Personally, I prefer the fork 1 + u over the perhaps more obvious >:@u
Other than that, I kind of like your ndr.
Thanks,
--
Raul
On Mon, Jul 27, 2015 at 11:47 AM, Dan Bron <j...@bron.us> wrote:
>
> Raul wrote:
>> twosC=: #:~ 2 #~ 1 + {:@$@#:
>
> The clause {:@$@#: does a lot of work (computationally speaking, not
> notationally speaking) to determine the number of bits required. There is a
> cheaper way.
>
> But the problem with “cheaper ways” is I always have to come up with them and
> then teach J what they are. Just for once, I’d like J to teach *me* how to
> do it better.
>
> Well, today is that day:
>
> 2&#. b. _1
> ($&2@>:@(2&(<.@^.))@(1&>.)@(>./)@:|@, #: ]) :.(2&#.)
>
> Thus [1]:
>
> ndr NB. Number of Digits Required
> 10&$: :( >:@<.@^. 1 >. >./@:|@, )
>
> And so:
>
> twosC =: #:~ 2 #~ 1 + {:@$@#:
> twosC2 =: #:~ 2 #~ 1 + 2&ndr
>
> (twosC2 -: twosC) i:4
> 1
>
> Comparing performance:
>
> A=:i:1e7 NB. Unnecessarily large
> Q=:10 timespacex&> '{:@$@#: A';'2&ndr A’
>
> Q
> 0.501709 5.36873e8
> 0.204981 5.36873e8
>
> 0.01 round %/Q [ load'numeric'
> 2.45 1
>
> Of course this difference is only showing up with unrealistically large
> inputs, and in that case will be swamped by the calculation and manifestation
> of the final #: array in twosC … but, it was a fun opportunity to show off
> n&#. b. _1 (one of my favorite J tricks).
>
> -Dan
>
> [1] I really think ndr or some variant should be included in the standard
> library. I also think I shouldn’t have to load’numeric’ to get something as
> useful and frequently-needed as “round”.
>
>
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