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Date:      Sun, 12 Aug 2012 23:12:13 -0000
From:      Stephen Montgomery-Smith <stephen@missouri.edu>
To:        Bruce Evans <brde@optusnet.com.au>
Cc:        Diane Bruce <db@db.net>, 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>, Peter Jeremy <peter@rulingia.com>, Warner Losh <imp@bsdimp.com>
Subject:   Re: Use of C99 extra long double math functions after r236148
Message-ID:  <500C79A1.6080809@missouri.edu>
Resent-Message-ID: <20120812231206.GR20453@server.rulingia.com>
In-Reply-To: <20120723015912.K5029@besplex.bde.org>
References:  <20120714120432.GA70706@server.rulingia.com> <20120717200931.U6624@besplex.bde.org> <5006D13D.2080702@missouri.edu> <20120718205625.GA409@troutmask.apl.washington.edu> <500725F2.7060603@missouri.edu> <20120719025345.GA1376@troutmask.apl.washington.edu> <50077987.1080307@missouri.edu> <20120719032706.GA1558@troutmask.apl.washington.edu> <5007826D.7060806@missouri.edu> <5007AD41.9070000@missouri.edu> <20120719205347.T2601@besplex.bde.org> <50084322.7020401@missouri.edu> <20120720035001.W4053@besplex.bde.org> <50085441.4090305@missouri.edu> <20120720162953.N2162@besplex.bde.org> <20120720184114.B2790@besplex.bde.org> <50097128.6030405@missouri.edu> <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>

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So now that people pointed out that casinh is available in mpc, I no 
longer need the interface to pari.  I used mpc with 300 bit precision.

I tested out the casinh program.  After a small tweek, the worst case 
ULP is about 2.5 or 3.  Edge cases close to I do very well, with a ULP 
of about 0.5.  I am very pleased with how well it performs.

I looked at Peter Jeremy's code for catanh, and I notice that he hasn't 
yet worked to get optimal ULP, since he has concentrated on the handling 
of the edge cases.

If Peter is OK with me butting in, I'll could try to work on getting 
optimal ULP for catanh.  I think it will be easier to analyze than 
casinh, since no csqrts need to be involved.  I anticipate that the hard 
case will be when z is close to the imaginary axis, and moderately large 
(like 1e-5 + 10*I).



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