"http://www.w3.org/TR/html4/strict.dtd">
<html>
<head>
+ <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<title>LLVM Alias Analysis Infrastructure</title>
<link rel="stylesheet" href="llvm.css" type="text/css">
</head>
<body>
-<div class="doc_title">
+<h1>
LLVM Alias Analysis Infrastructure
-</div>
+</h1>
<ol>
<li><a href="#introduction">Introduction</a></li>
<li><a href="#chaining"><tt>AliasAnalysis</tt> chaining behavior</a></li>
<li><a href="#updating">Updating analysis results for transformations</a></li>
<li><a href="#implefficiency">Efficiency Issues</a></li>
- <li><a href="#passmanager">Pass Manager Issues</a></li>
+ <li><a href="#limitations">Limitations</a></li>
</ul>
</li>
</div>
<!-- *********************************************************************** -->
-<div class="doc_section">
+<h2>
<a name="introduction">Introduction</a>
-</div>
+</h2>
<!-- *********************************************************************** -->
-<div class="doc_text">
+<div>
<p>Alias Analysis (aka Pointer Analysis) is a class of techniques which attempt
to determine whether or not two pointers ever can point to the same object in
</div>
<!-- *********************************************************************** -->
-<div class="doc_section">
+<h2>
<a name="overview"><tt>AliasAnalysis</tt> Class Overview</a>
-</div>
+</h2>
<!-- *********************************************************************** -->
-<div class="doc_text">
+<div>
<p>The <a
href="http://llvm.org/doxygen/classllvm_1_1AliasAnalysis.html"><tt>AliasAnalysis</tt></a>
call. The <tt>AliasAnalysis</tt> interface also exposes some helper methods
which allow you to get mod/ref information for arbitrary instructions.</p>
-</div>
+<p>All <tt>AliasAnalysis</tt> interfaces require that in queries involving
+multiple values, values which are not
+<a href="LangRef.html#constants">constants</a> are all defined within the
+same function.</p>
<!-- ======================================================================= -->
-<div class="doc_subsection">
+<h3>
<a name="pointers">Representation of Pointers</a>
-</div>
+</h3>
-<div class="doc_text">
+<div>
<p>Most importantly, the <tt>AliasAnalysis</tt> class provides several methods
which are used to query whether or not two memory objects alias, whether
</div>
<!-- ======================================================================= -->
-<div class="doc_subsection">
+<h3>
<a name="alias">The <tt>alias</tt> method</a>
-</div>
+</h3>
-<div class="doc_text">
-The <tt>alias</tt> method is the primary interface used to determine whether or
-not two memory objects alias each other. It takes two memory objects as input
-and returns MustAlias, MayAlias, or NoAlias as appropriate.
-</div>
+<div>
+<p>The <tt>alias</tt> method is the primary interface used to determine whether
+or not two memory objects alias each other. It takes two memory objects as
+input and returns MustAlias, PartialAlias, MayAlias, or NoAlias as
+appropriate.</p>
+
+<p>Like all <tt>AliasAnalysis</tt> interfaces, the <tt>alias</tt> method requires
+that either the two pointer values be defined within the same function, or at
+least one of the values is a <a href="LangRef.html#constants">constant</a>.</p>
<!-- _______________________________________________________________________ -->
-<div class="doc_subsubsection">
+<h4>
<a name="MustMayNo">Must, May, and No Alias Responses</a>
-</div>
+</h4>
-<div class="doc_text">
+<div>
<p>The NoAlias response may be used when there is never an immediate dependence
between any memory reference <i>based</i> on one pointer and any memory
reference <i>based</i> the other. The most obvious example is when the two
and reallocation.</p>
<p>As an exception to this is with the
-<a href="LangRef.html#noalias"><tt>noalias</tt></a> keyword. AliasAnalysis
-implementations may choose to ignore the "irrelevant" dependencies, provided
-their clients do not need to be aware of these dependencies for correctness.</p>
+<a href="LangRef.html#noalias"><tt>noalias</tt></a> keyword; the "irrelevant"
+dependencies are ignored.</p>
<p>The MayAlias response is used whenever the two pointers might refer to the
-same object. If the two memory objects overlap, but do not start at the same
-location, return MayAlias.</p>
+same object.</p>
+
+<p>The PartialAlias response is used when the two memory objects are known
+to be overlapping in some way, but do not start at the same address.</p>
<p>The MustAlias response may only be returned if the two memory objects are
guaranteed to always start at exactly the same location. A MustAlias response
</div>
+</div>
+
<!-- ======================================================================= -->
-<div class="doc_subsection">
+<h3>
<a name="ModRefInfo">The <tt>getModRefInfo</tt> methods</a>
-</div>
+</h3>
-<div class="doc_text">
+<div>
<p>The <tt>getModRefInfo</tt> methods return information about whether the
execution of an instruction can read or modify a memory location. Mod/Ref
<p>The <tt>AliasAnalysis</tt> class also provides a <tt>getModRefInfo</tt>
method for testing dependencies between function calls. This method takes two
-call sites (CS1 & CS2), returns NoModRef if the two calls refer to disjoint
-memory locations, Ref if CS1 reads memory written by CS2, Mod if CS1 writes to
-memory read or written by CS2, or ModRef if CS1 might read or write memory
-accessed by CS2. Note that this relation is not commutative.</p>
+call sites (CS1 & CS2), returns NoModRef if neither call writes to memory
+read or written by the other, Ref if CS1 reads memory written by CS2, Mod if CS1
+writes to memory read or written by CS2, or ModRef if CS1 might read or write
+memory written to by CS2. Note that this relation is not commutative.</p>
</div>
<!-- ======================================================================= -->
-<div class="doc_subsection">
+<h3>
<a name="OtherItfs">Other useful <tt>AliasAnalysis</tt> methods</a>
-</div>
+</h3>
-<div class="doc_text">
+<div>
<p>
Several other tidbits of information are often collected by various alias
analysis implementations and can be put to good use by various clients.
</p>
-</div>
-
<!-- _______________________________________________________________________ -->
-<div class="doc_subsubsection">
+<h4>
The <tt>pointsToConstantMemory</tt> method
-</div>
+</h4>
-<div class="doc_text">
+<div>
<p>The <tt>pointsToConstantMemory</tt> method returns true if and only if the
analysis can prove that the pointer only points to unchanging memory locations
</div>
<!-- _______________________________________________________________________ -->
-<div class="doc_subsubsection">
+<h4>
<a name="simplemodref">The <tt>doesNotAccessMemory</tt> and
<tt>onlyReadsMemory</tt> methods</a>
-</div>
+</h4>
-<div class="doc_text">
+<div>
<p>These methods are used to provide very simple mod/ref information for
function calls. The <tt>doesNotAccessMemory</tt> method returns true for a
</div>
+</div>
+
+</div>
+
<!-- *********************************************************************** -->
-<div class="doc_section">
+<h2>
<a name="writingnew">Writing a new <tt>AliasAnalysis</tt> Implementation</a>
-</div>
+</h2>
<!-- *********************************************************************** -->
-<div class="doc_text">
+<div>
<p>Writing a new alias analysis implementation for LLVM is quite
straight-forward. There are already several implementations that you can use
For a examples, take a look at the <a href="#impls">various alias analysis
implementations</a> included with LLVM.</p>
-</div>
-
<!-- ======================================================================= -->
-<div class="doc_subsection">
+<h3>
<a name="passsubclasses">Different Pass styles</a>
-</div>
+</h3>
-<div class="doc_text">
+<div>
<p>The first step to determining what type of <a
href="WritingAnLLVMPass.html">LLVM pass</a> you need to use for your Alias
</div>
<!-- ======================================================================= -->
-<div class="doc_subsection">
+<h3>
<a name="requiredcalls">Required initialization calls</a>
-</div>
+</h3>
-<div class="doc_text">
+<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
</div>
<!-- ======================================================================= -->
-<div class="doc_subsection">
+<h3>
<a name="interfaces">Interfaces which may be specified</a>
-</div>
+</h3>
-<div class="doc_text">
+<div>
<p>All of the <a
href="/doxygen/classllvm_1_1AliasAnalysis.html"><tt>AliasAnalysis</tt></a>
<!-- ======================================================================= -->
-<div class="doc_subsection">
+<h3>
<a name="chaining"><tt>AliasAnalysis</tt> chaining behavior</a>
-</div>
+</h3>
-<div class="doc_text">
+<div>
-<p>With only two special exceptions (the <tt><a
-href="#basic-aa">basicaa</a></tt> and <a href="#no-aa"><tt>no-aa</tt></a>
-passes) every alias analysis pass chains to another alias analysis
+<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
<!-- ======================================================================= -->
-<div class="doc_subsection">
+<h3>
<a name="updating">Updating analysis results for transformations</a>
-</div>
+</h3>
-<div class="doc_text">
+<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
</p>
<p>
-The <tt>AliasAnalysis</tt> interface exposes two methods which are used to
+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>
-</div>
<!-- _______________________________________________________________________ -->
-<div class="doc_subsubsection">The <tt>deleteValue</tt> method</div>
+<h4>The <tt>deleteValue</tt> method</h4>
-<div class="doc_text">
+<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
</div>
<!-- _______________________________________________________________________ -->
-<div class="doc_subsubsection">The <tt>copyValue</tt> method</div>
+<h4>The <tt>copyValue</tt> method</h4>
-<div class="doc_text">
+<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
</div>
<!-- _______________________________________________________________________ -->
-<div class="doc_subsubsection">The <tt>replaceWithNewValue</tt> method</div>
+<h4>The <tt>replaceWithNewValue</tt> method</h4>
-<div class="doc_text">
+<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>
+
<!-- ======================================================================= -->
-<div class="doc_subsection">
+<h3>
<a name="implefficiency">Efficiency Issues</a>
-</div>
+</h3>
-<div class="doc_text">
+<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
</div>
<!-- ======================================================================= -->
-<div class="doc_subsection">
- <a name="passmanager">Pass Manager Issues</a>
-</div>
+<h3>
+ <a name="limitations">Limitations</a>
+</h3>
-<div class="doc_text">
+<div>
-<p>PassManager support for alternative AliasAnalysis implementation
-has some issues.</p>
+<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
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.</tt>
+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
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>
<!-- *********************************************************************** -->
-<div class="doc_section">
+<h2>
<a name="using">Using alias analysis results</a>
-</div>
+</h2>
<!-- *********************************************************************** -->
-<div class="doc_text">
+<div>
<p>There are several different ways to use alias analysis results. In order of
preference, these are...</p>
-</div>
-
<!-- ======================================================================= -->
-<div class="doc_subsection">
+<h3>
<a name="memdep">Using the <tt>MemoryDependenceAnalysis</tt> Pass</a>
-</div>
+</h3>
-<div class="doc_text">
+<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
</div>
<!-- ======================================================================= -->
-<div class="doc_subsection">
+<h3>
<a name="ast">Using the <tt>AliasSetTracker</tt> class</a>
-</div>
+</h3>
-<div class="doc_text">
+<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
duration of the loop nest. Both of these transformations only apply if the
pointer argument is loop-invariant.</p>
-</div>
-
<!-- _______________________________________________________________________ -->
-<div class="doc_subsubsection">
+<h4>
The AliasSetTracker implementation
-</div>
+</h4>
-<div class="doc_text">
+<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
</div>
+</div>
+
<!-- ======================================================================= -->
-<div class="doc_subsection">
+<h3>
<a name="direct">Using the <tt>AliasAnalysis</tt> interface directly</a>
-</div>
+</h3>
-<div class="doc_text">
+<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
</div>
+</div>
+
<!-- *********************************************************************** -->
-<div class="doc_section">
+<h2>
<a name="exist">Existing alias analysis implementations and clients</a>
-</div>
+</h2>
<!-- *********************************************************************** -->
-<div class="doc_text">
+<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
be aware of the <a href="#aliasanalysis-debug">the clients</a> that are useful
for monitoring and evaluating different implementations.</p>
-</div>
-
<!-- ======================================================================= -->
-<div class="doc_subsection">
+<h3>
<a name="impls">Available <tt>AliasAnalysis</tt> implementations</a>
-</div>
+</h3>
-<div class="doc_text">
+<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> and
-<a href="#basic-aa"><tt>-basicaa</tt></a> implementations, all of these <a
-href="#chaining">chain</a> to other alias analysis implementations.</p>
-
-</div>
+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>
<!-- _______________________________________________________________________ -->
-<div class="doc_subsubsection">
+<h4>
<a name="no-aa">The <tt>-no-aa</tt> pass</a>
-</div>
+</h4>
-<div class="doc_text">
+<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
</div>
<!-- _______________________________________________________________________ -->
-<div class="doc_subsubsection">
+<h4>
<a name="basic-aa">The <tt>-basicaa</tt> pass</a>
-</div>
+</h4>
-<div class="doc_text">
+<div>
-<p>The <tt>-basicaa</tt> pass is the default LLVM alias analysis. It is an
-aggressive local analysis that "knows" many important facts:</p>
+<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
</div>
<!-- _______________________________________________________________________ -->
-<div class="doc_subsubsection">
+<h4>
<a name="globalsmodref">The <tt>-globalsmodref-aa</tt> pass</a>
-</div>
+</h4>
-<div class="doc_text">
+<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
</div>
<!-- _______________________________________________________________________ -->
-<div class="doc_subsubsection">
+<h4>
<a name="steens-aa">The <tt>-steens-aa</tt> pass</a>
-</div>
+</h4>
-<div class="doc_text">
+<div>
<p>The <tt>-steens-aa</tt> pass implements a variation on the well-known
"Steensgaard's algorithm" for interprocedural alias analysis. Steensgaard's
</div>
<!-- _______________________________________________________________________ -->
-<div class="doc_subsubsection">
+<h4>
<a name="ds-aa">The <tt>-ds-aa</tt> pass</a>
-</div>
+</h4>
-<div class="doc_text">
+<div>
<p>The <tt>-ds-aa</tt> pass implements the full Data Structure Analysis
algorithm. Data Structure Analysis is a modular unification-based,
</div>
<!-- _______________________________________________________________________ -->
-<div class="doc_subsubsection">
+<h4>
<a name="scev-aa">The <tt>-scev-aa</tt> pass</a>
-</div>
+</h4>
-<div class="doc_text">
+<div>
<p>The <tt>-scev-aa</tt> pass implements AliasAnalysis queries by
translating them into ScalarEvolution queries. This gives it a
</div>
+</div>
+
<!-- ======================================================================= -->
-<div class="doc_subsection">
+<h3>
<a name="aliasanalysis-xforms">Alias analysis driven transformations</a>
-</div>
+</h3>
-<div class="doc_text">
+<div>
LLVM includes several alias-analysis driven transformations which can be used
with any of the implementations above.
-</div>
<!-- _______________________________________________________________________ -->
-<div class="doc_subsubsection">
+<h4>
<a name="adce">The <tt>-adce</tt> pass</a>
-</div>
+</h4>
-<div class="doc_text">
+<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
<!-- _______________________________________________________________________ -->
-<div class="doc_subsubsection">
+<h4>
<a name="licm">The <tt>-licm</tt> pass</a>
-</div>
+</h4>
-<div class="doc_text">
+<div>
<p>The <tt>-licm</tt> pass implements various Loop Invariant Code Motion related
transformations. It uses the <tt>AliasAnalysis</tt> interface for several
</div>
<!-- _______________________________________________________________________ -->
-<div class="doc_subsubsection">
+<h4>
<a name="argpromotion">The <tt>-argpromotion</tt> pass</a>
-</div>
+</h4>
-<div class="doc_text">
+<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
</div>
<!-- _______________________________________________________________________ -->
-<div class="doc_subsubsection">
+<h4>
<a name="gvn">The <tt>-gvn</tt>, <tt>-memcpyopt</tt>, and <tt>-dse</tt>
passes</a>
-</div>
+</h4>
-<div class="doc_text">
+<div>
<p>These passes use AliasAnalysis information to reason about loads and stores.
</p>
</div>
+</div>
+
<!-- ======================================================================= -->
-<div class="doc_subsection">
+<h3>
<a name="aliasanalysis-debug">Clients for debugging and evaluation of
implementations</a>
-</div>
+</h3>
-<div class="doc_text">
+<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>
-</div>
-
<!-- _______________________________________________________________________ -->
-<div class="doc_subsubsection">
+<h4>
<a name="print-alias-sets">The <tt>-print-alias-sets</tt> pass</a>
-</div>
+</h4>
-<div class="doc_text">
+<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
<!-- _______________________________________________________________________ -->
-<div class="doc_subsubsection">
+<h4>
<a name="count-aa">The <tt>-count-aa</tt> pass</a>
-</div>
+</h4>
-<div class="doc_text">
+<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
</div>
<!-- _______________________________________________________________________ -->
-<div class="doc_subsubsection">
+<h4>
<a name="aa-eval">The <tt>-aa-eval</tt> pass</a>
-</div>
+</h4>
-<div class="doc_text">
+<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
</div>
+</div>
+
+</div>
+
<!-- *********************************************************************** -->
-<div class="doc_section">
+<h2>
<a name="memdep">Memory Dependence Analysis</a>
-</div>
+</h2>
<!-- *********************************************************************** -->
-<div class="doc_text">
+<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,
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>
+ <a href="http://llvm.org/">LLVM Compiler Infrastructure</a><br>
Last modified: $Date$
</address>