A Memory Bandwidth-Efficient Hybrid Radix Sort on GPUs

Sorting is at the core of many database operations, such as index creation, sort-merge joins, and user-requested output sorting. As GPUs are emerging as a promising platform to accelerate various operations, sorting on GPUs becomes a viable endeavour. Over the past few years, several improvements have been proposed for sorting on GPUs, leading to the first radix sort implementations that achieve a sorting rate of over one billion 32-bit keys per second. Yet, state-of-the-art approaches are heavily memory bandwidth-bound, as they require substantially more memory transfers than their CPU-based counterparts. Our work proposes a novel approach that almost halves the amount of memory transfers and, therefore, considerably lifts the memory bandwidth limitation. Being able to sort two gigabytes of eight-byte records in as little as 50 milliseconds, our approach achieves a 2.32-fold improvement over the state-of-the-art GPU-based radix sort for uniform distributions, sustaining a minimum speed-up of no less than a factor of 1.66 for skewed distributions. To address inputs that either do not reside on the GPU or exceed the available device memory, we build on our efficient GPU sorting approach with a pipelined heterogeneous sorting algorithm that mitigates the overhead associated with PCIe data transfers. Comparing the end-to-end sorting performance to the state-of-the-art CPU-based radix sort running 16 threads, our heterogeneous approach achieves a 2.06-fold and a 1.53-fold improvement for sorting 64 GB key-value pairs with a skewed and a uniform distribution, respectively.Comment: 16 pages, accepted at SIGMOD 201

Massiv-Parallele Algorithmen zum Laden von Daten auf Moderner Hardware

While systems face an ever-growing amount of data that needs to be ingested, queried and analysed, processors are seeing only moderate improvements in sequential processing performance. This thesis addresses the fundamental shift towards increasingly parallel processors and contributes multiple massively parallel algorithms to accelerate different stages of the ingestion pipeline, such as data parsing and sorting.Systeme sehen sich mit einer stetig anwachsenden Menge an Daten konfrontiert, die geladen und analysiert, sowie Anfragen darauf bearbeitet werden müssen. Gleichzeitig nimmt die sequentielle Verarbeitungsgeschwindigkeit von Prozessoren nur noch moderat zu. Diese Arbeit adressiert den Wandel hin zu zunehmend parallelen Prozessoren und leistet mit mehreren massiv-parallelen Algorithmen einen Beitrag um unterschiedliche Phasen der Datenverarbeitung wie zum Beispiel Parsing und Sortierung zu beschleunigen

On the programmability of multi-GPU computing systems

Multi-GPU systems are widely used in High Performance Computing environments to accelerate scientific computations. This trend is expected to continue as integrated GPUs will be introduced to processors used in multi-socket servers and servers will pack a higher number of GPUs per node. GPUs are currently connected to the system through the PCI Express interconnect, which provides limited bandwidth (compared to the bandwidth of the memory in GPUs) and it often becomes a bottleneck for performance scalability. Current programming models present GPUs as isolated devices with their own memory, even if they share the host memory with the CPU. Programmers explicitly manage allocations in all GPU memories and use primitives to communicate data between GPUs. Furthermore, programmers are required to use mechanisms such as command queues and inter-GPU synchronization. This explicit model harms the maintainability of the code and introduces new sources for potential errors. The first proposal of this thesis is the HPE model. HPE builds a simple, consistent programming interface based on three major features. (1) All device address spaces are combined with the host address space to form a Unified Virtual Address Space. (2) Programs are provided with an Asymmetric Distributed Shared Memory system for all the GPUs in the system. It allows to allocate memory objects that can be accessed by any GPU or CPU. (3) Every CPU thread can request a data exchange between any two GPUs, through simple memory copy calls. Such a simple interface allows HPE to provide always the optimal implementation; eliminating the need for application code to handle different system topologies. Experimental results show improvements on real applications that range from 5% in compute-bound benchmarks to 2.6x in communication-bound benchmarks. HPE transparently implements sophisticated communication schemes that can deliver up to a 2.9x speedup in I/O device transfers. The second proposal of this thesis is a shared memory programming model that exploits the new GPU capabilities for remote memory accesses to remove the need for explicit communication between GPUs. This model turns a multi-GPU system into a shared memory system with NUMA characteristics. In order to validate the viability of the model we also perform an exhaustive performance analysis of remote memory accesses over PCIe. We show that the unique characteristics of the GPU execution model and memory hierarchy help to hide the costs of remote memory accesses. Results show that PCI Express 3.0 is able to hide the costs of up to a 10% of remote memory accesses depending on the access pattern, while caching of remote memory accesses can have a large performance impact on kernel performance. Finally, we introduce AMGE, a programming interface, compiler support and runtime system that automatically executes computations that are programmed for a single GPU across all the GPUs in the system. The programming interface provides a data type for multidimensional arrays that allows for robust, transparent distribution of arrays across all GPU memories. The compiler extracts the dimensionality information from the type of each array, and is able to determine the access pattern in each dimension of the array. The runtime system uses the compiler-provided information to automatically choose the best computation and data distribution configuration to minimize inter-GPU communication and memory footprint. This model effectively frees programmers from the task of decomposing and distributing computation and data to exploit several GPUs. AMGE achieves almost linear speedups for a wide range of dense computation benchmarks on a real 4-GPU system with an interconnect with moderate bandwidth. We show that irregular computations can also benefit from AMGE, too.Los sistemas multi-GPU son muy comúnmente utilizados en entornos de computación de altas prestaciones para acelerar cálculos científicos. Esta tendencia continuará con la introducción de GPUs integradas en los procesadores de los servidores procesador y con una mayor densidad de GPUs por nodo. Las GPUs actualmente se contectan al sistema a través de una interconexión PCI Express, que provee un ancho de banda reducido (comparado con las memorias de las GPUs) y habitualmente se convierte en el cuello de botella para escalar el rendimiento. Los modelos de programación actuales exponen las GPUs como dispositivos aislados con su propia memoria, incluso si comparten la memoria física con la CPU. Los programadores manejan diferentes reservas en todas las memorias de GPU y usan primitivas para comunicar datos entre GPUs. Además, los programadores deben utilizar mecanismos como colas de comandos y sincronicación entre GPUs. Este modelo explícito empeora la programabilidad del código e introduce nuevas fuentes de errores potenciales. La primera propuesta de esta tesis es el modelo HPE. HPE construye una interfaz de programaci ón consistente basada en tres características principales. (1) Todos los espacios de direcciones de los dispositivos son combinados para formar un espacio de direcciones unificado. (2) Los programas usan un sistema asimétrico distribuido de memoria compartida para todas las GPUs del sistema, que permite declarar objetos de memoria que pueden ser accedidos por cualquier GPU o CPU. (3) Cada hilo de ejecución de la CPU puede lanzar un intercambio de datos entre dos GPUs a través de simples llamadas de copia de memoria. Esta interfaz simplificada permite a HPE usar la implementaci ón óptima; sinque la aplicación contemple diferentes topologías de sistema. Los resultados experimentales muestran mejoras en aplicaciones reales que van desde un 5% en aplicaciones limitadas por el cómputo a 2.6x aplicaciones imitadas por la comunicación. HPE implementa sofisticados esquemas de transferencia para dispositivos de E/S que proporcionan mejoras de rendimiento de 2.9x. La segunda propuesta de esta tesis es un modelo de programación basado en memoria compartida que aprovecha las nuevas capacidades acceso remoto de memoria de las GPUs para eliminar la comunicación explícita entre memorias de GPU. Este modelo convierte un sistema multi-GPU en un sistema de memoria compartida con características NUMA. Para validar la viabilidad del modelo realizamos un anlásis exhaustivo del rendimiento los accessos de memoria remotos sobre PCIe. Los resultados muestran que PCI Express 3.0 elimina los costes de hasta un 10% de accesos remotos, dependiendo en el patrón de acceso, mientras que guardar los accesos remotos en memorias cache tiene un gran inpacto en el rendimiento de las computaciones. Finalmente, presentamos AMGE, una interfaz de programación con soporte de compilación y un sistema que ejecuta, de forma automática, computaciones programadas para una única GPU en todas las GPUs del sistema. La interfaz de programación proporciona un tipo de datos para arreglos multidimensionales que permite una distribuci ón transparente y robusta de los datos en todas las memorias de GPU. El compilador extrae la información sobre la dimensionalidad de cada arreglo y puede determinar el patrón de acceso en cada dimensión de forma individual. El sistema utiliza, en tiempo de ejecución, la información del compilador para elegir la mejor descomposición de la computación y los datos para minimizar la comunicación entre GPUs y el uso de memoria. AMGE consigue mejoras de rendimiento que crecen de forma lineal con el número de GPUs para un amplio abanico de computaciones densas en un sistema real con 4 GPUs. También mostramos que las computaciones con patrones irregulares también se pueden beneficiar de AMGE

Comparison based sorting for systems with multiple GPUs

As a basic building block of many applications, sorting algorithms that efficiently run on modern machines are key for the performance of these applications. With the recent shift to using GPUs for general purpose compuing, researches have proposed several sorting algorithms for single-GPU systems. However, some workstations and HPC systems have multiple GPUs, and applications running on them are designed to use all available GPUs in the system. In this paper we present a high performance multi-GPU merge sort algorithm that solves the problem of sorting data distributed across several GPUs. Our merge sort algorithm first sorts the data on each GPU using an existing single-GPU sorting algorithm. Then, a series of merge steps produce a globally sorted array distributed across all the GPUs in the system. This merge phase is enabled by a novel pivot selection algorithm that ensures that merge steps always distribute data evenly among all GPUs. We also present the implementation of our sorting algorithm in CUDA, as well as a novel inter-GPU communication technique that enables this pivot selection algorithm. Experimental results show that an efficient implementation of our algorithm achieves a speed up of 1.9x when running on two GPUs and 3.3x when running on four GPUs, compared to sorting on a single GPU. At the same time, it is able to sort two and four times more records, compared to sorting on one GPU.Peer ReviewedPostprint (published version

Comparison based sorting for systems with multiple GPUs

As a basic building block of many applications, sorting algorithms that efficiently run on modern machines are key for the performance of these applications. With the recent shift to using GPUs for general purpose compuing, researches have proposed several sorting algorithms for single-GPU systems. However, some workstations and HPC systems have multiple GPUs, and applications running on them are designed to use all available GPUs in the system. In this paper we present a high performance multi-GPU merge sort algorithm that solves the problem of sorting data distributed across several GPUs. Our merge sort algorithm first sorts the data on each GPU using an existing single-GPU sorting algorithm. Then, a series of merge steps produce a globally sorted array distributed across all the GPUs in the system. This merge phase is enabled by a novel pivot selection algorithm that ensures that merge steps always distribute data evenly among all GPUs. We also present the implementation of our sorting algorithm in CUDA, as well as a novel inter-GPU communication technique that enables this pivot selection algorithm. Experimental results show that an efficient implementation of our algorithm achieves a speed up of 1.9x when running on two GPUs and 3.3x when running on four GPUs, compared to sorting on a single GPU. At the same time, it is able to sort two and four times more records, compared to sorting on one GPU.Peer Reviewe