diff --git a/src/math/big/int_test.go b/src/math/big/int_test.go
index 9930ed016a..7ef2b3907f 100644
--- a/src/math/big/int_test.go
+++ b/src/math/big/int_test.go
@@ -1727,3 +1727,29 @@ func BenchmarkIntSqr(b *testing.B) {
 		})
 	}
 }
+
+func benchmarkDiv(b *testing.B, aSize, bSize int) {
+	var r = rand.New(rand.NewSource(1234))
+	aa := randInt(r, uint(aSize))
+	bb := randInt(r, uint(bSize))
+	if aa.Cmp(bb) < 0 {
+		aa, bb = bb, aa
+	}
+	x := new(Int)
+	y := new(Int)
+
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		x.DivMod(aa, bb, y)
+	}
+}
+
+func BenchmarkDiv(b *testing.B) {
+	min, max, step := 10, 100000, 10
+	for i := min; i <= max; i *= step {
+		j := 2 * i
+		b.Run(fmt.Sprintf("%d/%d", j, i), func(b *testing.B) {
+			benchmarkDiv(b, j, i)
+		})
+	}
+}
diff --git a/src/math/big/nat.go b/src/math/big/nat.go
index a6f79edccc..5f5cf5c3e4 100644
--- a/src/math/big/nat.go
+++ b/src/math/big/nat.go
@@ -680,43 +680,36 @@ func putNat(x *nat) {
 
 var natPool sync.Pool
 
-// q = (uIn-r)/v, with 0 <= r < y
+// q = (uIn-r)/vIn, with 0 <= r < y
 // Uses z as storage for q, and u as storage for r if possible.
 // See Knuth, Volume 2, section 4.3.1, Algorithm D.
 // Preconditions:
-//    len(v) >= 2
-//    len(uIn) >= len(v)
-func (z nat) divLarge(u, uIn, v nat) (q, r nat) {
-	n := len(v)
+//    len(vIn) >= 2
+//    len(uIn) >= len(vIn)
+//    u must not alias z
+func (z nat) divLarge(u, uIn, vIn nat) (q, r nat) {
+	n := len(vIn)
 	m := len(uIn) - n
 
-	// determine if z can be reused
-	// TODO(gri) should find a better solution - this if statement
-	//           is very costly (see e.g. time pidigits -s -n 10000)
-	if alias(z, u) || alias(z, uIn) || alias(z, v) {
-		z = nil // z is an alias for u or uIn or v - cannot reuse
+	// D1.
+	shift := nlz(vIn[n-1])
+	// do not modify vIn, it may be used by another goroutine simultaneously
+	vp := getNat(n)
+	v := *vp
+	shlVU(v, vIn, shift)
+
+	// u may safely alias uIn or vIn, the value of uIn is used to set u and vIn was already used
+	u = u.make(len(uIn) + 1)
+	u[len(uIn)] = shlVU(u[0:len(uIn)], uIn, shift)
+
+	// z may safely alias uIn or vIn, both values were used already
+	if alias(z, u) {
+		z = nil // z is an alias for u - cannot reuse
 	}
 	q = z.make(m + 1)
 
 	qhatvp := getNat(n + 1)
 	qhatv := *qhatvp
-	if alias(u, uIn) || alias(u, v) {
-		u = nil // u is an alias for uIn or v - cannot reuse
-	}
-	u = u.make(len(uIn) + 1)
-	u.clear() // TODO(gri) no need to clear if we allocated a new u
-
-	// D1.
-	var v1p *nat
-	shift := nlz(v[n-1])
-	if shift > 0 {
-		// do not modify v, it may be used by another goroutine simultaneously
-		v1p = getNat(n)
-		v1 := *v1p
-		shlVU(v1, v, shift)
-		v = v1
-	}
-	u[len(uIn)] = shlVU(u[0:len(uIn)], uIn, shift)
 
 	// D2.
 	vn1 := v[n-1]
@@ -756,9 +749,8 @@ func (z nat) divLarge(u, uIn, v nat) (q, r nat) {
 
 		q[j] = qhat
 	}
-	if v1p != nil {
-		putNat(v1p)
-	}
+
+	putNat(vp)
 	putNat(qhatvp)
 
 	q = q.norm()