7 Concluding Remarks

27 slopes, in the worst case, the proposed method could result in a serial execution. In this case, more dependence information, such as the magnitude of dependence vectors, may be required for computing a more eecient BDV set. Even though only a two-dimensional iteration space was considered in this paper, a similar algorithm can be extended to a multiple-dimensional iteration space. However, detailed study and experiments for a multiple-level nested loop will be our future work. Acknowledgement The authors would like to thank Dr. Pen-Chung Yew, Dr. Zhiyuan Li, and anonymous referees for their many useful suggestions and comments. References 1] P. Tang and P.-C. Yew, \Processor self-scheduling for multiple-nested parallel loops," in Pro-\On the number of operations simultaneously ex-ecutable in Fortran-like programs and their resulting speedup," IEEE Transactions on Computers , vol. 26 Speedup 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 p 3 p p 3 p p p p 3 p p p p 3 p p p p 3 p p p p 3 p p p p 3 p p p p p p 3 p p p p p p 3 p p p p p p 3 p p p p p p 3 p p p p p p p p 3 p p p p p p p p 3 p p p p p p p p 3 p + p p + p p p p + p p p p + p p p p + p p p p + p p p p + p p p p p p + p p p p p p + p p p p p p + p p p p p p + p p p p p p p p + p p p p p p p p + p p p p p p p p + p 2 p p2 p p p p2 p p p p 2 p p p p 2 p p p p2 p p p p2 p p p p p p 2 p p p p p p 2 p p p p p p 2 p p p p p p 2 p p p p p p p p 2 p p p p p p p p 2 p p p p p p p …