When taking a long list of pseudo random positive integers most of which are
far greater than the base, I expect about the same frequency for each first
digit from 1 to base-1. This seems to hold if the base is a power of 10, but
for other bases, e.g. base 24, I get rather unexpected results. See program
below. Someone has an idea how this can happen?
Thanks, Jos
#lang racket
(require racket/unsafe/ops racket/fixnum)
(define (first-digit n base)
(if (unsafe-fx< n base) n
(first-digit (unsafe-fxquotient n base) base)))
(define (first-digit-frequencies lon base)
(let ((v (make-fxvector (unsafe-fx- base 1) 0)))
(for ((n lon))
(let ((d (unsafe-fx- (first-digit n base) 1)))
(unsafe-vector-set! v d
(unsafe-fx+ (unsafe-vector-ref v d) 1))))
v))
(define (test vector-length number-size base)
(random-seed 1)
(let*
((lon (build-list
vector-length
(lambda (x) (add1 (random number-size)))))
(v (begin
(collect-garbage)
(collect-garbage)
(collect-garbage)
(time (first-digit-frequencies lon base)))))
(for/list ((f (in-fxvector v))) f)))
(test 1000000 1000000 10)
; cpu time: 171 real time: 171 gc time: 0
; (110963 111566 111299 111200 111218 110865 110476 111079 111334)
; all frequencies close to 1000000/9 as expected.
(test 1000000 1000000 100)
; cpu time: 124 real time: 125 gc time: 0
; list of frequencies all close to 1000000/99 as expected.
(test 1000000 1000000 24)
; cpu time: 171 real time: 172 gc time: 0
; (346114 346260 19220 remanining numbers close to 14500)
; Surprise! Expected all frequencies to be close to 1000000/23
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