In both versions of the code, if you give a single "exponent" n, the code
would produce a single answer for S(n). Internally, it would keep a single
intermediate result. If what it's doing is what you suspect (accuse! :-)
it of doing, you can verify it by using space=:7!:2
space '10 next 1 0'
space '20 next 1 0'
and look at the grow of the space consumption.
BTW, since the function is extremely fast growing,
5^.2^1023
440.582
441 next 1 0
1.76105e308 1.32079e308
442 next 1 0
_ _
If you are not interested in rational numbers, the function has only a few
possible answers. If you are worried about time/space, one approach may be
to recompute a vector S of length 442 of all possible results, and then
define next=: {&S .
On Thu, Dec 20, 2012 at 5:28 AM, alessandro codenotti <cod...@live.it>wrote:
>
> I think I badly explained myself, or maybe i completely misunderstood the
> code:
>
> > next=.5&(0 3 + *)
>
> the verb next simply applies the "multiply by five and add 3" to is right
> argument a number of times given by is left argument, right?
>
> > (i. 20) next 1 0
>
> this instruction, first applies 0 times "next" to 1 0, then applies once
> "next" to 1 0, then applies twice "next" to 1 0, ... , then applies 20
> times "next" to 1 0, right?
>
> this mean that S(0) has been calculated 20 times, S(1) has been calculated
> 19 times, S(n) has been calculated 20-n times since every time the function
> next restarts from
> the first term (which is 1 0), right?
>
> What i mean is that with something like the following pseudo-code S(n) is
> calculated once avoiding a huge waste of time and memory:
>
> S(1)=1 0
> for i=2 to 20 do
> S(i)=.3+5*S(i-1)
> end
>
> My question then was if the code:
>
> > next=.0 3+*&5
> > 20 next@]^:(i.@[) 1 0
>
> has the same problem or not and, in case of a positive answer, how can i
> translate my pseudo-code in J avoiding an explicit loop.
>
> It may be that I completely misunderstood your code and the problem that
> is worring me doesn't exist at all but I'm really a beginner in J...
>
> Alessandro
>
>
>
>
>
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