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A GNU Manual
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<p>
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Previous: <a rel="previous" accesskey="p" href="Dependency-analysis.html#Dependency-analysis">Dependency analysis</a>,
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Up: <a rel="up" accesskey="u" href="Loop-Analysis-and-Representation.html#Loop-Analysis-and-Representation">Loop Analysis and Representation</a>
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</div>
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<h3 class="section">15.9 Omega a solver for linear programming problems</h3>
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<p><a name="index-Omega-a-solver-for-linear-programming-problems-3240"></a>
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The data dependence analysis contains several solvers triggered
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sequentially from the less complex ones to the more sophisticated.
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For ensuring the consistency of the results of these solvers, a data
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dependence check pass has been implemented based on two different
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solvers. The second method that has been integrated to GCC is based
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on the Omega dependence solver, written in the 1990's by William Pugh
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and David Wonnacott. Data dependence tests can be formulated using a
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subset of the Presburger arithmetics that can be translated to linear
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constraint systems. These linear constraint systems can then be
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solved using the Omega solver.
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<p>The Omega solver is using Fourier-Motzkin's algorithm for variable
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elimination: a linear constraint system containing <code>n</code> variables
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is reduced to a linear constraint system with <code>n-1</code> variables.
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The Omega solver can also be used for solving other problems that can
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be expressed under the form of a system of linear equalities and
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inequalities. The Omega solver is known to have an exponential worst
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case, also known under the name of “omega nightmare” in the
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literature, but in practice, the omega test is known to be efficient
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for the common data dependence tests.
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<p>The interface used by the Omega solver for describing the linear
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programming problems is described in <samp><span class="file">omega.h</span></samp>, and the solver is
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<code>omega_solve_problem</code>.
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