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: Stephen Montgomery-Smith <[email protected]>, [email protected], [email protected] Subject: Re: bin/170206: complex arcsinh, log, etc. Date: Fri, 27 Jul 2012 09:45:02 -0500
On 07/27/2012 09:26 AM, Bruce Evans wrote: > % hm1 = -1; > % for (i=0;i<12;i++) hm1 += val[i]; > % return (cpack(0.5 * log1p(hm1), atan2(y, x))); > > It is the trailing terms that I think don't work right here. You sort > them and add from high to low, but normally it is necessary to add > from low to high (consider terms [1, DBL_EPSILON/2, DBL_EPSILON/4]). > Adding from high to low cancels with the -1 term, but then only > particular values work right. Also, I don't see how adding the low > terms without extra precision preserves enough precision. I understand what you are saying. But in this case adding in order of smallest to largest (adding -1 last) won't work. If all the signs in the same direction, it would work. But -1 has the wrong sign. But I can also tell you that I haven't thought my algorithm through every special case. I can tell you it seems to work in all the examples I tried. But I don't have a mathematical proof. _______________________________________________ [email protected] mailing list http://lists.freebsd.org/mailman/listinfo/freebsd-bugs To unsubscribe, send any mail to "[email protected]"
