math/big: better test coverage, misc. cleanups

Change-Id: I4ce5cee63093d917095bf90f4e11123f7ec0f93c
Reviewed-on: https://go-review.googlesource.com/2964Reviewed-by: Alan Donovan <adonovan@google.com>

src/math/big/int.go

@@ -736,7 +736,7 @@ func (z *Int) binaryGCD(a, b *Int) *Int {
 
 // ProbablyPrime performs n Miller-Rabin tests to check whether x is prime.
 // If it returns true, x is prime with probability 1 - 1/4^n.
-// If it returns false, x is not prime. n must be >0.
+// If it returns false, x is not prime. n must be > 0.
 func (x *Int) ProbablyPrime(n int) bool {
 	if n <= 0 {
 		panic("non-positive n for ProbablyPrime")

src/math/big/int_test.go

@@ -621,6 +621,44 @@ func TestDivisionSigns(t *testing.T) {
 	}
 }
 
+var bitTests = []nat{
+	nil,
+	{0},
+	{1},
+	{0, 1, 2, 3, 4},
+	{4, 3, 2, 1, 0},
+	{4, 3, 2, 1, 0, 0, 0, 0},
+}
+
+func norm(x nat) nat {
+	i := len(x)
+	for i > 0 && x[i-1] == 0 {
+		i--
+	}
+	return x[:i]
+}
+
+func TestBits(t *testing.T) {
+	for _, test := range bitTests {
+		var z Int
+		z.neg = true
+		got := z.SetBits(test)
+		want := norm(test)
+		if got.abs.cmp(want) != 0 {
+			t.Errorf("SetBits(%v) = %v; want %v", test, got.abs, want)
+		}
+
+		if got.neg {
+			t.Errorf("SetBits(%v): got negative result")
+		}
+
+		bits := nat(z.Bits())
+		if bits.cmp(want) != 0 {
+			t.Errorf("%v.Bits() = %v; want %v", z.abs, bits, want)
+		}
+	}
+}
+
 func checkSetBytes(b []byte) bool {
 	hex1 := hex.EncodeToString(new(Int).SetBytes(b).Bytes())
 	hex2 := hex.EncodeToString(b)
@@ -962,6 +1000,8 @@ var primes = []string{
 }
 
 var composites = []string{
+	"0",
+	"1",
 	"21284175091214687912771199898307297748211672914763848041968395774954376176754",
 	"6084766654921918907427900243509372380954290099172559290432744450051395395951",
 	"84594350493221918389213352992032324280367711247940675652888030554255915464401",

src/math/big/nat.go

@@ -610,7 +610,7 @@ func (x nat) bitLen() int {
 const MaxBase = 'z' - 'a' + 10 + 1 // = hexValue('z') + 1
 
 func hexValue(ch rune) Word {
-	d := int(MaxBase + 1) // illegal base
+	d := int(MaxBase + 1) // invalid base
 	switch {
 	case '0' <= ch && ch <= '9':
 		d = int(ch - '0')
@@ -634,9 +634,9 @@ func hexValue(ch rune) Word {
 // ``0b'' or ``0B'' prefix selects base 2. Otherwise the selected base is 10.
 //
 func (z nat) scan(r io.RuneScanner, base int) (nat, int, error) {
-	// reject illegal bases
+	// reject invalid bases
 	if base < 0 || base == 1 || MaxBase < base {
-		return z, 0, errors.New("illegal number base")
+		return z, 0, errors.New("invalid number base")
 	}
 
 	// one char look-ahead
@@ -728,7 +728,13 @@ const (
 // decimalString returns a decimal representation of x.
 // It calls x.string with the charset "0123456789".
 func (x nat) decimalString() string {
-	return x.string(lowercaseDigits[0:10])
+	return x.string(lowercaseDigits[:10])
+}
+
+// hexString returns a hexadecimal representation of x.
+// It calls x.string with the charset "0123456789abcdef".
+func (x nat) hexString() string {
+	return x.string(lowercaseDigits[:16])
 }
 
 // string converts x to a string using digits from a charset; a digit with
@@ -739,8 +745,8 @@ func (x nat) string(charset string) string {
 
 	// special cases
 	switch {
-	case b < 2 || MaxBase > 256:
-		panic("illegal base")
+	case b < 2 || b > 256:
+		panic("invalid character set length")
 	case len(x) == 0:
 		return string(charset[0])
 	}

src/math/big/nat_test.go

@@ -243,16 +243,28 @@ var strTests = []struct {
 	{nil, "01", "0"},
 	{nat{1}, "01", "1"},
 	{nat{0xc5}, "01", "11000101"},
-	{nat{03271}, lowercaseDigits[0:8], "3271"},
-	{nat{10}, lowercaseDigits[0:10], "10"},
-	{nat{1234567890}, uppercaseDigits[0:10], "1234567890"},
-	{nat{0xdeadbeef}, lowercaseDigits[0:16], "deadbeef"},
-	{nat{0xdeadbeef}, uppercaseDigits[0:16], "DEADBEEF"},
-	{nat{0x229be7}, lowercaseDigits[0:17], "1a2b3c"},
-	{nat{0x309663e6}, uppercaseDigits[0:32], "O9COV6"},
+	{nat{03271}, lowercaseDigits[:8], "3271"},
+	{nat{10}, lowercaseDigits[:10], "10"},
+	{nat{1234567890}, uppercaseDigits[:10], "1234567890"},
+	{nat{0xdeadbeef}, lowercaseDigits[:16], "deadbeef"},
+	{nat{0xdeadbeef}, uppercaseDigits[:16], "DEADBEEF"},
+	{nat{0x229be7}, lowercaseDigits[:17], "1a2b3c"},
+	{nat{0x309663e6}, uppercaseDigits[:32], "O9COV6"},
 }
 
 func TestString(t *testing.T) {
+	// test invalid character set explicitly
+	var panicStr string
+	func() {
+		defer func() {
+			panicStr = recover().(string)
+		}()
+		natOne.string("0")
+	}()
+	if panicStr != "invalid character set length" {
+		t.Errorf("expected panic for invalid character set")
+	}
+
 	for _, a := range strTests {
 		s := a.x.string(a.c)
 		if s != a.s {
@@ -474,8 +486,8 @@ func ScanHelper(b *testing.B, base int, x, y Word) {
 	z = z.expWW(x, y)
 
 	var s string
-	s = z.string(lowercaseDigits[0:base])
-	if t := toString(z, lowercaseDigits[0:base]); t != s {
+	s = z.string(lowercaseDigits[:base])
+	if t := toString(z, lowercaseDigits[:base]); t != s {
 		b.Fatalf("scanning: got %s; want %s", s, t)
 	}
 	b.StartTimer()
@@ -513,11 +525,11 @@ func StringHelper(b *testing.B, base int, x, y Word) {
 	b.StopTimer()
 	var z nat
 	z = z.expWW(x, y)
-	z.string(lowercaseDigits[0:base]) // warm divisor cache
+	z.string(lowercaseDigits[:base]) // warm divisor cache
 	b.StartTimer()
 
 	for i := 0; i < b.N; i++ {
-		_ = z.string(lowercaseDigits[0:base])
+		_ = z.string(lowercaseDigits[:base])
 	}
 }
 
@@ -552,11 +564,11 @@ func LeafSizeHelper(b *testing.B, base Word, size int) {
 		b.StopTimer()
 		var z nat
 		z = z.expWW(base, Word(d))           // build target number
-		_ = z.string(lowercaseDigits[0:base]) // warm divisor cache
+		_ = z.string(lowercaseDigits[:base]) // warm divisor cache
 		b.StartTimer()
 
 		for i := 0; i < b.N; i++ {
-			_ = z.string(lowercaseDigits[0:base])
+			_ = z.string(lowercaseDigits[:base])
 		}
 	}
 
@@ -581,8 +593,8 @@ func TestStringPowers(t *testing.T) {
 	for b = 2; b <= 16; b++ {
 		for p = 0; p <= 512; p++ {
 			x := nat(nil).expWW(b, p)
-			xs := x.string(lowercaseDigits[0:b])
-			xs2 := toString(x, lowercaseDigits[0:b])
+			xs := x.string(lowercaseDigits[:b])
+			xs2 := toString(x, lowercaseDigits[:b])
 			if xs != xs2 {
 				t.Errorf("failed at %d ** %d in base %d: %s != %s", b, p, b, xs, xs2)
 			}
@@ -691,20 +703,30 @@ func TestModW(t *testing.T) {
 }
 
 func TestTrailingZeroBits(t *testing.T) {
+	// test 0 case explicitly
+	if n := trailingZeroBits(0); n != 0 {
+		t.Errorf("got trailingZeroBits(0) = %d; want 0", n)
+	}
+
 	x := Word(1)
-	for i := uint(0); i <= _W; i++ {
+	for i := uint(0); i < _W; i++ {
 		n := trailingZeroBits(x)
-		if n != i%_W {
+		if n != i {
 			t.Errorf("got trailingZeroBits(%#x) = %d; want %d", x, n, i%_W)
 		}
 		x <<= 1
 	}
 
+	// test 0 case explicitly
+	if n := nat(nil).trailingZeroBits(); n != 0 {
+		t.Errorf("got nat(nil).trailingZeroBits() = %d; want 0", n)
+	}
+
 	y := nat(nil).set(natOne)
 	for i := uint(0); i <= 3*_W; i++ {
 		n := y.trailingZeroBits()
 		if n != i {
-			t.Errorf("got 0x%s.trailingZeroBits() = %d; want %d", y.string(lowercaseDigits[0:16]), n, i)
+			t.Errorf("got 0x%s.trailingZeroBits() = %d; want %d", y.hexString(), n, i)
 		}
 		y = y.shl(y, 1)
 	}