fs/bcachefs/mean_and_variance.c

   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
  47 u128_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 }
  61 EXPORT_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  */
  67 s64 mean_and_variance_get_mean(struct mean_and_variance s)
  68 {
  69         return s.n ? div64_u64(s.sum, s.n) : 0;
  70 }
  71 EXPORT_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  */
  79 u64 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 }
  90 EXPORT_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  */
  96 u32 mean_and_variance_get_stddev(struct mean_and_variance s)
  97 {
  98         return int_sqrt64(mean_and_variance_get_variance(s));
  99 }
 100 EXPORT_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  */
 112 void 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 }
 133 EXPORT_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  */
 140 s64 mean_and_variance_weighted_get_mean(struct mean_and_variance_weighted s,
 141                 u8 weight)
 142 {
 143         return fast_divpow2(s.mean, weight);
 144 }
 145 EXPORT_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  */
 152 u64 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 }
 158 EXPORT_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  */
 165 u32 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 }
 170 EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_stddev);
 171
 172 MODULE_AUTHOR("Daniel B. Hill");
 173 MODULE_LICENSE("GPL");