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

[Frederick H. Pitts]

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
>