
Date: Sat, 23 Feb 2019 10:08:58 0500 From: Rich Felker <dalias@...c.org> To: musl@...ts.openwall.com Cc: Shane Seelig <stseelig@...l.com> Subject: Re: x87 asin and acos On Sat, Feb 23, 2019 at 09:21:08AM 0500, Shane Seelig wrote: > Currently 'asin' uses the algorithm: > arcsin(x) == arctan(x/(sqrt((1x)(1+x)))) > If the following algorithm were to be used instead, an 'fadd' could be > removed. > arcsin(x) == arctan(x/(sqrt(1x**2))) They don't seem to be numerically equal. For example, if x is smaller than sqrt(LDBL_EPSILON/2), 1x**2 is 1, but (1x)*(1+x) is not. I don't recall the process of writing the function in detail, but I'm pretty sure this matters to the result, especially since sqrt then expands the magnitude of the error. Rich
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