1/* SPDX-License-Identifier: GPL-2.0 */
2#ifndef MEAN_AND_VARIANCE_H_
3#define MEAN_AND_VARIANCE_H_
4
5#include <linux/types.h>
6#include <linux/limits.h>
7#include <linux/math.h>
8#include <linux/math64.h>
9
10#define SQRT_U64_MAX 4294967295ULL
11
12/*
13 * u128_u: u128 user mode, because not all architectures support a real int128
14 * type
15 *
16 * We don't use this version in userspace, because in userspace we link with
17 * Rust and rustc has issues with u128.
18 */
19
20#if defined(__SIZEOF_INT128__) && defined(__KERNEL__) && !defined(CONFIG_PARISC)
21
22typedef struct {
23 unsigned __int128 v;
24} __aligned(16) u128_u;
25
26static inline u128_u u64_to_u128(u64 a)
27{
28 return (u128_u) { .v = a };
29}
30
31static inline u64 u128_lo(u128_u a)
32{
33 return a.v;
34}
35
36static inline u64 u128_hi(u128_u a)
37{
38 return a.v >> 64;
39}
40
41static inline u128_u u128_add(u128_u a, u128_u b)
42{
43 a.v += b.v;
44 return a;
45}
46
47static inline u128_u u128_sub(u128_u a, u128_u b)
48{
49 a.v -= b.v;
50 return a;
51}
52
53static inline u128_u u128_shl(u128_u a, s8 shift)
54{
55 a.v <<= shift;
56 return a;
57}
58
59static inline u128_u u128_square(u64 a)
60{
61 u128_u b = u64_to_u128(a);
62
63 b.v *= b.v;
64 return b;
65}
66
67#else
68
69typedef struct {
70 u64 hi, lo;
71} __aligned(16) u128_u;
72
73/* conversions */
74
75static inline u128_u u64_to_u128(u64 a)
76{
77 return (u128_u) { .lo = a };
78}
79
80static inline u64 u128_lo(u128_u a)
81{
82 return a.lo;
83}
84
85static inline u64 u128_hi(u128_u a)
86{
87 return a.hi;
88}
89
90/* arithmetic */
91
92static inline u128_u u128_add(u128_u a, u128_u b)
93{
94 u128_u c;
95
96 c.lo = a.lo + b.lo;
97 c.hi = a.hi + b.hi + (c.lo < a.lo);
98 return c;
99}
100
101static inline u128_u u128_sub(u128_u a, u128_u b)
102{
103 u128_u c;
104
105 c.lo = a.lo - b.lo;
106 c.hi = a.hi - b.hi - (c.lo > a.lo);
107 return c;
108}
109
110static inline u128_u u128_shl(u128_u i, s8 shift)
111{
112 u128_u r;
113
114 r.lo = i.lo << shift;
115 if (shift < 64)
116 r.hi = (i.hi << shift) | (i.lo >> (64 - shift));
117 else {
118 r.hi = i.lo << (shift - 64);
119 r.lo = 0;
120 }
121 return r;
122}
123
124static inline u128_u u128_square(u64 i)
125{
126 u128_u r;
127 u64 h = i >> 32, l = i & U32_MAX;
128
129 r = u128_shl(u64_to_u128(h*h), 64);
130 r = u128_add(r, u128_shl(u64_to_u128(h*l), 32));
131 r = u128_add(r, u128_shl(u64_to_u128(l*h), 32));
132 r = u128_add(r, u64_to_u128(l*l));
133 return r;
134}
135
136#endif
137
138static inline u128_u u64s_to_u128(u64 hi, u64 lo)
139{
140 u128_u c = u64_to_u128(a: hi);
141
142 c = u128_shl(a: c, shift: 64);
143 c = u128_add(a: c, b: u64_to_u128(a: lo));
144 return c;
145}
146
147u128_u u128_div(u128_u n, u64 d);
148
149struct mean_and_variance {
150 s64 n;
151 s64 sum;
152 u128_u sum_squares;
153};
154
155/* expontentially weighted variant */
156struct mean_and_variance_weighted {
157 s64 mean;
158 u64 variance;
159};
160
161/**
162 * fast_divpow2() - fast approximation for n / (1 << d)
163 * @n: numerator
164 * @d: the power of 2 denominator.
165 *
166 * note: this rounds towards 0.
167 */
168static inline s64 fast_divpow2(s64 n, u8 d)
169{
170 return (n + ((n < 0) ? ((1 << d) - 1) : 0)) >> d;
171}
172
173/**
174 * mean_and_variance_update() - update a mean_and_variance struct @s1 with a new sample @v1
175 * and return it.
176 * @s1: the mean_and_variance to update.
177 * @v1: the new sample.
178 *
179 * see linked pdf equation 12.
180 */
181static inline void
182mean_and_variance_update(struct mean_and_variance *s, s64 v)
183{
184 s->n++;
185 s->sum += v;
186 s->sum_squares = u128_add(a: s->sum_squares, b: u128_square(abs(v)));
187}
188
189s64 mean_and_variance_get_mean(struct mean_and_variance s);
190u64 mean_and_variance_get_variance(struct mean_and_variance s1);
191u32 mean_and_variance_get_stddev(struct mean_and_variance s);
192
193void mean_and_variance_weighted_update(struct mean_and_variance_weighted *s,
194 s64 v, bool initted, u8 weight);
195
196s64 mean_and_variance_weighted_get_mean(struct mean_and_variance_weighted s,
197 u8 weight);
198u64 mean_and_variance_weighted_get_variance(struct mean_and_variance_weighted s,
199 u8 weight);
200u32 mean_and_variance_weighted_get_stddev(struct mean_and_variance_weighted s,
201 u8 weight);
202
203#endif // MEAN_AND_VAIRANCE_H_
204

source code of linux/fs/bcachefs/mean_and_variance.h