big: Add bitwise methods for Int

R=gri
CC=golang-dev
https://golang.org/cl/987041

src/pkg/big/int.go

@@ -408,3 +408,145 @@ func (z *Int) Rsh(x *Int, n uint) *Int {
 	z.abs = z.abs.shr(x.abs, n)
 	return z
 }
+
+// And sets z = x & y and returns z.
+func (z *Int) And(x, y *Int) *Int {
+	if x.neg == y.neg {
+		if x.neg {
+			// (-x) & (-y) == ^(x-1) & ^(y-1) == ^((x-1) | (y-1)) == -(((x-1) | (y-1)) + 1)
+			x1 := nat{}.sub(x.abs, natOne)
+			y1 := z.abs.sub(y.abs, natOne)
+			z.neg = true
+			z.abs = z.abs.add(z.abs.or(x1, y1), natOne)
+			return z
+		}
+
+		// x & y == x & y
+		z.neg = false
+		z.abs = z.abs.and(x.abs, y.abs)
+		return z
+	}
+
+	// x.neg != y.neg
+	if x.neg {
+		x, y = y, x // & is symmetric
+	}
+
+	// x & (-y) == x & ^(y-1) == x &^ (y-1)
+	y1 := z.abs.sub(y.abs, natOne)
+	z.neg = false
+	z.abs = z.abs.andNot(x.abs, y1)
+	return z
+}
+
+
+// AndNot sets z = x &^ y and returns z.
+func (z *Int) AndNot(x, y *Int) *Int {
+	if x.neg == y.neg {
+		if x.neg {
+			// (-x) &^ (-y) == ^(x-1) &^ ^(y-1) == ^(x-1) & (y-1) == (y-1) &^ (x-1)
+			x1 := nat{}.sub(x.abs, natOne)
+			y1 := z.abs.sub(y.abs, natOne)
+			z.neg = false
+			z.abs = z.abs.andNot(y1, x1)
+			return z
+		}
+
+		// x &^ y == x &^ y
+		z.neg = false
+		z.abs = z.abs.andNot(x.abs, y.abs)
+		return z
+	}
+
+	if x.neg {
+		// (-x) &^ y == ^(x-1) &^ y == ^(x-1) & ^y == ^((x-1) | y) == -(((x-1) | y) + 1)
+		x1 := z.abs.sub(x.abs, natOne)
+		z.neg = true
+		z.abs = z.abs.add(z.abs.or(x1, y.abs), natOne)
+		return z
+	}
+
+	// x &^ (-y) == x &^ ^(y-1) == x & (y-1)
+	y1 := z.abs.add(y.abs, natOne)
+	z.neg = false
+	z.abs = z.abs.and(x.abs, y1)
+	return z
+}
+
+
+// Or sets z = x | y and returns z.
+func (z *Int) Or(x, y *Int) *Int {
+	if x.neg == y.neg {
+		if x.neg {
+			// (-x) | (-y) == ^(x-1) | ^(y-1) == ^((x-1) & (y-1)) == -(((x-1) & (y-1)) + 1)
+			x1 := nat{}.sub(x.abs, natOne)
+			y1 := z.abs.sub(y.abs, natOne)
+			z.neg = true
+			z.abs = z.abs.add(z.abs.and(x1, y1), natOne)
+			return z
+		}
+
+		// x | y == x | y
+		z.neg = false
+		z.abs = z.abs.or(x.abs, y.abs)
+		return z
+	}
+
+	// x.neg != y.neg
+	if x.neg {
+		x, y = y, x // | is symmetric
+	}
+
+	// x | (-y) == x | ^(y-1) == ^((y-1) &^ x) == -(^((y-1) &^ x) + 1)
+	y1 := z.abs.sub(y.abs, natOne)
+	z.neg = true
+	z.abs = z.abs.add(z.abs.andNot(y1, x.abs), natOne)
+	return z
+}
+
+
+// Xor sets z = x ^ y and returns z.
+func (z *Int) Xor(x, y *Int) *Int {
+	if x.neg == y.neg {
+		if x.neg {
+			// (-x) ^ (-y) == ^(x-1) ^ ^(y-1) == (x-1) ^ (y-1)
+			x1 := nat{}.sub(x.abs, natOne)
+			y1 := z.abs.sub(y.abs, natOne)
+			z.neg = false
+			z.abs = z.abs.xor(x1, y1)
+			return z
+		}
+
+		// x ^ y == x ^ y
+		z.neg = false
+		z.abs = z.abs.xor(x.abs, y.abs)
+		return z
+	}
+
+	// x.neg != y.neg
+	if x.neg {
+		x, y = y, x // | is symmetric
+	}
+
+	// x ^ (-y) == x ^ ^(y-1) == ^(x ^ (y-1)) == -((x ^ (y-1)) + 1)
+	y1 := z.abs.sub(y.abs, natOne)
+	z.neg = true
+	z.abs = z.abs.add(z.abs.xor(x.abs, y1), natOne)
+	return z
+}
+
+
+// Not sets z = ^x and returns z.
+func (z *Int) Not(x *Int) *Int {
+	if x.neg {
+		// ^(-x) == ^(^(x-1)) == x-1
+		z.neg = false
+		z.abs = z.abs.sub(x.abs, natOne)
+		return z
+	}
+
+	// ^x == -x-1 == -(x+1)
+	z.neg = true
+	z.abs = z.abs.add(x.abs, natOne)
+	return z
+}

src/pkg/big/int_test.go

@@ -709,3 +709,129 @@ func TestInt64(t *testing.T) {
 		}
 	}
 }
+
+
+type bitwiseTest struct {
+	x, y                 string
+	and, or, xor, andNot string
+}
+
+var bitwiseTests = []bitwiseTest{
+	bitwiseTest{"0x00", "0x00", "0x00", "0x00", "0x00", "0x00"},
+	bitwiseTest{"0x00", "0x01", "0x00", "0x01", "0x01", "0x00"},
+	bitwiseTest{"0x01", "0x00", "0x00", "0x01", "0x01", "0x01"},
+	bitwiseTest{"-0x01", "0x00", "0x00", "-0x01", "-0x01", "-0x01"},
+	bitwiseTest{"0x00", "-0x01", "0x00", "-0x01", "-0x01", "0x00"},
+	bitwiseTest{"0x01", "0x01", "0x01", "0x01", "0x00", "0x00"},
+	bitwiseTest{"-0x01", "-0x01", "-0x01", "-0x01", "0x00", "0x00"},
+	bitwiseTest{"0x07", "0x08", "0x00", "0x0f", "0x0f", "0x07"},
+	bitwiseTest{"0x05", "0x0f", "0x05", "0x0f", "0x0a", "0x00"},
+	bitwiseTest{"0x013ff6", "0x9a4e", "0x1a46", "0x01bffe", "0x01a5b8", "0x0125b0"},
+	bitwiseTest{"-0x013ff6", "0x9a4e", "0x800a", "-0x0125b2", "-0x01a5bc", "-0x01c000"},
+	bitwiseTest{"-0x013ff6", "-0x9a4e", "-0x01bffe", "-0x1a46", "0x01a5b8", "0x8008"},
+	bitwiseTest{
+		"0x1000009dc6e3d9822cba04129bcbe3401",
+		"0xb9bd7d543685789d57cb918e833af352559021483cdb05cc21fd",
+		"0x1000001186210100001000009048c2001",
+		"0xb9bd7d543685789d57cb918e8bfeff7fddb2ebe87dfbbdfe35fd",
+		"0xb9bd7d543685789d57ca918e8ae69d6fcdb2eae87df2b97215fc",
+		"0x8c40c2d8822caa04120b8321400",
+	},
+	bitwiseTest{
+		"0x1000009dc6e3d9822cba04129bcbe3401",
+		"-0xb9bd7d543685789d57cb918e833af352559021483cdb05cc21fd",
+		"0x8c40c2d8822caa04120b8321401",
+		"-0xb9bd7d543685789d57ca918e82229142459020483cd2014001fd",
+		"-0xb9bd7d543685789d57ca918e8ae69d6fcdb2eae87df2b97215fe",
+		"0x1000001186210100001000009048c2000",
+	},
+	bitwiseTest{
+		"-0x1000009dc6e3d9822cba04129bcbe3401",
+		"-0xb9bd7d543685789d57cb918e833af352559021483cdb05cc21fd",
+		"-0xb9bd7d543685789d57cb918e8bfeff7fddb2ebe87dfbbdfe35fd",
+		"-0x1000001186210100001000009048c2001",
+		"0xb9bd7d543685789d57ca918e8ae69d6fcdb2eae87df2b97215fc",
+		"0xb9bd7d543685789d57ca918e82229142459020483cd2014001fc",
+	},
+}
+
+
+type bitFun func(z, x, y *Int) *Int
+
+func testBitFun(t *testing.T, msg string, f bitFun, x, y *Int, exp string) {
+	expected := new(Int)
+	expected.SetString(exp, 16)
+
+	out := f(new(Int), x, y)
+	if out.Cmp(expected) != 0 {
+		println("Test failed")
+		t.Errorf("%s: got %s want %s", msg, out, expected)
+	}
+}
+
+
+func testBitFunSelf(t *testing.T, msg string, f bitFun, x, y *Int, exp string) {
+	expected := new(Int)
+	expected.SetString(exp, 16)
+
+	x = f(x, x, y)
+	if x.Cmp(expected) != 0 {
+		println("Test failed")
+		t.Errorf("%s: got %s want %s", msg, x, expected)
+	}
+}
+
+
+func TestBitwise(t *testing.T) {
+	x := new(Int)
+	y := new(Int)
+	for _, test := range bitwiseTests {
+		x.SetString(test.x, 16)
+		y.SetString(test.y, 16)
+
+		testBitFun(t, "and", (*Int).And, x, y, test.and)
+		testBitFunSelf(t, "and", (*Int).And, x, y, test.and)
+		testBitFun(t, "andNot", (*Int).AndNot, x, y, test.andNot)
+		testBitFunSelf(t, "andNot", (*Int).AndNot, x, y, test.andNot)
+		testBitFun(t, "or", (*Int).Or, x, y, test.or)
+		testBitFunSelf(t, "or", (*Int).Or, x, y, test.or)
+		testBitFun(t, "xor", (*Int).Xor, x, y, test.xor)
+		testBitFunSelf(t, "xor", (*Int).Xor, x, y, test.xor)
+	}
+}
+
+
+type notTest struct {
+	in  string
+	out string
+}
+
+var notTests = []notTest{
+	notTest{"0", "-1"},
+	notTest{"1", "-2"},
+	notTest{"7", "-8"},
+	notTest{"0", "-1"},
+	notTest{"-81910", "81909"},
+	notTest{
+		"298472983472983471903246121093472394872319615612417471234712061",
+		"-298472983472983471903246121093472394872319615612417471234712062",
+	},
+}
+
+func TestNot(t *testing.T) {
+	in := new(Int)
+	out := new(Int)
+	expected := new(Int)
+	for i, test := range notTests {
+		in.SetString(test.in, 10)
+		expected.SetString(test.out, 10)
+		out = out.Not(in)
+		if out.Cmp(expected) != 0 {
+			t.Errorf("#%d: got %s want %s", i, out, expected)
+		}
+		out = out.Not(out)
+		if out.Cmp(in) != 0 {
+			t.Errorf("#%d: got %s want %s", i, out, in)
+		}
+	}
+}

src/pkg/big/nat.go

@@ -629,7 +629,7 @@ func hexValue(ch byte) int {
 }
 
 
-// scanN returns the natural number corresponding to the
+// scan returns the natural number corresponding to the
 // longest possible prefix of s representing a natural number in a
 // given conversion base, the actual conversion base used, and the
 // prefix length. The syntax of natural numbers follows the syntax
@@ -833,6 +833,81 @@ func (z nat) shiftRightDeprecated(x nat, n uint) nat {
 }
 
 
+func (z nat) and(x, y nat) nat {
+	m := len(x)
+	n := len(y)
+	if m > n {
+		m = n
+	}
+	// m <= n
+
+	z = z.make(m)
+	for i := 0; i < m; i++ {
+		z[i] = x[i] & y[i]
+	}
+
+	return z.norm()
+}
+
+
+func (z nat) andNot(x, y nat) nat {
+	m := len(x)
+	n := len(y)
+	if n > m {
+		n = m
+	}
+	// m >= n
+
+	z = z.make(m)
+	for i := 0; i < n; i++ {
+		z[i] = x[i] &^ y[i]
+	}
+	copy(z[n:m], x[n:m])
+
+	return z.norm()
+}
+
+
+func (z nat) or(x, y nat) nat {
+	m := len(x)
+	n := len(y)
+	s := x
+	if m < n {
+		n, m = m, n
+		s = y
+	}
+	// n >= m
+
+	z = z.make(n)
+	for i := 0; i < m; i++ {
+		z[i] = x[i] | y[i]
+	}
+	copy(z[m:n], s[m:n])
+
+	return z.norm()
+}
+
+
+func (z nat) xor(x, y nat) nat {
+	m := len(x)
+	n := len(y)
+	s := x
+	if n < m {
+		n, m = m, n
+		s = y
+	}
+	// n >= m
+
+	z = z.make(n)
+	for i := 0; i < m; i++ {
+		z[i] = x[i] ^ y[i]
+	}
+	copy(z[m:n], s[m:n])
+
+	return z.norm()
+}
+
+
 // greaterThan returns true iff (x1<<_W + x2) > (y1<<_W + y2)
 func greaterThan(x1, x2, y1, y2 Word) bool { return x1 > y1 || x1 == y1 && x2 > y2 }
 

src/pkg/big/nat_test.go

@@ -173,37 +173,37 @@ func BenchmarkMul(b *testing.B) {
 }
 
 
-type strN struct {
+type str struct {
 	x nat
 	b int
 	s string
 }
 
 
-var tabN = []strN{
+var tab = []str{
-	strN{nil, 10, "0"},
+	str{nil, 10, "0"},
-	strN{nat{1}, 10, "1"},
+	str{nat{1}, 10, "1"},
-	strN{nat{10}, 10, "10"},
+	str{nat{10}, 10, "10"},
-	strN{nat{1234567890}, 10, "1234567890"},
+	str{nat{1234567890}, 10, "1234567890"},
 }
 
 
 func TestString(t *testing.T) {
-	for _, a := range tabN {
+	for _, a := range tab {
 		s := a.x.string(a.b)
 		if s != a.s {
-			t.Errorf("stringN%+v\n\tgot s = %s; want %s", a, s, a.s)
+			t.Errorf("string%+v\n\tgot s = %s; want %s", a, s, a.s)
 		}
 
 		x, b, n := nat(nil).scan(a.s, a.b)
 		if x.cmp(a.x) != 0 {
-			t.Errorf("scanN%+v\n\tgot z = %v; want %v", a, x, a.x)
+			t.Errorf("scan%+v\n\tgot z = %v; want %v", a, x, a.x)
 		}
 		if b != a.b {
-			t.Errorf("scanN%+v\n\tgot b = %d; want %d", a, b, a.b)
+			t.Errorf("scan%+v\n\tgot b = %d; want %d", a, b, a.b)
 		}
 		if n != len(a.s) {
-			t.Errorf("scanN%+v\n\tgot n = %d; want %d", a, n, len(a.s))
+			t.Errorf("scan%+v\n\tgot n = %d; want %d", a, n, len(a.s))
 		}
 	}
 }