Dependence Testing and Vectorization of Multimedia Agents

Wepresent a dependence testing algorithm that considers the short width of modern SIMD registers in a typical microprocessor. The test works by solving the dependence system with the generalized GCD algorithm and then simplifying the solution equations for a particular set of dependence distances. We start by simplifying each solution lattice to generate points that satisfy some small constant dependence distance that corresponds to the width of the register being used. We use the Power Test to efficiently perform Fourier-Motzkin Variable Elimination on the simplified systems in order to determine if dependences exist. The improvements described in this paper also extend our SIMD dependence test to loops with symbolic and triangular lower and upper bounds as well as array indices that contain unknown symbolic additive constants. The resulting analysis is used to guide the vectorization pass of a dynamic multimedia compiler used to compile software agents that process audio, video and image data. We fully detail the proposed dependence test in this paper, including the related work.