Loop monotonic statements

A statement is considered to be monotonic with respect to a loop if its execution, during the successive iterations of a given execution of the loop, assigns a monotonically increasing or decreasing sequence of values to a variable. We present static analysis techniques to identify loop monotonic statements. The knowledge of loop monotonicity characteristics of statements which compute array subscript expressions is of significant value in a number of applications. We illustrate the use of this information in improving the efficiency of run-time array bound checking, run-time dependence testing, and on-the-fly detection of access anomalies. Given that a significant percentage of subscript expressions are monotonic, substantial savings can be expected by using these techniques