Jokerjar
BANNED | Редактировать | Профиль | Сообщение | Цитировать | Сообщить модератору
unit UMathServices;
{©Drkb v.3(2007): www.drkb.ru,
®Vit (Vitaly Nevzorov) - nevzorov@yahoo.com}
interface
Type TProgress = procedure(Done:real);
{Собственно экспортные функции}
Function ulFact(First:String):string;
Function ulSum(First, Second :string):string;
Function ulSub(First, Second :string):string;
Function ulMPL(First, Second :string):string;
Function ulPower(First, Second :string):string;
function UlDiv(First, Second:String; Precision:integer):String; {Precision - не истинная точность а количество знаков учитываемых после запятой сверх тех которые значимы. Все знаки уже существующие в делимом и делителе в любом случае учитываются}
{Call back function for long operations}
var OnProgress: TProgress;
implementation
Uses SysUtils;
type TMathArray=array of integer;
Type TNumber=record
int, frac:TMathArray;
sign:boolean;
end;
var n1, n2:TNumber;
Procedure Str2Number(s:string; var n:TNumber);
var i, j, l:integer;
begin
if s='' then
begin
setlength(n.int , 0);
setlength(n.frac , 0);
exit;
end;
l:=length(s);
if s[1]='-' then
begin
s:=copy(s,2,l);
l:=l-1;
n.sign:=false;
end
else
n.sign:=true;
j:=pos('.', s);
if j>0 then
begin
setlength(n.int , j-1);
for i:=1 to j-1 do n.int[i-1]:=strtoint(s[j-i]);
setlength(n.frac , l-j);
for i:=1 to l-j do n.frac[i-1]:=strtoint(s[l-i+1]);
end
else
begin
setlength(n.int,l);
for i:=1 to l do n.int[i-1]:=strtoint(s[l-i+1]);
setlength(n.frac,0);
end;
end;
Function Num2Array(Var n:TNumber; var a:TMathArray):integer;
var i:integer;
begin
result:=length(n.frac);
setlength(a,length(n.int)+result);
for i:=0 to length(a)-1 do if i<result then a[i]:=n.frac[i] else a[i]:=n.int[i-result];
end;
Procedure MultiplyArray(var a1, a2, a:TMathArray);
var i, j:integer;
b:boolean;
begin
{checking for zero, 1}
for i:=length(a2)-1 downto 0 do
begin
for j:=length(a1)-1 downto 0 do
begin
a[j+i]:=a[j+i]+(a2[i]*a1[j]);
end;
end;
repeat
b:=true;
for i:=0 to length(a)-1 do
if a[i]>9 then
begin
b:=false;
try
a[i+1]:=a[i+1]+1;
except
setlength(a, length(a)+1);
a[i+1]:=a[i+1]+1;
end;
a[i]:=a[i]-10;
end;
until b;
end;
Procedure Array2Num(Var n:TNumber; var a:TMathArray; frac:integer; sign:boolean);
var i:integer;
begin
setlength(n.frac,frac);
setlength(n.int,length(a)-frac);
for i:=0 to length(a)-1 do
begin
if i<frac then n.frac[i]:=a[i] else n.int[i-frac]:=a[i];
end;
n.sign:=sign;
end;
Function Number2Str(var n:TNumber):string;
var i:integer;
s:string;
begin
result:='';
for i:=0 to high(n.int) do result:=inttostr(n.int[i])+result;
if length(n.frac)<>0 then
begin
for i:=0 to high(n.frac) do s:=inttostr(n.frac[i])+s;
result:=result+'.'+s;
end;
while (length(result)>1) and (result[1]='0') do delete(result,1,1);
if pos('.', result)>0 then while (length(result)>1) and (result[length(result)]='0') do delete(result,length(result),1);
if not n.sign then result:='-'+result;
setlength(n.int,0);
setlength(n.frac,0);
end;
Procedure DisposeNumber(var n:TNumber);
begin
setlength(n.int,0);
setlength(n.frac,0);
end;
Function ulFact(First:String):string;
var n1, n2:TNumber;
i:integer;
a, a1, a2:TMathArray;
max:integer;
begin
Str2Number('1', n1);
Str2Number('1', n2);
Num2Array(n1, a1);
Num2Array(n2, a2);
max:=strtoint(First);
for i:=1 to strtoint(First) do
begin
if Assigned(OnProgress) then OnProgress((i/max)*100);
setlength(a,length(a1)+length(a2)+1);
MultiplyArray(a1, a2, a);
setlength(a1,0);
setlength(a2,0);
a1:=a;
Str2Number(inttostr(i), n2);
Num2Array(n2, a2);
end;
Array2Num(n1, a1, 0, true);
result:=Number2Str(n1);
DisposeNumber(n1);
end;
Function ulPower(First, Second :string):string;
var i, j, c:integer;
a, a1, a2:TMathArray;
var n1:TNumber;
max:integer;
begin
j:=strtoint(Second);
if j=0 then
begin
result:='1';
exit;
end
else
if j=1 then
begin
result:=First;
exit;
end;
max:=j-1;
Str2Number(First, n1);
c:=Num2Array(n1, a1);
setlength(a,0);
setlength(a2,0);
a2:=a1;
for i:=1 to j-1 do
begin
if Assigned(OnProgress) then OnProgress((i/max)*100);
setlength(a,0);
setlength(a,length(a1)+length(a2)+1);
MultiplyArray(a1, a2, a);
setlength(a2,0);
a2:=a;
end;
setlength(a1,0);
setlength(a2,0);
c:=c*j;
if n1.sign then
Array2Num(n1, a, c, true)
else
if odd(j) then Array2Num(n1, a, c, false) else Array2Num(n1, a, c, true);
setlength(a,0);
result:=Number2Str(n1);
DisposeNumber(n1);
end;
Procedure MultiplyNumbers(var n1, n2 :TNumber);
var i:integer;
a, a1, a2:TMathArray;
begin
i:=Num2Array(n1, a1)+Num2Array(n2, a2);
setlength(a,length(a1)+length(a2)+1);
MultiplyArray(a1, a2, a);
setlength(a1,0);
setlength(a2,0);
Array2Num(n1, a, i, n1.sign=n2.sign);
DisposeNumber(n2);
setlength(a,0);
end;
Function ulMPL(First, Second :string):string;
var n1, n2:TNumber;
begin
Str2Number(First, n1);
Str2Number(Second, n2);
MultiplyNumbers(n1, n2);
result:=Number2Str(n1);
DisposeNumber(n1);
end;
Procedure AlignNumbers(var n1, n2:TNumber);
var i1, i2, i:integer;
begin
i1:=length(n1.int);
i2:=length(n2.int);
if i1>i2 then setlength(n2.int, i1);
if i2>i1 then setlength(n1.int, i2);
i1:=length(n1.frac);
i2:=length(n2.frac);
if i1>i2 then
begin
setlength(n2.frac, i1);
for i:=i1-1 downto 0 do
begin
if i-(i1-i2)>0 then n2.frac[i]:=n2.frac[i-(i1-i2)] else n2.frac[i]:=0;
end;
end;
if i2>i1 then
begin
setlength(n1.frac, i2);
for i:=i2-1 downto 0 do
begin
if i-(i2-i1)>0 then n1.frac[i]:=n1.frac[i-(i2-i1)] else n1.frac[i]:=0;
end;
end;
end;
Function SubInteger(a1,a2:TMathArray):integer;
var i:integer;
b:boolean;
begin
result:=0;
if length(a1)=0 then exit;
for i:=0 to length(a1)-1 do a1[i]:=a1[i]-a2[i];
repeat
b:=true;
for i:=0 to length(a1)-1 do
if a1[i]<0 then
begin
b:=false;
if i=length(a1)-1 then
begin
result:=-1;
a1[i]:=a1[i]+10;
b:=true;
end
else
begin
a1[i+1]:=a1[i+1]-1;
a1[i]:=a1[i]+10;
end;
end;
until b;
end;
Procedure AssignNumber(out n1:TNumber; const n2:TNumber);
var i:integer;
begin
Setlength(n1.int, length(n2.int));
for i:=0 to length(n2.int)-1 do n1.int[i]:=n2.int[i];
Setlength(n1.frac, length(n2.frac));
for i:=0 to length(n2.frac)-1 do n1.frac[i]:=n2.frac[i];
n1.sign:=n2.sign;
end;
Procedure SubNumber(var n1, n2 : TNumber);
var i:integer;
n:TNumber;
begin
AlignNumbers(n1, n2);
i:=subInteger(n1.frac, n2.frac);
n1.int[0]:=n1.int[0]+i;
DisposeNumber(n);
AssignNumber(n, n1);
i:=subInteger(n1.int, n2.int);
if i<0 then
begin
subInteger(n2.int, n.int);
AssignNumber(n1, n2);
end
else
begin
DisposeNumber(n2);
end;
end;
Function SumInteger(a1,a2:TMathArray):integer;
var i:integer;
b:boolean;
begin
result:=0;
if length(a1)=0 then exit;
for i:=0 to length(a1)-1 do a1[i]:=a1[i]+a2[i];
repeat
b:=true;
for i:=0 to length(a1)-1 do
if a1[i]>9 then
begin
b:=false;
if i=length(a1)-1 then
begin
result:=1;
a1[i]:=a1[i]-10;
b:=true;
end
else
begin
a1[i+1]:=a1[i+1]+1;
a1[i]:=a1[i]-10;
end;
end;
until b;
end;
Procedure SumNumber(var n1, n2:TNumber);
var i:integer;
begin
AlignNumbers(n1, n2);
i:=sumInteger(n1.frac, n2.frac);
n1.int[0]:=n1.int[0]+i;
i:=sumInteger(n1.int, n2.int);
if i>0 then
begin
setlength(n1.int, length(n1.int)+1);
n1.int[length(n1.int)-1]:=i;
end;
DisposeNumber(n2);
end;
Procedure SumNumbers(var n1, n2:TNumber);
begin
if n1.sign and n2.sign then
begin
SumNumber(n1, n2);
n1.sign:=true;
end
else
if (not n1.sign) and (not n2.sign) then
begin
SumNumber(n1, n2);
n1.sign:=False;
end
else
if (not n1.sign) and n2.sign then
begin
SubNumber(n2, n1);
AssignNumber(n1, n2);
end
else
begin
SubNumber(n1, n2);
end;
end;
Function ulSum(First, Second :string):string;
begin
Str2Number(First, n1);
Str2Number(Second, n2);
SumNumbers(n1, n2);
result:=Number2Str(n1);
DisposeNumber(n1);
end;
Function ulSub(First, Second :string):string;
begin
Str2Number(First, n1);
Str2Number(Second, n2);
n2.sign:=not n2.sign;
SumNumbers(n1, n2);
result:=Number2Str(n1);
DisposeNumber(n1);
end;
function DupChr(const X:Char;Count:Integer):AnsiString;
begin
if Count>0 then begin
SetLength(Result,Count);
if Length(Result)=Count then FillChar(Result[1],Count,X);
end;
end;
function StrCmp(X,Y:AnsiString):Integer;
var
I,J:Integer;
begin
I:=Length(X);
J:=Length(Y);
if I=0 then begin
Result:=J;
Exit;
end;
if J=0 then begin
Result:=I;
Exit;
end;
if X[1]=#45 then begin
if Y[1]=#45 then begin
X:=Copy(X,2,I);
Y:=Copy(Y,2,J);
end else begin
Result:=-1;
Exit;
end;
end else if Y[1]=#45 then begin
Result:=1;
Exit;
end;
Result:=I-J;
if Result=0 then Result:=CompareStr(X,Y);
end;
function StrDiv(X,Y:AnsiString):AnsiString;
var
I,J:Integer;
S,V:Boolean;
T1,T2:AnsiString;
R:string;
max:integer;
begin
Result:=#48;
R:=#48;
I:=Length(X);
J:=Length(Y);
S:=False;
V:=False;
if I=0 then Exit;
if (J=0) OR (Y[1]=#48) then begin
Result:='';
R:='';
Exit;
end;
if X[1]=#45 then begin
Dec(I);
V:=True;
X:=Copy(X,2,I);
if Y[1]=#45 then begin
Dec(J);
Y:=Copy(Y,2,J)
end else S:=True;
end else if Y[1]=#45 then begin
Dec(J);
Y:=Copy(Y,2,J);
S:=True;
end;
Dec(I,J);
if I<0 then begin
R:=X;
Exit;
end;
T2:=DupChr(#48,I);
T1:=Y+T2;
T2:=#49+T2;
max:= Length(T1);
while Length(T1)>=J do begin
while StrCmp(X,T1)>=0 do begin
X:=UlSub(X,T1);
Result:=UlSum(Result,T2);
end;
SetLength(T1,Length(T1)-1);
SetLength(T2,Length(T2)-1);
if Assigned(OnProgress) then OnProgress(100-(Length(T1)/max)*100);
end;
R:=X;
if S then if Result[1]<>#48 then Result:=#45+Result;
if V then if R[1]<>#48 then R:=#45+R;
end;
Function Mul10(First:string; Second:integer):string;
var s:string;
i, j:integer;
begin
if pos('.',First)=0 then
begin
s:='';
For i:=0 to Second-1 do s:=s+'0';
Result:=First+s;
end
else
begin
s:='';
j:=length(First)-pos('.',First);
if (second-j)>0 then For i:=0 to Second-j-1 do s:=s+'0';
First:=First+s;
j:=pos('.',First);
First:=StringReplace(First,'.','',[]);
insert('.',First,j+second);
while (length(First)>0) and (First[length(First)]='0') do delete(First,length(First),1);
while (length(First)>0) and (First[length(First)]='.') do delete(First,length(First),1);
Result:=First;
end;
end;
Function Div10(First:string; Second:integer):string;
var s:string;
i:integer;
begin
s:='';
For i:=0 to Second do s:=s+'0';
s:=s+First;
Insert('.', s, length(s)-Second+1);
while (length(s)>0) and (s[1]='0') do delete(s,1,1);
if pos('.',s)>0 then
while (length(s)>0) and (s[length(s)]='0') do delete(s,length(s),1);
if (length(s)>0) and (s[length(s)]='.') then delete(s,length(s),1);
Result:=s;
end;
function UlDiv(First, Second:String; Precision:integer):String;
begin
First:=Mul10(First, Precision);
result:=Div10(StrDiv(First, Second), Precision);
end;
end. |
