| U. Schwiegelshohn, F. Gasperoni, and K. Ebciolu. On optimal parallelization of arbitrary loops. Journal of Parallel and Distributed Computing, 11:130134, 1991. |
....schedules that exhibit a cyclic pattern are particularly interesting since they can be described by loops. A cyclic schedule is a schedule such that (v; k) c v k, for some c v 2 N 2 Optimality for arbitrary loops is in general not easy to discuss as shown by Schwiegelshohn et al. [28]. 3 For some architectures, the delay of an operation may depend on both dependent operations and on the nature of the dependence (anti, ow, or output) The delay is then placed on edges and not vertices. We chose this model for making the discussion simpler, but this can be generalized. 3 ....
U. Schwiegelshohn, F. Gasperoni, and K. Ebciolu. On optimal parallelization of arbitrary loops. Journal of Parallel and Distributed Computing, 11:130134, 1991.
....and a nite number 1 We put good in quotation marks because the technique remains of course a heuristic. Loop compaction itself is NP complete in the case of resource constraints : 2 Optimality for arbitrary loops is in general not easy to discuss as shown by Schwiegelshohn et al. [25]. 3 of non pipelined homogeneous functional units. Despite this simpli ed model, our algorithm can still be used in practice for more sophisticated resource models (even if the theoretical guarantee that we give is no longer true) Indeed, the loop shifting technique that we develop is the rst ....
U. Schwiegelshohn, F. Gasperoni, and K. Ebciolu. On optimal parallelization of arbitrary loops. Journal of Parallel and Distributed Computing, 11:130134, 1991.
....adequately address what software pipelining algorithms can and cannot achieve. Results in this line of development include a software pipelining algorithm that generates optimal code for loops without conditional tests [AN88a] and a proof that optimal software pipelining is impossible in general [SGE91] However, this work has largely ignored resource constraints. Existing software pipelining algorithms handle resource constraints in a variety of ways. Some algorithms deal with only weak forms of resource constraints e.g. the number of operations that can be executed in parallel. Others ....
....to duplicate those operations onto each branch of the conditional after it has been scheduled. 8 On Optimal Software Pipelining In this section we briefly review research on the limitations of software pipelining, especially a result showing that optimal software pipelining is unachievable [SGE91] Given this result, we show that our algorithm is as good as possible in the sense that it can produce arbitrarily good schedules. Research in software pipelining has naturally focused on discovering algorithms for computing pipelined schedules, both in general and for specific machines. ....
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U. Schwiegelshohn, F. Gasperoni, and K. Ebcioglu. On optimal parallelization of arbitrary loops. Journal of Parallel and Distributed Computing, 11(2):130--134, 1991.
....number of L iterations can be executed concurrently. However, even under the restrictive condition that for all operation op in L and for every i 1 there be a dependence chain from op[i] to op[i 1] one can show that cyclic branching systems with no asymptotic 1 optimum for L and w exist [53]. This solves an open problem posed by several researchers [4,59] Theorem 6.4.1 There exists a cyclic branching system L with recurrent dependences, core operation set O and such that 8 op 2 O d(op; op) 6= and 8 R 2 d(op; op) oe(R) 1 for which no asymptotic 1 optimum exists for L and ....
U. Schwiegelshohn, F. Gasperoni, and K. Ebcio glu, On optimal parallelization of arbitrary loops, Journal of Parallel and Distributed Computing, 11 (1991), pp. 130--134.
No context found.
U. Schwiegelshohn, F. Gasperoni, and K. Ebciolu. On optimal parallelization of arbitrary loops. Journal of Parallel and Distributed Computing, 11:130134, 1991.
No context found.
U. Schwiegelshohn, F. Gasperoni, and K. Ebciolu. On optimal parallelization of arbitrary loops. Journal of Parallel and Distributed Computing, 11:130134, 1991.
No context found.
U. Schwiegelshohn, F. Gasperoni, and K. Ebcioglu. On Optimal Parallelization of Arbitrary Loops. Journal of Parallel and Distributed Computing, 11(2):130--134, 1991.
No context found.
U. Schwiegelshohn, F. Gasperoni, and K. Ebcio glu. On Optimal Parallelization of Arbitrary Loops. Journal of Parallel and Distributed Computing, 11(2):130--134, 1991.
No context found.
U. Schwiegelshohn, F. Gasperoni, and K. Ebcio glu. On Optimal Parallelization of Arbitrary Loops. Journal of Parallel and Distributed Computing, 11(2):130--134, 1991.
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