Date: Fri, 27 Jul 2012 09:39:55 -0500 From: Stephen Montgomery-Smith <stephen@missouri.edu> To: Bruce Evans <brde@optusnet.com.au> Cc: freebsd-bugs@freebsd.org, FreeBSD-gnats-submit@freebsd.org, Stephen Montgomery-Smith <stephen@freebsd.org> Subject: Re: bin/170206: complex arcsinh, log, etc. Message-ID: <5012A83B.3010404@missouri.edu> In-Reply-To: <20120727233939.A7820@besplex.bde.org> References: <201207270247.q6R2lkeR021134@wilberforce.math.missouri.edu> <20120727233939.A7820@besplex.bde.org>
index | next in thread | previous in thread | raw e-mail
On 07/27/2012 09:26 AM, Bruce Evans wrote: > On Wed, 25 Jul 2012, Stephen Montgomery-Smith wrote: > >> This function seems to be able to compute clog with a worst case >> relative error of 4 or 5 ULP. >> ... > > I lost your previous reply about this after reading just the first part. > Please resend if interested. > > First part recovered by vidcontrol: > > VC> > I'm still working on testing and fixing clog. Haven't got near > the more > VC> > complex functions. > VC> > > VC> > For clog, the worst case that I've found so far has x^2+y^2-1 ~= > 1e-47: > VC> > > VC> > x = > 0.999999999999999555910790149937383830547332763671875000000000 > VC> > y = > VC> > 0.0000000298023223876953091912775497878893005143652317201485857367516 > VC> > (need high precision decimal or these rounded to 53 bits > binary) > VC> > x^2+y^2-1 = 1.0947644252537633366591637369e-47 > VC> VC> That is exactly 2^(-156). So maybe triple quad precision really > is enough. > > Hmm. But you need 53 more value bits after the 156. Quadruple precision > gives 3 to spare. I didn't notice that this number was exactly a power > of 2, but just added 15-17 for the value bits in decimal to 47 to get over > 60. I think one should be able to prove mathematically that if the number is as small as 1e-47, only the first one or two bits of the mantissa will be non-zero. I think that if more than triple double precision is needed, it is only one or two more bits more than triple double precision.home | help
Want to link to this message? Use this
URL: <https://mail-archive.FreeBSD.org/cgi/mid.cgi?5012A83B.3010404>