From mboxrd@z Thu Jan 1 00:00:00 1970 X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on inbox.vuxu.org X-Spam-Level: X-Spam-Status: No, score=-3.3 required=5.0 tests=DKIM_SIGNED,DKIM_VALID, MAILING_LIST_MULTI,NICE_REPLY_A,RCVD_IN_DNSWL_MED,UNPARSEABLE_RELAY autolearn=ham autolearn_force=no version=3.4.4 Received: (qmail 6065 invoked from network); 26 Mar 2021 15:37:42 -0000 Received: from zero.zsh.org (94.142.241.90) by inbox.vuxu.org with ESMTPUTF8; 26 Mar 2021 15:37:42 -0000 ARC-Seal: i=1; cv=none; a=rsa-sha256; d=zsh.org; s=rsa-20200801; t=1616773062; b=H2AiqkcYrf09XKq8wYzCTzMgh9BZu9Ae2gBSyniumT1MZqgE3sxvbPiCS35HKwQvl7iW6+qXzq 0ibfwGoIJVZXO/57LIKTMLP5wfI5TTJD4f7fq5lnkT+45vszcLQdBUV1sZUyk05bQYQhvIwxrE D8Chl4wKXN/Vay75C2QUuM/sBO1zp7HlM7vZ00v4WKJKseAEYZVNWZZobDr2qJr1tZ9zPxLjhg ij8Kl9GLbp3lqR8RghGbMD3lTo8TGHiANR0smO16oKGmx6lHR3ZAzdGJT7Z0MVAqKehPkLr/pQ gqA2uylRBMIuh7mMx7JDk46PemAMP+CYStn+iCfFXJ36oA==; ARC-Authentication-Results: i=1; zsh.org; iprev=pass (mta01.eastlink.ca) smtp.remote-ip=24.224.136.30; dmarc=none header.from=eastlink.ca; arc=none ARC-Message-Signature: i=1; a=rsa-sha256; c=relaxed; d=zsh.org; s=rsa-20200801; t=1616773062; bh=fOxPfNlsBaOtAKhf+wVU/90vkx2EbXarVlbfDBGHACc=; h=List-Archive:List-Owner:List-Post:List-Unsubscribe:List-Subscribe:List-Help: List-Id:Sender:Content-Transfer-Encoding:Content-Type:In-Reply-To: MIME-Version:Date:Message-ID:From:References:To:Subject:DKIM-Signature; b=WwpgPeYoSM81GJHiNq5zwFOaJPXZWSHAZjoELw8q3WhqTM+yEUf+ge6iiRTawfJSCCwfSaarzu blTIHUrHUCkONKQhb0VQXXkBvjVbpobBcyAAzxekPnvsd/TR0U2KWBEbxilCcGAuxu1Dp/SDX2 sVYAKFcM6m3SamUffBooHuiloZt1ggum4xffBi2L76pP6QLgcsiyDKvHDYarqmn7arKHvahgdy b/O5ZU61lwyW5RwdC56cT2xpQgUBvyLTNm9FejIQN8I8zlpuR+09qamHzfF16VB7B8fD/xqf6M EGtkpg8K6Lit9kZkQ0KtBPSY3JmyON5oBtJEeDaAuPfW3g==; DKIM-Signature: v=1; a=rsa-sha256; q=dns/txt; c=relaxed/relaxed; d=zsh.org; s=rsa-20200801; h=List-Archive:List-Owner:List-Post:List-Unsubscribe: List-Subscribe:List-Help:List-Id:Sender:Content-transfer-encoding: Content-type:In-reply-to:MIME-version:Date:Message-id:From:References:To: Subject:Reply-To:Cc:Content-ID:Content-Description:Resent-Date:Resent-From: Resent-Sender:Resent-To:Resent-Cc:Resent-Message-ID; bh=wG+y1xhMRGIwFRabdnMbCQkK6+Qq3Sed79XSfFsns8w=; b=RJifE1jZJOv6DDYLFnJqMbxinS KEWRElLCzd/D/tcHfnT+eFUlGFBId+ocdz6NpxQ5wJTkrjT2J2XJ3xlgApDH2BPkKTowFoBPjjeYY vCxLRNBTBhVczXu0I36YPsIO/bm3OSMAdhKyCIy6BVHuPYqcaJqPMI8sICME7zblSlbSffghzD5D5 /UyZKonsdrl3vYIcKZiXI8RbBkRTxzl4EVLGmBZFqNPRK5HWNXHAzI9eeIXBkXb/xC8bZfi1DuWKI oqXfHCKC1xS7vDm0X4+YmurGsG0ao2dmr9ueV0Z5jw6xJP1ZWhvf662Lh+Z3sJmCoWlgUyOi8ReUc vdpsyyXg==; Received: from authenticated user by zero.zsh.org with local id 1lPoVZ-000IPw-Jf; Fri, 26 Mar 2021 15:36:21 +0000 Authentication-Results: zsh.org; iprev=pass (mta01.eastlink.ca) smtp.remote-ip=24.224.136.30; dmarc=none header.from=eastlink.ca; arc=none Received: from mta01.eastlink.ca ([24.224.136.30]:44136) by zero.zsh.org with esmtps (TLS1.2:ECDHE-RSA-AES128-GCM-SHA256:128) id 1lPoV3-000H7e-HR; Fri, 26 Mar 2021 15:35:49 +0000 Received: from csp02.eastlink.ca ([71.7.199.167]) by mta01.eastlink.ca (Oracle Communications Messaging Server 8.0.2.2.20180531 64bit (built May 31 2018)) with ESMTPS id <0QQL0046W029OEH0@mta01.eastlink.ca> for zsh-users@zsh.org; Fri, 26 Mar 2021 12:35:48 -0300 (ADT) Received: from [192.168.0.2] ([24.207.90.194]) by Eastlink with ESMTP id PoV1lJtFt54V7PoV1lOEzk; Fri, 26 Mar 2021 12:35:48 -0300 X-Authority-Analysis: v=2.4 cv=PJ/KRdmC c=1 sm=1 tr=0 ts=605dff54 a=zv49KfEsxEDzuN5AGO7r0Q==:117 a=zv49KfEsxEDzuN5AGO7r0Q==:17 a=IkcTkHD0fZMA:10 a=wpF38avAJe6T2jC1zh0A:9 a=QEXdDO2ut3YA:10 a=fCgQI5UlmZDRPDxm0A3o:22 X-Vade-Cause: gggruggvucftvghtrhhoucdtuddrgeduledrudehvddgkedtucetufdoteggodetrfdotffvucfrrhhofhhilhgvmecugfetuffvnffkpffmpdfqfgfvnecuuegrihhlohhuthemuceftddtnecunecujfgurhepuffvfhfhkffffgggjggtgfesthekredttdefjeenucfhrhhomheptfgrhicutehnughrvgifshcuoehrrgihrghnughrvgifshesvggrshhtlhhinhhkrdgtrgeqnecuggftrfgrthhtvghrnhepkedvueeuffefhfdvueeiteffvddtvdejgeeujeekieduheeiteeiheegtedvhfefnecukfhppedvgedrvddtjedrledtrdduleegnecuvehluhhsthgvrhfuihiivgeptdenucfrrghrrghmpehinhgvthepvdegrddvtdejrdeltddrudelgedphhgvlhhopegludelvddrudeikedrtddrvdgnpdhmrghilhhfrhhomheprhgrhigrnhgurhgvfihssegvrghsthhlihhnkhdrtggrpdhrtghpthhtohepiihshhdquhhsvghrshesiihshhdrohhrghdpghgvthdqkghiphfrrghsshifugepthhruhgv X-Vade-Score: 0 X-Vade-State: 0 X-EL-IP-NOAUTH: 24.207.90.194 Subject: Re: arithmetic anomaly To: zsh-users@zsh.org References: <0227b30d-4f09-2c8b-1248-557859d875ce@eastlink.ca> <91303-1616717760.288585@Iyj2.F9RA.VD0P> <6d70bc8d-73d3-7866-6485-ee89dafdebc9@eastlink.ca> From: Ray Andrews Message-id: <691e63e8-aff6-cce6-d7b4-7bf6de10363a@eastlink.ca> Date: Fri, 26 Mar 2021 08:35:47 -0700 User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:78.0) Gecko/20100101 Thunderbird/78.8.0 MIME-version: 1.0 In-reply-to: Content-type: text/plain; charset=utf-8; format=flowed Content-transfer-encoding: 8bit Content-language: en-US X-Seq: 26611 Archived-At: X-Loop: zsh-users@zsh.org Errors-To: zsh-users-owner@zsh.org Precedence: list Precedence: bulk Sender: zsh-users-request@zsh.org X-no-archive: yes List-Id: List-Help: List-Subscribe: List-Unsubscribe: List-Post: List-Owner: List-Archive: Archived-At: On 2021-03-26 7:49 a.m., Roman Perepelitsa wrote: > > Aborted based on which condition? If the result of an operation is not > representable exactly in a double? If so, then even `1. / 10` would > abort because the real number 0.1 is not representable. > Ha!  You have a point there!  The article you linked talked about some of these issues, but surely in my case it's simply a plain fact that no decimal past 15 can be accurate ever?  Perhaps in practice this is not so easy to distinguish but we used to end rounding errors with that (what's it called?) the 'S' on it's side, the 'approximation' symbol.  Anyway, it's easy for me to preach since I don't have to figure out how this would work in practice.  It's easy to talk about but perhaps not so easy to code.  For now I'm awake to the issue: no accuracy past 15 digits. > Roman.