Date: Sun, 12 Aug 2012 23:12:28 -0000 From: Peter Jeremy <peter@rulingia.com> To: Stephen Montgomery-Smith <stephen@missouri.edu> Cc: Diane Bruce <db@db.net>, Bruce Evans <brde@optusnet.com.au>, John Baldwin <jhb@freebsd.org>, David Chisnall <theraven@freebsd.org>, Bruce Evans <bde@freebsd.org>, Steve Kargl <sgk@troutmask.apl.washington.edu>, David Schultz <das@freebsd.org>, Warner Losh <imp@bsdimp.com> Subject: Re: Use of C99 extra long double math functions after r236148 Message-ID: <20120722231300.GA8033@server.rulingia.com> Resent-Message-ID: <20120812231221.GS20453@server.rulingia.com> In-Reply-To: <500C79A1.6080809@missouri.edu> References: <20120721032448.X5744@besplex.bde.org> <5009BD6C.9050301@missouri.edu> <20120721123522.T877@besplex.bde.org> <500A2565.9090009@missouri.edu> <20120721181204.A1702@besplex.bde.org> <500B594D.1020305@missouri.edu> <20120722125300.P2246@besplex.bde.org> <500C1B1A.5070107@missouri.edu> <20120723015912.K5029@besplex.bde.org> <500C79A1.6080809@missouri.edu>
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On 2012-Jul-22 17:07:29 -0500, Stephen Montgomery-Smith <stephen@missouri.e=
du> wrote:
>I tested out the casinh program. After a small tweek, the worst case=20
>ULP is about 2.5 or 3. Edge cases close to I do very well, with a ULP=20
>of about 0.5. I am very pleased with how well it performs.
That's excellent. I think the exception handling in clog() needs some
work - in particular, input NaNs should be returned, rather than
returning new default NaNs.
>I looked at Peter Jeremy's code for catanh, and I notice that he hasn't=20
>yet worked to get optimal ULP, since he has concentrated on the handling=
=20
>of the edge cases.
As I've previously mentioned, I believe handling the exception cases
can be done completely independently of handling the "normal" cases
and I was focussing on the former since it is just a (simple) matter
of implementing the text in n1256 G.6.2.3.
>If Peter is OK with me butting in, I'll could try to work on getting=20
>optimal ULP for catanh. I think it will be easier to analyze than=20
>casinh, since no csqrts need to be involved. I anticipate that the hard=
=20
>case will be when z is close to the imaginary axis, and moderately large=
=20
>(like 1e-5 + 10*I).
The "normal" cases are (algorithmetically with '^' as exponentiation):
catanh(z) =3D clog((1+z)/(1-z))/2
=3D (clog(1+z) - clog(1-z))/2
catanh(x+I*y) =3D log((y^2 + (1+x)^2)/(y^2 + (1-x)^2))/4 + I*atan2(y^2, 1-x=
^2-y^2)/2
None of these approaches behave cleanly when |z| is close to 1. If
you have some insights, feel free to work on it.
--=20
Peter Jeremy
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