Re: What to do about tgammal?

From: Steve Kargl <sgk_at_troutmask.apl.washington.edu>
Date: Sat, 18 Dec 2021 03:52:22 UTC 
On Tue, Dec 14, 2021 at 10:21:55PM +0000, Mark Murray wrote:
> On 14 Dec 2021, at 21:51, Steve Kargl <sgk@troutmask.apl.washington.edu> wrote:
> > Interval          max ULP          x at Max ULP
> > [6,1755.1]        0.873414 at 1.480588145237629047468e+03
> > [1.0662,6]        0.861508 at 1.999467927053585410537e+00
> > [1.01e-17,1.0661] 0.938041 at 1.023286481537296307856e+00
> > [-1.9999,-1.0001] 3.157770 at -1.246957268051453610329e+00
> > [-2.9999,-2.0001] 2.987659 at -2.220949465449893090070e+00
> > 
> > Note, 1.01e-17 can be reduced to soemthing like 1.01e-19 or
> 
> Extra diffs most welcome!
> 

Hi Mark,

Don't know if you noticed, but I borroewed a few cpu cycles
from grimoire.  My WIP is already better than the imprecise.c
kludge from theraven@.  I need to work out the details of 
computing logl(x) in extra precision or see if I can leverage
what Bruce did a few years ago.  Anywho, current results:

Interval tested for tgammal: [128,1755]
count: 1000000
  xm =  1.71195767195767195767195767195767183e+03L
libm =  7.79438030237108165017007606176403036e+4790L
mpfr =  7.79438030237108165017007606175285456e+4790L
 ULP = 14869.19517

Interval tested for tgammal: [16,128]
count: 1000000
  xm =  1.27687183687183687183687183687183690e+02L
libm =  6.61421998891483212224382625339007663e+212L
mpfr =  6.61421998891483212224382625338960267e+212L
 ULP = 731.00958

Interval tested for tgammal: [10,16]
count: 1000000
  xm =  1.54261654261654261654261654261654251e+01L
libm =  2.74203137295418912508367515208072654e+11L
mpfr =  2.74203137295418912508367515208073861e+11L
 ULP = 45.61161

Interval tested for tgammal: [1.2446e-60,10]
count: 1000000
  xm =  6.26200626138006138006138006138006065e-02L
libm =  1.54507103764516989381203274093299079e+01L
mpfr =  1.54507103764516989381203274093299091e+01L
 ULP = 0.76751




-- 
Steve