| Eigenmann, R., Hoeflinger, J., Li, Z., and Padua, D. 1992. Experience in the automatic parallelizationof four Perfect-Benchmarkprograms. In U. Banerjee, D. Gelernter, A. Nicolau, and D. Padua (Eds.), Workshop on Languages and Compilers for Parallel Computing, pp. 65--83. Springer-Verlag. LNCS no. 589. |
.... linear induction variables, but can often take the form of polynomial and geometric induction expressions, periodic sequences, monotonic sequences, and wrap around variables: Eigenmann et al. note one scientific code where a speedup of eight was obtained by recognizing a geometric sequence [Eigenmann, Hoeflinger, Li, and Padua 1992]. Current compilers recognize specific forms of these expressions by ad hoc pattern recognition algorithms. Consider the following Fortran loop: np1 = n 1 j = n do i = 1, n B(i) A(j) A(i) 2.0 j = i C(i) B(i) B(np1) enddo In the absence of any aggressive analysis, two ....
....may be assigned. 5. EXTENSIONS FOR LOOP STRUCTURES Several researchers studying parallelizing compilers have pointed out specific types of nested induction variable forms that, while relatively infrequent, can lead to significant parallelism if the subscript expressions can be classified [Eigenmann, Hoeflinger, Li, and Padua 1992; Haghighat and Polychronopoulos 1992] A typical example is a triangular loop containing a polynomial induction variable, similar to the Fortran program and its SSA form shown in Figures 9 and 10. 7 Here k is a polynomial in the outer loop because it is linearly incremented in the inner loop, ....
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Eigenmann, R., Hoeflinger, J., Li, Z., and Padua, D. 1992. Experience in the automatic parallelizationof four Perfect-Benchmarkprograms. In U. Banerjee, D. Gelernter, A. Nicolau, and D. Padua (Eds.), Workshop on Languages and Compilers for Parallel Computing, pp. 65--83. Springer-Verlag. LNCS no. 589.
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