From nobody Sat Dec 18 10:41:14 2021 X-Original-To: freebsd-hackers@mlmmj.nyi.freebsd.org Received: from mx1.freebsd.org (mx1.freebsd.org [IPv6:2610:1c1:1:606c::19:1]) by mlmmj.nyi.freebsd.org (Postfix) with ESMTP id 9C65218E327C; Sat, 18 Dec 2021 10:41:18 +0000 (UTC) (envelope-from markm@FreeBSD.org) Received: from smtp.freebsd.org (smtp.freebsd.org [IPv6:2610:1c1:1:606c::24b:4]) (using TLSv1.3 with cipher TLS_AES_256_GCM_SHA384 (256/256 bits) key-exchange X25519 server-signature RSA-PSS (4096 bits) server-digest SHA256 client-signature RSA-PSS (4096 bits) client-digest SHA256) (Client CN "smtp.freebsd.org", Issuer "R3" (verified OK)) by mx1.freebsd.org (Postfix) with ESMTPS id 4JGMpQ26Hnz4kBs; Sat, 18 Dec 2021 10:41:18 +0000 (UTC) (envelope-from markm@FreeBSD.org) Received: from smtpclient.apple (unknown [IPv6:2a02:8011:300b:42:6dfc:850d:c1cd:d820]) (using TLSv1.2 with cipher ECDHE-RSA-AES256-GCM-SHA384 (256/256 bits)) (Client did not present a certificate) (Authenticated sender: markm) by smtp.freebsd.org (Postfix) with ESMTPSA id A3CC220844; Sat, 18 Dec 2021 10:41:17 +0000 (UTC) (envelope-from markm@FreeBSD.org) Content-Type: multipart/signed; boundary="Apple-Mail=_D858C349-81E9-4783-9A72-6F9F7568A1F2"; protocol="application/pgp-signature"; micalg=pgp-sha512 List-Id: Technical discussions relating to FreeBSD <freebsd-hackers.freebsd.org> List-Archive: https://lists.freebsd.org/archives/freebsd-hackers List-Help: <mailto:freebsd-hackers+help@freebsd.org> List-Post: <mailto:freebsd-hackers@freebsd.org> List-Subscribe: <mailto:freebsd-hackers+subscribe@freebsd.org> List-Unsubscribe: <mailto:freebsd-hackers+unsubscribe@freebsd.org> Sender: owner-freebsd-hackers@freebsd.org Mime-Version: 1.0 (Mac OS X Mail 15.0 \(3693.20.0.1.32\)) Subject: Re: What to do about tgammal? From: Mark Murray <markm@FreeBSD.org> In-Reply-To: <20211218035222.GA68916@troutmask.apl.washington.edu> Date: Sat, 18 Dec 2021 10:41:14 +0000 Cc: freebsd-hackers@freebsd.org, freebsd-current@freebsd.org Content-Transfer-Encoding: quoted-printable Message-Id: <6C888EBF-1734-4EDC-8DBF-D2BA2454C37D@FreeBSD.org> 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> To: Steve Kargl <sgk@troutmask.apl.washington.edu> X-Mailer: Apple Mail (2.3693.20.0.1.32) ARC-Message-Signature: i=1; a=rsa-sha256; c=relaxed/relaxed; d=freebsd.org; s=dkim; t=1639824078; h=from:from:reply-to:subject:subject:date:date:message-id:message-id: to:to:cc:cc:mime-version:mime-version:content-type:content-type: content-transfer-encoding:content-transfer-encoding: in-reply-to:in-reply-to:references:references; bh=/Ad3Lky0eNnvICrh1CZUgIH6Hu4GiGCutuqmFdwq1ow=; b=szq2Z/cwOKBb/3GIcFVjdmlT3Tt6dvTWNRiU/KYR8hRFbWMJ70MMBuGVdTb9bP6ekiozGg sQfmk/47PpDFd7y2TljtnfBW9SlKTemCfsGgcA4c8NDcsbvXpRYMgIkQN1IO+5A6UNo4Wd IporNE203CF2bdihJQmKcVtoXPiEaZlRci8/uT1bhZC0aWkvpJhZyGGt+cGkAvcF6vQ/2V JLcgK2tiIlk5AA09/S1hz1XQsy3gXnP/Qx3kDxc825mM4J7nsUBWNpov1yjenooNutd3vw z89JUbgnRKQnsuza1RPe7w6TJHC3dzECd8RHOaLpWS4oAFYuQoRGha/RhcfgcQ== ARC-Seal: i=1; s=dkim; d=freebsd.org; t=1639824078; a=rsa-sha256; cv=none; b=BVUsGMuoDwGcMRGoQL7wZ9UXzFE5uxTN2DzHwscP2uxA22GazGjk6wml3v4gPGBwDxuG92 Vbzmlwo0Pv2ZrcQIBtu1ahHLsPq9LqCdeBNlG1k/gjjNGwhxw7jqYdBRrizIQUcKbVJ+Pd 0ZPn3N7vcDb+BQkmFgOnalPPILIsX/2g+qM63C+4SWv1M3eHXiJoWCSuBL6hAXCk4IyNjh HSodVlseGiHJZC1HJNVjm1hVD1fxDT6cwkn5AIEx/JiBjhRBqmwxEt2Lysp5OUwPv9T2sZ aXiaHCZclcWbzxWvP4TM0rrp2k/SR31hiO23Gv+AHdQ9Mdu7DV6rgST8tJokpw== ARC-Authentication-Results: i=1; mx1.freebsd.org; none X-ThisMailContainsUnwantedMimeParts: N --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--