function ln ( x : number ) : number;
	var	a, b, temp : number;
		shift, logbase : integer;

	begin
	logbase := crude_estimate_of_ln(x)/ln(BASE);
	if 2*logbase<Digits then begin
		shift := Digits div 2 - logbase + 1;
		ln := ln( x * BASE**shift ) - shift*LNBASE
		end
	else	begin
		a := 1.0;	b := 4/x;
		while a-b>sqrteps do begin
			temp := a;
			a := (a+b) / 2;
			b := sqrt( temp*b )
			end;
		ln := Pi / (a+b)
		end
	end;