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From: Rich Felker <dalias@libc.org>
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Subject: Re: x87 asin and acos
Date: Sat, 23 Feb 2019 10:08:58 -0500
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Cc: Shane Seelig <stseelig@mail.com>
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On Sat, Feb 23, 2019 at 09:21:08AM -0500, Shane Seelig wrote:
> Currently 'asin' uses the algorithm:
> 	arcsin(x) == arctan(x/(sqrt((1-x)(1+x))))
> If the following algorithm were to be used instead, an 'fadd' could be
> removed.
> 	arcsin(x) == arctan(x/(sqrt(1-x**2)))

They don't seem to be numerically equal. For example, if x is smaller
than sqrt(LDBL_EPSILON/2), 1-x**2 is 1, but (1-x)*(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