linux/lib/math/int_log.c

// SPDX-License-Identifier: LGPL-2.1-or-later
/*
 * Provides fixed-point logarithm operations.
 *
 * Copyright (C) 2006 Christoph Pfister (christophpfister@gmail.com)
 */

#include <linux/bitops.h>
#include <linux/export.h>
#include <linux/int_log.h>
#include <linux/kernel.h>
#include <linux/types.h>

#include <asm/bug.h>

static const unsigned short logtable[256] = {
	0x0000, 0x0171, 0x02e0, 0x044e, 0x05ba, 0x0725, 0x088e, 0x09f7,
	0x0b5d, 0x0cc3, 0x0e27, 0x0f8a, 0x10eb, 0x124b, 0x13aa, 0x1508,
	0x1664, 0x17bf, 0x1919, 0x1a71, 0x1bc8, 0x1d1e, 0x1e73, 0x1fc6,
	0x2119, 0x226a, 0x23ba, 0x2508, 0x2656, 0x27a2, 0x28ed, 0x2a37,
	0x2b80, 0x2cc8, 0x2e0f, 0x2f54, 0x3098, 0x31dc, 0x331e, 0x345f,
	0x359f, 0x36de, 0x381b, 0x3958, 0x3a94, 0x3bce, 0x3d08, 0x3e41,
	0x3f78, 0x40af, 0x41e4, 0x4319, 0x444c, 0x457f, 0x46b0, 0x47e1,
	0x4910, 0x4a3f, 0x4b6c, 0x4c99, 0x4dc5, 0x4eef, 0x5019, 0x5142,
	0x526a, 0x5391, 0x54b7, 0x55dc, 0x5700, 0x5824, 0x5946, 0x5a68,
	0x5b89, 0x5ca8, 0x5dc7, 0x5ee5, 0x6003, 0x611f, 0x623a, 0x6355,
	0x646f, 0x6588, 0x66a0, 0x67b7, 0x68ce, 0x69e4, 0x6af8, 0x6c0c,
	0x6d20, 0x6e32, 0x6f44, 0x7055, 0x7165, 0x7274, 0x7383, 0x7490,
	0x759d, 0x76aa, 0x77b5, 0x78c0, 0x79ca, 0x7ad3, 0x7bdb, 0x7ce3,
	0x7dea, 0x7ef0, 0x7ff6, 0x80fb, 0x81ff, 0x8302, 0x8405, 0x8507,
	0x8608, 0x8709, 0x8809, 0x8908, 0x8a06, 0x8b04, 0x8c01, 0x8cfe,
	0x8dfa, 0x8ef5, 0x8fef, 0x90e9, 0x91e2, 0x92db, 0x93d2, 0x94ca,
	0x95c0, 0x96b6, 0x97ab, 0x98a0, 0x9994, 0x9a87, 0x9b7a, 0x9c6c,
	0x9d5e, 0x9e4f, 0x9f3f, 0xa02e, 0xa11e, 0xa20c, 0xa2fa, 0xa3e7,
	0xa4d4, 0xa5c0, 0xa6ab, 0xa796, 0xa881, 0xa96a, 0xaa53, 0xab3c,
	0xac24, 0xad0c, 0xadf2, 0xaed9, 0xafbe, 0xb0a4, 0xb188, 0xb26c,
	0xb350, 0xb433, 0xb515, 0xb5f7, 0xb6d9, 0xb7ba, 0xb89a, 0xb97a,
	0xba59, 0xbb38, 0xbc16, 0xbcf4, 0xbdd1, 0xbead, 0xbf8a, 0xc065,
	0xc140, 0xc21b, 0xc2f5, 0xc3cf, 0xc4a8, 0xc580, 0xc658, 0xc730,
	0xc807, 0xc8de, 0xc9b4, 0xca8a, 0xcb5f, 0xcc34, 0xcd08, 0xcddc,
	0xceaf, 0xcf82, 0xd054, 0xd126, 0xd1f7, 0xd2c8, 0xd399, 0xd469,
	0xd538, 0xd607, 0xd6d6, 0xd7a4, 0xd872, 0xd93f, 0xda0c, 0xdad9,
	0xdba5, 0xdc70, 0xdd3b, 0xde06, 0xded0, 0xdf9a, 0xe063, 0xe12c,
	0xe1f5, 0xe2bd, 0xe385, 0xe44c, 0xe513, 0xe5d9, 0xe69f, 0xe765,
	0xe82a, 0xe8ef, 0xe9b3, 0xea77, 0xeb3b, 0xebfe, 0xecc1, 0xed83,
	0xee45, 0xef06, 0xefc8, 0xf088, 0xf149, 0xf209, 0xf2c8, 0xf387,
	0xf446, 0xf505, 0xf5c3, 0xf680, 0xf73e, 0xf7fb, 0xf8b7, 0xf973,
	0xfa2f, 0xfaea, 0xfba5, 0xfc60, 0xfd1a, 0xfdd4, 0xfe8e, 0xff47,
};

unsigned int intlog2(u32 value)
{
	/**
	 *	returns: log2(value) * 2^24
	 *	wrong result if value = 0 (log2(0) is undefined)
	 */
	unsigned int msb;
	unsigned int logentry;
	unsigned int significand;
	unsigned int interpolation;

	if (unlikely(value == 0)) {
		WARN_ON(1);
		return 0;
	}

	/* first detect the msb (count begins at 0) */
	msb = fls(value) - 1;

	/**
	 *	now we use a logtable after the following method:
	 *
	 *	log2(2^x * y) * 2^24 = x * 2^24 + log2(y) * 2^24
	 *	where x = msb and therefore 1 <= y < 2
	 *	first y is determined by shifting the value left
	 *	so that msb is bit 31
	 *		0x00231f56 -> 0x8C7D5800
	 *	the result is y * 2^31 -> "significand"
	 *	then the highest 9 bits are used for a table lookup
	 *	the highest bit is discarded because it's always set
	 *	the highest nine bits in our example are 100011000
	 *	so we would use the entry 0x18
	 */
	significand = value << (31 - msb);
	logentry = (significand >> 23) % ARRAY_SIZE(logtable);

	/**
	 *	last step we do is interpolation because of the
	 *	limitations of the log table the error is that part of
	 *	the significand which isn't used for lookup then we
	 *	compute the ratio between the error and the next table entry
	 *	and interpolate it between the log table entry used and the
	 *	next one the biggest error possible is 0x7fffff
	 *	(in our example it's 0x7D5800)
	 *	needed value for next table entry is 0x800000
	 *	so the interpolation is
	 *	(error / 0x800000) * (logtable_next - logtable_current)
	 *	in the implementation the division is moved to the end for
	 *	better accuracy there is also an overflow correction if
	 *	logtable_next is 256
	 */
	interpolation = ((significand & 0x7fffff) *
			((logtable[(logentry + 1) % ARRAY_SIZE(logtable)] -
			  logtable[logentry]) & 0xffff)) >> 15;

	/* now we return the result */
	return ((msb << 24) + (logtable[logentry] << 8) + interpolation);
}
EXPORT_SYMBOL(intlog2);

unsigned int intlog10(u32 value)
{
	/**
	 *	returns: log10(value) * 2^24
	 *	wrong result if value = 0 (log10(0) is undefined)
	 */
	u64 log;

	if (unlikely(value == 0)) {
		WARN_ON(1);
		return 0;
	}

	log = intlog2(value);

	/**
	 *	we use the following method:
	 *	log10(x) = log2(x) * log10(2)
	 */

	return (log * 646456993) >> 31;
}
EXPORT_SYMBOL(intlog10);