Data locality is critical to achieving high performance on large-scale parallel machines. Non-local data accesses result in communication that can greatly impact performance. Thus the mapping, or decomposition, of the computation and data onto the processors of a scalable parallel machine is a key issue in compiling programs for these architectures.

Loop fusion is a program transformation that merges multiple loops into one. It is effective for reducing the synchronization overhead of parallel loops and for improving data locality. This paper presents three results for fusion: (1) a new algorithm for fusing a collection of parallel and sequential loops, minimizing parallel loop synchronization while maximizing parallelism; (2) a proof that performing fusion to maximize data locality is NP-hard; and (3) two polynomial-time algorithms for improving data locality. These techniques also apply to loop distribution, which is shown to be essentially equivalent to loop fusion. Our approach is general enough to support other fusion heuristics. Preliminary experimental results validate our approach for improving performance by exploiting data locality and increasing the granularity of parallelism.

In order to perform powerful program optimizations, an exact interprocedural analysis of array data ow is needed. For that purpose, two new types of array region are introduced. IN and OUT regions represent the sets of array elements, the values of which are imported to or exported from the current statement or procedure. Among the various applications are: compilation of communications for message-passing machines, array privatization, compile-time optimization of local memory or cache behavior in hierarchical memory machines.

Applicable to arbitrary sequences and nests of loops, affine partitioning is a program transformation framework that unifies many previously proposed loop transformations, including unimodular transforms, fusion, fission, reindexing, scaling and statement reordering. Algorithms based on affine partitioning have been shown to be effective for parallelization and communication minimization. This paper presents algorithms that improve data locality using affine partitioning. Blocking and array contraction are two important optimizations that have been shown to be useful for data locality. Blocking creates a set of inner loops so that data brought into the faster levels of the memory hierarchy can be reused. Array contraction reduces an array to a scalar variable and thereby reduces the number of memory operations executed and the memory footprint. Loop transforms are often necessary to make blocking and array contraction possible.

In this paper we propose a method for applying the loop fusion and array contraction optimizations across a collection of loop nests. Loop fusion and array contraction are techniques that can reduce array communication between fused loops by transforming array references into simple scalar references. In previous work we investigated the problem of performing loop interchange and loop reversal on individual loop nests so as to maximize the number of array accesses that are potential candidates for array contraction [SG91]. This paper extends our previous work by taking into account the data dependence constraints imposed by loop fusion and investigating how the loop nests should be fused together so as to maximize the number of array accesses that are actually optimized by array contraction. We propose an efficient method called collective loop fusion that partitions a collection of loop nests into fusible clusters. After an optimized partition is obtained, loop fusion and array contr...

The SUIF Explorer is an interactive parallelization tool that is more effective than previous systems in minimizing the number of lines of code that require programmer assistance. First, the interprocedural analyses in the SUIF system is successful in parallelizing many coarse-grain loops, thus minimizing the number of spurious dependences requiring attention. Second, the system uses dynamic execution analyzers to identify those important loops that are likely to be parallelizable. Third, the SUIF Explorer is the first to apply program slicing to aid programmers in interactive parallelization. The system guides the programmer in the parallelization process using a set of sophisticated visualization techniques. This paper demonstrates the effectiveness of the SUIF Explorer with three case studies. The programmer was able to speed up all three programs by examining only a small fraction of the program and privatizing a few variables. 1. Introduction Exploiting coarse-grain parallelism i...

Array languages such as Fortran 90, HPF and ZPL have many benefits in simplifying array-based computations and expressing data parallelism. However, they can suffer large performance penalties because they introduce intermediate arrays---both at the source level and during the compilation process---which increase memory usage and pollute the cache. Most compilers address this problem by simply scalarizing the array language and relying on a scalar language compiler to perform loop fusion and array contraction. We instead show that there are advantages to performing a form of loop fusion and array contraction at the array level. This paper describes this approach and explains its advantages. Experimental results show that our scheme typically yields runtime improvements of greater than 20% and sometimes up to 400%. In addition, it yields superior memory use when compared against commercial compilers and exhibits comparable memory use when compared with scalar languages. We also explore ...

Abstract—Recently, several experimental studies have been conducted on block data layout in conjunction with tiling as a data transformation technique to improve cache performance. In this paper, we analyze cache and TLB performance of such alternate layouts (including block data layout and Morton layout) when used in conjunction with tiling. We derive a tight lower bound on TLB performance for standard matrix access patterns, and show that block data layout and Morton layout achieve this bound. To improve cache performance, block data layout is used in concert with tiling. Based on the cache and TLB performance analysis, we propose a data block size selection algorithm that finds a tight range for optimal block size. To validate our analysis, we conducted simulations and experiments using tiled matrix multiplication, LU decomposition, and Cholesky factorization. For matrix multiplication, simulation results using UltraSparc II parameters show that tiling and block data layout with a block size given by our block size selection algorithm, reduces up to 93 percent of TLB misses compared with other techniques (copying, padding, etc.). The total miss cost is reduced considerably. Experiments on several platforms (UltraSparc II and III, Alpha, and Pentium III) show that tiling with block data layout achieves up to 50 percent performance improvement over other techniques that use conventional layouts. Morton layout is also analyzed and compared with block data layout. Experimental results show that matrix multiplication using block data layout is up to 15 percent faster than that using Morton data layout. Index Terms—Block data layout, tiling, TLB misses, cache misses, memory hierarchy. 1

In this paper, we propose memory reduction as a new approach to data locality enhancement. Under this approach, we use the compiler to reduce the size of the data repeatedly referenced in a collection of nested loops. Between their reuses, the data will more likely remain in higher-speed memory devices, such as the cache. Specically, we present an optimal algorithm to combine loop shifting, loop fusion and array contraction to reduce the temporary array storage required to execute a collection of loops. When applied to 20 benchmark programs, our technique reduces the memory requirement, counting both the data and the code, by 51% on average. The transformed programs gain a speedup of 1.40 on average, due to the reduced footprint and, consequently, the improved data locality. Categories and Subject Descriptors D.3.4 [Programming Languages]: Processors|compil- ers, optimization General Terms Languages Keywords Array contraction, data locality, loop fusion, loop shifting 1.

While data parallelism is well-suited from algorithmic, architectural, and linguistic considerations to serve as a basis for portable parallel programming, its characteristic fine-grained parallelism makes the efficient implementation of data-parallel languages on MIMD machines a challenging task. The design, implementation, and evaluation of an optimizing compiler are presented for an applicative nested data-parallel language called VCODE targeted at the Encore Multimax, a shared-memory multiprocessor. The source language supports nested aggregate data types; aggregate operations including elementwise forms, scans, reductions, and permutations; and conditionals and recursion for control flow. A small set of graph-theoretic compile-time optimizations reduce the overheads on MIMDmachines in several ways: by increasing the grain size of the output program, by reducing synchronization and storage requirements, and by improving locality of reference. The two key ideas behind these...