diff --git a/src/pkg/big/arith.go b/src/pkg/big/arith.go
index 1c481caabc6..d5060bb88fa 100644
--- a/src/pkg/big/arith.go
+++ b/src/pkg/big/arith.go
@@ -211,19 +211,32 @@ func divStep(x1, x0, y Word) (q, r Word) {
 }
 
 
-// Number of leading zeros in x.
-func leadingZeros(x Word) (n uint) {
-	if x == 0 {
-		return _W
+// Length of x in bits.
+func bitLen(x Word) (n int) {
+	for ; x >= 0x100; x >>= 8 {
+		n += 8
 	}
-	for x&(1<<(_W-1)) == 0 {
+	for ; x > 0; x >>= 1 {
 		n++
-		x <<= 1
 	}
 	return
 }
 
 
+// log2 computes the integer binary logarithm of x.
+// The result is the integer n for which 2^n <= x < 2^(n+1).
+// If x == 0, the result is -1.
+func log2(x Word) int {
+	return bitLen(x) - 1
+}
+
+
+// Number of leading zeros in x.
+func leadingZeros(x Word) uint {
+	return uint(_W - bitLen(x))
+}
+
+
 // q = (x1<<_W + x0 - r)/y
 func divWW_g(x1, x0, y Word) (q, r Word) {
 	if x1 == 0 {
diff --git a/src/pkg/big/nat.go b/src/pkg/big/nat.go
index ff8e806b242..acec53d5b52 100644
--- a/src/pkg/big/nat.go
+++ b/src/pkg/big/nat.go
@@ -165,9 +165,8 @@ func (z nat) sub(x, y nat) nat {
 	if c != 0 {
 		panic("underflow")
 	}
-	z = z.norm()
 
-	return z
+	return z.norm()
 }
 
 
@@ -495,7 +494,7 @@ func (z nat) divW(x nat, y Word) (q nat, r Word) {
 		q = z.set(x) // result is x
 		return
 	case m == 0:
-		q = z.set(nil) // result is 0
+		q = z.make(0) // result is 0
 		return
 	}
 	// m > 0
@@ -553,10 +552,10 @@ func (z nat) divLarge(z2, uIn, v nat) (q, r nat) {
 	q = z.make(m + 1)
 
 	// D1.
-	shift := uint(leadingZeroBits(v[n-1]))
+	shift := leadingZeros(v[n-1])
 	v.shiftLeftDeprecated(v, shift)
 	u.shiftLeftDeprecated(uIn, shift)
-	u[len(uIn)] = uIn[len(uIn)-1] >> (_W - uint(shift))
+	u[len(uIn)] = uIn[len(uIn)-1] >> (_W - shift)
 
 	// D2.
 	for j := m; j >= 0; j-- {
@@ -605,26 +604,12 @@ func (z nat) divLarge(z2, uIn, v nat) (q, r nat) {
 }
 
 
-// log2 computes the integer binary logarithm of x.
-// The result is the integer n for which 2^n <= x < 2^(n+1).
-// If x == 0, the result is -1.
-func log2(x Word) int {
-	n := -1
-	for ; x > 0; x >>= 1 {
-		n++
-	}
-	return n
-}
-
-
-// log2 computes the integer binary logarithm of x.
-// The result is the integer n for which 2^n <= x < 2^(n+1).
-// If x == 0, the result is -1.
-func (x nat) log2() int {
+// Length of x in bits. x must be normalized.
+func (x nat) bitLen() int {
 	if i := len(x) - 1; i >= 0 {
-		return i*_W + log2(x[i])
+		return i*_W + bitLen(x[i])
 	}
-	return -1
+	return 0
 }
 
 
@@ -703,7 +688,7 @@ func (x nat) string(base int) string {
 	}
 
 	// allocate buffer for conversion
-	i := (x.log2()+1)/log2(Word(base)) + 1 // +1: round up
+	i := x.bitLen()/log2(Word(base)) + 1 // +1: round up
 	s := make([]byte, i)
 
 	// don't destroy x
@@ -721,24 +706,6 @@ func (x nat) string(base int) string {
 }
 
 
-// leadingZeroBits returns the number of leading zero bits in x.
-func leadingZeroBits(x Word) int {
-	c := 0
-	if x < 1<<(_W/2) {
-		x <<= _W / 2
-		c = _W / 2
-	}
-
-	for i := 0; x != 0; i++ {
-		if x&(1<<(_W-1)) != 0 {
-			return i + c
-		}
-		x <<= 1
-	}
-
-	return _W
-}
-
 const deBruijn32 = 0x077CB531
 
 var deBruijn32Lookup = []byte{
@@ -997,16 +964,6 @@ func (z nat) expNN(x, y, m nat) nat {
 }
 
 
-// len returns the bit length of z.
-func (z nat) len() int {
-	if len(z) == 0 {
-		return 0
-	}
-
-	return (len(z)-1)*_W + (_W - leadingZeroBits(z[len(z)-1]))
-}
-
-
 // probablyPrime performs reps Miller-Rabin tests to check whether n is prime.
 // If it returns true, n is prime with probability 1 - 1/4^reps.
 // If it returns false, n is not prime.
@@ -1063,7 +1020,7 @@ func (n nat) probablyPrime(reps int) bool {
 	rand := rand.New(rand.NewSource(int64(n[0])))
 
 	var x, y, quotient nat
-	nm3Len := nm3.len()
+	nm3Len := nm3.bitLen()
 
 NextRandom:
 	for i := 0; i < reps; i++ {
diff --git a/src/pkg/big/nat_test.go b/src/pkg/big/nat_test.go
index bf637b0daa9..f9adf3dd499 100644
--- a/src/pkg/big/nat_test.go
+++ b/src/pkg/big/nat_test.go
@@ -209,11 +209,11 @@ func TestString(t *testing.T) {
 }
 
 
-func TestLeadingZeroBits(t *testing.T) {
-	var x Word = 1 << (_W - 1)
+func TestLeadingZeros(t *testing.T) {
+	var x Word = _B >> 1
 	for i := 0; i <= _W; i++ {
-		if leadingZeroBits(x) != i {
-			t.Errorf("failed at %x: got %d want %d", x, leadingZeroBits(x), i)
+		if int(leadingZeros(x)) != i {
+			t.Errorf("failed at %x: got %d want %d", x, leadingZeros(x), i)
 		}
 		x >>= 1
 	}