From: Damian McGuckin <damianm@esi.com.au>
To: musl@lists.openwall.com
Subject: ATANH
Date: Wed, 27 Feb 2019 13:59:41 +1100 (AEDT) [thread overview]
Message-ID: <alpine.LRH.2.02.1902271353470.18595@key0.esi.com.au> (raw)
The comments for this routine say:
* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5)
There is a point where atanh(x) can be approximated by just x to machine
precision. This is where the exponent of x is less than some number, or
where x itself is less than some number.
In MUSL, for the 80-bit version, directly from the code, this is
2^(-LDBL_MANT_DIG/2) = 0x1.0p-32;
Interestingly, this same number, is used double atanh and float atanhf.
Note that in fdlibm, 0x1.0p-28 is used for all types
In fact, isn't
x * (1 + x^2/3) == x (after roundoff)
if
x < 2^(p/2),
i.e. 0x1.0p-26 for double, 0x1.0p-12 for float.
Note that for 80-bit wide, it is 0x1.0p-32 agreeing with MUSL!!
Regards - Damian
Pacific Engineering Systems International, 277-279 Broadway, Glebe NSW 2037
Ph:+61-2-8571-0847 .. Fx:+61-2-9692-9623 | unsolicited email not wanted here
Views & opinions here are mine and not those of any past or present employer
next reply other threads:[~2019-02-27 2:59 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
2019-02-27 2:59 Damian McGuckin [this message]
2019-02-27 10:38 ` ATANH Szabolcs Nagy
Reply instructions:
You may reply publicly to this message via plain-text email
using any one of the following methods:
* Save the following mbox file, import it into your mail client,
and reply-to-all from there: mbox
Avoid top-posting and favor interleaved quoting:
https://en.wikipedia.org/wiki/Posting_style#Interleaved_style
* Reply using the --to, --cc, and --in-reply-to
switches of git-send-email(1):
git send-email \
--in-reply-to=alpine.LRH.2.02.1902271353470.18595@key0.esi.com.au \
--to=damianm@esi.com.au \
--cc=musl@lists.openwall.com \
/path/to/YOUR_REPLY
https://kernel.org/pub/software/scm/git/docs/git-send-email.html
* If your mail client supports setting the In-Reply-To header
via mailto: links, try the mailto: link
Be sure your reply has a Subject: header at the top and a blank line
before the message body.
Code repositories for project(s) associated with this public inbox
https://git.vuxu.org/mirror/musl/
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).