From: Rich Felker <dalias@libc.org>
To: musl@lists.openwall.com
Cc: Shane Seelig <stseelig@mail.com>
Subject: Re: x87 asin and acos
Date: Sat, 23 Feb 2019 10:08:58 -0500 [thread overview]
Message-ID: <20190223150858.GM23599@brightrain.aerifal.cx> (raw)
In-Reply-To: <e5a4695c-2333-f496-88ab-51b2241696e6@mail.com>
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
next prev parent reply other threads:[~2019-02-23 15:08 UTC|newest]
Thread overview: 6+ messages / expand[flat|nested] mbox.gz Atom feed top
2019-02-23 14:21 Shane Seelig
2019-02-23 15:08 ` Rich Felker [this message]
2019-02-23 19:57 ` Rich Felker
2019-02-24 2:53 ` Damian McGuckin
2019-02-23 20:30 ` Szabolcs Nagy
2019-02-23 20:36 ` Szabolcs Nagy
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