From: Vincent Lefevre <vincent@vinc17.net>
To: zsh-workers@zsh.org
Subject: Re: zsh converts a floating-point number to string with too much precision
Date: Sat, 21 Dec 2019 22:28:25 +0100 [thread overview]
Message-ID: <20191221212825.GA849755@zira.vinc17.org> (raw)
In-Reply-To: <20191221084736.bokldw7tzxw3thn3@chaz.gmail.com>
On 2019-12-21 08:47:36 +0000, Stephane Chazelas wrote:
> OK, I think I see what you mean.
>
> So on a system (with a compiler) where C doubles are implemented
> as IEEE 754 double precision, both 1.1 and 1.1000000000000001
> are represented as the same binary double (whose exact value is
> 1.100000000000000088817841970012523233890533447265625).
>
> So you're saying echo $((1.1000000000000001)) and echo $((1.1))
> should output 1.1, because even though 1.1000000000000001 is
> closer to that value than 1.1000000000000000, zsh should pick
> the latter because people prefer to see shorter number
> representations and in that case it doesn't matter which one we
> pick as both lead to the same double.
I now remember that our Handbook of Floating-Point Arithmetic covers
this issue (Section 4.9.2.1 "Output conversion: from radix 2 to
radix 10" in the 2nd edition). But it just gives references
--------------------------------------------------------------------
"[...] Steele and White designed an algorithm for that. Their
algorithm was later improved by Burger and Dybvig [86], and by
Gay [211]. Gay's code is available for anyone to use, and is
very robust.(17) Faster yet more complex algorithms have been
introduced by Loitsch [394] and Andrysco et al. [16]. [...]"
(17) At the time of writing this book, it can be obtained at
http://www.netlib.org/fp/ (file dtoa.c).
--------------------------------------------------------------------
and Burger and Dybvig's high-level algorithm.
--
Vincent Lefèvre <vincent@vinc17.net> - Web: <https://www.vinc17.net/>
100% accessible validated (X)HTML - Blog: <https://www.vinc17.net/blog/>
Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)
next prev parent reply other threads:[~2019-12-21 21:29 UTC|newest]
Thread overview: 12+ messages / expand[flat|nested] mbox.gz Atom feed top
2019-12-20 1:37 Vincent Lefevre
2019-12-20 3:38 ` Mikael Magnusson
2019-12-20 16:58 ` Stephane Chazelas
2019-12-20 17:12 ` Roman Perepelitsa
2019-12-21 0:50 ` Vincent Lefevre
2019-12-21 8:47 ` Stephane Chazelas
2019-12-21 9:43 ` Roman Perepelitsa
2019-12-21 17:56 ` Stephane Chazelas
2019-12-21 18:11 ` Stephane Chazelas
2019-12-21 18:20 ` Roman Perepelitsa
2019-12-21 21:28 ` Vincent Lefevre [this message]
2019-12-21 1:00 ` Vincent Lefevre
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=20191221212825.GA849755@zira.vinc17.org \
--to=vincent@vinc17.net \
--cc=zsh-workers@zsh.org \
/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/zsh/
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).