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
|
// SPDX-License-Identifier: GPL-2.0
/*
* Functions for incremental mean and variance.
*
* This program is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 as published by
* the Free Software Foundation.
*
* This program is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
* more details.
*
* Copyright © 2022 Daniel B. Hill
*
* Author: Daniel B. Hill <daniel@gluo.nz>
*
* Description:
*
* This is includes some incremental algorithms for mean and variance calculation
*
* Derived from the paper: https://fanf2.user.srcf.net/hermes/doc/antiforgery/stats.pdf
*
* Create a struct and if it's the weighted variant set the w field (weight = 2^k).
*
* Use mean_and_variance[_weighted]_update() on the struct to update it's state.
*
* Use the mean_and_variance[_weighted]_get_* functions to calculate the mean and variance, some computation
* is deferred to these functions for performance reasons.
*
* see lib/math/mean_and_variance_test.c for examples of usage.
*
* DO NOT access the mean and variance fields of the weighted variants directly.
* DO NOT change the weight after calling update.
*/
#include <linux/bug.h>
#include <linux/compiler.h>
#include <linux/export.h>
#include <linux/limits.h>
#include <linux/math.h>
#include <linux/math64.h>
#include <linux/module.h>
#include "mean_and_variance.h"
u128_u u128_div(u128_u n, u64 d)
{
u128_u r;
u64 rem;
u64 hi = u128_hi(n);
u64 lo = u128_lo(n);
u64 h = hi & ((u64) U32_MAX << 32);
u64 l = (hi & (u64) U32_MAX) << 32;
r = u128_shl(u64_to_u128(div64_u64_rem(h, d, &rem)), 64);
r = u128_add(r, u128_shl(u64_to_u128(div64_u64_rem(l + (rem << 32), d, &rem)), 32));
r = u128_add(r, u64_to_u128(div64_u64_rem(lo + (rem << 32), d, &rem)));
return r;
}
EXPORT_SYMBOL_GPL(u128_div);
/**
* mean_and_variance_get_mean() - get mean from @s
* @s: mean and variance number of samples and their sums
*/
s64 mean_and_variance_get_mean(struct mean_and_variance s)
{
return s.n ? div64_u64(s.sum, s.n) : 0;
}
EXPORT_SYMBOL_GPL(mean_and_variance_get_mean);
/**
* mean_and_variance_get_variance() - get variance from @s1
* @s1: mean and variance number of samples and sums
*
* see linked pdf equation 12.
*/
u64 mean_and_variance_get_variance(struct mean_and_variance s1)
{
if (s1.n) {
u128_u s2 = u128_div(s1.sum_squares, s1.n);
u64 s3 = abs(mean_and_variance_get_mean(s1));
return u128_lo(u128_sub(s2, u128_square(s3)));
} else {
return 0;
}
}
EXPORT_SYMBOL_GPL(mean_and_variance_get_variance);
/**
* mean_and_variance_get_stddev() - get standard deviation from @s
* @s: mean and variance number of samples and their sums
*/
u32 mean_and_variance_get_stddev(struct mean_and_variance s)
{
return int_sqrt64(mean_and_variance_get_variance(s));
}
EXPORT_SYMBOL_GPL(mean_and_variance_get_stddev);
/**
* mean_and_variance_weighted_update() - exponentially weighted variant of mean_and_variance_update()
* @s: mean and variance number of samples and their sums
* @x: new value to include in the &mean_and_variance_weighted
*
* see linked pdf: function derived from equations 140-143 where alpha = 2^w.
* values are stored bitshifted for performance and added precision.
*/
void mean_and_variance_weighted_update(struct mean_and_variance_weighted *s, s64 x)
{
// previous weighted variance.
u8 w = s->weight;
u64 var_w0 = s->variance;
// new value weighted.
s64 x_w = x << w;
s64 diff_w = x_w - s->mean;
s64 diff = fast_divpow2(diff_w, w);
// new mean weighted.
s64 u_w1 = s->mean + diff;
if (!s->init) {
s->mean = x_w;
s->variance = 0;
} else {
s->mean = u_w1;
s->variance = ((var_w0 << w) - var_w0 + ((diff_w * (x_w - u_w1)) >> w)) >> w;
}
s->init = true;
}
EXPORT_SYMBOL_GPL(mean_and_variance_weighted_update);
/**
* mean_and_variance_weighted_get_mean() - get mean from @s
* @s: mean and variance number of samples and their sums
*/
s64 mean_and_variance_weighted_get_mean(struct mean_and_variance_weighted s)
{
return fast_divpow2(s.mean, s.weight);
}
EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_mean);
/**
* mean_and_variance_weighted_get_variance() -- get variance from @s
* @s: mean and variance number of samples and their sums
*/
u64 mean_and_variance_weighted_get_variance(struct mean_and_variance_weighted s)
{
// always positive don't need fast divpow2
return s.variance >> s.weight;
}
EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_variance);
/**
* mean_and_variance_weighted_get_stddev() - get standard deviation from @s
* @s: mean and variance number of samples and their sums
*/
u32 mean_and_variance_weighted_get_stddev(struct mean_and_variance_weighted s)
{
return int_sqrt64(mean_and_variance_weighted_get_variance(s));
}
EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_stddev);
MODULE_AUTHOR("Daniel B. Hill");
MODULE_LICENSE("GPL");
|
