Chain-based scheduling: Part I - loop transformations and code generation

Chain-based scheduling [1] is an efficient partitioning and scheduling scheme for nested loops on distributed-memory multicomputers. The idea is to take advantage of the regular data dependence structure of a nested loop to overlap and pipeline the communication and computation. Most partitioning and scheduling algorithms proposed for nested loops on multicomputers [1,2,3] are graph algorithms on the iteration space of the nested loop. The graph algorithms for partitioning and scheduling are too expensive (at least O(N), where N is the total number of iterations) to be implemented in parallelizing compilers. Graph algorithms also need large data structures to store the result of the partitioning and scheduling. In this paper, we propose compiler loop transformations and the code generation to generate chain-based parallel codes for nested loops on multicomputers. The cost of the loop transformations is O(nd), where n is the number of nesting loops and d is the number of data dependences. Both n and d are very small in real programs. The loop transformations and code generation for chain-based partitioning and scheduling enable parallelizing compilers to generate parallel codes which contain all partitioning and scheduling information that the parallel processors need at run time

Compiler Optimization Techniques for Scheduling and Reducing Overhead

Exploiting parallelism in loops in programs is an important factor in realizing the potential performance of processors today. This dissertation develops and evaluates several compiler optimizations aimed at improving the performance of loops on processors. An important feature of a class of scientific computing problems is the regularity exhibited by their access patterns. Chapter 2 presents an approach of optimizing the address generation of these problems that results in the following: (i) elimination of redundant arithmetic computation by recognizing and exploiting the presence of common sub-expressions across different iterations in stencil codes; and (ii) conversion of as many array references to scalar accesses as possible, which leads to reduced execution time, decrease in address arithmetic overhead, access to data in registers as opposed to caches, etc. With the advent of VLIW processors, the exploitation of fine-grain instruction-level parallelism has become a major challenge to optimizing compilers. Fine-grain scheduling of inner loops has received a lot of attention, little work has been done in the area of applying it to nested loops. Chapter 3 presents an approach to fine-grain scheduling of nested loops by formulating the problem of finding theminimum iteration initiation interval as one of finding a rational affine schedule for each statement in the body of a perfectly nested loop which is then solved using linear programming. Frequent synchronization on multiprocessors is expensive due to its high cost. Chapter 4 presents a method for eliminating redundant synchronization for nested loops. In nested loops, a dependence may be redundant in only a portion of the iteration space. A characterization of the non-uniformity of the redundancy of a dependence is developed in terms of the relation between the dependences and the shape and size of the iteration space. Exploiting locality is critical for achieving high level of performance on a parallel machine. Chapter 5 presents an approach using the concept of affinity regions to find transformations such that a suitable iteration-to-processor mapping can be found for a sequence of loop nests accessing shared arrays. This not only improves the data locality but significantly reduces communication overhead

Compilation Techniques for High-Performance Embedded Systems with Multiple Processors

Institute for Computing Systems ArchitectureDespite the progress made in developing more advanced compilers for embedded systems, programming of embedded high-performance computing systems based on Digital Signal Processors (DSPs) is still a highly skilled manual task. This is true for single-processor systems, and even more for embedded systems based on multiple DSPs. Compilers often fail to optimise existing DSP codes written in C due to the employed programming style. Parallelisation is hampered by the complex multiple address space memory architecture, which can be found in most commercial multi-DSP configurations. This thesis develops an integrated optimisation and parallelisation strategy that can deal with low-level C codes and produces optimised parallel code for a homogeneous multi-DSP architecture with distributed physical memory and multiple logical address spaces. In a first step, low-level programming idioms are identified and recovered. This enables the application of high-level code and data transformations well-known in the field of scientific computing. Iterative feedback-driven search for “good” transformation sequences is being investigated. A novel approach to parallelisation based on a unified data and loop transformation framework is presented and evaluated. Performance optimisation is achieved through exploitation of data locality on the one hand, and utilisation of DSP-specific architectural features such as Direct Memory Access (DMA) transfers on the other hand. The proposed methodology is evaluated against two benchmark suites (DSPstone & UTDSP) and four different high-performance DSPs, one of which is part of a commercial four processor multi-DSP board also used for evaluation. Experiments confirm the effectiveness of the program recovery techniques as enablers of high-level transformations and automatic parallelisation. Source-to-source transformations of DSP codes yield an average speedup of 2.21 across four different DSP architectures. The parallelisation scheme is – in conjunction with a set of locality optimisations – able to produce linear and even super-linear speedups on a number of relevant DSP kernels and applications

Loop parallelization: revisiting framework of unimodular transformations

The paper extends the framework of linear loop transformations adding a new nonlinear step at the transformation process. The current framework of linear loop transformation cannot identify a significant fraction of parallelism. For this reason, we present a method to complement it with some basic transformations in order to extract the maximum loop parallelism in perfect nested loops with tight recurrences in the dependence graph. The parallelizing algorithm solves the important problem of deciding the set of transformations to apply in order to maximize the degree of parallelism, the number of parallel loops within a loop nest, and presents a way of generating efficient transformed code that exploits coarse grain parallelism on a MIMD systemPeer ReviewedPostprint (published version

Center for Aeronautics and Space Information Sciences

This report summarizes the research done during 1991/92 under the Center for Aeronautics and Space Information Science (CASIS) program. The topics covered are computer architecture, networking, and neural nets

Automatic Parallelization of Tiled Stencil Loop Nests on GPUs

This thesis attempts to design and implement a compiler framework based on the polyhedral model. The compiler automatically parallelizes loop nests; especially stencil kernels, into efficient GPU code by loop tiling transformations which the polyhedral model describes. To enhance parallel performance, we introduce three practically efficient techniques to process different types of loop nests. The experimental results of our compiler framework have demonstrated that these advanced techniques can outperform previous approaches. Firstly, we aim to find efficient tiling transformations without violating data dependences. How to select a tile's shape and size is an open issue that is performance-critical and influenced by GPU's hardware constraints. We propose an approach to determine the tile shapes out of consideration for improving two-level parallelism of GPUs. The new approach finds appropriate tiling hyperplanes by embedding parallelism-enhancing constraints into the polyhedral model to maximize intra-tile, i.e., intra-SM parallelism. This improves the load balance among the streaming processors (SPs), which execute a wavefront of loop iterations within a tile. We eliminate parallelism-hindering false dependences to optimize inter-tile, i.e., inter-SM parallelism. This improves the load balance among the streaming multiprocessors (SMs), which execute a wavefront of tiles. Furthermore, to avoid combinatorial explosion of tile size's configurations, we present a model-driven approach to automating tile size selection that is performance-critical for loop tiling transformations, especially for DOACROSS loop nests. Our tile size selection model accurately estimates the execution times of tiled loop nests running on GPUs. The selected tile sizes lead to the performance results that are close to the best observed for a range of problem sizes tested. Finally, to address the difficulty and low-performance of parallelizing widely used SOR stencil loop nests, we present a new tiled parallel SOR method, called MLSOR, which admits more efficient data-parallel SIMD execution on GPUs. Unlike the previous two approaches that are dependence-preserving, the basic idea is to algorithmically restructure a stencil kernel based on a non-dependence-preserving parallelization scheme to avoid pipelining for higher parallelism. The new approach can be implemented in compilers through a pattern matching pass to optimize SOR-like DOACROSS loop nests on GPUs

Directions in parallel programming: HPF, shared virtual memory and object parallelism in pC++

Fortran and C++ are the dominant programming languages used in scientific computation. Consequently, extensions to these languages are the most popular for programming massively parallel computers. We discuss two such approaches to parallel Fortran and one approach to C++. The High Performance Fortran Forum has designed HPF with the intent of supporting data parallelism on Fortran 90 applications. HPF works by asking the user to help the compiler distribute and align the data structures with the distributed memory modules in the system. Fortran-S takes a different approach in which the data distribution is managed by the operating system and the user provides annotations to indicate parallel control regions. In the case of C++, we look at pC++ which is based on a concurrent aggregate parallel model

Automatic Data and Computation Mapping for Distributed-Memory Machines.

Distributed memory parallel computers offer enormous computation power, scalability and flexibility. However, these machines are difficult to program and this limits their widespread use. An important characteristic of these machines is the difference in the access time for data in local versus non-local memory; non-local memory accesses are much slower than local memory accesses. This is also a characteristic of shared memory machines but to a less degree. Therefore it is essential that as far as possible, the data that needs to be accessed by a processor during the execution of the computation assigned to it reside in its local memory rather than in some other processor\u27s memory. Several research projects have concluded that proper mapping of data is key to realizing the performance potential of distributed memory machines. Current language design efforts such as Fortran D and High Performance Fortran (HPF) are based on this. It is our thesis that for many practical codes, it is possible to derive good mappings through a combination of algorithms and systematic procedures. We view mapping as consisting of wo phases, alignment followed by distribution. For the alignment phase we present three constraint-based methods--one based on a linear programming formulation of the problem; the second formulates the alignment problem as a constrained optimization problem using Lagrange multipliers; the third method uses a heuristic to decide which constraints to leave unsatisfied (based on the penalty of increased communication incurred in doing so) in order to find a mapping. In addressing the distribution phase, we have developed two methods that integrate the placement of computation--loop nests in our case--with the mapping of data. For one distributed dimension, our approach finds the best combination of data and computation mapping that results in low communication overhead; this is done by choosing a loop order that allows message vectorization. In the second method, we introduce the distribution preference graph and the operations on this graph allow us to integrate loop restructuring transformations and data mapping. These techniques produce mappings that have been used in efficient hand-coded implementations of several benchmark codes

Optimization within a Unified Transformation Framework

Programmers typically want to write scientific programs in a high level language with semantics based on a sequential execution model. To execute efficiently on a parallel machine, however, a program typically needs to contain explicit parallelism and possibly explicit communication and synchronization. So, we need compilers to convert programs from the first of these forms to the second. There are two basic choices to be made when parallelizing a program. First, the computations of the program need to be distributed amongst the set of available processors. Second, the computations on each processor need to be ordered. My contribution has been the development of simple mathematical abstractions for representing these choices and the development of new algorithms for making these choices. I have developed a new framework that achieves good performance by minimizing communication between processors, minimizing the time processors spend waiting for messages from other processors, and ordering data accesses so as to exploit the memory hierarchy. This framework can be used by optimizing compilers, as well as by interactive transformation tools. The state of the art for vectorizing compilers is already quite good, but much work remains to bring parallelizing compilers up to the same standard. The main contribution of my work can be summarized as improving this situation by replacing existing ad hoc parallelization techniques with a sound underlying foundation on which future work can be built. (Also cross-referenced as UMIACS-TR-96-93

From ALPHA to imperative code : a transformational compiler for an array based functional language

Practical parallel programming demands that the details of distributing data to processors and inter- processor communication be managed by the compiler. These tasks quickly become too di cult for a programmer to do by hand for all but the simplest parallel programs. Yet, many parallel languages still require the programmer to manage much of the the parallelism. I discuss the synthesis of parallel imperative code from algorithms written in a functional language called Alpha. Alpha is based on systems of a ne recurrence equations and was designed to specify algorithms for regular array architectures. Being a functional language, Alpha implicitly supports the expression of both concurrency and communication. Thus, the programmer is freed from having to explicitly manage the parallelism. Using the information derived from static analysis, Alpha can be transformed into a form suitable for generating imperative parallel code through a series of provably correct program transformations. The kinds of analysis needed to generate e cient code for array-based functional programs are a generalization of dependency analysis, usage analysis, and scheduling techniques used in systolic array synthesis