Date: Sun, 25 Aug 2013 10:58:17 -0700 From: Steve Kargl <sgk@troutmask.apl.washington.edu> To: Bruce Evans <brde@optusnet.com.au> Cc: freebsd-numerics@FreeBSD.org Subject: Re: (2nd time) tweaks to erff() threshold values Message-ID: <20130825175817.GA60599@troutmask.apl.washington.edu> In-Reply-To: <20130825171910.GA60396@troutmask.apl.washington.edu> References: <20130822213315.GA6708@troutmask.apl.washington.edu> <20130823202257.Q1593@besplex.bde.org> <20130823165744.GA47369@troutmask.apl.washington.edu> <20130824202102.GA54981@troutmask.apl.washington.edu> <20130825023029.GA56772@troutmask.apl.washington.edu> <20130825171910.GA60396@troutmask.apl.washington.edu>
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On Sun, Aug 25, 2013 at 10:19:10AM -0700, Steve Kargl wrote: > > Note**2, I did not record a domain and range as my routine that > generates plots seems to give a really messed up result for > the range [-0.08, 0.06]. However, the error estimate from > solving the Remes matrix equation is err = 0x1.39c84809b7ed2p-38. Found the bug in the graphing routine. /* * Domain [0.84375, 1.25], range ~[-1.954e-10,1.940e-11]: * |(erf(x) - erx) - p(x)/q(x)| < 2**-36. */ > +pa0 = 1.35131621e-08F, /* 0x1.d04f08p-27 */ > +pa1 = 4.15107518e-01F, /* 0x1.a911f2p-2 */ > +pa2 = -1.63339108e-01F, /* -0x1.4e84bcp-3 */ > +pa3 = 1.12098485e-01F, /* 0x1.cb27c8p-4 */ > +qa1 = 6.06513679e-01F, /* 0x1.3688f6p-1 */ > +qa2 = 5.43227255e-01F, /* 0x1.1621e2p-1 */ > +qa3 = 1.74396917e-01F, /* 0x1.652a36p-3 */ > +qa4 = 5.88681065e-02F, /* 0x1.e23f5ep-5 */ Note, the range and 2**-36 estimate are from the results of the Remes algorithm run with 1024-bits of precision. The above coefficients were simply rounded to single precision, as I haven't investigated a better method for running, yet. -- Steve
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