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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