REM  QBASIC

DECLARE FUNCTION p! (b!)
DECLARE FUNCTION f! (b!)
CLS

SCREEN 11
WINDOW (-.5, 6.5)-(1.5, 3.5)
LINE (0, 4)-(0, 6.2832)
LINE (1, 4)-(1, 6.2832)
LINE (0, 4)-(1, 4)
LINE (0, 6.2832)-(1, 6.2832)

FOR b = 0 TO 1 STEP .005
   PSET (b, f(b))
   PSET (b, p(b))
NEXT b

FOR b = 0 TO 1.01 STEP .05
   PRINT USING "##.## %"; (f(b) - p(b)) / f(b) * 100
NEXT b

SLEEP 0
SCREEN 0
END

FUNCTION f (b)
   h = .002
   s = (b + 1) / 2
   FOR x = h TO 1.57 STEP h
      s = s + SQR(SIN(x) ^ 2 + (b * COS(x)) ^ 2)
   NEXT x
   f = 4 * h * s
END FUNCTION

FUNCTION p (b)
   p = 2.28 * b ^ 1.44 + 4
END FUNCTION

Var
 f:Text;
 i:Byte;
 r:Real;

Const
 a1 = 0.4630151;
 a2 = 0.1077812;
 b1 = 0.2452727;
 b2 = 0.0412496;

Function Ell_Int(ba:real):real;
var
 n,m:real;
begin
 m:=SQRT(1-Sqr(ba));
 n:=1-m;
 Ell_Int:=((1+a1*n+a2*n*n)+(b1*n + b2*n*n)*ln(1/n))*4;
end;

Function Ell_App(ba:real):real;
begin
 Ell_App:=((Pi*2-4)*Exp(1.44*ln(ba))+4);
end;

Begin
 Assign(f,'D:\Ell.dat');
 Rewrite(f);
 for i:=1 to 100 do
  begin
   r:=0.01*i;
   writeln(f,r:4:2,Ell_Int(r):15:5,Ell_App(r):15:5,Abs((Ell_App(r)-Ell_Int(r))/(Ell_App(r)+Ell_Int(r)))*200:15:5);
  end;
 Close(f);
End.