[LUAU] doing 'e'

[Jim Thompson]

Jim Thompson wrote:

> or lisp
>
> (setq service_list  (mapcar  #'string-downcase TempServiceList))

Lets see a perl/python/... equivalent to this lisp exercise for 
obtaining 'e':

* (defun uniform ()
"the uniform random variable on the interval (0,1)"
  (random 1.0 ))
UNIFORM

*  (defun wait-time (&optional ignore-me)
"the number of uniform random variates when their sum first exceeds 1"
  (do ((count 0 (1+ count))
       (total 0 (+ total (uniform))))
      ((> total 1) count)))

WAIT-TIME

;; I put the optional parameter in wait-time to support this use:
* (mapcar #'wait-time '(1 1 1 1 1 1 1 1 1 1 1 1 1 1 1))
(2 2 2 2 2 2 2 3 3 4 3 2 4 3 2)

;; The wait-times are smallish integers. Let's try to see what their 
average is.
* (defun avg-wait-time (trials)
  (let ((sum 0))
    (dotimes (i trials) (incf sum (wait-time)))
    (/ sum trials 1.0)))

AVG-WAIT-TIME

;; Can you guess the limiting value of the average wait time?
* (mapcar #'avg-wait-time '(1 10 100 1000 10000 100000 1000000))

(2.0 2.9 2.71 2.726 2.7118 2.71774 2.719146)
* (mapcar #'avg-wait-time '(1 10 100 1000 10000 100000 1000000 10000000))

(2.0 3.0 2.77 2.71 2.7093 2.72287 2.717509 2.7183373)
* (mapcar #'avg-wait-time '(1 10 100 1000 10000 100000 1000000 10000000000))
(2.0 2.9 2.72 2.721 2.7164 2.71576 2.71782 2.7182744)

Euler's number, 'e', is approximately 2.7182818284590452354, and this is 
a highly-inefficient way to extract it, but
the function does tend toward 'e'.)

Jim