On Mon, 28 Nov 2005, Steve Kargl wrote:
On Mon, Nov 28, 2005 at 11:16:27AM +0100, Andre Oppermann wrote:
Bruce Evans wrote:
...
lib/msun/src e_lgammaf_r.c
Log:
Fixed about 50 million errors of infinity ulps and about 3 million errors
of between 1.0 and 1.8509 ulps for lgammaf(x) with x between -2**-21 and
-2**-70.
What is an ULP and are you going to write a paper on how FreeBSD has
the best, fastest and most precise msun library of all OSs?
Units in the Last Place.
http://docs.sun.com/source/806-3568/ncg_goldberg.html
Yes, that is probably the best reference. Knuth is also good. See
also ieee(3) and <float.h>. The expression b**(1-p) (FLT_EPSILON,
etc.) in <float.h> is 1 ulp according to 1 sentence in Knuth, but this
is only 1 ulp for values normalized to be >= 1.0 and < 2.0. Generally,
an ulp is just like FLT_EPSILON, with the epsilon normalized to the
same precision as the value instead of the value normalized to the same
precision as the epsilon.
I don't like writing papers, and rarely read them these days. ISTR
reading the Goldberg one when it was first published not long before
I almost stopped reading many technical paper papers.
Hopefully at least Sun still knows everything in docs.sun.com and has the
most precise if not the fastest libm.
The history of {t,l}gamma's precision is interesting. The old BSD
libm one (actually not so old; it is by McIlroy in {Oct,Nov} 1992)
tries much harder than the (1993) fdlibm one to be precise. We still
use it for tgamma. For lgamma, I think it achieves more precision for
positive args. On negative args, it comments that "all bets are off"
because cases like lgamma(-2.4...) have a result near 0. Such cases
are especially hard to make precise and lgamma's implementation is
especially unsuitable for making them precise (it uses essentially
lgamma(x) = log(f(x)/g(x)) = log(f(x)) - log(g(x)), where f(x) and
g(x) are large, so almost all precision is lost to cancellation when
the difference is small).
Bruce
_______________________________________________
cvs-all@freebsd.org mailing list
http://lists.freebsd.org/mailman/listinfo/cvs-all
To unsubscribe, send any mail to "[EMAIL PROTECTED]"
