xref: /linux/include/linux/log2.h (revision 4f2c0a4acffbec01079c28f839422e64ddeff004)
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
21 static __always_inline __attribute__((const))
__ilog2_u32(u32 n)22 int __ilog2_u32(u32 n)
23 {
24 	return fls(n) - 1;
25 }
26 #endif
27 
28 #ifndef CONFIG_ARCH_HAS_ILOG2_U64
29 static __always_inline __attribute__((const))
__ilog2_u64(u64 n)30 int __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  */
44 static inline __attribute__((const))
is_power_of_2(unsigned long n)45 bool 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  */
54 static inline __attribute__((const))
__roundup_pow_of_two(unsigned long n)55 unsigned 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  */
64 static inline __attribute__((const))
__rounddown_pow_of_two(unsigned long n)65 unsigned 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 
198 static inline __attribute_const__
__order_base_2(unsigned long n)199 int __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 
225 static inline __attribute__((const))
__bits_per(unsigned long n)226 int __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 #endif /* _LINUX_LOG2_H */
259