Computational Physics on Graphics Processing Units

The use of graphics processing units for scientific computations is an emerging strategy that can significantly speed up various different algorithms. In this review, we discuss advances made in the field of computational physics, focusing on classical molecular dynamics, and on quantum simulations for electronic structure calculations using the density functional theory, wave function techniques, and quantum field theory.Comment: Proceedings of the 11th International Conference, PARA 2012, Helsinki, Finland, June 10-13, 201

Performance and power optimizations in chip multiprocessors for throughput-aware computation

The so-called "power (or power density) wall" has caused core frequency (and single-thread performance) to slow down, giving rise to the era of multi-core/multi-thread processors. For example, the IBM POWER4 processor, released in 2001, incorporated two single-thread cores into the same chip. In 2010, IBM released the POWER7 processor with eight 4-thread cores in the same chip, for a total capacity of 32 execution contexts. The ever increasing number of cores and threads gives rise to new opportunities and challenges for software and hardware architects. At software level, applications can benefit from the abundant number of execution contexts to boost throughput. But this challenges programmers to create highly-parallel applications and operating systems capable of scheduling them correctly. At hardware level, the increasing core and thread count puts pressure on the memory interface, because memory bandwidth grows at a slower pace ---phenomenon known as the "bandwidth (or memory) wall". In addition to memory bandwidth issues, chip power consumption rises due to manufacturers' difficulty to lower operating voltages sufficiently every processor generation. This thesis presents innovations to improve bandwidth and power consumption in chip multiprocessors (CMPs) for throughput-aware computation: a bandwidth-optimized last-level cache (LLC), a bandwidth-optimized vector register file, and a power/performance-aware thread placement heuristic. In contrast to state-of-the-art LLC designs, our organization avoids data replication and, hence, does not require keeping data coherent. Instead, the address space is statically distributed all over the LLC (in a fine-grained interleaving fashion). The absence of data replication increases the cache effective capacity, which results in better hit rates and higher bandwidth compared to a coherent LLC. We use double buffering to hide the extra access latency due to the lack of data replication. The proposed vector register file is composed of thousands of registers and organized as an aggregation of banks. We leverage such organization to attach small special-function "local computation elements" (LCEs) to each bank. This approach ---referred to as the "processor-in-regfile" (PIR) strategy--- overcomes the limited number of register file ports. Because each LCE is a SIMD computation element and all of them can proceed concurrently, the PIR strategy constitutes a highly-parallel super-wide-SIMD device (ideal for throughput-aware computation). Finally, we present a heuristic to reduce chip power consumption by dynamically placing software (application) threads across hardware (physical) threads. The heuristic gathers chip-level power and performance information at runtime to infer characteristics of the applications being executed. For example, if an application's threads share data, the heuristic may decide to place them in fewer cores to favor inter-thread data sharing and communication. In such case, the number of active cores decreases, which is a good opportunity to switch off the unused cores to save power. It is increasingly harder to find bulletproof (micro-)architectural solutions for the bandwidth and power scalability limitations in CMPs. Consequently, we think that architects should attack those problems from different flanks simultaneously, with complementary innovations. This thesis contributes with a battery of solutions to alleviate those problems in the context of throughput-aware computation: 1) proposing a bandwidth-optimized LLC; 2) proposing a bandwidth-optimized register file organization; and 3) proposing a simple technique to improve power-performance efficiency.El excesivo consumo de potencia de los procesadores actuales ha desacelerado el incremento en la frecuencia operativa de los mismos para dar lugar a la era de los procesadores con múltiples núcleos y múltiples hilos de ejecución. Por ejemplo, el procesador POWER7 de IBM, lanzado al mercado en 2010, incorpora ocho núcleos en el mismo chip, con cuatro hilos de ejecución por núcleo. Esto da lugar a nuevas oportunidades y desafíos para los arquitectos de software y hardware. A nivel de software, las aplicaciones pueden beneficiarse del abundante número de núcleos e hilos de ejecución para aumentar el rendimiento. Pero esto obliga a los programadores a crear aplicaciones altamente paralelas y sistemas operativos capaces de planificar correctamente la ejecución de las mismas. A nivel de hardware, el creciente número de núcleos e hilos de ejecución ejerce presión sobre la interfaz de memoria, ya que el ancho de banda de memoria crece a un ritmo más lento. Además de los problemas de ancho de banda de memoria, el consumo de energía del chip se eleva debido a la dificultad de los fabricantes para reducir suficientemente los voltajes de operación entre generaciones de procesadores. Esta tesis presenta innovaciones para mejorar el ancho de banda y consumo de energía en procesadores multinúcleo en el ámbito de la computación orientada a rendimiento ("throughput-aware computation"): una memoria caché de último nivel ("last-level cache" o LLC) optimizada para ancho de banda, un banco de registros vectorial optimizado para ancho de banda, y una heurística para planificar la ejecución de aplicaciones paralelas orientada a mejorar la eficiencia del consumo de potencia y desempeño. En contraste con los diseños de LLC de última generación, nuestra organización evita la duplicación de datos y, por tanto, no requiere de técnicas de coherencia. El espacio de direcciones de memoria se distribuye estáticamente en la LLC con un entrelazado de grano fino. La ausencia de replicación de datos aumenta la capacidad efectiva de la memoria caché, lo que se traduce en mejores tasas de acierto y mayor ancho de banda en comparación con una LLC coherente. Utilizamos la técnica de "doble buffering" para ocultar la latencia adicional necesaria para acceder a datos remotos. El banco de registros vectorial propuesto se compone de miles de registros y se organiza como una agregación de bancos. Incorporamos a cada banco una pequeña unidad de cómputo de propósito especial ("local computation element" o LCE). Este enfoque ---que llamamos "computación en banco de registros"--- permite superar el número limitado de puertos en el banco de registros. Debido a que cada LCE es una unidad de cómputo con soporte SIMD ("single instruction, multiple data") y todas ellas pueden proceder de forma concurrente, la estrategia de "computación en banco de registros" constituye un dispositivo SIMD altamente paralelo. Por último, presentamos una heurística para planificar la ejecución de aplicaciones paralelas orientada a reducir el consumo de energía del chip, colocando dinámicamente los hilos de ejecución a nivel de software entre los hilos de ejecución a nivel de hardware. La heurística obtiene, en tiempo de ejecución, información de consumo de potencia y desempeño del chip para inferir las características de las aplicaciones. Por ejemplo, si los hilos de ejecución a nivel de software comparten datos significativamente, la heurística puede decidir colocarlos en un menor número de núcleos para favorecer el intercambio de datos entre ellos. En tal caso, los núcleos no utilizados se pueden apagar para ahorrar energía. Cada vez es más difícil encontrar soluciones de arquitectura "a prueba de balas" para resolver las limitaciones de escalabilidad de los procesadores actuales. En consecuencia, creemos que los arquitectos deben atacar dichos problemas desde diferentes flancos simultáneamente, con innovaciones complementarias

High Performance P3M N-body code: CUBEP3M

This paper presents CUBEP3M, a publicly-available high performance cosmological N-body code and describes many utilities and extensions that have been added to the standard package. These include a memory-light runtime SO halo finder, a non-Gaussian initial conditions generator, and a system of unique particle identification. CUBEP3M is fast, its accuracy is tuneable to optimize speed or memory, and has been run on more than 27,000 cores, achieving within a factor of two of ideal weak scaling even at this problem size. The code can be run in an extra-lean mode where the peak memory imprint for large runs is as low as 37 bytes per particles, which is almost two times leaner than other widely used N-body codes. However, load imbalances can increase this requirement by a factor of two, such that fast configurations with all the utilities enabled and load imbalances factored in require between 70 and 120 bytes per particles. CUBEP3M is well designed to study large scales cosmological systems, where imbalances are not too large and adaptive time-stepping not essential. It has already been used for a broad number of science applications that require either large samples of non-linear realizations or very large dark matter N-body simulations, including cosmological reionization, halo formation, baryonic acoustic oscillations, weak lensing or non-Gaussian statistics. We discuss the structure, the accuracy, known systematic effects and the scaling performance of the code and its utilities, when applicable.Comment: 20 pages, 17 figures, added halo profiles, updated to match MNRAS accepted versio

Implementation Techniques for the Truncated Fourier Transform

We study various algorithms for the Truncated Fourier Transform (TFT) which is a variation of the Discrete Fourier Transform (DFT) that allows one to work with an input vector of arbitrary size without zero padding. After a review of the original algorithms for the forward and inverse TFT introduced by J. van der Hoeven, we consider the variation of D. Harvey as well as that of J. Johnson and L.C. Meng. Both variations are based on Cooley-Tukey like formulas. The former is called strict general radix as it strictly follows the specifications proposed by J. van der Hoeven, while the latter is called relaxed general radix as it requires some zero padding so as to improve data flow which supports full vectorization and parallelization. In this thesis, we report on an implementation of the relaxed general radix forward TFT and a strict general radix inverse TFT. We have three objectives. First, obtaining a software tool generating optimized code forward and inverse TFT, extending the previous work of S. Covanov dedicated to FFT code generation. Second, comparing the practical efficiency of the strict and relaxed general radix schemes. Third, investigating the parallelization of one-dimensional TFT algorithms. Our experimental results show that, in practice, the relaxed general radix forward TFT can reach similar performance (in terms of running time, clock cycles and cache misses) as the optimized FFT code of the BPAS library (on input vectors on which both codes apply without zero padding). Moreover, for an input vector whose size ranges between two consecutive values for which FFT does not require zero padding, our relaxed TFT generated code provides an effective implementation. Unfortunately, the same satisfactory observation does not hold for the strict radix scheme when comparing the inverse TFT and FFT. As for parallelization, here again the relaxed general radix scheme is satisfactory while the strict general radix is not. For instance, w.r.t. to the FFT code, the parallel forward TFT code has a speedup factor of 5.31 and 6.78 for an input vector of size 2^23 and 2^26 respectively

Accelerating Pattern Recognition Algorithms On Parallel Computing Architectures

The move to more parallel computing architectures places more responsibility on the programmer to achieve greater performance. The programmer must now have a greater understanding of the underlying architecture and the inherent algorithmic parallelism. Using parallel computing architectures for exploiting algorithmic parallelism can be a complex task. This dissertation demonstrates various techniques for using parallel computing architectures to exploit algorithmic parallelism. Specifically, three pattern recognition (PR) approaches are examined for acceleration across multiple parallel computing architectures, namely field programmable gate arrays (FPGAs) and general purpose graphical processing units (GPGPUs). Phase-only filter correlation for fingerprint identification was studied as the first PR approach. This approach\u27s sensitivity to angular rotations, scaling, and missing data was surveyed. Additionally, a novel FPGA implementation of this algorithm was created using fixed point computations, deep pipelining, and four computation phases. Communication and computation were overlapped to efficiently process large fingerprint galleries. The FPGA implementation showed approximately a 47 times speedup over a central processing unit (CPU) implementation with negligible impact on precision. For the second PR approach, a spiking neural network (SNN) algorithm for a character recognition application was examined. A novel FPGA implementation of the approach was developed incorporating a scalable modular SNN processing element (PE) to efficiently perform neural computations. The modular SNN PE incorporated streaming memory, fixed point computation, and deep pipelining. This design showed speedups of approximately 3.3 and 8.5 times over CPU implementations for 624 and 9,264 sized neural networks, respectively. Results indicate that the PE design could scale to process larger sized networks easily. Finally for the third PR approach, cellular simultaneous recurrent networks (CSRNs) were investigated for GPGPU acceleration. Particularly, the applications of maze traversal and face recognition were studied. Novel GPGPU implementations were developed employing varying quantities of task-level, data-level, and instruction-level parallelism to achieve efficient runtime performance. Furthermore, the performance of the face recognition application was examined across a heterogeneous cluster of multi-core and GPGPU architectures. A combination of multi-core processors and GPGPUs achieved roughly a 996 times speedup over a single-core CPU implementation. From examining these PR approaches for acceleration, this dissertation presents useful techniques and insight applicable to other algorithms to improve performance when designing a parallel implementation