You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
86 lines
4.0 KiB
HTML
86 lines
4.0 KiB
HTML
4 years ago
|
<html lang="en">
|
||
|
|
<head>
|
||
|
|
<title>Omega - GNU Compiler Collection (GCC) Internals</title>
|
||
|
|
<meta http-equiv="Content-Type" content="text/html">
|
||
|
|
<meta name="description" content="GNU Compiler Collection (GCC) Internals">
|
||
|
|
<meta name="generator" content="makeinfo 4.13">
|
||
|
|
<link title="Top" rel="start" href="index.html#Top">
|
||
|
|
<link rel="up" href="Loop-Analysis-and-Representation.html#Loop-Analysis-and-Representation" title="Loop Analysis and Representation">
|
||
|
|
<link rel="prev" href="Dependency-analysis.html#Dependency-analysis" title="Dependency analysis">
|
||
|
|
<link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage">
|
||
|
|
<!--
|
||
|
|
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.-->
|
||
|
|
<meta http-equiv="Content-Style-Type" content="text/css">
|
||
|
|
<style type="text/css"><!--
|
||
|
|
pre.display { font-family:inherit }
|
||
|
|
pre.format { font-family:inherit }
|
||
|
|
pre.smalldisplay { font-family:inherit; font-size:smaller }
|
||
|
|
pre.smallformat { font-family:inherit; font-size:smaller }
|
||
|
|
pre.smallexample { font-size:smaller }
|
||
|
|
pre.smalllisp { font-size:smaller }
|
||
|
|
span.sc { font-variant:small-caps }
|
||
|
|
span.roman { font-family:serif; font-weight:normal; }
|
||
|
|
span.sansserif { font-family:sans-serif; font-weight:normal; }
|
||
|
|
--></style>
|
||
|
|
</head>
|
||
|
|
<body>
|
||
|
|
<div class="node">
|
||
|
|
<a name="Omega"></a>
|
||
|
|
<p>
|
||
|
|
Previous: <a rel="previous" accesskey="p" href="Dependency-analysis.html#Dependency-analysis">Dependency analysis</a>,
|
||
|
|
Up: <a rel="up" accesskey="u" href="Loop-Analysis-and-Representation.html#Loop-Analysis-and-Representation">Loop Analysis and Representation</a>
|
||
|
|
<hr>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<h3 class="section">15.9 Omega a solver for linear programming problems</h3>
|
||
|
|
|
||
|
|
<p><a name="index-Omega-a-solver-for-linear-programming-problems-3240"></a>
|
||
|
|
The data dependence analysis contains several solvers triggered
|
||
|
|
sequentially from the less complex ones to the more sophisticated.
|
||
|
|
For ensuring the consistency of the results of these solvers, a data
|
||
|
|
dependence check pass has been implemented based on two different
|
||
|
|
solvers. The second method that has been integrated to GCC is based
|
||
|
|
on the Omega dependence solver, written in the 1990's by William Pugh
|
||
|
|
and David Wonnacott. Data dependence tests can be formulated using a
|
||
|
|
subset of the Presburger arithmetics that can be translated to linear
|
||
|
|
constraint systems. These linear constraint systems can then be
|
||
|
|
solved using the Omega solver.
|
||
|
|
|
||
|
|
<p>The Omega solver is using Fourier-Motzkin's algorithm for variable
|
||
|
|
elimination: a linear constraint system containing <code>n</code> variables
|
||
|
|
is reduced to a linear constraint system with <code>n-1</code> variables.
|
||
|
|
The Omega solver can also be used for solving other problems that can
|
||
|
|
be expressed under the form of a system of linear equalities and
|
||
|
|
inequalities. The Omega solver is known to have an exponential worst
|
||
|
|
case, also known under the name of “omega nightmare” in the
|
||
|
|
literature, but in practice, the omega test is known to be efficient
|
||
|
|
for the common data dependence tests.
|
||
|
|
|
||
|
|
<p>The interface used by the Omega solver for describing the linear
|
||
|
|
programming problems is described in <samp><span class="file">omega.h</span></samp>, and the solver is
|
||
|
|
<code>omega_solve_problem</code>.
|
||
|
|
|
||
|
|
<!-- Copyright (C) 1988-2015 Free Software Foundation, Inc. -->
|
||
|
|
<!-- This is part of the GCC manual. -->
|
||
|
|
<!-- For copying conditions, see the file gcc.texi. -->
|
||
|
|
</body></html>
|
||
|
|
|