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 inline __attribute__((const))
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 inline __attribute__((const))
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))
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))
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))
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 const_ilog2(n) : \
160 (sizeof(n) <= 4) ? \
161 __ilog2_u32(n) : \
162 __ilog2_u64(n) \
163 )
164
165 /**
166 * roundup_pow_of_two - round the given value up to nearest power of two
167 * @n: parameter
168 *
169 * round the given value up to the nearest power of two
170 * - the result is undefined when n == 0
171 * - this can be used to initialise global variables from constant data
172 */
173 #define roundup_pow_of_two(n) \
174 ( \
175 __builtin_constant_p(n) ? ( \
176 (n == 1) ? 1 : \
177 (1UL << (ilog2((n) - 1) + 1)) \
178 ) : \
179 __roundup_pow_of_two(n) \
180 )
181
182 /**
183 * rounddown_pow_of_two - round the given value down to nearest power of two
184 * @n: parameter
185 *
186 * round the given value down to the nearest power of two
187 * - the result is undefined when n == 0
188 * - this can be used to initialise global variables from constant data
189 */
190 #define rounddown_pow_of_two(n) \
191 ( \
192 __builtin_constant_p(n) ? ( \
193 (1UL << ilog2(n))) : \
194 __rounddown_pow_of_two(n) \
195 )
196
197 static inline __attribute_const__
198 int __order_base_2(unsigned long n)
199 {
200 return n > 1 ? ilog2(n - 1) + 1 : 0;
201 }
202
203 /**
204 * order_base_2 - calculate the (rounded up) base 2 order of the argument
205 * @n: parameter
206 *
207 * The first few values calculated by this routine:
208 * ob2(0) = 0
209 * ob2(1) = 0
210 * ob2(2) = 1
211 * ob2(3) = 2
212 * ob2(4) = 2
213 * ob2(5) = 3
214 * ... and so on.
215 */
216 #define order_base_2(n) \
217 ( \
218 __builtin_constant_p(n) ? ( \
219 ((n) == 0 || (n) == 1) ? 0 : \
220 ilog2((n) - 1) + 1) : \
221 __order_base_2(n) \
222 )
223
224 static inline __attribute__((const))
225 int __bits_per(unsigned long n)
226 {
227 if (n < 2)
228 return 1;
229 if (is_power_of_2(n))
230 return order_base_2(n) + 1;
231 return order_base_2(n);
232 }
233
234 /**
235 * bits_per - calculate the number of bits required for the argument
236 * @n: parameter
237 *
238 * This is constant-capable and can be used for compile time
239 * initializations, e.g bitfields.
240 *
241 * The first few values calculated by this routine:
242 * bf(0) = 1
243 * bf(1) = 1
244 * bf(2) = 2
245 * bf(3) = 2
246 * bf(4) = 3
247 * ... and so on.
248 */
249 #define bits_per(n) \
250 ( \
251 __builtin_constant_p(n) ? ( \
252 ((n) == 0 || (n) == 1) \
253 ? 1 : ilog2(n) + 1 \
254 ) : \
255 __bits_per(n) \
256 )
257 #endif /* _LINUX_LOG2_H */