1 /* libFLAC - Free Lossless Audio Codec library
2  * Copyright (C) 2000-2009  Josh Coalson
3  * Copyright (C) 2011-2016  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) ((uint32_t)((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 	uint32_t 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 -= (int)(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, (uint32_t)(-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 	uint32_t 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 -= (int)(bits-16); // defined, but cast to int to avoid ubsan assert.
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, (uint32_t)(-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[],uint32_t data_len,float residual_bits_per_sample[FLAC__MAX_FIXED_ORDER+1])217 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])
218 #else
219 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])
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 	uint32_t 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] = (float)((total_error_0 > 0) ? log(M_LN2 * (double)total_error_0 / (double)data_len) / M_LN2 : 0.0);
259 	residual_bits_per_sample[1] = (float)((total_error_1 > 0) ? log(M_LN2 * (double)total_error_1 / (double)data_len) / M_LN2 : 0.0);
260 	residual_bits_per_sample[2] = (float)((total_error_2 > 0) ? log(M_LN2 * (double)total_error_2 / (double)data_len) / M_LN2 : 0.0);
261 	residual_bits_per_sample[3] = (float)((total_error_3 > 0) ? log(M_LN2 * (double)total_error_3 / (double)data_len) / M_LN2 : 0.0);
262 	residual_bits_per_sample[4] = (float)((total_error_4 > 0) ? log(M_LN2 * (double)total_error_4 / (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[],uint32_t data_len,float residual_bits_per_sample[FLAC__MAX_FIXED_ORDER+1])275 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])
276 #else
277 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])
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 	uint32_t 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] = (float)((total_error_0 > 0) ? log(M_LN2 * (double)total_error_0 / (double)data_len) / M_LN2 : 0.0);
321 	residual_bits_per_sample[1] = (float)((total_error_1 > 0) ? log(M_LN2 * (double)total_error_1 / (double)data_len) / M_LN2 : 0.0);
322 	residual_bits_per_sample[2] = (float)((total_error_2 > 0) ? log(M_LN2 * (double)total_error_2 / (double)data_len) / M_LN2 : 0.0);
323 	residual_bits_per_sample[3] = (float)((total_error_3 > 0) ? log(M_LN2 * (double)total_error_3 / (double)data_len) / M_LN2 : 0.0);
324 	residual_bits_per_sample[4] = (float)((total_error_4 > 0) ? log(M_LN2 * (double)total_error_4 / (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[],uint32_t data_len,uint32_t order,FLAC__int32 residual[])336 void FLAC__fixed_compute_residual(const FLAC__int32 data[], uint32_t data_len, uint32_t 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 				residual[i] = data[i] - 2*data[i-1] + data[i-2];
353 			break;
354 		case 3:
355 			for(i = 0; i < idata_len; i++)
356 				residual[i] = data[i] - 3*data[i-1] + 3*data[i-2] - data[i-3];
357 			break;
358 		case 4:
359 			for(i = 0; i < idata_len; i++)
360 				residual[i] = data[i] - 4*data[i-1] + 6*data[i-2] - 4*data[i-3] + data[i-4];
361 			break;
362 		default:
363 			FLAC__ASSERT(0);
364 	}
365 }
366 
FLAC__fixed_restore_signal(const FLAC__int32 residual[],uint32_t data_len,uint32_t order,FLAC__int32 data[])367 void FLAC__fixed_restore_signal(const FLAC__int32 residual[], uint32_t data_len, uint32_t order, FLAC__int32 data[])
368 {
369 	int i, idata_len = (int)data_len;
370 
371 	switch(order) {
372 		case 0:
373 			FLAC__ASSERT(sizeof(residual[0]) == sizeof(data[0]));
374 			memcpy(data, residual, sizeof(residual[0])*data_len);
375 			break;
376 		case 1:
377 			for(i = 0; i < idata_len; i++)
378 				data[i] = residual[i] + data[i-1];
379 			break;
380 		case 2:
381 			for(i = 0; i < idata_len; i++)
382 				data[i] = residual[i] + 2*data[i-1] - data[i-2];
383 			break;
384 		case 3:
385 			for(i = 0; i < idata_len; i++)
386 				data[i] = residual[i] + 3*data[i-1] - 3*data[i-2] + data[i-3];
387 			break;
388 		case 4:
389 			for(i = 0; i < idata_len; i++)
390 				data[i] = residual[i] + 4*data[i-1] - 6*data[i-2] + 4*data[i-3] - data[i-4];
391 			break;
392 		default:
393 			FLAC__ASSERT(0);
394 	}
395 }
396