```   1/* Integer base 2 logarithm calculation
2 *
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
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```
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