From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: X-Original-To: caml-list@sympa.inria.fr Delivered-To: caml-list@sympa.inria.fr Received: from mail2-relais-roc.national.inria.fr (mail2-relais-roc.national.inria.fr [192.134.164.83]) by sympa.inria.fr (Postfix) with ESMTPS id F0B437F8F2 for ; Tue, 3 Jun 2014 14:48:10 +0200 (CEST) Received-SPF: None (mail2-smtp-roc.national.inria.fr: no sender authenticity information available from domain of yminsky@janestreet.com) identity=pra; client-ip=38.105.200.112; receiver=mail2-smtp-roc.national.inria.fr; envelope-from="yminsky@janestreet.com"; x-sender="yminsky@janestreet.com"; x-conformance=sidf_compatible Received-SPF: Pass (mail2-smtp-roc.national.inria.fr: domain of yminsky@janestreet.com designates 38.105.200.112 as permitted sender) identity=mailfrom; client-ip=38.105.200.112; receiver=mail2-smtp-roc.national.inria.fr; envelope-from="yminsky@janestreet.com"; x-sender="yminsky@janestreet.com"; x-conformance=sidf_compatible; x-record-type="v=spf1" Received-SPF: None (mail2-smtp-roc.national.inria.fr: no sender authenticity information available from domain of postmaster@mxout1.mail.janestreet.com) identity=helo; client-ip=38.105.200.112; receiver=mail2-smtp-roc.national.inria.fr; envelope-from="yminsky@janestreet.com"; x-sender="postmaster@mxout1.mail.janestreet.com"; x-conformance=sidf_compatible X-IronPort-Anti-Spam-Filtered: true X-IronPort-Anti-Spam-Result: AlYBAF3DjVMmachwnGdsb2JhbABZg1lYgmyqDJVmAYEFCBYOAQEBAQEGFgk8giUBAQEEEhEdAQEjCQsBDwsLDQICCAEdAgIhARIBBQEKEgYTEgwEiAwDEQMCCKElaoowd4R/AQWZcQMKhUIRBoEqiAmDCYE/VweCdYFLhGMFkyeBeIE+i3+EAxgphQSBUg X-IPAS-Result: AlYBAF3DjVMmachwnGdsb2JhbABZg1lYgmyqDJVmAYEFCBYOAQEBAQEGFgk8giUBAQEEEhEdAQEjCQsBDwsLDQICCAEdAgIhARIBBQEKEgYTEgwEiAwDEQMCCKElaoowd4R/AQWZcQMKhUIRBoEqiAmDCYE/VweCdYFLhGMFkyeBeIE+i3+EAxgphQSBUg X-IronPort-AV: E=Sophos;i="4.98,965,1392159600"; d="scan'208";a="77788815" Received: from mxout1.mail.janestreet.com ([38.105.200.112]) by mail2-smtp-roc.national.inria.fr with ESMTP/TLS/DHE-RSA-AES256-SHA; 03 Jun 2014 14:48:09 +0200 Received: from tot-smtp.delacy.com ([172.27.22.15] helo=tot-smtp) by mxout1.mail.janestreet.com with esmtps (TLSv1.2:DHE-RSA-AES256-GCM-SHA384:256) (Exim 4.82) (envelope-from ) id 1Wro8O-0005Y0-12 for caml-list@inria.fr; Tue, 03 Jun 2014 08:48:08 -0400 Received: from tot-dmz-mxgoog1.delacy.com ([172.27.224.14] helo=mxgoog2.janestreet.com) by tot-smtp with esmtps (TLSv1:AES256-SHA:256) (Exim 4.72) (envelope-from ) id 1Wro8N-0005Pa-SZ for caml-list@inria.fr; Tue, 03 Jun 2014 08:48:07 -0400 Received: from mail-lb0-f178.google.com ([209.85.217.178]) by mxgoog2.janestreet.com with esmtp (Exim 4.76) (envelope-from ) id 1Wro8N-0007F0-MP for caml-list@inria.fr; Tue, 03 Jun 2014 08:48:07 -0400 Received: by mail-lb0-f178.google.com with SMTP id w7so3352784lbi.37 for ; Tue, 03 Jun 2014 05:48:07 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=janestreet.com; s=google; h=mime-version:in-reply-to:references:date:message-id:subject:from:to :cc:content-type; bh=QlpEfV6WLQ7dORICyAgbHfXYymHVv/0aKycoDi3VEgI=; b=StqdxZLVAdnqEeBVHTFn+vroI189jw5PEwSARg26RyixzMsmty2bEcDmWy5npvhxNL VZsL+YnwItEphVmtUfy9AQFcjqc6rdxlXiSjQObQ0+veR8eVXQr8wgyB1C/6qIcQtWcE 30YF8a0My2D5mTnqP3w3GPhZpOXiHSwVVZztM= X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20130820; h=x-gm-message-state:mime-version:in-reply-to:references:date :message-id:subject:from:to:cc:content-type; bh=QlpEfV6WLQ7dORICyAgbHfXYymHVv/0aKycoDi3VEgI=; b=bjWU8hMDd07+BtfDPqtRwrwkSChzXrrxcEEbSNhbE3AIxx6S3cLWEQE95QMenwmQOj O8oZwTxKwnm8GUdHhY8QdGuVgzT1mGgfrp3DoQwpsh4IyLezfG/PZ040FWgwihcWLuwd XxUuTFcvip1Q25rJ99xxHAu3022DIr1Dqo8B58ZTU0KC3yivc+8uDD7MFkUNW41OolxV WYAXreqP36DKYwVeRtsvNQg6eCP3UcL/1NCt+KGesVwfmoVhcg1A4b9Vpefxgx2Lxk+V d/qm43CIsvzQpayUIPSNuwX/fh6fQQGh4arrQjdsV9ENLWemoSdzAxjxX3ePMcBzFa6P BzXg== X-Gm-Message-State: ALoCoQmi6MQwGzedkoHFSyT8zPXmdZ23wYNzicLQPLY3ZZvaep9n+z8BXcoZ81n3n918Zpiv24biVa/YCrV2lNNJAxrAKUeARyQvAKWveNnsC2QPNV9ailpfSCgOoq2V5RNu9TUwG5eP X-Received: by 10.152.5.98 with SMTP id r2mr3042274lar.59.1401799686989; Tue, 03 Jun 2014 05:48:06 -0700 (PDT) MIME-Version: 1.0 X-Received: by 10.152.5.98 with SMTP id r2mr3042259lar.59.1401799686853; Tue, 03 Jun 2014 05:48:06 -0700 (PDT) Received: by 10.112.3.39 with HTTP; Tue, 3 Jun 2014 05:48:06 -0700 (PDT) In-Reply-To: References: <543099239773658961@orange.fr> <1401716071976.85ecb8da@Nodemailer> Date: Tue, 3 Jun 2014 08:48:06 -0400 Message-ID: From: Yaron Minsky To: Gabriel Scherer Cc: Andrew Herron , Damien Guichard , Caml List , David Powers Content-Type: text/plain; charset=UTF-8 Subject: Re: [Caml-list] Why AVL-tree? The following summary of what we do with respect to Maps and Sets in Core was written by David Powers (who isn't yet subscribe to the list, so he asked me to forward it on.) In Core we use a slight modification of the AVL tree found in the standard library. I think the biggest change (other than the interface) is that we add a specialized constructor (Leaf of 'key * 'value) as a specialization of Node (left * key * value * right) to limit allocation. It's a nice speed bump and doesn't do too much damage to the readability of the code. We also spent a bunch of time last summer working through the research papers of the last 10 years to see if we could find an implementation we liked better. I'd have to pull up the full history of the project to give real details, but we tried at least all of the following: - red-black trees - left-leaning red-black trees - treaps (including a variant that stored entropy in the spare bits in the variant tag) - splay trees - weight balanced trees - AVL trees with GADT enforcement of the invariants - 1-2 brother trees I'll lead with the caveat that benchmarking is hard, and these structures shine in different ways depending on the type of workload you throw at them. Each implementation below was also mostly a first-pass to understand the structure and do simple tests, so there may be more speed gold in the hills. Your mileage may vary. That said, our conclusions at the end: - red black trees are hard to code and understand (mostly due to remove), and don't show a real performance win. - treaps are a wonderful structure in terms of code simplicity, but getting enough randomness quickly enough is too costly to make them a win over AVL trees (you need to allocate just as much and you need to generate randomness) - splay trees are in our tree, but are too special purpose to be a general win. - Weight balanced trees are a nice structure, and are used in other languages/libraries. They were neither better or worse than AVL trees. - AVL trees with GADT enforcement work, but were actually slower than straightforward AVL trees at the time we tested them. There is some extra matching due to the variant having more cases, so perhaps this isn't surprising. It's also likely that we didn't carry the 2-imbalance trick into the GADT version, which might have skewed the result. - 1-2 brother trees were the best of the lot, and we actually produced a version of the code that we felt was an overall win (or tie) for all workloads. Unfortunately, the optimizations we needed to get us there made the code much longer and harder to understand than the AVL tree code. We just couldn't convince ourselves that it was worth it. Probably the most important point is that nothing we did above gave a general win of more than 10-20% in the tight loop case. Given that, we kept our tweaked AVL tree implementation. If you want to be very very fast, you probably can't get away with a map, and if you just want to be "fast enough" the AVL tree we have is a nice set of tradeoffs for code complexity. On Mon, Jun 2, 2014 at 11:06 AM, Gabriel Scherer wrote: > Note that OCaml's balanced trees are not exactly what is usually > called AVL, as the imbalance between different branches can be at most > 2 (+1 on one side and -1 on the other) instead of just 1 as the > traditional definition assumes. > > On Mon, Jun 2, 2014 at 3:34 PM, Andrew Herron wrote: >> Wikipedia has some notes on the difference: >> >> http://en.wikipedia.org/wiki/AVL_tree >> >> AVL has faster lookup, so maybe they decided to optimise for that. >> >> It's different to some other languages I've seen, but then so is their >> decision to not use a tail recursive List.map. Each to their own, it's not >> hard to implement the alternative :) >> >> >> On Mon, Jun 2, 2014 at 11:21 PM, Damien Guichard >> wrote: >>> >>> >>> Red-black tree would spare a machine word per node, because a red-black >>> tree doesn't need depth information. >>> Hence the reason is either historical or a space/speed trade-off >>> (comparing two depths may be faster than pattern matching). >>> >>> Regards, >>> >>> damien guichard >>> >>> Hi, list, >>> >>> Just from the curiosity, why balanced binary trees used in Set and Map are >>> AVL-trees, not their alternative, say, red-black trees? Is there a deep >>> reason for it, or just a historical one? >>> >>> Best, >>> -- >>> Yoriyuki Yamagata >>> http://yoriyuki.info/ >>> >>> >> > > -- > Caml-list mailing list. Subscription management and archives: > https://sympa.inria.fr/sympa/arc/caml-list > Beginner's list: http://groups.yahoo.com/group/ocaml_beginners > Bug reports: http://caml.inria.fr/bin/caml-bugs