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| <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. |
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