program pifreem; {1000 Stellen von pi mit der Formel von Freeman}
 uses crt,dos;    {pi=32*atn(1/10)-16*atn(1/515)-4*atn(1/239)}

 const n=1005;    {5 Sicherheitsstellen}
 var ta,te:real;
     i,j,k,m,nr,di:integer;
     c,d,q,u,x,h,mi,se,hs:word;
     a:array[1..2,1..n] of word;

 procedure divi(y:word);
 begin
  c:=0;for j:=1 to n+1 do
  begin x:=a[nr,j]+c;q:=x div y;a[nr,j]:=q;
  d:=x-y*q;c:=10*d;end;
 end;

 procedure mult(y:word);
 begin
  for j:=1 to n+1 do a[nr,j]:=y*a[nr,j];
  for j:=n+1 downto 2 do
  begin u:=a[nr,j] div 10;a[nr,j-1]:=a[nr,j-1]+u;
  a[nr,j]:=a[nr,j] mod 10;end;
 end;

 procedure atn;
 begin
  a[nr,1]:=1;k:=trunc(n*ln(10)/ln(m)/2);
  for i:=k downto 1 do
  begin
   divi(2*i+1);mult(2*i-1);divi(m);divi(m);
   for j:=2 to n-1 do a[nr,j]:=9-a[nr,j];
   a[nr,n]:=10-a[nr,n];
  end;
  divi(m);
 end;

  procedure subtr;
  begin
   for i:=n downto 2 do
   begin
    di:=a[1,i]-a[2,i];
    if di<0 then begin di:=di+10;a[1,i-1]:=a[1,i-1]-1;end;
    a[1,i]:=di;
   end;
  end;

  Begin
   clrscr;writeln;
   gettime(h,mi,se,hs);ta:=3600*h+60*mi+se+hs/100;
   nr:=1;m:=10;atn;mult(8);
   nr:=2;m:=515;atn;mult(4);subtr;
   m:=239;atn;subtr;
   nr:=1;mult(4);write('   ');
   for i:=1 to n-4 do
   begin
    write(a[1,i]);if i=1 then write('.');
    if ((i-1) mod 4=0) then write(' ');
   end;
   writeln('...');
   gettime(h,mi,se,hs);te:=3600*h+60*mi+se+hs/100;
   writeln(' 1000 Stellen in ',te-ta:3:2,' Sekunden');
   repeat until keypressed;
  End.

  {G. F. Freeman, Math. Gazette 42(1958), S.285; zit. von Werner Scholz:
  "Geschichte der Approximation der Zahl Pi", 3. verb. Version, Internet}


























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