bcachefs: Mean and variance

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>

1 files changed, 153 insertions, 0 deletions

diff --git a/fs/bcachefs/mean_and_variance_test.c b/fs/bcachefs/mean_and_variance_test.c
new file mode 100644
index 000000000000..2b4cf9b1781b
--- /dev/null
+++ b/fs/bcachefs/mean_and_variance_test.c
@@ -0,0 +1,153 @@
+// SPDX-License-Identifier: GPL-2.0
+#include <kunit/test.h>
+
+#include "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 = { .weight = 2 };
+
+	s.weight = 2;
+
+	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);
+
+	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);
+
+	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) { .weight = 2 };
+
+	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);
+
+	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);
+
+	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 = { .weight = 8 };
+	s64 i;
+
+	for (i = 10; i <= 100; i += 10)
+		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) { .weight = 8 };
+
+	for (i = -10; i >= -100; i -= 10)
+		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_u a  = u64s_to_u128(0, U64_MAX);
+	u128_u a1 = u64s_to_u128(0, 1);
+	u128_u b  = u64s_to_u128(1, 0);
+	u128_u c  = u64s_to_u128(0, 1LLU << 63);
+	u128_u c2 = u64s_to_u128(U64_MAX, U64_MAX);
+
+	KUNIT_EXPECT_EQ(test, u128_hi(u128_add(a, a1)), 1);
+	KUNIT_EXPECT_EQ(test, u128_lo(u128_add(a, a1)), 0);
+	KUNIT_EXPECT_EQ(test, u128_hi(u128_add(a1, a)), 1);
+	KUNIT_EXPECT_EQ(test, u128_lo(u128_add(a1, a)), 0);
+
+	KUNIT_EXPECT_EQ(test, u128_lo(u128_sub(b, a1)), U64_MAX);
+	KUNIT_EXPECT_EQ(test, u128_hi(u128_sub(b, a1)), 0);
+
+	KUNIT_EXPECT_EQ(test, u128_hi(u128_shl(c, 1)), 1);
+	KUNIT_EXPECT_EQ(test, u128_lo(u128_shl(c, 1)), 0);
+
+	KUNIT_EXPECT_EQ(test, u128_hi(u128_square(U64_MAX)), U64_MAX - 1);
+	KUNIT_EXPECT_EQ(test, u128_lo(u128_square(U64_MAX)), 1);
+
+	KUNIT_EXPECT_EQ(test, u128_lo(u128_div(b, 2)), 1LLU << 63);
+
+	KUNIT_EXPECT_EQ(test, u128_hi(u128_div(c2, 2)), U64_MAX >> 1);
+	KUNIT_EXPECT_EQ(test, u128_lo(u128_div(c2, 2)), U64_MAX);
+
+	KUNIT_EXPECT_EQ(test, u128_hi(u128_div(u128_shl(u64_to_u128(U64_MAX), 32), 2)), U32_MAX >> 1);
+	KUNIT_EXPECT_EQ(test, u128_lo(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");