Re: Elisp manual, node "Comparison of Numbers"

[Lennart Borgman <lennart.borgman.073@student.lu.se>]

Kim F. Storm wrote:
> 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!
>   
Hm. It is the relative distance from 0.