begin
library A0, A1, A4, A5, A12, A15;

  comment Specimen ALGOL program from Appendix 1 of KDF9 ALGOL manual.
                 This is a program for a practically arising problem.
                 It illustrates the use of many of the facilities available to the
                 ALGOL user;

   real alpha, lambda, Delta alpha;
   integer i, f1, f2, f3, f4, f5;

   real procedure erfc (z); value z; real z;

       begin comment This procedure evaluates the complementary
                                 error function of z using the trapezoidal rule.
                                 It halves the interval until the required accuracy
                                 is attained, but avoids repeating the evaluation of
                                 ordinates more than once;

		real x, h, J0, J1;
		integer n, i;

		h := 0.1; J0 := 0; n := 0; i := 1;

	   R:	J1 := J0;

		for n := n, n + i while n × h × (n × h + 2 × z) < 11.51 do
		   begin
		      x := z + n × h;
				J0 := J0 + exp(-(x^2)) × (if n = 0 then 0.5 else 1);
		   end 	;

		if abs(1 - 2 × J1/J0) > 0.00001 then
		   begin
		      i := 2; n := 1; h := h/2;
				goto R
		   end 	;

		erfc := 1.128379 × J0 × h

	end erfc;

   open (20);

	Delta alpha := read (20); close (20);

	comment Delta alpha is the only input data item required by the program;

	open (10);

	write text (10,
	            {
	              Propagation$of$an$Impulse$into$a$Viscous-locking$Medium
	              {cccc}
	              {ssss}
	              Delta$alpha$=$
	            }
	           );

      write (10, format ({d.ddddccc}), Delta alpha);

      write text(10,
                 {
                   {ssss}
                   alpha
                   {sssss}
                   {sssss}
                   {sss}
                   lambda
                   {sssssss}
                   {sssssss}
                   {ss}
                   lambda.sqrt(2alpha)
                   {s}
                   g
                   {cc}
                   {ssss}
                   0.0000
                   {sssss}
                   {sssss}
                   {sss}
                   INFINITY
                   {sssss}
                   {sssss}
                   {sss}
                   1.00000
                   {sssss}
                   {sssss}
                   {sss}
                   1.00000
                   {c}
                 }
                );

      f1 := format ({ssssd.dddd});
      f2 := format ({12sd.ddddº+nd});
      f3 := format ({12sd.ddddd});
      f4 := format ({13sd.dddddcc});
      f5 := format ({13sd.dddddc});

      i := 1;

	for alpha := Delta alpha step Delta alpha until 1.0 do
	    begin
	       real l1, l2;

			 i := i + 1;
			 lambda := (1 - alpha)/sqrt (2 × alpha);
			 if alpha = 1 then goto SKIP;

	Repeat:
	       l1 := lambda;

		    l2 := sqrt (0.886227 × (1-alpha)/alpha × l1 × erfc (l1) × exp(+l1^2));
			 lambda := l2 + 0.835 × alpha × (l2-l1);

			 if abs (1-l2/lambda)>º-5 then goto Repeat;

	  SKIP:
	       write (10, f1, alpha);
          write (10, f2, lambda);
  		    write (10, f3, lambda × sqrt (2 × alpha));
		    write (10,
		           if i - i ÷ 5 × 5 = 0 then f4 else f5,
                   if lambda > .70710678
                     then 2 × lambda^2 × alpha × (1-alpha)
			            else
			              if lambda ± 0
			                  then alpha × (1 - alpha) × exp (lambda^2) / (lambda × 2.3282180)
				               else 0.48394
				    )
	    end;

   newline(10, 2);

	close (10)

end
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0.1;

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