[PATCH 31/32] lib: add mean and variance module.

Kent Overstreet
2023-05-09T17:01:14Z

From: Daniel Hill <daniel@gluo.nz>

This module provides a fast 64bit implementation of basic statistics
functions, including mean, variance and standard deviation in both
weighted and unweighted variants, the unweighted variant has a 32bit
limitation per sample to prevent overflow when squaring.

Signed-off-by: Daniel Hill <daniel@gluo.nz>
Signed-off-by: Kent Overstreet <kent.overstreet@linux.dev>
---
MAINTAINERS | 9 ++
include/linux/mean_and_variance.h | 219 ++++++++++++++++++++++++++++++
lib/Kconfig.debug | 9 ++
lib/math/Kconfig | 3 +
lib/math/Makefile | 2 +
lib/math/mean_and_variance.c | 136 +++++++++++++++++++
lib/math/mean_and_variance_test.c | 155 +++++++++++++++++++++
7 files changed, 533 insertions(+)
create mode 100644 include/linux/mean_and_variance.h
create mode 100644 lib/math/mean_and_variance.c
create mode 100644 lib/math/mean_and_variance_test.c

diff --git a/MAINTAINERS b/MAINTAINERS
index c550f5909e..dbf3c33c31 100644
--- a/MAINTAINERS
+++ b/MAINTAINERS
@@ -12767,6 +12767,15 @@ F: Documentation/devicetree/bindings/net/ieee802154/mcr20a.txt
F: drivers/net/ieee802154/mcr20a.c
F: drivers/net/ieee802154/mcr20a.h

+MEAN AND VARIANCE LIBRARY
+M: Daniel B. Hill <daniel@gluo.nz>
+M: Kent Overstreet <kent.overstreet@linux.dev>
+S: Maintained
+T: git https://github.com/YellowOnion/linux/
+F: include/linux/mean_and_variance.h
+F: lib/math/mean_and_variance.c
+F: lib/math/mean_and_variance_test.c
+
MEASUREMENT COMPUTING CIO-DAC IIO DRIVER
M: William Breathitt Gray <william.gray@linaro.org>
L: linux-iio@vger.kernel.org
diff --git a/include/linux/mean_and_variance.h b/include/linux/mean_and_variance.h
new file mode 100644
index 0000000000..89540628e8
--- /dev/null
+++ b/include/linux/mean_and_variance.h
@@ -0,0 +1,219 @@
+/* SPDX-License-Identifier: GPL-2.0 */
+#ifndef MEAN_AND_VARIANCE_H_
+#define MEAN_AND_VARIANCE_H_
+
+#include <linux/types.h>
+#include <linux/limits.h>
+#include <linux/math64.h>
+
+#define SQRT_U64_MAX 4294967295ULL
+
+
+#if defined(CONFIG_ARCH_SUPPORTS_INT128) && defined(__SIZEOF_INT128__)
+
+typedef unsigned __int128 u128;
+
+static inline u128 u64_to_u128(u64 a)
+{
+ return (u128)a;
+}
+
+static inline u64 u128_to_u64(u128 a)
+{
+ return (u64)a;
+}
+
+static inline u64 u128_shr64_to_u64(u128 a)
+{
+ return (u64)(a >> 64);
+}
+
+static inline u128 u128_add(u128 a, u128 b)
+{
+ return a + b;
+}
+
+static inline u128 u128_sub(u128 a, u128 b)
+{
+ return a - b;
+}
+
+static inline u128 u128_shl(u128 i, s8 shift)
+{
+ return i << shift;
+}
+
+static inline u128 u128_shl64_add(u64 a, u64 b)
+{
+ return ((u128)a << 64) + b;
+}
+
+static inline u128 u128_square(u64 i)
+{
+ return i*i;
+}
+
+#else
+
+typedef struct {
+ u64 hi, lo;
+} u128;
+
+static inline u128 u64_to_u128(u64 a)
+{
+ return (u128){ .lo = a };
+}
+
+static inline u64 u128_to_u64(u128 a)
+{
+ return a.lo;
+}
+
+static inline u64 u128_shr64_to_u64(u128 a)
+{
+ return a.hi;
+}
+
+static inline u128 u128_add(u128 a, u128 b)
+{
+ u128 c;
+
+ c.lo = a.lo + b.lo;
+ c.hi = a.hi + b.hi + (c.lo < a.lo);
+ return c;
+}
+
+static inline u128 u128_sub(u128 a, u128 b)
+{
+ u128 c;
+
+ c.lo = a.lo - b.lo;
+ c.hi = a.hi - b.hi - (c.lo > a.lo);
+ return c;
+}
+
+static inline u128 u128_shl(u128 i, s8 shift)
+{
+ u128 r;
+
+ r.lo = i.lo << shift;
+ if (shift < 64)
+ r.hi = (i.hi << shift) | (i.lo >> (64 - shift));
+ else {
+ r.hi = i.lo << (shift - 64);
+ r.lo = 0;
+ }
+ return r;
+}
+
+static inline u128 u128_shl64_add(u64 a, u64 b)
+{
+ return u128_add(u128_shl(u64_to_u128(a), 64), u64_to_u128(b));
+}
+
+static inline u128 u128_square(u64 i)
+{
+ u128 r;
+ u64 h = i >> 32, l = i & (u64)U32_MAX;
+
+ r = u128_shl(u64_to_u128(h*h), 64);
+ r = u128_add(r, u128_shl(u64_to_u128(h*l), 32));
+ r = u128_add(r, u128_shl(u64_to_u128(l*h), 32));
+ r = u128_add(r, u64_to_u128(l*l));
+ return r;
+}
+
+#endif
+
+static inline u128 u128_div(u128 n, u64 d)
+{
+ u128 r;
+ u64 rem;
+ u64 hi = u128_shr64_to_u64(n);
+ u64 lo = u128_to_u64(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;
+}
+
+struct mean_and_variance {
+ s64 n;
+ s64 sum;
+ u128 sum_squares;
+};
+
+/* expontentially weighted variant */
+struct mean_and_variance_weighted {
+ bool init;
+ u8 w;
+ s64 mean;
+ u64 variance;
+};
+
+/**
+ * fast_divpow2() - fast approximation for n / (1 << d)
+ * @n: numerator
+ * @d: the power of 2 denominator.
+ *
+ * note: this rounds towards 0.
+ */
+static inline s64 fast_divpow2(s64 n, u8 d)
+{
+ return (n + ((n < 0) ? ((1 << d) - 1) : 0)) >> d;
+}
+
+static inline struct mean_and_variance
+mean_and_variance_update_inlined(struct mean_and_variance s1, s64 v1)
+{
+ struct mean_and_variance s2;
+ u64 v2 = abs(v1);
+
+ s2.n = s1.n + 1;
+ s2.sum = s1.sum + v1;
+ s2.sum_squares = u128_add(s1.sum_squares, u128_square(v2));
+ return s2;
+}
+
+static inline struct mean_and_variance_weighted
+mean_and_variance_weighted_update_inlined(struct mean_and_variance_weighted s1, s64 x)
+{
+ struct mean_and_variance_weighted s2;
+ // previous weighted variance.
+ u64 var_w0 = s1.variance;
+ u8 w = s2.w = s1.w;
+ // new value weighted.
+ s64 x_w = x << w;
+ s64 diff_w = x_w - s1.mean;
+ s64 diff = fast_divpow2(diff_w, w);
+ // new mean weighted.
+ s64 u_w1 = s1.mean + diff;
+
+ BUG_ON(w % 2 != 0);
+
+ if (!s1.init) {
+ s2.mean = x_w;
+ s2.variance = 0;
+ } else {
+ s2.mean = u_w1;
+ s2.variance = ((var_w0 << w) - var_w0 + ((diff_w * (x_w - u_w1)) >> w)) >> w;
+ }
+ s2.init = true;
+
+ return s2;
+}
+
+struct mean_and_variance mean_and_variance_update(struct mean_and_variance s1, s64 v1);
+ s64 mean_and_variance_get_mean(struct mean_and_variance s);
+ u64 mean_and_variance_get_variance(struct mean_and_variance s1);
+ u32 mean_and_variance_get_stddev(struct mean_and_variance s);
+
+struct mean_and_variance_weighted mean_and_variance_weighted_update(struct mean_and_variance_weighted s1, s64 v1);
+ s64 mean_and_variance_weighted_get_mean(struct mean_and_variance_weighted s);
+ u64 mean_and_variance_weighted_get_variance(struct mean_and_variance_weighted s);
+ u32 mean_and_variance_weighted_get_stddev(struct mean_and_variance_weighted s);
+
+#endif // MEAN_AND_VAIRANCE_H_
diff --git a/lib/Kconfig.debug b/lib/Kconfig.debug
index 3dba7a9aff..9ca88e0027 100644
--- a/lib/Kconfig.debug
+++ b/lib/Kconfig.debug
@@ -2101,6 +2101,15 @@ config CPUMASK_KUNIT_TEST

If unsure, say N.

+config MEAN_AND_VARIANCE_UNIT_TEST
+ tristate "mean_and_variance unit tests" if !KUNIT_ALL_TESTS
+ depends on KUNIT
+ select MEAN_AND_VARIANCE
+ default KUNIT_ALL_TESTS
+ help
+ This option enables the kunit tests for mean_and_variance module.
+ If unsure, say N.
+
config TEST_LIST_SORT
tristate "Linked list sorting test" if !KUNIT_ALL_TESTS
depends on KUNIT
diff --git a/lib/math/Kconfig b/lib/math/Kconfig
index 0634b428d0..7530ae9a35 100644
--- a/lib/math/Kconfig
+++ b/lib/math/Kconfig
@@ -15,3 +15,6 @@ config PRIME_NUMBERS

config RATIONAL
tristate
+
+config MEAN_AND_VARIANCE
+ tristate
diff --git a/lib/math/Makefile b/lib/math/Makefile
index bfac26ddfc..2ef1487e01 100644
--- a/lib/math/Makefile
+++ b/lib/math/Makefile
@@ -4,6 +4,8 @@ obj-y += div64.o gcd.o lcm.o int_pow.o int_sqrt.o reciprocal_div.o
obj-$(CONFIG_CORDIC) += cordic.o
obj-$(CONFIG_PRIME_NUMBERS) += prime_numbers.o
obj-$(CONFIG_RATIONAL) += rational.o
+obj-$(CONFIG_MEAN_AND_VARIANCE) += mean_and_variance.o

obj-$(CONFIG_TEST_DIV64) += test_div64.o
obj-$(CONFIG_RATIONAL_KUNIT_TEST) += rational-test.o
+obj-$(CONFIG_MEAN_AND_VARIANCE_UNIT_TEST) += mean_and_variance_test.o
diff --git a/lib/math/mean_and_variance.c b/lib/math/mean_and_variance.c
new file mode 100644
index 0000000000..6e315d3a13
--- /dev/null
+++ b/lib/math/mean_and_variance.c
@@ -0,0 +1,136 @@
+// 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/mean_and_variance.h>
+#include <linux/module.h>
+
+/**
+ * mean_and_variance_update() - update a mean_and_variance struct @s1 with a new sample @v1
+ * and return it.
+ * @s1: the mean_and_variance to update.
+ * @v1: the new sample.
+ *
+ * see linked pdf equation 12.
+ */
+struct mean_and_variance mean_and_variance_update(struct mean_and_variance s1, s64 v1)
+{
+ return mean_and_variance_update_inlined(s1, v1);
+}
+EXPORT_SYMBOL_GPL(mean_and_variance_update);
+
+/**
+ * mean_and_variance_get_mean() - get mean from @s
+ */
+s64 mean_and_variance_get_mean(struct mean_and_variance s)
+{
+ return div64_u64(s.sum, s.n);
+}
+EXPORT_SYMBOL_GPL(mean_and_variance_get_mean);
+
+/**
+ * mean_and_variance_get_variance() - get variance from @s1
+ *
+ * see linked pdf equation 12.
+ */
+u64 mean_and_variance_get_variance(struct mean_and_variance s1)
+{
+ u128 s2 = u128_div(s1.sum_squares, s1.n);
+ u64 s3 = abs(mean_and_variance_get_mean(s1));
+
+ return u128_to_u64(u128_sub(s2, u128_square(s3)));
+}
+EXPORT_SYMBOL_GPL(mean_and_variance_get_variance);
+
+/**
+ * mean_and_variance_get_stddev() - get standard deviation from @s
+ */
+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()
+ * @s1: ..
+ * @s2: ..
+ *
+ * see linked pdf: function derived from equations 140-143 where alpha = 2^w.
+ * values are stored bitshifted for performance and added precision.
+ */
+struct mean_and_variance_weighted mean_and_variance_weighted_update(struct mean_and_variance_weighted s1,
+ s64 x)
+{
+ return mean_and_variance_weighted_update_inlined(s1, x);
+}
+EXPORT_SYMBOL_GPL(mean_and_variance_weighted_update);
+
+/**
+ * mean_and_variance_weighted_get_mean() - get mean from @s
+ */
+s64 mean_and_variance_weighted_get_mean(struct mean_and_variance_weighted s)
+{
+ return fast_divpow2(s.mean, s.w);
+}
+EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_mean);
+
+/**
+ * mean_and_variance_weighted_get_variance() -- get variance from @s
+ */
+u64 mean_and_variance_weighted_get_variance(struct mean_and_variance_weighted s)
+{
+ // always positive don't need fast divpow2
+ return s.variance >> s.w;
+}
+EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_variance);
+
+/**
+ * mean_and_variance_weighted_get_stddev() - get standard deviation from @s
+ */
+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");
diff --git a/lib/math/mean_and_variance_test.c b/lib/math/mean_and_variance_test.c
new file mode 100644
index 0000000000..79a96d7307
--- /dev/null
+++ b/lib/math/mean_and_variance_test.c
@@ -0,0 +1,155 @@
+// SPDX-License-Identifier: GPL-2.0
+#include <kunit/test.h>
+#include <linux/mean_and_variance.h>
+
+#define MAX_SQR (SQRT_U64_MAX*SQRT_U64_MAX)
+
+static void mean_and_variance_basic_test(struct kunit *test)
+{
+ struct mean_and_variance s = {};
+
+ s = mean_and_variance_update(s, 2);
+ s = mean_and_variance_update(s, 2);
+
+ KUNIT_EXPECT_EQ(test, mean_and_variance_get_mean(s), 2);
+ KUNIT_EXPECT_EQ(test, mean_and_variance_get_variance(s), 0);
+ KUNIT_EXPECT_EQ(test, s.n, 2);
+
+ s = mean_and_variance_update(s, 4);
+ s = mean_and_variance_update(s, 4);
+
+ KUNIT_EXPECT_EQ(test, mean_and_variance_get_mean(s), 3);
+ KUNIT_EXPECT_EQ(test, mean_and_variance_get_variance(s), 1);
+ KUNIT_EXPECT_EQ(test, s.n, 4);
+}
+
+/*
+ * Test values computed using a spreadsheet from the psuedocode at the bottom:
+ * https://fanf2.user.srcf.net/hermes/doc/antiforgery/stats.pdf
+ */
+
+static void mean_and_variance_weighted_test(struct kunit *test)
+{
+ struct mean_and_variance_weighted s = {};
+
+ s.w = 2;
+
+ s = mean_and_variance_weighted_update(s, 10);
+ KUNIT_EXPECT_EQ(test, mean_and_variance_weighted_get_mean(s), 10);
+ KUNIT_EXPECT_EQ(test, mean_and_variance_weighted_get_variance(s), 0);
+
+ s = mean_and_variance_weighted_update(s, 20);
+ KUNIT_EXPECT_EQ(test, mean_and_variance_weighted_get_mean(s), 12);
+ KUNIT_EXPECT_EQ(test, mean_and_variance_weighted_get_variance(s), 18);
+
+ s = mean_and_variance_weighted_update(s, 30);
+ KUNIT_EXPECT_EQ(test, mean_and_variance_weighted_get_mean(s), 16);
+ KUNIT_EXPECT_EQ(test, mean_and_variance_weighted_get_variance(s), 72);
+
+ s = (struct mean_and_variance_weighted){};
+ s.w = 2;
+
+ s = mean_and_variance_weighted_update(s, -10);
+ KUNIT_EXPECT_EQ(test, mean_and_variance_weighted_get_mean(s), -10);
+ KUNIT_EXPECT_EQ(test, mean_and_variance_weighted_get_variance(s), 0);
+
+ s = mean_and_variance_weighted_update(s, -20);
+ KUNIT_EXPECT_EQ(test, mean_and_variance_weighted_get_mean(s), -12);
+ KUNIT_EXPECT_EQ(test, mean_and_variance_weighted_get_variance(s), 18);
+
+ s = mean_and_variance_weighted_update(s, -30);
+ KUNIT_EXPECT_EQ(test, mean_and_variance_weighted_get_mean(s), -16);
+ KUNIT_EXPECT_EQ(test, mean_and_variance_weighted_get_variance(s), 72);
+
+}
+
+static void mean_and_variance_weighted_advanced_test(struct kunit *test)
+{
+ struct mean_and_variance_weighted s = {};
+ s64 i;
+
+ s.w = 8;
+ for (i = 10; i <= 100; i += 10)
+ s = mean_and_variance_weighted_update(s, i);
+
+ KUNIT_EXPECT_EQ(test, mean_and_variance_weighted_get_mean(s), 11);
+ KUNIT_EXPECT_EQ(test, mean_and_variance_weighted_get_variance(s), 107);
+
+ s = (struct mean_and_variance_weighted){};
+
+ s.w = 8;
+ for (i = -10; i >= -100; i -= 10)
+ s = mean_and_variance_weighted_update(s, i);
+
+ KUNIT_EXPECT_EQ(test, mean_and_variance_weighted_get_mean(s), -11);
+ KUNIT_EXPECT_EQ(test, mean_and_variance_weighted_get_variance(s), 107);
+
+}
+
+static void mean_and_variance_fast_divpow2(struct kunit *test)
+{
+ s64 i;
+ u8 d;
+
+ for (i = 0; i < 100; i++) {
+ d = 0;
+ KUNIT_EXPECT_EQ(test, fast_divpow2(i, d), div_u64(i, 1LLU << d));
+ KUNIT_EXPECT_EQ(test, abs(fast_divpow2(-i, d)), div_u64(i, 1LLU << d));
+ for (d = 1; d < 32; d++) {
+ KUNIT_EXPECT_EQ_MSG(test, abs(fast_divpow2(i, d)),
+ div_u64(i, 1 << d), "%lld %u", i, d);
+ KUNIT_EXPECT_EQ_MSG(test, abs(fast_divpow2(-i, d)),
+ div_u64(i, 1 << d), "%lld %u", -i, d);
+ }
+ }
+}
+
+static void mean_and_variance_u128_basic_test(struct kunit *test)
+{
+ u128 a = u128_shl64_add(0, U64_MAX);
+ u128 a1 = u128_shl64_add(0, 1);
+ u128 b = u128_shl64_add(1, 0);
+ u128 c = u128_shl64_add(0, 1LLU << 63);
+ u128 c2 = u128_shl64_add(U64_MAX, U64_MAX);
+
+ KUNIT_EXPECT_EQ(test, u128_shr64_to_u64(u128_add(a, a1)), 1);
+ KUNIT_EXPECT_EQ(test, u128_to_u64(u128_add(a, a1)), 0);
+ KUNIT_EXPECT_EQ(test, u128_shr64_to_u64(u128_add(a1, a)), 1);
+ KUNIT_EXPECT_EQ(test, u128_to_u64(u128_add(a1, a)), 0);
+
+ KUNIT_EXPECT_EQ(test, u128_to_u64(u128_sub(b, a1)), U64_MAX);
+ KUNIT_EXPECT_EQ(test, u128_shr64_to_u64(u128_sub(b, a1)), 0);
+
+ KUNIT_EXPECT_EQ(test, u128_shr64_to_u64(u128_shl(c, 1)), 1);
+ KUNIT_EXPECT_EQ(test, u128_to_u64(u128_shl(c, 1)), 0);
+
+ KUNIT_EXPECT_EQ(test, u128_shr64_to_u64(u128_square(U64_MAX)), U64_MAX - 1);
+ KUNIT_EXPECT_EQ(test, u128_to_u64(u128_square(U64_MAX)), 1);
+
+ KUNIT_EXPECT_EQ(test, u128_to_u64(u128_div(b, 2)), 1LLU << 63);
+
+ KUNIT_EXPECT_EQ(test, u128_shr64_to_u64(u128_div(c2, 2)), U64_MAX >> 1);
+ KUNIT_EXPECT_EQ(test, u128_to_u64(u128_div(c2, 2)), U64_MAX);
+
+ KUNIT_EXPECT_EQ(test, u128_shr64_to_u64(u128_div(u128_shl(u64_to_u128(U64_MAX), 32), 2)), U32_MAX >> 1);
+ KUNIT_EXPECT_EQ(test, u128_to_u64(u128_div(u128_shl(u64_to_u128(U64_MAX), 32), 2)), U64_MAX << 31);
+}
+
+static struct kunit_case mean_and_variance_test_cases[] = {
+ KUNIT_CASE(mean_and_variance_fast_divpow2),
+ KUNIT_CASE(mean_and_variance_u128_basic_test),
+ KUNIT_CASE(mean_and_variance_basic_test),
+ KUNIT_CASE(mean_and_variance_weighted_test),
+ KUNIT_CASE(mean_and_variance_weighted_advanced_test),
+ {}
+};
+
+static struct kunit_suite mean_and_variance_test_suite = {
+.name = "mean and variance tests",
+.test_cases = mean_and_variance_test_cases
+};
+
+kunit_test_suite(mean_and_variance_test_suite);
+
+MODULE_AUTHOR("Daniel B. Hill");
+MODULE_LICENSE("GPL");
--
2.40.1