math/big: minor performance tuning

Reuse temporary slice to avoid extra allocations
(originally done correctly by remyoudompheng@gmail.com
in https://golang.org/cl/6345075/).

benchmark           old ns/op    new ns/op    delta
BenchmarkHilbert      6252790      6262304   +0.15%
BenchmarkMul         45827438     45301002   -1.15%

R=r
CC=golang-dev
https://golang.org/cl/6346097

src/pkg/math/big/nat.go

@@ -438,8 +438,9 @@ func (z nat) mul(x, y nat) nat {
 
 		// add x0*y1*b
 		x0 := x0.norm()
-		y1 := y[k:] // y1 is normalized because y is
-		addAt(z, t.mul(x0, y1), k)
+		y1 := y[k:]       // y1 is normalized because y is
+		t = t.mul(x0, y1) // update t so we don't lose t's underlying array
+		addAt(z, t, k)
 
 		// add xi*y0<<i, xi*y1*b<<(i+k)
 		y0 := y0.norm()
@@ -449,8 +450,10 @@ func (z nat) mul(x, y nat) nat {
 				xi = xi[:k]
 			}
 			xi = xi.norm()
-			addAt(z, t.mul(xi, y0), i)
-			addAt(z, t.mul(xi, y1), i+k)
+			t = t.mul(xi, y0)
+			addAt(z, t, i)
+			t = t.mul(xi, y1)
+			addAt(z, t, i+k)
 		}
 	}
 
@@ -1232,7 +1235,7 @@ func (z nat) random(rand *rand.Rand, limit nat, n int) nat {
 // reuses the storage of z if possible.
 func (z nat) expNN(x, y, m nat) nat {
 	if alias(z, x) || alias(z, y) {
-		// We cannot allow in place modification of x or y.
+		// We cannot allow in-place modification of x or y.
 		z = nil
 	}
 

src/pkg/math/big/nat_test.go

@@ -179,7 +179,7 @@ func allocBytes(f func()) uint64 {
 
 // TestMulUnbalanced tests that multiplying numbers of different lengths
 // does not cause deep recursion and in turn allocate too much memory.
-// test case for issue 3807
+// Test case for issue 3807.
 func TestMulUnbalanced(t *testing.T) {
 	x := rndNat(50000)
 	y := rndNat(40)
@@ -201,7 +201,7 @@ func rndNat(n int) nat {
 	for i := 0; i < n; i++ {
 		x[i] = Word(rnd.Int63()<<1 + rnd.Int63n(2))
 	}
-	return x
+	return x.norm()
 }
 
 func BenchmarkMul(b *testing.B) {