Extending conventional flow analysis to deal with array references

Traditional optimization-oriented flow analysis provides methods for solving a wide assortment of problems (e.g., forward and backward problems; problems with confluence operators of union, intersection, etc.). Traditional methods deal extremely well with scalar variables because it is easy to determine whether or not two scalar variable references refer to the same memory location(s). Traditional methods, on the other hand, deal with references to array variables by ignoring the fact that they are array variables, i.e., by treating them as though they were references to scalar variables; the reason is, of course, that it is more difficult to determine whether two references to the same array variable refer to the same memory location(s). Using methods derived from the field of array subscript analysis, we have developed methods for the enhancement of the flow analysis of code containing array references. In the present paper we present some elementary results which are useful in solving flow problems which require must kill information, problems such as ud-chaining, du-chaining, and live variable analysis. In a later paper we will show how the principles underlying these results may be extended to the solution of problems requiring must not killinformation, problems such as global common subexpressions.