[gambit-list] Any rational-number->string with infinite precision for decimal output? (i.e. d.ddddd rather than x/y)
Marc Feeley
feeley at iro.umontreal.ca
Wed Jan 15 22:11:19 EST 2014
On Jan 15, 2014, at 8:12 PM, Mikael <mikael.rcv at gmail.com> wrote:
>
>
> 2014/1/15 Marc Feeley <feeley at iro.umontreal.ca>
>
> On Jan 15, 2014, at 5:04 PM, Mikael <mikael.rcv at gmail.com> wrote:
>
> > 2014/1/15 Mikael <mikael.rcv at gmail.com>
> > I believe you addressed now how to detect whether a rational has inifinite decimals - yes I got aware there's an algorithm to do this too, (even while it's iterative - would be nice to understand how fast it is, anyhow) neat.
> >
> > Yeah if anyone has an example implementation of such an algorithm |has-infinite-decimals?| feel free to post :)
>
> It is really very simple. I’ll let you think about it some more before posting a solution…
>
> Marc
>
>
> I trust it's both simple and elegant - implementing something and do not have the proper focus on math in this moment;
>
> It just struck me that it's an awesome symmetry that there's this full support both re input, handling and output (per algorithm I suggested in previous email, guess that's how fast at is goes) of these, and the dot on the i in this respect would be the ability to check that a number has a finite number of decimals - saw an algorithm but didn't take it to the level of implementing it - , that was all I was thinking today.
>
> Mikael
The following algorithm is not optimal, but it has the virtue of being simple. It puts the repeating decimals in […] if there are any (in other words 1/3 prints as 0.[3] meaning 0.33333333...).
Marc
(define (println-decimal n) ;; n is a positive real
(define (generator frac states digits)
(if (= frac 0)
(reverse digits)
(let ((seen (member frac states)))
(if seen
(let* ((i (- (length seen) 1))
(len (length states)))
(append (reverse (list-tail digits (- len i)))
'(#\[)
(list-tail (reverse digits) i)
'(#\])))
(let* ((frac*10 (* 10 frac))
(digit (truncate frac*10)))
(generator (- frac*10 digit)
(cons frac states)
(cons digit digits)))))))
(println
(let* ((exact (inexact->exact n))
(int (truncate exact)))
(list int #\. (generator (- exact int) '() '())))))
(println-decimal 1/1024)
(println-decimal 1/999)
(println-decimal 5/700)
(println-decimal 0.1)
(println-decimal 0.2)
(println-decimal 0.3)
(println-decimal (* 4 (atan 1)))
(println-decimal (expt 1/3 7))
;; output:
;;
;; 0.0009765625
;; 0.[001]
;; 0.00[714285]
;; 0.1000000000000000055511151231257827021181583404541015625
;; 0.200000000000000011102230246251565404236316680908203125
;; 0.299999999999999988897769753748434595763683319091796875
;; 3.141592653589793115997963468544185161590576171875
;; 0.[000457247370827617741197988111568358481938728852309099222679469593049839963420210333790580704160951074531321444901691815272062185642432556012802926383173296753543667123914037494284407864654778235025148605395518975765889346136259716506630086877]
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