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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 1.5.0.2 (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)))
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.

```