Date: Sun, 08 Jul 2012 14:06:46 -0500 From: Stephen Montgomery-Smith <stephen@missouri.edu> To: freebsd-current@freebsd.org Subject: Re: Use of C99 extra long double math functions after r236148 Message-ID: <4FF9DA46.2010502@missouri.edu> In-Reply-To: <210816F0-7ED7-4481-ABFF-C94A700A3EA0@bsdimp.com> References: <4FC3A154.8030702@missouri.edu> <20120528203159.GA76340@troutmask.apl.washington.edu> <4FC3EBDA.2080502@missouri.edu> <20120528221731.GA76723@troutmask.apl.washington.edu> <4FC40449.3040602@missouri.edu> <20120528233035.GA77157@troutmask.apl.washington.edu> <4FC40DEA.8030703@missouri.edu> <20120529000756.GA77386@troutmask.apl.washington.edu> <4FC43C8F.5090509@missouri.edu> <20120529045612.GB4445@server.rulingia.com> <20120708124047.GA44061@zim.MIT.EDU> <210816F0-7ED7-4481-ABFF-C94A700A3EA0@bsdimp.com>
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Here is a technical question. I know that people always talk about ulp's in the context of how good a function implementation is. I think the ulp is the number of base 2 digits at the end of the mantissa that we cannot rely on. So if one were to write a naive implementation of lexp(x) that used Taylor's series if x is positive, and 1/lexp(-x) is x is negative - well one could fairly easily estimate an upper bound on the ulp, but it wouldn't be low (like ulp=1 or 2), but probably rather higher (ulp of the order of 10 or 20). So do people really work hard to get that last drop of ulp out of their calculations? Would a ulp=10 be considered unacceptable? Also, looking through the source code for the FreeBSD implementation of exp, I saw that they used some rather smart rational function. (I don't know how they came up with it.) Presumably a big part of the issue is to make the functions work rather fast. And a naive implementation of Taylor's series wouldn't be fast. But if people want lexp rather than exp, they must have already decided that accuracy is more important than speed.home | help
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