[racket] a small programming exercise

Mine's basically the same as everyone else's, except I find the first
digit using math instead of string conversion.

#lang racket

;; Compute the base-10 logarithm of a number
(define (log10 x)
  (/ (log x) (log 10)))

; Compute the first (base-10) digit of a number
(define (first-digit n)
  (inexact->exact (floor (/ n (expt 10 (floor (log10 n)))))))

; Table of occurrences
(define table (make-vector 10 0))

; Update the table of occurrences
(define (update-table n)
  (let ([i (first-digit n)])
    (vector-set! table i (add1 (vector-ref table i)))))

; Display the table
(define (distribution count)
  (map (lambda (n)
         (list n (exact->inexact (/ (vector-ref table n) count))))
       '(1 2 3 4 5 6 7 8 9)))

; Display the distribution of first digits in a list
(define (benford l)
  (begin
    (for-each update-table l)
    (distribution (length l))))

; Display the distribution of a list of random numbers
(benford (filter positive? (build-list 1000 (lambda (n) (random (add1 n))))))
==>
'((1 0.25075528700906347)
  (2 0.1782477341389728)
  (3 0.15709969788519637)
  (4 0.11379657603222558)
  (5 0.08459214501510574)
  (6 0.07653575025176233)
  (7 0.050352467270896276)
  (8 0.044310171198388724)
  (9 0.044310171198388724))