Re: Elisp manual, node "Comparison of Numbers"

[David Kastrup <dak@gnu.org>]

Lennart Borgman <lennart.borgman.073@student.lu.se> writes:

> 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.

It is merely the distance from 0, not the "relative distance".

-- 
David Kastrup, Kriemhildstr. 15, 44793 Bochum