/* libFLAC - Free Lossless Audio Codec library
* Copyright (C) 2004-2009 Josh Coalson
* Copyright (C) 2011-2025 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 "FLAC/assert.h"
#include "share/compat.h"
#include "private/float.h"
#ifdef FLAC__INTEGER_ONLY_LIBRARY
const FLAC__fixedpoint FLAC__FP_ZERO = 0;
const FLAC__fixedpoint FLAC__FP_ONE_HALF = 0x00008000;
const FLAC__fixedpoint FLAC__FP_ONE = 0x00010000;
const FLAC__fixedpoint FLAC__FP_LN2 = 45426;
const FLAC__fixedpoint FLAC__FP_E = 178145;
/* Lookup tables for Knuth's logarithm algorithm */
#define LOG2_LOOKUP_PRECISION 16
static const FLAC__uint32 log2_lookup[][LOG2_LOOKUP_PRECISION] = {
{
/*
* 0 fraction bits
*/
/* undefined */ 0x00000000,
/* lg(2/1) = */ 0x00000001,
/* lg(4/3) = */ 0x00000000,
/* lg(8/7) = */ 0x00000000,
/* lg(16/15) = */ 0x00000000,
/* lg(32/31) = */ 0x00000000,
/* lg(64/63) = */ 0x00000000,
/* lg(128/127) = */ 0x00000000,
/* lg(256/255) = */ 0x00000000,
/* lg(512/511) = */ 0x00000000,
/* lg(1024/1023) = */ 0x00000000,
/* lg(2048/2047) = */ 0x00000000,
/* lg(4096/4095) = */ 0x00000000,
/* lg(8192/8191) = */ 0x00000000,
/* lg(16384/16383) = */ 0x00000000,
/* lg(32768/32767) = */ 0x00000000
},
{
/*
* 4 fraction bits
*/
/* undefined */ 0x00000000,
/* lg(2/1) = */ 0x00000010,
/* lg(4/3) = */ 0x00000007,
/* lg(8/7) = */ 0x00000003,
/* lg(16/15) = */ 0x00000001,
/* lg(32/31) = */ 0x00000001,
/* lg(64/63) = */ 0x00000000,
/* lg(128/127) = */ 0x00000000,
/* lg(256/255) = */ 0x00000000,
/* lg(512/511) = */ 0x00000000,
/* lg(1024/1023) = */ 0x00000000,
/* lg(2048/2047) = */ 0x00000000,
/* lg(4096/4095) = */ 0x00000000,
/* lg(8192/8191) = */ 0x00000000,
/* lg(16384/16383) = */ 0x00000000,
/* lg(32768/32767) = */ 0x00000000
},
{
/*
* 8 fraction bits
*/
/* undefined */ 0x00000000,
/* lg(2/1) = */ 0x00000100,
/* lg(4/3) = */ 0x0000006a,
/* lg(8/7) = */ 0x00000031,
/* lg(16/15) = */ 0x00000018,
/* lg(32/31) = */ 0x0000000c,
/* lg(64/63) = */ 0x00000006,
/* lg(128/127) = */ 0x00000003,
/* lg(256/255) = */ 0x00000001,
/* lg(512/511) = */ 0x00000001,
/* lg(1024/1023) = */ 0x00000000,
/* lg(2048/2047) = */ 0x00000000,
/* lg(4096/4095) = */ 0x00000000,
/* lg(8192/8191) = */ 0x00000000,
/* lg(16384/16383) = */ 0x00000000,
/* lg(32768/32767) = */ 0x00000000
},
{
/*
* 12 fraction bits
*/
/* undefined */ 0x00000000,
/* lg(2/1) = */ 0x00001000,
/* lg(4/3) = */ 0x000006a4,
/* lg(8/7) = */ 0x00000315,
/* lg(16/15) = */ 0x0000017d,
/* lg(32/31) = */ 0x000000bc,
/* lg(64/63) = */ 0x0000005d,
/* lg(128/127) = */ 0x0000002e,
/* lg(256/255) = */ 0x00000017,
/* lg(512/511) = */ 0x0000000c,
/* lg(1024/1023) = */ 0x00000006,
/* lg(2048/2047) = */ 0x00000003,
/* lg(4096/4095) = */ 0x00000001,
/* lg(8192/8191) = */ 0x00000001,
/* lg(16384/16383) = */ 0x00000000,
/* lg(32768/32767) = */ 0x00000000
},
{
/*
* 16 fraction bits
*/
/* undefined */ 0x00000000,
/* lg(2/1) = */ 0x00010000,
/* lg(4/3) = */ 0x00006a40,
/* lg(8/7) = */ 0x00003151,
/* lg(16/15) = */ 0x000017d6,
/* lg(32/31) = */ 0x00000bba,
/* lg(64/63) = */ 0x000005d1,
/* lg(128/127) = */ 0x000002e6,
/* lg(256/255) = */ 0x00000172,
/* lg(512/511) = */ 0x000000b9,
/* lg(1024/1023) = */ 0x0000005c,
/* lg(2048/2047) = */ 0x0000002e,
/* lg(4096/4095) = */ 0x00000017,
/* lg(8192/8191) = */ 0x0000000c,
/* lg(16384/16383) = */ 0x00000006,
/* lg(32768/32767) = */ 0x00000003
},
{
/*
* 20 fraction bits
*/
/* undefined */ 0x00000000,
/* lg(2/1) = */ 0x00100000,
/* lg(4/3) = */ 0x0006a3fe,
/* lg(8/7) = */ 0x00031513,
/* lg(16/15) = */ 0x00017d60,
/* lg(32/31) = */ 0x0000bb9d,
/* lg(64/63) = */ 0x00005d10,
/* lg(128/127) = */ 0x00002e59,
/* lg(256/255) = */ 0x00001721,
/* lg(512/511) = */ 0x00000b8e,
/* lg(1024/1023) = */ 0x000005c6,
/* lg(2048/2047) = */ 0x000002e3,
/* lg(4096/4095) = */ 0x00000171,
/* lg(8192/8191) = */ 0x000000b9,
/* lg(16384/16383) = */ 0x0000005c,
/* lg(32768/32767) = */ 0x0000002e
},
{
/*
* 24 fraction bits
*/
/* undefined */ 0x00000000,
/* lg(2/1) = */ 0x01000000,
/* lg(4/3) = */ 0x006a3fe6,
/* lg(8/7) = */ 0x00315130,
/* lg(16/15) = */ 0x0017d605,
/* lg(32/31) = */ 0x000bb9ca,
/* lg(64/63) = */ 0x0005d0fc,
/* lg(128/127) = */ 0x0002e58f,
/* lg(256/255) = */ 0x0001720e,
/* lg(512/511) = */ 0x0000b8d8,
/* lg(1024/1023) = */ 0x00005c61,
/* lg(2048/2047) = */ 0x00002e2d,
/* lg(4096/4095) = */ 0x00001716,
/* lg(8192/8191) = */ 0x00000b8b,
/* lg(16384/16383) = */ 0x000005c5,
/* lg(32768/32767) = */ 0x000002e3
},
{
/*
* 28 fraction bits
*/
/* undefined */ 0x00000000,
/* lg(2/1) = */ 0x10000000,
/* lg(4/3) = */ 0x06a3fe5c,
/* lg(8/7) = */ 0x03151301,
/* lg(16/15) = */ 0x017d6049,
/* lg(32/31) = */ 0x00bb9ca6,
/* lg(64/63) = */ 0x005d0fba,
/* lg(128/127) = */ 0x002e58f7,
/* lg(256/255) = */ 0x001720da,
/* lg(512/511) = */ 0x000b8d87,
/* lg(1024/1023) = */ 0x0005c60b,
/* lg(2048/2047) = */ 0x0002e2d7,
/* lg(4096/4095) = */ 0x00017160,
/* lg(8192/8191) = */ 0x0000b8ad,
/* lg(16384/16383) = */ 0x00005c56,
/* lg(32768/32767) = */ 0x00002e2b
}
};
#if 0
static const FLAC__uint64 log2_lookup_wide[] = {
{
/*
* 32 fraction bits
*/
/* undefined */ 0x00000000,
/* lg(2/1) = */ FLAC__U64L(0x100000000),
/* lg(4/3) = */ FLAC__U64L(0x6a3fe5c6),
/* lg(8/7) = */ FLAC__U64L(0x31513015),
/* lg(16/15) = */ FLAC__U64L(0x17d60497),
/* lg(32/31) = */ FLAC__U64L(0x0bb9ca65),
/* lg(64/63) = */ FLAC__U64L(0x05d0fba2),
/* lg(128/127) = */ FLAC__U64L(0x02e58f74),
/* lg(256/255) = */ FLAC__U64L(0x01720d9c),
/* lg(512/511) = */ FLAC__U64L(0x00b8d875),
/* lg(1024/1023) = */ FLAC__U64L(0x005c60aa),
/* lg(2048/2047) = */ FLAC__U64L(0x002e2d72),
/* lg(4096/4095) = */ FLAC__U64L(0x00171600),
/* lg(8192/8191) = */ FLAC__U64L(0x000b8ad2),
/* lg(16384/16383) = */ FLAC__U64L(0x0005c55d),
/* lg(32768/32767) = */ FLAC__U64L(0x0002e2ac)
},
{
/*
* 48 fraction bits
*/
/* undefined */ 0x00000000,
/* lg(2/1) = */ FLAC__U64L(0x1000000000000),
/* lg(4/3) = */ FLAC__U64L(0x6a3fe5c60429),
/* lg(8/7) = */ FLAC__U64L(0x315130157f7a),
/* lg(16/15) = */ FLAC__U64L(0x17d60496cfbb),
/* lg(32/31) = */ FLAC__U64L(0xbb9ca64ecac),
/* lg(64/63) = */ FLAC__U64L(0x5d0fba187cd),
/* lg(128/127) = */ FLAC__U64L(0x2e58f7441ee),
/* lg(256/255) = */ FLAC__U64L(0x1720d9c06a8),
/* lg(512/511) = */ FLAC__U64L(0xb8d8752173),
/* lg(1024/1023) = */ FLAC__U64L(0x5c60aa252e),
/* lg(2048/2047) = */ FLAC__U64L(0x2e2d71b0d8),
/* lg(4096/4095) = */ FLAC__U64L(0x1716001719),
/* lg(8192/8191) = */ FLAC__U64L(0xb8ad1de1b),
/* lg(16384/16383) = */ FLAC__U64L(0x5c55d640d),
/* lg(32768/32767) = */ FLAC__U64L(0x2e2abcf52)
}
};
#endif
FLAC__uint32 FLAC__fixedpoint_log2(FLAC__uint32 x, uint32_t fracbits, uint32_t precision)
{
const FLAC__uint32 ONE = (1u << fracbits);
const FLAC__uint32 *table = log2_lookup[fracbits >> 2];
FLAC__ASSERT(fracbits < 32);
FLAC__ASSERT((fracbits & 0x3) == 0);
if(x < ONE)
return 0;
if(precision > LOG2_LOOKUP_PRECISION)
precision = LOG2_LOOKUP_PRECISION;
/* Knuth's algorithm for computing logarithms, optimized for base-2 with lookup tables */
{
FLAC__uint32 y = 0;
FLAC__uint32 z = x >> 1, k = 1;
while (x > ONE && k < precision) {
if (x - z >= ONE) {
x -= z;
z = x >> k;
y += table[k];
}
else {
z >>= 1;
k++;
}
}
return y;
}
}
#endif /* defined FLAC__INTEGER_ONLY_LIBRARY */