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touched bigint

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This commit is contained in:
hyung-hwan
2014-03-04 14:32:49 +00:00
parent 77abff6346
commit 3be78f2cdf
3 changed files with 167 additions and 158 deletions
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266
lib/h2-scheme-bigint.adb
View File

@ -196,12 +196,12 @@ package body Bigint is
generic
with function Operator (X: in Object_Integer;
Y: in Object_Integer) return Object_Integer;
procedure Plain_Integer_Op (Interp: access Interpreter_Record;
procedure Plain_Integer_Op (Interp: in out Interpreter_Record;
X: in out Object_Pointer;
Y: in out Object_Pointer;
Z: out Object_Pointer);
procedure Plain_Integer_Op (Interp: access Interpreter_Record;
procedure Plain_Integer_Op (Interp: in out Interpreter_Record;
X: in out Object_Pointer;
Y: in out Object_Pointer;
Z: out Object_Pointer) is
@ -219,25 +219,25 @@ package body Bigint is
return;
exception
when Constraint_Error =>
Push_Top (Interp.all, A'Unchecked_Access);
Push_Top (Interp.all, B'Unchecked_Access);
Push_Top (Interp, A'Unchecked_Access);
Push_Top (Interp, B'Unchecked_Access);
-- TODO: allocate A and B from a non-GC heap.
-- I know that pointers returned by Make_Bigint here are short-lived
-- and not needed after actual operation. non-GC heap is a better choice.
A := Make_Bigint(Interp, Value => G);
B := Make_Bigint(Interp, Value => H);
Pop_Tops (Interp.all, 2);
A := Make_Bigint(Interp.Self, Value => G);
B := Make_Bigint(Interp.Self, Value => H);
Pop_Tops (Interp, 2);
end;
else
Push_Top (Interp.all, A'Unchecked_Access);
Push_Top (Interp.all, B'Unchecked_Access);
Push_Top (Interp, A'Unchecked_Access);
Push_Top (Interp, B'Unchecked_Access);
if Is_Integer(A) then
A := Make_Bigint(Interp, Value => Pointer_To_Integer(A));
A := Make_Bigint(Interp.Self, Value => Pointer_To_Integer(A));
end if;
if Is_Integer(B) then
B := Make_Bigint(Interp, Value => Pointer_To_Integer(B));
B := Make_Bigint(Interp.Self, Value => Pointer_To_Integer(B));
end if;
Pop_Tops (Interp.all, 2);
Pop_Tops (Interp, 2);
end if;
X := A;
@ -252,43 +252,51 @@ package body Bigint is
-----------------------------------------------------------------------------
procedure Add_Unsigned_Array (X: in Object_Half_Word_Array;
XS: in Half_Word_Object_Size;
Y: in Object_Half_Word_Array;
YS: in Half_Word_Object_Size;
Z: in out Object_Half_Word_Array) is
pragma Inline (Add_Unsigned_Array);
pragma Assert (XS >= YS);
W: Object_Word;
Carry: Object_Half_Word := 0;
begin
for I in 1 .. YS loop
W := Object_Word(X(I)) + Object_Word(Y(I)) + Object_Word(Carry);
Carry := Get_High(W);
Z(I) := Get_Low(W);
end loop;
for I in YS + 1 .. XS loop
W := Object_Word(X(I)) + Object_Word(Carry);
Carry := Get_High(W);
Z(I) := Get_Low(W);
end loop;
Z(XS + 1) := Carry;
end Add_Unsigned_Array;
function Add_Unsigned (Interp: access Interpreter_Record;
X: in Object_Pointer;
Y: in Object_Pointer) return Object_Pointer is
A, B: aliased Object_Pointer;
Z: Object_Pointer;
W: Object_Word;
Carry: Object_Half_Word := 0;
Last: Half_Word_Object_Size;
begin
if X.Size >= Y.Size then
A := X;
B := Y;
Last := X.Size + 1;
else
A := Y;
B := X;
Last := Y.Size + 1;
end if;
Push_Top (Interp.all, A'Unchecked_Access);
Push_Top (Interp.all, B'Unchecked_Access);
Z := Make_Bigint (Interp.Self, Last);
Z := Make_Bigint (Interp.Self, A.Size + 1);
Pop_Tops (Interp.all, 2);
for I in 1 .. B.Size loop
W := Object_Word(A.Half_Word_Slot(I)) + Object_Word(B.Half_Word_Slot(I)) + Object_Word(Carry);
Carry := Get_High(W);
Z.Half_Word_Slot(I) := Get_Low(W);
end loop;
for I in B.Size + 1 .. A.Size loop
W := Object_Word(A.Half_Word_Slot(I)) + Object_Word(Carry);
Carry := Get_High(W);
Z.Half_Word_Slot(I) := Get_Low(W);
end loop;
Z.Half_Word_Slot(Last) := Carry;
Add_Unsigned_Array (A.Half_Word_Slot, A.Size, B.Half_Word_Slot, B.Size, Z.Half_Word_Slot);
return Z;
end Add_Unsigned;
@ -325,7 +333,6 @@ package body Bigint is
pragma Assert (Borrow = 0);
end Subtract_Unsigned_Array;
function Subtract_Unsigned (Interp: access Interpreter_Record;
X: in Object_Pointer;
Y: in Object_Pointer) return Object_Pointer is
@ -344,7 +351,7 @@ package body Bigint is
Push_Top (Interp.all, B'Unchecked_Access);
Z := Make_Bigint (Interp.Self, A.Size); -- Assume X.Size >= Y.Size.
Pop_Tops (Interp.all, 2);
Subtract_Unsigned_Array (A.Half_Word_Slot, A.Size, B.Half_Word_SLot, B.Size, Z.Half_Word_Slot);
return Z;
end Subtract_Unsigned;
@ -408,7 +415,7 @@ package body Bigint is
return Z;
end Multiply_Unsigned;
procedure Divide_Unsigned (Interp: access Interpreter_Record;
procedure Divide_Unsigned (Interp: in out Interpreter_Record;
X: in Object_Pointer;
Y: in Object_Pointer;
Q: out Object_Pointer;
@ -417,7 +424,6 @@ package body Bigint is
B: aliased Object_Pointer := Y;
Quo: aliased Object_Pointer;
Remn: aliased Object_Pointer;
Dend: aliased Object_Pointer; -- Dividend
Sor: aliased Object_Pointer; -- Divisor
Tmp: Object_Pointer;
@ -426,35 +432,24 @@ package body Bigint is
Dend_Size: Half_Word_Object_Size;
Sor_Size: Half_Word_Object_Size;
Tmp_Size: Half_Word_Object_Size;
Cand_Size: Half_Word_Object_Size;
Cand_W: Object_Word;
Cand: Object_Half_Word_Array (1 .. 2);
Cand_Size: Half_Word_Object_Size;
begin
pragma Assert (not Is_Less_Unsigned(A, B)); -- The caller must ensure that X >= Y
-- 823456 / 93
-- 823456 930000 : (8 / 9) => 0,
-- 823456 93000 : (82 / 9) => 9,
-- 9 * 93000 => 837000
-- 837000 > 823456
-- 8 * 93000 => 664000
-- 664000 <= 823456
Push_Top (Interp.all, A'Unchecked_Access);
Push_Top (Interp.all, B'Unchecked_Access);
Push_Top (Interp.all, Quo'Unchecked_Access);
Push_Top (Interp.all, Remn'Unchecked_Access);
Push_Top (Interp.all, Dend'Unchecked_Access);
Push_Top (Interp.all, Sor'Unchecked_Access);
Push_Top (Interp, A'Unchecked_Access);
Push_Top (Interp, B'Unchecked_Access);
Push_Top (Interp, Quo'Unchecked_Access);
Push_Top (Interp, Dend'Unchecked_Access);
Push_Top (Interp, Sor'Unchecked_Access);
Quo := Make_Bigint (Interp.Self, A.Size);
Remn := Make_Bigint (Interp.Self, A.Size);
Dend := Make_Bigint (Interp.Self, A.Size);
Sor := Make_Bigint (Interp.Self, A.Size);
Tmp := Make_Bigint (Interp.Self, A.Size + B.Size);
Pop_Tops (Interp.all, 6);
Tmp := Make_Bigint (Interp.Self, A.Size + 2); -- Is it enough? A.Size + B.Size is safer
Pop_Tops (Interp, 5);
Dend_Size := A.Size;
Sor_Size := A.Size;
@ -463,10 +458,10 @@ package body Bigint is
Sor.Half_Word_Slot(1 + Diff .. B.Size + Diff) := B.Half_Word_Slot;
for I in reverse B.Size .. A.Size loop
if Is_Less_Unsigned_Array(Dend.Half_Word_Slot, Dend_Size, Sor.Half_Word_Slot, Sor_Size) then
Quo.Half_Word_Slot(I) := 0;
else
if not Is_Less_Unsigned_Array(Dend.Half_Word_Slot, Dend_Size, Sor.Half_Word_Slot, Sor_Size) then
if Dend_Size > Sor_Size then
-- Take the 2 high digits from the dividend and
-- the highest digit from the divisor and guess the quotient digits.
Cand_W := Make_Word(Dend.Half_Word_Slot(Dend_Size - 1), Dend.Half_Word_Slot(Dend_Size));
Cand_W := Cand_W / Object_Word(Sor.Half_Word_Slot(Sor_Size));
Cand(1) := Get_Low(Cand_W);
@ -477,21 +472,34 @@ package body Bigint is
Cand_Size := 1;
end if;
else
-- Take the highest digit from the dividend and the divisor
-- and guess the quotient digit.
Cand(1) := Dend.Half_Word_Slot(Dend_Size) / Sor.Half_Word_Slot(Sor_Size);
Cand_Size := 1;
end if;
-- Multiply the divisor and the quotient candidate.
Tmp.Half_Word_Slot := (others => 0);
Multiply_Unsigned_Array (Cand, Cand_Size, Sor.Half_Word_Slot, Sor_Size, Tmp.Half_Word_Slot);
Tmp_Size := Count_Effective_Slots(Tmp);
-- Check if the divident is less than the multiplication result.
if Is_Less_Unsigned_Array(Dend.Half_Word_Slot, Dend_Size, Tmp.Half_Word_Slot, Tmp_Size) then
-- If so, decrement the candidate by 1.
Quo.Half_Word_Slot(I) := Cand(1) - 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);
-- 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;
@ -505,106 +513,95 @@ package body Bigint is
end loop;
Q := Quo;
R := Remn;
R := Dend;
end Divide_Unsigned;
-----------------------------------------------------------------------------
function Add (Interp: access Interpreter_Record;
X: in Object_Pointer;
Y: in Object_Pointer) return Object_Pointer is
Z: Object_Pointer;
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
return Z;
end if;
if A.Sign /= B.Sign then
if A.Sign = Negative_Sign then
Z := Subtract (Interp, B, A);
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
Z := Subtract (Interp, A, B);
Sign := A.Sign;
Z := Add_Unsigned (Interp.Self, A, B);
Z.Sign := Sign;
end if;
else
Sign := A.Sign;
Z := Add_Unsigned (Interp, A, B);
Z.Sign := Sign;
Z := Normalize(Interp.Self, Z);
end if;
return Normalize(Interp, Z);
end Add;
function Subtract (Interp: access Interpreter_Record;
X: in Object_Pointer;
Y: in Object_Pointer) return Object_Pointer is
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;
Z: Object_Pointer;
Sign: Object_Sign;
begin
Subtract_Integers (Interp, A, B, Z);
if Z /= null then
return Z;
end if;
if A.Sign /= B.Sign then
Sign := A.Sign;
Z := Add_Unsigned (Interp, 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, B, A);
if Z = null then
if A.Sign /= B.Sign then
Sign := A.Sign;
Z := Add_Unsigned(Interp.Self, A, B);
Z.Sign := Sign;
else
Sign := A.Sign;
Z := Subtract_Unsigned (Interp, A, B);
Z.Sign := Sign;
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;
return Normalize(Interp, Z);
end Subtract;
function Multiply (Interp: access Interpreter_Record;
X: in Object_Pointer;
Y: in Object_Pointer) return Object_Pointer is
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;
Z: Object_Pointer;
Sign: Object_Sign;
begin
Multiply_Integers (Interp, A, B, Z);
if Z /= null then
return 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;
-- 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, A, B);
Z.Sign := Sign;
return Normalize(Interp, Z);
end Multiply;
procedure Divide (Interp: access Interpreter_Record;
procedure Divide (Interp: in out Interpreter_Record;
X: in Object_Pointer;
Y: in Object_Pointer;
Q: out Object_Pointer;
@ -649,15 +646,22 @@ package body Bigint is
C.Sign := Sign;
D.Sign := Sign;
Push_Top (Interp.all, C'Unchecked_Access);
Push_Top (Interp.all, D'Unchecked_Access);
C := Normalize(Interp, C);
D := Normalize(Interp, D);
Pop_Tops (Interp.all, 2);
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;

35
lib/h2-scheme.adb
View File

@ -2661,32 +2661,35 @@ B: aliased Object_Pointer;
begin
Push_Top (Interp, A'Unchecked_Access);
Push_Top (Interp, B'Unchecked_Access);
--A := Make_Bigint (Interp.Self, Value => 16#0FFFFFFF_FFFFFFFF#);
--B := Make_Bigint (Interp.Self, Value => 16#0FFFFFFF_FFFFFFFF#);
--A := Make_Bigint(Interp.Self, Value => 16#0FFFFFFF_FFFFFFFF#);
--B := Make_Bigint(Interp.Self, Value => 16#0FFFFFFF_FFFFFFFF#);
--for I in 1 .. 11 loop
--A := Bigint.Add (Interp.Self, A, B);
--A := Bigint.Add(Interp.Self, A, B);
--end loop;
A := Make_Bigint (Interp.Self, Value => 16#FFFF_00000001#);
--B := Make_Bigint (Interp.Self, Value => 16#FFFF_0000000F#);
B := Make_Bigint (Interp.Self, Value => 16#FFFFFF_00000001#);
A := Make_Bigint(Interp.Self, Value => 16#FFFF_00000001#);
--B := Make_Bigint(Interp.Self, Value => 16#FFFF_0000000F#);
B := Make_Bigint(Interp.Self, Value => 16#FFFFFF_00000001#);
B.sign := Negative_Sign;
A := Make_Bigint (Interp.Self, Size => 10);
A.Half_Word_Slot(10) := 16#FFFFFFFF#;
A := Bigint.Multiply (Interp.Self, A, integer_to_pointer(2));
A := Bigint.Add (Interp.Self, A, A);
A := Make_Bigint(Interp.Self, Size => 4);
A.Half_Word_Slot(4) := 16#11FFFFFF#;
Bigint.Multiply(Interp, A, integer_to_pointer(2), A);
Bigint.Add(Interp, A, A, A);
--A := Bigint.Divide (Interp.Self, A, integer_to_pointer(0));
B := Make_Bigint(Interp.Self, Size => 4);
B.Half_Word_Slot(4) := 16#22FFFFFF#;
Bigint.Subtract(Interp, B, integer_to_pointer(1), B);
--A := Bigint.Divide(Interp, A, integer_to_pointer(0));
print (interp, A);
print (interp, B);
declare
q, r: object_Pointer;
begin
--Bigint.Divide (Interp.Self, integer_to_pointer(-10), integer_to_pointer(6), Q, R);
Bigint.Divide (Interp.Self, A, integer_to_pointer(-2), Q, R);
print (interp, Q);
print (interp, R);
--Bigint.Divide (Interp, integer_to_pointer(-10), integer_to_pointer(6), Q, R);
Bigint.Divide (Interp, A, B, Q, R);
ada.text_io.put ("Q => "); print (interp, Q);
ada.text_io.put ("R => "); print (interp, R);
end;
Pop_tops (Interp, 2);
end;

24
lib/h2-scheme.ads
View File

@ -402,7 +402,6 @@ package H2.Scheme is
end case;
end record;
-- -----------------------------------------------------------------------------
-- The nil/true/false object are represented by special pointer values.
@ -605,19 +604,22 @@ private
pragma Inline (Get_Low);
pragma Inline (Make_Word);
function Add (Interp: access Interpreter_Record;
X: in Object_Pointer;
Y: in Object_Pointer) return Object_Pointer;
procedure Add (Interp: in out Interpreter_Record;
X: in Object_Pointer;
Y: in Object_Pointer;
Z: out Object_Pointer);
function Subtract (Interp: access Interpreter_Record;
X: in Object_Pointer;
Y: in Object_Pointer) return Object_Pointer;
procedure Subtract (Interp: in out Interpreter_Record;
X: in Object_Pointer;
Y: in Object_Pointer;
Z: out Object_Pointer);
function Multiply (Interp: access Interpreter_Record;
X: in Object_Pointer;
Y: in Object_Pointer) return Object_Pointer;
procedure Multiply (Interp: in out Interpreter_Record;
X: in Object_Pointer;
Y: in Object_Pointer;
Z: out Object_Pointer);
procedure Divide (Interp: access Interpreter_Record;
procedure Divide (Interp: in out Interpreter_Record;
X: in Object_Pointer;
Y: in Object_Pointer;
Q: out Object_Pointer;