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From: Richard Addison-Wood <richard@wetafx.co.nz> To: nobody@gcc.gnu.org Cc: gcc-prs@gcc.gnu.org, Subject: Re: optimization/9654: extra-precision fp comparisons are less accurate Date: Fri, 14 Feb 2003 03:56:00 -0000 [thread overview] Message-ID: <20030214035601.23499.qmail@sources.redhat.com> (raw) The following reply was made to PR optimization/9654; it has been noted by GNATS. From: Richard Addison-Wood <richard@wetafx.co.nz> To: rearnsha@gcc.gnu.org Cc: gcc-gnats@gcc.gnu.org, gcc-bugs@gcc.gnu.org Subject: Re: optimization/9654: extra-precision fp comparisons are less accurate Date: Fri, 14 Feb 2003 16:48:38 +1300 It's quite reasonable to assume that acos(1-0.5*DBL_EPSILON) will not be 0. For a value of d that is nearly 1: acos(d) == sqrt(1-d*d) is a good approximation (certainly within representational limits ieee754 double precision). The point to notice here is that if d is distinguishable from 1, d*d will be even more distinguishable from 1. All told, it very reasonable to expect: acos(1-0.5*DBL_EPSILON) == sqrt(DBL_EPSILON) which is a value that is not particularly close to 0. However, it is still close enough to 0 so that: sin(sqrt(DBL_EPSILON)) == sqrt(DBL_EPSILON) is a good approximation. Of course, this discourse into acos(), sin(), and sqrt() is beside the point. With code like this: if (d < 1.0) { arglessthanone(d); } it should be the case that the arglessthanone() function should not see an argument value that is greater than or equal to 1.0.
next reply other threads:[~2003-02-14 3:56 UTC|newest] Thread overview: 5+ messages / expand[flat|nested] mbox.gz Atom feed top 2003-02-14 3:56 Richard Addison-Wood [this message] -- strict thread matches above, loose matches on Subject: below -- 2003-02-16 15:30 ebotcazou 2003-02-14 12:26 Richard Earnshaw 2003-02-12 17:56 rearnsha 2003-02-11 4:06 richard
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