Date: Tue, 14 Aug 2012 22:31:35 -0500 From: Stephen Montgomery-Smith <stephen@missouri.edu> To: freebsd-numerics@freebsd.org Subject: Re: Complex arg-trig functions Message-ID: <502B1817.5070401@missouri.edu> In-Reply-To: <502A9B99.7090309@missouri.edu> References: <5017111E.6060003@missouri.edu> <501C361D.4010807@missouri.edu> <20120804165555.X1231@besplex.bde.org> <501D51D7.1020101@missouri.edu> <20120805030609.R3101@besplex.bde.org> <501D9C36.2040207@missouri.edu> <20120805175106.X3574@besplex.bde.org> <501EC015.3000808@missouri.edu> <20120805191954.GA50379@troutmask.apl.washington.edu> <20120807205725.GA10572@server.rulingia.com> <20120809025220.N4114@besplex.bde.org> <5027F07E.9060409@missouri.edu> <20120814003614.H3692@besplex.bde.org> <50295887.2010608@missouri.edu> <20120814055931.Q4897@besplex.bde.org> <50297468.20902@missouri.edu> <20120814173931.V934@besplex.bde.org> <502A820C.6060804@missouri.edu> <502A8494.2050707@missouri.edu> <502A9B99.7090309@missouri.edu>
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I was looking through the code e_acosh.c, and it made me realize I could get a small fraction more ULP in catrig.c by making the replacements: 216c216 < *rx = log1p(Am1 + sqrt(Am1*(A+1))); --- > *rx = log1p(Am1 + sqrt(2*Am1 + Am1*Am1)); 282c282 < *sqrt_A2my2 = sqrt(Amy*(A+y)); --- > *sqrt_A2my2 = sqrt(2*y*Amy + Amy*Amy); I'm not quite sure if the second replacement makes much difference, but the first replacement seemed quite effective.
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