From owner-sc22wg5+sc22wg5-dom8=www.open-std.org@open-std.org Wed Aug 24 15:57:14 2016 Return-Path: X-Original-To: sc22wg5-dom8 Delivered-To: sc22wg5-dom8@www.open-std.org Received: by www.open-std.org (Postfix, from userid 521) id BF31E35872B; Wed, 24 Aug 2016 15:57:14 +0200 (CEST) Delivered-To: sc22wg5@open-std.org Received: from mail-wm0-f48.google.com (mail-wm0-f48.google.com [74.125.82.48]) (using TLSv1 with cipher AES128-SHA (128/128 bits)) (No client certificate requested) by www.open-std.org (Postfix) with ESMTP id D562D3568F8 for ; Wed, 24 Aug 2016 15:57:11 +0200 (CEST) Received: by mail-wm0-f48.google.com with SMTP id q128so203003171wma.1 for ; Wed, 24 Aug 2016 06:57:11 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=bris-ac-uk.20150623.gappssmtp.com; s=20150623; h=date:from:message-id:to:subject:reply-to:in-reply-to; bh=vihC15relBO/HqM11BrgpLQ15skrswTw8y3ZAtiqVSs=; b=JzybshRR0CUOkuF2tc44RQkz9n9+obtTysex80R2T9QwqFL3ui81+4ssgvwqwamys3 0OhyqOMcZ6REvsptvVqGMOGXVAwkR6Pn1zfL5Oe1lkZvKUjqmvmXfUF+YeDko4c3vUWv g0iU1ZJoVJ29dMg2g1SqHSOxMeDo7OOv/CHYsDkM7XDsuPmHinqK1P2+Q87JSKwi78vD EQ7l2Lg3xknRUMX0+8RTCOj3fQxnYZINlhps5pmmW2qLgJWe3Kykvm71kmoFLDbJu4EN uv9G2FcV1KtB9w22KR8o3WL+5Gd959poZ+GyuuwgTXDu93Hih4YA3VBNBWhOjruprYiE 2D/A== X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20130820; h=x-gm-message-state:date:from:message-id:to:subject:reply-to :in-reply-to; bh=vihC15relBO/HqM11BrgpLQ15skrswTw8y3ZAtiqVSs=; b=P9rOw8qxiVKHaolgd7sNJr+63v/uVsWRfiIiiHHPz41mkOTP4VFOl2dkKvYzRULacn IljNVTlUeQqVKIB1neUopdqs9Wq/fkvZosjTGPIiiGKY4nvUwE21mbDlBd2Nmx16Gtbx 6KoX8VuiwhQx84LRfqaMurL7EvmqqHaivzGlxW8PbULiH0aeCJOtt/C77Kky2bDHXHz0 sQpFjOj5UUItbg8wdVray8W2Hmm1AhiyJsmsG4D2xN7hoZr5S3HdY6JYdrmtwci9Vxsl vqIpitd8o5fw2CwveZmnWRUIjC4kqo7UjNsMTvtpUi41Du/hMac3evknA8nQ20BTA1vM ZiOg== X-Gm-Message-State: AEkooutGsChCC0fpj6RPFrCS/V5jOfwHCETapAXze0XBm+MuSJ2Ca0GtNrrszoDeRr5huR+T X-Received: by 10.194.78.74 with SMTP id z10mr2822075wjw.68.1472047030607; Wed, 24 Aug 2016 06:57:10 -0700 (PDT) Received: from mech-as222.men.bris.ac.uk (mech-as222.men.bris.ac.uk. [137.222.170.4]) by smtp.gmail.com with ESMTPSA id q65sm10739652wmd.24.2016.08.24.06.57.09 for (version=TLS1_2 cipher=ECDHE-RSA-AES128-GCM-SHA256 bits=128/128); Wed, 24 Aug 2016 06:57:10 -0700 (PDT) Received: from mech-as222.men.bris.ac.uk (localhost [127.0.0.1]) by mech-as222.men.bris.ac.uk (8.15.2/8.15.2) with ESMTP id u7ODv9mv083791 for ; Wed, 24 Aug 2016 14:57:09 +0100 (BST) (envelope-from mexas@mech-as222.men.bris.ac.uk) Received: (from mexas@localhost) by mech-as222.men.bris.ac.uk (8.15.2/8.15.2/Submit) id u7ODv9Lk083790 for sc22wg5@open-std.org; Wed, 24 Aug 2016 14:57:09 +0100 (BST) (envelope-from mexas) Date: Wed, 24 Aug 2016 14:57:09 +0100 (BST) From: Anton Shterenlikht Message-Id: <201608241357.u7ODv9Lk083790@mech-as222.men.bris.ac.uk> To: sc22wg5@open-std.org Subject: Re: (j3.2006) (SC22WG5.5780) edits to clarify SQRT treatment of negative zero, for comments Reply-To: mexas@bris.ac.uk In-Reply-To: Sender: owner-sc22wg5@open-std.org Precedence: bulk >From: Robert Corbett >> >> and negative zero [394:31-395:3], and SQRT(X) >> is mathematically equivalent to EXP( 0.5 * LOG(X) ). > >They are not mathematically equivalent when X is zero. >In that case, SQRT(X) is well-defined, but the expression >EXP( 0.5 * LOG(X) ) is mathematical nonsense, because the >log of zero is undefined. The real part of log of zero is well defined - it is minus infinity. Hence exp( log(x) ) is also well defined - it is zero. With ieee 754, when infinity is a valid numerical value, the two expressions are computationally equivalent too. 3 out of 3 compilers agree with me: complex :: z z = cmplx( 0.0, 0.0 ) write (*,*) log( z ) write (*,*) exp( log( z ) ) end gives: (-Infinity,0.) (0.,0.) Yes, log of zero is not allowed by [394:28-29]. Perhaps this restriction should be relaxed, e.g. as was suggested in F03/0042: http://j3-fortran.org/doc/meeting/210/16-006.txt - for real X, when X is zero, LOG(X) is minus infinity for both positive and negative zero X. - for complex X, when X is zero, the real part of LOG(X) is minus infinity, the imaginary part of LOG(X) is a processor dependent value between -pi and +pi. Such addition would help write portable complex algebra programs for systems supporting ieee 754. Anton