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 */
211
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