diff --git a/src/pkg/math/big/arith.go b/src/pkg/math/big/arith.go
index 0a02a4ef59b..f30951ef0f6 100644
--- a/src/pkg/math/big/arith.go
+++ b/src/pkg/math/big/arith.go
@@ -80,10 +80,22 @@ func mulAddWWW_g(x, y, c Word) (z1, z0 Word) {
 
 // Length of x in bits.
 func bitLen(x Word) (n int) {
-	for ; x >= 0x100; x >>= 8 {
+	for ; x >= 0x8000; x >>= 16 {
+		n += 16
+	}
+	if x >= 0x80 {
+		x >>= 8
 		n += 8
 	}
-	for ; x > 0; x >>= 1 {
+	if x >= 0x8 {
+		x >>= 4
+		n += 4
+	}
+	if x >= 0x2 {
+		x >>= 2
+		n += 2
+	}
+	if x >= 0x1 {
 		n++
 	}
 	return
diff --git a/src/pkg/math/big/arith_test.go b/src/pkg/math/big/arith_test.go
index b6c56c39ef4..106cd92d856 100644
--- a/src/pkg/math/big/arith_test.go
+++ b/src/pkg/math/big/arith_test.go
@@ -333,3 +333,25 @@ func TestMulAddWWW(t *testing.T) {
 		}
 	}
 }
+
+// runs b.N iterations of bitLen called on a Word containing (1 << nbits)-1.
+func benchmarkBitLenN(b *testing.B, nbits uint) {
+	testword := Word((uint64(1) << nbits) - 1)
+	for i := 0; i < b.N; i++ {
+		bitLen(testword)
+	}
+}
+
+// Individual bitLen tests.  Numbers chosen to examine both sides
+// of powers-of-two boundaries.
+func BenchmarkBitLen0(b *testing.B)  { benchmarkBitLenN(b, 0) }
+func BenchmarkBitLen1(b *testing.B)  { benchmarkBitLenN(b, 1) }
+func BenchmarkBitLen2(b *testing.B)  { benchmarkBitLenN(b, 2) }
+func BenchmarkBitLen3(b *testing.B)  { benchmarkBitLenN(b, 3) }
+func BenchmarkBitLen4(b *testing.B)  { benchmarkBitLenN(b, 4) }
+func BenchmarkBitLen5(b *testing.B)  { benchmarkBitLenN(b, 5) }
+func BenchmarkBitLen8(b *testing.B)  { benchmarkBitLenN(b, 8) }
+func BenchmarkBitLen9(b *testing.B)  { benchmarkBitLenN(b, 9) }
+func BenchmarkBitLen16(b *testing.B) { benchmarkBitLenN(b, 16) }
+func BenchmarkBitLen17(b *testing.B) { benchmarkBitLenN(b, 17) }
+func BenchmarkBitLen31(b *testing.B) { benchmarkBitLenN(b, 31) }