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// 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
* @initted: caller must track whether this is the first use or not
* @weight: ewma weight
*
* 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, bool initted, u8 weight)
{
// previous weighted variance.
u8 w = 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 (!initted) {
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;
}
}
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
* @weight: ewma weight
*/
s64 mean_and_variance_weighted_get_mean(struct mean_and_variance_weighted s,
u8 weight)
{
return fast_divpow2(s.mean, 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
* @weight: ewma weight
*/
u64 mean_and_variance_weighted_get_variance(struct mean_and_variance_weighted s,
u8 weight)
{
// always positive don't need fast divpow2
return s.variance >> 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
* @weight: ewma weight
*/
u32 mean_and_variance_weighted_get_stddev(struct mean_and_variance_weighted s,
u8 weight)
{
return int_sqrt64(mean_and_variance_weighted_get_variance(s, weight));
}
EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_stddev);
MODULE_AUTHOR("Daniel B. Hill");
MODULE_LICENSE("GPL");
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