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

Interactive Data Exploration with Smart Drill-Down

We present {\em smart drill-down}, an operator for interactively exploring a relational table to discover and summarize "interesting" groups of tuples. Each group of tuples is described by a {\em rule}. For instance, the rule $(a, b, \star, 1000)$ tells us that there are a thousand tuples with value $a$ in the first column and $b$ in the second column (and any value in the third column). Smart drill-down presents an analyst with a list of rules that together describe interesting aspects of the table. The analyst can tailor the definition of interesting, and can interactively apply smart drill-down on an existing rule to explore that part of the table. We demonstrate that the underlying optimization problems are {\sc NP-Hard}, and describe an algorithm for finding the approximately optimal list of rules to display when the user uses a smart drill-down, and a dynamic sampling scheme for efficiently interacting with large tables. Finally, we perform experiments on real datasets on our experimental prototype to demonstrate the usefulness of smart drill-down and study the performance of our algorithms

Autotuning wavefront patterns for heterogeneous architectures

Manual tuning of applications for heterogeneous parallel systems is tedious and complex. Optimizations are often not portable, and the whole process must be repeated when moving to a new system, or sometimes even to a different problem size. Pattern based parallel programming models were originally designed to provide programmers with an abstract layer, hiding tedious parallel boilerplate code, and allowing a focus on only application specific issues. However, the constrained algorithmic model associated with each pattern also enables the creation of pattern-specific optimization strategies. These can capture more complex variations than would be accessible by analysis of equivalent unstructured source code. These variations create complex optimization spaces. Machine learning offers well established techniques for exploring such spaces. In this thesis we use machine learning to create autotuning strategies for heterogeneous parallel implementations of applications which follow the wavefront pattern. In a wavefront, computation starts from one corner of the problem grid and proceeds diagonally like a wave to the opposite corner in either two or three dimensions. Our framework partitions and optimizes the work created by these applications across systems comprising multicore CPUs and multiple GPU accelerators. The tuning opportunities for a wavefront include controlling the amount of computation to be offloaded onto GPU accelerators, choosing the number of CPU and GPU threads to process tasks, tiling for both CPU and GPU memory structures, and trading redundant halo computation against communication for multiple GPUs. Our exhaustive search of the problem space shows that these parameters are very sensitive to the combination of architecture, wavefront instance and problem size. We design and investigate a family of autotuning strategies, targeting single and multiple CPU + GPU systems, and both two and three dimensional wavefront instances. These yield an average of 87% of the performance found by offline exhaustive search, with up to 99% in some cases

Tuning the Computational Effort: An Adaptive Accuracy-aware Approach Across System Layers

This thesis introduces a novel methodology to realize accuracy-aware systems, which will help designers integrate accuracy awareness into their systems. It proposes an adaptive accuracy-aware approach across system layers that addresses current challenges in that domain, combining and tuning accuracy-aware methods on different system layers. To widen the scope of accuracy-aware computing including approximate computing for other domains, this thesis presents innovative accuracy-aware methods and techniques for different system layers. The required tuning of the accuracy-aware methods is integrated into a configuration layer that tunes the available knobs of the accuracy-aware methods integrated into a system

Automated Compilation Framework for Scratchpad-based Real-Time Systems

ScratchPad Memory (SPM) is highly adopted in real-time systems as it exhibits a predictable behaviour. SPM is software-managed by explicitly inserting instructions to move code and data transfers between the SPM and the main memory. However, it is a tedious job to decide how to manage the SPM and to manually modify the code to insert memory transfers. Hence, an automated compilation tool is essential to efficiently utilize the SPM. Another key problem with SPM is the latency suffered by the system due to memory transfers. Hiding this latency is important for high-performance systems. In this thesis, we address the problems of managing SPM and reducing the impact of memory latency. To realize the automation of our work, we develop a compilation framework based on the LLVM compiler to analyze and transform the program code. We exploit our framework to improve the performance of the execution of single and multi-tasks in real-time systems. For the single task execution, Worst-Case Execution Time (WCET) is of great importance to assure correct and safe behaviour of the system. So, we propose a WCET-driven allocation technique for data SPM that employs software prefetching to efficiently manage the SPM and to overlap the memory transfer and the task execution in a predictable way. On the other hand, multi-tasking requires the system to be schedulable such that all the tasks can meet their timing requirements. However, executing multiple tasks on a multi-processor platform suffers from the contention of the accesses to the shared main memory. To avoid the contention, several scheduling techniques adopted the 3-phase execution model which executes the task as a sequence of memory and computation phases. This provides the means to avoid the contention as well as to hide the memory latency by using a Direct Memory Access (DMA) engine. Executing memory transfers using the DMA allows overlapping the memory transfers with the computations on the processor. Using the 3-phase model in systems with limited sizes of local SPM may necessitate a segmentation of the task. Automating the segmentation process is necessary especially for systems with large task sets. Hence, we propose a set of efficient segmentation algorithms that follow the 3-phase execution model. The application of these algorithms shows a significant improvement in the system schedulability. For our segmentation algorithms to be more applicable, we extend the 3-phase model to allow programs with multiple paths represented as conditional Directed Acyclic Graphs (DAGs), unlike the previous works that targeted sequential programs. We also introduce a multi-steaming model to exploit the benefits of prefetching by overlapping the memory and computation phases of the same task, which was not allowed in the previous approaches. By combining the automated compilation with the proposed algorithms, we are able to achieve our goal to efficiently manage data SPM in real-time systems

Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization

International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM