package body math_lib is

	-- function which returns the square root of a floating point number

	function sqrt(A : float) return float is
		guess, delt : float;
	begin
		if a = 0.0 then
			return 0.0;
		elsif a = 1.0 then
			return 1.0;
		else
			guess := a / 2.0;
			delt := 1.0;
			while guess ** 2 > a loop
				guess := guess / 2.0;
			end loop;
			while abs(guess ** 2 - a) > 0.0001 loop
				while (guess + delt) ** 2 > a loop
					if delt < 1.0e-6 then
						return guess;
					end if;
					delt := delt / 2.0;
				end loop;
				guess := guess + delt;
			end loop;
			return guess;
		end if;
	end sqrt;

	-- function which returns the natural log of a floating point number.

	function ln(a : float) return float is
		x1 : float