Date: Sun, 12 Aug 2012 23:07:48 -0000 From: Stephen Montgomery-Smith <stephen@missouri.edu> To: Steve Kargl <sgk@troutmask.apl.washington.edu> Cc: Diane Bruce <db@db.net>, John Baldwin <jhb@freebsd.org>, David Chisnall <theraven@freebsd.org>, Bruce Evans <bde@freebsd.org>, Bruce Evans <brde@optusnet.com.au>, 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: <500725F2.7060603@missouri.edu> Resent-Message-ID: <20120812230741.GB20453@server.rulingia.com> In-Reply-To: <20120718205625.GA409@troutmask.apl.washington.edu> References: <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> <20120718205625.GA409@troutmask.apl.washington.edu>
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On 07/18/2012 03:56 PM, Steve Kargl wrote: > On Wed, Jul 18, 2012 at 10:07:41AM -0500, Stephen Montgomery-Smith wrote: >> >>> The most obvious immediate difficulty in translating the above into C is >>> that y*y and z*z may overflow when the result shouldn't. >> >> This will be a lot easier than I originally expected. When we are in >> conditions when overflow might occur, we can simply make the approximations >> sqrt(y*y-1) = y >> csqrt(z*z+1) = signum(x)*z >> because in floating point arithmetic, these will not be approximations, >> but true exactly. And I am thinking that the test I will use for when >> to use these approximations will be (y==y+1) and (z==z+1) respectively. >> (I would use (z*z==z*z+1) but that test has the overflow problem.) > > I could be mistaken, but I believe that you need to raise the > inexact flag with these approximations because in fact you > are doing floating point math. > Thanks for this observation. I am looking through the C99 standard, trying to understand the inexact flag. But I am struggling to interpret it. Am I to understand that the inexact flag should be set anytime a floating point operation produces an answer that is not guaranteed exact? For example, should 1.0/3.0 and sqrt(2.0) raise the inexact flag?
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