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Linux kernel mirror (for testing)
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1// SPDX-License-Identifier: GPL-2.0
2/*
3 * Functions for incremental mean and variance.
4 *
5 * This program is free software; you can redistribute it and/or modify it
6 * under the terms of the GNU General Public License version 2 as published by
7 * the Free Software Foundation.
8 *
9 * This program is distributed in the hope that it will be useful, but WITHOUT
10 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
11 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
12 * more details.
13 *
14 * Copyright © 2022 Daniel B. Hill
15 *
16 * Author: Daniel B. Hill <daniel@gluo.nz>
17 *
18 * Description:
19 *
20 * This is includes some incremental algorithms for mean and variance calculation
21 *
22 * Derived from the paper: https://fanf2.user.srcf.net/hermes/doc/antiforgery/stats.pdf
23 *
24 * Create a struct and if it's the weighted variant set the w field (weight = 2^k).
25 *
26 * Use mean_and_variance[_weighted]_update() on the struct to update it's state.
27 *
28 * Use the mean_and_variance[_weighted]_get_* functions to calculate the mean and variance, some computation
29 * is deferred to these functions for performance reasons.
30 *
31 * see lib/math/mean_and_variance_test.c for examples of usage.
32 *
33 * DO NOT access the mean and variance fields of the weighted variants directly.
34 * DO NOT change the weight after calling update.
35 */
36
37#include <linux/bug.h>
38#include <linux/compiler.h>
39#include <linux/export.h>
40#include <linux/limits.h>
41#include <linux/math.h>
42#include <linux/math64.h>
43#include <linux/module.h>
44
45#include "mean_and_variance.h"
46
47u128_u u128_div(u128_u n, u64 d)
48{
49 u128_u r;
50 u64 rem;
51 u64 hi = u128_hi(n);
52 u64 lo = u128_lo(n);
53 u64 h = hi & ((u64) U32_MAX << 32);
54 u64 l = (hi & (u64) U32_MAX) << 32;
55
56 r = u128_shl(u64_to_u128(div64_u64_rem(h, d, &rem)), 64);
57 r = u128_add(r, u128_shl(u64_to_u128(div64_u64_rem(l + (rem << 32), d, &rem)), 32));
58 r = u128_add(r, u64_to_u128(div64_u64_rem(lo + (rem << 32), d, &rem)));
59 return r;
60}
61EXPORT_SYMBOL_GPL(u128_div);
62
63/**
64 * mean_and_variance_get_mean() - get mean from @s
65 */
66s64 mean_and_variance_get_mean(struct mean_and_variance s)
67{
68 return s.n ? div64_u64(s.sum, s.n) : 0;
69}
70EXPORT_SYMBOL_GPL(mean_and_variance_get_mean);
71
72/**
73 * mean_and_variance_get_variance() - get variance from @s1
74 *
75 * see linked pdf equation 12.
76 */
77u64 mean_and_variance_get_variance(struct mean_and_variance s1)
78{
79 if (s1.n) {
80 u128_u s2 = u128_div(s1.sum_squares, s1.n);
81 u64 s3 = abs(mean_and_variance_get_mean(s1));
82
83 return u128_lo(u128_sub(s2, u128_square(s3)));
84 } else {
85 return 0;
86 }
87}
88EXPORT_SYMBOL_GPL(mean_and_variance_get_variance);
89
90/**
91 * mean_and_variance_get_stddev() - get standard deviation from @s
92 */
93u32 mean_and_variance_get_stddev(struct mean_and_variance s)
94{
95 return int_sqrt64(mean_and_variance_get_variance(s));
96}
97EXPORT_SYMBOL_GPL(mean_and_variance_get_stddev);
98
99/**
100 * mean_and_variance_weighted_update() - exponentially weighted variant of mean_and_variance_update()
101 * @s1: ..
102 * @s2: ..
103 *
104 * see linked pdf: function derived from equations 140-143 where alpha = 2^w.
105 * values are stored bitshifted for performance and added precision.
106 */
107void mean_and_variance_weighted_update(struct mean_and_variance_weighted *s, s64 x)
108{
109 // previous weighted variance.
110 u8 w = s->weight;
111 u64 var_w0 = s->variance;
112 // new value weighted.
113 s64 x_w = x << w;
114 s64 diff_w = x_w - s->mean;
115 s64 diff = fast_divpow2(diff_w, w);
116 // new mean weighted.
117 s64 u_w1 = s->mean + diff;
118
119 if (!s->init) {
120 s->mean = x_w;
121 s->variance = 0;
122 } else {
123 s->mean = u_w1;
124 s->variance = ((var_w0 << w) - var_w0 + ((diff_w * (x_w - u_w1)) >> w)) >> w;
125 }
126 s->init = true;
127}
128EXPORT_SYMBOL_GPL(mean_and_variance_weighted_update);
129
130/**
131 * mean_and_variance_weighted_get_mean() - get mean from @s
132 */
133s64 mean_and_variance_weighted_get_mean(struct mean_and_variance_weighted s)
134{
135 return fast_divpow2(s.mean, s.weight);
136}
137EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_mean);
138
139/**
140 * mean_and_variance_weighted_get_variance() -- get variance from @s
141 */
142u64 mean_and_variance_weighted_get_variance(struct mean_and_variance_weighted s)
143{
144 // always positive don't need fast divpow2
145 return s.variance >> s.weight;
146}
147EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_variance);
148
149/**
150 * mean_and_variance_weighted_get_stddev() - get standard deviation from @s
151 */
152u32 mean_and_variance_weighted_get_stddev(struct mean_and_variance_weighted s)
153{
154 return int_sqrt64(mean_and_variance_weighted_get_variance(s));
155}
156EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_stddev);
157
158MODULE_AUTHOR("Daniel B. Hill");
159MODULE_LICENSE("GPL");