| <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> |
| <html> |
| <!-- Copyright (C) 1988-2015 Free Software Foundation, Inc. |
| |
| Permission is granted to copy, distribute and/or modify this document |
| under the terms of the GNU Free Documentation License, Version 1.3 or |
| any later version published by the Free Software Foundation; with the |
| Invariant Sections being "Funding Free Software", the Front-Cover |
| Texts being (a) (see below), and with the Back-Cover Texts being (b) |
| (see below). A copy of the license is included in the section entitled |
| "GNU Free Documentation License". |
| |
| (a) The FSF's Front-Cover Text is: |
| |
| A GNU Manual |
| |
| (b) The FSF's Back-Cover Text is: |
| |
| You have freedom to copy and modify this GNU Manual, like GNU |
| software. Copies published by the Free Software Foundation raise |
| funds for GNU development. --> |
| <!-- Created by GNU Texinfo 5.2, http://www.gnu.org/software/texinfo/ --> |
| <head> |
| <title>GNU Compiler Collection (GCC) Internals: Scalar evolutions</title> |
| |
| <meta name="description" content="GNU Compiler Collection (GCC) Internals: Scalar evolutions"> |
| <meta name="keywords" content="GNU Compiler Collection (GCC) Internals: Scalar evolutions"> |
| <meta name="resource-type" content="document"> |
| <meta name="distribution" content="global"> |
| <meta name="Generator" content="makeinfo"> |
| <meta http-equiv="Content-Type" content="text/html; charset=utf-8"> |
| <link href="index.html#Top" rel="start" title="Top"> |
| <link href="Option-Index.html#Option-Index" rel="index" title="Option Index"> |
| <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents"> |
| <link href="Loop-Analysis-and-Representation.html#Loop-Analysis-and-Representation" rel="up" title="Loop Analysis and Representation"> |
| <link href="loop_002div.html#loop_002div" rel="next" title="loop-iv"> |
| <link href="LCSSA.html#LCSSA" rel="prev" title="LCSSA"> |
| <style type="text/css"> |
| <!-- |
| a.summary-letter {text-decoration: none} |
| blockquote.smallquotation {font-size: smaller} |
| div.display {margin-left: 3.2em} |
| div.example {margin-left: 3.2em} |
| div.indentedblock {margin-left: 3.2em} |
| div.lisp {margin-left: 3.2em} |
| div.smalldisplay {margin-left: 3.2em} |
| div.smallexample {margin-left: 3.2em} |
| div.smallindentedblock {margin-left: 3.2em; font-size: smaller} |
| div.smalllisp {margin-left: 3.2em} |
| kbd {font-style:oblique} |
| pre.display {font-family: inherit} |
| pre.format {font-family: inherit} |
| pre.menu-comment {font-family: serif} |
| pre.menu-preformatted {font-family: serif} |
| pre.smalldisplay {font-family: inherit; font-size: smaller} |
| pre.smallexample {font-size: smaller} |
| pre.smallformat {font-family: inherit; font-size: smaller} |
| pre.smalllisp {font-size: smaller} |
| span.nocodebreak {white-space:nowrap} |
| span.nolinebreak {white-space:nowrap} |
| span.roman {font-family:serif; font-weight:normal} |
| span.sansserif {font-family:sans-serif; font-weight:normal} |
| ul.no-bullet {list-style: none} |
| --> |
| </style> |
| |
| |
| </head> |
| |
| <body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000"> |
| <a name="Scalar-evolutions"></a> |
| <div class="header"> |
| <p> |
| Next: <a href="loop_002div.html#loop_002div" accesskey="n" rel="next">loop-iv</a>, Previous: <a href="LCSSA.html#LCSSA" accesskey="p" rel="prev">LCSSA</a>, Up: <a href="Loop-Analysis-and-Representation.html#Loop-Analysis-and-Representation" accesskey="u" rel="up">Loop Analysis and Representation</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Option-Index.html#Option-Index" title="Index" rel="index">Index</a>]</p> |
| </div> |
| <hr> |
| <a name="Scalar-evolutions-1"></a> |
| <h3 class="section">15.5 Scalar evolutions</h3> |
| <a name="index-Scalar-evolutions"></a> |
| <a name="index-IV-analysis-on-GIMPLE"></a> |
| |
| <p>Scalar evolutions (SCEV) are used to represent results of induction |
| variable analysis on GIMPLE. They enable us to represent variables with |
| complicated behavior in a simple and consistent way (we only use it to |
| express values of polynomial induction variables, but it is possible to |
| extend it). The interfaces to SCEV analysis are declared in |
| <samp>tree-scalar-evolution.h</samp>. To use scalar evolutions analysis, |
| <code>scev_initialize</code> must be used. To stop using SCEV, |
| <code>scev_finalize</code> should be used. SCEV analysis caches results in |
| order to save time and memory. This cache however is made invalid by |
| most of the loop transformations, including removal of code. If such a |
| transformation is performed, <code>scev_reset</code> must be called to clean |
| the caches. |
| </p> |
| <p>Given an SSA name, its behavior in loops can be analyzed using the |
| <code>analyze_scalar_evolution</code> function. The returned SCEV however |
| does not have to be fully analyzed and it may contain references to |
| other SSA names defined in the loop. To resolve these (potentially |
| recursive) references, <code>instantiate_parameters</code> or |
| <code>resolve_mixers</code> functions must be used. |
| <code>instantiate_parameters</code> is useful when you use the results of SCEV |
| only for some analysis, and when you work with whole nest of loops at |
| once. It will try replacing all SSA names by their SCEV in all loops, |
| including the super-loops of the current loop, thus providing a complete |
| information about the behavior of the variable in the loop nest. |
| <code>resolve_mixers</code> is useful if you work with only one loop at a |
| time, and if you possibly need to create code based on the value of the |
| induction variable. It will only resolve the SSA names defined in the |
| current loop, leaving the SSA names defined outside unchanged, even if |
| their evolution in the outer loops is known. |
| </p> |
| <p>The SCEV is a normal tree expression, except for the fact that it may |
| contain several special tree nodes. One of them is |
| <code>SCEV_NOT_KNOWN</code>, used for SSA names whose value cannot be |
| expressed. The other one is <code>POLYNOMIAL_CHREC</code>. Polynomial chrec |
| has three arguments – base, step and loop (both base and step may |
| contain further polynomial chrecs). Type of the expression and of base |
| and step must be the same. A variable has evolution |
| <code>POLYNOMIAL_CHREC(base, step, loop)</code> if it is (in the specified |
| loop) equivalent to <code>x_1</code> in the following example |
| </p> |
| <div class="smallexample"> |
| <pre class="smallexample">while (…) |
| { |
| x_1 = phi (base, x_2); |
| x_2 = x_1 + step; |
| } |
| </pre></div> |
| |
| <p>Note that this includes the language restrictions on the operations. |
| For example, if we compile C code and <code>x</code> has signed type, then the |
| overflow in addition would cause undefined behavior, and we may assume |
| that this does not happen. Hence, the value with this SCEV cannot |
| overflow (which restricts the number of iterations of such a loop). |
| </p> |
| <p>In many cases, one wants to restrict the attention just to affine |
| induction variables. In this case, the extra expressive power of SCEV |
| is not useful, and may complicate the optimizations. In this case, |
| <code>simple_iv</code> function may be used to analyze a value – the result |
| is a loop-invariant base and step. |
| </p> |
| <hr> |
| <div class="header"> |
| <p> |
| Next: <a href="loop_002div.html#loop_002div" accesskey="n" rel="next">loop-iv</a>, Previous: <a href="LCSSA.html#LCSSA" accesskey="p" rel="prev">LCSSA</a>, Up: <a href="Loop-Analysis-and-Representation.html#Loop-Analysis-and-Representation" accesskey="u" rel="up">Loop Analysis and Representation</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Option-Index.html#Option-Index" title="Index" rel="index">Index</a>]</p> |
| </div> |
| |
| |
| |
| </body> |
| </html> |
