Fix issue.

ext/stats/percentile.go

@@ -11,6 +11,9 @@ import (
 	"github.com/ncruces/sort/quick"
 )
 
+// Compatible with:
+// https://sqlite.org/src/file/ext/misc/percentile.c
+
 const (
 	median = iota
 	percentile_100

ext/stats/welford.go

@@ -7,12 +7,10 @@ import (
 )
 
 // Welford's algorithm with Kahan summation:
+// The effect of truncation in statistical computation [van Reeken, AJ 1970]
 // https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Welford's_online_algorithm
 // https://en.wikipedia.org/wiki/Kahan_summation_algorithm
 
-// See also:
-// https://duckdb.org/docs/sql/aggregates.html#statistical-aggregates
-
 type welford struct {
 	m1, m2 kahan
 	n      int64
@@ -39,17 +37,22 @@ func (w welford) stddev_samp() float64 {
 }
 
 func (w *welford) enqueue(x float64) {
-	w.n++
+	n := w.n + 1
+	w.n = n
 	d1 := x - w.m1.hi - w.m1.lo
-	w.m1.add(d1 / float64(w.n))
+	w.m1.add(d1 / float64(n))
 	d2 := x - w.m1.hi - w.m1.lo
 	w.m2.add(d1 * d2)
 }
 
 func (w *welford) dequeue(x float64) {
-	w.n--
+	n := w.n - 1
+	w.n = n
+	if n <= 0 {
+		return
+	}
 	d1 := x - w.m1.hi - w.m1.lo
-	w.m1.sub(d1 / float64(w.n))
+	w.m1.sub(d1 / float64(n))
 	d2 := x - w.m1.hi - w.m1.lo
 	w.m2.sub(d1 * d2)
 }
@@ -139,11 +142,12 @@ func (w welford2) regr_json() string {
 }
 
 func (w *welford2) enqueue(y, x float64) {
-	w.n++
+	n := w.n + 1
+	w.n = n
 	d1y := y - w.m1y.hi - w.m1y.lo
 	d1x := x - w.m1x.hi - w.m1x.lo
-	w.m1y.add(d1y / float64(w.n))
-	w.m1x.add(d1x / float64(w.n))
+	w.m1y.add(d1y / float64(n))
+	w.m1x.add(d1x / float64(n))
 	d2y := y - w.m1y.hi - w.m1y.lo
 	d2x := x - w.m1x.hi - w.m1x.lo
 	w.m2y.add(d1y * d2y)
@@ -152,11 +156,15 @@ func (w *welford2) enqueue(y, x float64) {
 }
 
 func (w *welford2) dequeue(y, x float64) {
-	w.n--
+	n := w.n - 1
+	w.n = n
+	if n <= 0 {
+		return
+	}
 	d1y := y - w.m1y.hi - w.m1y.lo
 	d1x := x - w.m1x.hi - w.m1x.lo
-	w.m1y.sub(d1y / float64(w.n))
-	w.m1x.sub(d1x / float64(w.n))
+	w.m1y.sub(d1y / float64(n))
+	w.m1x.sub(d1x / float64(n))
 	d2y := y - w.m1y.hi - w.m1y.lo
 	d2x := x - w.m1x.hi - w.m1x.lo
 	w.m2y.sub(d1y * d2y)

ext/stats/welford_test.go

@@ -37,6 +37,16 @@ func Test_welford(t *testing.T) {
 	if s1.var_pop() != s2.var_pop() {
 		t.Errorf("got %v, want %v", s1, s2)
 	}
+
+	s1.dequeue(16)
+	s1.dequeue(7)
+	s1.dequeue(13)
+	s1.enqueue(16)
+	s1.enqueue(7)
+	s1.enqueue(13)
+	if s1.var_pop() != s2.var_pop() {
+		t.Errorf("got %v, want %v", s1, s2)
+	}
 }
 
 func Test_covar(t *testing.T) {
@@ -65,6 +75,18 @@ func Test_covar(t *testing.T) {
 	if c1.covar_pop() != c2.covar_pop() {
 		t.Errorf("got %v, want %v", c1.covar_pop(), c2.covar_pop())
 	}
+
+	c1.dequeue(2, 60)
+	c1.dequeue(5, 80)
+	c1.dequeue(4, 75)
+	c1.dequeue(7, 90)
+	c1.enqueue(2, 60)
+	c1.enqueue(5, 80)
+	c1.enqueue(4, 75)
+	c1.enqueue(7, 90)
+	if c1.covar_pop() != c2.covar_pop() {
+		t.Errorf("got %v, want %v", c1.covar_pop(), c2.covar_pop())
+	}
 }
 
 func Test_correlation(t *testing.T) {