1/* Integer base 2 logarithm calculation
2 *
3 * Copyright (C) 2006 Red Hat, Inc. All Rights Reserved.
4 * Written by David Howells (dhowells@redhat.com)
5 *
6 * This program is free software; you can redistribute it and/or
7 * modify it under the terms of the GNU General Public License
8 * as published by the Free Software Foundation; either version
9 * 2 of the License, or (at your option) any later version.
10 */
11
12#ifndef _LINUX_LOG2_H
13#define _LINUX_LOG2_H
14
15#include <linux/types.h>
16#include <linux/bitops.h>
17
18/*
19 * deal with unrepresentable constant logarithms
20 */
21extern __attribute__((const, noreturn))
22int ____ilog2_NaN(void);
23
24/*
25 * non-constant log of base 2 calculators
26 * - the arch may override these in asm/bitops.h if they can be implemented
27 *   more efficiently than using fls() and fls64()
28 * - the arch is not required to handle n==0 if implementing the fallback
29 */
30#ifndef CONFIG_ARCH_HAS_ILOG2_U32
31static inline __attribute__((const))
32int __ilog2_u32(u32 n)
33{
34	return fls(n) - 1;
35}
36#endif
37
38#ifndef CONFIG_ARCH_HAS_ILOG2_U64
39static inline __attribute__((const))
40int __ilog2_u64(u64 n)
41{
42	return fls64(n) - 1;
43}
44#endif
45
46/*
47 *  Determine whether some value is a power of two, where zero is
48 * *not* considered a power of two.
49 */
50
51static inline __attribute__((const))
52bool is_power_of_2(unsigned long n)
53{
54	return (n != 0 && ((n & (n - 1)) == 0));
55}
56
57/*
58 * round up to nearest power of two
59 */
60static inline __attribute__((const))
61unsigned long __roundup_pow_of_two(unsigned long n)
62{
63	return 1UL << fls_long(n - 1);
64}
65
66/*
67 * round down to nearest power of two
68 */
69static inline __attribute__((const))
70unsigned long __rounddown_pow_of_two(unsigned long n)
71{
72	return 1UL << (fls_long(n) - 1);
73}
74
75/**
76 * ilog2 - log of base 2 of 32-bit or a 64-bit unsigned value
77 * @n - parameter
78 *
79 * constant-capable log of base 2 calculation
80 * - this can be used to initialise global variables from constant data, hence
81 *   the massive ternary operator construction
82 *
83 * selects the appropriately-sized optimised version depending on sizeof(n)
84 */
85#define ilog2(n)				\
86(						\
87	__builtin_constant_p(n) ? (		\
88		(n) < 1 ? ____ilog2_NaN() :	\
89		(n) & (1ULL << 63) ? 63 :	\
90		(n) & (1ULL << 62) ? 62 :	\
91		(n) & (1ULL << 61) ? 61 :	\
92		(n) & (1ULL << 60) ? 60 :	\
93		(n) & (1ULL << 59) ? 59 :	\
94		(n) & (1ULL << 58) ? 58 :	\
95		(n) & (1ULL << 57) ? 57 :	\
96		(n) & (1ULL << 56) ? 56 :	\
97		(n) & (1ULL << 55) ? 55 :	\
98		(n) & (1ULL << 54) ? 54 :	\
99		(n) & (1ULL << 53) ? 53 :	\
100		(n) & (1ULL << 52) ? 52 :	\
101		(n) & (1ULL << 51) ? 51 :	\
102		(n) & (1ULL << 50) ? 50 :	\
103		(n) & (1ULL << 49) ? 49 :	\
104		(n) & (1ULL << 48) ? 48 :	\
105		(n) & (1ULL << 47) ? 47 :	\
106		(n) & (1ULL << 46) ? 46 :	\
107		(n) & (1ULL << 45) ? 45 :	\
108		(n) & (1ULL << 44) ? 44 :	\
109		(n) & (1ULL << 43) ? 43 :	\
110		(n) & (1ULL << 42) ? 42 :	\
111		(n) & (1ULL << 41) ? 41 :	\
112		(n) & (1ULL << 40) ? 40 :	\
113		(n) & (1ULL << 39) ? 39 :	\
114		(n) & (1ULL << 38) ? 38 :	\
115		(n) & (1ULL << 37) ? 37 :	\
116		(n) & (1ULL << 36) ? 36 :	\
117		(n) & (1ULL << 35) ? 35 :	\
118		(n) & (1ULL << 34) ? 34 :	\
119		(n) & (1ULL << 33) ? 33 :	\
120		(n) & (1ULL << 32) ? 32 :	\
121		(n) & (1ULL << 31) ? 31 :	\
122		(n) & (1ULL << 30) ? 30 :	\
123		(n) & (1ULL << 29) ? 29 :	\
124		(n) & (1ULL << 28) ? 28 :	\
125		(n) & (1ULL << 27) ? 27 :	\
126		(n) & (1ULL << 26) ? 26 :	\
127		(n) & (1ULL << 25) ? 25 :	\
128		(n) & (1ULL << 24) ? 24 :	\
129		(n) & (1ULL << 23) ? 23 :	\
130		(n) & (1ULL << 22) ? 22 :	\
131		(n) & (1ULL << 21) ? 21 :	\
132		(n) & (1ULL << 20) ? 20 :	\
133		(n) & (1ULL << 19) ? 19 :	\
134		(n) & (1ULL << 18) ? 18 :	\
135		(n) & (1ULL << 17) ? 17 :	\
136		(n) & (1ULL << 16) ? 16 :	\
137		(n) & (1ULL << 15) ? 15 :	\
138		(n) & (1ULL << 14) ? 14 :	\
139		(n) & (1ULL << 13) ? 13 :	\
140		(n) & (1ULL << 12) ? 12 :	\
141		(n) & (1ULL << 11) ? 11 :	\
142		(n) & (1ULL << 10) ? 10 :	\
143		(n) & (1ULL <<  9) ?  9 :	\
144		(n) & (1ULL <<  8) ?  8 :	\
145		(n) & (1ULL <<  7) ?  7 :	\
146		(n) & (1ULL <<  6) ?  6 :	\
147		(n) & (1ULL <<  5) ?  5 :	\
148		(n) & (1ULL <<  4) ?  4 :	\
149		(n) & (1ULL <<  3) ?  3 :	\
150		(n) & (1ULL <<  2) ?  2 :	\
151		(n) & (1ULL <<  1) ?  1 :	\
152		(n) & (1ULL <<  0) ?  0 :	\
153		____ilog2_NaN()			\
154				   ) :		\
155	(sizeof(n) <= 4) ?			\
156	__ilog2_u32(n) :			\
157	__ilog2_u64(n)				\
158 )
159
160/**
161 * roundup_pow_of_two - round the given value up to nearest power of two
162 * @n - parameter
163 *
164 * round the given value up to the nearest power of two
165 * - the result is undefined when n == 0
166 * - this can be used to initialise global variables from constant data
167 */
168#define roundup_pow_of_two(n)			\
169(						\
170	__builtin_constant_p(n) ? (		\
171		(n == 1) ? 1 :			\
172		(1UL << (ilog2((n) - 1) + 1))	\
173				   ) :		\
174	__roundup_pow_of_two(n)			\
175 )
176
177/**
178 * rounddown_pow_of_two - round the given value down to nearest power of two
179 * @n - parameter
180 *
181 * round the given value down to the nearest power of two
182 * - the result is undefined when n == 0
183 * - this can be used to initialise global variables from constant data
184 */
185#define rounddown_pow_of_two(n)			\
186(						\
187	__builtin_constant_p(n) ? (		\
188		(1UL << ilog2(n))) :		\
189	__rounddown_pow_of_two(n)		\
190 )
191
192/**
193 * order_base_2 - calculate the (rounded up) base 2 order of the argument
194 * @n: parameter
195 *
196 * The first few values calculated by this routine:
197 *  ob2(0) = 0
198 *  ob2(1) = 0
199 *  ob2(2) = 1
200 *  ob2(3) = 2
201 *  ob2(4) = 2
202 *  ob2(5) = 3
203 *  ... and so on.
204 */
205
206#define order_base_2(n) ilog2(roundup_pow_of_two(n))
207
208#endif /* _LINUX_LOG2_H */
209