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Re: Elisp manual, node "Comparison of Numbers"

From: Lennart Borgman
Subject: Re: Elisp manual, node "Comparison of Numbers"
Date: Mon, 29 May 2006 15:54:05 +0200
User-agent: Thunderbird (Windows/20060308)

Kim F. Storm wrote:
David Kastrup <address@hidden> writes:

"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)))

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.

Hm. It is the relative distance from 0.

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