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Misha Brukmana97e6cb2004-07-01 15:33:24 +00006 <title>LLVM Alias Analysis Infrastructure</title>
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Chris Lattner9f648752003-03-04 19:37:49 +000010
NAKAMURA Takumi05d02652011-04-18 23:59:50 +000011<h1>
Misha Brukmana97e6cb2004-07-01 15:33:24 +000012 LLVM Alias Analysis Infrastructure
NAKAMURA Takumi05d02652011-04-18 23:59:50 +000013</h1>
Chris Lattner9f648752003-03-04 19:37:49 +000014
15<ol>
Misha Brukmanb2154252003-10-23 02:29:42 +000016 <li><a href="#introduction">Introduction</a></li>
Chris Lattner9f648752003-03-04 19:37:49 +000017
Chris Lattnerccc80652004-05-23 21:04:01 +000018 <li><a href="#overview"><tt>AliasAnalysis</tt> Class Overview</a>
Chris Lattner9f648752003-03-04 19:37:49 +000019 <ul>
Misha Brukmanb2154252003-10-23 02:29:42 +000020 <li><a href="#pointers">Representation of Pointers</a></li>
Chris Lattnerccc80652004-05-23 21:04:01 +000021 <li><a href="#alias">The <tt>alias</tt> method</a></li>
Misha Brukmanb2154252003-10-23 02:29:42 +000022 <li><a href="#ModRefInfo">The <tt>getModRefInfo</tt> methods</a></li>
Chris Lattnerccc80652004-05-23 21:04:01 +000023 <li><a href="#OtherItfs">Other useful <tt>AliasAnalysis</tt> methods</a></li>
24 </ul>
25 </li>
Chris Lattner9f648752003-03-04 19:37:49 +000026
Chris Lattnerccc80652004-05-23 21:04:01 +000027 <li><a href="#writingnew">Writing a new <tt>AliasAnalysis</tt> Implementation</a>
Chris Lattner9f648752003-03-04 19:37:49 +000028 <ul>
Misha Brukmanb2154252003-10-23 02:29:42 +000029 <li><a href="#passsubclasses">Different Pass styles</a></li>
30 <li><a href="#requiredcalls">Required initialization calls</a></li>
31 <li><a href="#interfaces">Interfaces which may be specified</a></li>
Chris Lattnerccc80652004-05-23 21:04:01 +000032 <li><a href="#chaining"><tt>AliasAnalysis</tt> chaining behavior</a></li>
33 <li><a href="#updating">Updating analysis results for transformations</a></li>
Misha Brukmanb2154252003-10-23 02:29:42 +000034 <li><a href="#implefficiency">Efficiency Issues</a></li>
Dan Gohman01e59882010-12-15 23:09:41 +000035 <li><a href="#limitations">Limitations</a></li>
Chris Lattnerccc80652004-05-23 21:04:01 +000036 </ul>
37 </li>
Chris Lattner9f648752003-03-04 19:37:49 +000038
Chris Lattnerccc80652004-05-23 21:04:01 +000039 <li><a href="#using">Using alias analysis results</a>
Chris Lattner9f648752003-03-04 19:37:49 +000040 <ul>
Chris Lattner4f4365e2009-04-25 21:11:37 +000041 <li><a href="#memdep">Using the <tt>MemoryDependenceAnalysis</tt> Pass</a></li>
Misha Brukmanb2154252003-10-23 02:29:42 +000042 <li><a href="#ast">Using the <tt>AliasSetTracker</tt> class</a></li>
Chris Lattnerccc80652004-05-23 21:04:01 +000043 <li><a href="#direct">Using the <tt>AliasAnalysis</tt> interface directly</a></li>
44 </ul>
45 </li>
Misha Brukman3896be22003-10-24 18:06:11 +000046
Chris Lattnerccc80652004-05-23 21:04:01 +000047 <li><a href="#exist">Existing alias analysis implementations and clients</a>
Chris Lattner9f648752003-03-04 19:37:49 +000048 <ul>
Chris Lattnerccc80652004-05-23 21:04:01 +000049 <li><a href="#impls">Available <tt>AliasAnalysis</tt> implementations</a></li>
50 <li><a href="#aliasanalysis-xforms">Alias analysis driven transformations</a></li>
Misha Brukmana97e6cb2004-07-01 15:33:24 +000051 <li><a href="#aliasanalysis-debug">Clients for debugging and evaluation of
52 implementations</a></li>
Chris Lattnerccc80652004-05-23 21:04:01 +000053 </ul>
54 </li>
Owen Andersond8b47282007-10-02 00:44:20 +000055 <li><a href="#memdep">Memory Dependence Analysis</a></li>
Misha Brukmanb2154252003-10-23 02:29:42 +000056</ol>
Chris Lattner9f648752003-03-04 19:37:49 +000057
Chris Lattnerccc80652004-05-23 21:04:01 +000058<div class="doc_author">
59 <p>Written by <a href="mailto:sabre@nondot.org">Chris Lattner</a></p>
Misha Brukman3896be22003-10-24 18:06:11 +000060</div>
Chris Lattner9f648752003-03-04 19:37:49 +000061
Chris Lattner9f648752003-03-04 19:37:49 +000062<!-- *********************************************************************** -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +000063<h2>
Misha Brukmancd11e452003-10-22 23:27:16 +000064 <a name="introduction">Introduction</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +000065</h2>
Chris Lattner9f648752003-03-04 19:37:49 +000066<!-- *********************************************************************** -->
67
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +000068<div>
Misha Brukman1f254d52003-11-21 22:30:25 +000069
Chris Lattnerccc80652004-05-23 21:04:01 +000070<p>Alias Analysis (aka Pointer Analysis) is a class of techniques which attempt
71to determine whether or not two pointers ever can point to the same object in
72memory. There are many different algorithms for alias analysis and many
73different ways of classifying them: flow-sensitive vs flow-insensitive,
74context-sensitive vs context-insensitive, field-sensitive vs field-insensitive,
75unification-based vs subset-based, etc. Traditionally, alias analyses respond
Duncan Sands8036ca42007-03-30 12:22:09 +000076to a query with a <a href="#MustMayNo">Must, May, or No</a> alias response,
Chris Lattnerccc80652004-05-23 21:04:01 +000077indicating that two pointers always point to the same object, might point to the
78same object, or are known to never point to the same object.</p>
Misha Brukman1f254d52003-11-21 22:30:25 +000079
Chris Lattnerccc80652004-05-23 21:04:01 +000080<p>The LLVM <a
Reid Spencer05fe4b02006-03-14 05:39:39 +000081href="http://llvm.org/doxygen/classllvm_1_1AliasAnalysis.html"><tt>AliasAnalysis</tt></a>
Chris Lattnerccc80652004-05-23 21:04:01 +000082class is the primary interface used by clients and implementations of alias
83analyses in the LLVM system. This class is the common interface between clients
84of alias analysis information and the implementations providing it, and is
85designed to support a wide range of implementations and clients (but currently
86all clients are assumed to be flow-insensitive). In addition to simple alias
87analysis information, this class exposes Mod/Ref information from those
88implementations which can provide it, allowing for powerful analyses and
89transformations to work well together.</p>
Misha Brukman1f254d52003-11-21 22:30:25 +000090
91<p>This document contains information necessary to successfully implement this
Chris Lattner9f648752003-03-04 19:37:49 +000092interface, use it, and to test both sides. It also explains some of the finer
93points about what exactly results mean. If you feel that something is unclear
Misha Brukmancd11e452003-10-22 23:27:16 +000094or should be added, please <a href="mailto:sabre@nondot.org">let me
Misha Brukman1f254d52003-11-21 22:30:25 +000095know</a>.</p>
96
Misha Brukmancd11e452003-10-22 23:27:16 +000097</div>
Chris Lattner9f648752003-03-04 19:37:49 +000098
99<!-- *********************************************************************** -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000100<h2>
Chris Lattnerccc80652004-05-23 21:04:01 +0000101 <a name="overview"><tt>AliasAnalysis</tt> Class Overview</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000102</h2>
Chris Lattner9f648752003-03-04 19:37:49 +0000103<!-- *********************************************************************** -->
104
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000105<div>
Misha Brukman1f254d52003-11-21 22:30:25 +0000106
Chris Lattnerccc80652004-05-23 21:04:01 +0000107<p>The <a
Reid Spencer05fe4b02006-03-14 05:39:39 +0000108href="http://llvm.org/doxygen/classllvm_1_1AliasAnalysis.html"><tt>AliasAnalysis</tt></a>
Chris Lattnerccc80652004-05-23 21:04:01 +0000109class defines the interface that the various alias analysis implementations
110should support. This class exports two important enums: <tt>AliasResult</tt>
111and <tt>ModRefResult</tt> which represent the result of an alias query or a
112mod/ref query, respectively.</p>
Misha Brukman1f254d52003-11-21 22:30:25 +0000113
Chris Lattnerccc80652004-05-23 21:04:01 +0000114<p>The <tt>AliasAnalysis</tt> interface exposes information about memory,
115represented in several different ways. In particular, memory objects are
116represented as a starting address and size, and function calls are represented
117as the actual <tt>call</tt> or <tt>invoke</tt> instructions that performs the
118call. The <tt>AliasAnalysis</tt> interface also exposes some helper methods
119which allow you to get mod/ref information for arbitrary instructions.</p>
Misha Brukman1f254d52003-11-21 22:30:25 +0000120
Dan Gohman9e86f432010-07-07 14:27:09 +0000121<p>All <tt>AliasAnalysis</tt> interfaces require that in queries involving
122multiple values, values which are not
123<a href="LangRef.html#constants">constants</a> are all defined within the
124same function.</p>
125
Chris Lattner9f648752003-03-04 19:37:49 +0000126<!-- ======================================================================= -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000127<h3>
Misha Brukmancd11e452003-10-22 23:27:16 +0000128 <a name="pointers">Representation of Pointers</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000129</h3>
Chris Lattner9f648752003-03-04 19:37:49 +0000130
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000131<div>
Misha Brukman3896be22003-10-24 18:06:11 +0000132
Chris Lattnerccc80652004-05-23 21:04:01 +0000133<p>Most importantly, the <tt>AliasAnalysis</tt> class provides several methods
134which are used to query whether or not two memory objects alias, whether
135function calls can modify or read a memory object, etc. For all of these
136queries, memory objects are represented as a pair of their starting address (a
137symbolic LLVM <tt>Value*</tt>) and a static size.</p>
Misha Brukman3896be22003-10-24 18:06:11 +0000138
139<p>Representing memory objects as a starting address and a size is critically
Chris Lattnerccc80652004-05-23 21:04:01 +0000140important for correct Alias Analyses. For example, consider this (silly, but
141possible) C code:</p>
Misha Brukman3896be22003-10-24 18:06:11 +0000142
Misha Brukman294611a2004-07-28 22:18:33 +0000143<div class="doc_code">
Chris Lattner9f648752003-03-04 19:37:49 +0000144<pre>
Misha Brukman294611a2004-07-28 22:18:33 +0000145int i;
146char C[2];
147char A[10];
148/* ... */
149for (i = 0; i != 10; ++i) {
150 C[0] = A[i]; /* One byte store */
151 C[1] = A[9-i]; /* One byte store */
152}
Chris Lattner9f648752003-03-04 19:37:49 +0000153</pre>
Misha Brukman294611a2004-07-28 22:18:33 +0000154</div>
Misha Brukman3896be22003-10-24 18:06:11 +0000155
156<p>In this case, the <tt>basicaa</tt> pass will disambiguate the stores to
Chris Lattner9f648752003-03-04 19:37:49 +0000157<tt>C[0]</tt> and <tt>C[1]</tt> because they are accesses to two distinct
158locations one byte apart, and the accesses are each one byte. In this case, the
159LICM pass can use store motion to remove the stores from the loop. In
Misha Brukman3896be22003-10-24 18:06:11 +0000160constrast, the following code:</p>
161
Misha Brukman294611a2004-07-28 22:18:33 +0000162<div class="doc_code">
Chris Lattner9f648752003-03-04 19:37:49 +0000163<pre>
Misha Brukman294611a2004-07-28 22:18:33 +0000164int i;
165char C[2];
166char A[10];
167/* ... */
168for (i = 0; i != 10; ++i) {
169 ((short*)C)[0] = A[i]; /* Two byte store! */
170 C[1] = A[9-i]; /* One byte store */
171}
Chris Lattner9f648752003-03-04 19:37:49 +0000172</pre>
Misha Brukman294611a2004-07-28 22:18:33 +0000173</div>
Misha Brukman3896be22003-10-24 18:06:11 +0000174
175<p>In this case, the two stores to C do alias each other, because the access to
176the <tt>&amp;C[0]</tt> element is a two byte access. If size information wasn't
Chris Lattner9f648752003-03-04 19:37:49 +0000177available in the query, even the first case would have to conservatively assume
Misha Brukman3896be22003-10-24 18:06:11 +0000178that the accesses alias.</p>
179
Misha Brukmancd11e452003-10-22 23:27:16 +0000180</div>
Chris Lattner9f648752003-03-04 19:37:49 +0000181
182<!-- ======================================================================= -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000183<h3>
Chris Lattnerccc80652004-05-23 21:04:01 +0000184 <a name="alias">The <tt>alias</tt> method</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000185</h3>
Chris Lattnerccc80652004-05-23 21:04:01 +0000186
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000187<div>
Dan Gohman9e86f432010-07-07 14:27:09 +0000188<p>The <tt>alias</tt> method is the primary interface used to determine whether
189or not two memory objects alias each other. It takes two memory objects as
Dan Gohman4a34cbd2010-12-10 19:38:58 +0000190input and returns MustAlias, PartialAlias, MayAlias, or NoAlias as
191appropriate.</p>
Dan Gohman9e86f432010-07-07 14:27:09 +0000192
193<p>Like all <tt>AliasAnalysis</tt> interfaces, the <tt>alias</tt> method requires
194that either the two pointer values be defined within the same function, or at
195least one of the values is a <a href="LangRef.html#constants">constant</a>.</p>
Chris Lattnerccc80652004-05-23 21:04:01 +0000196
197<!-- _______________________________________________________________________ -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000198<h4>
Misha Brukmancd11e452003-10-22 23:27:16 +0000199 <a name="MustMayNo">Must, May, and No Alias Responses</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000200</h4>
Chris Lattner9f648752003-03-04 19:37:49 +0000201
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000202<div>
Dan Gohman1e109622010-07-02 18:41:32 +0000203<p>The NoAlias response may be used when there is never an immediate dependence
204between any memory reference <i>based</i> on one pointer and any memory
205reference <i>based</i> the other. The most obvious example is when the two
206pointers point to non-overlapping memory ranges. Another is when the two
207pointers are only ever used for reading memory. Another is when the memory is
208freed and reallocated between accesses through one pointer and accesses through
209the other -- in this case, there is a dependence, but it's mediated by the free
210and reallocation.</p>
Misha Brukman3896be22003-10-24 18:06:11 +0000211
Dan Gohmanefca7f92010-07-02 23:46:54 +0000212<p>As an exception to this is with the
Dan Gohman9e86f432010-07-07 14:27:09 +0000213<a href="LangRef.html#noalias"><tt>noalias</tt></a> keyword; the "irrelevant"
214dependencies are ignored.</p>
Dan Gohmanefca7f92010-07-02 23:46:54 +0000215
Nick Lewycky01557ce2008-12-14 21:08:48 +0000216<p>The MayAlias response is used whenever the two pointers might refer to the
Dan Gohman4a34cbd2010-12-10 19:38:58 +0000217same object.</p>
218
219<p>The PartialAlias response is used when the two memory objects are known
220to be overlapping in some way, but do not start at the same address.</p>
Misha Brukman3896be22003-10-24 18:06:11 +0000221
Nick Lewycky01557ce2008-12-14 21:08:48 +0000222<p>The MustAlias response may only be returned if the two memory objects are
223guaranteed to always start at exactly the same location. A MustAlias response
224implies that the pointers compare equal.</p>
Misha Brukman3896be22003-10-24 18:06:11 +0000225
Misha Brukmancd11e452003-10-22 23:27:16 +0000226</div>
Chris Lattner9f648752003-03-04 19:37:49 +0000227
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000228</div>
229
Chris Lattner9f648752003-03-04 19:37:49 +0000230<!-- ======================================================================= -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000231<h3>
Misha Brukmancd11e452003-10-22 23:27:16 +0000232 <a name="ModRefInfo">The <tt>getModRefInfo</tt> methods</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000233</h3>
Chris Lattner9f648752003-03-04 19:37:49 +0000234
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000235<div>
Misha Brukman3896be22003-10-24 18:06:11 +0000236
237<p>The <tt>getModRefInfo</tt> methods return information about whether the
Chris Lattner9f648752003-03-04 19:37:49 +0000238execution of an instruction can read or modify a memory location. Mod/Ref
Chris Lattnerccc80652004-05-23 21:04:01 +0000239information is always conservative: if an instruction <b>might</b> read or write
240a location, ModRef is returned.</p>
241
242<p>The <tt>AliasAnalysis</tt> class also provides a <tt>getModRefInfo</tt>
243method for testing dependencies between function calls. This method takes two
Dan Gohman39429e22010-08-30 23:47:24 +0000244call sites (CS1 &amp; CS2), returns NoModRef if neither call writes to memory
245read or written by the other, Ref if CS1 reads memory written by CS2, Mod if CS1
246writes to memory read or written by CS2, or ModRef if CS1 might read or write
247memory written to by CS2. Note that this relation is not commutative.</p>
Misha Brukman3896be22003-10-24 18:06:11 +0000248
Misha Brukmancd11e452003-10-22 23:27:16 +0000249</div>
Chris Lattner9f648752003-03-04 19:37:49 +0000250
Chris Lattnerccc80652004-05-23 21:04:01 +0000251
252<!-- ======================================================================= -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000253<h3>
Chris Lattnerccc80652004-05-23 21:04:01 +0000254 <a name="OtherItfs">Other useful <tt>AliasAnalysis</tt> methods</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000255</h3>
Chris Lattnerccc80652004-05-23 21:04:01 +0000256
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000257<div>
Chris Lattnerccc80652004-05-23 21:04:01 +0000258
259<p>
260Several other tidbits of information are often collected by various alias
261analysis implementations and can be put to good use by various clients.
262</p>
263
Chris Lattnerccc80652004-05-23 21:04:01 +0000264<!-- _______________________________________________________________________ -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000265<h4>
Chris Lattnerccc80652004-05-23 21:04:01 +0000266 The <tt>pointsToConstantMemory</tt> method
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000267</h4>
Chris Lattnerccc80652004-05-23 21:04:01 +0000268
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000269<div>
Chris Lattnerccc80652004-05-23 21:04:01 +0000270
271<p>The <tt>pointsToConstantMemory</tt> method returns true if and only if the
272analysis can prove that the pointer only points to unchanging memory locations
273(functions, constant global variables, and the null pointer). This information
274can be used to refine mod/ref information: it is impossible for an unchanging
275memory location to be modified.</p>
276
277</div>
278
Chris Lattnerccc80652004-05-23 21:04:01 +0000279<!-- _______________________________________________________________________ -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000280<h4>
Chris Lattnerccc80652004-05-23 21:04:01 +0000281 <a name="simplemodref">The <tt>doesNotAccessMemory</tt> and
282 <tt>onlyReadsMemory</tt> methods</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000283</h4>
Chris Lattnerccc80652004-05-23 21:04:01 +0000284
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000285<div>
Chris Lattnerccc80652004-05-23 21:04:01 +0000286
287<p>These methods are used to provide very simple mod/ref information for
288function calls. The <tt>doesNotAccessMemory</tt> method returns true for a
289function if the analysis can prove that the function never reads or writes to
290memory, or if the function only reads from constant memory. Functions with this
291property are side-effect free and only depend on their input arguments, allowing
292them to be eliminated if they form common subexpressions or be hoisted out of
293loops. Many common functions behave this way (e.g., <tt>sin</tt> and
294<tt>cos</tt>) but many others do not (e.g., <tt>acos</tt>, which modifies the
295<tt>errno</tt> variable).</p>
296
297<p>The <tt>onlyReadsMemory</tt> method returns true for a function if analysis
298can prove that (at most) the function only reads from non-volatile memory.
299Functions with this property are side-effect free, only depending on their input
300arguments and the state of memory when they are called. This property allows
301calls to these functions to be eliminated and moved around, as long as there is
302no store instruction that changes the contents of memory. Note that all
303functions that satisfy the <tt>doesNotAccessMemory</tt> method also satisfies
304<tt>onlyReadsMemory</tt>.</p>
305
306</div>
307
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000308</div>
309
310</div>
311
Chris Lattner9f648752003-03-04 19:37:49 +0000312<!-- *********************************************************************** -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000313<h2>
Chris Lattnerccc80652004-05-23 21:04:01 +0000314 <a name="writingnew">Writing a new <tt>AliasAnalysis</tt> Implementation</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000315</h2>
Chris Lattner9f648752003-03-04 19:37:49 +0000316<!-- *********************************************************************** -->
317
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000318<div>
Misha Brukman3896be22003-10-24 18:06:11 +0000319
320<p>Writing a new alias analysis implementation for LLVM is quite
321straight-forward. There are already several implementations that you can use
322for examples, and the following information should help fill in any details.
Chris Lattnerccc80652004-05-23 21:04:01 +0000323For a examples, take a look at the <a href="#impls">various alias analysis
324implementations</a> included with LLVM.</p>
Misha Brukman3896be22003-10-24 18:06:11 +0000325
Chris Lattner9f648752003-03-04 19:37:49 +0000326<!-- ======================================================================= -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000327<h3>
Misha Brukmancd11e452003-10-22 23:27:16 +0000328 <a name="passsubclasses">Different Pass styles</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000329</h3>
Chris Lattner9f648752003-03-04 19:37:49 +0000330
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000331<div>
Misha Brukman3896be22003-10-24 18:06:11 +0000332
333<p>The first step to determining what type of <a
334href="WritingAnLLVMPass.html">LLVM pass</a> you need to use for your Alias
335Analysis. As is the case with most other analyses and transformations, the
336answer should be fairly obvious from what type of problem you are trying to
337solve:</p>
338
Chris Lattner9f648752003-03-04 19:37:49 +0000339<ol>
Misha Brukmancd11e452003-10-22 23:27:16 +0000340 <li>If you require interprocedural analysis, it should be a
341 <tt>Pass</tt>.</li>
Chris Lattnerccc80652004-05-23 21:04:01 +0000342 <li>If you are a function-local analysis, subclass <tt>FunctionPass</tt>.</li>
Misha Brukmancd11e452003-10-22 23:27:16 +0000343 <li>If you don't need to look at the program at all, subclass
344 <tt>ImmutablePass</tt>.</li>
345</ol>
Misha Brukman3896be22003-10-24 18:06:11 +0000346
347<p>In addition to the pass that you subclass, you should also inherit from the
Misha Brukman700fd492003-05-07 21:47:16 +0000348<tt>AliasAnalysis</tt> interface, of course, and use the
Chris Lattner9f648752003-03-04 19:37:49 +0000349<tt>RegisterAnalysisGroup</tt> template to register as an implementation of
Misha Brukman3896be22003-10-24 18:06:11 +0000350<tt>AliasAnalysis</tt>.</p>
351
Misha Brukmancd11e452003-10-22 23:27:16 +0000352</div>
Chris Lattner9f648752003-03-04 19:37:49 +0000353
354<!-- ======================================================================= -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000355<h3>
Misha Brukmancd11e452003-10-22 23:27:16 +0000356 <a name="requiredcalls">Required initialization calls</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000357</h3>
Chris Lattner9f648752003-03-04 19:37:49 +0000358
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000359<div>
Misha Brukman3896be22003-10-24 18:06:11 +0000360
Chris Lattnerccc80652004-05-23 21:04:01 +0000361<p>Your subclass of <tt>AliasAnalysis</tt> is required to invoke two methods on
362the <tt>AliasAnalysis</tt> base class: <tt>getAnalysisUsage</tt> and
Chris Lattner9f648752003-03-04 19:37:49 +0000363<tt>InitializeAliasAnalysis</tt>. In particular, your implementation of
364<tt>getAnalysisUsage</tt> should explicitly call into the
365<tt>AliasAnalysis::getAnalysisUsage</tt> method in addition to doing any
366declaring any pass dependencies your pass has. Thus you should have something
Misha Brukman3896be22003-10-24 18:06:11 +0000367like this:</p>
368
Misha Brukman294611a2004-07-28 22:18:33 +0000369<div class="doc_code">
Chris Lattner9f648752003-03-04 19:37:49 +0000370<pre>
Misha Brukman294611a2004-07-28 22:18:33 +0000371void getAnalysisUsage(AnalysisUsage &amp;AU) const {
372 AliasAnalysis::getAnalysisUsage(AU);
373 <i>// declare your dependencies here.</i>
374}
Chris Lattner9f648752003-03-04 19:37:49 +0000375</pre>
Misha Brukman294611a2004-07-28 22:18:33 +0000376</div>
Misha Brukman3896be22003-10-24 18:06:11 +0000377
378<p>Additionally, your must invoke the <tt>InitializeAliasAnalysis</tt> method
379from your analysis run method (<tt>run</tt> for a <tt>Pass</tt>,
Chris Lattnerccc80652004-05-23 21:04:01 +0000380<tt>runOnFunction</tt> for a <tt>FunctionPass</tt>, or <tt>InitializePass</tt>
381for an <tt>ImmutablePass</tt>). For example (as part of a <tt>Pass</tt>):</p>
Misha Brukman3896be22003-10-24 18:06:11 +0000382
Misha Brukman294611a2004-07-28 22:18:33 +0000383<div class="doc_code">
Chris Lattner9f648752003-03-04 19:37:49 +0000384<pre>
Misha Brukman294611a2004-07-28 22:18:33 +0000385bool run(Module &amp;M) {
386 InitializeAliasAnalysis(this);
387 <i>// Perform analysis here...</i>
388 return false;
389}
Chris Lattner9f648752003-03-04 19:37:49 +0000390</pre>
Misha Brukman294611a2004-07-28 22:18:33 +0000391</div>
Misha Brukman3896be22003-10-24 18:06:11 +0000392
Misha Brukmancd11e452003-10-22 23:27:16 +0000393</div>
Chris Lattner9f648752003-03-04 19:37:49 +0000394
395<!-- ======================================================================= -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000396<h3>
Misha Brukmancd11e452003-10-22 23:27:16 +0000397 <a name="interfaces">Interfaces which may be specified</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000398</h3>
Chris Lattner9f648752003-03-04 19:37:49 +0000399
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000400<div>
Misha Brukman3896be22003-10-24 18:06:11 +0000401
Chris Lattnerccc80652004-05-23 21:04:01 +0000402<p>All of the <a
403href="/doxygen/classllvm_1_1AliasAnalysis.html"><tt>AliasAnalysis</tt></a>
404virtual methods default to providing <a href="#chaining">chaining</a> to another
405alias analysis implementation, which ends up returning conservatively correct
406information (returning "May" Alias and "Mod/Ref" for alias and mod/ref queries
Misha Brukman3896be22003-10-24 18:06:11 +0000407respectively). Depending on the capabilities of the analysis you are
408implementing, you just override the interfaces you can improve.</p>
409
Misha Brukmancd11e452003-10-22 23:27:16 +0000410</div>
Chris Lattner9f648752003-03-04 19:37:49 +0000411
Chris Lattnerccc80652004-05-23 21:04:01 +0000412
413
Chris Lattner9f648752003-03-04 19:37:49 +0000414<!-- ======================================================================= -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000415<h3>
Chris Lattnerccc80652004-05-23 21:04:01 +0000416 <a name="chaining"><tt>AliasAnalysis</tt> chaining behavior</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000417</h3>
Chris Lattner9f648752003-03-04 19:37:49 +0000418
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000419<div>
Misha Brukman3896be22003-10-24 18:06:11 +0000420
Chris Lattnerccc80652004-05-23 21:04:01 +0000421<p>With only two special exceptions (the <tt><a
422href="#basic-aa">basicaa</a></tt> and <a href="#no-aa"><tt>no-aa</tt></a>
423passes) every alias analysis pass chains to another alias analysis
424implementation (for example, the user can specify "<tt>-basicaa -ds-aa
Chris Lattnera9cf1962010-03-01 19:24:17 +0000425-licm</tt>" to get the maximum benefit from both alias
Chris Lattnerccc80652004-05-23 21:04:01 +0000426analyses). The alias analysis class automatically takes care of most of this
427for methods that you don't override. For methods that you do override, in code
428paths that return a conservative MayAlias or Mod/Ref result, simply return
429whatever the superclass computes. For example:</p>
Misha Brukman3896be22003-10-24 18:06:11 +0000430
Misha Brukman294611a2004-07-28 22:18:33 +0000431<div class="doc_code">
Chris Lattnerccc80652004-05-23 21:04:01 +0000432<pre>
Misha Brukman294611a2004-07-28 22:18:33 +0000433AliasAnalysis::AliasResult alias(const Value *V1, unsigned V1Size,
434 const Value *V2, unsigned V2Size) {
435 if (...)
436 return NoAlias;
437 ...
Chris Lattnerccc80652004-05-23 21:04:01 +0000438
Misha Brukman294611a2004-07-28 22:18:33 +0000439 <i>// Couldn't determine a must or no-alias result.</i>
440 return AliasAnalysis::alias(V1, V1Size, V2, V2Size);
441}
Chris Lattnerccc80652004-05-23 21:04:01 +0000442</pre>
Misha Brukman294611a2004-07-28 22:18:33 +0000443</div>
Chris Lattnerccc80652004-05-23 21:04:01 +0000444
445<p>In addition to analysis queries, you must make sure to unconditionally pass
446LLVM <a href="#updating">update notification</a> methods to the superclass as
447well if you override them, which allows all alias analyses in a change to be
448updated.</p>
449
450</div>
451
452
453<!-- ======================================================================= -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000454<h3>
Chris Lattnerccc80652004-05-23 21:04:01 +0000455 <a name="updating">Updating analysis results for transformations</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000456</h3>
Chris Lattnerccc80652004-05-23 21:04:01 +0000457
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000458<div>
Chris Lattnerccc80652004-05-23 21:04:01 +0000459<p>
460Alias analysis information is initially computed for a static snapshot of the
461program, but clients will use this information to make transformations to the
462code. All but the most trivial forms of alias analysis will need to have their
463analysis results updated to reflect the changes made by these transformations.
464</p>
465
466<p>
Owen Andersonab6acc62011-01-03 21:38:41 +0000467The <tt>AliasAnalysis</tt> interface exposes four methods which are used to
Chris Lattnerccc80652004-05-23 21:04:01 +0000468communicate program changes from the clients to the analysis implementations.
469Various alias analysis implementations should use these methods to ensure that
470their internal data structures are kept up-to-date as the program changes (for
471example, when an instruction is deleted), and clients of alias analysis must be
472sure to call these interfaces appropriately.
473</p>
Chris Lattnerccc80652004-05-23 21:04:01 +0000474
475<!-- _______________________________________________________________________ -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000476<h4>The <tt>deleteValue</tt> method</h4>
Chris Lattnerccc80652004-05-23 21:04:01 +0000477
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000478<div>
Chris Lattnerccc80652004-05-23 21:04:01 +0000479The <tt>deleteValue</tt> method is called by transformations when they remove an
480instruction or any other value from the program (including values that do not
481use pointers). Typically alias analyses keep data structures that have entries
482for each value in the program. When this method is called, they should remove
483any entries for the specified value, if they exist.
484</div>
485
Chris Lattnerccc80652004-05-23 21:04:01 +0000486<!-- _______________________________________________________________________ -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000487<h4>The <tt>copyValue</tt> method</h4>
Chris Lattnerccc80652004-05-23 21:04:01 +0000488
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000489<div>
Chris Lattnerccc80652004-05-23 21:04:01 +0000490The <tt>copyValue</tt> method is used when a new value is introduced into the
491program. There is no way to introduce a value into the program that did not
492exist before (this doesn't make sense for a safe compiler transformation), so
493this is the only way to introduce a new value. This method indicates that the
494new value has exactly the same properties as the value being copied.
495</div>
496
Chris Lattnerccc80652004-05-23 21:04:01 +0000497<!-- _______________________________________________________________________ -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000498<h4>The <tt>replaceWithNewValue</tt> method</h4>
Chris Lattnerccc80652004-05-23 21:04:01 +0000499
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000500<div>
Chris Lattnerccc80652004-05-23 21:04:01 +0000501This method is a simple helper method that is provided to make clients easier to
502use. It is implemented by copying the old analysis information to the new
503value, then deleting the old value. This method cannot be overridden by alias
504analysis implementations.
Misha Brukmancd11e452003-10-22 23:27:16 +0000505</div>
Chris Lattner9f648752003-03-04 19:37:49 +0000506
Owen Andersonab6acc62011-01-03 21:38:41 +0000507<!-- _______________________________________________________________________ -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000508<h4>The <tt>addEscapingUse</tt> method</h4>
Owen Andersonab6acc62011-01-03 21:38:41 +0000509
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000510<div>
Owen Andersonab6acc62011-01-03 21:38:41 +0000511<p>The <tt>addEscapingUse</tt> method is used when the uses of a pointer
512value have changed in ways that may invalidate precomputed analysis information.
513Implementations may either use this callback to provide conservative responses
514for points whose uses have change since analysis time, or may recompute some
515or all of their internal state to continue providing accurate responses.</p>
516
517<p>In general, any new use of a pointer value is considered an escaping use,
518and must be reported through this callback, <em>except</em> for the
519uses below:</p>
520
521<ul>
522 <li>A <tt>bitcast</tt> or <tt>getelementptr</tt> of the pointer</li>
523 <li>A <tt>store</tt> through the pointer (but not a <tt>store</tt>
524 <em>of</em> the pointer)</li>
525 <li>A <tt>load</tt> through the pointer</li>
526</ul>
527</div>
528
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000529</div>
530
Chris Lattner9f648752003-03-04 19:37:49 +0000531<!-- ======================================================================= -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000532<h3>
Misha Brukmancd11e452003-10-22 23:27:16 +0000533 <a name="implefficiency">Efficiency Issues</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000534</h3>
Chris Lattner9f648752003-03-04 19:37:49 +0000535
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000536<div>
Misha Brukman3896be22003-10-24 18:06:11 +0000537
538<p>From the LLVM perspective, the only thing you need to do to provide an
539efficient alias analysis is to make sure that alias analysis <b>queries</b> are
540serviced quickly. The actual calculation of the alias analysis results (the
541"run" method) is only performed once, but many (perhaps duplicate) queries may
542be performed. Because of this, try to move as much computation to the run
543method as possible (within reason).</p>
544
Misha Brukmancd11e452003-10-22 23:27:16 +0000545</div>
Chris Lattner9f648752003-03-04 19:37:49 +0000546
Dan Gohman3f43dc32010-06-24 19:34:03 +0000547<!-- ======================================================================= -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000548<h3>
Dan Gohman49e41c52010-12-15 18:45:20 +0000549 <a name="limitations">Limitations</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000550</h3>
Dan Gohman3f43dc32010-06-24 19:34:03 +0000551
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000552<div>
Dan Gohman3f43dc32010-06-24 19:34:03 +0000553
Dan Gohman49e41c52010-12-15 18:45:20 +0000554<p>The AliasAnalysis infrastructure has several limitations which make
555writing a new <tt>AliasAnalysis</tt> implementation difficult.</p>
Dan Gohman3f43dc32010-06-24 19:34:03 +0000556
557<p>There is no way to override the default alias analysis. It would
558be very useful to be able to do something like "opt -my-aa -O2" and
559have it use -my-aa for all passes which need AliasAnalysis, but there
560is currently no support for that, short of changing the source code
561and recompiling. Similarly, there is also no way of setting a chain
562of analyses as the default.</p>
563
564<p>There is no way for transform passes to declare that they preserve
565<tt>AliasAnalysis</tt> implementations. The <tt>AliasAnalysis</tt>
566interface includes <tt>deleteValue</tt> and <tt>copyValue</tt> methods
567which are intended to allow a pass to keep an AliasAnalysis consistent,
568however there's no way for a pass to declare in its
569<tt>getAnalysisUsage</tt> that it does so. Some passes attempt to use
570<tt>AU.addPreserved&lt;AliasAnalysis&gt;</tt>, however this doesn't
NAKAMURA Takumi4d6deb02011-04-09 09:51:57 +0000571actually have any effect.</p>
Dan Gohman3f43dc32010-06-24 19:34:03 +0000572
573<p><tt>AliasAnalysisCounter</tt> (<tt>-count-aa</tt>) and <tt>AliasDebugger</tt>
574(<tt>-debug-aa</tt>) are implemented as <tt>ModulePass</tt> classes, so if your
575alias analysis uses <tt>FunctionPass</tt>, it won't be able to use
576these utilities. If you try to use them, the pass manager will
577silently route alias analysis queries directly to
578<tt>BasicAliasAnalysis</tt> instead.</p>
579
580<p>Similarly, the <tt>opt -p</tt> option introduces <tt>ModulePass</tt>
581passes between each pass, which prevents the use of <tt>FunctionPass</tt>
582alias analysis passes.</p>
583
Dan Gohman49e41c52010-12-15 18:45:20 +0000584<p>The <tt>AliasAnalysis</tt> API does have functions for notifying
585implementations when values are deleted or copied, however these
586aren't sufficient. There are many other ways that LLVM IR can be
587modified which could be relevant to <tt>AliasAnalysis</tt>
588implementations which can not be expressed.</p>
589
590<p>The <tt>AliasAnalysisDebugger</tt> utility seems to suggest that
591<tt>AliasAnalysis</tt> implementations can expect that they will be
592informed of any relevant <tt>Value</tt> before it appears in an
593alias query. However, popular clients such as <tt>GVN</tt> don't
594support this, and are known to trigger errors when run with the
595<tt>AliasAnalysisDebugger</tt>.</p>
596
597<p>Due to several of the above limitations, the most obvious use for
598the <tt>AliasAnalysisCounter</tt> utility, collecting stats on all
599alias queries in a compilation, doesn't work, even if the
600<tt>AliasAnalysis</tt> implementations don't use <tt>FunctionPass</tt>.
601There's no way to set a default, much less a default sequence,
602and there's no way to preserve it.</p>
603
604<p>The <tt>AliasSetTracker</tt> class (which is used by <tt>LICM</tt>
605makes a non-deterministic number of alias queries. This can cause stats
606collected by <tt>AliasAnalysisCounter</tt> to have fluctuations among
607identical runs, for example. Another consequence is that debugging
608techniques involving pausing execution after a predetermined number
609of queries can be unreliable.</p>
610
611<p>Many alias queries can be reformulated in terms of other alias
612queries. When multiple <tt>AliasAnalysis</tt> queries are chained together,
613it would make sense to start those queries from the beginning of the chain,
614with care taken to avoid infinite looping, however currently an
615implementation which wants to do this can only start such queries
616from itself.</p>
617
Dan Gohman3f43dc32010-06-24 19:34:03 +0000618</div>
619
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000620</div>
621
Chris Lattner9f648752003-03-04 19:37:49 +0000622<!-- *********************************************************************** -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000623<h2>
Chris Lattnerccc80652004-05-23 21:04:01 +0000624 <a name="using">Using alias analysis results</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000625</h2>
Chris Lattner9f648752003-03-04 19:37:49 +0000626<!-- *********************************************************************** -->
627
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000628<div>
Misha Brukman3896be22003-10-24 18:06:11 +0000629
630<p>There are several different ways to use alias analysis results. In order of
631preference, these are...</p>
632
Chris Lattner9f648752003-03-04 19:37:49 +0000633<!-- ======================================================================= -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000634<h3>
Chris Lattner4f4365e2009-04-25 21:11:37 +0000635 <a name="memdep">Using the <tt>MemoryDependenceAnalysis</tt> Pass</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000636</h3>
Chris Lattner9f648752003-03-04 19:37:49 +0000637
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000638<div>
Misha Brukman3896be22003-10-24 18:06:11 +0000639
Chris Lattner4f4365e2009-04-25 21:11:37 +0000640<p>The <tt>memdep</tt> pass uses alias analysis to provide high-level dependence
641information about memory-using instructions. This will tell you which store
642feeds into a load, for example. It uses caching and other techniques to be
643efficient, and is used by Dead Store Elimination, GVN, and memcpy optimizations.
644</p>
Misha Brukman3896be22003-10-24 18:06:11 +0000645
Misha Brukmancd11e452003-10-22 23:27:16 +0000646</div>
Chris Lattner9f648752003-03-04 19:37:49 +0000647
648<!-- ======================================================================= -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000649<h3>
Misha Brukmancd11e452003-10-22 23:27:16 +0000650 <a name="ast">Using the <tt>AliasSetTracker</tt> class</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000651</h3>
Chris Lattner9f648752003-03-04 19:37:49 +0000652
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000653<div>
Misha Brukman3896be22003-10-24 18:06:11 +0000654
655<p>Many transformations need information about alias <b>sets</b> that are active
656in some scope, rather than information about pairwise aliasing. The <tt><a
Misha Brukman294611a2004-07-28 22:18:33 +0000657href="/doxygen/classllvm_1_1AliasSetTracker.html">AliasSetTracker</a></tt> class
658is used to efficiently build these Alias Sets from the pairwise alias analysis
Chris Lattnerccc80652004-05-23 21:04:01 +0000659information provided by the <tt>AliasAnalysis</tt> interface.</p>
Misha Brukman3896be22003-10-24 18:06:11 +0000660
Chris Lattnerccc80652004-05-23 21:04:01 +0000661<p>First you initialize the AliasSetTracker by using the "<tt>add</tt>" methods
662to add information about various potentially aliasing instructions in the scope
663you are interested in. Once all of the alias sets are completed, your pass
664should simply iterate through the constructed alias sets, using the
665<tt>AliasSetTracker</tt> <tt>begin()</tt>/<tt>end()</tt> methods.</p>
Misha Brukman3896be22003-10-24 18:06:11 +0000666
667<p>The <tt>AliasSet</tt>s formed by the <tt>AliasSetTracker</tt> are guaranteed
Chris Lattner539ca702003-12-19 08:43:07 +0000668to be disjoint, calculate mod/ref information and volatility for the set, and
669keep track of whether or not all of the pointers in the set are Must aliases.
670The AliasSetTracker also makes sure that sets are properly folded due to call
Misha Brukman3896be22003-10-24 18:06:11 +0000671instructions, and can provide a list of pointers in each set.</p>
672
673<p>As an example user of this, the <a href="/doxygen/structLICM.html">Loop
Chris Lattnerccc80652004-05-23 21:04:01 +0000674Invariant Code Motion</a> pass uses <tt>AliasSetTracker</tt>s to calculate alias
675sets for each loop nest. If an <tt>AliasSet</tt> in a loop is not modified,
676then all load instructions from that set may be hoisted out of the loop. If any
677alias sets are stored to <b>and</b> are must alias sets, then the stores may be
678sunk to outside of the loop, promoting the memory location to a register for the
679duration of the loop nest. Both of these transformations only apply if the
680pointer argument is loop-invariant.</p>
Misha Brukman3896be22003-10-24 18:06:11 +0000681
Chris Lattnerccc80652004-05-23 21:04:01 +0000682<!-- _______________________________________________________________________ -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000683<h4>
Chris Lattner539ca702003-12-19 08:43:07 +0000684 The AliasSetTracker implementation
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000685</h4>
Chris Lattner539ca702003-12-19 08:43:07 +0000686
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000687<div>
Chris Lattner539ca702003-12-19 08:43:07 +0000688
689<p>The AliasSetTracker class is implemented to be as efficient as possible. It
690uses the union-find algorithm to efficiently merge AliasSets when a pointer is
691inserted into the AliasSetTracker that aliases multiple sets. The primary data
692structure is a hash table mapping pointers to the AliasSet they are in.</p>
693
694<p>The AliasSetTracker class must maintain a list of all of the LLVM Value*'s
695that are in each AliasSet. Since the hash table already has entries for each
696LLVM Value* of interest, the AliasesSets thread the linked list through these
697hash-table nodes to avoid having to allocate memory unnecessarily, and to make
698merging alias sets extremely efficient (the linked list merge is constant time).
699</p>
700
701<p>You shouldn't need to understand these details if you are just a client of
702the AliasSetTracker, but if you look at the code, hopefully this brief
703description will help make sense of why things are designed the way they
704are.</p>
705
706</div>
707
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000708</div>
709
Chris Lattner9f648752003-03-04 19:37:49 +0000710<!-- ======================================================================= -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000711<h3>
Chris Lattnerccc80652004-05-23 21:04:01 +0000712 <a name="direct">Using the <tt>AliasAnalysis</tt> interface directly</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000713</h3>
Chris Lattner9f648752003-03-04 19:37:49 +0000714
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000715<div>
Misha Brukman3896be22003-10-24 18:06:11 +0000716
Chris Lattnerccc80652004-05-23 21:04:01 +0000717<p>If neither of these utility class are what your pass needs, you should use
718the interfaces exposed by the <tt>AliasAnalysis</tt> class directly. Try to use
719the higher-level methods when possible (e.g., use mod/ref information instead of
720the <a href="#alias"><tt>alias</tt></a> method directly if possible) to get the
721best precision and efficiency.</p>
Misha Brukman3896be22003-10-24 18:06:11 +0000722
Misha Brukmancd11e452003-10-22 23:27:16 +0000723</div>
Chris Lattner9f648752003-03-04 19:37:49 +0000724
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000725</div>
726
Chris Lattner9f648752003-03-04 19:37:49 +0000727<!-- *********************************************************************** -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000728<h2>
Chris Lattnerccc80652004-05-23 21:04:01 +0000729 <a name="exist">Existing alias analysis implementations and clients</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000730</h2>
Chris Lattner9f648752003-03-04 19:37:49 +0000731<!-- *********************************************************************** -->
732
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000733<div>
Misha Brukman3896be22003-10-24 18:06:11 +0000734
Chris Lattnerccc80652004-05-23 21:04:01 +0000735<p>If you're going to be working with the LLVM alias analysis infrastructure,
736you should know what clients and implementations of alias analysis are
737available. In particular, if you are implementing an alias analysis, you should
738be aware of the <a href="#aliasanalysis-debug">the clients</a> that are useful
739for monitoring and evaluating different implementations.</p>
Misha Brukman3896be22003-10-24 18:06:11 +0000740
Chris Lattner9f648752003-03-04 19:37:49 +0000741<!-- ======================================================================= -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000742<h3>
Chris Lattnerccc80652004-05-23 21:04:01 +0000743 <a name="impls">Available <tt>AliasAnalysis</tt> implementations</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000744</h3>
Chris Lattnerccc80652004-05-23 21:04:01 +0000745
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000746<div>
Chris Lattnerccc80652004-05-23 21:04:01 +0000747
748<p>This section lists the various implementations of the <tt>AliasAnalysis</tt>
Dan Gohmanb0b0da72011-05-24 22:01:32 +0000749interface. With the exception of the <a href="#no-aa"><tt>-no-aa</tt></a>
750implementation, all of these <a href="#chaining">chain</a> to other alias
751analysis implementations.</p>
Chris Lattnerccc80652004-05-23 21:04:01 +0000752
Chris Lattnerccc80652004-05-23 21:04:01 +0000753<!-- _______________________________________________________________________ -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000754<h4>
Misha Brukmancd11e452003-10-22 23:27:16 +0000755 <a name="no-aa">The <tt>-no-aa</tt> pass</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000756</h4>
Chris Lattner9f648752003-03-04 19:37:49 +0000757
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000758<div>
Misha Brukman3896be22003-10-24 18:06:11 +0000759
Chris Lattnerccc80652004-05-23 21:04:01 +0000760<p>The <tt>-no-aa</tt> pass is just like what it sounds: an alias analysis that
761never returns any useful information. This pass can be useful if you think that
762alias analysis is doing something wrong and are trying to narrow down a
763problem.</p>
764
765</div>
766
Chris Lattnerccc80652004-05-23 21:04:01 +0000767<!-- _______________________________________________________________________ -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000768<h4>
Chris Lattnerccc80652004-05-23 21:04:01 +0000769 <a name="basic-aa">The <tt>-basicaa</tt> pass</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000770</h4>
Chris Lattnerccc80652004-05-23 21:04:01 +0000771
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000772<div>
Chris Lattnerccc80652004-05-23 21:04:01 +0000773
Dan Gohmanc66712f2010-11-15 18:07:16 +0000774<p>The <tt>-basicaa</tt> pass is an aggressive local analysis that "knows"
775many important facts:</p>
Chris Lattnerccc80652004-05-23 21:04:01 +0000776
777<ul>
778<li>Distinct globals, stack allocations, and heap allocations can never
779 alias.</li>
780<li>Globals, stack allocations, and heap allocations never alias the null
781 pointer.</li>
782<li>Different fields of a structure do not alias.</li>
783<li>Indexes into arrays with statically differing subscripts cannot alias.</li>
784<li>Many common standard C library functions <a
785 href="#simplemodref">never access memory or only read memory</a>.</li>
786<li>Pointers that obviously point to constant globals
787 "<tt>pointToConstantMemory</tt>".</li>
788<li>Function calls can not modify or references stack allocations if they never
789 escape from the function that allocates them (a common case for automatic
790 arrays).</li>
791</ul>
792
793</div>
794
Chris Lattner100a4f82004-06-28 19:19:47 +0000795<!-- _______________________________________________________________________ -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000796<h4>
Chris Lattner100a4f82004-06-28 19:19:47 +0000797 <a name="globalsmodref">The <tt>-globalsmodref-aa</tt> pass</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000798</h4>
Chris Lattner100a4f82004-06-28 19:19:47 +0000799
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000800<div>
Chris Lattner100a4f82004-06-28 19:19:47 +0000801
802<p>This pass implements a simple context-sensitive mod/ref and alias analysis
Chris Lattnerccb354b2004-07-27 07:50:07 +0000803for internal global variables that don't "have their address taken". If a
804global does not have its address taken, the pass knows that no pointers alias
805the global. This pass also keeps track of functions that it knows never access
Chris Lattner4f4365e2009-04-25 21:11:37 +0000806memory or never read memory. This allows certain optimizations (e.g. GVN) to
Chris Lattnerccb354b2004-07-27 07:50:07 +0000807eliminate call instructions entirely.
Chris Lattner100a4f82004-06-28 19:19:47 +0000808</p>
809
810<p>The real power of this pass is that it provides context-sensitive mod/ref
811information for call instructions. This allows the optimizer to know that
812calls to a function do not clobber or read the value of the global, allowing
813loads and stores to be eliminated.</p>
814
815<p>Note that this pass is somewhat limited in its scope (only support
816non-address taken globals), but is very quick analysis.</p>
817</div>
Chris Lattnerccc80652004-05-23 21:04:01 +0000818
819<!-- _______________________________________________________________________ -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000820<h4>
Chris Lattnerccc80652004-05-23 21:04:01 +0000821 <a name="steens-aa">The <tt>-steens-aa</tt> pass</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000822</h4>
Chris Lattnerccc80652004-05-23 21:04:01 +0000823
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000824<div>
Chris Lattnerccc80652004-05-23 21:04:01 +0000825
826<p>The <tt>-steens-aa</tt> pass implements a variation on the well-known
827"Steensgaard's algorithm" for interprocedural alias analysis. Steensgaard's
828algorithm is a unification-based, flow-insensitive, context-insensitive, and
829field-insensitive alias analysis that is also very scalable (effectively linear
830time).</p>
831
832<p>The LLVM <tt>-steens-aa</tt> pass implements a "speculatively
833field-<b>sensitive</b>" version of Steensgaard's algorithm using the Data
834Structure Analysis framework. This gives it substantially more precision than
835the standard algorithm while maintaining excellent analysis scalability.</p>
836
Chris Lattnerd6e0dd12007-07-03 04:41:50 +0000837<p>Note that <tt>-steens-aa</tt> is available in the optional "poolalloc"
838module, it is not part of the LLVM core.</p>
839
Chris Lattnerccc80652004-05-23 21:04:01 +0000840</div>
841
842<!-- _______________________________________________________________________ -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000843<h4>
Chris Lattnerccc80652004-05-23 21:04:01 +0000844 <a name="ds-aa">The <tt>-ds-aa</tt> pass</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000845</h4>
Chris Lattnerccc80652004-05-23 21:04:01 +0000846
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000847<div>
Chris Lattnerccc80652004-05-23 21:04:01 +0000848
849<p>The <tt>-ds-aa</tt> pass implements the full Data Structure Analysis
850algorithm. Data Structure Analysis is a modular unification-based,
851flow-insensitive, context-<b>sensitive</b>, and speculatively
852field-<b>sensitive</b> alias analysis that is also quite scalable, usually at
853O(n*log(n)).</p>
854
855<p>This algorithm is capable of responding to a full variety of alias analysis
856queries, and can provide context-sensitive mod/ref information as well. The
857only major facility not implemented so far is support for must-alias
858information.</p>
Misha Brukman3896be22003-10-24 18:06:11 +0000859
Chris Lattnerd6e0dd12007-07-03 04:41:50 +0000860<p>Note that <tt>-ds-aa</tt> is available in the optional "poolalloc"
861module, it is not part of the LLVM core.</p>
862
Misha Brukmancd11e452003-10-22 23:27:16 +0000863</div>
Chris Lattner9f648752003-03-04 19:37:49 +0000864
Dan Gohman85dfca62010-06-28 22:09:52 +0000865<!-- _______________________________________________________________________ -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000866<h4>
Dan Gohman85dfca62010-06-28 22:09:52 +0000867 <a name="scev-aa">The <tt>-scev-aa</tt> pass</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000868</h4>
Dan Gohman85dfca62010-06-28 22:09:52 +0000869
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000870<div>
Dan Gohman85dfca62010-06-28 22:09:52 +0000871
872<p>The <tt>-scev-aa</tt> pass implements AliasAnalysis queries by
873translating them into ScalarEvolution queries. This gives it a
874more complete understanding of <tt>getelementptr</tt> instructions
875and loop induction variables than other alias analyses have.</p>
876
877</div>
Chris Lattner9f648752003-03-04 19:37:49 +0000878
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000879</div>
880
Chris Lattner9f648752003-03-04 19:37:49 +0000881<!-- ======================================================================= -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000882<h3>
Chris Lattnerccc80652004-05-23 21:04:01 +0000883 <a name="aliasanalysis-xforms">Alias analysis driven transformations</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000884</h3>
Chris Lattnerccc80652004-05-23 21:04:01 +0000885
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000886<div>
Chris Lattnerccc80652004-05-23 21:04:01 +0000887LLVM includes several alias-analysis driven transformations which can be used
888with any of the implementations above.
Chris Lattnerccc80652004-05-23 21:04:01 +0000889
890<!-- _______________________________________________________________________ -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000891<h4>
Chris Lattnerccc80652004-05-23 21:04:01 +0000892 <a name="adce">The <tt>-adce</tt> pass</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000893</h4>
Chris Lattnerccc80652004-05-23 21:04:01 +0000894
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000895<div>
Chris Lattnerccc80652004-05-23 21:04:01 +0000896
897<p>The <tt>-adce</tt> pass, which implements Aggressive Dead Code Elimination
898uses the <tt>AliasAnalysis</tt> interface to delete calls to functions that do
899not have side-effects and are not used.</p>
900
901</div>
902
903
904<!-- _______________________________________________________________________ -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000905<h4>
Chris Lattnerccc80652004-05-23 21:04:01 +0000906 <a name="licm">The <tt>-licm</tt> pass</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000907</h4>
Chris Lattnerccc80652004-05-23 21:04:01 +0000908
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000909<div>
Chris Lattnerccc80652004-05-23 21:04:01 +0000910
911<p>The <tt>-licm</tt> pass implements various Loop Invariant Code Motion related
912transformations. It uses the <tt>AliasAnalysis</tt> interface for several
913different transformations:</p>
914
915<ul>
916<li>It uses mod/ref information to hoist or sink load instructions out of loops
917if there are no instructions in the loop that modifies the memory loaded.</li>
918
919<li>It uses mod/ref information to hoist function calls out of loops that do not
920write to memory and are loop-invariant.</li>
921
922<li>If uses alias information to promote memory objects that are loaded and
923stored to in loops to live in a register instead. It can do this if there are
924no may aliases to the loaded/stored memory location.</li>
925</ul>
926
927</div>
928
929<!-- _______________________________________________________________________ -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000930<h4>
Chris Lattnerccc80652004-05-23 21:04:01 +0000931 <a name="argpromotion">The <tt>-argpromotion</tt> pass</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000932</h4>
Chris Lattnerccc80652004-05-23 21:04:01 +0000933
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000934<div>
Chris Lattnerccc80652004-05-23 21:04:01 +0000935<p>
936The <tt>-argpromotion</tt> pass promotes by-reference arguments to be passed in
937by-value instead. In particular, if pointer arguments are only loaded from it
938passes in the value loaded instead of the address to the function. This pass
939uses alias information to make sure that the value loaded from the argument
940pointer is not modified between the entry of the function and any load of the
941pointer.</p>
942</div>
943
944<!-- _______________________________________________________________________ -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000945<h4>
Chris Lattner4f4365e2009-04-25 21:11:37 +0000946 <a name="gvn">The <tt>-gvn</tt>, <tt>-memcpyopt</tt>, and <tt>-dse</tt>
947 passes</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000948</h4>
Chris Lattnerccc80652004-05-23 21:04:01 +0000949
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000950<div>
Misha Brukman294611a2004-07-28 22:18:33 +0000951
Chris Lattner4f4365e2009-04-25 21:11:37 +0000952<p>These passes use AliasAnalysis information to reason about loads and stores.
953</p>
Chris Lattnerccc80652004-05-23 21:04:01 +0000954
955</div>
956
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000957</div>
958
Chris Lattnerccc80652004-05-23 21:04:01 +0000959<!-- ======================================================================= -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000960<h3>
Misha Brukman294611a2004-07-28 22:18:33 +0000961 <a name="aliasanalysis-debug">Clients for debugging and evaluation of
962 implementations</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000963</h3>
Chris Lattnerccc80652004-05-23 21:04:01 +0000964
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000965<div>
Chris Lattnerccc80652004-05-23 21:04:01 +0000966
Misha Brukman294611a2004-07-28 22:18:33 +0000967<p>These passes are useful for evaluating the various alias analysis
Chris Lattnera9cf1962010-03-01 19:24:17 +0000968implementations. You can use them with commands like '<tt>opt -ds-aa
Misha Brukman294611a2004-07-28 22:18:33 +0000969-aa-eval foo.bc -disable-output -stats</tt>'.</p>
970
Chris Lattnerccc80652004-05-23 21:04:01 +0000971<!-- _______________________________________________________________________ -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000972<h4>
Misha Brukmancd11e452003-10-22 23:27:16 +0000973 <a name="print-alias-sets">The <tt>-print-alias-sets</tt> pass</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000974</h4>
Chris Lattner9f648752003-03-04 19:37:49 +0000975
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000976<div>
Misha Brukman3896be22003-10-24 18:06:11 +0000977
978<p>The <tt>-print-alias-sets</tt> pass is exposed as part of the
Chris Lattner05d5c9d2006-01-03 06:04:48 +0000979<tt>opt</tt> tool to print out the Alias Sets formed by the <a
Chris Lattner9f648752003-03-04 19:37:49 +0000980href="#ast"><tt>AliasSetTracker</tt></a> class. This is useful if you're using
Chris Lattner05d5c9d2006-01-03 06:04:48 +0000981the <tt>AliasSetTracker</tt> class. To use it, use something like:</p>
982
983<div class="doc_code">
984<pre>
985% opt -ds-aa -print-alias-sets -disable-output
986</pre>
987</div>
Misha Brukman3896be22003-10-24 18:06:11 +0000988
Misha Brukmancd11e452003-10-22 23:27:16 +0000989</div>
Chris Lattner9f648752003-03-04 19:37:49 +0000990
Chris Lattnerccc80652004-05-23 21:04:01 +0000991
992<!-- _______________________________________________________________________ -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000993<h4>
Misha Brukmancd11e452003-10-22 23:27:16 +0000994 <a name="count-aa">The <tt>-count-aa</tt> pass</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +0000995</h4>
Chris Lattner9f648752003-03-04 19:37:49 +0000996
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +0000997<div>
Misha Brukman3896be22003-10-24 18:06:11 +0000998
999<p>The <tt>-count-aa</tt> pass is useful to see how many queries a particular
Misha Brukman294611a2004-07-28 22:18:33 +00001000pass is making and what responses are returned by the alias analysis. As an
1001example,</p>
Misha Brukman3896be22003-10-24 18:06:11 +00001002
Misha Brukman294611a2004-07-28 22:18:33 +00001003<div class="doc_code">
Chris Lattner9f648752003-03-04 19:37:49 +00001004<pre>
Misha Brukman294611a2004-07-28 22:18:33 +00001005% opt -basicaa -count-aa -ds-aa -count-aa -licm
Chris Lattner9f648752003-03-04 19:37:49 +00001006</pre>
Misha Brukman294611a2004-07-28 22:18:33 +00001007</div>
Misha Brukman3896be22003-10-24 18:06:11 +00001008
Misha Brukman294611a2004-07-28 22:18:33 +00001009<p>will print out how many queries (and what responses are returned) by the
1010<tt>-licm</tt> pass (of the <tt>-ds-aa</tt> pass) and how many queries are made
1011of the <tt>-basicaa</tt> pass by the <tt>-ds-aa</tt> pass. This can be useful
1012when debugging a transformation or an alias analysis implementation.</p>
Misha Brukman3896be22003-10-24 18:06:11 +00001013
Misha Brukmancd11e452003-10-22 23:27:16 +00001014</div>
Chris Lattner9f648752003-03-04 19:37:49 +00001015
Chris Lattnerccc80652004-05-23 21:04:01 +00001016<!-- _______________________________________________________________________ -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +00001017<h4>
Misha Brukmancd11e452003-10-22 23:27:16 +00001018 <a name="aa-eval">The <tt>-aa-eval</tt> pass</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +00001019</h4>
Chris Lattner9f648752003-03-04 19:37:49 +00001020
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +00001021<div>
Misha Brukman3896be22003-10-24 18:06:11 +00001022
1023<p>The <tt>-aa-eval</tt> pass simply iterates through all pairs of pointers in a
Chris Lattner9f648752003-03-04 19:37:49 +00001024function and asks an alias analysis whether or not the pointers alias. This
1025gives an indication of the precision of the alias analysis. Statistics are
Chris Lattnerccc80652004-05-23 21:04:01 +00001026printed indicating the percent of no/may/must aliases found (a more precise
1027algorithm will have a lower number of may aliases).</p>
Misha Brukman3896be22003-10-24 18:06:11 +00001028
Misha Brukmancd11e452003-10-22 23:27:16 +00001029</div>
Chris Lattner9f648752003-03-04 19:37:49 +00001030
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +00001031</div>
1032
1033</div>
1034
Chris Lattner9f648752003-03-04 19:37:49 +00001035<!-- *********************************************************************** -->
NAKAMURA Takumi05d02652011-04-18 23:59:50 +00001036<h2>
Owen Anderson5a726b82007-10-02 00:43:25 +00001037 <a name="memdep">Memory Dependence Analysis</a>
NAKAMURA Takumi05d02652011-04-18 23:59:50 +00001038</h2>
Owen Anderson5a726b82007-10-02 00:43:25 +00001039<!-- *********************************************************************** -->
1040
NAKAMURA Takumi074eeaa2011-04-21 01:52:00 +00001041<div>
Owen Anderson5a726b82007-10-02 00:43:25 +00001042
1043<p>If you're just looking to be a client of alias analysis information, consider
1044using the Memory Dependence Analysis interface instead. MemDep is a lazy,
1045caching layer on top of alias analysis that is able to answer the question of
1046what preceding memory operations a given instruction depends on, either at an
1047intra- or inter-block level. Because of its laziness and caching
1048policy, using MemDep can be a significant performance win over accessing alias
1049analysis directly.</p>
1050
1051</div>
1052
1053<!-- *********************************************************************** -->
Chris Lattner9f648752003-03-04 19:37:49 +00001054
Misha Brukman3896be22003-10-24 18:06:11 +00001055<hr>
Misha Brukman915cab22003-11-22 01:26:21 +00001056<address>
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Misha Brukman915cab22003-11-22 01:26:21 +00001061
1062 <a href="mailto:sabre@nondot.org">Chris Lattner</a><br>
NAKAMURA Takumib9a33632011-04-09 02:13:37 +00001063 <a href="http://llvm.org/">LLVM Compiler Infrastructure</a><br>
Misha Brukman915cab22003-11-22 01:26:21 +00001064 Last modified: $Date$
1065</address>
Misha Brukmancd11e452003-10-22 23:27:16 +00001066
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