Citation:
Mohamed Tadjouddine, Frances Bodman, John D. Pryce & Shaun A. Forth, Improving
the Performance of the Vertex Elimination Algorithm for Derivative Calculation.
Automatic Differentiation: Applications, Theory, and Implementations, Bücker,
M.; Corliss, G.; Hovland, P.; Naumann, U.; Norris, B. (Eds.) Lecture Notes in
Computational Science & Engineering, Volume 50, 2006, p111-120
Abstract:
In previous work [TOMS, 2004, 30(3), 266--299], we used Markowitz-like
heuristics aiming to find elimination sequences that minimise the number of
floating-point operations (flops) for vertex elimination Jacobian code. We also
used the depth-first traversal algorithm to reorder the statements of the
Jacobian code with the aim of reducing the number of memory accesses. In this
work, we study the effects of reducing flops or memory accesses within the
vertex elimination algorithm for Jacobian calculation. On RISC processors, we
observed that for data residing in registers, the number of flops gives a good
estimate of the execution time, while for out-of-register data, the execution
time is dominated by the time for memory access operations. We also present a
statement reordering scheme based on a greedy-list scheduling algorithm using
ranking functions. This statement reordering will enable us to trade-off the
exploitation of the instruction level parallelism of such processors with the
reduction in memory accesses.
