668 lines
21 KiB
Ada
668 lines
21 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_Array (X: in Object_Half_Word_Array;
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XS: in Half_Word_Object_Size;
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Y: in Object_Half_Word_Array;
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YS: in Half_Word_Object_Size) return Standard.Boolean is
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pragma Inline (Is_Less_Unsigned_Array);
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begin
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if XS /= YS then
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return XS < YS;
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end if;
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for I in reverse X'Range loop
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if X(I) /= Y(I) then
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return X(I) < Y(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_Array;
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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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return Is_Less_Unsigned_Array (X.Half_Word_Slot, X.Size, Y.Half_Word_Slot, Y.Size);
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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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pragma Inline (Is_Zero);
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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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function Is_One_Unsigned (X: in Object_Pointer) return Standard.Boolean is
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pragma Inline (Is_One_Unsigned);
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begin
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return X.Size = 1 and then X.Half_Word_Slot(1) = 1;
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end Is_One_Unsigned;
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-----------------------------------------------------------------------------
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function Copy_Upto (Interp: access Interpreter_Record;
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X: in Object_Pointer;
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Last: in Half_Word_Object_Size) return Object_Pointer is
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pragma Assert (Last < X.Size);
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A: aliased Object_Pointer := X;
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Z: Object_Pointer;
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begin
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Push_Top (Interp.all, A'Unchecked_Access);
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Z := Make_Bigint(Interp, Size => Last);
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Pop_Tops (Interp.all, 1);
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Z.Sign := A.Sign;
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Z.Half_Word_Slot := A.Half_Word_Slot(1 .. Last);
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return Z;
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end Copy_Upto;
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function Count_Effective_Slots (X: in Object_Pointer) return Half_Word_Object_Size is
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pragma Inline (Count_Effective_Slots);
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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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return Last;
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end Count_Effective_Slots;
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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;
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begin
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Last := Count_Effective_Slots(X);
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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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-- No compaction is needed. return it as it is
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return X;
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end if;
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-- Remove unneeded slots and clone meaningful contents only.
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return Copy_Upto(Interp, X, Last);
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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: in out 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: in out 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, A'Unchecked_Access);
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Push_Top (Interp, 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.Self, Value => G);
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B := Make_Bigint(Interp.Self, Value => H);
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Pop_Tops (Interp, 2);
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end;
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else
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Push_Top (Interp, A'Unchecked_Access);
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Push_Top (Interp, B'Unchecked_Access);
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if Is_Integer(A) then
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A := Make_Bigint(Interp.Self, 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.Self, Value => Pointer_To_Integer(B));
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end if;
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Pop_Tops (Interp, 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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procedure Add_Unsigned_Array (X: in Object_Half_Word_Array;
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XS: in Half_Word_Object_Size;
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Y: in Object_Half_Word_Array;
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YS: in Half_Word_Object_Size;
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Z: in out Object_Half_Word_Array) is
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pragma Inline (Add_Unsigned_Array);
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pragma Assert (XS >= YS);
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W: Object_Word;
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Carry: Object_Half_Word := 0;
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begin
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for I in 1 .. YS loop
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W := Object_Word(X(I)) + Object_Word(Y(I)) + Object_Word(Carry);
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Carry := Get_High(W);
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Z(I) := Get_Low(W);
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end loop;
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for I in YS + 1 .. XS loop
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W := Object_Word(X(I)) + Object_Word(Carry);
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Carry := Get_High(W);
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Z(I) := Get_Low(W);
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end loop;
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Z(XS + 1) := Carry;
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end Add_Unsigned_Array;
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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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A, B: aliased Object_Pointer;
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Z: Object_Pointer;
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begin
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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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else
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A := Y;
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B := X;
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end if;
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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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Z := Make_Bigint (Interp.Self, A.Size + 1);
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Pop_Tops (Interp.all, 2);
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Add_Unsigned_Array (A.Half_Word_Slot, A.Size, B.Half_Word_Slot, B.Size, Z.Half_Word_Slot);
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return Z;
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end Add_Unsigned;
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procedure Subtract_Unsigned_Array (X: in Object_Half_Word_Array;
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XS: in Half_Word_Object_Size;
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Y: in Object_Half_Word_Array;
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YS: in Half_Word_Object_Size;
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Z: in out Object_Half_Word_Array) is
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W: Object_Word;
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Borrowed_Word: constant Object_Word := Object_Word(Object_Half_Word'Last) + 1;
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Borrow: Object_Half_Word := 0;
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begin
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for I in 1 .. YS loop
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W := Object_Word(Y(I)) + Object_Word(Borrow);
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if Object_Word(X(I)) >= W then
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Z(I) := X(I) - Object_Half_Word(W);
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Borrow := 0;
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else
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Z(I) := Object_Half_Word(Borrowed_Word + Object_Word(X(I)) - W);
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Borrow := 1;
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end if;
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end loop;
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for I in YS + 1 .. XS loop
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if X(I) >= Borrow then
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Z(I) := X(I) - Object_Half_Word(Borrow);
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Borrow := 0;
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else
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Z(I) := Object_Half_Word(Borrowed_Word + Object_Word(X(I)) - Object_Word(Borrow));
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Borrow := 1;
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end if;
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end loop;
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pragma Assert (Borrow = 0);
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end Subtract_Unsigned_Array;
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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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pragma Inline (Subtract_Unsigned);
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A: aliased Object_Pointer := X;
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B: aliased Object_Pointer := Y;
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Z: Object_Pointer;
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W: Object_Word;
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Borrowed_Word: constant Object_Word := Object_Word(Object_Half_Word'Last) + 1;
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Borrow: Object_Half_Word := 0;
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begin
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pragma Assert (not Is_Less_Unsigned(A, B)); -- The caller must ensure that X >= Y
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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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Z := Make_Bigint (Interp.Self, A.Size); -- Assume X.Size >= Y.Size.
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Pop_Tops (Interp.all, 2);
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Subtract_Unsigned_Array (A.Half_Word_Slot, A.Size, B.Half_Word_SLot, B.Size, Z.Half_Word_Slot);
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return Z;
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end Subtract_Unsigned;
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procedure Multiply_Unsigned_Array (X: in Object_Half_Word_Array;
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XS: in Half_Word_Object_Size;
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Y: in Object_Half_Word_Array;
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YS: in Half_Word_Object_Size;
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Z: in out Object_Half_Word_Array) is
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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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for I in 1 .. YS loop
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if Y(I) = 0 then
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Z(XS + I) := 0;
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else
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Carry := 0;
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for J in 1 .. XS loop
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W := Object_Word(X(J)) * Object_Word(Y(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(Index);
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if Low < Z(Index) then
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High := High + 1;
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end if;
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Z(Index) := Low;
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Carry := High;
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end loop;
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Z(XS + I) := Carry;
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end if;
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end loop;
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end Multiply_Unsigned_Array;
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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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pragma Inline (Multiply_Unsigned);
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A: aliased Object_Pointer := X;
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B: aliased Object_Pointer := Y;
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Z: Object_Pointer;
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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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Z := Make_Bigint (Interp.Self, A.Size + B.Size);
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Pop_Tops (Interp.all, 2);
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Multiply_Unsigned_Array (A.Half_Word_Slot, A.Size, B.Half_Word_Slot, B.Size, Z.Half_Word_Slot);
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return Z;
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end Multiply_Unsigned;
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procedure Divide_Unsigned (Interp: in out Interpreter_Record;
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X: in Object_Pointer;
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Y: in Object_Pointer;
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Q: out Object_Pointer;
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R: 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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Quo: aliased Object_Pointer;
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Dend: aliased Object_Pointer; -- Dividend
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Sor: aliased Object_Pointer; -- Divisor
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Tmp: Object_Pointer;
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Diff: Half_Word_Object_Size;
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Dend_Size: Half_Word_Object_Size;
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Sor_Size: Half_Word_Object_Size;
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Tmp_Size: Half_Word_Object_Size;
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Cand_W: Object_Word;
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Cand: Object_Half_Word_Array (1 .. 2);
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Cand_Size: Half_Word_Object_Size;
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begin
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pragma Assert (not Is_Less_Unsigned(A, B)); -- The caller must ensure that X >= Y
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Push_Top (Interp, A'Unchecked_Access);
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Push_Top (Interp, B'Unchecked_Access);
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Push_Top (Interp, Quo'Unchecked_Access);
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Push_Top (Interp, Dend'Unchecked_Access);
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Push_Top (Interp, Sor'Unchecked_Access);
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Quo := Make_Bigint (Interp.Self, A.Size);
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Dend := Make_Bigint (Interp.Self, A.Size);
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Sor := Make_Bigint (Interp.Self, A.Size);
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Tmp := Make_Bigint (Interp.Self, A.Size + 2); -- Is it enough? A.Size + B.Size is safer
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Pop_Tops (Interp, 5);
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Dend_Size := A.Size;
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Sor_Size := A.Size;
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Diff := A.Size - B.Size;
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Dend.Half_Word_Slot := A.Half_Word_Slot;
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Sor.Half_Word_Slot(1 + Diff .. B.Size + Diff) := B.Half_Word_Slot;
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for I in reverse B.Size .. A.Size loop
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if not Is_Less_Unsigned_Array(Dend.Half_Word_Slot, Dend_Size, Sor.Half_Word_Slot, Sor_Size) then
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if Dend_Size > Sor_Size then
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-- Take the 2 high digits from the dividend and
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-- the highest digit from the divisor and guess the quotient digits.
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Cand_W := Make_Word(Dend.Half_Word_Slot(Dend_Size - 1), Dend.Half_Word_Slot(Dend_Size));
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Cand_W := Cand_W / Object_Word(Sor.Half_Word_Slot(Sor_Size));
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Cand(1) := Get_Low(Cand_W);
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Cand(2) := Get_High(Cand_W);
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if Cand(2) > 0 then
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Cand_Size := 2;
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else
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Cand_Size := 1;
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end if;
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else
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-- Take the highest digit from the dividend and the divisor
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-- and guess the quotient digit.
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Cand(1) := Dend.Half_Word_Slot(Dend_Size) / Sor.Half_Word_Slot(Sor_Size);
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Cand_Size := 1;
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end if;
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-- Multiply the divisor and the quotient candidate.
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Tmp.Half_Word_Slot := (others => 0);
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Multiply_Unsigned_Array (Cand, Cand_Size, Sor.Half_Word_Slot, Sor_Size, Tmp.Half_Word_Slot);
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Tmp_Size := Count_Effective_Slots(Tmp);
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-- Check if the divident is less than the multiplication result.
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if Is_Less_Unsigned_Array(Dend.Half_Word_Slot, Dend_Size, Tmp.Half_Word_Slot, Tmp_Size) then
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-- If so, decrement the candidate by 1.
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Quo.Half_Word_Slot(I) := Cand(1) - 1;
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|
|
|
-- Dividend := Dividend - Tmp
|
|
Subtract_Unsigned_Array (Dend.Half_Word_Slot, Dend_Size, Tmp.Half_Word_Slot, Tmp_Size, Dend.Half_Word_Slot);
|
|
Dend_Size := Count_Effective_Slots(Dend);
|
|
|
|
-- Divident := Dividdent - Divisor
|
|
Subtract_Unsigned_Array (Dend.Half_Word_Slot, Dend_Size, Sor.Half_Word_Slot, Sor_Size, Dend.Half_Word_Slot);
|
|
Dend_Size := Count_Effective_Slots(Dend);
|
|
else
|
|
-- If not, the candidate is the right guess.
|
|
Quo.Half_Word_Slot(I) := Cand(1);
|
|
|
|
-- Dividend := Dividend - Tmp
|
|
Subtract_Unsigned_Array (Dend.Half_Word_Slot, Dend_Size, Tmp.Half_Word_Slot, Tmp_Size, Dend.Half_Word_Slot);
|
|
Dend_Size := Count_Effective_Slots(Dend);
|
|
end if;
|
|
end if;
|
|
|
|
-- Shift the divisor right by 1 slot
|
|
pragma Assert (I = Sor_Size);
|
|
Sor_Size := Sor_Size - 1;
|
|
Sor.Half_Word_Slot(1 .. Sor_Size) := Sor.Half_Word_Slot(2 .. I);
|
|
Sor.Half_Word_Slot(I) := 0;
|
|
end loop;
|
|
|
|
Q := Quo;
|
|
R := Dend;
|
|
end Divide_Unsigned;
|
|
|
|
-----------------------------------------------------------------------------
|
|
|
|
procedure Add (Interp: in out Interpreter_Record;
|
|
X: in Object_Pointer;
|
|
Y: in Object_Pointer;
|
|
Z: out Object_Pointer) is
|
|
A: Object_Pointer := X;
|
|
B: Object_Pointer := Y;
|
|
Sign: Object_Sign;
|
|
begin
|
|
Add_Integers (Interp, A, B, Z);
|
|
if Z = null then
|
|
if A.Sign /= B.Sign then
|
|
if A.Sign = Negative_Sign then
|
|
Subtract (Interp, B, A, Z);
|
|
else
|
|
Subtract (Interp, A, B, Z);
|
|
end if;
|
|
else
|
|
Sign := A.Sign;
|
|
Z := Add_Unsigned (Interp.Self, A, B);
|
|
Z.Sign := Sign;
|
|
end if;
|
|
Z := Normalize(Interp.Self, Z);
|
|
end if;
|
|
end Add;
|
|
|
|
procedure Subtract (Interp: in out Interpreter_Record;
|
|
X: in Object_Pointer;
|
|
Y: in Object_Pointer;
|
|
Z: out Object_Pointer) is
|
|
A: Object_Pointer := X;
|
|
B: Object_Pointer := Y;
|
|
Sign: Object_Sign;
|
|
begin
|
|
Subtract_Integers (Interp, A, B, Z);
|
|
if Z = null then
|
|
if A.Sign /= B.Sign then
|
|
Sign := A.Sign;
|
|
Z := Add_Unsigned(Interp.Self, A, B);
|
|
Z.Sign := Sign;
|
|
else
|
|
if Is_Less_Unsigned(A, B) then
|
|
--Sign := Object_Sign'Val(not Object_Sign'Pos(A.Sign)); -- opposite A.Sign
|
|
if A.Sign = Negative_Sign then
|
|
Sign := Positive_Sign;
|
|
else
|
|
Sign := Negative_Sign;
|
|
end if;
|
|
Z := Subtract_Unsigned(Interp.Self, B, A);
|
|
Z.Sign := Sign;
|
|
else
|
|
Sign := A.Sign;
|
|
Z := Subtract_Unsigned(Interp.Self, A, B);
|
|
Z.Sign := Sign;
|
|
end if;
|
|
end if;
|
|
Z := Normalize(Interp.Self, Z);
|
|
end if;
|
|
end Subtract;
|
|
|
|
procedure Multiply (Interp: in out Interpreter_Record;
|
|
X: in Object_Pointer;
|
|
Y: in Object_Pointer;
|
|
Z: out Object_Pointer) is
|
|
A: Object_Pointer := X;
|
|
B: Object_Pointer := Y;
|
|
Sign: Object_Sign;
|
|
begin
|
|
Multiply_Integers (Interp, A, B, Z);
|
|
if Z = null then
|
|
-- Determine the sign earlier than any object allocation
|
|
-- to avoid GC side-effects because A and B are not pushed
|
|
-- as temporarry object pointers.
|
|
if A.Sign = B.Sign then
|
|
Sign := Positive_Sign;
|
|
else
|
|
Sign := Negative_Sign;
|
|
end if;
|
|
Z := Multiply_Unsigned (Interp.Self, A, B);
|
|
Z.Sign := Sign;
|
|
Z := Normalize(Interp.Self, Z);
|
|
end if;
|
|
end Multiply;
|
|
|
|
procedure Divide (Interp: in out Interpreter_Record;
|
|
X: in Object_Pointer;
|
|
Y: in Object_Pointer;
|
|
Q: out Object_Pointer;
|
|
R: out Object_Pointer) is
|
|
A: Object_Pointer := X;
|
|
B: Object_Pointer := Y;
|
|
C: aliased Object_Pointer;
|
|
D: aliased Object_Pointer;
|
|
Sign: Object_Sign;
|
|
begin
|
|
if (Is_Integer(Y) and then Pointer_To_Integer(Y) = 0) or else
|
|
(Is_Bigint(Y) and then Is_Zero(Y)) then
|
|
raise Divide_By_Zero_Error;
|
|
end if;
|
|
|
|
Divide_Integers (Interp, A, B, Q);
|
|
if Q /= null then
|
|
-- remainder operation must succeed if division was ok.
|
|
R := Integer_To_Pointer(Pointer_To_Integer(A) rem Pointer_To_Integer(B));
|
|
return;
|
|
end if;
|
|
|
|
if Is_Equal(A, B) then
|
|
Q := Integer_To_Pointer(1);
|
|
R := Integer_To_Pointer(0);
|
|
return;
|
|
elsif Is_Less_Unsigned(A, B) then
|
|
Q := Integer_To_Pointer(0);
|
|
R := A;
|
|
return;
|
|
end if;
|
|
|
|
-- Determine the sign earlier than any object allocation
|
|
-- to avoid GC side-effects because A and B are not pushed
|
|
-- as temporarry object pointers.
|
|
if A.Sign = B.Sign then
|
|
Sign := Positive_Sign;
|
|
else
|
|
Sign := Negative_Sign;
|
|
end if;
|
|
Divide_Unsigned (Interp, A, B, C, D);
|
|
C.Sign := Sign;
|
|
D.Sign := Sign;
|
|
|
|
Push_Top (Interp, C'Unchecked_Access);
|
|
Push_Top (Interp, D'Unchecked_Access);
|
|
C := Normalize(Interp.Self, C);
|
|
D := Normalize(Interp.Self, D);
|
|
Pop_Tops (Interp, 2);
|
|
|
|
Q := C;
|
|
R := D;
|
|
end Divide;
|
|
|
|
procedure To_String (Interp: in out Interpreter_Record;
|
|
X: in Object_Pointer;
|
|
Radix: in Object_Half_Word;
|
|
Z: out Object_Pointer) is
|
|
begin
|
|
null;
|
|
end To_String;
|
|
end Bigint;
|
|
|