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

Split Tiling for GPUs: Automatic Parallelization Using Trapezoidal Tiles to Reconcile Parallelism and Locality, avoiding Divergence and Load Imbalance

International audienceTiling is a key technology to increase data reuse in computation kernels. For computations structured as one sequential outer "time" loop enclosing a set of parallel inner loops, the option of tiling only the parallel inner loops is generally not profitable because it does not enable enough data reuse. To combine parallelism and locality, several tiling algorithms propose to tile the time loop together with one or more of the parallel inner loops. However, all these algorithms have some limitations: they are either limited to special computation patterns, require the redundant execution of certain iterations (overlapped tiling), or require the use of wavefront parallelism which makes the parallel workload unbalanced. One approach to tiling that addresses most of these issues is split tiling, where tiles are subdivided into a sequence of trapezoidal computation steps. In this paper, we develop an approach to generate split tiled code for GPUs in the PPCG polyhedral code generator. We propose a generic algorithm to calculate an affine schedule and index-set splitting that enable us to perform tiling for locality and synchronization avoidance, while simultaneously maintaining parallelism, without the need for skewing or redundant computations. Our algorithm performs split tiling for an arbitrary number of dimensions and without the need to construct any large integer linear programming problem. The method and its implementation are evaluated on standard stencil kernels and compared with a state-of-the-art polyhedral compiler and with a domain-specific stencil compiler, both targeting CUDA GPUs

Tiling Optimization For Nested Loops On Gpus

Optimizing nested loops has been considered as an important topic and widely studied in parallel programming. With the development of GPU architectures, the performance of these computations can be significantly boosted with the massively parallel hardware. General matrix-matrix multiplication is a typical example where executing such an algorithm on GPUs outperforms the performance obtained on other multicore CPUs. However, achieving ideal performance on GPUs usually requires a lot of human effort to manage the massively parallel computation resources. Therefore, the efficient implementation of optimizing nested loops on GPUs became a popular topic in recent years. We present our work based on the tiling strategy in this dissertation to address three kinds of popular problems. Different kinds of computations bring in different latency issues where dependencies in the computation may result in insufficient parallelism and the performance of computations without dependencies may be degraded due to intensive memory accesses. In this thesis, we tackle the challenges for each kind of problem and believe that other computations performed in nested loops can also benefit from the presented techniques. We improve a parallel approximation algorithm for the problem of scheduling jobs on parallel identical machines to minimize makespan with a high-dimensional tiling method. The algorithm is designed and optimized for solving this kind of problem efficiently on GPUs. Because the algorithm is based on a higher-dimensional dynamic programming approach, where dimensionality refers to the number of variables in the dynamic programming equation characterizing the problem, the existing implementation suffers from the pain of dimensionality and cannot fully utilize GPU resources. We design a novel data-partitioning technique to accelerate the higher-dimensional dynamic programming component of the algorithm. Both the load imbalance and exceeding memory capacity issues are addressed in our GPU solution. We present performance results to demonstrate how our proposed design improves the GPU utilization and makes it possible to solve large higher-dimensional dynamic programming problems within the limited GPU memory. Experimental results show that the GPU implementation achieves up to 25X speedup compared to the best existing OpenMP implementation. In addition, we focus on optimizing wavefront parallelism on GPUs. Wavefront parallelism is a well-known technique for exploiting the concurrency of applications that execute nested loops with uniform data dependencies. Recent research on such applications, which range from sequence alignment tools to partial differential equation solvers, has used GPUs to benefit from the massively parallel computing resources. Wavefront parallelism faces the load imbalance issue because the parallelism is passing along the diagonal. The tiling method has been introduced as a popular solution to address this issue. However, the use of hyperplane tiles increases the cost of synchronization and leads to poor data locality. In this paper, we present a highly optimized implementation of the wavefront parallelism technique that harnesses the GPU architecture. A balanced workload and maximum resource utilization are achieved with an extremely low synchronization overhead. We design the kernel configuration to significantly reduce the minimum number of synchronizations required and also introduce an inter-block lock to minimize the overhead of each synchronization. We evaluate the performance of our proposed technique for four different applications: Sequence Alignment, Edit Distance, Summed-Area Table, and 2DSOR. The performance results demonstrate that our method achieves speedups of up to six times compared to the previous best-known hyperplane tiling-based GPU implementation. Finally, we extend the hyperplane tiling to high order 2D stencil computations. Unlike wavefront parallelism that has dependence in the spatial dimension, dependence remains only across two adjacent time steps along the temporal dimension in stencil computations. Even if the no-dependence property significantly increases the parallelism obtained in the spatial dimensions, full parallelism may not be efficient on GPUs. Due to the limited cache capacity owned by each streaming multiprocessor, full parallelism can be obtained on global memory only, which has high latency to access. Therefore, the tiling technique can be applied to improve the memory efficiency by caching the small tiled blocks. Because the widely studied tiling methods, like overlapped tiling and split tiling, have considerable computation overhead caused by load imbalance or extra operations, we propose a time skewed tiling method, which is designed upon the GPU architecture. We work around the serialized computation issue and coordinate the intra-tile parallelism and inter-tile parallelism to minimize the load imbalance caused by pipelined processing. Moreover, we address the high-order stencil computations in our development, which has not been comprehensively studied. The proposed method achieves up to 3.5X performance improvement when the stencil computation is performed on a Moore neighborhood pattern

Loop parallelization automation for graphics processing units

A technology that allows extending GPU capabilities to deal with data volumes that outfit internal GPU’s memory capacity is proposed. It involves loop tiling and data serialization and can be applied to utilize clusters consisting of several GPUs. Applicability criterion is specified and a semi-automatic proof-of-concept software tool is implemented. The experiment to demonstrate the feasibility of the proposed technology is described

Polyhedral+Dataflow Graphs

This research presents an intermediate compiler representation that is designed for optimization, and emphasizes the temporary storage requirements and execution schedule of a given computation to guide optimization decisions. The representation is expressed as a dataflow graph that describes computational statements and data mappings within the polyhedral compilation model. The targeted applications include both the regular and irregular scientific domains. The intermediate representation can be integrated into existing compiler infrastructures. A specification language implemented as a domain specific language in C++ describes the graph components and the transformations that can be applied. The visual representation allows users to reason about optimizations. Graph variants can be translated into source code or other representation. The language, intermediate representation, and associated transformations have been applied to improve the performance of differential equation solvers, or sparse matrix operations, tensor decomposition, and structured multigrid methods

Tools for efficient Deep Learning

In the era of Deep Learning (DL), there is a fast-growing demand for building and deploying Deep Neural Networks (DNNs) on various platforms. This thesis proposes five tools to address the challenges for designing DNNs that are efficient in time, in resources and in power consumption. We first present Aegis and SPGC to address the challenges in improving the memory efficiency of DL training and inference. Aegis makes mixed precision training (MPT) stabler by layer-wise gradient scaling. Empirical experiments show that Aegis can improve MPT accuracy by at most 4\%. SPGC focuses on structured pruning: replacing standard convolution with group convolution (GConv) to avoid irregular sparsity. SPGC formulates GConv pruning as a channel permutation problem and proposes a novel heuristic polynomial-time algorithm. Common DNNs pruned by SPGC have maximally 1\% higher accuracy than prior work. This thesis also addresses the challenges lying in the gap between DNN descriptions and executables by Polygeist for software and POLSCA for hardware. Many novel techniques, e.g. statement splitting and memory partitioning, are explored and used to expand polyhedral optimisation. Polygeist can speed up software execution in sequential and parallel by 2.53 and 9.47 times on Polybench/C. POLSCA achieves 1.5 times speedup over hardware designs directly generated from high-level synthesis on Polybench/C. Moreover, this thesis presents Deacon, a framework that generates FPGA-based DNN accelerators of streaming architectures with advanced pipelining techniques to address the challenges from heterogeneous convolution and residual connections. Deacon provides fine-grained pipelining, graph-level optimisation, and heuristic exploration by graph colouring. Compared with prior designs, Deacon shows resource/power consumption efficiency improvement of 1.2x/3.5x for MobileNets and 1.0x/2.8x for SqueezeNets. All these tools are open source, some of which have already gained public engagement. We believe they can make efficient deep learning applications easier to build and deploy.Open Acces

Performance and Memory Space Optimizations for Embedded Systems

Embedded systems have three common principles: real-time performance, low power consumption, and low price (limited hardware). Embedded computers use chip multiprocessors (CMPs) to meet these expectations. However, one of the major problems is lack of efficient software support for CMPs; in particular, automated code parallelizers are needed. The aim of this study is to explore various ways to increase performance, as well as reducing resource usage and energy consumption for embedded systems. We use code restructuring, loop scheduling, data transformation, code and data placement, and scratch-pad memory (SPM) management as our tools in different embedded system scenarios. The majority of our work is focused on loop scheduling. Main contributions of our work are: We propose a memory saving strategy that exploits the value locality in array data by storing arrays in a compressed form. Based on the compressed forms of the input arrays, our approach automatically determines the compressed forms of the output arrays and also automatically restructures the code. We propose and evaluate a compiler-directed code scheduling scheme, which considers both parallelism and data locality. It analyzes the code using a locality parallelism graph representation, and assigns the nodes of this graph to processors.We also introduce an Integer Linear Programming based formulation of the scheduling problem. We propose a compiler-based SPM conscious loop scheduling strategy for array/loop based embedded applications. The method is to distribute loop iterations across parallel processors in an SPM-conscious manner. The compiler identifies potential SPM hits and misses, and distributes loop iterations such that the processors have close execution times. We present an SPM management technique using Markov chain based data access. We propose a compiler directed integrated code and data placement scheme for 2-D mesh based CMP architectures. Using a Code-Data Affinity Graph (CDAG) to represent the relationship between loop iterations and array data, it assigns the sets of loop iterations to processing cores and sets of data blocks to on-chip memories. We present a memory bank aware dynamic loop scheduling scheme for array intensive applications.The goal is to minimize the number of memory banks needed for executing the group of loop iterations

Un framework pour l'exécution efficace d'applications sur GPU et CPU+GPU

Technological limitations faced by the semi-conductor manufacturers in the early 2000's restricted the increase in performance of the sequential computation units. Nowadays, the trend is to increase the number of processor cores per socket and to progressively use the GPU cards for highly parallel computations. Complexity of the recent architectures makes it difficult to statically predict the performance of a program. We describe a reliable and accurate parallel loop nests execution time prediction method on GPUs based on three stages: static code generation, offline profiling, and online prediction. In addition, we present two techniques to fully exploit the computing resources at disposal on a system. The first technique consists in jointly using CPU and GPU for executing a code. In order to achieve higher performance, it is mandatory to consider load balance, in particular by predicting execution time. The runtime uses the profiling results and the scheduler computes the execution times and adjusts the load distributed to the processors. The second technique, puts CPU and GPU in a competition: instances of the considered code are simultaneously executed on CPU and GPU. The winner of the competition notifies its completion to the other instance, implying the termination of the latter.Les verrous technologiques rencontrés par les fabricants de semi-conducteurs au début des années deux-mille ont abrogé la flambée des performances des unités de calculs séquentielles. La tendance actuelle est à la multiplication du nombre de cœurs de processeur par socket et à l'utilisation progressive des cartes GPU pour des calculs hautement parallèles. La complexité des architectures récentes rend difficile l'estimation statique des performances d'un programme. Nous décrivons une méthode fiable et précise de prédiction du temps d'exécution de nids de boucles parallèles sur GPU basée sur trois étapes : la génération de code, le profilage offline et la prédiction online. En outre, nous présentons deux techniques pour exploiter l'ensemble des ressources disponibles d'un système pour la performance. La première consiste en l'utilisation conjointe des CPUs et GPUs pour l'exécution d'un code. Afin de préserver les performances il est nécessaire de considérer la répartition de charge, notamment en prédisant les temps d'exécution. Le runtime utilise les résultats du profilage et un ordonnanceur calcule des temps d'exécution et ajuste la charge distribuée aux processeurs. La seconde technique présentée met le CPU et le GPU en compétition : des instances du code cible sont exécutées simultanément sur CPU et GPU. Le vainqueur de la compétition notifie sa complétion à l'autre instance, impliquant son arrêt

Doctor of Philosophy in Computer Science

dissertationStencil computations are operations on structured grids. They are frequently found in partial differential equation solvers, making their performance critical to a range of scientific applications. On modern architectures where data movement costs dominate computation, optimizing stencil computations is a challenging task. Typically, domain scientists must reduce and orchestrate data movement to tackle the memory bandwidth and latency bottlenecks. Furthermore, optimized code must map efficiently to ever increasing parallelism on a chip. This dissertation studies several stencils with varying arithmetic intensities, thus requiring contrasting optimization strategies. Stencils traditionally have low arithmetic intensity, making their performance limited by memory bandwidth. Contemporary higher-order stencils are designed to require smaller grids, hence less memory, but are bound by increased floating-point operations. This dissertation develops communication-avoiding optimizations to reduce data movement in memory-bound stencils. For higher-order stencils, a novel transformation, partial sums, is designed to reduce the number of floating-point operations and improve register reuse. These optimizations are implemented in a compiler framework, which is further extended to generate parallel code targeting multicores and graphics processor units (GPUs). The augmented compiler framework is then combined with autotuning to productively address stencil optimization challenges. Autotuning explores a search space of possible implementations of a computation to find the optimal code for an execution context. In this dissertation, autotuning is used to compose sequences of optimizations to drive the augmented compiler framework. This compiler-directed autotuning approach is used to optimize stencils in the context of a linear solver, Geometric Multigrid (GMG). GMG uses sequences of stencil computations, and presents greater optimization challenges than isolated stencils, as interactions between stencils must also be considered. The efficacy of our approach is demonstrated by comparing the performance of generated code against manually tuned code, over commercial compiler-generated code, and against analytic performance bounds. Generated code outperforms manually optimized codes on multicores and GPUs. Against Intel's compiler on multicores, generated code achieves up to 4x speedup for stencils, and 3x for the solver. On GPUs, generated code achieves 80% of an analytically computed performance bound