make stdev calculation more numerically stable (#3984)

ydb/core/mind/hive/hive.h

@@ -1,5 +1,6 @@
 #pragma once
 #include <bitset>
+#include <ranges>
 
 #include <util/generic/queue.h>
 #include <util/random/random.h>
@@ -201,20 +202,33 @@ TResourceNormalizedValues NormalizeRawValues(const TResourceRawValues& values, c
 NMetrics::EResource GetDominantResourceType(const TResourceRawValues& values, const TResourceRawValues& maximum);
 NMetrics::EResource GetDominantResourceType(const TResourceNormalizedValues& normValues);
 
+// https://en.wikipedia.org/wiki/Kahan_summation_algorithm
+template<std::ranges::range TRange>
+std::ranges::range_value_t<TRange> StableSum(const TRange& values) {
+    using TValue = std::ranges::range_value_t<TRange>;
+    TValue sum{};
+    TValue correction{};
+    for (const auto& x : values) {
+        TValue y = x - correction;
+        TValue tmp = sum + y;
+        correction = (tmp - sum) - y;
+        sum = tmp;
+    }
+    return sum;
+}
+
 template <typename... ResourceTypes>
 inline std::tuple<ResourceTypes...> GetStDev(const TVector<std::tuple<ResourceTypes...>>& values) {
     std::tuple<ResourceTypes...> sum;
     if (values.empty())
         return sum;
-    for (const auto& v : values) {
-        sum = sum + v;
-    }
+    sum = StableSum(values);
     auto mean = sum / values.size();
-    sum = std::tuple<ResourceTypes...>();
-    for (const auto& v : values) {
-        auto diff = v - mean;
-        sum = sum + diff * diff;
-    }
+    auto quadraticDev = [&] (const std::tuple<ResourceTypes...>& value) {
+        auto diff = value - mean;
+        return diff * diff;
+    };
+    sum = StableSum(values | std::views::transform(quadraticDev));
     auto div = sum / values.size();
     auto st_dev = sqrt(div);
     return tuple_cast<ResourceTypes...>::cast(st_dev);

ydb/core/mind/hive/hive_impl_ut.cpp

@@ -193,4 +193,22 @@ Y_UNIT_TEST_SUITE(THiveImplTest) {
         Ctest << "HIVE_TABLET_BALANCE_STRATEGY_RANDOM" << Endl;
         CheckSpeedAndDistribution(allTablets, BalanceTablets<NKikimrConfig::THiveConfig::HIVE_TABLET_BALANCE_STRATEGY_RANDOM>, EResourceToBalance::Memory);
     }
+
+    Y_UNIT_TEST(TestStDev) {
+        using TSingleResource = std::tuple<double>;
+
+        TVector<TSingleResource> values(100, 50.0 / 1'000'000);
+        values.front() = 51.0 / 1'000'000;
+
+        double stDev1 = std::get<0>(GetStDev(values));
+
+        std::swap(values.front(), values.back());
+
+        double stDev2 = std::get<0>(GetStDev(values));
+
+        double expectedStDev = sqrt(0.9703) / 1'000'000;
+
+        UNIT_ASSERT_DOUBLES_EQUAL(expectedStDev, stDev1, 1e-6);
+        UNIT_ASSERT_VALUES_EQUAL(stDev1, stDev2);
+    }
 }