log2.h

  1/* SPDX-License-Identifier: GPL-2.0-or-later */
  2/* Integer base 2 logarithm calculation
  3 *
  4 * Copyright (C) 2006 Red Hat, Inc. All Rights Reserved.
  5 * Written by David Howells (dhowells@redhat.com)
  6 */
  7
  8#ifndef _LINUX_LOG2_H
  9#define _LINUX_LOG2_H
 10
 11#include <linux/types.h>
 12#include <linux/bitops.h>
 13
 14/*
 15 * non-constant log of base 2 calculators
 16 * - the arch may override these in asm/bitops.h if they can be implemented
 17 *   more efficiently than using fls() and fls64()
 18 * - the arch is not required to handle n==0 if implementing the fallback
 19 */
 20#ifndef CONFIG_ARCH_HAS_ILOG2_U32
 21static __always_inline __attribute__((const))
 22int __ilog2_u32(u32 n)
 23{
 24	return fls(n) - 1;
 25}
 26#endif
 27
 28#ifndef CONFIG_ARCH_HAS_ILOG2_U64
 29static __always_inline __attribute__((const))
 30int __ilog2_u64(u64 n)
 31{
 32	return fls64(n) - 1;
 33}
 34#endif
 35
 36/**
 37 * is_power_of_2() - check if a value is a power of two
 38 * @n: the value to check
 39 *
 40 * Determine whether some value is a power of two, where zero is
 41 * *not* considered a power of two.
 42 * Return: true if @n is a power of 2, otherwise false.
 43 */
 44static __always_inline __attribute__((const))
 45bool is_power_of_2(unsigned long n)
 46{
 47	return (n != 0 && ((n & (n - 1)) == 0));
 48}
 49
 50/**
 51 * __roundup_pow_of_two() - round up to nearest power of two
 52 * @n: value to round up
 53 */
 54static inline __attribute__((const))
 55unsigned long __roundup_pow_of_two(unsigned long n)
 56{
 57	return 1UL << fls_long(n - 1);
 58}
 59
 60/**
 61 * __rounddown_pow_of_two() - round down to nearest power of two
 62 * @n: value to round down
 63 */
 64static inline __attribute__((const))
 65unsigned long __rounddown_pow_of_two(unsigned long n)
 66{
 67	return 1UL << (fls_long(n) - 1);
 68}
 69
 70/**
 71 * const_ilog2 - log base 2 of 32-bit or a 64-bit constant unsigned value
 72 * @n: parameter
 73 *
 74 * Use this where sparse expects a true constant expression, e.g. for array
 75 * indices.
 76 */
 77#define const_ilog2(n)				\
 78(						\
 79	__builtin_constant_p(n) ? (		\
 80		(n) < 2 ? 0 :			\
 81		(n) & (1ULL << 63) ? 63 :	\
 82		(n) & (1ULL << 62) ? 62 :	\
 83		(n) & (1ULL << 61) ? 61 :	\
 84		(n) & (1ULL << 60) ? 60 :	\
 85		(n) & (1ULL << 59) ? 59 :	\
 86		(n) & (1ULL << 58) ? 58 :	\
 87		(n) & (1ULL << 57) ? 57 :	\
 88		(n) & (1ULL << 56) ? 56 :	\
 89		(n) & (1ULL << 55) ? 55 :	\
 90		(n) & (1ULL << 54) ? 54 :	\
 91		(n) & (1ULL << 53) ? 53 :	\
 92		(n) & (1ULL << 52) ? 52 :	\
 93		(n) & (1ULL << 51) ? 51 :	\
 94		(n) & (1ULL << 50) ? 50 :	\
 95		(n) & (1ULL << 49) ? 49 :	\
 96		(n) & (1ULL << 48) ? 48 :	\
 97		(n) & (1ULL << 47) ? 47 :	\
 98		(n) & (1ULL << 46) ? 46 :	\
 99		(n) & (1ULL << 45) ? 45 :	\
100		(n) & (1ULL << 44) ? 44 :	\
101		(n) & (1ULL << 43) ? 43 :	\
102		(n) & (1ULL << 42) ? 42 :	\
103		(n) & (1ULL << 41) ? 41 :	\
104		(n) & (1ULL << 40) ? 40 :	\
105		(n) & (1ULL << 39) ? 39 :	\
106		(n) & (1ULL << 38) ? 38 :	\
107		(n) & (1ULL << 37) ? 37 :	\
108		(n) & (1ULL << 36) ? 36 :	\
109		(n) & (1ULL << 35) ? 35 :	\
110		(n) & (1ULL << 34) ? 34 :	\
111		(n) & (1ULL << 33) ? 33 :	\
112		(n) & (1ULL << 32) ? 32 :	\
113		(n) & (1ULL << 31) ? 31 :	\
114		(n) & (1ULL << 30) ? 30 :	\
115		(n) & (1ULL << 29) ? 29 :	\
116		(n) & (1ULL << 28) ? 28 :	\
117		(n) & (1ULL << 27) ? 27 :	\
118		(n) & (1ULL << 26) ? 26 :	\
119		(n) & (1ULL << 25) ? 25 :	\
120		(n) & (1ULL << 24) ? 24 :	\
121		(n) & (1ULL << 23) ? 23 :	\
122		(n) & (1ULL << 22) ? 22 :	\
123		(n) & (1ULL << 21) ? 21 :	\
124		(n) & (1ULL << 20) ? 20 :	\
125		(n) & (1ULL << 19) ? 19 :	\
126		(n) & (1ULL << 18) ? 18 :	\
127		(n) & (1ULL << 17) ? 17 :	\
128		(n) & (1ULL << 16) ? 16 :	\
129		(n) & (1ULL << 15) ? 15 :	\
130		(n) & (1ULL << 14) ? 14 :	\
131		(n) & (1ULL << 13) ? 13 :	\
132		(n) & (1ULL << 12) ? 12 :	\
133		(n) & (1ULL << 11) ? 11 :	\
134		(n) & (1ULL << 10) ? 10 :	\
135		(n) & (1ULL <<  9) ?  9 :	\
136		(n) & (1ULL <<  8) ?  8 :	\
137		(n) & (1ULL <<  7) ?  7 :	\
138		(n) & (1ULL <<  6) ?  6 :	\
139		(n) & (1ULL <<  5) ?  5 :	\
140		(n) & (1ULL <<  4) ?  4 :	\
141		(n) & (1ULL <<  3) ?  3 :	\
142		(n) & (1ULL <<  2) ?  2 :	\
143		1) :				\
144	-1)
145
146/**
147 * ilog2 - log base 2 of 32-bit or a 64-bit unsigned value
148 * @n: parameter
149 *
150 * constant-capable log of base 2 calculation
151 * - this can be used to initialise global variables from constant data, hence
152 * the massive ternary operator construction
153 *
154 * selects the appropriately-sized optimised version depending on sizeof(n)
155 */
156#define ilog2(n) \
157( \
158	__builtin_constant_p(n) ?	\
159	((n) < 2 ? 0 :			\
160	 63 - __builtin_clzll(n)) :	\
161	(sizeof(n) <= 4) ?		\
162	__ilog2_u32(n) :		\
163	__ilog2_u64(n)			\
164 )
165
166/**
167 * roundup_pow_of_two - round the given value up to nearest power of two
168 * @n: parameter
169 *
170 * round the given value up to the nearest power of two
171 * - the result is undefined when n == 0
172 * - this can be used to initialise global variables from constant data
173 */
174#define roundup_pow_of_two(n)			\
175(						\
176	__builtin_constant_p(n) ? (		\
177		((n) == 1) ? 1 :		\
178		(1UL << (ilog2((n) - 1) + 1))	\
179				   ) :		\
180	__roundup_pow_of_two(n)			\
181 )
182
183/**
184 * rounddown_pow_of_two - round the given value down to nearest power of two
185 * @n: parameter
186 *
187 * round the given value down to the nearest power of two
188 * - the result is undefined when n == 0
189 * - this can be used to initialise global variables from constant data
190 */
191#define rounddown_pow_of_two(n)			\
192(						\
193	__builtin_constant_p(n) ? (		\
194		(1UL << ilog2(n))) :		\
195	__rounddown_pow_of_two(n)		\
196 )
197
198static inline __attribute_const__
199int __order_base_2(unsigned long n)
200{
201	return n > 1 ? ilog2(n - 1) + 1 : 0;
202}
203
204/**
205 * order_base_2 - calculate the (rounded up) base 2 order of the argument
206 * @n: parameter
207 *
208 * The first few values calculated by this routine:
209 *  ob2(0) = 0
210 *  ob2(1) = 0
211 *  ob2(2) = 1
212 *  ob2(3) = 2
213 *  ob2(4) = 2
214 *  ob2(5) = 3
215 *  ... and so on.
216 */
217#define order_base_2(n)				\
218(						\
219	__builtin_constant_p(n) ? (		\
220		((n) == 0 || (n) == 1) ? 0 :	\
221		ilog2((n) - 1) + 1) :		\
222	__order_base_2(n)			\
223)
224
225static inline __attribute__((const))
226int __bits_per(unsigned long n)
227{
228	if (n < 2)
229		return 1;
230	if (is_power_of_2(n))
231		return order_base_2(n) + 1;
232	return order_base_2(n);
233}
234
235/**
236 * bits_per - calculate the number of bits required for the argument
237 * @n: parameter
238 *
239 * This is constant-capable and can be used for compile time
240 * initializations, e.g bitfields.
241 *
242 * The first few values calculated by this routine:
243 * bf(0) = 1
244 * bf(1) = 1
245 * bf(2) = 2
246 * bf(3) = 2
247 * bf(4) = 3
248 * ... and so on.
249 */
250#define bits_per(n)				\
251(						\
252	__builtin_constant_p(n) ? (		\
253		((n) == 0 || (n) == 1)		\
254			? 1 : ilog2(n) + 1	\
255	) :					\
256	__bits_per(n)				\
257)
258
259/**
260 * max_pow_of_two_factor - return highest power-of-2 factor
261 * @n: parameter
262 *
263 * find highest power-of-2 which is evenly divisible into n.
264 * 0 is returned for n == 0 or 1.
265 */
266static inline __attribute__((const))
267unsigned int max_pow_of_two_factor(unsigned int n)
268{
269	return n & -n;
270}
271
272#endif /* _LINUX_LOG2_H */