Long-float variant giving more precision to numerical computations.

If you want to test the accuracy of a Bessel function subroutine, you
should test it near some difficult points, not at 1.0. Probably a
difficult place is near a zero of the Bessel function, especially
a zero that is far from the origin.
 
I would not conclude that Slatec is almost accurate enough for
double-double;
in fact, if the library is really well designed, it should be just barely
good enough for the maximum precision which was anticipated for its use.
any higher accuracy is wasted effort!

RJF

> -----Original Message-----
> From: maxima-bounces at math.utexas.edu 
> [mailto:maxima-bounces at math.utexas.edu] On Behalf Of Douglas Crosher
> Sent: Tuesday, February 26, 2008 8:09 AM
> To: Raymond Toy
> Cc: Maxima List
> Subject: Re: [Maxima] Long-float variant giving more 
> precision to numerical computations.
> 
> Raymond Toy wrote:
> > Douglas Crosher wrote:
> >>
> >> The slatec Fortran source comments suggests it is precise 
> enough for
> >> double-double float.  The code can be re-translated, 
> maintaining the
> >> constant precision, using the following hack patch.
> ...
> > Finally got around to applying this patch to f2cl.  I tried it with 
> > quadpack, and the translation looks good.  Unfortunately, the 
> > translation won't work because the f2cl-lib functions need 
> to be changed 
> > to support double-double-float.  A quick hack of f2cl-lib gives 
> > something that runs, but one simple test of quadpack dqag produces 
> > results that aren't very accurate.
> 
> Slatec seems to be almost accurate enough for double-double floats.
> For example:
> 
> (slatec:dbesj0 1w0)
> 0.76519768655796655144971752610269
> 
> Expected:
> 0.76519768655796655144971752610266322090927428975532524...
> 
> The code calculates the number of coefficients needed at 
> runtime which uses the
> result of (d1mach 3), a value of (scale-float 1w0 -100) seems to pass.
> 
> Regards
> Douglas Crosher
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