Floating point coercion problem?

[John M. Canning <jc@cvl.umd.edu>]

   Thank you for your reponse about the floating point co-processor (my v1.3.2
documentation is packed in a box waiting to be moved to another building).

   Here is a floating point problem that could be a problem with the IEEE
floating point representation or MACL's integer to floating point conversion.
Consider the following function which should always return T:

(defun foo (x) (<= (- (+ x (sqrt 2)) x) (sqrt 2)))

But in MACL

(foo 6) => T
(foo 7) => nil

This table summarizes foo's results for some integers:

  x          foo
  --------   -------
  0-6        T
  7-30       nil
  31-126     T
  127-2046   nil
  2047-4094  T
  4095-9999  nil

(I only tested up to 9999).

  Furthermore, the error generated by adding and subtracting the same integer
is greater than long-float-epsilon.
(- (- (+ 7 (sqrt 2)) 7) (sqrt 2)) => 6.661338147750939E-16
long-float-epsilon => 1.1107651257114E-16

        - John Canning