1// SPDX-License-Identifier: GPL-2.0
  2/*
  3 * Functions for incremental mean and variance.
  4 *
  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.
  8 *
  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
 12 * more details.
 13 *
 14 * Copyright © 2022 Daniel B. Hill
 15 *
 16 * Author: Daniel B. Hill <daniel@gluo.nz>
 17 *
 18 * Description:
 19 *
 20 * This is includes some incremental algorithms for mean and variance calculation
 21 *
 22 * Derived from the paper: https://fanf2.user.srcf.net/hermes/doc/antiforgery/stats.pdf
 23 *
 24 * Create a struct and if it's the weighted variant set the w field (weight = 2^k).
 25 *
 26 * Use mean_and_variance[_weighted]_update() on the struct to update it's state.
 27 *
 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.
 30 *
 31 * see lib/math/mean_and_variance_test.c for examples of usage.
 32 *
 33 * DO NOT access the mean and variance fields of the weighted variants directly.
 34 * DO NOT change the weight after calling update.
 35 */
 36
 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>
 44
 45#include "mean_and_variance.h"
 46
 47u128_u u128_div(u128_u n, u64 d)
 48{
 49	u128_u r;
 50	u64 rem;
 51	u64 hi = u128_hi(n);
 52	u64 lo = u128_lo(n);
 53	u64  h =  hi & ((u64) U32_MAX  << 32);
 54	u64  l = (hi &  (u64) U32_MAX) << 32;
 55
 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)));
 59	return r;
 60}
 61EXPORT_SYMBOL_GPL(u128_div);
 62
 63/**
 64 * mean_and_variance_get_mean() - get mean from @s
 65 * @s: mean and variance number of samples and their sums
 66 */
 67s64 mean_and_variance_get_mean(struct mean_and_variance s)
 68{
 69	return s.n ? div64_u64(s.sum, s.n) : 0;
 70}
 71EXPORT_SYMBOL_GPL(mean_and_variance_get_mean);
 72
 73/**
 74 * mean_and_variance_get_variance() -  get variance from @s1
 75 * @s1: mean and variance number of samples and sums
 76 *
 77 * see linked pdf equation 12.
 78 */
 79u64 mean_and_variance_get_variance(struct mean_and_variance s1)
 80{
 81	if (s1.n) {
 82		u128_u s2 = u128_div(s1.sum_squares, s1.n);
 83		u64  s3 = abs(mean_and_variance_get_mean(s1));
 84
 85		return u128_lo(u128_sub(s2, u128_square(s3)));
 86	} else {
 87		return 0;
 88	}
 89}
 90EXPORT_SYMBOL_GPL(mean_and_variance_get_variance);
 91
 92/**
 93 * mean_and_variance_get_stddev() - get standard deviation from @s
 94 * @s: mean and variance number of samples and their sums
 95 */
 96u32 mean_and_variance_get_stddev(struct mean_and_variance s)
 97{
 98	return int_sqrt64(mean_and_variance_get_variance(s));
 99}
100EXPORT_SYMBOL_GPL(mean_and_variance_get_stddev);
101
102/**
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
106 * @initted: caller must track whether this is the first use or not
107 * @weight: ewma weight
108 *
109 * see linked pdf: function derived from equations 140-143 where alpha = 2^w.
110 * values are stored bitshifted for performance and added precision.
111 */
112void mean_and_variance_weighted_update(struct mean_and_variance_weighted *s,
113		s64 x, bool initted, u8 weight)
114{
115	// previous weighted variance.
116	u8 w		= weight;
117	u64 var_w0	= s->variance;
118	// new value weighted.
119	s64 x_w		= x << w;
120	s64 diff_w	= x_w - s->mean;
121	s64 diff	= fast_divpow2(diff_w, w);
122	// new mean weighted.
123	s64 u_w1	= s->mean + diff;
124
125	if (!initted) {
126		s->mean = x_w;
127		s->variance = 0;
128	} else {
129		s->mean = u_w1;
130		s->variance = ((var_w0 << w) - var_w0 + ((diff_w * (x_w - u_w1)) >> w)) >> w;
131	}
132}
133EXPORT_SYMBOL_GPL(mean_and_variance_weighted_update);
134
135/**
136 * mean_and_variance_weighted_get_mean() - get mean from @s
137 * @s: mean and variance number of samples and their sums
138 * @weight: ewma weight
139 */
140s64 mean_and_variance_weighted_get_mean(struct mean_and_variance_weighted s,
141		u8 weight)
142{
143	return fast_divpow2(s.mean, weight);
144}
145EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_mean);
146
147/**
148 * mean_and_variance_weighted_get_variance() -- get variance from @s
149 * @s: mean and variance number of samples and their sums
150 * @weight: ewma weight
151 */
152u64 mean_and_variance_weighted_get_variance(struct mean_and_variance_weighted s,
153		u8 weight)
154{
155	// always positive don't need fast divpow2
156	return s.variance >> weight;
157}
158EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_variance);
159
160/**
161 * mean_and_variance_weighted_get_stddev() - get standard deviation from @s
162 * @s: mean and variance number of samples and their sums
163 * @weight: ewma weight
164 */
165u32 mean_and_variance_weighted_get_stddev(struct mean_and_variance_weighted s,
166		u8 weight)
167{
168	return int_sqrt64(mean_and_variance_weighted_get_variance(s, weight));
169}
170EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_stddev);
171
172MODULE_AUTHOR("Daniel B. Hill");
173MODULE_LICENSE("GPL");