X Don't move data to new page on split if load is append-like

Else a lot of time is then spent moving data forth and back with memcpy
on further appends.

btree.go

@@ -366,6 +366,12 @@ func (t *Tree) Delete(k interface{} /*K*/) (ok bool) {
 		}
 	}
 
+	// don't leave previously active data page with < 50% load
+	if t.hitD != nil && t.hitD.c < kd && t.hitP != nil {
+		//println("refill")
+		t.refill(t.hitP, t.hitD, t.hitPi)
+	}
+
 	// data page not quickly found - search and descent from root
 	pi := -1
 	var p *x
@@ -744,6 +750,12 @@ func (t *Tree) Set(k interface{} /*K*/, v interface{} /*V*/) {
 		}
 	}
 
+	// don't leave previously active data page with < 50% load
+	if t.hitD != nil && t.hitD.c < kd && t.hitP != nil {
+		//println("refill")
+		t.refill(t.hitP, t.hitD, t.hitPi)
+	}
+
 	// data page not quickly found - search and descent from root
 	pi := -1
 	var p *x
@@ -895,6 +907,12 @@ func (t *Tree) Put(k interface{} /*K*/, upd func(oldV interface{} /*V*/, exists
 		}
 	}
 
+	// don't leave previously active data page with < 50% load
+	if t.hitD != nil && t.hitD.c < kd && t.hitP != nil {
+		//println("refill")
+		t.refill(t.hitP, t.hitD, t.hitPi)
+	}
+
 	// data page not quickly found - search and descent from root
 	t.hitKminSet, t.hitKmaxSet = false, false // initially [-∞, +∞)
 	t.hitPKminSet, t.hitPKmaxSet = false, false
@@ -984,13 +1002,19 @@ func (t *Tree) split(p *x, q *d, pi, i int, k interface{} /*K*/, v interface{} /
 	q.n = r
 	r.p = q
 
+	// don't copy on sequential bulk-set pattern
+	if i == 2*kd {
+		t.insert(r, 0, k, v)
+	} else {
 		copy(r.d[:], q.d[kd:2*kd])
 		for i := range q.d[kd:] {
 			q.d[kd+i] = zde
 		}
 		q.c = kd
 		r.c = kd
+	}
 
+	// XXX vs ^^^ (not adding elements)
 	if pi >= 0 {
 		p.insert(pi, r.d[0].k, r)
 	} else {
@@ -1002,7 +1026,10 @@ func (t *Tree) split(p *x, q *d, pi, i int, k interface{} /*K*/, v interface{} /
 	}
 
 	if i > kd {
+		// XXX vvv try to merge with ^^^ t.insert(r, 0, k, v)
+		if i < 2*kd {
 			t.insert(r, i-kd, k, v)
+		}
 		t.setHitKmin(p.x[pi].k)
 		if pi+1 < p.c { // k=+∞ @p.c
 			t.setHitKmax(p.x[pi+1].k)
@@ -1057,6 +1084,8 @@ func (t *Tree) underflow(p *x, q *d, pi int) {
 	t.ver++
 	l, r := p.siblings(pi)
 
+	// TODO don't move 1 elements for bulk-delete patterb (see split for bulk-set case)
+
 	if l != nil && l.c+q.c >= 2*kd {
 		l.mvR(q, 1)
 		p.x[pi-1].k = q.d[0].k
@@ -1177,6 +1206,47 @@ func (t *Tree) underflowX(p *x, q *x, pi int, i int) (*x, int) {
 	return q, i
 }
 
+// refill refills data page to have >= 50% load taking data entries from siblings
+// if siblings have not enough entries for such refill, the data page in question is concatenated into one of them.
+// XXX naming -> fillup ?
+func (t *Tree) refill(p *x, q *d, pi int) {
+	t.ver++
+	l, r := p.siblings(pi)
+
+	δl := 0
+	δr := 0
+	if l != nil {
+		δl = l.c - kd
+	}
+	if r != nil {
+		δr = r.c - kd
+	}
+
+	if q.c + δl + δr < kd {
+		// cannot refill - concatenate into l or r
+		if l != nil {
+			t.cat(p, l, q, pi-1)
+		} else {
+			t.cat(p, q, r, pi)
+		}
+		return
+	}
+
+	// refill from siblings
+	δ := kd - q.c
+	δl = δ * δl / (δl + δr)
+	δr = δ - δl
+
+	if δl != 0 {
+		l.mvR(q, δl)
+		p.x[pi-1].k = q.d[0].k
+	}
+	if δr != 0 {
+		q.mvL(r, δr)
+		p.x[pi].k = r.d[0].k
+	}
+}
+
 // ----------------------------------------------------------------- Enumerator
 
 // Close recycles e to a pool for possible later reuse. No references to e

example/int.go

@@ -366,6 +366,12 @@ func (t *Tree) Delete(k int) (ok bool) {
 		}
 	}
 
+	// don't leave previously active data page with < 50% load
+	if t.hitD != nil && t.hitD.c < kd && t.hitP != nil {
+		//println("refill")
+		t.refill(t.hitP, t.hitD, t.hitPi)
+	}
+
 	// data page not quickly found - search and descent from root
 	pi := -1
 	var p *x
@@ -744,6 +750,12 @@ func (t *Tree) Set(k int, v int) {
 		}
 	}
 
+	// don't leave previously active data page with < 50% load
+	if t.hitD != nil && t.hitD.c < kd && t.hitP != nil {
+		//println("refill")
+		t.refill(t.hitP, t.hitD, t.hitPi)
+	}
+
 	// data page not quickly found - search and descent from root
 	pi := -1
 	var p *x
@@ -895,6 +907,12 @@ func (t *Tree) Put(k int, upd func(oldV int, exists bool) (newV int, write bool)
 		}
 	}
 
+	// don't leave previously active data page with < 50% load
+	if t.hitD != nil && t.hitD.c < kd && t.hitP != nil {
+		//println("refill")
+		t.refill(t.hitP, t.hitD, t.hitPi)
+	}
+
 	// data page not quickly found - search and descent from root
 	t.hitKminSet, t.hitKmaxSet = false, false // initially [-∞, +∞)
 	t.hitPKminSet, t.hitPKmaxSet = false, false
@@ -984,13 +1002,19 @@ func (t *Tree) split(p *x, q *d, pi, i int, k int, v int) {
 	q.n = r
 	r.p = q
 
+	// don't copy on sequential bulk-set pattern
+	if i == 2*kd {
+		t.insert(r, 0, k, v)
+	} else {
 		copy(r.d[:], q.d[kd:2*kd])
 		for i := range q.d[kd:] {
 			q.d[kd+i] = zde
 		}
 		q.c = kd
 		r.c = kd
+	}
 
+	// XXX vs ^^^ (not adding elements)
 	if pi >= 0 {
 		p.insert(pi, r.d[0].k, r)
 	} else {
@@ -1002,7 +1026,10 @@ func (t *Tree) split(p *x, q *d, pi, i int, k int, v int) {
 	}
 
 	if i > kd {
+		// XXX vvv try to merge with ^^^ t.insert(r, 0, k, v)
+		if i < 2*kd {
 			t.insert(r, i-kd, k, v)
+		}
 		t.setHitKmin(p.x[pi].k)
 		if pi+1 < p.c { // k=+∞ @p.c
 			t.setHitKmax(p.x[pi+1].k)
@@ -1057,6 +1084,8 @@ func (t *Tree) underflow(p *x, q *d, pi int) {
 	t.ver++
 	l, r := p.siblings(pi)
 
+	// TODO don't move 1 elements for bulk-delete patterb (see split for bulk-set case)
+
 	if l != nil && l.c+q.c >= 2*kd {
 		l.mvR(q, 1)
 		p.x[pi-1].k = q.d[0].k
@@ -1177,6 +1206,47 @@ func (t *Tree) underflowX(p *x, q *x, pi int, i int) (*x, int) {
 	return q, i
 }
 
+// refill refills data page to have >= 50% load taking data entries from siblings
+// if siblings have not enough entries for such refill, the data page in question is concatenated into one of them.
+// XXX naming -> fillup ?
+func (t *Tree) refill(p *x, q *d, pi int) {
+	t.ver++
+	l, r := p.siblings(pi)
+
+	δl := 0
+	δr := 0
+	if l != nil {
+		δl = l.c - kd
+	}
+	if r != nil {
+		δr = r.c - kd
+	}
+
+	if q.c + δl + δr < kd {
+		// cannot refill - concatenate into l or r
+		if l != nil {
+			t.cat(p, l, q, pi-1)
+		} else {
+			t.cat(p, q, r, pi)
+		}
+		return
+	}
+
+	// refill from siblings
+	δ := kd - q.c
+	δl = δ * δl / (δl + δr)
+	δr = δ - δl
+
+	if δl != 0 {
+		l.mvR(q, δl)
+		p.x[pi-1].k = q.d[0].k
+	}
+	if δr != 0 {
+		q.mvL(r, δr)
+		p.x[pi].k = r.d[0].k
+	}
+}
+
 // ----------------------------------------------------------------- Enumerator
 
 // Close recycles e to a pool for possible later reuse. No references to e