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https://github.com/golang/go
synced 2024-11-26 04:07:59 -07:00
implemented outstanding bit ops on negative integerts
R=rsc DELTA=195 (146 added, 1 deleted, 48 changed) OCL=31895 CL=31931
This commit is contained in:
Robert Griesemer
parent
90ffb7b8f5
commit
2b1ec70d0f
@ -110,10 +110,10 @@ func dump(x []digit) {
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type Natural []digit;
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var (
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natZero Natural = Natural{};
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natOne Natural = Natural{1};
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natTwo Natural = Natural{2};
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natTen Natural = Natural{10};
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natZero = Natural{};
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natOne = Natural{1};
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natTwo = Natural{2};
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natTen = Natural{10};
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)
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@ -588,7 +588,7 @@ func (x Natural) Shr(s uint) Natural {
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}
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// And returns the ``bitwise and'' x & y for the binary representation of x and y.
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// And returns the ``bitwise and'' x & y for the 2's-complement representation of x and y.
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//
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func (x Natural) And(y Natural) Natural {
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n := len(x);
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@ -614,7 +614,7 @@ func copy(z, x []digit) {
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}
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// AndNot returns the ``bitwise clear'' x &^ y for the binary representation of x and y.
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// AndNot returns the ``bitwise clear'' x &^ y for the 2's-complement representation of x and y.
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//
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func (x Natural) AndNot(y Natural) Natural {
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n := len(x);
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@ -633,7 +633,7 @@ func (x Natural) AndNot(y Natural) Natural {
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}
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// Or returns the ``bitwise or'' x | y for the binary representation of x and y.
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// Or returns the ``bitwise or'' x | y for the 2's-complement representation of x and y.
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//
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func (x Natural) Or(y Natural) Natural {
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n := len(x);
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@ -652,7 +652,7 @@ func (x Natural) Or(y Natural) Natural {
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}
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// Xor returns the ``bitwise exclusive or'' x ^ y for the binary representation of x and y.
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// Xor returns the ``bitwise exclusive or'' x ^ y for the 2's-complement representation of x and y.
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//
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func (x Natural) Xor(y Natural) Natural {
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n := len(x);
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@ -1230,68 +1230,135 @@ func (x *Integer) Shl(s uint) *Integer {
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}
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// The bitwise operations on integers are defined on the 2's-complement
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// representation of integers. From
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//
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// -x == ^x + 1 (1) 2's complement representation
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//
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// follows:
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//
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// -(x) == ^(x) + 1
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// -(-x) == ^(-x) + 1
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// x-1 == ^(-x)
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// ^(x-1) == -x (2)
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//
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// Using (1) and (2), operations on negative integers of the form -x are
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// converted to operations on negated positive integers of the form ~(x-1).
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// Shr implements ``shift right'' x >> s. It returns x / 2^s.
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// Implementation restriction: Shl is not yet implemented for negative x.
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//
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func (x *Integer) Shr(s uint) *Integer {
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if !x.sign {
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return MakeInt(false, x.mant.Shr(s));
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if x.sign {
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// (-x) >> s == ^(x-1) >> s == ^((x-1) >> s) == -(((x-1) >> s) + 1)
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return MakeInt(true, x.mant.Sub(natOne).Shr(s).Add(natOne));
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}
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panic("UNIMPLEMENTED Integer.Shr of negative value");
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return nil;
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return MakeInt(false, x.mant.Shr(s));
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}
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// And returns the ``bitwise and'' x & y for the binary representation of x and y.
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// Implementation restriction: And is not implemented for negative integers.
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// Not returns the ``bitwise not'' ^x for the 2's-complement representation of x.
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func (x *Integer) Not() *Integer {
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if x.sign {
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// ^(-x) == ^(^(x-1)) == x-1
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return MakeInt(false, x.mant.Sub(natOne));
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}
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// ^x == -x-1 == -(x+1)
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return MakeInt(true, x.mant.Add(natOne));
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}
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// And returns the ``bitwise and'' x & y for the 2's-complement representation of x and y.
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//
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func (x *Integer) And(y *Integer) *Integer {
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if !x.sign && !y.sign {
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if x.sign == y.sign {
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if x.sign {
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// (-x) & (-y) == ^(x-1) & ^(y-1) == ^((x-1) | (y-1)) == -(((x-1) | (y-1)) + 1)
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return MakeInt(true, x.mant.Sub(natOne).Or(y.mant.Sub(natOne)).Add(natOne));
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}
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// x & y == x & y
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return MakeInt(false, x.mant.And(y.mant));
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}
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panic("UNIMPLEMENTED Integer.And of negative values");
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return nil;
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// x.sign != y.sign
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if x.sign {
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x, y = y, x; // & is symmetric
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}
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// x & (-y) == x & ^(y-1) == x &^ (y-1)
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return MakeInt(false, x.mant.AndNot(y.mant.Sub(natOne)));
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}
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// AndNot returns the ``bitwise clear'' x &^ y for the binary representation of x and y.
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// Implementation restriction: AndNot is not implemented for negative integers.
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// AndNot returns the ``bitwise clear'' x &^ y for the 2's-complement representation of x and y.
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//
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func (x *Integer) AndNot(y *Integer) *Integer {
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if !x.sign && !y.sign {
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if x.sign == y.sign {
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if x.sign {
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// (-x) &^ (-y) == ^(x-1) &^ ^(y-1) == ^(x-1) & (y-1) == (y-1) &^ (x-1)
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return MakeInt(false, y.mant.Sub(natOne).AndNot(x.mant.Sub(natOne)));
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}
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// x &^ y == x &^ y
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return MakeInt(false, x.mant.AndNot(y.mant));
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}
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panic("UNIMPLEMENTED Integer.AndNot of negative values");
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return nil;
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if x.sign {
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// (-x) &^ y == ^(x-1) &^ y == ^(x-1) & ^y == ^((x-1) | y) == -(((x-1) | y) + 1)
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return MakeInt(true, x.mant.Sub(natOne).Or(y.mant).Add(natOne));
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}
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// x &^ (-y) == x &^ ^(y-1) == x & (y-1)
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return MakeInt(false, x.mant.And(y.mant.Sub(natOne)));
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}
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// Or returns the ``bitwise or'' x | y for the binary representation of x and y.
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// Implementation restriction: Or is not implemented for negative integers.
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// Or returns the ``bitwise or'' x | y for the 2's-complement representation of x and y.
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//
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func (x *Integer) Or(y *Integer) *Integer {
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if !x.sign && !y.sign {
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if x.sign == y.sign {
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if x.sign {
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// (-x) | (-y) == ^(x-1) | ^(y-1) == ^((x-1) & (y-1)) == -(((x-1) & (y-1)) + 1)
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return MakeInt(true, x.mant.Sub(natOne).And(y.mant.Sub(natOne)).Add(natOne));
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}
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// x | y == x | y
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return MakeInt(false, x.mant.Or(y.mant));
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}
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panic("UNIMPLEMENTED Integer.Or of negative values");
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return nil;
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// x.sign != y.sign
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if x.sign {
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x, y = y, x; // | or symmetric
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}
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// x | (-y) == x | ^(y-1) == ^((y-1) &^ x) == -(^((y-1) &^ x) + 1)
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return MakeInt(true, y.mant.Sub(natOne).AndNot(x.mant).Add(natOne));
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}
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// Xor returns the ``bitwise xor'' x | y for the binary representation of x and y.
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// Implementation restriction: Xor is not implemented for negative integers.
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// Xor returns the ``bitwise xor'' x | y for the 2's-complement representation of x and y.
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//
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func (x *Integer) Xor(y *Integer) *Integer {
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if !x.sign && !y.sign {
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if x.sign == y.sign {
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if x.sign {
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// (-x) ^ (-y) == ^(x-1) ^ ^(y-1) == (x-1) ^ (y-1)
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return MakeInt(false, x.mant.Sub(natOne).Xor(y.mant.Sub(natOne)));
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}
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// x ^ y == x ^ y
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return MakeInt(false, x.mant.Xor(y.mant));
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}
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panic("UNIMPLEMENTED Integer.Xor of negative values");
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return nil;
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// x.sign != y.sign
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if x.sign {
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x, y = y, x; // ^ is symmetric
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}
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// x ^ (-y) == x ^ ^(y-1) == ^(x ^ (y-1)) == -((x ^ (y-1)) + 1)
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return MakeInt(true, x.mant.Xor(y.mant.Sub(natOne)).Add(natOne));
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}
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@ -467,8 +467,9 @@ func TestIntShift(t *testing.T) {
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}
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test_msg = "IntShift4R";
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//int_eq(0, Int(-43).Shr(1), Int(-43 >> 1));
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//int_eq(1, ip.Neg().Shr(10), ip.Neg().Div(Int(1).Shl(10)));
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int_eq(0, Int(-43).Shr(1), Int(-43 >> 1));
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int_eq(0, Int(-1024).Shr(100), Int(-1));
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int_eq(1, ip.Neg().Shr(10), ip.Neg().Div(Int(1).Shl(10)));
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}
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@ -507,6 +508,83 @@ func TestNatBitOps(t *testing.T) {
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}
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func TestIntBitOps1(t *testing.T) {
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tester = t;
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test_msg = "IntBitOps1";
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type T struct { x, y int64 };
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a := []T {
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T{ +7, +3 },
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T{ +7, -3 },
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T{ -7, +3 },
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T{ -7, -3 },
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};
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for i := uint(0); i < uint(len(a)); i++ {
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e := &a[i];
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int_eq(4*i+0, Int(e.x).And(Int(e.y)), Int(e.x & e.y));
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int_eq(4*i+1, Int(e.x).AndNot(Int(e.y)), Int(e.x &^ e.y));
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int_eq(4*i+2, Int(e.x).Or(Int(e.y)), Int(e.x | e.y));
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int_eq(4*i+3, Int(e.x).Xor(Int(e.y)), Int(e.x ^ e.y));
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}
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}
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func TestIntBitOps2(t *testing.T) {
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tester = t;
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test_msg = "IntNot";
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int_eq(0, Int(-2).Not(), Int( 1));
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int_eq(0, Int(-1).Not(), Int( 0));
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int_eq(0, Int( 0).Not(), Int(-1));
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int_eq(0, Int( 1).Not(), Int(-2));
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int_eq(0, Int( 2).Not(), Int(-3));
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test_msg = "IntAnd";
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for x := int64(-15); x < 5; x++ {
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bx := Int(x);
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for y := int64(-5); y < 15; y++ {
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by := Int(y);
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for i := uint(50); i < 70; i++ { // shift across 64bit boundary
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int_eq(i, bx.Shl(i).And(by.Shl(i)), Int(x & y).Shl(i));
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}
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}
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}
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test_msg = "IntAndNot";
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for x := int64(-15); x < 5; x++ {
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bx := Int(x);
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for y := int64(-5); y < 15; y++ {
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by := Int(y);
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for i := uint(50); i < 70; i++ { // shift across 64bit boundary
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int_eq(2*i+0, bx.Shl(i).AndNot(by.Shl(i)), Int(x &^ y).Shl(i));
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int_eq(2*i+1, bx.Shl(i).And(by.Shl(i).Not()), Int(x &^ y).Shl(i));
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}
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}
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}
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test_msg = "IntOr";
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for x := int64(-15); x < 5; x++ {
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bx := Int(x);
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for y := int64(-5); y < 15; y++ {
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by := Int(y);
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for i := uint(50); i < 70; i++ { // shift across 64bit boundary
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int_eq(i, bx.Shl(i).Or(by.Shl(i)), Int(x | y).Shl(i));
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}
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}
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}
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test_msg = "IntXor";
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for x := int64(-15); x < 5; x++ {
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bx := Int(x);
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for y := int64(-5); y < 15; y++ {
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by := Int(y);
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for i := uint(50); i < 70; i++ { // shift across 64bit boundary
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int_eq(i, bx.Shl(i).Xor(by.Shl(i)), Int(x ^ y).Shl(i));
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}
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}
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}
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}
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func TestNatCmp(t *testing.T) {
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tester = t;
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test_msg = "NatCmp";
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