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160 lines
4.5 KiB
C
160 lines
4.5 KiB
C
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// SPDX-License-Identifier: GPL-2.0
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/*
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* Functions for incremental mean and variance.
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*
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* This program is free software; you can redistribute it and/or modify it
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* under the terms of the GNU General Public License version 2 as published by
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* the Free Software Foundation.
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*
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* This program is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
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* more details.
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*
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* Copyright © 2022 Daniel B. Hill
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*
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* Author: Daniel B. Hill <daniel@gluo.nz>
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*
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* Description:
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*
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* This is includes some incremental algorithms for mean and variance calculation
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*
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* Derived from the paper: https://fanf2.user.srcf.net/hermes/doc/antiforgery/stats.pdf
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*
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* Create a struct and if it's the weighted variant set the w field (weight = 2^k).
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*
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* Use mean_and_variance[_weighted]_update() on the struct to update it's state.
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*
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* Use the mean_and_variance[_weighted]_get_* functions to calculate the mean and variance, some computation
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* is deferred to these functions for performance reasons.
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*
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* see lib/math/mean_and_variance_test.c for examples of usage.
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*
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* DO NOT access the mean and variance fields of the weighted variants directly.
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* DO NOT change the weight after calling update.
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*/
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#include <linux/bug.h>
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#include <linux/compiler.h>
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#include <linux/export.h>
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#include <linux/limits.h>
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#include <linux/math.h>
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#include <linux/math64.h>
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#include <linux/module.h>
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#include "mean_and_variance.h"
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u128_u u128_div(u128_u n, u64 d)
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{
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u128_u r;
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u64 rem;
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u64 hi = u128_hi(n);
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u64 lo = u128_lo(n);
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u64 h = hi & ((u64) U32_MAX << 32);
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u64 l = (hi & (u64) U32_MAX) << 32;
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r = u128_shl(u64_to_u128(div64_u64_rem(h, d, &rem)), 64);
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r = u128_add(r, u128_shl(u64_to_u128(div64_u64_rem(l + (rem << 32), d, &rem)), 32));
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r = u128_add(r, u64_to_u128(div64_u64_rem(lo + (rem << 32), d, &rem)));
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return r;
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}
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EXPORT_SYMBOL_GPL(u128_div);
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/**
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* mean_and_variance_get_mean() - get mean from @s
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*/
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s64 mean_and_variance_get_mean(struct mean_and_variance s)
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{
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return s.n ? div64_u64(s.sum, s.n) : 0;
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}
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EXPORT_SYMBOL_GPL(mean_and_variance_get_mean);
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/**
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* mean_and_variance_get_variance() - get variance from @s1
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*
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* see linked pdf equation 12.
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*/
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u64 mean_and_variance_get_variance(struct mean_and_variance s1)
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{
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if (s1.n) {
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u128_u s2 = u128_div(s1.sum_squares, s1.n);
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u64 s3 = abs(mean_and_variance_get_mean(s1));
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return u128_lo(u128_sub(s2, u128_square(s3)));
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} else {
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return 0;
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}
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}
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EXPORT_SYMBOL_GPL(mean_and_variance_get_variance);
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/**
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* mean_and_variance_get_stddev() - get standard deviation from @s
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*/
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u32 mean_and_variance_get_stddev(struct mean_and_variance s)
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{
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return int_sqrt64(mean_and_variance_get_variance(s));
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}
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EXPORT_SYMBOL_GPL(mean_and_variance_get_stddev);
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/**
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* mean_and_variance_weighted_update() - exponentially weighted variant of mean_and_variance_update()
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* @s1: ..
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* @s2: ..
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*
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* see linked pdf: function derived from equations 140-143 where alpha = 2^w.
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* values are stored bitshifted for performance and added precision.
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*/
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void mean_and_variance_weighted_update(struct mean_and_variance_weighted *s, s64 x)
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{
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// previous weighted variance.
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u8 w = s->weight;
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u64 var_w0 = s->variance;
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// new value weighted.
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s64 x_w = x << w;
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s64 diff_w = x_w - s->mean;
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s64 diff = fast_divpow2(diff_w, w);
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// new mean weighted.
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s64 u_w1 = s->mean + diff;
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if (!s->init) {
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s->mean = x_w;
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s->variance = 0;
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} else {
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s->mean = u_w1;
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s->variance = ((var_w0 << w) - var_w0 + ((diff_w * (x_w - u_w1)) >> w)) >> w;
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}
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s->init = true;
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}
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EXPORT_SYMBOL_GPL(mean_and_variance_weighted_update);
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/**
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* mean_and_variance_weighted_get_mean() - get mean from @s
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*/
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s64 mean_and_variance_weighted_get_mean(struct mean_and_variance_weighted s)
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{
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return fast_divpow2(s.mean, s.weight);
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}
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EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_mean);
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/**
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* mean_and_variance_weighted_get_variance() -- get variance from @s
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*/
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u64 mean_and_variance_weighted_get_variance(struct mean_and_variance_weighted s)
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{
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// always positive don't need fast divpow2
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return s.variance >> s.weight;
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}
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EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_variance);
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/**
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* mean_and_variance_weighted_get_stddev() - get standard deviation from @s
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*/
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u32 mean_and_variance_weighted_get_stddev(struct mean_and_variance_weighted s)
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{
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return int_sqrt64(mean_and_variance_weighted_get_variance(s));
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}
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EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_stddev);
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MODULE_AUTHOR("Daniel B. Hill");
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MODULE_LICENSE("GPL");
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