An improved nonlinear data dependence test
To further parallelize large-scale nonlinear scientific computing applications, some data dependence techniques for nonlinear subscripts, especially for quadratic subscripts, were proposed in the past. The quadratic programming (QP) test and polynomial variable interval (PVI) test are two representative techniques. The QP test, which serves as an exact but time-consuming technique, always gives conservative results when the coefficient matrix of the quadratic terms is not positive semi-definite, while the PVI test will lose efficiency when there exist mixed polynomials in the dependence equation. Focusing on the dependences caused by quadratic subscripts in nonlinear and irregular programs, we propose an improved nonlinear data dependence test in this paper. We first normalize a quadratic equation which is written in a general form, and determine whether the canonical equation is integer solvable in the region of interest based on the interval equation theory. Experimental results show that, compared with the QP test, our method maintains a much lower time complexity. Furthermore, it can detect more general dependences than other dependence testing methods like the PVI test in terms of quadratic subscripts.
data dependence test nonlinear subscript interval equation parallelizing compiler