Path: csiph.com!v102.xanadu-bbs.net!xanadu-bbs.net!feeder.erje.net!eu.feeder.erje.net!newsfeed.xs4all.nl!newsfeed2.news.xs4all.nl!xs4all!newsgate.cistron.nl!newsgate.news.xs4all.nl!post.news.xs4all.nl!not-for-mail Return-Path: X-Original-To: python-list@python.org Delivered-To: python-list@mail.python.org X-Spam-Status: OK 0.004 X-Spam-Evidence: '*H*': 0.99; '*S*': 0.00; 'output': 0.05; 'skip:` 10': 0.07; 'expected.': 0.09; 'received:80.91': 0.09; 'received:80.91.229': 0.09; 'received:gmane.org': 0.09; 'received:list': 0.09; 'bug': 0.12; 'exactly,': 0.16; 'expecting': 0.16; 'message-id:@post.gmane.org': 0.16; 'propagation': 0.16; 'range,': 0.16; 'received:80.91.229.3': 0.16; 'received:plane.gmane.org': 0.16; 'all.': 0.16; 'wrote:': 0.18; 'module': 0.19; 'header:User-Agent:1': 0.23; 'error': 0.23; 'skip:` 20': 0.24; 'certain': 0.27; 'header:X-Complaints-To:1': 0.27; 'point': 0.28; 'function': 0.29; 'absolute': 0.30; 'compared': 0.30; 'too.': 0.31; '-0700,': 0.31; 'decimal': 0.31; "we're": 0.32; 'skip:d 20': 0.34; 'but': 0.35; 'library.': 0.36; 'charset:us-ascii': 0.36; 'to:addr:python-list': 0.38; 'expect': 0.39; 'to:addr:python.org': 0.39; 'enough': 0.39; 'received:org': 0.40; "you're": 0.61; 'more': 0.64; 'close': 0.67; 'believe': 0.68; 'natural': 0.68; 'results': 0.69; 'partial': 0.84; 'received:86': 0.91 X-Injected-Via-Gmane: http://gmane.org/ To: python-list@python.org From: Mark Dickinson Subject: Re: Bug in Decimal?? Date: Sun, 4 May 2014 10:53:06 +0000 (UTC) References: <973d2677-03c6-464a-8c88-f07282806468@googlegroups.com> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit X-Gmane-NNTP-Posting-Host: sea.gmane.org User-Agent: Loom/3.14 (http://gmane.org/) X-Loom-IP: 86.30.244.11 (Mozilla/5.0 (Macintosh; Intel Mac OS X 10_9_2) AppleWebKit/537.75.14 (KHTML, like Gecko) Version/7.0.3 Safari/537.75.14) X-BeenThere: python-list@python.org X-Mailman-Version: 2.1.15 Precedence: list List-Id: General discussion list for the Python programming language List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Newsgroups: comp.lang.python Message-ID: Lines: 28 NNTP-Posting-Host: 2001:888:2000:d::a6 X-Trace: 1399200803 news.xs4all.nl 2952 [2001:888:2000:d::a6]:34665 X-Complaints-To: abuse@xs4all.nl Xref: csiph.com comp.lang.python:70908 On Tue, 29 Apr 2014 19:37:17 -0700, pleasedontspam wrote: > Hello, I believe I found a bug in the Decimal library. The natural logarithm > results seem to be off in a certain range, as compared with Wolfram Alpha. I had a quick look: this isn't a bug - it's just the result of propagation of the error in "partial" to "final". In more detail: we've got a working precision of 2016 significant figures. For any small x, we have (1 + x) / (1 - x) = 1 + 2x + 2x^2 + 2x^3 + .... For your value of x, `Decimal('1e-1007'), we've got enough precision to store 1 + 2x + 2x^2 exactly, but that's all. So partial has an absolute error of around 2x^3, or 2e-3021. And since the derivative of the natural log function is almost exactly 1 at the point we're interested in, we expect the absolute error in the output to be close to 2e-3021, too. And that's *precisely* what you're seeing: the Decimal module is giving you a result that's exactly `Decimal('2e-1007') - Decimal('1.3e-3021')`, while the result you were expecting is `Decimal('2e-1007') + Decimal('0.7e-3021')`. A difference of exactly `Decimal('2e-3021')`, as expected. -- Mark