log2.h

/* Integer base 2 logarithm calculation
 *
 * Copyright (C) 2006 Red Hat, Inc. All Rights Reserved.
 * Written by David Howells (dhowells@redhat.com)
 *
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License
 * as published by the Free Software Foundation; either version
 * 2 of the License, or (at your option) any later version.
 */

#ifndef __LOG2_H__
#define __LOG2_H__

#include <sys/types.h>

static __always_inline int fls(int x)
{
	return x ? sizeof(x) * 8 - __builtin_clz(x) : 0;
}

/*
 * deal with unrepresentable constant logarithms
 */
extern __attribute__((const, noreturn))
int ____ilog2_NaN(void);

/*
 * non-constant log of base 2 calculators
 * - the arch may override these in asm/bitops.h if they can be implemented
 *   more efficiently than using fls() and fls64()
 * - the arch is not required to handle n==0 if implementing the fallback
 */
static inline __attribute__((const))
int __ilog2_u32(u_int32_t n)
{
	return fls(n) - 1;
}

/*
 *  Determine whether some value is a power of two, where zero is
 * *not* considered a power of two.
 */

static inline __attribute__((const))
int is_power_of_2(unsigned long n)
{
	return (n != 0 && ((n & (n - 1)) == 0));
}

/**
 * ilog2 - log of base 2 of 32-bit or a 64-bit unsigned value
 * @n - parameter
 *
 * constant-capable log of base 2 calculation
 * - this can be used to initialise global variables from constant data, hence
 *   the massive ternary operator construction
 *
 * selects the appropriately-sized optimised version depending on sizeof(n)
 */
#define ilog2(n)				\
(						\
	__builtin_constant_p(n) ? (		\
		(n) < 1 ? ____ilog2_NaN() :	\
		(n) & (1ULL << 63) ? 63 :	\
		(n) & (1ULL << 62) ? 62 :	\
		(n) & (1ULL << 61) ? 61 :	\
		(n) & (1ULL << 60) ? 60 :	\
		(n) & (1ULL << 59) ? 59 :	\
		(n) & (1ULL << 58) ? 58 :	\
		(n) & (1ULL << 57) ? 57 :	\
		(n) & (1ULL << 56) ? 56 :	\
		(n) & (1ULL << 55) ? 55 :	\
		(n) & (1ULL << 54) ? 54 :	\
		(n) & (1ULL << 53) ? 53 :	\
		(n) & (1ULL << 52) ? 52 :	\
		(n) & (1ULL << 51) ? 51 :	\
		(n) & (1ULL << 50) ? 50 :	\
		(n) & (1ULL << 49) ? 49 :	\
		(n) & (1ULL << 48) ? 48 :	\
		(n) & (1ULL << 47) ? 47 :	\
		(n) & (1ULL << 46) ? 46 :	\
		(n) & (1ULL << 45) ? 45 :	\
		(n) & (1ULL << 44) ? 44 :	\
		(n) & (1ULL << 43) ? 43 :	\
		(n) & (1ULL << 42) ? 42 :	\
		(n) & (1ULL << 41) ? 41 :	\
		(n) & (1ULL << 40) ? 40 :	\
		(n) & (1ULL << 39) ? 39 :	\
		(n) & (1ULL << 38) ? 38 :	\
		(n) & (1ULL << 37) ? 37 :	\
		(n) & (1ULL << 36) ? 36 :	\
		(n) & (1ULL << 35) ? 35 :	\
		(n) & (1ULL << 34) ? 34 :	\
		(n) & (1ULL << 33) ? 33 :	\
		(n) & (1ULL << 32) ? 32 :	\
		(n) & (1ULL << 31) ? 31 :	\
		(n) & (1ULL << 30) ? 30 :	\
		(n) & (1ULL << 29) ? 29 :	\
		(n) & (1ULL << 28) ? 28 :	\
		(n) & (1ULL << 27) ? 27 :	\
		(n) & (1ULL << 26) ? 26 :	\
		(n) & (1ULL << 25) ? 25 :	\
		(n) & (1ULL << 24) ? 24 :	\
		(n) & (1ULL << 23) ? 23 :	\
		(n) & (1ULL << 22) ? 22 :	\
		(n) & (1ULL << 21) ? 21 :	\
		(n) & (1ULL << 20) ? 20 :	\
		(n) & (1ULL << 19) ? 19 :	\
		(n) & (1ULL << 18) ? 18 :	\
		(n) & (1ULL << 17) ? 17 :	\
		(n) & (1ULL << 16) ? 16 :	\
		(n) & (1ULL << 15) ? 15 :	\
		(n) & (1ULL << 14) ? 14 :	\
		(n) & (1ULL << 13) ? 13 :	\
		(n) & (1ULL << 12) ? 12 :	\
		(n) & (1ULL << 11) ? 11 :	\
		(n) & (1ULL << 10) ? 10 :	\
		(n) & (1ULL <<  9) ?  9 :	\
		(n) & (1ULL <<  8) ?  8 :	\
		(n) & (1ULL <<  7) ?  7 :	\
		(n) & (1ULL <<  6) ?  6 :	\
		(n) & (1ULL <<  5) ?  5 :	\
		(n) & (1ULL <<  4) ?  4 :	\
		(n) & (1ULL <<  3) ?  3 :	\
		(n) & (1ULL <<  2) ?  2 :	\
		(n) & (1ULL <<  1) ?  1 :	\
		(n) & (1ULL <<  0) ?  0 :	\
		____ilog2_NaN()			\
				   ) :		\
	__ilog2_u32(n)				\
 )

/**
 * roundup_pow_of_two - round the given value up to nearest power of two
 * @n - parameter
 *
 * round the given value up to the nearest power of two
 * - the result is undefined when n == 0
 * - this can be used to initialise global variables from constant data
 */
#define roundup_pow_of_two(n)			\
(						\
	__builtin_constant_p(n) ? (		\
		(n == 1) ? 1 :			\
		(1UL << (ilog2((n) - 1) + 1))	\
				   ) :		\
	__roundup_pow_of_two(n)			\
 )

/**
 * rounddown_pow_of_two - round the given value down to nearest power of two
 * @n - parameter
 *
 * round the given value down to the nearest power of two
 * - the result is undefined when n == 0
 * - this can be used to initialise global variables from constant data
 */
#define rounddown_pow_of_two(n)			\
(						\
	__builtin_constant_p(n) ? (		\
		(1UL << ilog2(n))) :		\
	__rounddown_pow_of_two(n)		\
 )

/**
 * order_base_2 - calculate the (rounded up) base 2 order of the argument
 * @n: parameter
 *
 * The first few values calculated by this routine:
 *  ob2(0) = 0
 *  ob2(1) = 0
 *  ob2(2) = 1
 *  ob2(3) = 2
 *  ob2(4) = 2
 *  ob2(5) = 3
 *  ... and so on.
 */

#define order_base_2(n) ilog2(roundup_pow_of_two(n))

#endif /* _LINUX_LOG2_H */