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
>