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Re: acos / asin accuracy
- From: "Carlos O'Donell" <carlos at systemhalted dot org>
- To: "Henri Verbeet" <hverbeet at gmail dot com>
- Cc: libc-help at sourceware dot org
- Date: Sun, 21 Sep 2008 12:35:55 -0400
- Subject: Re: acos / asin accuracy
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On Sun, Sep 21, 2008 at 11:04 AM, Henri Verbeet <firstname.lastname@example.org> wrote:
> Acos and asin in sysdeps/i386/fpu are implemented as "atan2(sqrt(1 -
> x*x), x)" and "atan2(x, sqrt(1 - x*x))"
> and http://sources.redhat.com/git/?p=glibc.git;a=blob_plain;f=sysdeps/i386/fpu/e_asin.S;hb=HEAD).
> The expression "1-x*x" is bad for accuracy, especially for values of x
> close to -1 or 1 (x*x introduces rounding error, subtracting from 1
> cancels most of the remaining significant digits out). Obviously the
> problem is worse when using single precision. A much better way would
> be to use (1-x)*(1+x) instead.
Do you have a patch, with before and after results, including the
results of running the glibc math testsuite?
> I would have filed a bug in bugzilla for this, but it appears bugzilla
> doesn't send the confirmation mails for new accounts (as other people
> already noted).
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