Polly's Polyhedral Scheduling in the Presence of Reductions

The polyhedral model provides a powerful mathematical abstraction to enable effective optimization of loop nests with respect to a given optimization goal, e.g., exploiting parallelism. Unexploited reduction properties are a frequent reason for polyhedral optimizers to assume parallelism prohibiting dependences. To our knowledge, no polyhedral loop optimizer available in any production compiler provides support for reductions. In this paper, we show that leveraging the parallelism of reductions can lead to a significant performance increase. We give a precise, dependence based, definition of reductions and discuss ways to extend polyhedral optimization to exploit the associativity and commutativity of reduction computations. We have implemented a reduction-enabled scheduling approach in the Polly polyhedral optimizer and evaluate it on the standard Polybench 3.2 benchmark suite. We were able to detect and model all 52 arithmetic reductions and achieve speedups up to 2.21$\times$ on a quad core machine by exploiting the multidimensional reduction in the BiCG benchmark.Comment: Presented at the IMPACT15 worksho

Fine grain software pipelining of non-vectorizable nested loops

This paper presents a new technique to parallelize nested loops at the statement level. It transforms sequential nested loops, either vectorizable or not, into parallel ones. Previously, the wavefront method was used to parallelize non-vectorizable nested loops. However, in order to reduce the complexity of parallelization, the wavefront method regards an iteration as an unbreakable scheduling unit and draws parallelism through iteration overlapping. Our technique takes a statement rather than an iteration as the scheduling unit and exploits parallelism by overlapping the statements in all dimensions. In this paper, we show how this finer grain parallelization can be achieved with reasonable computational complexity, and the effectiveness of the resulting method in exploiting parallelism

Dynamic Loop Scheduling Using MPI Passive-Target Remote Memory Access

Scientific applications often contain large computationally-intensive parallel loops. Loop scheduling techniques aim to achieve load balanced executions of such applications. For distributed-memory systems, existing dynamic loop scheduling (DLS) libraries are typically MPI-based, and employ a master-worker execution model to assign variably-sized chunks of loop iterations. The master-worker execution model may adversely impact performance due to the master-level contention. This work proposes a distributed chunk-calculation approach that does not require the master-worker execution scheme. Moreover, it considers the novel features in the latest MPI standards, such as passive-target remote memory access, shared-memory window creation, and atomic read-modify-write operations. To evaluate the proposed approach, five well-known DLS techniques, two applications, and two heterogeneous hardware setups have been considered. The DLS techniques implemented using the proposed approach outperformed their counterparts implemented using the traditional master-worker execution model

N-Dimensional Perfect Pipelining

In this paper, we introduce a technique to parallelize nested loops at the fine grain level. It is a generalization of Perfect Pipelining which was developed to parallelize a single-nested loop at the fine grain level. Previous techniques that can parallelize nested loops, e.g. DOACROSS or Wavefront method, mostly belong to the coarse grain approach. We explain our method, contrast it with the coarse grain techniques, and show the benefits of parallelizing nested loops at the fine grain level

Loop Coalescing and Scheduling for Barrier MIMD Architectures

Barrier MIMDs are asynchronous Multiple Instruction stream Multiple Data stream architectures capable of parallel execution of variable execution time instructions and arbitrary control flow (e.g., while loops and calls); however, they differ from conventional MlMDs in that the need for run-time synchronization is significantly reduced. This work considers the problem of scheduling nested loop structures on a barrier MIMD. The basic approach employs loop coalescing, a technique for transforming a multiply-nested loop into a single loop. Loop coalescing is extended to nested triangular loops, in which inner loop bounds are functions of outer loop indices. Also, a more efficient scheme to generate the original loop indices from the coalesced index is proposed for the case of constant loop bounds. These results are general, and can be applied to extend previous work using loop coalescing techniques. We concentrate on using loop coalescing for scheduling barrier MIMDs, and show how previous work in loop transformations [Wol89], [Pol88] and linear scheduling theory [ShF88], rShO901 cart be applied to this problem