The following reply was made to PR bin/170206; it has been noted by GNATS. From: Stephen Montgomery-Smith <[email protected]> To: Bruce Evans <[email protected]> Cc: [email protected], [email protected], Stephen Montgomery-Smith <[email protected]> Subject: Re: bin/170206: complex arcsinh, log, etc. Date: Sat, 28 Jul 2012 18:12:07 -0500
On 07/28/2012 11:15 AM, Stephen Montgomery-Smith wrote: > 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.) And I should add that I just realized that ULP isn't quite the same as relative error, so an extra factor of up to 2 could make its way into the calculations. _______________________________________________ [email protected] mailing list http://lists.freebsd.org/mailman/listinfo/freebsd-bugs To unsubscribe, send any mail to "[email protected]"
