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 inline 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 struct mean_and_variance s2;
75 s2.sum_squares = u128_add(s1.sum_squares, u128_square(v2));
78 EXPORT_SYMBOL_GPL(mean_and_variance_update);
81 * mean_and_variance_get_mean() - get mean from @s
83 s64 mean_and_variance_get_mean(struct mean_and_variance s)
85 return div64_u64(s.sum, s.n);
87 EXPORT_SYMBOL_GPL(mean_and_variance_get_mean);
90 * mean_and_variance_get_variance() - get variance from @s1
92 * see linked pdf equation 12.
94 u64 mean_and_variance_get_variance(struct mean_and_variance s1)
96 u128 s2 = u128_div(s1.sum_squares, s1.n);
97 u64 s3 = abs(mean_and_variance_get_mean(s1));
99 return u128_to_u64(u128_sub(s2, u128_square(s3)));
101 EXPORT_SYMBOL_GPL(mean_and_variance_get_variance);
104 * mean_and_variance_get_stddev() - get standard deviation from @s
106 u32 mean_and_variance_get_stddev(struct mean_and_variance s)
108 return int_sqrt64(mean_and_variance_get_variance(s));
110 EXPORT_SYMBOL_GPL(mean_and_variance_get_stddev);
113 * mean_and_variance_weighted_update() - exponentially weighted variant of mean_and_variance_update()
117 * see linked pdf: function derived from equations 140-143 where alpha = 2^w.
118 * values are stored bitshifted for performance and added precision.
120 struct mean_and_variance_weighted mean_and_variance_weighted_update(struct mean_and_variance_weighted s1,
123 struct mean_and_variance_weighted s2;
124 // previous weighted variance.
125 u64 var_w0 = s1.variance;
127 // new value weighted.
129 s64 diff_w = x_w - s1.mean;
130 s64 diff = fast_divpow2(diff_w, w);
131 // new mean weighted.
132 s64 u_w1 = s1.mean + diff;
141 s2.variance = ((var_w0 << w) - var_w0 + ((diff_w * (x_w - u_w1)) >> w)) >> w;
147 EXPORT_SYMBOL_GPL(mean_and_variance_weighted_update);
150 * mean_and_variance_weighted_get_mean() - get mean from @s
152 s64 mean_and_variance_weighted_get_mean(struct mean_and_variance_weighted s)
154 return fast_divpow2(s.mean, s.w);
156 EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_mean);
159 * mean_and_variance_weighted_get_variance() -- get variance from @s
161 u64 mean_and_variance_weighted_get_variance(struct mean_and_variance_weighted s)
163 // always positive don't need fast divpow2
164 return s.variance >> s.w;
166 EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_variance);
169 * mean_and_variance_weighted_get_stddev() - get standard deviation from @s
171 u32 mean_and_variance_weighted_get_stddev(struct mean_and_variance_weighted s)
173 return int_sqrt64(mean_and_variance_weighted_get_variance(s));
175 EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_stddev);
177 MODULE_AUTHOR("Daniel B. Hill");
178 MODULE_LICENSE("GPL");