Date: Tue, 28 Jun 2005 20:30:14 GMT From: David Schultz <das@FreeBSD.ORG> To: freebsd-standards@FreeBSD.org Subject: Re: standards/82654: C99 long double math functions are missing Message-ID: <200506282030.j5SKUEZI059621@freefall.freebsd.org>
next in thread | raw e-mail | index | archive | help
The following reply was made to PR standards/82654; it has been noted by GNATS. From: David Schultz <das@FreeBSD.ORG> To: "Steven G. Kargl" <kargl@troutmask.apl.washington.edu> Cc: FreeBSD-gnats-submit@FreeBSD.ORG Subject: Re: standards/82654: C99 long double math functions are missing Date: Tue, 28 Jun 2005 16:19:48 -0400 On Sat, Jun 25, 2005, Steven G. Kargl wrote: > The enclosed patch implements logl(), log10l(), sqrtl(), and cbrtl(). > I'm sure someone will want bit twiddling or assembly code, but the > c code works on both i386 and amd64. Cool. I don't have much time to look at this right now, but I definitely will want to go through this later. I have some general comments about accuracy, though. IEEE-754 says that algebraic functions (sqrt and cbrt in this case) should always produce correctly rounded results. The sqrt() and sqrtf() implementations handle this by computing an extra bit of the result, and using this bit and whether the remainder is 0 or not to determine which way to round. This can be a bit tricky to get right, but it can probably be done straightforwardly by following fdlibm's example. Simply using native floating-point arithmetic as you have done will probably not suffice, unfortunately, so this is something that definitely needs to be fixed. The transcendental functions (e.g. logl() and log10l()) are not required to be correctly rounded because it is not known how to ensure correct rounding in a bounded amount of time. However, the guarantee made by fdlibm and most other math libraries is that it will always be correctly rounded, except for a small percentage of cases that are very close to halfway between two representable numbers. For illustration, this might mean that 0.125000000000001 gets rounded to 0.12 instead of 0.13 if we had two decimal digits of accuracy. Now, technically speaking, there's no *requirement* that these transcendental functions be reasonably accurate. The old BSD math library often gave errors of several ulps or worse on particular ``bad'' inputs. But it is certainly desirable that they work at least as well as their double and float counterparts. One could argue that most people don't care about the last few bits of accuracy, but some people do (think Intel Pentium bug), and I worry that adding routines with mediocre accuracy now will mean that nobody will bother writing better ones later. Consider, for instance, that glibc's implementations of fma() and most of the complex math functions have been broken for years because they were implemented by people who wanted to claim standards conformance without fully understanding what they were doing. Then again, I can't argue too much against your implementations given that nobody seems to have implemented more accurate BSD-licensed routines yet. If you'd like, I can point you to what are considered the cutting- edge papers on how to implement these functions in software, but I don't have time to work on it myself in the forseeable future. Two other minor points: - Looking briefly at your logl() and log10l() implementations, I'm concerned about accuracy at inputs very close to 0. - From my notes, the ``lowest-hanging fruit'', i.e. the unimplemented long double functions that would be the easiest to implement accurately, are fmodl(), remainderl(), and remquol(). These are easy mainly because they can be implemented as modified versions of their double counterparts, with a minimal amount of special- casing for various long double implementations. By the way, it's really great that someone has taken an interest in this. One of these days, I should have more time to work on it... --David
Want to link to this message? Use this URL: <https://mail-archive.FreeBSD.org/cgi/mid.cgi?200506282030.j5SKUEZI059621>