--- /dev/null
+// 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
+ *
+ * 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)
+{
+ // previous weighted variance.
+ u8 w = s->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 (!s->init) {
+ 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;
+ }
+ s->init = true;
+}
+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
+ */
+s64 mean_and_variance_weighted_get_mean(struct mean_and_variance_weighted s)
+{
+ return fast_divpow2(s.mean, s.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
+ */
+u64 mean_and_variance_weighted_get_variance(struct mean_and_variance_weighted s)
+{
+ // always positive don't need fast divpow2
+ return s.variance >> s.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
+ */
+u32 mean_and_variance_weighted_get_stddev(struct mean_and_variance_weighted s)
+{
+ return int_sqrt64(mean_and_variance_weighted_get_variance(s));
+}
+EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_stddev);
+
+MODULE_AUTHOR("Daniel B. Hill");
+MODULE_LICENSE("GPL");
projects / bcachefs-tools-debian / blobdiff