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