From -2280020165790101792 X-Google-Thread: f78e5,4ba9dcb1ae436e16 X-Google-Attributes: gidf78e5,public X-Google-Language: ENGLISH,ASCII-7-bit Path: g2news1.google.com!news2.google.com!proxad.net!proxad.net!194.159.246.34.MISMATCH!peer-uk.news.demon.net!kibo.news.demon.net!news.demon.co.uk!demon!stump.algebra.com!devnull From: kuyper@wizard.net (James Kuyper) Newsgroups: comp.std.c++ Subject: Re: Pi, Euler Number, and perhaps other 'natural' constants? Date: Sun, 1 Aug 2004 11:11:20 GMT Organization: http://groups.google.com Lines: 39 Sender: mail2news@demon.net Approved: fjh@cs.mu.oz.au (Fergus Henderson , moderator of comp.std.c++) Message-ID: <8b42afac.0408010210.7d10bd55@posting.google.com> References: <5cydnSisJNo4yJncRVn-sQ@speakeasy.net> NNTP-Posting-Host: news.news.demon.net Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: news.demon.co.uk 1091358691 24163 158.152.254.254 (1 Aug 2004 11:11:31 GMT) X-Complaints-To: abuse@demon.net NNTP-Posting-Date: Sun, 1 Aug 2004 11:11:31 +0000 (UTC) X-Robomod: STUMP, ichudov@algebra.com (Igor Chudov) X-Spam-Checker-Version: SpamAssassin 2.60-mulga_r1 (1.212-2003-09-23-exp) on mulga.cs.mu.OZ.AU X-Spam-Status: No, hits=-3.8 required=5.2 tests=AWL,BAYES_00 autolearn=ham version=2.60-mulga_r1 X-Received: (from fjh@localhost) by mulga.cs.mu.OZ.AU (8.12.10+Sun/8.12.9/Submit) id i71BBKT3024631; Sun, 1 Aug 2004 21:11:20 +1000 (EST) X-Path: comp-std-cpp-robomod!not-for-mail X-NNTP-Posting-Date: Sun, 1 Aug 2004 10:10:09 +0000 (UTC) X-Spam-Level: X-Delivered-To: std-c++@ucar.edu X-Authentication-Warning: mulga.cs.mu.OZ.AU: fjh set sender to devnull@stump.algebra.com using -f X-Newsgroups: comp.std.c++ Xref: g2news1.google.com comp.std.c++:1511 pfefferd@hotmail.co.il.nospam ("Daniel Pfeffer") wrote in message news:... .. > The _mathematical_ value of pi is known to a very high accuracy. The > _machine_ representation of PI depends on the size of the mantissa, the > rounding mode, etc. Even in a single environment, the value of PI can change > because of a difference in the rounding mode of the environment (e.g. round > towards negative infinity will always give a result that differs from round > round towards positive infinity). > > These rounding mode differences are not unimportant. For example, correct > interval arithmetic relies on the presence of both of the above rounding > modes. > > I am aware that the FP rounding mode is defined in std::numeric_limits<>, > and that it is currently constant for each FP type. However, if the C99 > mechanisms are incorporated into C++0x, this will have to change. If C99's hexadecimal constants are also incorporated, it will be possible to define PI in a way that doesn't get rounded, at least for machines where FLT_RADIX is a power of 2. >> We should have "std::pi" as a double, accurate to the last bit >> of a double, even if it has to be calculated offline and >> stored as a hex float. This is worth doing, because it's >> a huge pain to do that and it only needs to be done once. > > > > See above. The actual value may change (by 1 ulp), depending on the > environment's current rounding mode. Not if stored as a hex float, at least if FLT_RADIX is a power of 2. --- [ comp.std.c++ is moderated. To submit articles, try just posting with ] [ your news-reader. If that fails, use mailto:std-c++@ncar.ucar.edu ] [ --- Please see the FAQ before posting. --- ] [ FAQ: http://www.jamesd.demon.co.uk/csc/faq.html ]