include/linux/log2.h

   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 */