1 // SPDX-License-Identifier: GPL-2.0
3 * Functions for incremental mean and variance.
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.
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
14 * Copyright © 2022 Daniel B. Hill
16 * Author: Daniel B. Hill <daniel@gluo.nz>
20 * This is includes some incremental algorithms for mean and variance calculation
22 * Derived from the paper: https://fanf2.user.srcf.net/hermes/doc/antiforgery/stats.pdf
24 * Create a struct and if it's the weighted variant set the w field (weight = 2^k).
26 * Use mean_and_variance[_weighted]_update() on the struct to update it's state.
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.
31 * see lib/math/mean_and_variance_test.c for examples of usage.
33 * DO NOT access the mean and variance fields of the weighted variants directly.
34 * DO NOT change the weight after calling update.
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/mean_and_variance.h>
44 #include <linux/module.h>
45 #include <linux/printbuf.h>
49 * fast_divpow2() - fast approximation for n / (1 << d)
51 * @d: the power of 2 denominator.
53 * note: this rounds towards 0.
55 s64 fast_divpow2(s64 n, u8 d)
57 return (n + ((n < 0) ? ((1 << d) - 1) : 0)) >> d;
61 * mean_and_variance_update() - update a mean_and_variance struct @s1 with a new sample @v1
63 * @s1: the mean_and_variance to update.
64 * @v1: the new sample.
66 * see linked pdf equation 12.
68 struct mean_and_variance mean_and_variance_update(struct mean_and_variance s1, s64 v1)
70 return mean_and_variance_update_inlined(s1, v1);
72 EXPORT_SYMBOL_GPL(mean_and_variance_update);
75 * mean_and_variance_get_mean() - get mean from @s
77 s64 mean_and_variance_get_mean(struct mean_and_variance s)
79 return div64_u64(s.sum, s.n);
81 EXPORT_SYMBOL_GPL(mean_and_variance_get_mean);
84 * mean_and_variance_get_variance() - get variance from @s1
86 * see linked pdf equation 12.
88 u64 mean_and_variance_get_variance(struct mean_and_variance s1)
90 u128 s2 = u128_div(s1.sum_squares, s1.n);
91 u64 s3 = abs(mean_and_variance_get_mean(s1));
93 return u128_to_u64(u128_sub(s2, u128_square(s3)));
95 EXPORT_SYMBOL_GPL(mean_and_variance_get_variance);
98 * mean_and_variance_get_stddev() - get standard deviation from @s
100 u32 mean_and_variance_get_stddev(struct mean_and_variance s)
102 return int_sqrt64(mean_and_variance_get_variance(s));
104 EXPORT_SYMBOL_GPL(mean_and_variance_get_stddev);
107 * mean_and_variance_weighted_update() - exponentially weighted variant of mean_and_variance_update()
111 * see linked pdf: function derived from equations 140-143 where alpha = 2^w.
112 * values are stored bitshifted for performance and added precision.
114 struct mean_and_variance_weighted mean_and_variance_weighted_update(struct mean_and_variance_weighted s1,
117 return mean_and_variance_weighted_update_inlined(s1, x);
119 EXPORT_SYMBOL_GPL(mean_and_variance_weighted_update);
122 * mean_and_variance_weighted_get_mean() - get mean from @s
124 s64 mean_and_variance_weighted_get_mean(struct mean_and_variance_weighted s)
126 return fast_divpow2(s.mean, s.w);
128 EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_mean);
131 * mean_and_variance_weighted_get_variance() -- get variance from @s
133 u64 mean_and_variance_weighted_get_variance(struct mean_and_variance_weighted s)
135 // always positive don't need fast divpow2
136 return s.variance >> s.w;
138 EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_variance);
141 * mean_and_variance_weighted_get_stddev() - get standard deviation from @s
143 u32 mean_and_variance_weighted_get_stddev(struct mean_and_variance_weighted s)
145 return int_sqrt64(mean_and_variance_weighted_get_variance(s));
147 EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_stddev);
149 MODULE_AUTHOR("Daniel B. Hill");
150 MODULE_LICENSE("GPL");