diff --git a/src/math/big/gcd_test.go b/src/math/big/gcd_test.go
index c0b9f58..a929bf5 100644
--- a/src/math/big/gcd_test.go
+++ b/src/math/big/gcd_test.go
@@ -20,13 +20,27 @@
 }
 
 func runGCD(b *testing.B, aSize, bSize uint) {
+	b.Run("WithoutXY", func(b *testing.B) {
+		runGCDExt(b, aSize, bSize, false)
+	})
+	b.Run("WithXY", func(b *testing.B) {
+		runGCDExt(b, aSize, bSize, true)
+	})
+}
+
+func runGCDExt(b *testing.B, aSize, bSize uint, calcXY bool) {
 	b.StopTimer()
 	var r = rand.New(rand.NewSource(1234))
 	aa := randInt(r, aSize)
 	bb := randInt(r, bSize)
+	var x, y *Int
+	if calcXY {
+		x = new(Int)
+		y = new(Int)
+	}
 	b.StartTimer()
 	for i := 0; i < b.N; i++ {
-		new(Int).GCD(nil, nil, aa, bb)
+		new(Int).GCD(x, y, aa, bb)
 	}
 }
 
diff --git a/src/math/big/int.go b/src/math/big/int.go
index 67ab704..f2a75d1 100644
--- a/src/math/big/int.go
+++ b/src/math/big/int.go
@@ -459,11 +459,11 @@
 	q := new(Int)
 	temp := new(Int)
 
+	r := new(Int)
 	for len(B.abs) > 0 {
-		r := new(Int)
 		q, r = q.QuoRem(A, B, r)
 
-		A, B = B, r
+		A, B, r = B, r, A
 
 		temp.Set(X)
 		X.Mul(X, q)
diff --git a/src/math/big/nat.go b/src/math/big/nat.go
index 7668b64..2e65d2a7 100644
--- a/src/math/big/nat.go
+++ b/src/math/big/nat.go
@@ -8,7 +8,10 @@
 
 package big
 
-import "math/rand"
+import (
+	"math/rand"
+	"sync"
+)
 
 // An unsigned integer x of the form
 //
@@ -539,6 +542,21 @@
 	return
 }
 
+// getNat returns a nat of len n. The contents may not be zero.
+func getNat(n int) nat {
+	var z nat
+	if v := natPool.Get(); v != nil {
+		z = v.(nat)
+	}
+	return z.make(n)
+}
+
+func putNat(x nat) {
+	natPool.Put(x)
+}
+
+var natPool sync.Pool
+
 // q = (uIn-r)/v, 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.
@@ -557,7 +575,7 @@
 	}
 	q = z.make(m + 1)
 
-	qhatv := make(nat, n+1)
+	qhatv := getNat(n + 1)
 	if alias(u, uIn) || alias(u, v) {
 		u = nil // u is an alias for uIn or v - cannot reuse
 	}
@@ -565,10 +583,11 @@
 	u.clear() // TODO(gri) no need to clear if we allocated a new u
 
 	// D1.
+	var v1 nat
 	shift := nlz(v[n-1])
 	if shift > 0 {
 		// do not modify v, it may be used by another goroutine simultaneously
-		v1 := make(nat, n)
+		v1 = getNat(n)
 		shlVU(v1, v, shift)
 		v = v1
 	}
@@ -609,6 +628,10 @@
 
 		q[j] = qhat
 	}
+	if v1 != nil {
+		putNat(v1)
+	}
+	putNat(qhatv)
 
 	q = q.norm()
 	shrVU(u, u, shift)