# distinguishing usual numbers, infinities and NaN

In a Scheme program, I need to distinguish infinities and NaN values. In Guile, it's simple, it's just the functions inf? and nan?. But when I took another implementation, I got troubles. I spent a lot of time and tried everything -- =, eq?, equal?, but nothing helped. Fortunately, after a break, I found a simple universal solution.

Let's see what happens if we compare (by <) the values.

Code:

``````(for-each (lambda (left)
(for-each (lambda (right)
(display (< left right))(display " "))
(list (/ 0.0 0.0) (/ 1.0 0.0) (/ -1.0 0.0) 777))
(newline))
(list (/ 0.0 0.0) (/ 1.0 0.0) (/ -1.0 0.0) 777))
``````

The table:

```  <   | NaN +inf -inf 777
-------------------------
NaN   |  #f  #f   #f  #f
+inf  |  #f  #f   #f  #f
-inf  |  #f  #t   #f  #t
777   |  #f  #t   #f  #f
```

Similar tables can be got for > and =. With this table, it's easy to differentiate the type of a variable x. For example:

* If it is greater than -inf and less that +inf, it's an usual number.
* Otherwise: if it is greater than -inf, then it's +inf; if it is less than +inf, then it's -inf.
* Otherwise, it's NaN.

The code uses another algorithm of the same style.

``````(define gx:nan? (lambda (x) (not (or (< x 777) (> x -777)))))
(define gx:inf? (lambda (x)
(if (and (< x (/ 1.0 0.0)) (> x (/ -1.0 0.0)))
#f
(not (gx:nan? x)))))
``````

Testing:

``````(map gx:inf? (list (/ 0.0 0.0) (/ 1.0 0.0) (/ -1.0 0.0) 777))
===> (#f #t #t #f)

(map gx:nan? (list (/ 0.0 0.0) (/ 1.0 0.0) (/ -1.0 0.0) 777))
===> (#t #f #f #f)
``````
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