[i] = residual[i] + 3*data[i-1] - 3*data[i-2] + data[i-3];
422 for(i = 0; i < idata_len; i++)
423 #if 1 /* OPT: may be faster with some compilers on some systems */
424 data[i] = residual[i] + ((data[i-1]+data[i-3])<<2) - ((data[i-2]<<2) + (data[i-2]<<1)) - data[i-4];
426 data[i] = residual[i] + 4*data[i-1] - 6*data[i-2] + 4*data[i-3] - data[i-4];