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  * SPDX-License-Identifier:     GPL-2.0+
   7  */
   8
   9 #ifndef _LINUX_LOG2_H
  10 #define _LINUX_LOG2_H
  11
  12 #include <linux/types.h>
  13 #include <linux/bitops.h>
  14
  15 /*
  16  * deal with unrepresentable constant logarithms
  17  */
  18 extern __attribute__((const, noreturn))
  19 int ____ilog2_NaN(void);
  20
  21 /*
  22  * non-constant log of base 2 calculators
  23  * - the arch may override these in asm/bitops.h if they can be implemented
  24  *   more efficiently than using fls() and fls64()
  25  * - the arch is not required to handle n==0 if implementing the fallback
  26  */
  27 #ifndef CONFIG_ARCH_HAS_ILOG2_U32
  28 static inline __attribute__((const))
  29 int __ilog2_u32(u32 n)
  30 {
  31         return fls(n) - 1;
  32 }
  33 #endif
  34
  35 #ifndef CONFIG_ARCH_HAS_ILOG2_U64
  36 static inline __attribute__((const))
  37 int __ilog2_u64(u64 n)
  38 {
  39         return fls64(n) - 1;
  40 }
  41 #endif
  42
  43 /*
  44  *  Determine whether some value is a power of two, where zero is
  45  * *not* considered a power of two.
  46  */
  47
  48 static inline __attribute__((const))
  49 bool is_power_of_2(unsigned long n)
  50 {
  51         return (n != 0 && ((n & (n - 1)) == 0));
  52 }
  53
  54 /*
  55  * round up to nearest power of two
  56  */
  57 static inline __attribute__((const))
  58 unsigned long __roundup_pow_of_two(unsigned long n)
  59 {
  60         return 1UL << fls_long(n - 1);
  61 }
  62
  63 /*
  64  * round down to nearest power of two
  65  */
  66 static inline __attribute__((const))
  67 unsigned long __rounddown_pow_of_two(unsigned long n)
  68 {
  69         return 1UL << (fls_long(n) - 1);
  70 }
  71
  72 /**
  73  * ilog2 - log of base 2 of 32-bit or a 64-bit unsigned value
  74  * @n - parameter
  75  *
  76  * constant-capable log of base 2 calculation
  77  * - this can be used to initialise global variables from constant data, hence
  78  *   the massive ternary operator construction
  79  *
  80  * selects the appropriately-sized optimised version depending on sizeof(n)
  81  */
  82 #define ilog2(n)                                \
  83 (                                               \
  84         __builtin_constant_p(n) ? (             \
  85                 (n) < 1 ? ____ilog2_NaN() :     \
  86                 (n) & (1ULL << 63) ? 63 :       \
  87                 (n) & (1ULL << 62) ? 62 :       \
  88                 (n) & (1ULL << 61) ? 61 :       \
  89                 (n) & (1ULL << 60) ? 60 :       \
  90                 (n) & (1ULL << 59) ? 59 :       \
  91                 (n) & (1ULL << 58) ? 58 :       \
  92                 (n) & (1ULL << 57) ? 57 :       \
  93                 (n) & (1ULL << 56) ? 56 :       \
  94                 (n) & (1ULL << 55) ? 55 :       \
  95                 (n) & (1ULL << 54) ? 54 :       \
  96                 (n) & (1ULL << 53) ? 53 :       \
  97                 (n) & (1ULL << 52) ? 52 :       \
  98                 (n) & (1ULL << 51) ? 51 :       \
  99                 (n) & (1ULL << 50) ? 50 :       \
 100                 (n) & (1ULL << 49) ? 49 :       \
 101                 (n) & (1ULL << 48) ? 48 :       \
 102                 (n) & (1ULL << 47) ? 47 :       \
 103                 (n) & (1ULL << 46) ? 46 :       \
 104                 (n) & (1ULL << 45) ? 45 :       \
 105                 (n) & (1ULL << 44) ? 44 :       \
 106                 (n) & (1ULL << 43) ? 43 :       \
 107                 (n) & (1ULL << 42) ? 42 :       \
 108                 (n) & (1ULL << 41) ? 41 :       \
 109                 (n) & (1ULL << 40) ? 40 :       \
 110                 (n) & (1ULL << 39) ? 39 :       \
 111                 (n) & (1ULL << 38) ? 38 :       \
 112                 (n) & (1ULL << 37) ? 37 :       \
 113                 (n) & (1ULL << 36) ? 36 :       \
 114                 (n) & (1ULL << 35) ? 35 :       \
 115                 (n) & (1ULL << 34) ? 34 :       \
 116                 (n) & (1ULL << 33) ? 33 :       \
 117                 (n) & (1ULL << 32) ? 32 :       \
 118                 (n) & (1ULL << 31) ? 31 :       \
 119                 (n) & (1ULL << 30) ? 30 :       \
 120                 (n) & (1ULL << 29) ? 29 :       \
 121                 (n) & (1ULL << 28) ? 28 :       \
 122                 (n) & (1ULL << 27) ? 27 :       \
 123                 (n) & (1ULL << 26) ? 26 :       \
 124                 (n) & (1ULL << 25) ? 25 :       \
 125                 (n) & (1ULL << 24) ? 24 :       \
 126                 (n) & (1ULL << 23) ? 23 :       \
 127                 (n) & (1ULL << 22) ? 22 :       \
 128                 (n) & (1ULL << 21) ? 21 :       \
 129                 (n) & (1ULL << 20) ? 20 :       \
 130                 (n) & (1ULL << 19) ? 19 :       \
 131                 (n) & (1ULL << 18) ? 18 :       \
 132                 (n) & (1ULL << 17) ? 17 :       \
 133                 (n) & (1ULL << 16) ? 16 :       \
 134                 (n) & (1ULL << 15) ? 15 :       \
 135                 (n) & (1ULL << 14) ? 14 :       \
 136                 (n) & (1ULL << 13) ? 13 :       \
 137                 (n) & (1ULL << 12) ? 12 :       \
 138                 (n) & (1ULL << 11) ? 11 :       \
 139                 (n) & (1ULL << 10) ? 10 :       \
 140                 (n) & (1ULL <<  9) ?  9 :       \
 141                 (n) & (1ULL <<  8) ?  8 :       \
 142                 (n) & (1ULL <<  7) ?  7 :       \
 143                 (n) & (1ULL <<  6) ?  6 :       \
 144                 (n) & (1ULL <<  5) ?  5 :       \
 145                 (n) & (1ULL <<  4) ?  4 :       \
 146                 (n) & (1ULL <<  3) ?  3 :       \
 147                 (n) & (1ULL <<  2) ?  2 :       \
 148                 (n) & (1ULL <<  1) ?  1 :       \
 149                 (n) & (1ULL <<  0) ?  0 :       \
 150                 ____ilog2_NaN()                 \
 151                                    ) :          \
 152         (sizeof(n) <= 4) ?                      \
 153         __ilog2_u32(n) :                        \
 154         __ilog2_u64(n)                          \
 155  )
 156
 157 /**
 158  * roundup_pow_of_two - round the given value up to nearest power of two
 159  * @n - parameter
 160  *
 161  * round the given value up to the nearest power of two
 162  * - the result is undefined when n == 0
 163  * - this can be used to initialise global variables from constant data
 164  */
 165 #define roundup_pow_of_two(n)                   \
 166 (                                               \
 167         __builtin_constant_p(n) ? (             \
 168                 (n == 1) ? 1 :                  \
 169                 (1UL << (ilog2((n) - 1) + 1))   \
 170                                    ) :          \
 171         __roundup_pow_of_two(n)                 \
 172  )
 173
 174 /**
 175  * rounddown_pow_of_two - round the given value down to nearest power of two
 176  * @n - parameter
 177  *
 178  * round the given value down to the nearest power of two
 179  * - the result is undefined when n == 0
 180  * - this can be used to initialise global variables from constant data
 181  */
 182 #define rounddown_pow_of_two(n)                 \
 183 (                                               \
 184         __builtin_constant_p(n) ? (             \
 185                 (1UL << ilog2(n))) :            \
 186         __rounddown_pow_of_two(n)               \
 187  )
 188
 189 /**
 190  * order_base_2 - calculate the (rounded up) base 2 order of the argument
 191  * @n: parameter
 192  *
 193  * The first few values calculated by this routine:
 194  *  ob2(0) = 0
 195  *  ob2(1) = 0
 196  *  ob2(2) = 1
 197  *  ob2(3) = 2
 198  *  ob2(4) = 2
 199  *  ob2(5) = 3
 200  *  ... and so on.
 201  */
 202
 203 #define order_base_2(n) ilog2(roundup_pow_of_two(n))
 204
 205 #endif /* _LINUX_LOG2_H */