<table border="1" cellspacing="0" cellpadding="8">
    <tr>
        <th>Issue</th>
        <td>
            <a href=https://github.com/llvm/llvm-project/issues/122942>122942</a>
        </td>
    </tr>

    <tr>
        <th>Summary</th>
        <td>
            [mlir][presburger] "Isolated" local variables can produce crash or unexpected results in IntegerRelation/PresburgerRelation routines
        </td>
    </tr>

    <tr>
      <th>Labels</th>
      <td>
            mlir:presburger
      </td>
    </tr>

    <tr>
      <th>Assignees</th>
      <td>
            christopherbate
      </td>
    </tr>

    <tr>
      <th>Reporter</th>
      <td>
          christopherbate
      </td>
    </tr>
</table>

<pre>
    I've noticed an issue where "isolated" local variables can cause problems in the elimination of non-div locals (IntegerRelation -> PresburgerRelation) as well as in the set subtraction algorithm (`getSetDifference` in `PresburgerRelation.cpp`).

By "isolated" I mean that there is a local defined in the IntegerRelation system, but there may not be a constraint that links the local to other variables. This sounds contrived, but it can happen if a user constructs an IntegerRelation from an AffineMap where one of the domain variables is not used to calculate the range. Invoking `IntegerRelation::getRangeSet` would then turn all the domain variables into locals, resulting in a local which is not related to any other variable in the system.

If you then try to compute the "non-div local" representation, I noticed that the number of disjuncts can become much larger than if the local is eliminated (e.g. 2x for each unused local). Furthermore, I will sporadically run into an unreachable here https://github.com/llvm/llvm-project/blob/main/mlir/lib/Analysis/Presburger/Simplex.cpp#L1463. Will update this issue with a concise reproducer.

As a workaround, I added a routine to eliminate such locals whenever I construct an IntegerRelation. It doesn't look like any of the existing simplification routines in `IntegerRelation` know how to remove with such locals.


   
</pre>
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