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1
/* Integer base 2 logarithm calculation
1
/* Integer base 2 logarithm calculation
2
 *
2
 *
3
 * Copyright (C) 2006 Red Hat, Inc. All Rights Reserved.
3
 * Copyright (C) 2006 Red Hat, Inc. All Rights Reserved.
4
 * Written by David Howells (dhowells@redhat.com)
4
 * Written by David Howells (dhowells@redhat.com)
5
 *
5
 *
6
 * This program is free software; you can redistribute it and/or
6
 * This program is free software; you can redistribute it and/or
7
 * modify it under the terms of the GNU General Public License
7
 * modify it under the terms of the GNU General Public License
8
 * as published by the Free Software Foundation; either version
8
 * as published by the Free Software Foundation; either version
9
 * 2 of the License, or (at your option) any later version.
9
 * 2 of the License, or (at your option) any later version.
10
 */
10
 */
11
 
11
 
12
#ifndef _LINUX_LOG2_H
12
#ifndef _LINUX_LOG2_H
13
#define _LINUX_LOG2_H
13
#define _LINUX_LOG2_H
14
 
14
 
15
#include 
15
#include 
16
#include 
16
#include 
17
 
17
 
18
/*
18
/*
19
 * deal with unrepresentable constant logarithms
-
 
20
 */
-
 
21
extern __attribute__((const, noreturn))
-
 
22
int ____ilog2_NaN(void);
-
 
23
 
-
 
24
/*
-
 
25
 * non-constant log of base 2 calculators
19
 * non-constant log of base 2 calculators
26
 * - the arch may override these in asm/bitops.h if they can be implemented
20
 * - the arch may override these in asm/bitops.h if they can be implemented
27
 *   more efficiently than using fls() and fls64()
21
 *   more efficiently than using fls() and fls64()
28
 * - the arch is not required to handle n==0 if implementing the fallback
22
 * - the arch is not required to handle n==0 if implementing the fallback
29
 */
23
 */
30
#ifndef CONFIG_ARCH_HAS_ILOG2_U32
24
#ifndef CONFIG_ARCH_HAS_ILOG2_U32
31
static inline __attribute__((const))
25
static inline __attribute__((const))
32
int __ilog2_u32(u32 n)
26
int __ilog2_u32(u32 n)
33
{
27
{
34
	return fls(n) - 1;
28
	return fls(n) - 1;
35
}
29
}
36
#endif
30
#endif
37
 
31
 
38
#ifndef CONFIG_ARCH_HAS_ILOG2_U64
32
#ifndef CONFIG_ARCH_HAS_ILOG2_U64
39
static inline __attribute__((const))
33
static inline __attribute__((const))
40
int __ilog2_u64(u64 n)
34
int __ilog2_u64(u64 n)
41
{
35
{
42
	return fls64(n) - 1;
36
	return fls64(n) - 1;
43
}
37
}
44
#endif
38
#endif
45
 
39
 
46
/*
40
/*
47
 *  Determine whether some value is a power of two, where zero is
41
 *  Determine whether some value is a power of two, where zero is
48
 * *not* considered a power of two.
42
 * *not* considered a power of two.
49
 */
43
 */
50
 
44
 
51
static inline __attribute__((const))
45
static inline __attribute__((const))
52
bool is_power_of_2(unsigned long n)
46
bool is_power_of_2(unsigned long n)
53
{
47
{
54
	return (n != 0 && ((n & (n - 1)) == 0));
48
	return (n != 0 && ((n & (n - 1)) == 0));
55
}
49
}
56
 
50
 
57
/*
51
/*
58
 * round up to nearest power of two
52
 * round up to nearest power of two
59
 */
53
 */
60
static inline __attribute__((const))
54
static inline __attribute__((const))
61
unsigned long __roundup_pow_of_two(unsigned long n)
55
unsigned long __roundup_pow_of_two(unsigned long n)
62
{
56
{
63
	return 1UL << fls_long(n - 1);
57
	return 1UL << fls_long(n - 1);
64
}
58
}
65
 
59
 
66
/*
60
/*
67
 * round down to nearest power of two
61
 * round down to nearest power of two
68
 */
62
 */
69
static inline __attribute__((const))
63
static inline __attribute__((const))
70
unsigned long __rounddown_pow_of_two(unsigned long n)
64
unsigned long __rounddown_pow_of_two(unsigned long n)
71
{
65
{
72
	return 1UL << (fls_long(n) - 1);
66
	return 1UL << (fls_long(n) - 1);
73
}
67
}
74
 
68
 
75
/**
69
/**
76
 * ilog2 - log of base 2 of 32-bit or a 64-bit unsigned value
70
 * ilog2 - log of base 2 of 32-bit or a 64-bit unsigned value
77
 * @n - parameter
71
 * @n - parameter
78
 *
72
 *
79
 * constant-capable log of base 2 calculation
73
 * constant-capable log of base 2 calculation
80
 * - this can be used to initialise global variables from constant data, hence
74
 * - this can be used to initialise global variables from constant data, hence
81
 *   the massive ternary operator construction
75
 *   the massive ternary operator construction
82
 *
76
 *
83
 * selects the appropriately-sized optimised version depending on sizeof(n)
77
 * selects the appropriately-sized optimised version depending on sizeof(n)
84
 */
78
 */
85
#define ilog2(n)				\
79
#define ilog2(n)				\
86
(						\
80
(						\
87
	__builtin_constant_p(n) ? (		\
81
	__builtin_constant_p(n) ? (		\
88
		(n) < 1 ? ____ilog2_NaN() :	\
82
		(n) < 2 ? 0 :			\
89
		(n) & (1ULL << 63) ? 63 :	\
83
		(n) & (1ULL << 63) ? 63 :	\
90
		(n) & (1ULL << 62) ? 62 :	\
84
		(n) & (1ULL << 62) ? 62 :	\
91
		(n) & (1ULL << 61) ? 61 :	\
85
		(n) & (1ULL << 61) ? 61 :	\
92
		(n) & (1ULL << 60) ? 60 :	\
86
		(n) & (1ULL << 60) ? 60 :	\
93
		(n) & (1ULL << 59) ? 59 :	\
87
		(n) & (1ULL << 59) ? 59 :	\
94
		(n) & (1ULL << 58) ? 58 :	\
88
		(n) & (1ULL << 58) ? 58 :	\
95
		(n) & (1ULL << 57) ? 57 :	\
89
		(n) & (1ULL << 57) ? 57 :	\
96
		(n) & (1ULL << 56) ? 56 :	\
90
		(n) & (1ULL << 56) ? 56 :	\
97
		(n) & (1ULL << 55) ? 55 :	\
91
		(n) & (1ULL << 55) ? 55 :	\
98
		(n) & (1ULL << 54) ? 54 :	\
92
		(n) & (1ULL << 54) ? 54 :	\
99
		(n) & (1ULL << 53) ? 53 :	\
93
		(n) & (1ULL << 53) ? 53 :	\
100
		(n) & (1ULL << 52) ? 52 :	\
94
		(n) & (1ULL << 52) ? 52 :	\
101
		(n) & (1ULL << 51) ? 51 :	\
95
		(n) & (1ULL << 51) ? 51 :	\
102
		(n) & (1ULL << 50) ? 50 :	\
96
		(n) & (1ULL << 50) ? 50 :	\
103
		(n) & (1ULL << 49) ? 49 :	\
97
		(n) & (1ULL << 49) ? 49 :	\
104
		(n) & (1ULL << 48) ? 48 :	\
98
		(n) & (1ULL << 48) ? 48 :	\
105
		(n) & (1ULL << 47) ? 47 :	\
99
		(n) & (1ULL << 47) ? 47 :	\
106
		(n) & (1ULL << 46) ? 46 :	\
100
		(n) & (1ULL << 46) ? 46 :	\
107
		(n) & (1ULL << 45) ? 45 :	\
101
		(n) & (1ULL << 45) ? 45 :	\
108
		(n) & (1ULL << 44) ? 44 :	\
102
		(n) & (1ULL << 44) ? 44 :	\
109
		(n) & (1ULL << 43) ? 43 :	\
103
		(n) & (1ULL << 43) ? 43 :	\
110
		(n) & (1ULL << 42) ? 42 :	\
104
		(n) & (1ULL << 42) ? 42 :	\
111
		(n) & (1ULL << 41) ? 41 :	\
105
		(n) & (1ULL << 41) ? 41 :	\
112
		(n) & (1ULL << 40) ? 40 :	\
106
		(n) & (1ULL << 40) ? 40 :	\
113
		(n) & (1ULL << 39) ? 39 :	\
107
		(n) & (1ULL << 39) ? 39 :	\
114
		(n) & (1ULL << 38) ? 38 :	\
108
		(n) & (1ULL << 38) ? 38 :	\
115
		(n) & (1ULL << 37) ? 37 :	\
109
		(n) & (1ULL << 37) ? 37 :	\
116
		(n) & (1ULL << 36) ? 36 :	\
110
		(n) & (1ULL << 36) ? 36 :	\
117
		(n) & (1ULL << 35) ? 35 :	\
111
		(n) & (1ULL << 35) ? 35 :	\
118
		(n) & (1ULL << 34) ? 34 :	\
112
		(n) & (1ULL << 34) ? 34 :	\
119
		(n) & (1ULL << 33) ? 33 :	\
113
		(n) & (1ULL << 33) ? 33 :	\
120
		(n) & (1ULL << 32) ? 32 :	\
114
		(n) & (1ULL << 32) ? 32 :	\
121
		(n) & (1ULL << 31) ? 31 :	\
115
		(n) & (1ULL << 31) ? 31 :	\
122
		(n) & (1ULL << 30) ? 30 :	\
116
		(n) & (1ULL << 30) ? 30 :	\
123
		(n) & (1ULL << 29) ? 29 :	\
117
		(n) & (1ULL << 29) ? 29 :	\
124
		(n) & (1ULL << 28) ? 28 :	\
118
		(n) & (1ULL << 28) ? 28 :	\
125
		(n) & (1ULL << 27) ? 27 :	\
119
		(n) & (1ULL << 27) ? 27 :	\
126
		(n) & (1ULL << 26) ? 26 :	\
120
		(n) & (1ULL << 26) ? 26 :	\
127
		(n) & (1ULL << 25) ? 25 :	\
121
		(n) & (1ULL << 25) ? 25 :	\
128
		(n) & (1ULL << 24) ? 24 :	\
122
		(n) & (1ULL << 24) ? 24 :	\
129
		(n) & (1ULL << 23) ? 23 :	\
123
		(n) & (1ULL << 23) ? 23 :	\
130
		(n) & (1ULL << 22) ? 22 :	\
124
		(n) & (1ULL << 22) ? 22 :	\
131
		(n) & (1ULL << 21) ? 21 :	\
125
		(n) & (1ULL << 21) ? 21 :	\
132
		(n) & (1ULL << 20) ? 20 :	\
126
		(n) & (1ULL << 20) ? 20 :	\
133
		(n) & (1ULL << 19) ? 19 :	\
127
		(n) & (1ULL << 19) ? 19 :	\
134
		(n) & (1ULL << 18) ? 18 :	\
128
		(n) & (1ULL << 18) ? 18 :	\
135
		(n) & (1ULL << 17) ? 17 :	\
129
		(n) & (1ULL << 17) ? 17 :	\
136
		(n) & (1ULL << 16) ? 16 :	\
130
		(n) & (1ULL << 16) ? 16 :	\
137
		(n) & (1ULL << 15) ? 15 :	\
131
		(n) & (1ULL << 15) ? 15 :	\
138
		(n) & (1ULL << 14) ? 14 :	\
132
		(n) & (1ULL << 14) ? 14 :	\
139
		(n) & (1ULL << 13) ? 13 :	\
133
		(n) & (1ULL << 13) ? 13 :	\
140
		(n) & (1ULL << 12) ? 12 :	\
134
		(n) & (1ULL << 12) ? 12 :	\
141
		(n) & (1ULL << 11) ? 11 :	\
135
		(n) & (1ULL << 11) ? 11 :	\
142
		(n) & (1ULL << 10) ? 10 :	\
136
		(n) & (1ULL << 10) ? 10 :	\
143
		(n) & (1ULL <<  9) ?  9 :	\
137
		(n) & (1ULL <<  9) ?  9 :	\
144
		(n) & (1ULL <<  8) ?  8 :	\
138
		(n) & (1ULL <<  8) ?  8 :	\
145
		(n) & (1ULL <<  7) ?  7 :	\
139
		(n) & (1ULL <<  7) ?  7 :	\
146
		(n) & (1ULL <<  6) ?  6 :	\
140
		(n) & (1ULL <<  6) ?  6 :	\
147
		(n) & (1ULL <<  5) ?  5 :	\
141
		(n) & (1ULL <<  5) ?  5 :	\
148
		(n) & (1ULL <<  4) ?  4 :	\
142
		(n) & (1ULL <<  4) ?  4 :	\
149
		(n) & (1ULL <<  3) ?  3 :	\
143
		(n) & (1ULL <<  3) ?  3 :	\
150
		(n) & (1ULL <<  2) ?  2 :	\
144
		(n) & (1ULL <<  2) ?  2 :	\
151
		(n) & (1ULL <<  1) ?  1 :	\
-
 
152
		(n) & (1ULL <<  0) ?  0 :	\
-
 
153
		____ilog2_NaN()			\
-
 
154
				   ) :		\
145
		1 ) :				\
155
	(sizeof(n) <= 4) ?			\
146
	(sizeof(n) <= 4) ?			\
156
	__ilog2_u32(n) :			\
147
	__ilog2_u32(n) :			\
157
	__ilog2_u64(n)				\
148
	__ilog2_u64(n)				\
158
 )
149
 )
159
 
150
 
160
/**
151
/**
161
 * roundup_pow_of_two - round the given value up to nearest power of two
152
 * roundup_pow_of_two - round the given value up to nearest power of two
162
 * @n - parameter
153
 * @n - parameter
163
 *
154
 *
164
 * round the given value up to the nearest power of two
155
 * round the given value up to the nearest power of two
165
 * - the result is undefined when n == 0
156
 * - the result is undefined when n == 0
166
 * - this can be used to initialise global variables from constant data
157
 * - this can be used to initialise global variables from constant data
167
 */
158
 */
168
#define roundup_pow_of_two(n)			\
159
#define roundup_pow_of_two(n)			\
169
(						\
160
(						\
170
	__builtin_constant_p(n) ? (		\
161
	__builtin_constant_p(n) ? (		\
171
		(n == 1) ? 1 :			\
162
		(n == 1) ? 1 :			\
172
		(1UL << (ilog2((n) - 1) + 1))	\
163
		(1UL << (ilog2((n) - 1) + 1))	\
173
				   ) :		\
164
				   ) :		\
174
	__roundup_pow_of_two(n)			\
165
	__roundup_pow_of_two(n)			\
175
 )
166
 )
176
 
167
 
177
/**
168
/**
178
 * rounddown_pow_of_two - round the given value down to nearest power of two
169
 * rounddown_pow_of_two - round the given value down to nearest power of two
179
 * @n - parameter
170
 * @n - parameter
180
 *
171
 *
181
 * round the given value down to the nearest power of two
172
 * round the given value down to the nearest power of two
182
 * - the result is undefined when n == 0
173
 * - the result is undefined when n == 0
183
 * - this can be used to initialise global variables from constant data
174
 * - this can be used to initialise global variables from constant data
184
 */
175
 */
185
#define rounddown_pow_of_two(n)			\
176
#define rounddown_pow_of_two(n)			\
186
(						\
177
(						\
187
	__builtin_constant_p(n) ? (		\
178
	__builtin_constant_p(n) ? (		\
188
		(1UL << ilog2(n))) :		\
179
		(1UL << ilog2(n))) :		\
189
	__rounddown_pow_of_two(n)		\
180
	__rounddown_pow_of_two(n)		\
190
 )
181
 )
191
 
182
 
192
/**
183
/**
193
 * order_base_2 - calculate the (rounded up) base 2 order of the argument
184
 * order_base_2 - calculate the (rounded up) base 2 order of the argument
194
 * @n: parameter
185
 * @n: parameter
195
 *
186
 *
196
 * The first few values calculated by this routine:
187
 * The first few values calculated by this routine:
197
 *  ob2(0) = 0
188
 *  ob2(0) = 0
198
 *  ob2(1) = 0
189
 *  ob2(1) = 0
199
 *  ob2(2) = 1
190
 *  ob2(2) = 1
200
 *  ob2(3) = 2
191
 *  ob2(3) = 2
201
 *  ob2(4) = 2
192
 *  ob2(4) = 2
202
 *  ob2(5) = 3
193
 *  ob2(5) = 3
203
 *  ... and so on.
194
 *  ... and so on.
204
 */
195
 */
-
 
196
 
205
 
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
#define order_base_2(n)				\
-
 
204
(						\
-
 
205
	__builtin_constant_p(n) ? (		\
-
 
206
		((n) == 0 || (n) == 1) ? 0 :	\
-
 
207
		ilog2((n) - 1) + 1) :		\
206
#define order_base_2(n) ilog2(roundup_pow_of_two(n))
208
	__order_base_2(n)			\
207
 
209
)
208
#endif /* _LINUX_LOG2_H */
210
#endif /* _LINUX_LOG2_H */