aboutsummaryrefslogtreecommitdiff
path: root/include/linux/math.h
blob: 439b8f0b9ebd3201b48cfe82c134e379d398dc3d (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
/* SPDX-License-Identifier: GPL-2.0 */
#ifndef _LINUX_MATH_H
#define _LINUX_MATH_H

#include <linux/types.h>
#include <asm/div64.h>
#include <uapi/linux/kernel.h>

/*
 * This looks more complex than it should be. But we need to
 * get the type for the ~ right in round_down (it needs to be
 * as wide as the result!), and we want to evaluate the macro
 * arguments just once each.
 */
#define __round_mask(x, y) ((__typeof__(x))((y)-1))

/**
 * round_up - round up to next specified power of 2
 * @x: the value to round
 * @y: multiple to round up to (must be a power of 2)
 *
 * Rounds @x up to next multiple of @y (which must be a power of 2).
 * To perform arbitrary rounding up, use roundup() below.
 */
#define round_up(x, y) ((((x)-1) | __round_mask(x, y))+1)

/**
 * round_down - round down to next specified power of 2
 * @x: the value to round
 * @y: multiple to round down to (must be a power of 2)
 *
 * Rounds @x down to next multiple of @y (which must be a power of 2).
 * To perform arbitrary rounding down, use rounddown() below.
 */
#define round_down(x, y) ((x) & ~__round_mask(x, y))

#define DIV_ROUND_UP __KERNEL_DIV_ROUND_UP

#define DIV_ROUND_DOWN_ULL(ll, d) \
	({ unsigned long long _tmp = (ll); do_div(_tmp, d); _tmp; })

#define DIV_ROUND_UP_ULL(ll, d) \
	DIV_ROUND_DOWN_ULL((unsigned long long)(ll) + (d) - 1, (d))

#if BITS_PER_LONG == 32
# define DIV_ROUND_UP_SECTOR_T(ll,d) DIV_ROUND_UP_ULL(ll, d)
#else
# define DIV_ROUND_UP_SECTOR_T(ll,d) DIV_ROUND_UP(ll,d)
#endif

/**
 * roundup - round up to the next specified multiple
 * @x: the value to up
 * @y: multiple to round up to
 *
 * Rounds @x up to next multiple of @y. If @y will always be a power
 * of 2, consider using the faster round_up().
 */
#define roundup(x, y) (					\
{							\
	typeof(y) __y = y;				\
	(((x) + (__y - 1)) / __y) * __y;		\
}							\
)
/**
 * rounddown - round down to next specified multiple
 * @x: the value to round
 * @y: multiple to round down to
 *
 * Rounds @x down to next multiple of @y. If @y will always be a power
 * of 2, consider using the faster round_down().
 */
#define rounddown(x, y) (				\
{							\
	typeof(x) __x = (x);				\
	__x - (__x % (y));				\
}							\
)

/*
 * Divide positive or negative dividend by positive or negative divisor
 * and round to closest integer. Result is undefined for negative
 * divisors if the dividend variable type is unsigned and for negative
 * dividends if the divisor variable type is unsigned.
 */
#define DIV_ROUND_CLOSEST(x, divisor)(			\
{							\
	typeof(x) __x = x;				\
	typeof(divisor) __d = divisor;			\
	(((typeof(x))-1) > 0 ||				\
	 ((typeof(divisor))-1) > 0 ||			\
	 (((__x) > 0) == ((__d) > 0))) ?		\
		(((__x) + ((__d) / 2)) / (__d)) :	\
		(((__x) - ((__d) / 2)) / (__d));	\
}							\
)
/*
 * Same as above but for u64 dividends. divisor must be a 32-bit
 * number.
 */
#define DIV_ROUND_CLOSEST_ULL(x, divisor)(		\
{							\
	typeof(divisor) __d = divisor;			\
	unsigned long long _tmp = (x) + (__d) / 2;	\
	do_div(_tmp, __d);				\
	_tmp;						\
}							\
)

#define __STRUCT_FRACT(type)				\
struct type##_fract {					\
	__##type numerator;				\
	__##type denominator;				\
};
__STRUCT_FRACT(s16)
__STRUCT_FRACT(u16)
__STRUCT_FRACT(s32)
__STRUCT_FRACT(u32)
#undef __STRUCT_FRACT

/*
 * Multiplies an integer by a fraction, while avoiding unnecessary
 * overflow or loss of precision.
 */
#define mult_frac(x, numer, denom)(			\
{							\
	typeof(x) quot = (x) / (denom);			\
	typeof(x) rem  = (x) % (denom);			\
	(quot * (numer)) + ((rem * (numer)) / (denom));	\
}							\
)

#define sector_div(a, b) do_div(a, b)

/**
 * abs - return absolute value of an argument
 * @x: the value.  If it is unsigned type, it is converted to signed type first.
 *     char is treated as if it was signed (regardless of whether it really is)
 *     but the macro's return type is preserved as char.
 *
 * Return: an absolute value of x.
 */
#define abs(x)	__abs_choose_expr(x, long long,				\
		__abs_choose_expr(x, long,				\
		__abs_choose_expr(x, int,				\
		__abs_choose_expr(x, short,				\
		__abs_choose_expr(x, char,				\
		__builtin_choose_expr(					\
			__builtin_types_compatible_p(typeof(x), char),	\
			(char)({ signed char __x = (x); __x<0?-__x:__x; }), \
			((void)0)))))))

#define __abs_choose_expr(x, type, other) __builtin_choose_expr(	\
	__builtin_types_compatible_p(typeof(x),   signed type) ||	\
	__builtin_types_compatible_p(typeof(x), unsigned type),		\
	({ signed type __x = (x); __x < 0 ? -__x : __x; }), other)

/**
 * reciprocal_scale - "scale" a value into range [0, ep_ro)
 * @val: value
 * @ep_ro: right open interval endpoint
 *
 * Perform a "reciprocal multiplication" in order to "scale" a value into
 * range [0, @ep_ro), where the upper interval endpoint is right-open.
 * This is useful, e.g. for accessing a index of an array containing
 * @ep_ro elements, for example. Think of it as sort of modulus, only that
 * the result isn't that of modulo. ;) Note that if initial input is a
 * small value, then result will return 0.
 *
 * Return: a result based on @val in interval [0, @ep_ro).
 */
static inline u32 reciprocal_scale(u32 val, u32 ep_ro)
{
	return (u32)(((u64) val * ep_ro) >> 32);
}

u64 int_pow(u64 base, unsigned int exp);
unsigned long int_sqrt(unsigned long);

#if BITS_PER_LONG < 64
u32 int_sqrt64(u64 x);
#else
static inline u32 int_sqrt64(u64 x)
{
	return (u32)int_sqrt(x);
}
#endif

#endif	/* _LINUX_MATH_H */