An exact data dependence testing method for quadratic expressions

Optimizing compilers relies on program analysis techniques to detect data dependence between program statements. Data dependence testing is a basic step in detecting loop-level parallelism in numerical program. Most studies indicate that data dependence tests cannot handle nonlinear-expression array subscripts. This study presents an exact dependence test that can handle quadratic expression array subscripts precisely. The proposed method detects whether a quadratic equation is monotonically increasing or decreasing, and then reduces the integer solution interval of each variable by repeated projection. When the effective solution interval for any variable shrinks to empty, no integer solutions exist for this quadratic equation; otherwise, all integer solutions can be found, implying that parallelism of a loop can be exploited.