math/big: more cleanups (msbxx, nlzxx functions)

Change-Id: Ibace718452b6dc029c5af5240117f5fc794c38cf
Reviewed-on: https://go-review.googlesource.com/10388Reviewed-by: Alan Donovan <adonovan@google.com>

src/math/big/arith.go

@@ -107,11 +107,26 @@ func log2(x Word) int {
 	return bitLen(x) - 1
 }
 
-// Number of leading zeros in x.
-func leadingZeros(x Word) uint {
+// nlz returns the number of leading zeros in x.
+func nlz(x Word) uint {
 	return uint(_W - bitLen(x))
 }
 
+// nlz64 returns the number of leading zeros in x.
+func nlz64(x uint64) uint {
+	switch _W {
+	case 32:
+		w := x >> 32
+		if w == 0 {
+			return 32 + nlz(Word(x))
+		}
+		return nlz(Word(w))
+	case 64:
+		return nlz(Word(x))
+	}
+	panic("unreachable")
+}
+
 // q = (u1<<_W + u0 - r)/y
 // Adapted from Warren, Hacker's Delight, p. 152.
 func divWW_g(u1, u0, v Word) (q, r Word) {
@@ -119,7 +134,7 @@ func divWW_g(u1, u0, v Word) (q, r Word) {
 		return 1<<_W - 1, 1<<_W - 1
 	}
 
-	s := leadingZeros(v)
+	s := nlz(v)
 	v <<= s
 
 	vn1 := v >> _W2

src/math/big/float.go

@@ -525,25 +525,6 @@ func (z *Float) round(sbit uint) {
 	return
 }
 
-// nlz returns the number of leading zero bits in x.
-func nlz(x Word) uint {
-	return _W - uint(bitLen(x))
-}
-
-func nlz64(x uint64) uint {
-	// TODO(gri) this can be done more nicely
-	if _W == 32 {
-		if x>>32 == 0 {
-			return 32 + nlz(Word(x))
-		}
-		return nlz(Word(x >> 32))
-	}
-	if _W == 64 {
-		return nlz(Word(x))
-	}
-	panic("unreachable")
-}
-
 func (z *Float) setBits64(neg bool, x uint64) *Float {
 	if z.prec == 0 {
 		z.prec = 64
@@ -732,25 +713,44 @@ func (z *Float) Copy(x *Float) *Float {
 	return z
 }
 
-func high32(x nat) uint32 {
-	// TODO(gri) This can be done more efficiently on 32bit platforms.
-	return uint32(high64(x) >> 32)
+// msb32 returns the 32 most significant bits of x.
+func msb32(x nat) uint32 {
+	i := len(x) - 1
+	if i < 0 {
+		return 0
+	}
+	if debugFloat && x[i]&(1<<(_W-1)) == 0 {
+		panic("x not normalized")
+	}
+	switch _W {
+	case 32:
+		return uint32(x[i])
+	case 64:
+		return uint32(x[i] >> 32)
+	}
+	panic("unreachable")
 }
 
-func high64(x nat) uint64 {
-	i := len(x)
-	if i == 0 {
+// msb64 returns the 64 most significant bits of x.
+func msb64(x nat) uint64 {
+	i := len(x) - 1
+	if i < 0 {
 		return 0
 	}
-	// i > 0
-	v := uint64(x[i-1])
-	if _W == 32 {
-		v <<= 32
-		if i > 1 {
-			v |= uint64(x[i-2])
+	if debugFloat && x[i]&(1<<(_W-1)) == 0 {
+		panic("x not normalized")
+	}
+	switch _W {
+	case 32:
+		v := uint64(x[i]) << 32
+		if i > 0 {
+			v |= uint64(x[i-1])
 		}
+		return v
+	case 64:
+		return uint64(x[i])
 	}
-	return v
+	panic("unreachable")
 }
 
 // Uint64 returns the unsigned integer resulting from truncating x
@@ -776,7 +776,7 @@ func (x *Float) Uint64() (uint64, Accuracy) {
 		// 1 <= x < Inf
 		if x.exp <= 64 {
 			// u = trunc(x) fits into a uint64
-			u := high64(x.mant) >> (64 - uint32(x.exp))
+			u := msb64(x.mant) >> (64 - uint32(x.exp))
 			if x.MinPrec() <= 64 {
 				return u, Exact
 			}
@@ -821,7 +821,7 @@ func (x *Float) Int64() (int64, Accuracy) {
 		// 1 <= |x| < +Inf
 		if x.exp <= 63 {
 			// i = trunc(x) fits into an int64 (excluding math.MinInt64)
-			i := int64(high64(x.mant) >> (64 - uint32(x.exp)))
+			i := int64(msb64(x.mant) >> (64 - uint32(x.exp)))
 			if x.neg {
 				i = -i
 			}
@@ -934,11 +934,11 @@ func (x *Float) Float32() (float32, Accuracy) {
 				return 0.0, Below
 			}
 			// bexp = 0
-			mant = high32(r.mant) >> (fbits - r.prec)
+			mant = msb32(r.mant) >> (fbits - r.prec)
 		} else {
 			// normal number: emin <= e <= emax
 			bexp = uint32(e+bias) << mbits
-			mant = high32(r.mant) >> ebits & (1<<mbits - 1) // cut off msb (implicit 1 bit)
+			mant = msb32(r.mant) >> ebits & (1<<mbits - 1) // cut off msb (implicit 1 bit)
 		}
 
 		return math.Float32frombits(sign | bexp | mant), r.acc
@@ -1041,11 +1041,11 @@ func (x *Float) Float64() (float64, Accuracy) {
 				return 0.0, Below
 			}
 			// bexp = 0
-			mant = high64(r.mant) >> (fbits - r.prec)
+			mant = msb64(r.mant) >> (fbits - r.prec)
 		} else {
 			// normal number: emin <= e <= emax
 			bexp = uint64(e+bias) << mbits
-			mant = high64(r.mant) >> ebits & (1<<mbits - 1) // cut off msb (implicit 1 bit)
+			mant = msb64(r.mant) >> ebits & (1<<mbits - 1) // cut off msb (implicit 1 bit)
 		}
 
 		return math.Float64frombits(sign | bexp | mant), r.acc

src/math/big/nat.go

@@ -572,7 +572,7 @@ func (z nat) divLarge(u, uIn, v nat) (q, r nat) {
 	u.clear() // TODO(gri) no need to clear if we allocated a new u
 
 	// D1.
-	shift := leadingZeros(v[n-1])
+	shift := nlz(v[n-1])
 	if shift > 0 {
 		// do not modify v, it may be used by another goroutine simultaneously
 		v1 := make(nat, n)
@@ -942,7 +942,7 @@ func (z nat) expNN(x, y, m nat) nat {
 	}
 
 	v := y[len(y)-1] // v > 0 because y is normalized and y > 0
-	shift := leadingZeros(v) + 1
+	shift := nlz(v) + 1
 	v <<= shift
 	var q nat
 

src/math/big/nat_test.go

@@ -205,11 +205,11 @@ func BenchmarkMul(b *testing.B) {
 	}
 }
 
-func TestLeadingZeros(t *testing.T) {
+func TestNLZ(t *testing.T) {
 	var x Word = _B >> 1
 	for i := 0; i <= _W; i++ {
-		if int(leadingZeros(x)) != i {
-			t.Errorf("failed at %x: got %d want %d", x, leadingZeros(x), i)
+		if int(nlz(x)) != i {
+			t.Errorf("failed at %x: got %d want %d", x, nlz(x), i)
 		}
 		x >>= 1
 	}