refactor(rust): Add remove_one to VarState for use in rolling variance

crates/polars-compute/src/var_cov.rs

@@ -61,7 +61,7 @@ impl VarState {
         }
     }
 
-    pub fn add_one(&mut self, x: f64) {
+    pub fn insert_one(&mut self, x: f64) {
         // Just a specialized version of
         // self.combine(&Self { weight: 1.0, mean: x, dp: 0.0 })
         let new_weight = self.weight + 1.0;
@@ -72,6 +72,17 @@ impl VarState {
         self.mean = new_mean;
     }
 
+    pub fn remove_one(&mut self, x: f64) {
+        // Just a specialized version of
+        // self.combine(&Self { weight: -1.0, mean: x, dp: 0.0 })
+        let new_weight = self.weight - 1.0;
+        let delta_mean = self.mean - x;
+        let new_mean = self.mean - delta_mean / new_weight;
+        self.dp += (new_mean - x) * delta_mean;
+        self.weight = new_weight;
+        self.mean = new_mean;
+    }
+
     pub fn combine(&mut self, other: &Self) {
         if other.weight == 0.0 {
             return;

crates/polars-expr/src/reduce/var_std.rs

@@ -77,7 +77,7 @@ impl<T: PolarsNumericType> Reducer for VarStdReducer<T> {
     #[inline(always)]
     fn reduce_one(&self, a: &mut Self::Value, b: Option<T::Native>, _seq_id: u64) {
         if let Some(x) = b {
-            a.add_one(x.as_());
+            a.insert_one(x.as_());
         }
     }