Re: [Bug-apl] Binomial function with extended exact result range beyond that of primitive function

[Elias Mårtenson]

Frederick,

Is you issue with monadic ! for integer arguments only? If so, since the are only 70 or so valid inputs to this function, the results can be precalculated and the implementation can simple dereference the result from an array.

For fractional parameters to monadic !, the result of the Gamma function has to be computed which of course is much more expensive.

Regards,

Elias

On 7 August 2014 11:15, Frederick H. Pitts <address@hidden> wrote:

Hello Juergen,

        I reran timing tests comparing the defined BINOM function with the
dyadic ! function after upgrading to SVN rev. 422. I saw no difference
in the BINOM and dyadic ! results and maybe a factor of 2 slowdown in
the dyadic ! which I attributed to the change in how monadic ! is
calculated.  I was hoping to see the dyadic ! produce exact integer
results up to the 9200000000000000000 upper limit on 64-bit GnuAPL
integers after the change. :-(.

        Is the change to monadic ! actually in SVN rev. 422?  Your email does
not say.

        If the change is there, then the 15-digit precision of double precision
numbers (even if the 15 digits are exact) simply isn't enough precision
to exactly calculate the binomial ! if the right argument to the latter
is 37 or greater.  BINOM gives exact results for right arguments up to
66 with a result that approaches the upper limit of 64-bit integers.

        I'm reporting this only to let you know that the change to monadic !
did not impact the dyadic !, if in fact the change is in SVN, other than
to slow it down.

Regards,

On Wed, 2014-08-06 at 17:29 +0200, Juergen Sauermann wrote:

> Hi Fred,
>
> I did a small rework of the monadic ! function. It should now be
> exact (well, as exact as ×/⍳N is) for integer arguments up to 170
> (i.e. the max integer before DOMAIN ERROR is thrown),
>
> Before it was calling tgamma() of libm.
>
> There are still many cases where GNU APL calls libm functions
> and replacing them all by more exact versions would be rather tedious.
> There are often speed-precision trade-offs involved. Normally the
> precision of libm functions is good enough. Let's fix issues on a
> case-by-case basis when we find them.
>
> /// Jürgen
>
>
> On 08/06/2014 03:06 AM, Frederick H. Pitts wrote:
>
> > Gentle people,
> >
> >     Please find attached binom.apl.tgz.  It contains the source for BINOM,
> > a defined function does what the primitive dyadic ! function does but
> > produces exact results over a larger range.
> >
> >         BINOM produces 1) the same results as ! over the range where !
> > produces exact integers, 2) exact integer results in range above that
> > produced by the ! but below the 9200000000000000000 upper limit of GNU
> > 64-bit integers and 3) floating point results that match those of !
> > above the 64-bit integer upper limit.
> >
> >     In the interest of full disclosure:
> > 1) The code is slow; 100 times slower than the primitive dyadic !.  But
> > then BINOM is interpreted while ! is compiled in to the interpreter.
> > 2) The code was presented in 1996 on comp.lang.apl by Jim Weigang and
> > others.
> >
> > Enjoy,
> >
> > Fred
> > Retired Chemical Engineer
>