unit
HugeInts;
interface
const
{$IFDEF
HugeInt_64 }
HugeIntSize = 64;
{$ELSE}{$IFDEF HugeInt_32 }
HugeIntSize = 32;
{$ELSE}{$IFDEF HugeInt_16 }
HugeIntSize = 16;
{$ELSE}
HugeIntSize = 8;
{$ENDIF}{$ENDIF}{$ENDIF}
HugeIntMSB = HugeIntSize-1;
type
HugeInt = array[0..HugeIntMSB]
of Byte;
const
HugeIntCarry: Boolean = False;
HugeIntDiv0: Boolean = False;
procedure
HugeInt_Min(var a: HugeInt); { a :=
-a }
procedure HugeInt_Inc(var a:
HugeInt); { a := a + 1
}
procedure HugeInt_Dec(var a: HugeInt);
{ a := a - 1 }
procedure HugeInt_Add(a,
b: HugeInt; var R: HugeInt); { R := a + b
}
procedure HugeInt_Sub(a, b: HugeInt; var R: HugeInt);
{ R := a - b }
procedure HugeInt_Mul(a, b:
HugeInt; var R: HugeInt); { R := a * b
}
procedure HugeInt_Div(a, b: HugeInt; var R: HugeInt);
{ R := a div b }
procedure HugeInt_Mod(a,
b: HugeInt; var R: HugeInt); { R := a mod b
}
function HugeInt_IsNeg(a: HugeInt):
Boolean;
function HugeInt_Zero(a: HugeInt):
Boolean;
function HugeInt_Odd(a: HugeInt):
Boolean;
function HugeInt_Comp(a, b: HugeInt): Integer;
{-1:a< 0; 1:a>}
procedure
HugeInt_Copy(Src: HugeInt; var Dest: HugeInt);{ Dest
:= Src }
procedure String2HugeInt(AString: string;
var a: HugeInt);
procedure Integer2HugeInt(AInteger: Integer;
var a: HugeInt);
procedure HugeInt2String(a: HugeInt;
var S: string);
implementation
procedure HugeInt_Copy(Src:
HugeInt; var Dest: HugeInt);
{ Dest := Src
}
begin
Move(Src, Dest, SizeOf(HugeInt));
end;{ HugeInt_Copy }
function HugeInt_IsNeg(a:
HugeInt): Boolean;
begin
HugeInt_IsNeg := a[HugeIntMSB] and $80 > 0;
end;{ HugeInt_IsNeg }
function HugeInt_Zero(a:
HugeInt): Boolean;
var i: Integer;
begin
HugeInt_Zero := False;
for i := 0 to HugeIntMSB
do
if a[i] <> 0 then
Exit;
HugeInt_Zero := True;
end;{
HugeInt_Zero }
function HugeInt_Odd(a: HugeInt):
Boolean;
begin
HugeInt_Odd := a[0] and 1 > 0;
end;{ HugeInt_Odd }
function HugeInt_HCD(a:
HugeInt): Integer;
var i: Integer;
begin
i := HugeIntMSB;
while (i > 0) and (a[i] =
0) do Dec(i);
HugeInt_HCD := i;
end;{
HugeInt_HCD }
procedure HugeInt_SHL(var a: HugeInt;
Digits: Integer);
{ Перемещение байтов переменной
"Digits" в левую часть,
байты "Digits" будут 'ослабевать' в MSB-части.
LSB-часть заполняется нулями. }
var t:
Integer;
b: HugeInt;
begin
if Digits > HugeIntMSB then
FillChar(a, SizeOf(HugeInt), 0)
else if Digits > 0 then
begin
Move(a[0], a[Digits],
HugeIntSize-Digits);
FillChar(a[0], Digits, 0);
end;{ else if
}
end;{ HugeInt_SHL
}
procedure HugeInt_SHR(var a: HugeInt; Digits:
Integer);
var t: Integer;
begin
if Digits > HugeIntMSB then
FillChar(a, SizeOf(HugeInt), 0)
else if Digits > 0 then
begin
Move(a[Digits], a[0],
HugeIntSize-Digits);
FillChar(a[HugeIntSize-Digits], Digits, 0);
end;{ else if
}
end;{ HugeInt_SHR
}
procedure HugeInt_Inc(var a: HugeInt);
{ a := a + 1 }
var
i: Integer;
h: Word;
begin
i := 0; h := 1;
repeat
h := h + a[i];
a[i] := Lo(h);
h := Hi(h);
Inc(i);
until (i > HugeIntMSB) or (h = 0);
HugeIntCarry := h > 0;
{$IFOPT R+ }
if HugeIntCarry then RunError(215);
{$ENDIF}
end;{ HugeInt_Inc }
procedure
HugeInt_Dec(var a: HugeInt);
{ a := a - 1
}
var Minus_1: HugeInt;
begin
{ самый простой способ }
FillChar(Minus_1, SizeOf(HugeInt), $FF);
{ -1 }
HugeInt_Add(a, Minus_1, a);
end;{
HugeInt_Dec }
procedure HugeInt_Min(var a:
HugeInt);
{ a := -a }
var i:
Integer;
begin
for i := 0 to HugeIntMSB
do
a[i] := not a[i];
HugeInt_Inc(a);
end;{ HugeInt_Min
}
function HugeInt_Comp(a, b: HugeInt): Integer;
{ a = b: ==0; a > b: ==1; a < b: ==-1
}
var
A_IsNeg, B_IsNeg: Boolean;
i: Integer;
begin
A_IsNeg := HugeInt_IsNeg(a);
B_IsNeg := HugeInt_IsNeg(b);
if A_IsNeg xor B_IsNeg then
if A_IsNeg then HugeInt_Comp := -1
else HugeInt_Comp := 1
else
begin
if A_IsNeg then HugeInt_Min(a);
if B_IsNeg then HugeInt_Min(b);
i := HugeIntMSB;
while (i > 0) and (a[i] =
b[i]) do Dec(i);
if A_IsNeg then { оба
отрицательные! }
if a[i] > b[i] then HugeInt_Comp := -1
else if a[i] < b[i] then HugeInt_Comp := 1
else HugeInt_Comp := 0
else { оба положительные }
if a[i] > b[i] then HugeInt_Comp := 1
else if a[i] < b[i] then HugeInt_Comp := -1
else HugeInt_Comp := 0;
end;{ else
}
end;{ HugeInt_Comp
}
procedure HugeInt_Add(a, b: HugeInt; var R:
HugeInt);
{ R := a + b }
var
i: Integer;
h: Word;
begin
h := 0;
for i := 0 to HugeIntMSB
do
begin
h := h + a[i] + b[i];
R[i] := Lo(h);
h := Hi(h);
end;{ for }
HugeIntCarry := h > 0;
{$IFOPT R+ }
if HugeIntCarry then RunError(215);
{$ENDIF}
end;{ HugeInt_Add }
procedure HugeInt_Sub(a, b:
HugeInt; var R: HugeInt);
{ R := a - b
}
var
i: Integer;
h: Word;
begin
HugeInt_Min(b);
HugeInt_Add(a, b, R);
end;{
HugeInt_Sub }
procedure HugeInt_Mul(a, b: HugeInt;
var R: HugeInt);
{ R := a * b
}
var
i, j, k: Integer;
A_end, B_end: Integer;
A_IsNeg, B_IsNeg: Boolean;
h: Word;
begin
A_IsNeg := HugeInt_IsNeg(a);
B_IsNeg := HugeInt_IsNeg(b);
if A_IsNeg then HugeInt_Min(a);
if B_IsNeg then HugeInt_Min(b);
A_End := HugeInt_HCD(a);
B_End := HugeInt_HCD(b);
FillChar(R, SizeOf(R), 0);
HugeIntCarry := False;
for i := 0 to A_end do
begin
h := 0;
for j:= 0 to B_end
do
if (i + j) < HugeIntSize then
begin
h := h + R[i+j] + a[i] * b[j];
R[i+j] := Lo(h);
h := Hi(h);
end;{ if }
k := i + B_End + 1;
while (k < HugeIntSize) and (h > 0) do
begin
h := h + R[k];
R[k] := Lo(h);
h := Hi(h);
Inc(k);
end;{ while }
HugeIntCarry := h > 0;
{$IFOPT R+}
if HugeIntCarry then RunError(215);
{$ENDIF}
end;{ for }
{ если все хорошо... }
if A_IsNeg xor B_IsNeg then
HugeInt_Min(R);
end;{ HugeInt_Mul
}
procedure HugeInt_DivMod(var a: HugeInt; b:
HugeInt; var R: HugeInt);
{ R := a div b a := a
mod b }
var
MaxShifts, s, q: Integer;
d, e: HugeInt;
A_IsNeg, B_IsNeg: Boolean;
begin
if HugeInt_Zero(b) then
begin
HugeIntDiv0 := True;
Exit;
end{ if }
else HugeIntDiv0 := False;
A_IsNeg := HugeInt_IsNeg(a);
B_IsNeg := HugeInt_IsNeg(b);
if A_IsNeg then HugeInt_Min(a);
if B_IsNeg then HugeInt_Min(b);
if HugeInt_Comp(a, b) < 0
then
{ a<b; нет необходимости деления
}
FillChar(R, SizeOf(R), 0)
else
begin
FillChar(R, SizeOf(R), 0);
repeat
Move(b, d, SizeOf(HugeInt));
{ сначала вычисляем количество перемещений
(сдвигов) }
MaxShifts := HugeInt_HCD(a) - HugeInt_HCD(b);
s := 0;
while (s <= MaxShifts) and (HugeInt_Comp(a, d)
>= 0) do
begin
Inc(s);
HugeInt_SHL(d, 1);
end;{ while }
Dec(s);
{ Создаем новую копию b }
Move(b, d, SizeOf(HugeInt));
{ Перемещаем (сдвигаем) d }
HugeInt_ShL(d, S);
{ Для добавление используем e = -d, это
быстрее чем вычитание d }
Move(d, e, SizeOf(HugeInt));
HugeInt_Min(e);
Q := 0;
{ пока a >= d вычисляем a := a+-d и
приращиваем Q}
while HugeInt_Comp(a, d) >= 0
do
begin
HugeInt_Add(a, e, a);
Inc(Q);
end;{ while }
{ Упс!, слишком много вычитаний; коррекция }
if HugeInt_IsNeg(a) then
begin
HugeInt_Add(a, d, a);
Dec(Q);
end;{ if }
HugeInt_SHL(R, 1);
R[0] := Q;
until HugeInt_Comp(a, b) < 0;
if A_IsNeg xor B_IsNeg then
HugeInt_Min(R);
end;{ else
}
end;{ HugeInt_Div }
procedure HugeInt_DivMod100(var a: HugeInt;
var R: Integer);
{ 256-тиричное деление - работает
только с
положительными числами: R := a mod 100; a:= a div 100;
}
var
Q: HugeInt;
S: Integer;
begin
R := 0; FillChar(Q, SizeOf(Q), 0);
S := HugeInt_HCD(a);
repeat
r := 256*R + a[S];
HugeInt_SHL(Q, 1);
Q[0] := R div 100;
R := R mod 100;
Dec(S);
until S < 0;
Move(Q, a, SizeOf(Q));
end;{
HugeInt_DivMod100 }
procedure HugeInt_Div(a, b: HugeInt;
var R: HugeInt);
begin
HugeInt_DivMod(a, b, R);
end;{
HugeInt_Div }
procedure HugeInt_Mod(a, b: HugeInt;
var R: HugeInt);
begin
HugeInt_DivMod(a, b, R);
Move(a, R, SizeOf(HugeInt));
end;{
HugeInt_Mod }
procedure HugeInt2String(a: HugeInt;
var S: string);
function Str100(i: Integer): string;
begin
Str100 := Chr(i div 10 + Ord('0')) + Chr(i mod 10 +
Ord('0'));
end;{ Str100
}
var
R: Integer;
Is_Neg: Boolean;
begin
S := '';
Is_Neg := HugeInt_IsNeg(a);
if Is_Neg then HugeInt_Min(a);
repeat
HugeInt_DivMod100(a, R);
Insert(Str100(R), S, 1);
until HugeInt_Zero(a) or (Length(S) = 254);
while (Length(S) > 1) and
(S[1] = '0') do
Delete(S, 1, 1);
if Is_Neg then Insert('-', S,
1);
end;{ HugeInt2String
}
procedure String_DivMod256(var S: string;
var R: Integer);
{ 10(00)-тиричное деление -
работает только с
положительными числами: R := S mod 256; S := S div 256
}
var Q: string;
begin
FillChar(Q, SizeOf(Q), 0);
R := 0;
while S <> '' do
begin
R := 10*R + Ord(S[1]) - Ord('0'); Delete(S, 1, 1);
Q := Q + Chr(R div 256 + Ord('0'));
R := R mod 256;
end;{ while }
while (Q <> '') and
(Q[1] = '0') do
Delete(Q, 1, 1);
S := Q;
end;{ String_DivMod256
}
procedure String2HugeInt(AString: string;
var a: HugeInt);
var
i, h: Integer;
Is_Neg: Boolean;
begin
if AString = '' then AString
:= '0';
Is_Neg := AString[1] = '-';
if Is_Neg then Delete(Astring, 1,
1);
i := 0;
while (AString <> '')
and (i <= HugeIntMSB) do
begin
String_DivMod256(AString, h);
a[i] := h;
Inc(i);
end;{ while }
if Is_Neg then HugeInt_Min(a);
end;{ String2HugeInt }
procedure
Integer2HugeInt(AInteger: Integer; var a: HugeInt);
var Is_Neg:
Boolean;
begin
Is_Neg := AInteger < 0;
if Is_Neg then AInteger := -AInteger;
FillChar(a, SizeOf(HugeInt), 0);
Move(AInteger, a, SizeOf(Integer));
if Is_Neg then HugeInt_Min(a);
end;{ Integer2HugeInt }
end.