Path: csiph.com!fu-berlin.de!uni-berlin.de!not-for-mail From: Random832 Newsgroups: comp.lang.python Subject: Re: math.frexp Date: Fri, 15 Jul 2016 14:28:05 -0400 Lines: 46 Message-ID: References: <5788cb76$0$1599$c3e8da3$5496439d@news.astraweb.com> <5789101c$0$1615$c3e8da3$5496439d@news.astraweb.com> <1468607285.2744204.667500217.193B8D54@webmail.messagingengine.com> Mime-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit X-Trace: news.uni-berlin.de xtguenPumhru8jKzM2hh2gEX7rZdsudf9oaZOnPKQ+OQ== Return-Path: X-Original-To: python-list@python.org Delivered-To: python-list@mail.python.org X-Spam-Status: OK 0.007 X-Spam-Evidence: '*H*': 0.99; '*S*': 0.00; 'else:': 0.03; 'ma,': 0.09; 'received:internal': 0.09; 'def': 0.13; 'b):': 0.16; 'message- id:@webmail.messagingengine.com': 0.16; 'received:10.202': 0.16; 'received:10.202.2': 0.16; 'received:66.111': 0.16; 'received:66.111.4': 0.16; 'received:io': 0.16; 'received:messagingengine.com': 0.16; 'received:psf.io': 0.16; 'wrote:': 0.16; 'math': 0.20; 'import': 0.24; 'header:In-Reply- To:1': 0.24; 'error': 0.27; 'fri,': 0.27; 'correct': 0.28; 'cases.': 0.29; '15,': 0.30; 'relative': 0.30; 'skip:_ 10': 0.32; "d'aprano": 0.33; 'steven': 0.33; 'attempt': 0.35; 'to:addr :python-list': 0.36; 'pm,': 0.36; 'subject:: ': 0.37; 'received:10': 0.37; 'received:66': 0.38; 'mean': 0.38; 'test': 0.39; 'to:addr:python.org': 0.40; 'header:Message-Id:1': 0.61; 'within': 0.64; 'of:': 0.66; 'jul': 0.72; 'answer,': 0.84 DKIM-Signature: v=1; a=rsa-sha1; c=relaxed/relaxed; d=fastmail.com; h= content-transfer-encoding:content-type:date:from:in-reply-to :message-id:mime-version:references:subject:to:x-sasl-enc :x-sasl-enc; s=mesmtp; bh=fPlaFXB/kOiTihvUd7Exry9m0Aw=; b=Ev5t86 rKNL/im5Bhd+NAb1VFnIJiCMaxTV5SnrjEAXGbZN/ABb6zr4VsxXqVRYCWy2GkLj H1q0rIHBn90nr1chXjP1ApW8xbxSH/e4cI6nJJa0uYf2AX3gahmxUn7TviFQLkbg 8Qmc+wUqc8oVKfvyhLqbnIfMG1WsnnzYBXKqk= DKIM-Signature: v=1; a=rsa-sha1; c=relaxed/relaxed; d= messagingengine.com; h=content-transfer-encoding:content-type :date:from:in-reply-to:message-id:mime-version:references :subject:to:x-sasl-enc:x-sasl-enc; s=smtpout; bh=fPlaFXB/kOiTihv Ud7Exry9m0Aw=; b=RRqGBKxdBFXNS5N0KlOuwSfF9JRCGNDUa4UxapAxAbfaVED QuPDMGAKtk2MGupBkIQDZexUGrxcsnmqI/9qoYBksCTy2ixag8+xF8qn57zcFzYk YcxISKgnZwQREmwmVTnU/18gJ8MY5DUM2FSz7oaKmu3A8cSHGtm2Xierk28E= X-Sasl-Enc: fxZj84g7qp/JoLJCDw2wtS9r+rwM78tbFhujAnDs++n5 1468607285 X-Mailer: MessagingEngine.com Webmail Interface - ajax-bf4e2c8f In-Reply-To: <5789101c$0$1615$c3e8da3$5496439d@news.astraweb.com> X-BeenThere: python-list@python.org X-Mailman-Version: 2.1.22 Precedence: list List-Id: General discussion list for the Python programming language List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-Mailman-Original-Message-ID: <1468607285.2744204.667500217.193B8D54@webmail.messagingengine.com> X-Mailman-Original-References: <5788cb76$0$1599$c3e8da3$5496439d@news.astraweb.com> <5789101c$0$1615$c3e8da3$5496439d@news.astraweb.com> Xref: csiph.com comp.lang.python:111484 On Fri, Jul 15, 2016, at 12:32, Steven D'Aprano wrote: > I can take the geometric mean of: > > [2.0**900, 2.0**920, 2.0**960, 2.0**980, 2.0**990] > > and get to within a relative error of 1e-14 of the correct answer, > 2**950: > > py> geometric_mean([2.0**900, 2.0**920, 2.0**960, 2.0**980, 2.0**990]) > 9.516908214257811e+285 > py> 2.0**950 > 9.516908214257812e+285 > > Here's one that's exact: > > py> geometric_mean([2e300, 4e300, 8e300, 16e300, 32e300]) > 8e+300 My own attempt gave an exact result for both test cases. from math import frexp as _frexp, ldexp def frexp(x): if type(x) is tuple: m, e1 = x m, e2 = _frexp(m) return m, e1 + e2 else: return _frexp(x) def _mul(a, b): ma, ea = frexp(a) mb, eb = frexp(b) return frexp((ma * mb, ea + eb)) def _product(values): return reduce(_mul, values) def geometric_mean(values): n = len(values) pm, pe = _product(values) me, re = divmod(pe, n) pm = ldexp(pm, re) return ldexp(pm**(1./n), me)