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<title>Common subexpression elimination</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Common subexpression elimination</span></span>

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<p>In <a href="Compiler_theory" class="mw-redirect" title="Compiler theory">compiler theory</a>, <b>common subexpression elimination</b> (<b>CSE</b>) is a <a href="Compiler_optimization" class="mw-redirect" title="Compiler optimization">compiler optimization</a> that searches for instances of identical <a href="Expression_(computer_science)" title="Expression (computer science)">expressions</a> (i.e., they all evaluate to the same value), and analyzes whether it is worthwhile replacing them with a single variable holding the computed value.<sup id="cite_ref-MuchnickAssociates1997_1-0" class="reference"><a href="#cite_note-MuchnickAssociates1997-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="Example">Example</h2></div>

<p>In the following code:

</p>

<pre>a = b * c + g;

d = b * c * e;

</pre>

<p>it may be worth transforming the code to:

</p>

<pre>tmp = b * c;

a = tmp + g;

d = tmp * e;

</pre>

<p>if the cost of storing and retrieving <code>tmp</code> is less than the cost of calculating <code>b * c</code> an extra time.

</p>

<div class="mw-heading mw-heading2"><h2 id="Principle">Principle</h2></div>

<p>The possibility to perform CSE is based on <a href="Available_expression" title="Available expression">available expression</a> analysis (a <a href="Data_flow_analysis" class="mw-redirect" title="Data flow analysis">data flow analysis</a>). An expression <code>b*c</code> is available at a point <i>p</i> in a program if:

</p>

<ul><li>every path from the initial node to p evaluates <code>b*c</code> before reaching <i>p</i>,</li>

<li>and there are no assignments to <code>b</code> or <code>c</code> after the evaluation but before <i>p</i>.</li></ul>

<p>The cost/benefit analysis performed by an optimizer will calculate whether the cost of the store to <code>tmp</code> is less than the cost of the multiplication; in practice other factors such as which values are held in which registers are also significant.

</p><p>Compiler writers distinguish two kinds of CSE:

</p>

<ul><li><b>local common subexpression elimination</b> works within a single <a href="Basic_block" title="Basic block">basic block</a></li>

<li><b>global common subexpression elimination</b> works on an entire procedure,</li></ul>

<p>Both kinds rely on <a href="Data_flow_analysis" class="mw-redirect" title="Data flow analysis">data flow analysis</a> of which expressions are available at which points in a program.

</p>

<div class="mw-heading mw-heading2"><h2 id="Benefits">Benefits</h2></div>

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<p>The benefits of performing CSE are great enough that it is a commonly used optimization.

</p><p>In simple cases like in the example above, programmers may manually eliminate the <a href="Duplicate_code" title="Duplicate code">duplicate expressions</a> while writing the code. The greatest source of CSEs are intermediate code sequences generated by the compiler, such as for <a href="Array_data_structure" class="mw-redirect" title="Array data structure">array</a> indexing calculations, where it is not possible for the developer to manually intervene. In some cases language features may create many duplicate expressions. For instance, <a href="C_(programming_language)" title="C (programming language)">C</a> <a href="Macro_(computer_science)" title="Macro (computer science)">macros</a>, where macro expansions may result in common subexpressions not apparent in the original source code.

</p><p>Compilers need to be judicious about the number of temporaries created to hold values. An excessive number of temporary values creates <a href="Register_pressure" class="mw-redirect" title="Register pressure">register pressure</a> possibly resulting in <a href="Register_spilling" class="mw-redirect" title="Register spilling">spilling registers</a> to memory, which may take longer than simply recomputing an arithmetic result when it is needed.

</p>

<ul><li><a href="Global_value_numbering" class="mw-redirect" title="Global value numbering">Global value numbering</a></li>

<li><a href="Loop-invariant_code_motion" title="Loop-invariant code motion">Loop-invariant code motion</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFSteven_MuchnickMuchnick_and_Associates1997" class="citation book cs1">Steven Muchnick; Muchnick and Associates (15 August 1997). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/advancedcompiler00much"><i>Advanced Compiler Design Implementation</i></a></span>. Morgan Kaufmann. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-55860-320-2</bdi>. <q>Common subexpression elimination.</q></cite></span>

</li>

</ol></div></div>

<ul><li><a href="Steven_S._Muchnick" class="mw-redirect" title="Steven S. Muchnick">Steven S. Muchnick</a>, <i><a rel="nofollow" class="external text" href="https://books.google.com/books?id=Pq7pHwG1_OkC&dq=%22Common+subexpression+elimination%22&pg=PA378">Advanced Compiler Design and Implementation</a></i> (<a href="Morgan_Kaufmann" class="mw-redirect" title="Morgan Kaufmann">Morgan Kaufmann</a>, 1997) pp. 378–396</li>

<li><a href="John_Cocke_(computer_scientist)" title="John Cocke (computer scientist)">John Cocke</a>. <a rel="nofollow" class="external text" href="http://dl.acm.org/citation.cfm?id=390013.808480">"Global Common Subexpression Elimination."</a> <i>Proceedings of a Symposium on Compiler Construction</i>, <i>ACM SIGPLAN Notices</i> 5(7), July 1970, pages 850–856.</li>

<li>Briggs, Preston, Cooper, Keith D., and Simpson, L. Taylor. "<a rel="nofollow" class="external text" href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.49.7975&rep=rep1&type=pdf">Value Numbering</a>." <i>Software-Practice and Experience</i>, 27(6), June 1997, pages 701-724.</li></ul>

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</style><div id="Compiler_optimizations253" style="font-size:114%;margin:0 4em"><a href="Optimizing_compiler" title="Optimizing compiler">Compiler optimizations</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Basic block</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Peephole_optimization" title="Peephole optimization">Peephole optimization</a></li>

<li><a href="Local_value_numbering" class="mw-redirect" title="Local value numbering">Local value numbering</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Loop_optimization" title="Loop optimization">Loop</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Automatic_parallelization" title="Automatic parallelization">Automatic parallelization</a></li>

<li><a href="Automatic_vectorization" title="Automatic vectorization">Automatic vectorization</a></li>

<li><a href="Induction_variable" title="Induction variable">Induction variable</a></li>

<li><a href="Loop_fusion" class="mw-redirect" title="Loop fusion">Loop fusion</a></li>

<li><a href="Loop-invariant_code_motion" title="Loop-invariant code motion">Loop-invariant code motion</a></li>

<li><a href="Loop_inversion" title="Loop inversion">Loop inversion</a></li>

<li><a href="Loop_interchange" title="Loop interchange">Loop interchange</a></li>

<li><a href="Loop_nest_optimization" title="Loop nest optimization">Loop nest optimization</a></li>

<li><a href="Loop_splitting" title="Loop splitting">Loop splitting</a></li>

<li><a href="Loop_unrolling" title="Loop unrolling">Loop unrolling</a></li>

<li><a href="Loop_unswitching" title="Loop unswitching">Loop unswitching</a></li>

<li><a href="Software_pipelining" title="Software pipelining">Software pipelining</a></li>

<li><a href="Strength_reduction" title="Strength reduction">Strength reduction</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Data-flow_analysis" title="Data-flow analysis">Data-flow<br>analysis</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Available_expression" title="Available expression">Available expression</a></li>

<li><a href="Constant_folding" title="Constant folding">Constant folding</a></li>

<li><a href="Dead_store" title="Dead store">Dead store</a> elimination</li>

<li><a href="Induction_variable_recognition_and_elimination" class="mw-redirect" title="Induction variable recognition and elimination">Induction variable recognition and elimination</a></li>

<li><a href="Live-variable_analysis" title="Live-variable analysis">Live-variable analysis</a></li>

<li><a href="Upwards_exposed_uses" title="Upwards exposed uses">Upwards exposed uses</a></li>

<li><a href="Use-define_chain" title="Use-define chain">Use-define chain</a></li>

<li><a href="Reaching_definition" title="Reaching definition">Reaching definitions</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Static_single-assignment_form" title="Static single-assignment form">SSA</a>-based</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Global_value_numbering" class="mw-redirect" title="Global value numbering">Global value numbering</a></li>

<li><a href="Sparse_conditional_constant_propagation" title="Sparse conditional constant propagation">Sparse conditional constant propagation</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Code_generation_(compiler)" title="Code generation (compiler)">Code generation</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Instruction_scheduling" title="Instruction scheduling">Instruction scheduling</a></li>

<li><a href="Instruction_selection" title="Instruction selection">Instruction selection</a></li>

<li><a href="Register_allocation" title="Register allocation">Register allocation</a></li>

<li><a href="Rematerialization" title="Rematerialization">Rematerialization</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Functional</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Deforestation_(computer_science)" title="Deforestation (computer science)">Deforestation</a></li>

<li><a href="Tail_call" title="Tail call">Tail-call elimination</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Global</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Interprocedural_optimization" title="Interprocedural optimization">Interprocedural optimization</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Bounds-checking_elimination" title="Bounds-checking elimination">Bounds-checking elimination</a></li>

<li><a href="Compile-time_function_execution" title="Compile-time function execution">Compile-time function execution</a></li>

<li><a href="Dead-code_elimination" title="Dead-code elimination">Dead-code elimination</a></li>

<li><a href="Expression_templates" title="Expression templates">Expression templates</a></li>

<li><a href="Inline_expansion" title="Inline expansion">Inline expansion</a></li>

<li><a href="Jump_threading" title="Jump threading">Jump threading</a></li>

<li><a href="Partial_evaluation" title="Partial evaluation">Partial evaluation</a></li>

<li><a href="Profile-guided_optimization" title="Profile-guided optimization">Profile-guided optimization</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Static analysis</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Alias_analysis" title="Alias analysis">Alias analysis</a></li>

<li><a href="Array-access_analysis" title="Array-access analysis">Array-access analysis</a></li>

<li><a href="Control-flow_analysis" title="Control-flow analysis">Control-flow analysis</a></li>

<li><a href="Data-flow_analysis" title="Data-flow analysis">Data-flow analysis</a></li>

<li><a href="Dependence_analysis" title="Dependence analysis">Dependence analysis</a></li>

<li><a href="Escape_analysis" title="Escape analysis">Escape analysis</a></li>

<li><a href="Pointer_analysis" title="Pointer analysis">Pointer analysis</a></li>

<li><a href="Shape_analysis_(program_analysis)" title="Shape analysis (program analysis)">Shape analysis</a></li>

<li><a href="Value_range_analysis" title="Value range analysis">Value range analysis</a></li></ul>

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