> First, y is converted to a number base x.
> Then we genereate an n-"digit" random number
> in a range 0.._1+x^n and if it is less than
> y we keep it and if it >:y we drop it
> and start over.
dice1 implements the description:
dice1=: 9999&$: : (4 : 0)"0
d=. x #.^:_1 y
while. 0 1 -: /:y,:z=. ?d do. end.
x#.z
)
The original "dice" is more complicated probably
due to optimizations. I am attempting to
understand what the optimizations are.
BTW, is it "obvious" that dice1 generates uniform
random numbers?
----- Original Message -----
From: Roger Hui <[EMAIL PROTECTED]>
Date: Thursday, July 13, 2006 1:52 pm
Subject: Re: [Jbeta] monadic '?' (and #. slowdown
> Thanks. But on the face of it the verb does
> not do the same as your description:
>
> dice=: 9999&$: : (4 : 0)"0
> y=. x #.^:_1 y-1
> label_again.
> l=.y =&{. r=.?1+{.y
> while. l *. r<&#y do.
> if. d>f=.y{~_1+#r=.r,d=.?x do. goto_again. end.
> l=.d=f
> end.
> x #. r,?x#~y-&#r
> )
>
> That is, "dice" does not generate n random digits.
> What it does is it generates random digits one
> by one, and depending on the digit d:
>
> d<i{y - keep it, and generate n-1-i more digits
> without further checking
> d=i{y - increment i and generate the next digit
> d>i{y - discard all digits and start from scratch
>
> Perhaps this is equivalent to your description,
> but the equivalence is not obvious to me.
>
> As well, if we "tweak" the verb and omit the
> "discard all digits" part but instead just
> discard the current digit d and generate
> another digit d1 and check again, that seems to
> satisfy your description of "uniform finite
> average number of discards". But you must have
> a reason for not doing that, otherwise you would
> have (I guess) gotten rid of the distasteful goto.
>
>
>
> ----- Original Message -----
> From: Andrew Nikitin <[EMAIL PROTECTED]>
> Date: Thursday, July 13, 2006 1:24 pm
> Subject: [Jbeta] monadic '?' (and #. slowdown
>
> > R&S HUI:
> > >So why are the numbers uniform?
> >
> > First, y is converted to a number base x (n digit vector) 0&{ is
> > highest"digit", _1&{ is the "lowest". Then we genereate an n-
> > "digit" random number
> > in
> > a range 0.._1+x^n and if it is less than y we keep it and if it
> > >:y we drop
> > it
> > and start over. Assuming uniform and independent distribution
> of
> > random"digits" we get uniformly distributed result. The way we
> > generate and check
> > digits promises uniformly finite average number of discarded
> > digits per
> > result (I
> > estimate this limit to be either 1 or 2).
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