The following reply was made to PR bin/170206; it has been noted by GNATS.
From: Stephen Montgomery-Smith <step...@missouri.edu>
To: Bruce Evans <b...@optusnet.com.au>
Cc: freebsd-bugs@freebsd.org, freebsd-gnats-sub...@freebsd.org,
Stephen Montgomery-Smith <step...@freebsd.org>
Subject: Re: bin/170206: complex arcsinh, log, etc.
Date: Sat, 28 Jul 2012 11:15:20 -0500
On 07/28/2012 10:46 AM, Stephen Montgomery-Smith wrote:
> OK. This clog really seems to work.
>
> x*x + y*y - 1 is computed with a ULP less than 0.8. The rest of the
> errors seem to be due to the implementation of log1p. The ULP of the
> final answer seems to be never bigger than a little over 2.
>
>
Also, I don't think the problem is due to the implementation of log1p.
If you do an error analysis of log(1+x) where x is about exp(-1)-1, and
x is correct to within 0.8 ULP, I suspect that about 2.5 ULP is the best
you can do for the final answer:
relative_error(log(1+x)) = fabs(1/((1+x) log(1+x))) * relative_error(x)
= 1.58 * relative_error(x)
Given that log1p has itself a ULP of about 1, and relative error in x is
0.8, and considering x=exp(-1)-1, this gives a ULP at around 1.58*0.8+1
= 2.3. And that is what I observed.
(Here "=" means approximately equal to.)
_______________________________________________
freebsd-bugs@freebsd.org mailing list
http://lists.freebsd.org/mailman/listinfo/freebsd-bugs
To unsubscribe, send any mail to "freebsd-bugs-unsubscr...@freebsd.org"
