Date: Sun, 12 Aug 2012 23:13:50 -0000 From: Bruce Evans <brde@optusnet.com.au> To: Bruce Evans <brde@optusnet.com.au> Cc: Diane Bruce <db@db.net>, John Baldwin <jhb@freebsd.org>, David Chisnall <theraven@freebsd.org>, Stephen Montgomery-Smith <stephen@missouri.edu>, 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: <20120719182849.T2190@besplex.bde.org> Resent-Message-ID: <20120812231342.GE20453@server.rulingia.com> In-Reply-To: <20120719144432.N1596@besplex.bde.org> References: <20120529045612.GB4445@server.rulingia.com> <20120711223247.GA9964@troutmask.apl.washington.edu> <20120713114100.GB83006@server.rulingia.com> <201207130818.38535.jhb@freebsd.org> <9EB2DA4F-19D7-4BA5-8811-D9451CB1D907@theravensnest.org> <C527B388-3537-406F-BA6D-2FA45B9EAA3B@FreeBSD.org> <20120713155805.GC81965@zim.MIT.EDU> <20120714120432.GA70706@server.rulingia.com> <20120717084457.U3890@besplex.bde.org> <5004A5C7.1040405@missouri.edu> <5004DEA9.1050001@missouri.edu> <20120717200931.U6624@besplex.bde.org> <5006D13D.2080702@missouri.edu> <20120719144432.N1596@besplex.bde.org>
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On Thu, 19 Jul 2012, Bruce Evans wrote: > On Wed, 18 Jul 2012, Stephen Montgomery-Smith wrote: > >> I went on a long road trip yesterday, so I didn't get any code written, but >> I did have a lot of thoughts about clog and casinh. >> >> First, the naive formula (here z=x+I*y) >> clog(z) = cpack(log(hypot(x,y)),atan2(x,y)) >> is going to work in a lot more edge cases then one might expect. This is >> because hypot and atan2, especially atan2, already do a rather good job >> getting the edge cases right. I am thinking in particular of when x or y >> are 0 or -0, or one of them is infinity or -infinity. > > Right, clog is deceptively simple. This is because it decomposes perfectly > into 2 real functions of 2 real variables and both of these functions are > standard and already implemented almost as well as possible. ISTR das > saying that it had a complicated case, but I don't see even one. atan2() Duh, I forget that log() must be applied to hypot(). You found the surprisingly large inaccuracies from (too-?) simple avoidance of overflow in hypot() soon after I first replied. Is there a problem even without overflow? I think log contracts any errors in hypot() so there isn't, but then why doesn't it contract any error in the overflow avoidance? Bruce
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