;;;; Math Utilities

;;; FIB computes the the Fibonacci function in the traditional
;;; recursive way.

(defun fib (n)
  (check-type n integer)
  ;; At this point we're sure we have an integer argument.
  ;; Now we can get down to some serious computation.
  (cond ((< n 0)
         ;; Hey, this is just supposed to be a simple example.
         ;; Did you really expect me to handle the general case?
         (error "FIB got ~D as an argument." n))
        ((< n 2) n)             ;fib[0]=0 and fib[1]=1
        ;; The cheap cases didn't work.
        ;; Nothing more to do but recurse.
        (t (+ (fib (- n 1))     ;The traditional formula
              (fib (- n 2)))))) ; is fib[n-1]+fib[n-2].