include/linux/log2.h

   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  * 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
  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
  31 static inline __attribute__((const))
  32 int __ilog2_u32(u32 n)
  33 {
  34         return fls(n) - 1;
  35 }
  36 #endif
  37
  38 #ifndef CONFIG_ARCH_HAS_ILOG2_U64
  39 static inline __attribute__((const))
  40 int __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
  51 static inline __attribute__((const))
  52 bool 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  */
  60 static inline __attribute__((const))
  61 unsigned 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  */
  69 static inline __attribute__((const))
  70 unsigned 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                 (n == 1) ? 0 :                  \
 189                 (1UL << ilog2(n))) :            \
 190         __rounddown_pow_of_two(n)               \
 191  )
 192
 193 /**
 194  * order_base_2 - calculate the (rounded up) base 2 order of the argument
 195  * @n: parameter
 196  *
 197  * The first few values calculated by this routine:
 198  *  ob2(0) = 0
 199  *  ob2(1) = 0
 200  *  ob2(2) = 1
 201  *  ob2(3) = 2
 202  *  ob2(4) = 2
 203  *  ob2(5) = 3
 204  *  ... and so on.
 205  */
 206
 207 #define order_base_2(n) ilog2(roundup_pow_of_two(n))
 208
 209 #endif /* _LINUX_LOG2_H */