% From the book
% PROLOG PROGRAMMING IN DEPTH
% by Michael A. Covington, Donald Nute, and Andre Vellino
% (Prentice Hall, 1997).
% Copyright 1997 Prentice-Hall, Inc.
% For educational use only

% File REALSQR2.PL
% From Chapter 2

% close_enough/2 and later version of real_square_root/2


close_enough(X,X) :- !.

close_enough(X,Y) :- X < Y,
                     Diff is Y-X,
                     Diff < 0.0001.

close_enough(X,Y) :- Y < X,
                     close_enough(Y,X).



real_square_root(X,nonexistent) :-                  % Clause 1
                         nonvar(X),
                         X < 0.0.

real_square_root(X,Y) :- nonvar(X),                 % Clause 2
                         X >= 0.0,
                         R is sqrt(X),
                         close_enough(R,Y).

real_square_root(X,Y) :- nonvar(X),                 % Clause 3
                         X > 0.0,
                         R is -sqrt(X),
                         close_enough(R,Y).

real_square_root(X,Y) :- nonvar(Y),                 % Clause 4
                         Ysquared is Y*Y,
                         close_enough(Ysquared,X).