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/module.h>
45 #include "mean_and_variance.h"
47 u128_u u128_div(u128_u n, u64 d)
53 u64 h = hi & ((u64) U32_MAX << 32);
54 u64 l = (hi & (u64) U32_MAX) << 32;
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)));
61 EXPORT_SYMBOL_GPL(u128_div);
64 * mean_and_variance_get_mean() - get mean from @s
65 * @s: mean and variance number of samples and their sums
67 s64 mean_and_variance_get_mean(struct mean_and_variance s)
69 return s.n ? div64_u64(s.sum, s.n) : 0;
71 EXPORT_SYMBOL_GPL(mean_and_variance_get_mean);
74 * mean_and_variance_get_variance() - get variance from @s1
75 * @s1: mean and variance number of samples and sums
77 * see linked pdf equation 12.
79 u64 mean_and_variance_get_variance(struct mean_and_variance s1)
82 u128_u s2 = u128_div(s1.sum_squares, s1.n);
83 u64 s3 = abs(mean_and_variance_get_mean(s1));
85 return u128_lo(u128_sub(s2, u128_square(s3)));
90 EXPORT_SYMBOL_GPL(mean_and_variance_get_variance);
93 * mean_and_variance_get_stddev() - get standard deviation from @s
94 * @s: mean and variance number of samples and their sums
96 u32 mean_and_variance_get_stddev(struct mean_and_variance s)
98 return int_sqrt64(mean_and_variance_get_variance(s));
100 EXPORT_SYMBOL_GPL(mean_and_variance_get_stddev);
103 * mean_and_variance_weighted_update() - exponentially weighted variant of mean_and_variance_update()
104 * @s: mean and variance number of samples and their sums
105 * @x: new value to include in the &mean_and_variance_weighted
107 * see linked pdf: function derived from equations 140-143 where alpha = 2^w.
108 * values are stored bitshifted for performance and added precision.
110 void mean_and_variance_weighted_update(struct mean_and_variance_weighted *s, s64 x)
112 // previous weighted variance.
114 u64 var_w0 = s->variance;
115 // new value weighted.
117 s64 diff_w = x_w - s->mean;
118 s64 diff = fast_divpow2(diff_w, w);
119 // new mean weighted.
120 s64 u_w1 = s->mean + diff;
127 s->variance = ((var_w0 << w) - var_w0 + ((diff_w * (x_w - u_w1)) >> w)) >> w;
131 EXPORT_SYMBOL_GPL(mean_and_variance_weighted_update);
134 * mean_and_variance_weighted_get_mean() - get mean from @s
135 * @s: mean and variance number of samples and their sums
137 s64 mean_and_variance_weighted_get_mean(struct mean_and_variance_weighted s)
139 return fast_divpow2(s.mean, s.weight);
141 EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_mean);
144 * mean_and_variance_weighted_get_variance() -- get variance from @s
145 * @s: mean and variance number of samples and their sums
147 u64 mean_and_variance_weighted_get_variance(struct mean_and_variance_weighted s)
149 // always positive don't need fast divpow2
150 return s.variance >> s.weight;
152 EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_variance);
155 * mean_and_variance_weighted_get_stddev() - get standard deviation from @s
156 * @s: mean and variance number of samples and their sums
158 u32 mean_and_variance_weighted_get_stddev(struct mean_and_variance_weighted s)
160 return int_sqrt64(mean_and_variance_weighted_get_variance(s));
162 EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_stddev);
164 MODULE_AUTHOR("Daniel B. Hill");
165 MODULE_LICENSE("GPL");