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      1 /* libFLAC - Free Lossless Audio Codec library
      2  * Copyright (C) 2004-2009  Josh Coalson
      3  * Copyright (C) 2011-2014  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 "FLAC/assert.h"
     38 #include "share/compat.h"
     39 #include "private/float.h"
     40 
     41 #ifdef FLAC__INTEGER_ONLY_LIBRARY
     42 
     43 const FLAC__fixedpoint FLAC__FP_ZERO = 0;
     44 const FLAC__fixedpoint FLAC__FP_ONE_HALF = 0x00008000;
     45 const FLAC__fixedpoint FLAC__FP_ONE = 0x00010000;
     46 const FLAC__fixedpoint FLAC__FP_LN2 = 45426;
     47 const FLAC__fixedpoint FLAC__FP_E = 178145;
     48 
     49 /* Lookup tables for Knuth's logarithm algorithm */
     50 #define LOG2_LOOKUP_PRECISION 16
     51 static const FLAC__uint32 log2_lookup[][LOG2_LOOKUP_PRECISION] = {
     52 	{
     53 		/*
     54 		 * 0 fraction bits
     55 		 */
     56 		/* undefined */ 0x00000000,
     57 		/* lg(2/1) = */ 0x00000001,
     58 		/* lg(4/3) = */ 0x00000000,
     59 		/* lg(8/7) = */ 0x00000000,
     60 		/* lg(16/15) = */ 0x00000000,
     61 		/* lg(32/31) = */ 0x00000000,
     62 		/* lg(64/63) = */ 0x00000000,
     63 		/* lg(128/127) = */ 0x00000000,
     64 		/* lg(256/255) = */ 0x00000000,
     65 		/* lg(512/511) = */ 0x00000000,
     66 		/* lg(1024/1023) = */ 0x00000000,
     67 		/* lg(2048/2047) = */ 0x00000000,
     68 		/* lg(4096/4095) = */ 0x00000000,
     69 		/* lg(8192/8191) = */ 0x00000000,
     70 		/* lg(16384/16383) = */ 0x00000000,
     71 		/* lg(32768/32767) = */ 0x00000000
     72 	},
     73 	{
     74 		/*
     75 		 * 4 fraction bits
     76 		 */
     77 		/* undefined */ 0x00000000,
     78 		/* lg(2/1) = */ 0x00000010,
     79 		/* lg(4/3) = */ 0x00000007,
     80 		/* lg(8/7) = */ 0x00000003,
     81 		/* lg(16/15) = */ 0x00000001,
     82 		/* lg(32/31) = */ 0x00000001,
     83 		/* lg(64/63) = */ 0x00000000,
     84 		/* lg(128/127) = */ 0x00000000,
     85 		/* lg(256/255) = */ 0x00000000,
     86 		/* lg(512/511) = */ 0x00000000,
     87 		/* lg(1024/1023) = */ 0x00000000,
     88 		/* lg(2048/2047) = */ 0x00000000,
     89 		/* lg(4096/4095) = */ 0x00000000,
     90 		/* lg(8192/8191) = */ 0x00000000,
     91 		/* lg(16384/16383) = */ 0x00000000,
     92 		/* lg(32768/32767) = */ 0x00000000
     93 	},
     94 	{
     95 		/*
     96 		 * 8 fraction bits
     97 		 */
     98 		/* undefined */ 0x00000000,
     99 		/* lg(2/1) = */ 0x00000100,
    100 		/* lg(4/3) = */ 0x0000006a,
    101 		/* lg(8/7) = */ 0x00000031,
    102 		/* lg(16/15) = */ 0x00000018,
    103 		/* lg(32/31) = */ 0x0000000c,
    104 		/* lg(64/63) = */ 0x00000006,
    105 		/* lg(128/127) = */ 0x00000003,
    106 		/* lg(256/255) = */ 0x00000001,
    107 		/* lg(512/511) = */ 0x00000001,
    108 		/* lg(1024/1023) = */ 0x00000000,
    109 		/* lg(2048/2047) = */ 0x00000000,
    110 		/* lg(4096/4095) = */ 0x00000000,
    111 		/* lg(8192/8191) = */ 0x00000000,
    112 		/* lg(16384/16383) = */ 0x00000000,
    113 		/* lg(32768/32767) = */ 0x00000000
    114 	},
    115 	{
    116 		/*
    117 		 * 12 fraction bits
    118 		 */
    119 		/* undefined */ 0x00000000,
    120 		/* lg(2/1) = */ 0x00001000,
    121 		/* lg(4/3) = */ 0x000006a4,
    122 		/* lg(8/7) = */ 0x00000315,
    123 		/* lg(16/15) = */ 0x0000017d,
    124 		/* lg(32/31) = */ 0x000000bc,
    125 		/* lg(64/63) = */ 0x0000005d,
    126 		/* lg(128/127) = */ 0x0000002e,
    127 		/* lg(256/255) = */ 0x00000017,
    128 		/* lg(512/511) = */ 0x0000000c,
    129 		/* lg(1024/1023) = */ 0x00000006,
    130 		/* lg(2048/2047) = */ 0x00000003,
    131 		/* lg(4096/4095) = */ 0x00000001,
    132 		/* lg(8192/8191) = */ 0x00000001,
    133 		/* lg(16384/16383) = */ 0x00000000,
    134 		/* lg(32768/32767) = */ 0x00000000
    135 	},
    136 	{
    137 		/*
    138 		 * 16 fraction bits
    139 		 */
    140 		/* undefined */ 0x00000000,
    141 		/* lg(2/1) = */ 0x00010000,
    142 		/* lg(4/3) = */ 0x00006a40,
    143 		/* lg(8/7) = */ 0x00003151,
    144 		/* lg(16/15) = */ 0x000017d6,
    145 		/* lg(32/31) = */ 0x00000bba,
    146 		/* lg(64/63) = */ 0x000005d1,
    147 		/* lg(128/127) = */ 0x000002e6,
    148 		/* lg(256/255) = */ 0x00000172,
    149 		/* lg(512/511) = */ 0x000000b9,
    150 		/* lg(1024/1023) = */ 0x0000005c,
    151 		/* lg(2048/2047) = */ 0x0000002e,
    152 		/* lg(4096/4095) = */ 0x00000017,
    153 		/* lg(8192/8191) = */ 0x0000000c,
    154 		/* lg(16384/16383) = */ 0x00000006,
    155 		/* lg(32768/32767) = */ 0x00000003
    156 	},
    157 	{
    158 		/*
    159 		 * 20 fraction bits
    160 		 */
    161 		/* undefined */ 0x00000000,
    162 		/* lg(2/1) = */ 0x00100000,
    163 		/* lg(4/3) = */ 0x0006a3fe,
    164 		/* lg(8/7) = */ 0x00031513,
    165 		/* lg(16/15) = */ 0x00017d60,
    166 		/* lg(32/31) = */ 0x0000bb9d,
    167 		/* lg(64/63) = */ 0x00005d10,
    168 		/* lg(128/127) = */ 0x00002e59,
    169 		/* lg(256/255) = */ 0x00001721,
    170 		/* lg(512/511) = */ 0x00000b8e,
    171 		/* lg(1024/1023) = */ 0x000005c6,
    172 		/* lg(2048/2047) = */ 0x000002e3,
    173 		/* lg(4096/4095) = */ 0x00000171,
    174 		/* lg(8192/8191) = */ 0x000000b9,
    175 		/* lg(16384/16383) = */ 0x0000005c,
    176 		/* lg(32768/32767) = */ 0x0000002e
    177 	},
    178 	{
    179 		/*
    180 		 * 24 fraction bits
    181 		 */
    182 		/* undefined */ 0x00000000,
    183 		/* lg(2/1) = */ 0x01000000,
    184 		/* lg(4/3) = */ 0x006a3fe6,
    185 		/* lg(8/7) = */ 0x00315130,
    186 		/* lg(16/15) = */ 0x0017d605,
    187 		/* lg(32/31) = */ 0x000bb9ca,
    188 		/* lg(64/63) = */ 0x0005d0fc,
    189 		/* lg(128/127) = */ 0x0002e58f,
    190 		/* lg(256/255) = */ 0x0001720e,
    191 		/* lg(512/511) = */ 0x0000b8d8,
    192 		/* lg(1024/1023) = */ 0x00005c61,
    193 		/* lg(2048/2047) = */ 0x00002e2d,
    194 		/* lg(4096/4095) = */ 0x00001716,
    195 		/* lg(8192/8191) = */ 0x00000b8b,
    196 		/* lg(16384/16383) = */ 0x000005c5,
    197 		/* lg(32768/32767) = */ 0x000002e3
    198 	},
    199 	{
    200 		/*
    201 		 * 28 fraction bits
    202 		 */
    203 		/* undefined */ 0x00000000,
    204 		/* lg(2/1) = */ 0x10000000,
    205 		/* lg(4/3) = */ 0x06a3fe5c,
    206 		/* lg(8/7) = */ 0x03151301,
    207 		/* lg(16/15) = */ 0x017d6049,
    208 		/* lg(32/31) = */ 0x00bb9ca6,
    209 		/* lg(64/63) = */ 0x005d0fba,
    210 		/* lg(128/127) = */ 0x002e58f7,
    211 		/* lg(256/255) = */ 0x001720da,
    212 		/* lg(512/511) = */ 0x000b8d87,
    213 		/* lg(1024/1023) = */ 0x0005c60b,
    214 		/* lg(2048/2047) = */ 0x0002e2d7,
    215 		/* lg(4096/4095) = */ 0x00017160,
    216 		/* lg(8192/8191) = */ 0x0000b8ad,
    217 		/* lg(16384/16383) = */ 0x00005c56,
    218 		/* lg(32768/32767) = */ 0x00002e2b
    219 	}
    220 };
    221 
    222 #if 0
    223 static const FLAC__uint64 log2_lookup_wide[] = {
    224 	{
    225 		/*
    226 		 * 32 fraction bits
    227 		 */
    228 		/* undefined */ 0x00000000,
    229 		/* lg(2/1) = */ FLAC__U64L(0x100000000),
    230 		/* lg(4/3) = */ FLAC__U64L(0x6a3fe5c6),
    231 		/* lg(8/7) = */ FLAC__U64L(0x31513015),
    232 		/* lg(16/15) = */ FLAC__U64L(0x17d60497),
    233 		/* lg(32/31) = */ FLAC__U64L(0x0bb9ca65),
    234 		/* lg(64/63) = */ FLAC__U64L(0x05d0fba2),
    235 		/* lg(128/127) = */ FLAC__U64L(0x02e58f74),
    236 		/* lg(256/255) = */ FLAC__U64L(0x01720d9c),
    237 		/* lg(512/511) = */ FLAC__U64L(0x00b8d875),
    238 		/* lg(1024/1023) = */ FLAC__U64L(0x005c60aa),
    239 		/* lg(2048/2047) = */ FLAC__U64L(0x002e2d72),
    240 		/* lg(4096/4095) = */ FLAC__U64L(0x00171600),
    241 		/* lg(8192/8191) = */ FLAC__U64L(0x000b8ad2),
    242 		/* lg(16384/16383) = */ FLAC__U64L(0x0005c55d),
    243 		/* lg(32768/32767) = */ FLAC__U64L(0x0002e2ac)
    244 	},
    245 	{
    246 		/*
    247 		 * 48 fraction bits
    248 		 */
    249 		/* undefined */ 0x00000000,
    250 		/* lg(2/1) = */ FLAC__U64L(0x1000000000000),
    251 		/* lg(4/3) = */ FLAC__U64L(0x6a3fe5c60429),
    252 		/* lg(8/7) = */ FLAC__U64L(0x315130157f7a),
    253 		/* lg(16/15) = */ FLAC__U64L(0x17d60496cfbb),
    254 		/* lg(32/31) = */ FLAC__U64L(0xbb9ca64ecac),
    255 		/* lg(64/63) = */ FLAC__U64L(0x5d0fba187cd),
    256 		/* lg(128/127) = */ FLAC__U64L(0x2e58f7441ee),
    257 		/* lg(256/255) = */ FLAC__U64L(0x1720d9c06a8),
    258 		/* lg(512/511) = */ FLAC__U64L(0xb8d8752173),
    259 		/* lg(1024/1023) = */ FLAC__U64L(0x5c60aa252e),
    260 		/* lg(2048/2047) = */ FLAC__U64L(0x2e2d71b0d8),
    261 		/* lg(4096/4095) = */ FLAC__U64L(0x1716001719),
    262 		/* lg(8192/8191) = */ FLAC__U64L(0xb8ad1de1b),
    263 		/* lg(16384/16383) = */ FLAC__U64L(0x5c55d640d),
    264 		/* lg(32768/32767) = */ FLAC__U64L(0x2e2abcf52)
    265 	}
    266 };
    267 #endif
    268 
    269 FLAC__uint32 FLAC__fixedpoint_log2(FLAC__uint32 x, unsigned fracbits, unsigned precision)
    270 {
    271 	const FLAC__uint32 ONE = (1u << fracbits);
    272 	const FLAC__uint32 *table = log2_lookup[fracbits >> 2];
    273 
    274 	FLAC__ASSERT(fracbits < 32);
    275 	FLAC__ASSERT((fracbits & 0x3) == 0);
    276 
    277 	if(x < ONE)
    278 		return 0;
    279 
    280 	if(precision > LOG2_LOOKUP_PRECISION)
    281 		precision = LOG2_LOOKUP_PRECISION;
    282 
    283 	/* Knuth's algorithm for computing logarithms, optimized for base-2 with lookup tables */
    284 	{
    285 		FLAC__uint32 y = 0;
    286 		FLAC__uint32 z = x >> 1, k = 1;
    287 		while (x > ONE && k < precision) {
    288 			if (x - z >= ONE) {
    289 				x -= z;
    290 				z = x >> k;
    291 				y += table[k];
    292 			}
    293 			else {
    294 				z >>= 1;
    295 				k++;
    296 			}
    297 		}
    298 		return y;
    299 	}
    300 }
    301 
    302 #endif /* defined FLAC__INTEGER_ONLY_LIBRARY */
    303