"Drew Adams" <address@hidden> writes:
I blindly got bit by this one. The Elisp manual gives this as an example of
how to test near equality of floating-point numbers:
(defvar fuzz-factor 1.0e-6)
(defun approx-equal (x y)
(or (and (= x 0) (= y 0))
(< (/ (abs (- x y))
(max (abs x) (abs y)))
fuzz-factor)))
When either x or y is 0.0, but not both, this gives nil no matter how close
the other number is to zero. I think this is more like what is needed:
(defun approx-equal (x y &optional fuzz)
(setq fuzz (or fuzz 1.0e-8))
(cond ((= x 0.0) (< y fuzz))
((= y 0.0) (< x fuzz))
(t (< (/ (abs (- x y)) (max (abs x) (abs y))) fuzz))))
The problem here is that fuzz is a _relative_ measure of equality, and
you employ it as an absolute measure here. I don't think it a good
idea at all that 1e-12 and 0.995e-12 are considered different, while
1e-8 and 0.0 are considered equal.