1 /* libFLAC - Free Lossless Audio Codec library
2 * Copyright (C) 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 #if HAVE_CONFIG_H
33 # include <config.h>
34 #endif
35
36 #include "FLAC/assert.h"
37
38 #include "private/float.h"
39
40 #ifdef FLAC__INTEGER_ONLY_LIBRARY
41
42 /* adjust for compilers that can't understand using LLU suffix for uint64_t literals */
43 #ifdef _MSC_VER
44 #define FLAC__U64L(x) x
45 #else
46 #define FLAC__U64L(x) x##LLU
47 #endif
48
49 const FLAC__fixedpoint FLAC__FP_ZERO = 0;
50 const FLAC__fixedpoint FLAC__FP_ONE_HALF = 0x00008000;
51 const FLAC__fixedpoint FLAC__FP_ONE = 0x00010000;
52 const FLAC__fixedpoint FLAC__FP_LN2 = 45426;
53 const FLAC__fixedpoint FLAC__FP_E = 178145;
54
55 /* Lookup tables for Knuth's logarithm algorithm */
56 #define LOG2_LOOKUP_PRECISION 16
57 static const FLAC__uint32 log2_lookup[][LOG2_LOOKUP_PRECISION] = {
58 {
59 /*
60 * 0 fraction bits
61 */
62 /* undefined */ 0x00000000,
63 /* lg(2/1) = */ 0x00000001,
64 /* lg(4/3) = */ 0x00000000,
65 /* lg(8/7) = */ 0x00000000,
66 /* lg(16/15) = */ 0x00000000,
67 /* lg(32/31) = */ 0x00000000,
68 /* lg(64/63) = */ 0x00000000,
69 /* lg(128/127) = */ 0x00000000,
70 /* lg(256/255) = */ 0x00000000,
71 /* lg(512/511) = */ 0x00000000,
72 /* lg(1024/1023) = */ 0x00000000,
73 /* lg(2048/2047) = */ 0x00000000,
74 /* lg(4096/4095) = */ 0x00000000,
75 /* lg(8192/8191) = */ 0x00000000,
76 /* lg(16384/16383) = */ 0x00000000,
77 /* lg(32768/32767) = */ 0x00000000
78 },
79 {
80 /*
81 * 4 fraction bits
82 */
83 /* undefined */ 0x00000000,
84 /* lg(2/1) = */ 0x00000010,
85 /* lg(4/3) = */ 0x00000007,
86 /* lg(8/7) = */ 0x00000003,
87 /* lg(16/15) = */ 0x00000001,
88 /* lg(32/31) = */ 0x00000001,
89 /* lg(64/63) = */ 0x00000000,
90 /* lg(128/127) = */ 0x00000000,
91 /* lg(256/255) = */ 0x00000000,
92 /* lg(512/511) = */ 0x00000000,
93 /* lg(1024/1023) = */ 0x00000000,
94 /* lg(2048/2047) = */ 0x00000000,
95 /* lg(4096/4095) = */ 0x00000000,
96 /* lg(8192/8191) = */ 0x00000000,
97 /* lg(16384/16383) = */ 0x00000000,
98 /* lg(32768/32767) = */ 0x00000000
99 },
100 {
101 /*
102 * 8 fraction bits
103 */
104 /* undefined */ 0x00000000,
105 /* lg(2/1) = */ 0x00000100,
106 /* lg(4/3) = */ 0x0000006a,
107 /* lg(8/7) = */ 0x00000031,
108 /* lg(16/15) = */ 0x00000018,
109 /* lg(32/31) = */ 0x0000000c,
110 /* lg(64/63) = */ 0x00000006,
111 /* lg(128/127) = */ 0x00000003,
112 /* lg(256/255) = */ 0x00000001,
113 /* lg(512/511) = */ 0x00000001,
114 /* lg(1024/1023) = */ 0x00000000,
115 /* lg(2048/2047) = */ 0x00000000,
116 /* lg(4096/4095) = */ 0x00000000,
117 /* lg(8192/8191) = */ 0x00000000,
118 /* lg(16384/16383) = */ 0x00000000,
119 /* lg(32768/32767) = */ 0x00000000
120 },
121 {
122 /*
123 * 12 fraction bits
124 */
125 /* undefined */ 0x00000000,
126 /* lg(2/1) = */ 0x00001000,
127 /* lg(4/3) = */ 0x000006a4,
128 /* lg(8/7) = */ 0x00000315,
129 /* lg(16/15) = */ 0x0000017d,
130 /* lg(32/31) = */ 0x000000bc,
131 /* lg(64/63) = */ 0x0000005d,
132 /* lg(128/127) = */ 0x0000002e,
133 /* lg(256/255) = */ 0x00000017,
134 /* lg(512/511) = */ 0x0000000c,
135 /* lg(1024/1023) = */ 0x00000006,
136 /* lg(2048/2047) = */ 0x00000003,
137 /* lg(4096/4095) = */ 0x00000001,
138 /* lg(8192/8191) = */ 0x00000001,
139 /* lg(16384/16383) = */ 0x00000000,
140 /* lg(32768/32767) = */ 0x00000000
141 },
142 {
143 /*
144 * 16 fraction bits
145 */
146 /* undefined */ 0x00000000,
147 /* lg(2/1) = */ 0x00010000,
148 /* lg(4/3) = */ 0x00006a40,
149 /* lg(8/7) = */ 0x00003151,
150 /* lg(16/15) = */ 0x000017d6,
151 /* lg(32/31) = */ 0x00000bba,
152 /* lg(64/63) = */ 0x000005d1,
153 /* lg(128/127) = */ 0x000002e6,
154 /* lg(256/255) = */ 0x00000172,
155 /* lg(512/511) = */ 0x000000b9,
156 /* lg(1024/1023) = */ 0x0000005c,
157 /* lg(2048/2047) = */ 0x0000002e,
158 /* lg(4096/4095) = */ 0x00000017,
159 /* lg(8192/8191) = */ 0x0000000c,
160 /* lg(16384/16383) = */ 0x00000006,
161 /* lg(32768/32767) = */ 0x00000003
162 },
163 {
164 /*
165 * 20 fraction bits
166 */
167 /* undefined */ 0x00000000,
168 /* lg(2/1) = */ 0x00100000,
169 /* lg(4/3) = */ 0x0006a3fe,
170 /* lg(8/7) = */ 0x00031513,
171 /* lg(16/15) = */ 0x00017d60,
172 /* lg(32/31) = */ 0x0000bb9d,
173 /* lg(64/63) = */ 0x00005d10,
174 /* lg(128/127) = */ 0x00002e59,
175 /* lg(256/255) = */ 0x00001721,
176 /* lg(512/511) = */ 0x00000b8e,
177 /* lg(1024/1023) = */ 0x000005c6,
178 /* lg(2048/2047) = */ 0x000002e3,
179 /* lg(4096/4095) = */ 0x00000171,
180 /* lg(8192/8191) = */ 0x000000b9,
181 /* lg(16384/16383) = */ 0x0000005c,
182 /* lg(32768/32767) = */ 0x0000002e
183 },
184 {
185 /*
186 * 24 fraction bits
187 */
188 /* undefined */ 0x00000000,
189 /* lg(2/1) = */ 0x01000000,
190 /* lg(4/3) = */ 0x006a3fe6,
191 /* lg(8/7) = */ 0x00315130,
192 /* lg(16/15) = */ 0x0017d605,
193 /* lg(32/31) = */ 0x000bb9ca,
194 /* lg(64/63) = */ 0x0005d0fc,
195 /* lg(128/127) = */ 0x0002e58f,
196 /* lg(256/255) = */ 0x0001720e,
197 /* lg(512/511) = */ 0x0000b8d8,
198 /* lg(1024/1023) = */ 0x00005c61,
199 /* lg(2048/2047) = */ 0x00002e2d,
200 /* lg(4096/4095) = */ 0x00001716,
201 /* lg(8192/8191) = */ 0x00000b8b,
202 /* lg(16384/16383) = */ 0x000005c5,
203 /* lg(32768/32767) = */ 0x000002e3
204 },
205 {
206 /*
207 * 28 fraction bits
208 */
209 /* undefined */ 0x00000000,
210 /* lg(2/1) = */ 0x10000000,
211 /* lg(4/3) = */ 0x06a3fe5c,
212 /* lg(8/7) = */ 0x03151301,
213 /* lg(16/15) = */ 0x017d6049,
214 /* lg(32/31) = */ 0x00bb9ca6,
215 /* lg(64/63) = */ 0x005d0fba,
216 /* lg(128/127) = */ 0x002e58f7,
217 /* lg(256/255) = */ 0x001720da,
218 /* lg(512/511) = */ 0x000b8d87,
219 /* lg(1024/1023) = */ 0x0005c60b,
220 /* lg(2048/2047) = */ 0x0002e2d7,
221 /* lg(4096/4095) = */ 0x00017160,
222 /* lg(8192/8191) = */ 0x0000b8ad,
223 /* lg(16384/16383) = */ 0x00005c56,
224 /* lg(32768/32767) = */ 0x00002e2b
225 }
226 };
227
228 #if 0
229 static const FLAC__uint64 log2_lookup_wide[] = {
230 {
231 /*
232 * 32 fraction bits
233 */
234 /* undefined */ 0x00000000,
235 /* lg(2/1) = */ FLAC__U64L(0x100000000),
236 /* lg(4/3) = */ FLAC__U64L(0x6a3fe5c6),
237 /* lg(8/7) = */ FLAC__U64L(0x31513015),
238 /* lg(16/15) = */ FLAC__U64L(0x17d60497),
239 /* lg(32/31) = */ FLAC__U64L(0x0bb9ca65),
240 /* lg(64/63) = */ FLAC__U64L(0x05d0fba2),
241 /* lg(128/127) = */ FLAC__U64L(0x02e58f74),
242 /* lg(256/255) = */ FLAC__U64L(0x01720d9c),
243 /* lg(512/511) = */ FLAC__U64L(0x00b8d875),
244 /* lg(1024/1023) = */ FLAC__U64L(0x005c60aa),
245 /* lg(2048/2047) = */ FLAC__U64L(0x002e2d72),
246 /* lg(4096/4095) = */ FLAC__U64L(0x00171600),
247 /* lg(8192/8191) = */ FLAC__U64L(0x000b8ad2),
248 /* lg(16384/16383) = */ FLAC__U64L(0x0005c55d),
249 /* lg(32768/32767) = */ FLAC__U64L(0x0002e2ac)
250 },
251 {
252 /*
253 * 48 fraction bits
254 */
255 /* undefined */ 0x00000000,
256 /* lg(2/1) = */ FLAC__U64L(0x1000000000000),
257 /* lg(4/3) = */ FLAC__U64L(0x6a3fe5c60429),
258 /* lg(8/7) = */ FLAC__U64L(0x315130157f7a),
259 /* lg(16/15) = */ FLAC__U64L(0x17d60496cfbb),
260 /* lg(32/31) = */ FLAC__U64L(0xbb9ca64ecac),
261 /* lg(64/63) = */ FLAC__U64L(0x5d0fba187cd),
262 /* lg(128/127) = */ FLAC__U64L(0x2e58f7441ee),
263 /* lg(256/255) = */ FLAC__U64L(0x1720d9c06a8),
264 /* lg(512/511) = */ FLAC__U64L(0xb8d8752173),
265 /* lg(1024/1023) = */ FLAC__U64L(0x5c60aa252e),
266 /* lg(2048/2047) = */ FLAC__U64L(0x2e2d71b0d8),
267 /* lg(4096/4095) = */ FLAC__U64L(0x1716001719),
268 /* lg(8192/8191) = */ FLAC__U64L(0xb8ad1de1b),
269 /* lg(16384/16383) = */ FLAC__U64L(0x5c55d640d),
270 /* lg(32768/32767) = */ FLAC__U64L(0x2e2abcf52)
271 }
272 };
273 #endif
274
FLAC__fixedpoint_log2(FLAC__uint32 x,unsigned fracbits,unsigned precision)275 FLAC__uint32 FLAC__fixedpoint_log2(FLAC__uint32 x, unsigned fracbits, unsigned precision)
276 {
277 const FLAC__uint32 ONE = (1u << fracbits);
278 const FLAC__uint32 *table = log2_lookup[fracbits >> 2];
279
280 FLAC__ASSERT(fracbits < 32);
281 FLAC__ASSERT((fracbits & 0x3) == 0);
282
283 if(x < ONE)
284 return 0;
285
286 if(precision > LOG2_LOOKUP_PRECISION)
287 precision = LOG2_LOOKUP_PRECISION;
288
289 /* Knuth's algorithm for computing logarithms, optimized for base-2 with lookup tables */
290 {
291 FLAC__uint32 y = 0;
292 FLAC__uint32 z = x >> 1, k = 1;
293 while (x > ONE && k < precision) {
294 if (x - z >= ONE) {
295 x -= z;
296 z = x >> k;
297 y += table[k];
298 }
299 else {
300 z >>= 1;
301 k++;
302 }
303 }
304 return y;
305 }
306 }
307
308 #endif /* defined FLAC__INTEGER_ONLY_LIBRARY */
309