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
25 static inline __attribute__((const))
__ilog2_u32(u32 n)26 int __ilog2_u32(u32 n)
27 {
28 	return fls(n) - 1;
29 }
30 #endif
31 
32 #ifndef CONFIG_ARCH_HAS_ILOG2_U64
33 static inline __attribute__((const))
__ilog2_u64(u64 n)34 int __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  */
48 static inline __attribute__((const))
is_power_of_2(unsigned long n)49 bool 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  */
58 static inline __attribute__((const))
__roundup_pow_of_two(unsigned long n)59 unsigned 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  */
68 static inline __attribute__((const))
__rounddown_pow_of_two(unsigned long n)69 unsigned 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 
201 static inline __attribute_const__
__order_base_2(unsigned long n)202 int __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