[Enhancement](agg-func) Make covar functions get greater precisions

be/src/vec/aggregate_functions/aggregate_function_covar.h

@@ -86,16 +86,26 @@ struct BaseData {
         count = 0;
     }
 
+    static double inf_to_nan(double val) {
+        // This function performs squaring operations, and due to differences in computation order,
+        // it might produce different values such as inf and nan.
+        // For performance reasons, we are uniformly changing it to nan
+        if (std::isinf(val)) [[unlikely]] {
+            return std::nan("");
+        }
+        return val;
+    };
+
     // Cov(X, Y) = E(XY) - E(X)E(Y)
     double get_pop_result() const {
         if (count == 1) {
             return 0.0;
         }
-        return sum_xy / count - sum_x * sum_y / (count * count);
+        return inf_to_nan((double)(sum_xy / count - sum_x / count * sum_y / count));
     }
 
     double get_samp_result() const {
-        return sum_xy / (count - 1) - sum_x * sum_y / (count * (count - 1));
+        return inf_to_nan((double)(sum_xy / (count - 1) - sum_x / count * sum_y / (count - 1)));
     }
 
     void merge(const BaseData& rhs) {
@@ -122,10 +132,10 @@ struct BaseData {
         count += 1;
     }
 
-    double sum_x;
-    double sum_y;
-    double sum_xy;
-    int64_t count;
+    long double sum_x {};
+    long double sum_y {};
+    long double sum_xy {};
+    int64_t count {};
 };
 
 template <typename T, typename Data>

be/src/vec/aggregate_functions/aggregate_function_stddev.h

@@ -78,7 +78,7 @@ struct BaseData {
             // it might produce different values such as inf and nan.
             // In MySQL, this will directly result in an error due to exceeding the double range.
             // For performance reasons, we are uniformly changing it to nan
-            if (std::isinf(val)) {
+            if (std::isinf(val)) [[unlikely]] {
                 return std::nan("");
             }
             return val;
@@ -107,8 +107,8 @@ struct BaseData {
         if (rhs.count == 0) {
             return;
         }
-        double delta = mean - rhs.mean;
-        double sum_count = count + rhs.count;
+        long double delta = mean - rhs.mean;
+        long double sum_count = count + rhs.count;
         mean = rhs.mean + delta * count / sum_count;
         m2 = rhs.m2 + m2 + (delta * delta) * rhs.count * count / sum_count;
         count = int64_t(sum_count);
@@ -119,16 +119,16 @@ struct BaseData {
                 assert_cast<const ColumnVector<T>&, TypeCheckOnRelease::DISABLE>(*column);
         double source_data = sources.get_data()[row_num];
 
-        double delta = source_data - mean;
-        double r = delta / (1 + count);
+        long double delta = source_data - mean;
+        long double r = delta / (1 + count);
         mean += r;
         m2 += count * delta * r;
         count += 1;
     }
 
-    double mean;
-    double m2;
-    int64_t count;
+    long double mean {};
+    long double m2 {};
+    int64_t count {};
 };
 
 template <typename T, typename Data>