include/linux/math.h

   1 /* SPDX-License-Identifier: GPL-2.0 */
   2 #ifndef _LINUX_MATH_H
   3 #define _LINUX_MATH_H
   4
   5 #include <linux/types.h>
   6 #include <asm/div64.h>
   7 #include <uapi/linux/kernel.h>
   8
   9 /*
  10  * This looks more complex than it should be. But we need to
  11  * get the type for the ~ right in round_down (it needs to be
  12  * as wide as the result!), and we want to evaluate the macro
  13  * arguments just once each.
  14  */
  15 #define __round_mask(x, y) ((__typeof__(x))((y)-1))
  16
  17 /**
  18  * round_up - round up to next specified power of 2
  19  * @x: the value to round
  20  * @y: multiple to round up to (must be a power of 2)
  21  *
  22  * Rounds @x up to next multiple of @y (which must be a power of 2).
  23  * To perform arbitrary rounding up, use roundup() below.
  24  */
  25 #define round_up(x, y) ((((x)-1) | __round_mask(x, y))+1)
  26
  27 /**
  28  * round_down - round down to next specified power of 2
  29  * @x: the value to round
  30  * @y: multiple to round down to (must be a power of 2)
  31  *
  32  * Rounds @x down to next multiple of @y (which must be a power of 2).
  33  * To perform arbitrary rounding down, use rounddown() below.
  34  */
  35 #define round_down(x, y) ((x) & ~__round_mask(x, y))
  36
  37 #define DIV_ROUND_UP __KERNEL_DIV_ROUND_UP
  38
  39 #define DIV_ROUND_DOWN_ULL(ll, d) \
  40         ({ unsigned long long _tmp = (ll); do_div(_tmp, d); _tmp; })
  41
  42 #define DIV_ROUND_UP_ULL(ll, d) \
  43         DIV_ROUND_DOWN_ULL((unsigned long long)(ll) + (d) - 1, (d))
  44
  45 #if BITS_PER_LONG == 32
  46 # define DIV_ROUND_UP_SECTOR_T(ll,d) DIV_ROUND_UP_ULL(ll, d)
  47 #else
  48 # define DIV_ROUND_UP_SECTOR_T(ll,d) DIV_ROUND_UP(ll,d)
  49 #endif
  50
  51 /**
  52  * roundup - round up to the next specified multiple
  53  * @x: the value to up
  54  * @y: multiple to round up to
  55  *
  56  * Rounds @x up to next multiple of @y. If @y will always be a power
  57  * of 2, consider using the faster round_up().
  58  */
  59 #define roundup(x, y) (                                 \
  60 {                                                       \
  61         typeof(y) __y = y;                              \
  62         (((x) + (__y - 1)) / __y) * __y;                \
  63 }                                                       \
  64 )
  65 /**
  66  * rounddown - round down to next specified multiple
  67  * @x: the value to round
  68  * @y: multiple to round down to
  69  *
  70  * Rounds @x down to next multiple of @y. If @y will always be a power
  71  * of 2, consider using the faster round_down().
  72  */
  73 #define rounddown(x, y) (                               \
  74 {                                                       \
  75         typeof(x) __x = (x);                            \
  76         __x - (__x % (y));                              \
  77 }                                                       \
  78 )
  79
  80 /*
  81  * Divide positive or negative dividend by positive or negative divisor
  82  * and round to closest integer. Result is undefined for negative
  83  * divisors if the dividend variable type is unsigned and for negative
  84  * dividends if the divisor variable type is unsigned.
  85  */
  86 #define DIV_ROUND_CLOSEST(x, divisor)(                  \
  87 {                                                       \
  88         typeof(x) __x = x;                              \
  89         typeof(divisor) __d = divisor;                  \
  90         (((typeof(x))-1) > 0 ||                         \
  91          ((typeof(divisor))-1) > 0 ||                   \
  92          (((__x) > 0) == ((__d) > 0))) ?                \
  93                 (((__x) + ((__d) / 2)) / (__d)) :       \
  94                 (((__x) - ((__d) / 2)) / (__d));        \
  95 }                                                       \
  96 )
  97 /*
  98  * Same as above but for u64 dividends. divisor must be a 32-bit
  99  * number.
 100  */
 101 #define DIV_ROUND_CLOSEST_ULL(x, divisor)(              \
 102 {                                                       \
 103         typeof(divisor) __d = divisor;                  \
 104         unsigned long long _tmp = (x) + (__d) / 2;      \
 105         do_div(_tmp, __d);                              \
 106         _tmp;                                           \
 107 }                                                       \
 108 )
 109
 110 #define __STRUCT_FRACT(type)                            \
 111 struct type##_fract {                                   \
 112         __##type numerator;                             \
 113         __##type denominator;                           \
 114 };
 115 __STRUCT_FRACT(s8)
 116 __STRUCT_FRACT(u8)
 117 __STRUCT_FRACT(s16)
 118 __STRUCT_FRACT(u16)
 119 __STRUCT_FRACT(s32)
 120 __STRUCT_FRACT(u32)
 121 #undef __STRUCT_FRACT
 122
 123 /* Calculate "x * n / d" without unnecessary overflow or loss of precision. */
 124 #define mult_frac(x, n, d)      \
 125 ({                              \
 126         typeof(x) x_ = (x);     \
 127         typeof(n) n_ = (n);     \
 128         typeof(d) d_ = (d);     \
 129                                 \
 130         typeof(x_) q = x_ / d_; \
 131         typeof(x_) r = x_ % d_; \
 132         q * n_ + r * n_ / d_;   \
 133 })
 134
 135 #define sector_div(a, b) do_div(a, b)
 136
 137 /**
 138  * abs - return absolute value of an argument
 139  * @x: the value.  If it is unsigned type, it is converted to signed type first.
 140  *     char is treated as if it was signed (regardless of whether it really is)
 141  *     but the macro's return type is preserved as char.
 142  *
 143  * Return: an absolute value of x.
 144  */
 145 #define abs(x)  __abs_choose_expr(x, long long,                         \
 146                 __abs_choose_expr(x, long,                              \
 147                 __abs_choose_expr(x, int,                               \
 148                 __abs_choose_expr(x, short,                             \
 149                 __abs_choose_expr(x, char,                              \
 150                 __builtin_choose_expr(                                  \
 151                         __builtin_types_compatible_p(typeof(x), char),  \
 152                         (char)({ signed char __x = (x); __x<0?-__x:__x; }), \
 153                         ((void)0)))))))
 154
 155 #define __abs_choose_expr(x, type, other) __builtin_choose_expr(        \
 156         __builtin_types_compatible_p(typeof(x),   signed type) ||       \
 157         __builtin_types_compatible_p(typeof(x), unsigned type),         \
 158         ({ signed type __x = (x); __x < 0 ? -__x : __x; }), other)
 159
 160 /**
 161  * abs_diff - return absolute value of the difference between the arguments
 162  * @a: the first argument
 163  * @b: the second argument
 164  *
 165  * @a and @b have to be of the same type. With this restriction we compare
 166  * signed to signed and unsigned to unsigned. The result is the subtraction
 167  * the smaller of the two from the bigger, hence result is always a positive
 168  * value.
 169  *
 170  * Return: an absolute value of the difference between the @a and @b.
 171  */
 172 #define abs_diff(a, b) ({                       \
 173         typeof(a) __a = (a);                    \
 174         typeof(b) __b = (b);                    \
 175         (void)(&__a == &__b);                   \
 176         __a > __b ? (__a - __b) : (__b - __a);  \
 177 })
 178
 179 /**
 180  * reciprocal_scale - "scale" a value into range [0, ep_ro)
 181  * @val: value
 182  * @ep_ro: right open interval endpoint
 183  *
 184  * Perform a "reciprocal multiplication" in order to "scale" a value into
 185  * range [0, @ep_ro), where the upper interval endpoint is right-open.
 186  * This is useful, e.g. for accessing a index of an array containing
 187  * @ep_ro elements, for example. Think of it as sort of modulus, only that
 188  * the result isn't that of modulo. ;) Note that if initial input is a
 189  * small value, then result will return 0.
 190  *
 191  * Return: a result based on @val in interval [0, @ep_ro).
 192  */
 193 static inline u32 reciprocal_scale(u32 val, u32 ep_ro)
 194 {
 195         return (u32)(((u64) val * ep_ro) >> 32);
 196 }
 197
 198 u64 int_pow(u64 base, unsigned int exp);
 199 unsigned long int_sqrt(unsigned long);
 200
 201 #if BITS_PER_LONG < 64
 202 u32 int_sqrt64(u64 x);
 203 #else
 204 static inline u32 int_sqrt64(u64 x)
 205 {
 206         return (u32)int_sqrt(x);
 207 }
 208 #endif
 209
 210 #endif  /* _LINUX_MATH_H */