Sorry, dice1 is wrong.
----- Original Message -----
From: Roger Hui <[EMAIL PROTECTED]>
Date: Thursday, July 13, 2006 2:09 pm
Subject: Re: [Jbeta] monadic '?' (and #. slowdown
> > 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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