471 lines
13 KiB
Ada
471 lines
13 KiB
Ada
with H2.Pool;
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separate (H2.Scheme)
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package body Bigint is
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use type System.Bit_Order;
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Big_Endian : constant := Standard.Boolean'Pos (
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System.Default_Bit_Order = System.High_Order_First
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);
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Little_Endian : constant := Standard.Boolean'Pos (
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System.Default_Bit_Order = System.Low_Order_First
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);
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--Half_Word_Bits: constant := Object_Pointer_Bits / 2;
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Half_Word_Bits: constant := Object_Half_Word'Size;
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Half_Word_Bytes: constant := Half_Word_Bits / System.Storage_Unit;
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type Word_Record is record
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Low: Object_Half_Word;
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High: Object_Half_Word;
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end record;
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for Word_Record use record
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--Low at 0 range 0 .. Half_Word_Bits - 1;
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--High at 0 range Half_Word_Bits .. Word_Bits - 1;
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Low at Half_Word_Bytes * (0 * Little_Endian + 1 * Big_Endian)
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range 0 .. Half_Word_Bits - 1;
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High at Half_Word_Bytes * (1 * Little_Endian + 0 * Big_Endian)
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range 0 .. Half_Word_Bits - 1;
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end record;
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for Word_Record'Size use Object_Word'Size;
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--for Word_Record'Size use Object_Pointer_Bits;
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--for Word_Record'Alignment use Object_Word'Alignment;
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--for Word_Record'Scalar_Storage_Order use System.High_Order_First;
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--for Word_Record'Bit_Order use System.High_Order_First;
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--for Word_Record'Bit_Order use System.Low_Order_First;
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-----------------------------------------------------------------------------
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function Get_Low (W: in Object_Word) return Object_Half_Word is
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R: Word_Record;
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for R'Address use W'Address;
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begin
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return R.Low;
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end Get_Low;
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function Get_High (W: in Object_Word) return Object_Half_Word is
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R: Word_Record;
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for R'Address use W'Address;
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begin
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return R.High;
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end Get_High;
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function Make_Word (L: in Object_Half_Word;
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H: in Object_Half_Word) return Object_Word is
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W: Object_Word;
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R: Word_Record;
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for R'Address use W'Address;
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begin
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R.Low := L;
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R.High := H;
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return W;
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end Make_Word;
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-----------------------------------------------------------------------------
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function Is_Less_Unsigned (X: in Object_Pointer;
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Y: in Object_Pointer) return Standard.Boolean is
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pragma Inline (Is_Less_Unsigned);
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begin
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if X.Size /= Y.Size then
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return X.Size < Y.Size;
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end if;
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for I in reverse X.Half_Word_Slot'Range loop
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if X.Half_Word_Slot(I) /= Y.Half_Word_Slot(I) then
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return X.Half_Word_Slot(I) < Y.Half_Word_Slot(I);
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end if;
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end loop;
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return Standard.False;
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end Is_Less_Unsigned;
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function Is_Less (X: in Object_Pointer;
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Y: in Object_Pointer) return Standard.Boolean is
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begin
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if X.Sign /= Y.Sign then
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return X.Sign = Negative_Sign;
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end if;
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return Is_Less_Unsigned (X, Y);
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end Is_Less;
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function Is_Equal (X: in Object_Pointer;
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Y: in Object_Pointer) return Standard.Boolean is
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begin
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return X.Sign = Y.Sign and then
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X.Size = Y.Size and then
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X.Half_Word_Slot = Y.Half_Word_Slot;
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end Is_Equal;
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function Is_Zero (X: in Object_Pointer) return Standard.Boolean is
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begin
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return X.Size = 1 and then X.Half_Word_Slot(1) = 0;
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end Is_Zero;
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-----------------------------------------------------------------------------
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function Normalize (Interp: access Interpreter_Record;
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X: in Object_Pointer) return Object_Pointer is
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Last: Half_Word_Object_Size := 1;
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begin
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for I in reverse 1 .. X.Size loop
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if X.Half_Word_Slot(I) /= 0 then
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Last := I;
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exit;
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end if;
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end loop;
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case Last is
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when 1 =>
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if X.Sign = Negative_Sign then
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return Integer_To_Pointer(-Object_Integer(X.Half_Word_Slot(1)));
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else
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return Integer_To_Pointer(Object_Integer(X.Half_Word_Slot(1)));
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end if;
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when 2 =>
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declare
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W: Object_Word := Make_Word (X.Half_Word_Slot(1), X.Half_Word_Slot(2));
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begin
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if X.Sign = Negative_Sign then
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if W in 0 .. Object_Word(-Object_Signed_Word(Object_Integer'First)) then
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return Integer_To_Pointer(-Object_Integer(W));
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end if;
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else
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if W in 0 .. Object_Word(Object_Integer'Last) then
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return Integer_To_Pointer(Object_Integer(W));
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end if;
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end if;
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end;
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when others =>
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null;
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end case;
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if X.Size = Last then
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return X;
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else
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return Make_Bigint(Interp, X, Last);
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end if;
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end Normalize;
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-----------------------------------------------------------------------------
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generic
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with function Operator (X: in Object_Integer;
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Y: in Object_Integer) return Object_Integer;
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procedure Plain_Integer_Op (Interp: access Interpreter_Record;
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X: in out Object_Pointer;
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Y: in out Object_Pointer;
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Z: out Object_Pointer);
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procedure Plain_Integer_Op (Interp: access Interpreter_Record;
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X: in out Object_Pointer;
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Y: in out Object_Pointer;
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Z: out Object_Pointer) is
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A: aliased Object_Pointer := X;
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B: aliased Object_Pointer := Y;
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begin
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if Is_Integer(A) and then Is_Integer(B) then
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declare
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G: Object_Integer := Pointer_To_Integer(A);
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H: Object_Integer := Pointer_To_Integer(B);
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begin
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X := A;
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Y := B;
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Z := Integer_To_Pointer(Operator(G, H));
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return;
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exception
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when Constraint_Error =>
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Push_Top (Interp.all, A'Unchecked_Access);
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Push_Top (Interp.all, B'Unchecked_Access);
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-- TODO: allocate A and B from a non-GC heap.
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-- I know that pointers returned by Make_Bigint here are short-lived
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-- and not needed after actual operation. non-GC heap is a better choice.
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A := Make_Bigint(Interp, Value => G);
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B := Make_Bigint(Interp, Value => H);
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Pop_Tops (Interp.all, 2);
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end;
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else
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Push_Top (Interp.all, A'Unchecked_Access);
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Push_Top (Interp.all, B'Unchecked_Access);
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if Is_Integer(A) then
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A := Make_Bigint(Interp, Value => Pointer_To_Integer(A));
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end if;
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if Is_Integer(B) then
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B := Make_Bigint(Interp, Value => Pointer_To_Integer(B));
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end if;
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Pop_Tops (Interp.all, 2);
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end if;
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X := A;
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Y := B;
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Z := null;
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end Plain_Integer_Op;
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procedure Add_Integers is new Plain_Integer_Op (Operator => "+");
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procedure Subtract_Integers is new Plain_Integer_Op (Operator => "-");
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procedure Multiply_Integers is new Plain_Integer_Op (Operator => "*");
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procedure Divide_Integers is new Plain_Integer_Op (Operator => "/");
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-----------------------------------------------------------------------------
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function Add_Unsigned (Interp: access Interpreter_Record;
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X: in Object_Pointer;
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Y: in Object_Pointer) return Object_Pointer is
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pragma Assert (Is_Bigint(X));
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pragma Assert (Is_Bigint(Y));
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A, B, Z: aliased Object_Pointer;
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W: Object_Word;
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Carry: Object_Half_Word;
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Last: Half_Word_Object_Size;
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begin
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Push_Top (Interp.all, A'Unchecked_Access);
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Push_Top (Interp.all, B'Unchecked_Access);
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Push_Top (Interp.all, Z'Unchecked_Access);
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if X.Size >= Y.Size then
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A := X;
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B := Y;
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Last := X.Size + 1;
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else
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A := Y;
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B := X;
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Last := Y.Size + 1;
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end if;
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Z := Make_Bigint (Interp.Self, Last);
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Carry := 0;
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for I in 1 .. B.Size loop
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W := Object_Word(A.Half_Word_Slot(I)) + Object_Word(B.Half_Word_Slot(I)) + Object_Word(Carry);
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Carry := Get_High(W);
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Z.Half_Word_Slot(I) := Get_Low(W);
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end loop;
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for I in B.Size + 1 .. A.Size loop
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W := Object_Word(A.Half_Word_Slot(I)) + Object_Word(Carry);
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Carry := Get_High(W);
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Z.Half_Word_Slot(I) := Get_Low(W);
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end loop;
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if Carry > 0 then
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Z.Half_Word_Slot(Last) := Carry;
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else
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declare
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T: Object_Pointer;
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begin
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T := Make_Bigint(Interp.Self, Last - 1);
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T.Half_Word_Slot := Z.Half_Word_Slot(1 .. Last - 1);
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Z := T;
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end;
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end if;
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Pop_Tops (Interp.all, 3);
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return Z;
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end Add_Unsigned;
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function Subtract_Unsigned (Interp: access Interpreter_Record;
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X: in Object_Pointer;
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Y: in Object_Pointer) return Object_Pointer is
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A, B, Z: aliased Object_Pointer;
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Last: Half_Word_Object_Size;
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Borrow: Object_Signed_Word;
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T: Object_Signed_Word;
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begin
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Push_Top (Interp.all, A'Unchecked_Access);
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Push_Top (Interp.all, B'Unchecked_Access);
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Push_Top (Interp.all, Z'Unchecked_Access);
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if X.Size >= Y.Size then
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A := X;
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B := Y;
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Last := X.Size;
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else
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A := Y;
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B := X;
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Last := Y.Size;
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end if;
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Z := Make_Bigint (Interp.Self, Last);
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Borrow := 0;
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for I in 1 .. B.Size loop
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T := Object_Signed_Word(A.Half_Word_Slot(I)) - Object_Signed_Word(B.Half_Word_Slot(I)) - Borrow;
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if T < 0 then
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Borrow := 1;
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Z.Half_Word_Slot(I) := Object_Half_Word(-T);
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else
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Borrow := 0;
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Z.Half_Word_Slot(I) := Object_Half_Word(T);
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end if;
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end loop;
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for I in B.Size + 1 .. A.Size loop
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T := Object_Signed_Word(A.Half_Word_Slot(I)) - Borrow;
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if T < 0 then
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Borrow := 1;
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Z.Half_Word_Slot(I) := Object_Half_Word(-T);
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else
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Borrow := 0;
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Z.Half_Word_Slot(I) := Object_Half_Word(T);
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end if;
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end loop;
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return Z;
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end Subtract_Unsigned;
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function Multiply_Unsigned (Interp: access Interpreter_Record;
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X: in Object_Pointer;
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Y: in Object_Pointer) return Object_Pointer is
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A, B, Z: aliased Object_Pointer;
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W: Object_Word;
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Low, High: Object_Half_Word;
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Carry: Object_Half_Word;
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Index: Half_Word_Object_Size;
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begin
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Push_Top (Interp.all, A'Unchecked_Access);
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Push_Top (Interp.all, B'Unchecked_Access);
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Push_Top (Interp.all, Z'Unchecked_Access);
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A := X;
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B := Y;
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Z := Make_Bigint (Interp.Self, A.Size + B.Size);
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--for I in B.Half_Word_Slot'Range loop
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for I in 1 .. B.Size loop
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if B.Half_Word_Slot(I) = 0 then
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Z.Half_Word_Slot(A.Size + I) := 0;
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else
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Carry := 0;
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--for J in A.Half_Word_Slot'Range loop
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for J in 1 .. A.Size loop
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W := Object_Word(A.Half_Word_Slot(J)) * Object_Word(B.Half_Word_Slot(I));
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Low := Get_Low(W);
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High := Get_High(W);
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Low := Low + Carry;
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if Low < Carry then
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High := High + 1;
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end if;
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Index := J + I - 1;
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Low := Low + Z.Half_Word_Slot(Index);
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if Low < Z.Half_Word_SLot(Index) then
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High := High + 1;
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end if;
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Z.Half_Word_Slot(Index) := Low;
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Carry := High;
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end loop;
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Z.Half_Word_Slot(A.Size + I) := Carry;
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end if;
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end loop;
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Pop_Tops (Interp.all, 3);
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return Z;
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end Multiply_Unsigned;
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-----------------------------------------------------------------------------
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function Add (Interp: access Interpreter_Record;
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X: in Object_Pointer;
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Y: in Object_Pointer) return Object_Pointer is
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Z: Object_Pointer;
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A: Object_Pointer := X;
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B: Object_Pointer := Y;
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Sign: Object_Sign;
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begin
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Add_Integers (Interp, A, B, Z);
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if Z /= null then
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return Z;
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end if;
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if A.Sign /= B.Sign then
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if A.Sign = Negative_Sign then
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Z := Subtract (Interp, B, A);
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else
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Z := Subtract (Interp, A, B);
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end if;
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else
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Sign := A.Sign;
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Z := Add_Unsigned (Interp, A, B);
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Z.Sign := Sign;
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end if;
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return Normalize(Interp, Z);
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end Add;
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function Subtract (Interp: access Interpreter_Record;
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X: in Object_Pointer;
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Y: in Object_Pointer) return Object_Pointer is
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Z: Object_Pointer;
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A: Object_Pointer := X;
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B: Object_Pointer := Y;
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Sign: Object_Sign;
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begin
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Subtract_Integers (Interp, A, B, Z);
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if Z /= null then
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return Z;
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end if;
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if A.Sign /= B.Sign then
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Sign := A.Sign;
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Z := Add_Unsigned (Interp, A, B);
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Z.Sign := Sign;
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else
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if Is_Less_Unsigned(A, B) then
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--Sign := Object_Sign'Val(not Object_Sign'Pos(A.Sign)); -- opposite A.Sign
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if A.Sign = Negative_Sign then
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Sign := Positive_Sign;
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else
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Sign := Negative_Sign;
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end if;
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Z := Subtract_Unsigned (Interp, B, A);
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Z.Sign := Sign;
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else
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Sign := A.Sign;
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Z := Subtract_Unsigned (Interp, A, B);
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Z.Sign := Sign;
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end if;
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end if;
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return Normalize(Interp, Z);
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end Subtract;
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function Multiply (Interp: access Interpreter_Record;
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X: in Object_Pointer;
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Y: in Object_Pointer) return Object_Pointer is
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Z: Object_Pointer;
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A: Object_Pointer := X;
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B: Object_Pointer := Y;
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Sign: Object_Sign;
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begin
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Multiply_Integers (Interp, A, B, Z);
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if Z /= null then
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return Z;
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end if;
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-- Determine the sign earlier than any object allocation
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-- to avoid GC side-effects because A and B are not pushed
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-- as temporarry object pointers.
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if A.Sign = B.Sign then
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Sign := Positive_Sign;
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else
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Sign := Negative_Sign;
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end if;
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Z := Multiply_Unsigned (Interp, A, B);
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Z.Sign := Sign;
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return Normalize(Interp, Z);
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end Multiply;
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end Bigint;
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