summaryrefslogtreecommitdiff
path: root/src/libFLAC/fixed.c
blob: 98f42a2f91c7174c19cd34c17ab1013a71eeafa2 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
/* libFLAC - Free Lossless Audio Codec library
 * Copyright (C) 2000-2009  Josh Coalson
 * Copyright (C) 2011-2016  Xiph.Org Foundation
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 *
 * - Redistributions of source code must retain the above copyright
 * notice, this list of conditions and the following disclaimer.
 *
 * - Redistributions in binary form must reproduce the above copyright
 * notice, this list of conditions and the following disclaimer in the
 * documentation and/or other materials provided with the distribution.
 *
 * - Neither the name of the Xiph.org Foundation nor the names of its
 * contributors may be used to endorse or promote products derived from
 * this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
 * A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR
 * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
 * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
 * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
 * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
 * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
 * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

#ifdef HAVE_CONFIG_H
#  include <config.h>
#endif

#include <math.h>
#include <string.h>
#include "share/compat.h"
#include "private/bitmath.h"
#include "private/fixed.h"
#include "private/macros.h"
#include "FLAC/assert.h"

#ifdef local_abs
#undef local_abs
#endif
#define local_abs(x) ((uint32_t)((x)<0? -(x) : (x)))

#ifdef FLAC__INTEGER_ONLY_LIBRARY
/* rbps stands for residual bits per sample
 *
 *             (ln(2) * err)
 * rbps = log  (-----------)
 *           2 (     n     )
 */
static FLAC__fixedpoint local__compute_rbps_integerized(FLAC__uint32 err, FLAC__uint32 n)
{
	FLAC__uint32 rbps;
	uint32_t bits; /* the number of bits required to represent a number */
	int fracbits; /* the number of bits of rbps that comprise the fractional part */

	FLAC__ASSERT(sizeof(rbps) == sizeof(FLAC__fixedpoint));
	FLAC__ASSERT(err > 0);
	FLAC__ASSERT(n > 0);

	FLAC__ASSERT(n <= FLAC__MAX_BLOCK_SIZE);
	if(err <= n)
		return 0;
	/*
	 * The above two things tell us 1) n fits in 16 bits; 2) err/n > 1.
	 * These allow us later to know we won't lose too much precision in the
	 * fixed-point division (err<<fracbits)/n.
	 */

	fracbits = (8*sizeof(err)) - (FLAC__bitmath_ilog2(err)+1);

	err <<= fracbits;
	err /= n;
	/* err now holds err/n with fracbits fractional bits */

	/*
	 * Whittle err down to 16 bits max.  16 significant bits is enough for
	 * our purposes.
	 */
	FLAC__ASSERT(err > 0);
	bits = FLAC__bitmath_ilog2(err)+1;
	if(bits > 16) {
		err >>= (bits-16);
		fracbits -= (bits-16);
	}
	rbps = (FLAC__uint32)err;

	/* Multiply by fixed-point version of ln(2), with 16 fractional bits */
	rbps *= FLAC__FP_LN2;
	fracbits += 16;
	FLAC__ASSERT(fracbits >= 0);

	/* FLAC__fixedpoint_log2 requires fracbits%4 to be 0 */
	{
		const int f = fracbits & 3;
		if(f) {
			rbps >>= f;
			fracbits -= f;
		}
	}

	rbps = FLAC__fixedpoint_log2(rbps, fracbits, (uint32_t)(-1));

	if(rbps == 0)
		return 0;

	/*
	 * The return value must have 16 fractional bits.  Since the whole part
	 * of the base-2 log of a 32 bit number must fit in 5 bits, and fracbits
	 * must be >= -3, these assertion allows us to be able to shift rbps
	 * left if necessary to get 16 fracbits without losing any bits of the
	 * whole part of rbps.
	 *
	 * There is a slight chance due to accumulated error that the whole part
	 * will require 6 bits, so we use 6 in the assertion.  Really though as
	 * long as it fits in 13 bits (32 - (16 - (-3))) we are fine.
	 */
	FLAC__ASSERT((int)FLAC__bitmath_ilog2(rbps)+1 <= fracbits + 6);
	FLAC__ASSERT(fracbits >= -3);

	/* now shift the decimal point into place */
	if(fracbits < 16)
		return rbps << (16-fracbits);
	else if(fracbits > 16)
		return rbps >> (fracbits-16);
	else
		return rbps;
}

static FLAC__fixedpoint local__compute_rbps_wide_integerized(FLAC__uint64 err, FLAC__uint32 n)
{
	FLAC__uint32 rbps;
	uint32_t bits; /* the number of bits required to represent a number */
	int fracbits; /* the number of bits of rbps that comprise the fractional part */

	FLAC__ASSERT(sizeof(rbps) == sizeof(FLAC__fixedpoint));
	FLAC__ASSERT(err > 0);
	FLAC__ASSERT(n > 0);

	FLAC__ASSERT(n <= FLAC__MAX_BLOCK_SIZE);
	if(err <= n)
		return 0;
	/*
	 * The above two things tell us 1) n fits in 16 bits; 2) err/n > 1.
	 * These allow us later to know we won't lose too much precision in the
	 * fixed-point division (err<<fracbits)/n.
	 */

	fracbits = (8*sizeof(err)) - (FLAC__bitmath_ilog2_wide(err)+1);

	err <<= fracbits;
	err /= n;
	/* err now holds err/n with fracbits fractional bits */

	/*
	 * Whittle err down to 16 bits max.  16 significant bits is enough for
	 * our purposes.
	 */
	FLAC__ASSERT(err > 0);
	bits = FLAC__bitmath_ilog2_wide(err)+1;
	if(bits > 16) {
		err >>= (bits-16);
		fracbits -= (bits-16);
	}
	rbps = (FLAC__uint32)err;

	/* Multiply by fixed-point version of ln(2), with 16 fractional bits */
	rbps *= FLAC__FP_LN2;
	fracbits += 16;
	FLAC__ASSERT(fracbits >= 0);

	/* FLAC__fixedpoint_log2 requires fracbits%4 to be 0 */
	{
		const int f = fracbits & 3;
		if(f) {
			rbps >>= f;
			fracbits -= f;
		}
	}

	rbps = FLAC__fixedpoint_log2(rbps, fracbits, (uint32_t)(-1));

	if(rbps == 0)
		return 0;

	/*
	 * The return value must have 16 fractional bits.  Since the whole part
	 * of the base-2 log of a 32 bit number must fit in 5 bits, and fracbits
	 * must be >= -3, these assertion allows us to be able to shift rbps
	 * left if necessary to get 16 fracbits without losing any bits of the
	 * whole part of rbps.
	 *
	 * There is a slight chance due to accumulated error that the whole part
	 * will require 6 bits, so we use 6 in the assertion.  Really though as
	 * long as it fits in 13 bits (32 - (16 - (-3))) we are fine.
	 */
	FLAC__ASSERT((int)FLAC__bitmath_ilog2(rbps)+1 <= fracbits + 6);
	FLAC__ASSERT(fracbits >= -3);

	/* now shift the decimal point into place */
	if(fracbits < 16)
		return rbps << (16-fracbits);
	else if(fracbits > 16)
		return rbps >> (fracbits-16);
	else
		return rbps;
}
#endif

#ifndef FLAC__INTEGER_ONLY_LIBRARY
uint32_t FLAC__fixed_compute_best_predictor(const FLAC__int32 data[], uint32_t data_len, float residual_bits_per_sample[FLAC__MAX_FIXED_ORDER+1])
#else
uint32_t FLAC__fixed_compute_best_predictor(const FLAC__int32 data[], uint32_t data_len, FLAC__fixedpoint residual_bits_per_sample[FLAC__MAX_FIXED_ORDER+1])
#endif
{
	FLAC__int32 last_error_0 = data[-1];
	FLAC__int32 last_error_1 = data[-1] - data[-2];
	FLAC__int32 last_error_2 = last_error_1 - (data[-2] - data[-3]);
	FLAC__int32 last_error_3 = last_error_2 - (data[-2] - 2*data[-3] + data[-4]);
	FLAC__int32 error, save;
	FLAC__uint32 total_error_0 = 0, total_error_1 = 0, total_error_2 = 0, total_error_3 = 0, total_error_4 = 0;
	uint32_t i, order;

	for(i = 0; i < data_len; i++) {
		error  = data[i]     ; total_error_0 += local_abs(error);                      save = error;
		error -= last_error_0; total_error_1 += local_abs(error); last_error_0 = save; save = error;
		error -= last_error_1; total_error_2 += local_abs(error); last_error_1 = save; save = error;
		error -= last_error_2; total_error_3 += local_abs(error); last_error_2 = save; save = error;
		error -= last_error_3; total_error_4 += local_abs(error); last_error_3 = save;
	}

	if(total_error_0 < flac_min(flac_min(flac_min(total_error_1, total_error_2), total_error_3), total_error_4))
		order = 0;
	else if(total_error_1 < flac_min(flac_min(total_error_2, total_error_3), total_error_4))
		order = 1;
	else if(total_error_2 < flac_min(total_error_3, total_error_4))
		order = 2;
	else if(total_error_3 < total_error_4)
		order = 3;
	else
		order = 4;

	/* Estimate the expected number of bits per residual signal sample. */
	/* 'total_error*' is linearly related to the variance of the residual */
	/* signal, so we use it directly to compute E(|x|) */
	FLAC__ASSERT(data_len > 0 || total_error_0 == 0);
	FLAC__ASSERT(data_len > 0 || total_error_1 == 0);
	FLAC__ASSERT(data_len > 0 || total_error_2 == 0);
	FLAC__ASSERT(data_len > 0 || total_error_3 == 0);
	FLAC__ASSERT(data_len > 0 || total_error_4 == 0);
#ifndef FLAC__INTEGER_ONLY_LIBRARY
	residual_bits_per_sample[0] = (float)((total_error_0 > 0) ? log(M_LN2 * (double)total_error_0 / (double)data_len) / M_LN2 : 0.0);
	residual_bits_per_sample[1] = (float)((total_error_1 > 0) ? log(M_LN2 * (double)total_error_1 / (double)data_len) / M_LN2 : 0.0);
	residual_bits_per_sample[2] = (float)((total_error_2 > 0) ? log(M_LN2 * (double)total_error_2 / (double)data_len) / M_LN2 : 0.0);
	residual_bits_per_sample[3] = (float)((total_error_3 > 0) ? log(M_LN2 * (double)total_error_3 / (double)data_len) / M_LN2 : 0.0);
	residual_bits_per_sample[4] = (float)((total_error_4 > 0) ? log(M_LN2 * (double)total_error_4 / (double)data_len) / M_LN2 : 0.0);
#else
	residual_bits_per_sample[0] = (total_error_0 > 0) ? local__compute_rbps_integerized(total_error_0, data_len) : 0;
	residual_bits_per_sample[1] = (total_error_1 > 0) ? local__compute_rbps_integerized(total_error_1, data_len) : 0;
	residual_bits_per_sample[2] = (total_error_2 > 0) ? local__compute_rbps_integerized(total_error_2, data_len) : 0;
	residual_bits_per_sample[3] = (total_error_3 > 0) ? local__compute_rbps_integerized(total_error_3, data_len) : 0;
	residual_bits_per_sample[4] = (total_error_4 > 0) ? local__compute_rbps_integerized(total_error_4, data_len) : 0;
#endif

	return order;
}

#ifndef FLAC__INTEGER_ONLY_LIBRARY
uint32_t FLAC__fixed_compute_best_predictor_wide(const FLAC__int32 data[], uint32_t data_len, float residual_bits_per_sample[FLAC__MAX_FIXED_ORDER+1])
#else
uint32_t FLAC__fixed_compute_best_predictor_wide(const FLAC__int32 data[], uint32_t data_len, FLAC__fixedpoint residual_bits_per_sample[FLAC__MAX_FIXED_ORDER+1])
#endif
{
	FLAC__int32 last_error_0 = data[-1];
	FLAC__int32 last_error_1 = data[-1] - data[-2];
	FLAC__int32 last_error_2 = last_error_1 - (data[-2] - data[-3]);
	FLAC__int32 last_error_3 = last_error_2 - (data[-2] - 2*data[-3] + data[-4]);
	FLAC__int32 error, save;
	/* total_error_* are 64-bits to avoid overflow when encoding
	 * erratic signals when the bits-per-sample and blocksize are
	 * large.
	 */
	FLAC__uint64 total_error_0 = 0, total_error_1 = 0, total_error_2 = 0, total_error_3 = 0, total_error_4 = 0;
	uint32_t i, order;

	for(i = 0; i < data_len; i++) {
		error  = data[i]     ; total_error_0 += local_abs(error);                      save = error;
		error -= last_error_0; total_error_1 += local_abs(error); last_error_0 = save; save = error;
		error -= last_error_1; total_error_2 += local_abs(error); last_error_1 = save; save = error;
		error -= last_error_2; total_error_3 += local_abs(error); last_error_2 = save; save = error;
		error -= last_error_3; total_error_4 += local_abs(error); last_error_3 = save;
	}

	if(total_error_0 < flac_min(flac_min(flac_min(total_error_1, total_error_2), total_error_3), total_error_4))
		order = 0;
	else if(total_error_1 < flac_min(flac_min(total_error_2, total_error_3), total_error_4))
		order = 1;
	else if(total_error_2 < flac_min(total_error_3, total_error_4))
		order = 2;
	else if(total_error_3 < total_error_4)
		order = 3;
	else
		order = 4;

	/* Estimate the expected number of bits per residual signal sample. */
	/* 'total_error*' is linearly related to the variance of the residual */
	/* signal, so we use it directly to compute E(|x|) */
	FLAC__ASSERT(data_len > 0 || total_error_0 == 0);
	FLAC__ASSERT(data_len > 0 || total_error_1 == 0);
	FLAC__ASSERT(data_len > 0 || total_error_2 == 0);
	FLAC__ASSERT(data_len > 0 || total_error_3 == 0);
	FLAC__ASSERT(data_len > 0 || total_error_4 == 0);
#ifndef FLAC__INTEGER_ONLY_LIBRARY
	residual_bits_per_sample[0] = (float)((total_error_0 > 0) ? log(M_LN2 * (double)total_error_0 / (double)data_len) / M_LN2 : 0.0);
	residual_bits_per_sample[1] = (float)((total_error_1 > 0) ? log(M_LN2 * (double)total_error_1 / (double)data_len) / M_LN2 : 0.0);
	residual_bits_per_sample[2] = (float)((total_error_2 > 0) ? log(M_LN2 * (double)total_error_2 / (double)data_len) / M_LN2 : 0.0);
	residual_bits_per_sample[3] = (float)((total_error_3 > 0) ? log(M_LN2 * (double)total_error_3 / (double)data_len) / M_LN2 : 0.0);
	residual_bits_per_sample[4] = (float)((total_error_4 > 0) ? log(M_LN2 * (double)total_error_4 / (double)data_len) / M_LN2 : 0.0);
#else
	residual_bits_per_sample[0] = (total_error_0 > 0) ? local__compute_rbps_wide_integerized(total_error_0, data_len) : 0;
	residual_bits_per_sample[1] = (total_error_1 > 0) ? local__compute_rbps_wide_integerized(total_error_1, data_len) : 0;
	residual_bits_per_sample[2] = (total_error_2 > 0) ? local__compute_rbps_wide_integerized(total_error_2, data_len) : 0;
	residual_bits_per_sample[3] = (total_error_3 > 0) ? local__compute_rbps_wide_integerized(total_error_3, data_len) : 0;
	residual_bits_per_sample[4] = (total_error_4 > 0) ? local__compute_rbps_wide_integerized(total_error_4, data_len) : 0;
#endif

	return order;
}

void FLAC__fixed_compute_residual(const FLAC__int32 data[], uint32_t data_len, uint32_t order, FLAC__int32 residual[])
{
	const int idata_len = (int)data_len;
	int i;

	switch(order) {
		case 0:
			FLAC__ASSERT(sizeof(residual[0]) == sizeof(data[0]));
			memcpy(residual, data, sizeof(residual[0])*data_len);
			break;
		case 1:
			for(i = 0; i < idata_len; i++)
				residual[i] = data[i] - data[i-1];
			break;
		case 2:
			for(i = 0; i < idata_len; i++)
				residual[i] = data[i] - 2*data[i-1] + data[i-2];
			break;
		case 3:
			for(i = 0; i < idata_len; i++)
				residual[i] = data[i] - 3*data[i-1] + 3*data[i-2] - data[i-3];
			break;
		case 4:
			for(i = 0; i < idata_len; i++)
				residual[i] = data[i] - 4*data[i-1] + 6*data[i-2] - 4*data[i-3] + data[i-4];
			break;
		default:
			FLAC__ASSERT(0);
	}
}

void FLAC__fixed_restore_signal(const FLAC__int32 residual[], uint32_t data_len, uint32_t order, FLAC__int32 data[])
{
	int i, idata_len = (int)data_len;

	switch(order) {
		case 0:
			FLAC__ASSERT(sizeof(residual[0]) == sizeof(data[0]));
			memcpy(data, residual, sizeof(residual[0])*data_len);
			break;
		case 1:
			for(i = 0; i < idata_len; i++)
				data[i] = residual[i] + data[i-1];
			break;
		case 2:
			for(i = 0; i < idata_len; i++)
				data[i] = residual[i] + 2*data[i-1] - data[i-2];
			break;
		case 3:
			for(i = 0; i < idata_len; i++)
				data[i] = residual[i] + 3*data[i-1] - 3*data[i-2] + data[i-3];
			break;
		case 4:
			for(i = 0; i < idata_len; i++)
				data[i] = residual[i] + 4*data[i-1] - 6*data[i-2] + 4*data[i-3] - data[i-4];
			break;
		default:
			FLAC__ASSERT(0);
	}
}