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<title>Loop-invariant code motion</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Loop-invariant code motion</span></span>

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<p>In <a href="Computer_programming" title="Computer programming">computer programming</a>, <a href="Loop-invariant_code" class="mw-redirect" title="Loop-invariant code">loop-invariant code</a> consists of statements or expressions (in an <a href="Imperative_programming" title="Imperative programming">imperative</a> <a href="Programming_language" title="Programming language">programming language</a>) that can be moved outside the body of a loop without affecting the semantics of the program. <b>Loop-invariant code motion</b> (also called <b>hoisting</b> or <b>scalar promotion</b>) is a <a href="Compiler_optimization" class="mw-redirect" title="Compiler optimization">compiler optimization</a> that performs this movement automatically.

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

<p>In the following code sample, two optimizations can be applied.

</p>

<span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>

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<p>Although the calculation <code>x = y + z</code> and <code>x * x</code> is loop-invariant, precautions must be taken before moving the code outside the loop. It is possible that the loop condition is <code>false</code> (for example, if <code>n</code> holds a negative value), and in such case, the loop body should not be executed at all. One way of guaranteeing correct behaviour is using a conditional branch outside of the loop. Evaluating the loop condition can have <a href="Side_effect_(computer_science)" title="Side effect (computer science)">side effects</a>, so an additional evaluation by the <code>if</code> construct should be compensated by replacing the <code>while</code> loop with a <code><a href="Do_while_loop" title="Do while loop">do {} while</a></code>. If the code used <code>do {} while</code> in the first place, the whole guarding process is not needed, as the loop body is guaranteed to execute at least once.

</p>

<span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="n">t1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">x</span><span class="p">;</span>

<span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>

</pre></div>

<p>This code can be optimized further. For example, <a href="Strength_reduction" title="Strength reduction">strength reduction</a> could remove the two multiplications inside the loop (<code>6*i</code> and <code>a[i]</code>), and <a href="Induction_variable" title="Induction variable">induction variable</a> elimination could then elide <code>i</code> completely. Since <code>6 * i</code> must be in lock step with <code>i</code> itself, there is no need to have both.

</p>

<div class="mw-heading mw-heading2"><h2 id="Invariant_code_detection">Invariant code detection</h2></div>

<p>Usually, a <a href="Reaching_definition" title="Reaching definition">reaching definitions analysis</a> is used to detect whether a statement or expression is loop invariant.

</p><p>For example, if all reaching definitions for the operands of some simple expression are outside of the loop, the expression can be moved out of the loop.

</p><p>Recent work by Moyen, Rubiano and Seiller uses data-flow dependence analysis <sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> to detect not only invariant commands but larger code fragments such as an inner loop. The analysis also detects quasi-invariants of arbitrary degrees, that is commands or code fragments that become invariant after a fixed number of iterations of the loop body. This technique was later used by Aubert, Rubiano, Rusch, and Seiller to automatically parallelise loops.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>

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

<p>Loop-invariant code which has been hoisted out of a loop is executed less often, providing a speedup. Another effect of this transformation is allowing constants to be stored in registers and not having to calculate the address and access the memory (or cache line) at each iteration.

</p><p>However, if too many variables are created, there will be high <a href="Register_pressure" class="mw-redirect" title="Register pressure">register pressure</a>, especially on processors with few registers, like the 32-bit <a href="X86" title="X86">x86</a>. If the compiler runs out of registers, some variables will be <a href="Register_spilling" class="mw-redirect" title="Register spilling">spilled</a>. To counteract this, the inverse optimization can be performed, <a href="Rematerialization" title="Rematerialization">rematerialization</a>.

</p>

<ul><li><a href="Code_motion" title="Code motion">Code motion</a></li>

<li><a href="Loop_invariant" title="Loop invariant">Loop invariant</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>

<ul><li>Aho, Alfred V.; Sethi, Ravi; & Ullman, Jeffrey D. (1986). Compilers: Principles, Techniques, and Tools. Addison Wesley. <style data-mw-deduplicate="TemplateStyles:r1238218222">

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</style><a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-201-10088-6</bdi>.</li></ul>

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

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<li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><cite id="CITEREFMoyenRubianoSeiller2017" class="citation book cs1">Moyen, Jean-Yves; Rubiano, Thomas; Seiller, Thomas (2017). "Loop Quasi-Invariant Chunk Detection". <i>Automated Technology for Verification and Analysis</i>. Lecture Notes in Computer Science. Vol. 10482. pp. <span class="nowrap">91–</span>108. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-319-68167-2_7">10.1007/978-3-319-68167-2_7</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-319-68166-5</bdi>.</cite></span>

</li>

<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite id="CITEREFAubertRubianoRuschSeiller2023" class="citation book cs1">Aubert, Clément; Rubiano, Thomas; Rusch, Neea; Seiller, Thomas (2023). "Distributing and Parallelizing Non-canonical Loops". <i>Verification, Model Checking, and Abstract Interpretation</i>. Lecture Notes in Computer Science. Vol. 13881. pp. <span class="nowrap">91–</span>108. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-031-24950-1_1">10.1007/978-3-031-24950-1_1</a>.</cite></span>

</li>

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

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20170806083023/http://www.compileroptimizations.com/category/hoisting.htm">Compiler Optimizations — Hoisting</a></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_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="Common_subexpression_elimination" title="Common subexpression elimination">Common subexpression elimination</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>

</div></td></tr></tbody></table></div></div><div><div class="zim-footer">

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