Date: Sat, 18 Dec 2021 10:41:14 +0000 From: Mark Murray <markm@FreeBSD.org> To: Steve Kargl <sgk@troutmask.apl.washington.edu> Cc: freebsd-hackers@freebsd.org, freebsd-current@freebsd.org Subject: Re: What to do about tgammal? Message-ID: <6C888EBF-1734-4EDC-8DBF-D2BA2454C37D@FreeBSD.org> In-Reply-To: <20211218035222.GA68916@troutmask.apl.washington.edu> References: <20211204185352.GA20452@troutmask.apl.washington.edu> <E5711C71-1095-4B6B-A33A-4CDFF123AB62@FreeBSD.org> <20211213022223.GA41440@troutmask.apl.washington.edu> <813F29E3-8478-4282-9518-5943DE7B5492@FreeBSD.org> <20211214215106.GA50381@troutmask.apl.washington.edu> <F63407DF-B7CF-4C7B-86AB-1D99EB6C6FC7@FreeBSD.org> <20211218035222.GA68916@troutmask.apl.washington.edu>
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--Apple-Mail=_D858C349-81E9-4783-9A72-6F9F7568A1F2 Content-Transfer-Encoding: quoted-printable Content-Type: text/plain; charset=us-ascii > On 18 Dec 2021, at 03:52, Steve Kargl = <sgk@troutmask.apl.washington.edu> wrote: >=20 > 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 >>>=20 >>> Note, 1.01e-17 can be reduced to soemthing like 1.01e-19 or >>=20 >> Extra diffs most welcome! >>=20 >=20 > Hi Mark, >=20 > Don't know if you noticed, but I borroewed a few cpu cycles > from grimoire. Didn't notice a thing! :-) > 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: >=20 > Interval tested for tgammal: [128,1755] > count: 1000000 > xm =3D 1.71195767195767195767195767195767183e+03L > libm =3D 7.79438030237108165017007606176403036e+4790L > mpfr =3D 7.79438030237108165017007606175285456e+4790L > ULP =3D 14869.19517 >=20 > Interval tested for tgammal: [16,128] > count: 1000000 > xm =3D 1.27687183687183687183687183687183690e+02L > libm =3D 6.61421998891483212224382625339007663e+212L > mpfr =3D 6.61421998891483212224382625338960267e+212L > ULP =3D 731.00958 >=20 > Interval tested for tgammal: [10,16] > count: 1000000 > xm =3D 1.54261654261654261654261654261654251e+01L > libm =3D 2.74203137295418912508367515208072654e+11L > mpfr =3D 2.74203137295418912508367515208073861e+11L > ULP =3D 45.61161 >=20 > Interval tested for tgammal: [1.2446e-60,10] > count: 1000000 > xm =3D 6.26200626138006138006138006138006065e-02L > libm =3D 1.54507103764516989381203274093299079e+01L > mpfr =3D 1.54507103764516989381203274093299091e+01L > ULP =3D 0.76751 Hmm. I think my understanding of ULP is missing something? I thought that ULP could not be greater than the mantissa size in bits? I.e., I thought it represents average rounding error (compared with "perfect rounding"), not truncation error, as the above very large ULPs suggest. M -- Mark R V Murray --Apple-Mail=_D858C349-81E9-4783-9A72-6F9F7568A1F2 Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename=signature.asc Content-Type: application/pgp-signature; name=signature.asc Content-Description: Message signed with OpenPGP -----BEGIN PGP SIGNATURE----- Version: GnuPG/MacGPG2 v2.2 Comment: GPGTools - http://gpgtools.org iQEzBAEBCgAdFiEEyzPHvybPbOpU9MCxQlsJDh9CUqAFAmG9usoACgkQQlsJDh9C UqA2bwf/aSpM0ZVX02od/89cMjwD+Hy5U4QemDhs+qHx0hPQn/Ry5SyEEeqjAJrA lde6OSxRhX3wBc5i/eN7vXdTz1WVj8C/QboXx0pkOBvVMOrb/9CpD5und8EIdekf f5QixS6vqXURjgLqRCdmOViCfG58KF+BcLJHZAtwl1EwoVTo28H/o+gx+2iA84oT qknObY4tKpMFqi5I5l7mmv7T/1Kiiwbe56KGAHvAMBY3u2048mOZpTGxJ/4qfSJI D/ZZLu51KAVx6mp8gRqUObxVoUpaUpYY8v1C/1Qbegmc7GGPnzcQPV28SWtB6kSw D3jkwnsxc1+GcIvHkFG2WE9Spaq5+w== =gzh1 -----END PGP SIGNATURE----- --Apple-Mail=_D858C349-81E9-4783-9A72-6F9F7568A1F2--
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