1068 lines
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HTML
1068 lines
40 KiB
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN"
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"http://www.w3.org/TR/html4/strict.dtd">
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<html>
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<head>
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<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
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<title>LLVM Alias Analysis Infrastructure</title>
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<link rel="stylesheet" href="llvm.css" type="text/css">
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</head>
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<body>
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<h1>
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LLVM Alias Analysis Infrastructure
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</h1>
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<ol>
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<li><a href="#introduction">Introduction</a></li>
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<li><a href="#overview"><tt>AliasAnalysis</tt> Class Overview</a>
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<ul>
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<li><a href="#pointers">Representation of Pointers</a></li>
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<li><a href="#alias">The <tt>alias</tt> method</a></li>
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<li><a href="#ModRefInfo">The <tt>getModRefInfo</tt> methods</a></li>
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<li><a href="#OtherItfs">Other useful <tt>AliasAnalysis</tt> methods</a></li>
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</ul>
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</li>
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<li><a href="#writingnew">Writing a new <tt>AliasAnalysis</tt> Implementation</a>
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<ul>
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<li><a href="#passsubclasses">Different Pass styles</a></li>
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<li><a href="#requiredcalls">Required initialization calls</a></li>
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<li><a href="#interfaces">Interfaces which may be specified</a></li>
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<li><a href="#chaining"><tt>AliasAnalysis</tt> chaining behavior</a></li>
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<li><a href="#updating">Updating analysis results for transformations</a></li>
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<li><a href="#implefficiency">Efficiency Issues</a></li>
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<li><a href="#limitations">Limitations</a></li>
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</ul>
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</li>
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<li><a href="#using">Using alias analysis results</a>
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<ul>
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<li><a href="#memdep">Using the <tt>MemoryDependenceAnalysis</tt> Pass</a></li>
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<li><a href="#ast">Using the <tt>AliasSetTracker</tt> class</a></li>
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<li><a href="#direct">Using the <tt>AliasAnalysis</tt> interface directly</a></li>
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</ul>
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</li>
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<li><a href="#exist">Existing alias analysis implementations and clients</a>
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<ul>
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<li><a href="#impls">Available <tt>AliasAnalysis</tt> implementations</a></li>
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<li><a href="#aliasanalysis-xforms">Alias analysis driven transformations</a></li>
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<li><a href="#aliasanalysis-debug">Clients for debugging and evaluation of
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implementations</a></li>
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</ul>
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</li>
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<li><a href="#memdep">Memory Dependence Analysis</a></li>
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</ol>
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<div class="doc_author">
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<p>Written by <a href="mailto:sabre@nondot.org">Chris Lattner</a></p>
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</div>
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<!-- *********************************************************************** -->
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<h2>
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<a name="introduction">Introduction</a>
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</h2>
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<!-- *********************************************************************** -->
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<div>
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<p>Alias Analysis (aka Pointer Analysis) is a class of techniques which attempt
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to determine whether or not two pointers ever can point to the same object in
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memory. There are many different algorithms for alias analysis and many
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different ways of classifying them: flow-sensitive vs flow-insensitive,
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context-sensitive vs context-insensitive, field-sensitive vs field-insensitive,
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unification-based vs subset-based, etc. Traditionally, alias analyses respond
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to a query with a <a href="#MustMayNo">Must, May, or No</a> alias response,
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indicating that two pointers always point to the same object, might point to the
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same object, or are known to never point to the same object.</p>
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<p>The LLVM <a
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href="http://llvm.org/doxygen/classllvm_1_1AliasAnalysis.html"><tt>AliasAnalysis</tt></a>
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class is the primary interface used by clients and implementations of alias
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analyses in the LLVM system. This class is the common interface between clients
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of alias analysis information and the implementations providing it, and is
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designed to support a wide range of implementations and clients (but currently
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all clients are assumed to be flow-insensitive). In addition to simple alias
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analysis information, this class exposes Mod/Ref information from those
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implementations which can provide it, allowing for powerful analyses and
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transformations to work well together.</p>
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<p>This document contains information necessary to successfully implement this
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interface, use it, and to test both sides. It also explains some of the finer
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points about what exactly results mean. If you feel that something is unclear
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or should be added, please <a href="mailto:sabre@nondot.org">let me
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know</a>.</p>
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</div>
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<!-- *********************************************************************** -->
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<h2>
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<a name="overview"><tt>AliasAnalysis</tt> Class Overview</a>
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</h2>
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<!-- *********************************************************************** -->
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<div>
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<p>The <a
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href="http://llvm.org/doxygen/classllvm_1_1AliasAnalysis.html"><tt>AliasAnalysis</tt></a>
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class defines the interface that the various alias analysis implementations
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should support. This class exports two important enums: <tt>AliasResult</tt>
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and <tt>ModRefResult</tt> which represent the result of an alias query or a
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mod/ref query, respectively.</p>
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<p>The <tt>AliasAnalysis</tt> interface exposes information about memory,
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represented in several different ways. In particular, memory objects are
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represented as a starting address and size, and function calls are represented
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as the actual <tt>call</tt> or <tt>invoke</tt> instructions that performs the
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call. The <tt>AliasAnalysis</tt> interface also exposes some helper methods
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which allow you to get mod/ref information for arbitrary instructions.</p>
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<p>All <tt>AliasAnalysis</tt> interfaces require that in queries involving
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multiple values, values which are not
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<a href="LangRef.html#constants">constants</a> are all defined within the
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same function.</p>
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<!-- ======================================================================= -->
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<h3>
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<a name="pointers">Representation of Pointers</a>
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</h3>
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<div>
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<p>Most importantly, the <tt>AliasAnalysis</tt> class provides several methods
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which are used to query whether or not two memory objects alias, whether
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function calls can modify or read a memory object, etc. For all of these
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queries, memory objects are represented as a pair of their starting address (a
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symbolic LLVM <tt>Value*</tt>) and a static size.</p>
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<p>Representing memory objects as a starting address and a size is critically
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important for correct Alias Analyses. For example, consider this (silly, but
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possible) C code:</p>
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<div class="doc_code">
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<pre>
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int i;
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char C[2];
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char A[10];
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/* ... */
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for (i = 0; i != 10; ++i) {
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C[0] = A[i]; /* One byte store */
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C[1] = A[9-i]; /* One byte store */
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}
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</pre>
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</div>
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<p>In this case, the <tt>basicaa</tt> pass will disambiguate the stores to
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<tt>C[0]</tt> and <tt>C[1]</tt> because they are accesses to two distinct
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locations one byte apart, and the accesses are each one byte. In this case, the
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LICM pass can use store motion to remove the stores from the loop. In
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constrast, the following code:</p>
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<div class="doc_code">
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<pre>
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int i;
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char C[2];
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char A[10];
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/* ... */
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for (i = 0; i != 10; ++i) {
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((short*)C)[0] = A[i]; /* Two byte store! */
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C[1] = A[9-i]; /* One byte store */
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}
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</pre>
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</div>
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<p>In this case, the two stores to C do alias each other, because the access to
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the <tt>&C[0]</tt> element is a two byte access. If size information wasn't
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available in the query, even the first case would have to conservatively assume
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that the accesses alias.</p>
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</div>
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<!-- ======================================================================= -->
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<h3>
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<a name="alias">The <tt>alias</tt> method</a>
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</h3>
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<div>
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<p>The <tt>alias</tt> method is the primary interface used to determine whether
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or not two memory objects alias each other. It takes two memory objects as
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input and returns MustAlias, PartialAlias, MayAlias, or NoAlias as
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appropriate.</p>
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<p>Like all <tt>AliasAnalysis</tt> interfaces, the <tt>alias</tt> method requires
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that either the two pointer values be defined within the same function, or at
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least one of the values is a <a href="LangRef.html#constants">constant</a>.</p>
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<!-- _______________________________________________________________________ -->
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<h4>
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<a name="MustMayNo">Must, May, and No Alias Responses</a>
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</h4>
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<div>
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<p>The NoAlias response may be used when there is never an immediate dependence
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between any memory reference <i>based</i> on one pointer and any memory
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reference <i>based</i> the other. The most obvious example is when the two
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pointers point to non-overlapping memory ranges. Another is when the two
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pointers are only ever used for reading memory. Another is when the memory is
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freed and reallocated between accesses through one pointer and accesses through
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the other -- in this case, there is a dependence, but it's mediated by the free
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and reallocation.</p>
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<p>As an exception to this is with the
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<a href="LangRef.html#noalias"><tt>noalias</tt></a> keyword; the "irrelevant"
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dependencies are ignored.</p>
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<p>The MayAlias response is used whenever the two pointers might refer to the
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same object.</p>
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<p>The PartialAlias response is used when the two memory objects are known
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to be overlapping in some way, but do not start at the same address.</p>
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<p>The MustAlias response may only be returned if the two memory objects are
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guaranteed to always start at exactly the same location. A MustAlias response
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implies that the pointers compare equal.</p>
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</div>
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</div>
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<!-- ======================================================================= -->
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<h3>
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<a name="ModRefInfo">The <tt>getModRefInfo</tt> methods</a>
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</h3>
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<div>
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<p>The <tt>getModRefInfo</tt> methods return information about whether the
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execution of an instruction can read or modify a memory location. Mod/Ref
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information is always conservative: if an instruction <b>might</b> read or write
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a location, ModRef is returned.</p>
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<p>The <tt>AliasAnalysis</tt> class also provides a <tt>getModRefInfo</tt>
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method for testing dependencies between function calls. This method takes two
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call sites (CS1 & CS2), returns NoModRef if neither call writes to memory
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read or written by the other, Ref if CS1 reads memory written by CS2, Mod if CS1
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writes to memory read or written by CS2, or ModRef if CS1 might read or write
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memory written to by CS2. Note that this relation is not commutative.</p>
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</div>
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<!-- ======================================================================= -->
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<h3>
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<a name="OtherItfs">Other useful <tt>AliasAnalysis</tt> methods</a>
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</h3>
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<div>
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<p>
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Several other tidbits of information are often collected by various alias
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analysis implementations and can be put to good use by various clients.
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</p>
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<!-- _______________________________________________________________________ -->
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<h4>
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The <tt>pointsToConstantMemory</tt> method
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</h4>
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<div>
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<p>The <tt>pointsToConstantMemory</tt> method returns true if and only if the
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analysis can prove that the pointer only points to unchanging memory locations
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(functions, constant global variables, and the null pointer). This information
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can be used to refine mod/ref information: it is impossible for an unchanging
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memory location to be modified.</p>
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</div>
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<!-- _______________________________________________________________________ -->
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<h4>
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<a name="simplemodref">The <tt>doesNotAccessMemory</tt> and
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<tt>onlyReadsMemory</tt> methods</a>
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</h4>
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<div>
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<p>These methods are used to provide very simple mod/ref information for
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function calls. The <tt>doesNotAccessMemory</tt> method returns true for a
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function if the analysis can prove that the function never reads or writes to
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memory, or if the function only reads from constant memory. Functions with this
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property are side-effect free and only depend on their input arguments, allowing
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them to be eliminated if they form common subexpressions or be hoisted out of
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loops. Many common functions behave this way (e.g., <tt>sin</tt> and
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<tt>cos</tt>) but many others do not (e.g., <tt>acos</tt>, which modifies the
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<tt>errno</tt> variable).</p>
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<p>The <tt>onlyReadsMemory</tt> method returns true for a function if analysis
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can prove that (at most) the function only reads from non-volatile memory.
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Functions with this property are side-effect free, only depending on their input
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arguments and the state of memory when they are called. This property allows
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calls to these functions to be eliminated and moved around, as long as there is
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no store instruction that changes the contents of memory. Note that all
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functions that satisfy the <tt>doesNotAccessMemory</tt> method also satisfies
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<tt>onlyReadsMemory</tt>.</p>
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</div>
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</div>
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</div>
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<!-- *********************************************************************** -->
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<h2>
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<a name="writingnew">Writing a new <tt>AliasAnalysis</tt> Implementation</a>
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</h2>
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<!-- *********************************************************************** -->
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<div>
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<p>Writing a new alias analysis implementation for LLVM is quite
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straight-forward. There are already several implementations that you can use
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for examples, and the following information should help fill in any details.
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For a examples, take a look at the <a href="#impls">various alias analysis
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implementations</a> included with LLVM.</p>
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<!-- ======================================================================= -->
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<h3>
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||
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<a name="passsubclasses">Different Pass styles</a>
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||
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</h3>
|
||
|
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|
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<div>
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<p>The first step to determining what type of <a
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href="WritingAnLLVMPass.html">LLVM pass</a> you need to use for your Alias
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Analysis. As is the case with most other analyses and transformations, the
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answer should be fairly obvious from what type of problem you are trying to
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solve:</p>
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<ol>
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<li>If you require interprocedural analysis, it should be a
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<tt>Pass</tt>.</li>
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<li>If you are a function-local analysis, subclass <tt>FunctionPass</tt>.</li>
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<li>If you don't need to look at the program at all, subclass
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<tt>ImmutablePass</tt>.</li>
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</ol>
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<p>In addition to the pass that you subclass, you should also inherit from the
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<tt>AliasAnalysis</tt> interface, of course, and use the
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|
|
<tt>RegisterAnalysisGroup</tt> template to register as an implementation of
|
||
|
|
<tt>AliasAnalysis</tt>.</p>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<!-- ======================================================================= -->
|
||
|
|
<h3>
|
||
|
|
<a name="requiredcalls">Required initialization calls</a>
|
||
|
|
</h3>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
|
||
|
|
<p>Your subclass of <tt>AliasAnalysis</tt> is required to invoke two methods on
|
||
|
|
the <tt>AliasAnalysis</tt> base class: <tt>getAnalysisUsage</tt> and
|
||
|
|
<tt>InitializeAliasAnalysis</tt>. In particular, your implementation of
|
||
|
|
<tt>getAnalysisUsage</tt> should explicitly call into the
|
||
|
|
<tt>AliasAnalysis::getAnalysisUsage</tt> method in addition to doing any
|
||
|
|
declaring any pass dependencies your pass has. Thus you should have something
|
||
|
|
like this:</p>
|
||
|
|
|
||
|
|
<div class="doc_code">
|
||
|
|
<pre>
|
||
|
|
void getAnalysisUsage(AnalysisUsage &AU) const {
|
||
|
|
AliasAnalysis::getAnalysisUsage(AU);
|
||
|
|
<i>// declare your dependencies here.</i>
|
||
|
|
}
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>Additionally, your must invoke the <tt>InitializeAliasAnalysis</tt> method
|
||
|
|
from your analysis run method (<tt>run</tt> for a <tt>Pass</tt>,
|
||
|
|
<tt>runOnFunction</tt> for a <tt>FunctionPass</tt>, or <tt>InitializePass</tt>
|
||
|
|
for an <tt>ImmutablePass</tt>). For example (as part of a <tt>Pass</tt>):</p>
|
||
|
|
|
||
|
|
<div class="doc_code">
|
||
|
|
<pre>
|
||
|
|
bool run(Module &M) {
|
||
|
|
InitializeAliasAnalysis(this);
|
||
|
|
<i>// Perform analysis here...</i>
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<!-- ======================================================================= -->
|
||
|
|
<h3>
|
||
|
|
<a name="interfaces">Interfaces which may be specified</a>
|
||
|
|
</h3>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
|
||
|
|
<p>All of the <a
|
||
|
|
href="/doxygen/classllvm_1_1AliasAnalysis.html"><tt>AliasAnalysis</tt></a>
|
||
|
|
virtual methods default to providing <a href="#chaining">chaining</a> to another
|
||
|
|
alias analysis implementation, which ends up returning conservatively correct
|
||
|
|
information (returning "May" Alias and "Mod/Ref" for alias and mod/ref queries
|
||
|
|
respectively). Depending on the capabilities of the analysis you are
|
||
|
|
implementing, you just override the interfaces you can improve.</p>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
<!-- ======================================================================= -->
|
||
|
|
<h3>
|
||
|
|
<a name="chaining"><tt>AliasAnalysis</tt> chaining behavior</a>
|
||
|
|
</h3>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
|
||
|
|
<p>With only one special exception (the <a href="#no-aa"><tt>no-aa</tt></a>
|
||
|
|
pass) every alias analysis pass chains to another alias analysis
|
||
|
|
implementation (for example, the user can specify "<tt>-basicaa -ds-aa
|
||
|
|
-licm</tt>" to get the maximum benefit from both alias
|
||
|
|
analyses). The alias analysis class automatically takes care of most of this
|
||
|
|
for methods that you don't override. For methods that you do override, in code
|
||
|
|
paths that return a conservative MayAlias or Mod/Ref result, simply return
|
||
|
|
whatever the superclass computes. For example:</p>
|
||
|
|
|
||
|
|
<div class="doc_code">
|
||
|
|
<pre>
|
||
|
|
AliasAnalysis::AliasResult alias(const Value *V1, unsigned V1Size,
|
||
|
|
const Value *V2, unsigned V2Size) {
|
||
|
|
if (...)
|
||
|
|
return NoAlias;
|
||
|
|
...
|
||
|
|
|
||
|
|
<i>// Couldn't determine a must or no-alias result.</i>
|
||
|
|
return AliasAnalysis::alias(V1, V1Size, V2, V2Size);
|
||
|
|
}
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>In addition to analysis queries, you must make sure to unconditionally pass
|
||
|
|
LLVM <a href="#updating">update notification</a> methods to the superclass as
|
||
|
|
well if you override them, which allows all alias analyses in a change to be
|
||
|
|
updated.</p>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
|
||
|
|
<!-- ======================================================================= -->
|
||
|
|
<h3>
|
||
|
|
<a name="updating">Updating analysis results for transformations</a>
|
||
|
|
</h3>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
<p>
|
||
|
|
Alias analysis information is initially computed for a static snapshot of the
|
||
|
|
program, but clients will use this information to make transformations to the
|
||
|
|
code. All but the most trivial forms of alias analysis will need to have their
|
||
|
|
analysis results updated to reflect the changes made by these transformations.
|
||
|
|
</p>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
The <tt>AliasAnalysis</tt> interface exposes four methods which are used to
|
||
|
|
communicate program changes from the clients to the analysis implementations.
|
||
|
|
Various alias analysis implementations should use these methods to ensure that
|
||
|
|
their internal data structures are kept up-to-date as the program changes (for
|
||
|
|
example, when an instruction is deleted), and clients of alias analysis must be
|
||
|
|
sure to call these interfaces appropriately.
|
||
|
|
</p>
|
||
|
|
|
||
|
|
<!-- _______________________________________________________________________ -->
|
||
|
|
<h4>The <tt>deleteValue</tt> method</h4>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
The <tt>deleteValue</tt> method is called by transformations when they remove an
|
||
|
|
instruction or any other value from the program (including values that do not
|
||
|
|
use pointers). Typically alias analyses keep data structures that have entries
|
||
|
|
for each value in the program. When this method is called, they should remove
|
||
|
|
any entries for the specified value, if they exist.
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<!-- _______________________________________________________________________ -->
|
||
|
|
<h4>The <tt>copyValue</tt> method</h4>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
The <tt>copyValue</tt> method is used when a new value is introduced into the
|
||
|
|
program. There is no way to introduce a value into the program that did not
|
||
|
|
exist before (this doesn't make sense for a safe compiler transformation), so
|
||
|
|
this is the only way to introduce a new value. This method indicates that the
|
||
|
|
new value has exactly the same properties as the value being copied.
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<!-- _______________________________________________________________________ -->
|
||
|
|
<h4>The <tt>replaceWithNewValue</tt> method</h4>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
This method is a simple helper method that is provided to make clients easier to
|
||
|
|
use. It is implemented by copying the old analysis information to the new
|
||
|
|
value, then deleting the old value. This method cannot be overridden by alias
|
||
|
|
analysis implementations.
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<!-- _______________________________________________________________________ -->
|
||
|
|
<h4>The <tt>addEscapingUse</tt> method</h4>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
<p>The <tt>addEscapingUse</tt> method is used when the uses of a pointer
|
||
|
|
value have changed in ways that may invalidate precomputed analysis information.
|
||
|
|
Implementations may either use this callback to provide conservative responses
|
||
|
|
for points whose uses have change since analysis time, or may recompute some
|
||
|
|
or all of their internal state to continue providing accurate responses.</p>
|
||
|
|
|
||
|
|
<p>In general, any new use of a pointer value is considered an escaping use,
|
||
|
|
and must be reported through this callback, <em>except</em> for the
|
||
|
|
uses below:</p>
|
||
|
|
|
||
|
|
<ul>
|
||
|
|
<li>A <tt>bitcast</tt> or <tt>getelementptr</tt> of the pointer</li>
|
||
|
|
<li>A <tt>store</tt> through the pointer (but not a <tt>store</tt>
|
||
|
|
<em>of</em> the pointer)</li>
|
||
|
|
<li>A <tt>load</tt> through the pointer</li>
|
||
|
|
</ul>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<!-- ======================================================================= -->
|
||
|
|
<h3>
|
||
|
|
<a name="implefficiency">Efficiency Issues</a>
|
||
|
|
</h3>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
|
||
|
|
<p>From the LLVM perspective, the only thing you need to do to provide an
|
||
|
|
efficient alias analysis is to make sure that alias analysis <b>queries</b> are
|
||
|
|
serviced quickly. The actual calculation of the alias analysis results (the
|
||
|
|
"run" method) is only performed once, but many (perhaps duplicate) queries may
|
||
|
|
be performed. Because of this, try to move as much computation to the run
|
||
|
|
method as possible (within reason).</p>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<!-- ======================================================================= -->
|
||
|
|
<h3>
|
||
|
|
<a name="limitations">Limitations</a>
|
||
|
|
</h3>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
|
||
|
|
<p>The AliasAnalysis infrastructure has several limitations which make
|
||
|
|
writing a new <tt>AliasAnalysis</tt> implementation difficult.</p>
|
||
|
|
|
||
|
|
<p>There is no way to override the default alias analysis. It would
|
||
|
|
be very useful to be able to do something like "opt -my-aa -O2" and
|
||
|
|
have it use -my-aa for all passes which need AliasAnalysis, but there
|
||
|
|
is currently no support for that, short of changing the source code
|
||
|
|
and recompiling. Similarly, there is also no way of setting a chain
|
||
|
|
of analyses as the default.</p>
|
||
|
|
|
||
|
|
<p>There is no way for transform passes to declare that they preserve
|
||
|
|
<tt>AliasAnalysis</tt> implementations. The <tt>AliasAnalysis</tt>
|
||
|
|
interface includes <tt>deleteValue</tt> and <tt>copyValue</tt> methods
|
||
|
|
which are intended to allow a pass to keep an AliasAnalysis consistent,
|
||
|
|
however there's no way for a pass to declare in its
|
||
|
|
<tt>getAnalysisUsage</tt> that it does so. Some passes attempt to use
|
||
|
|
<tt>AU.addPreserved<AliasAnalysis></tt>, however this doesn't
|
||
|
|
actually have any effect.</p>
|
||
|
|
|
||
|
|
<p><tt>AliasAnalysisCounter</tt> (<tt>-count-aa</tt>) and <tt>AliasDebugger</tt>
|
||
|
|
(<tt>-debug-aa</tt>) are implemented as <tt>ModulePass</tt> classes, so if your
|
||
|
|
alias analysis uses <tt>FunctionPass</tt>, it won't be able to use
|
||
|
|
these utilities. If you try to use them, the pass manager will
|
||
|
|
silently route alias analysis queries directly to
|
||
|
|
<tt>BasicAliasAnalysis</tt> instead.</p>
|
||
|
|
|
||
|
|
<p>Similarly, the <tt>opt -p</tt> option introduces <tt>ModulePass</tt>
|
||
|
|
passes between each pass, which prevents the use of <tt>FunctionPass</tt>
|
||
|
|
alias analysis passes.</p>
|
||
|
|
|
||
|
|
<p>The <tt>AliasAnalysis</tt> API does have functions for notifying
|
||
|
|
implementations when values are deleted or copied, however these
|
||
|
|
aren't sufficient. There are many other ways that LLVM IR can be
|
||
|
|
modified which could be relevant to <tt>AliasAnalysis</tt>
|
||
|
|
implementations which can not be expressed.</p>
|
||
|
|
|
||
|
|
<p>The <tt>AliasAnalysisDebugger</tt> utility seems to suggest that
|
||
|
|
<tt>AliasAnalysis</tt> implementations can expect that they will be
|
||
|
|
informed of any relevant <tt>Value</tt> before it appears in an
|
||
|
|
alias query. However, popular clients such as <tt>GVN</tt> don't
|
||
|
|
support this, and are known to trigger errors when run with the
|
||
|
|
<tt>AliasAnalysisDebugger</tt>.</p>
|
||
|
|
|
||
|
|
<p>Due to several of the above limitations, the most obvious use for
|
||
|
|
the <tt>AliasAnalysisCounter</tt> utility, collecting stats on all
|
||
|
|
alias queries in a compilation, doesn't work, even if the
|
||
|
|
<tt>AliasAnalysis</tt> implementations don't use <tt>FunctionPass</tt>.
|
||
|
|
There's no way to set a default, much less a default sequence,
|
||
|
|
and there's no way to preserve it.</p>
|
||
|
|
|
||
|
|
<p>The <tt>AliasSetTracker</tt> class (which is used by <tt>LICM</tt>
|
||
|
|
makes a non-deterministic number of alias queries. This can cause stats
|
||
|
|
collected by <tt>AliasAnalysisCounter</tt> to have fluctuations among
|
||
|
|
identical runs, for example. Another consequence is that debugging
|
||
|
|
techniques involving pausing execution after a predetermined number
|
||
|
|
of queries can be unreliable.</p>
|
||
|
|
|
||
|
|
<p>Many alias queries can be reformulated in terms of other alias
|
||
|
|
queries. When multiple <tt>AliasAnalysis</tt> queries are chained together,
|
||
|
|
it would make sense to start those queries from the beginning of the chain,
|
||
|
|
with care taken to avoid infinite looping, however currently an
|
||
|
|
implementation which wants to do this can only start such queries
|
||
|
|
from itself.</p>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<!-- *********************************************************************** -->
|
||
|
|
<h2>
|
||
|
|
<a name="using">Using alias analysis results</a>
|
||
|
|
</h2>
|
||
|
|
<!-- *********************************************************************** -->
|
||
|
|
|
||
|
|
<div>
|
||
|
|
|
||
|
|
<p>There are several different ways to use alias analysis results. In order of
|
||
|
|
preference, these are...</p>
|
||
|
|
|
||
|
|
<!-- ======================================================================= -->
|
||
|
|
<h3>
|
||
|
|
<a name="memdep">Using the <tt>MemoryDependenceAnalysis</tt> Pass</a>
|
||
|
|
</h3>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
|
||
|
|
<p>The <tt>memdep</tt> pass uses alias analysis to provide high-level dependence
|
||
|
|
information about memory-using instructions. This will tell you which store
|
||
|
|
feeds into a load, for example. It uses caching and other techniques to be
|
||
|
|
efficient, and is used by Dead Store Elimination, GVN, and memcpy optimizations.
|
||
|
|
</p>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<!-- ======================================================================= -->
|
||
|
|
<h3>
|
||
|
|
<a name="ast">Using the <tt>AliasSetTracker</tt> class</a>
|
||
|
|
</h3>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
|
||
|
|
<p>Many transformations need information about alias <b>sets</b> that are active
|
||
|
|
in some scope, rather than information about pairwise aliasing. The <tt><a
|
||
|
|
href="/doxygen/classllvm_1_1AliasSetTracker.html">AliasSetTracker</a></tt> class
|
||
|
|
is used to efficiently build these Alias Sets from the pairwise alias analysis
|
||
|
|
information provided by the <tt>AliasAnalysis</tt> interface.</p>
|
||
|
|
|
||
|
|
<p>First you initialize the AliasSetTracker by using the "<tt>add</tt>" methods
|
||
|
|
to add information about various potentially aliasing instructions in the scope
|
||
|
|
you are interested in. Once all of the alias sets are completed, your pass
|
||
|
|
should simply iterate through the constructed alias sets, using the
|
||
|
|
<tt>AliasSetTracker</tt> <tt>begin()</tt>/<tt>end()</tt> methods.</p>
|
||
|
|
|
||
|
|
<p>The <tt>AliasSet</tt>s formed by the <tt>AliasSetTracker</tt> are guaranteed
|
||
|
|
to be disjoint, calculate mod/ref information and volatility for the set, and
|
||
|
|
keep track of whether or not all of the pointers in the set are Must aliases.
|
||
|
|
The AliasSetTracker also makes sure that sets are properly folded due to call
|
||
|
|
instructions, and can provide a list of pointers in each set.</p>
|
||
|
|
|
||
|
|
<p>As an example user of this, the <a href="/doxygen/structLICM.html">Loop
|
||
|
|
Invariant Code Motion</a> pass uses <tt>AliasSetTracker</tt>s to calculate alias
|
||
|
|
sets for each loop nest. If an <tt>AliasSet</tt> in a loop is not modified,
|
||
|
|
then all load instructions from that set may be hoisted out of the loop. If any
|
||
|
|
alias sets are stored to <b>and</b> are must alias sets, then the stores may be
|
||
|
|
sunk to outside of the loop, promoting the memory location to a register for the
|
||
|
|
duration of the loop nest. Both of these transformations only apply if the
|
||
|
|
pointer argument is loop-invariant.</p>
|
||
|
|
|
||
|
|
<!-- _______________________________________________________________________ -->
|
||
|
|
<h4>
|
||
|
|
The AliasSetTracker implementation
|
||
|
|
</h4>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
|
||
|
|
<p>The AliasSetTracker class is implemented to be as efficient as possible. It
|
||
|
|
uses the union-find algorithm to efficiently merge AliasSets when a pointer is
|
||
|
|
inserted into the AliasSetTracker that aliases multiple sets. The primary data
|
||
|
|
structure is a hash table mapping pointers to the AliasSet they are in.</p>
|
||
|
|
|
||
|
|
<p>The AliasSetTracker class must maintain a list of all of the LLVM Value*'s
|
||
|
|
that are in each AliasSet. Since the hash table already has entries for each
|
||
|
|
LLVM Value* of interest, the AliasesSets thread the linked list through these
|
||
|
|
hash-table nodes to avoid having to allocate memory unnecessarily, and to make
|
||
|
|
merging alias sets extremely efficient (the linked list merge is constant time).
|
||
|
|
</p>
|
||
|
|
|
||
|
|
<p>You shouldn't need to understand these details if you are just a client of
|
||
|
|
the AliasSetTracker, but if you look at the code, hopefully this brief
|
||
|
|
description will help make sense of why things are designed the way they
|
||
|
|
are.</p>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<!-- ======================================================================= -->
|
||
|
|
<h3>
|
||
|
|
<a name="direct">Using the <tt>AliasAnalysis</tt> interface directly</a>
|
||
|
|
</h3>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
|
||
|
|
<p>If neither of these utility class are what your pass needs, you should use
|
||
|
|
the interfaces exposed by the <tt>AliasAnalysis</tt> class directly. Try to use
|
||
|
|
the higher-level methods when possible (e.g., use mod/ref information instead of
|
||
|
|
the <a href="#alias"><tt>alias</tt></a> method directly if possible) to get the
|
||
|
|
best precision and efficiency.</p>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<!-- *********************************************************************** -->
|
||
|
|
<h2>
|
||
|
|
<a name="exist">Existing alias analysis implementations and clients</a>
|
||
|
|
</h2>
|
||
|
|
<!-- *********************************************************************** -->
|
||
|
|
|
||
|
|
<div>
|
||
|
|
|
||
|
|
<p>If you're going to be working with the LLVM alias analysis infrastructure,
|
||
|
|
you should know what clients and implementations of alias analysis are
|
||
|
|
available. In particular, if you are implementing an alias analysis, you should
|
||
|
|
be aware of the <a href="#aliasanalysis-debug">the clients</a> that are useful
|
||
|
|
for monitoring and evaluating different implementations.</p>
|
||
|
|
|
||
|
|
<!-- ======================================================================= -->
|
||
|
|
<h3>
|
||
|
|
<a name="impls">Available <tt>AliasAnalysis</tt> implementations</a>
|
||
|
|
</h3>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
|
||
|
|
<p>This section lists the various implementations of the <tt>AliasAnalysis</tt>
|
||
|
|
interface. With the exception of the <a href="#no-aa"><tt>-no-aa</tt></a>
|
||
|
|
implementation, all of these <a href="#chaining">chain</a> to other alias
|
||
|
|
analysis implementations.</p>
|
||
|
|
|
||
|
|
<!-- _______________________________________________________________________ -->
|
||
|
|
<h4>
|
||
|
|
<a name="no-aa">The <tt>-no-aa</tt> pass</a>
|
||
|
|
</h4>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
|
||
|
|
<p>The <tt>-no-aa</tt> pass is just like what it sounds: an alias analysis that
|
||
|
|
never returns any useful information. This pass can be useful if you think that
|
||
|
|
alias analysis is doing something wrong and are trying to narrow down a
|
||
|
|
problem.</p>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<!-- _______________________________________________________________________ -->
|
||
|
|
<h4>
|
||
|
|
<a name="basic-aa">The <tt>-basicaa</tt> pass</a>
|
||
|
|
</h4>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
|
||
|
|
<p>The <tt>-basicaa</tt> pass is an aggressive local analysis that "knows"
|
||
|
|
many important facts:</p>
|
||
|
|
|
||
|
|
<ul>
|
||
|
|
<li>Distinct globals, stack allocations, and heap allocations can never
|
||
|
|
alias.</li>
|
||
|
|
<li>Globals, stack allocations, and heap allocations never alias the null
|
||
|
|
pointer.</li>
|
||
|
|
<li>Different fields of a structure do not alias.</li>
|
||
|
|
<li>Indexes into arrays with statically differing subscripts cannot alias.</li>
|
||
|
|
<li>Many common standard C library functions <a
|
||
|
|
href="#simplemodref">never access memory or only read memory</a>.</li>
|
||
|
|
<li>Pointers that obviously point to constant globals
|
||
|
|
"<tt>pointToConstantMemory</tt>".</li>
|
||
|
|
<li>Function calls can not modify or references stack allocations if they never
|
||
|
|
escape from the function that allocates them (a common case for automatic
|
||
|
|
arrays).</li>
|
||
|
|
</ul>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<!-- _______________________________________________________________________ -->
|
||
|
|
<h4>
|
||
|
|
<a name="globalsmodref">The <tt>-globalsmodref-aa</tt> pass</a>
|
||
|
|
</h4>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
|
||
|
|
<p>This pass implements a simple context-sensitive mod/ref and alias analysis
|
||
|
|
for internal global variables that don't "have their address taken". If a
|
||
|
|
global does not have its address taken, the pass knows that no pointers alias
|
||
|
|
the global. This pass also keeps track of functions that it knows never access
|
||
|
|
memory or never read memory. This allows certain optimizations (e.g. GVN) to
|
||
|
|
eliminate call instructions entirely.
|
||
|
|
</p>
|
||
|
|
|
||
|
|
<p>The real power of this pass is that it provides context-sensitive mod/ref
|
||
|
|
information for call instructions. This allows the optimizer to know that
|
||
|
|
calls to a function do not clobber or read the value of the global, allowing
|
||
|
|
loads and stores to be eliminated.</p>
|
||
|
|
|
||
|
|
<p>Note that this pass is somewhat limited in its scope (only support
|
||
|
|
non-address taken globals), but is very quick analysis.</p>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<!-- _______________________________________________________________________ -->
|
||
|
|
<h4>
|
||
|
|
<a name="steens-aa">The <tt>-steens-aa</tt> pass</a>
|
||
|
|
</h4>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
|
||
|
|
<p>The <tt>-steens-aa</tt> pass implements a variation on the well-known
|
||
|
|
"Steensgaard's algorithm" for interprocedural alias analysis. Steensgaard's
|
||
|
|
algorithm is a unification-based, flow-insensitive, context-insensitive, and
|
||
|
|
field-insensitive alias analysis that is also very scalable (effectively linear
|
||
|
|
time).</p>
|
||
|
|
|
||
|
|
<p>The LLVM <tt>-steens-aa</tt> pass implements a "speculatively
|
||
|
|
field-<b>sensitive</b>" version of Steensgaard's algorithm using the Data
|
||
|
|
Structure Analysis framework. This gives it substantially more precision than
|
||
|
|
the standard algorithm while maintaining excellent analysis scalability.</p>
|
||
|
|
|
||
|
|
<p>Note that <tt>-steens-aa</tt> is available in the optional "poolalloc"
|
||
|
|
module, it is not part of the LLVM core.</p>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<!-- _______________________________________________________________________ -->
|
||
|
|
<h4>
|
||
|
|
<a name="ds-aa">The <tt>-ds-aa</tt> pass</a>
|
||
|
|
</h4>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
|
||
|
|
<p>The <tt>-ds-aa</tt> pass implements the full Data Structure Analysis
|
||
|
|
algorithm. Data Structure Analysis is a modular unification-based,
|
||
|
|
flow-insensitive, context-<b>sensitive</b>, and speculatively
|
||
|
|
field-<b>sensitive</b> alias analysis that is also quite scalable, usually at
|
||
|
|
O(n*log(n)).</p>
|
||
|
|
|
||
|
|
<p>This algorithm is capable of responding to a full variety of alias analysis
|
||
|
|
queries, and can provide context-sensitive mod/ref information as well. The
|
||
|
|
only major facility not implemented so far is support for must-alias
|
||
|
|
information.</p>
|
||
|
|
|
||
|
|
<p>Note that <tt>-ds-aa</tt> is available in the optional "poolalloc"
|
||
|
|
module, it is not part of the LLVM core.</p>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<!-- _______________________________________________________________________ -->
|
||
|
|
<h4>
|
||
|
|
<a name="scev-aa">The <tt>-scev-aa</tt> pass</a>
|
||
|
|
</h4>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
|
||
|
|
<p>The <tt>-scev-aa</tt> pass implements AliasAnalysis queries by
|
||
|
|
translating them into ScalarEvolution queries. This gives it a
|
||
|
|
more complete understanding of <tt>getelementptr</tt> instructions
|
||
|
|
and loop induction variables than other alias analyses have.</p>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<!-- ======================================================================= -->
|
||
|
|
<h3>
|
||
|
|
<a name="aliasanalysis-xforms">Alias analysis driven transformations</a>
|
||
|
|
</h3>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
LLVM includes several alias-analysis driven transformations which can be used
|
||
|
|
with any of the implementations above.
|
||
|
|
|
||
|
|
<!-- _______________________________________________________________________ -->
|
||
|
|
<h4>
|
||
|
|
<a name="adce">The <tt>-adce</tt> pass</a>
|
||
|
|
</h4>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
|
||
|
|
<p>The <tt>-adce</tt> pass, which implements Aggressive Dead Code Elimination
|
||
|
|
uses the <tt>AliasAnalysis</tt> interface to delete calls to functions that do
|
||
|
|
not have side-effects and are not used.</p>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
|
||
|
|
<!-- _______________________________________________________________________ -->
|
||
|
|
<h4>
|
||
|
|
<a name="licm">The <tt>-licm</tt> pass</a>
|
||
|
|
</h4>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
|
||
|
|
<p>The <tt>-licm</tt> pass implements various Loop Invariant Code Motion related
|
||
|
|
transformations. It uses the <tt>AliasAnalysis</tt> interface for several
|
||
|
|
different transformations:</p>
|
||
|
|
|
||
|
|
<ul>
|
||
|
|
<li>It uses mod/ref information to hoist or sink load instructions out of loops
|
||
|
|
if there are no instructions in the loop that modifies the memory loaded.</li>
|
||
|
|
|
||
|
|
<li>It uses mod/ref information to hoist function calls out of loops that do not
|
||
|
|
write to memory and are loop-invariant.</li>
|
||
|
|
|
||
|
|
<li>If uses alias information to promote memory objects that are loaded and
|
||
|
|
stored to in loops to live in a register instead. It can do this if there are
|
||
|
|
no may aliases to the loaded/stored memory location.</li>
|
||
|
|
</ul>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<!-- _______________________________________________________________________ -->
|
||
|
|
<h4>
|
||
|
|
<a name="argpromotion">The <tt>-argpromotion</tt> pass</a>
|
||
|
|
</h4>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
<p>
|
||
|
|
The <tt>-argpromotion</tt> pass promotes by-reference arguments to be passed in
|
||
|
|
by-value instead. In particular, if pointer arguments are only loaded from it
|
||
|
|
passes in the value loaded instead of the address to the function. This pass
|
||
|
|
uses alias information to make sure that the value loaded from the argument
|
||
|
|
pointer is not modified between the entry of the function and any load of the
|
||
|
|
pointer.</p>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<!-- _______________________________________________________________________ -->
|
||
|
|
<h4>
|
||
|
|
<a name="gvn">The <tt>-gvn</tt>, <tt>-memcpyopt</tt>, and <tt>-dse</tt>
|
||
|
|
passes</a>
|
||
|
|
</h4>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
|
||
|
|
<p>These passes use AliasAnalysis information to reason about loads and stores.
|
||
|
|
</p>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<!-- ======================================================================= -->
|
||
|
|
<h3>
|
||
|
|
<a name="aliasanalysis-debug">Clients for debugging and evaluation of
|
||
|
|
implementations</a>
|
||
|
|
</h3>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
|
||
|
|
<p>These passes are useful for evaluating the various alias analysis
|
||
|
|
implementations. You can use them with commands like '<tt>opt -ds-aa
|
||
|
|
-aa-eval foo.bc -disable-output -stats</tt>'.</p>
|
||
|
|
|
||
|
|
<!-- _______________________________________________________________________ -->
|
||
|
|
<h4>
|
||
|
|
<a name="print-alias-sets">The <tt>-print-alias-sets</tt> pass</a>
|
||
|
|
</h4>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
|
||
|
|
<p>The <tt>-print-alias-sets</tt> pass is exposed as part of the
|
||
|
|
<tt>opt</tt> tool to print out the Alias Sets formed by the <a
|
||
|
|
href="#ast"><tt>AliasSetTracker</tt></a> class. This is useful if you're using
|
||
|
|
the <tt>AliasSetTracker</tt> class. To use it, use something like:</p>
|
||
|
|
|
||
|
|
<div class="doc_code">
|
||
|
|
<pre>
|
||
|
|
% opt -ds-aa -print-alias-sets -disable-output
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
|
||
|
|
<!-- _______________________________________________________________________ -->
|
||
|
|
<h4>
|
||
|
|
<a name="count-aa">The <tt>-count-aa</tt> pass</a>
|
||
|
|
</h4>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
|
||
|
|
<p>The <tt>-count-aa</tt> pass is useful to see how many queries a particular
|
||
|
|
pass is making and what responses are returned by the alias analysis. As an
|
||
|
|
example,</p>
|
||
|
|
|
||
|
|
<div class="doc_code">
|
||
|
|
<pre>
|
||
|
|
% opt -basicaa -count-aa -ds-aa -count-aa -licm
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>will print out how many queries (and what responses are returned) by the
|
||
|
|
<tt>-licm</tt> pass (of the <tt>-ds-aa</tt> pass) and how many queries are made
|
||
|
|
of the <tt>-basicaa</tt> pass by the <tt>-ds-aa</tt> pass. This can be useful
|
||
|
|
when debugging a transformation or an alias analysis implementation.</p>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<!-- _______________________________________________________________________ -->
|
||
|
|
<h4>
|
||
|
|
<a name="aa-eval">The <tt>-aa-eval</tt> pass</a>
|
||
|
|
</h4>
|
||
|
|
|
||
|
|
<div>
|
||
|
|
|
||
|
|
<p>The <tt>-aa-eval</tt> pass simply iterates through all pairs of pointers in a
|
||
|
|
function and asks an alias analysis whether or not the pointers alias. This
|
||
|
|
gives an indication of the precision of the alias analysis. Statistics are
|
||
|
|
printed indicating the percent of no/may/must aliases found (a more precise
|
||
|
|
algorithm will have a lower number of may aliases).</p>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<!-- *********************************************************************** -->
|
||
|
|
<h2>
|
||
|
|
<a name="memdep">Memory Dependence Analysis</a>
|
||
|
|
</h2>
|
||
|
|
<!-- *********************************************************************** -->
|
||
|
|
|
||
|
|
<div>
|
||
|
|
|
||
|
|
<p>If you're just looking to be a client of alias analysis information, consider
|
||
|
|
using the Memory Dependence Analysis interface instead. MemDep is a lazy,
|
||
|
|
caching layer on top of alias analysis that is able to answer the question of
|
||
|
|
what preceding memory operations a given instruction depends on, either at an
|
||
|
|
intra- or inter-block level. Because of its laziness and caching
|
||
|
|
policy, using MemDep can be a significant performance win over accessing alias
|
||
|
|
analysis directly.</p>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<!-- *********************************************************************** -->
|
||
|
|
|
||
|
|
<hr>
|
||
|
|
<address>
|
||
|
|
<a href="http://jigsaw.w3.org/css-validator/check/referer"><img
|
||
|
|
src="http://jigsaw.w3.org/css-validator/images/vcss-blue" alt="Valid CSS"></a>
|
||
|
|
<a href="http://validator.w3.org/check/referer"><img
|
||
|
|
src="http://www.w3.org/Icons/valid-html401-blue" alt="Valid HTML 4.01"></a>
|
||
|
|
|
||
|
|
<a href="mailto:sabre@nondot.org">Chris Lattner</a><br>
|
||
|
|
<a href="http://llvm.org/">LLVM Compiler Infrastructure</a><br>
|
||
|
|
Last modified: $Date: 2012-01-30 15:05:41 -0800 (Mon, 30 Jan 2012) $
|
||
|
|
</address>
|
||
|
|
|
||
|
|
</body>
|
||
|
|
</html>
|