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152 lines
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<title>GNU Compiler Collection (GCC) Internals: Scalar evolutions</title>
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<link href="Option-Index.html#Option-Index" rel="index" title="Option Index">
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<a name="Scalar-evolutions"></a>
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<div class="header">
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<p>
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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>
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</div>
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<hr>
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<a name="Scalar-evolutions-1"></a>
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<h3 class="section">15.5 Scalar evolutions</h3>
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<a name="index-Scalar-evolutions"></a>
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<a name="index-IV-analysis-on-GIMPLE"></a>
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<p>Scalar evolutions (SCEV) are used to represent results of induction
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variable analysis on GIMPLE. They enable us to represent variables with
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complicated behavior in a simple and consistent way (we only use it to
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express values of polynomial induction variables, but it is possible to
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extend it). The interfaces to SCEV analysis are declared in
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<samp>tree-scalar-evolution.h</samp>. To use scalar evolutions analysis,
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<code>scev_initialize</code> must be used. To stop using SCEV,
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<code>scev_finalize</code> should be used. SCEV analysis caches results in
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order to save time and memory. This cache however is made invalid by
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most of the loop transformations, including removal of code. If such a
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transformation is performed, <code>scev_reset</code> must be called to clean
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the caches.
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</p>
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<p>Given an SSA name, its behavior in loops can be analyzed using the
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<code>analyze_scalar_evolution</code> function. The returned SCEV however
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does not have to be fully analyzed and it may contain references to
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other SSA names defined in the loop. To resolve these (potentially
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recursive) references, <code>instantiate_parameters</code> or
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<code>resolve_mixers</code> functions must be used.
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<code>instantiate_parameters</code> is useful when you use the results of SCEV
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only for some analysis, and when you work with whole nest of loops at
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once. It will try replacing all SSA names by their SCEV in all loops,
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including the super-loops of the current loop, thus providing a complete
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information about the behavior of the variable in the loop nest.
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<code>resolve_mixers</code> is useful if you work with only one loop at a
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time, and if you possibly need to create code based on the value of the
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induction variable. It will only resolve the SSA names defined in the
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current loop, leaving the SSA names defined outside unchanged, even if
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their evolution in the outer loops is known.
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</p>
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<p>The SCEV is a normal tree expression, except for the fact that it may
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contain several special tree nodes. One of them is
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<code>SCEV_NOT_KNOWN</code>, used for SSA names whose value cannot be
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expressed. The other one is <code>POLYNOMIAL_CHREC</code>. Polynomial chrec
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has three arguments – base, step and loop (both base and step may
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contain further polynomial chrecs). Type of the expression and of base
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and step must be the same. A variable has evolution
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<code>POLYNOMIAL_CHREC(base, step, loop)</code> if it is (in the specified
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loop) equivalent to <code>x_1</code> in the following example
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</p>
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<div class="smallexample">
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<pre class="smallexample">while (…)
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{
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x_1 = phi (base, x_2);
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x_2 = x_1 + step;
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}
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</pre></div>
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<p>Note that this includes the language restrictions on the operations.
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For example, if we compile C code and <code>x</code> has signed type, then the
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overflow in addition would cause undefined behavior, and we may assume
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that this does not happen. Hence, the value with this SCEV cannot
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overflow (which restricts the number of iterations of such a loop).
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</p>
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<p>In many cases, one wants to restrict the attention just to affine
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induction variables. In this case, the extra expressive power of SCEV
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is not useful, and may complicate the optimizations. In this case,
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<code>simple_iv</code> function may be used to analyze a value – the result
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is a loop-invariant base and step.
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</p>
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<hr>
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<div class="header">
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<p>
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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>
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