Re: Elisp manual, node "Comparison of Numbers"

[storm@cua.dk (Kim F. Storm)]

David Kastrup <dak@gnu.org> writes:

> "Drew Adams" <drew.adams@oracle.com> 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.

Agree!

And:

 (approx-equal 0.0 -1.0e10) => t

-- 
Kim F. Storm <storm@cua.dk> http://www.cua.dk