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Date:      Sat, 15 Sep 2012 21:06:28 -0500
From:      Stephen Montgomery-Smith <stephen@missouri.edu>
To:        Bruce Evans <brde@optusnet.com.au>
Cc:        freebsd-numerics@freebsd.org
Subject:   Re: Complex arg-trig functions
Message-ID:  <50553424.2080902@missouri.edu>
In-Reply-To: <20120916041132.D6344@besplex.bde.org>
References:  <5017111E.6060003@missouri.edu> <20120814003614.H3692@besplex.bde.org> <50295F5C.6010800@missouri.edu> <20120814072946.S5260@besplex.bde.org> <50297CA5.5010900@missouri.edu> <50297E43.7090309@missouri.edu> <20120814201105.T934@besplex.bde.org> <502A780B.2010106@missouri.edu> <20120815223631.N1751@besplex.bde.org> <502C0CF8.8040003@missouri.edu> <20120906221028.O1542@besplex.bde.org> <5048D00B.8010401@missouri.edu> <504D3CCD.2050006@missouri.edu> <504FF726.9060001@missouri.edu> <20120912191556.F1078@besplex.bde.org> <20120912225847.J1771@besplex.bde.org> <50511B40.3070009@missouri.edu> <20120913204808.T1964@besplex.bde.org> <5051F59C.6000603@missouri.edu> <20120914014208.I2862@besplex.bde.org> <50526050.2070303@missouri.edu> <20120914212403.H1983@besplex.bde.org> <50538E28.6050400@missouri.edu> <20120915231032.C2669@besplex.bde.org> <50548E15.3010405@missouri.edu> <5054C027.2040008@missouri.edu> <5054C200.7090307@missouri.edu> <20120916041132.D6344@besplex.bde.org>

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One more thing I would like an opinion on.

In my code I check for |z| being small, and then use the approximations:
casinh(z) = z
cacos(z) = Pi - z
catanh(z) = z

However these approximations are not used in the papers by Hull et al, 
and the code works just fine if I don't include these in the code.

The only reason I put this code in is because I thought it would go a 
little faster in the cases that |z| is small.  Checking |z| is small 
takes no time at all.

So what do you think?  Should I keep these in the code or not?

Thanks, Stephen




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