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Parallelizing non-vectorizable loops for MIMD machines
Parallelizing a loop for MIMD machines can be described as a process of partitioning it into a number of relatively independent subloops. Previous approaches to partitioning non-vectorizable loops were mainly based on iteration pipelining which partitioned a loop based on iteration number and exploited parallelism by overlapping the execution of iterations. However, the amount of parallelism exploited this way is limited because the parallelism inside iterations has been ignored. In this paper, we present a new loop partitioning technique which can exploit both forms of parallelism - inside and across iterations. While inspired by the VLIW approach, our method is designed for more general, asynchronous, MIMD machines. In particular, our schedule takes the cost of communication into account, and attempts to balance it with respect to parallelism. We show our method is correct, efficient, and produces better schedules than previous iteration level approaches
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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
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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
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Fine-grain loop scheduling for MIMD machines
Previous algorithms for parallelizing loops on MIMD machines have been based on assigning one or more loop iterations to each processor, introducing synchronization as required. These methods exploit only iteration level parallelism, and ignore the parallelism that may exist at a lower level.In order to exploit parallelism both within and across iterations, our algorithm analyzes and schedules the loop at the statement level. The loop schedule reflects the expected communication and synchronization costs of the target machine. We provide test results that show that this algorithm can produce good speedup of loops on an MIMD machine
Clockwork graviton contributions to muon
The clockwork mechanism for gravity introduces a tower of massive graviton
modes, "clockwork gravitons," with a very compressed mass spectrum, whose
interaction strengths are much stronger than that of massless gravitons. In
this work, we compute the lowest order contributions of the clockwork gravitons
to the anomalous magnetic moment, , of muon in the context of extra
dimensional model with a five dimensional Planck mass, . We find that the
total contributions are rather insensitive to the detailed model parameters,
and determined mostly by the value of . In order to account for the
current muon anomaly, should be around , and the
size of the extra dimension has to be quite large, m.
For , the clockwork graviton contributions are too small
to explain the current muon anomaly. We also compare the clockwork
graviton contributions with other extra dimension models such as
Randall-Sundrum models or large extra dimension models. We find that the
leading contributions in the small curvature limit are universal, but the
cutoff-independent subleading contributions vary for different background
geometries and the clockwork geometry gives the smallest subleading
contributions.Comment: 14 pages, 4 figures: v3 minor corrections, to appear in PR
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