Optimization Techniques for Mapping Algorithms and Applications onto CUDA GPU Platforms and CPU-GPU Heterogeneous Platforms

An emerging trend in processor architecture seems to indicate the doubling of the number of cores per chip every two years with same or decreased clock speed. Of particular interest to this thesis is the class of many-core processors, which are becoming more attractive due to their high performance, low cost, and low power consumption. The main goal of this dissertation is to develop optimization techniques for mapping algorithms and applications onto CUDA GPUs and CPU-GPU heterogeneous platforms. The Fast Fourier transform (FFT) constitutes a fundamental tool in computational science and engineering, and hence a GPU-optimized implementation is of paramount importance. We first study the mapping of the 3D FFT onto the recent, CUDA GPUs and develop a new approach that minimizes the number of global memory accesses and overlaps the computations along the different dimensions. We obtain some of the fastest known implementations for the computation of multi-dimensional FFT. We then present a highly multithreaded FFT-based direct Poisson solver that is optimized for the recent NVIDIA GPUs. In addition to the massive multithreading, our algorithm carefully manages the multiple layers of the memory hierarchy so that all global memory accesses are coalesced into 128-bytes device memory transactions. As a result, we have achieved up to 375GFLOPS with a bandwidth of 120GB/s on the GTX 480. We further extend our methodology to deal with CPU-GPU based heterogeneous platforms for the case when the input is too large to fit on the GPU global memory. We develop optimization techniques for memory-bound, and computation-bound application. The main challenge here is to minimize data transfer between the CPU memory and the device memory and to overlap as much as possible these transfers with kernel execution. For memory-bounded applications, we achieve a near-peak effective PCIe bus bandwidth, 9-10GB/s and performance as high as 145 GFLOPS for multi-dimensional FFT computations and for solving the Poisson equation. We extend our CPU-GPU based software pipeline to a computation-bound application-DGEMM, and achieve the illusion of a memory of the CPU memory size and a computation throughput similar to a pure GPU

The Universe at Extreme Scale: Multi-Petaflop Sky Simulation on the BG/Q

Remarkable observational advances have established a compelling cross-validated model of the Universe. Yet, two key pillars of this model -- dark matter and dark energy -- remain mysterious. Sky surveys that map billions of galaxies to explore the `Dark Universe', demand a corresponding extreme-scale simulation capability; the HACC (Hybrid/Hardware Accelerated Cosmology Code) framework has been designed to deliver this level of performance now, and into the future. With its novel algorithmic structure, HACC allows flexible tuning across diverse architectures, including accelerated and multi-core systems. On the IBM BG/Q, HACC attains unprecedented scalable performance -- currently 13.94 PFlops at 69.2% of peak and 90% parallel efficiency on 1,572,864 cores with an equal number of MPI ranks, and a concurrency of 6.3 million. This level of performance was achieved at extreme problem sizes, including a benchmark run with more than 3.6 trillion particles, significantly larger than any cosmological simulation yet performed.Comment: 11 pages, 11 figures, final version of paper for talk presented at SC1

The fast multipole method at exascale

This thesis presents a top to bottom analysis on designing and implementing fast algorithms for current and future systems. We present new analysis, algorithmic techniques, and implementations of the Fast Multipole Method (FMM) for solving N- body problems. We target the FMM because it is broadly applicable to a variety of scientific particle simulations used to study electromagnetic, fluid, and gravitational phenomena, among others. Importantly, the FMM has asymptotically optimal time complexity with guaranteed approximation accuracy. As such, it is among the most attractive solutions for scalable particle simulation on future extreme scale systems. We specifically address two key challenges. The first challenge is how to engineer fast code for today’s platforms. We present the first in-depth study of multicore op- timizations and tuning for FMM, along with a systematic approach for transforming a conventionally-parallelized FMM into a highly-tuned one. We introduce novel opti- mizations that significantly improve the within-node scalability of the FMM, thereby enabling high-performance in the face of multicore and manycore systems. The second challenge is how to understand scalability on future systems. We present a new algorithmic complexity analysis of the FMM that considers both intra- and inter- node communication costs. Using these models, we present results for choosing the optimal algorithmic tuning parameter. This analysis also yields the surprising prediction that although the FMM is largely compute-bound today, and therefore highly scalable on current systems, the trajectory of processor architecture designs, if there are no significant changes could cause it to become communication-bound as early as the year 2015. This prediction suggests the utility of our analysis approach, which directly relates algorithmic and architectural characteristics, for enabling a new kind of highlevel algorithm-architecture co-design. To demonstrate the scientific significance of FMM, we present two applications namely, direct simulation of blood which is a multi-scale multi-physics problem and large-scale biomolecular electrostatics. MoBo (Moving Boundaries) is the infrastruc- ture for the direct numerical simulation of blood. It comprises of two key algorithmic components of which FMM is one. We were able to simulate blood flow using Stoke- sian dynamics on 200,000 cores of Jaguar, a peta-flop system and achieve a sustained performance of 0.7 Petaflop/s. The second application we propose as future work in this thesis is biomolecular electrostatics where we solve for the electrical potential using the boundary-integral formulation discretized with boundary element methods (BEM). The computational kernel in solving the large linear system is dense matrix vector multiply which we propose can be calculated using our scalable FMM. We propose to begin with the two dielectric problem where the electrostatic field is cal- culated using two continuum dielectric medium, the solvent and the molecule. This is only a first step to solving biologically challenging problems which have more than two dielectric medium, ion-exclusion layers, and solvent filled cavities. Finally, given the difficulty in producing high-performance scalable code, productivity is a key concern. Recently, numerical algorithms are being redesigned to take advantage of the architectural features of emerging multicore processors. These new classes of algorithms express fine-grained asynchronous parallelism and hence reduce the cost of synchronization. We performed the first extensive performance study of a recently proposed parallel programming model, called Concurrent Collections (CnC). In CnC, the programmer expresses her computation in terms of application-specific operations, partially-ordered by semantic scheduling constraints. The CnC model is well-suited to expressing asynchronous-parallel algorithms, so we evaluate CnC using two dense linear algebra algorithms in this style for execution on state-of-the-art mul- ticore systems. Our implementations in CnC was able to match and in some cases even exceed competing vendor-tuned and domain specific library codes. We combine these two distinct research efforts by expressing FMM in CnC, our approach tries to marry performance with productivity that will be critical on future systems. Looking forward, we would like to extend this to distributed memory machines, specifically implement FMM in the new distributed CnC, distCnC to express fine-grained paral- lelism which would require significant effort in alternative models.Ph.D

Heterogeneous parallel algorithms for computational fluid dynamics on unstructured meshes

Frontiers of computational fluid dynamics (CFD) are constantly expanding and eagerly demanding more computational resources. Currently, we are experiencing an rapid evolution in the high performance computing systems driven by power consumption constraints. New HPC nodes incorporate accelerators that are used as math co-processors for increasing the throughput and the FLOP per watt ratio. On the other hand, multi-core CPUs have turned into energy efficient system-on-chip architectures. By doing so, the main components of the node are fused and integrated into a single chip reducing the energy costs. Nowadays, several institutions and governments are investing in the research and development of different aspects of HPC that could lead to the next generations of supercomputers. This initiatives have entitled the problem as the exascale challenge. This goal can only be achieved by incorporating major changes in computer architecture, memory design and network interfaces. The CFD community faces an important challenge: keep the pace at the rapid changes in the HPC resources. The codes and formulations need to be re-design in other to exploit the different levels of parallelism and complex memory hierarchies of the new heterogeneous systems. The main characteristics demanded to the new CFD software are: memory awareness, extreme concurrency, modularity and portability. This thesis is devoted to the study of a CFD algorithm re-factoring for the adoption of new technologies. Our application context is the solution of incompressible flows (DNS or LES) on unstructured meshes. The first approach was using GPUs for accelerating the Poisson solver, that is the most computational intensive part of our application. The positive results obtained in this first step motivated us to port the complete time integration phase of our application. This requires a major redesign of the code. We propose a portable implementation model for CFD applications. The main idea was substituting stencil data structures and kernels by algebraic storage formats and operators. By doing so, the algorithm was restructured into a minimal set of algebraic operations. The implementation strategy consisted in the creation of a low-level algebraic layer for computations on CPUs and GPUs, and a high-level user-friendly discretization layer for CPUs that is fully localized at the preprocessing stage where performance does not play an important role. As a result, at the time-integration phase the code relies only on three algebraic kernels: sparse-matrix-vector product (SpMV), linear combination of two vectors (AXPY) and dot product (DOT). Such a simple set of basic linear algebra operations naturally provides the desired portability to any computing architecture. Special attention was paid at the development of data structures compatibles with the stream processing model. A detailed performance analysis was studied in both sequential and parallel execution engaging up to 128 GPUs in a hybrid CPU/GPU supercomputer. Moreover, we tested the portable implementation model of TermoFluids code in the Mont-Blanc mobile-based supercomputer. The re-design of the kernels exploits a heterogeneous execution model using both computing devices CPU and GPU of the ARM-based nodes. The load balancing between the two computing devices exploits a tabu search strategy that tunes the workload distribution during the preprocessing stage. A comparison of the Mont-Blanc prototypes with high-end supercomputers in terms of the achieved net performance and energy consumption provided some guidelines of the behavior of CFD applications in ARM-based architectures. Finally, we present a memory aware auto-tuned Poisson solver for problems with one Fourier diagonalizable direction. This work was developed and tested in the BlueGene/Q Vesta supercomputer, and aims at demonstrating the relevance of vectorization and memory awareness for fully exploiting the modern energy efficient CPUs.Las fronteras de la dinámica de fluidos computacional (CFD) están en constante expansión y demandan más y más recursos computacionales. Actualmente, estamos experimentando una evolución en los sistemas de computación de alto rendimiento (HPC) impulsado por restricciones de consumo de energía. Los nuevos nodos HPC incorporan aceleradores que se utilizan como co-procesadores para incrementar el rendimiento y la relación FLOP por vatio. Por otro lado, CPUs multi-core se han convertido en arquitecturas system-on-chip. Hoy en día, varias instituciones y gobiernos están invirtiendo en la investigación y desarrollo de los diferentes aspectos de HPC que podrían llevar a las próximas generaciones de superordenadores. Estas iniciativas han titulado el problema como el "exascale challenge". Este objetivo sólo puede lograrse mediante la incorporación de cambios importantes en: la arquitectura de ordenador, diseño de la memoria y las interfaces de red. La comunidad de CFD se enfrenta a un reto importante: mantener el ritmo a los rápidos cambios en las infraestructuras de HPC. Los códigos y formulaciones necesitan ser rediseñados para explotar los diferentes niveles de paralelismo y complejas jerarquías de memoria de los nuevos sistemas heterogéneos. Las principales características exigidas al nuevo software CFD son: estructuras de datos, la concurrencia extrema, modularidad y portabilidad. Esta tesis está dedicada al estudio de un modelo de implementation CFD para la adopción de nuevas tecnologías. Nuestro contexto de aplicación es la solución de los flujos incompresibles (DNS o LES) en mallas no estructuradas. El primer enfoque se basó en utilizar GPUs para acelerar el solver de Poisson. Los resultados positivos obtenidos en este primer paso nos motivaron a la portabilidad completa de la fase de integración temporal de nuestra aplicación. Esto requiere un importante rediseño del código. Proponemos un modelo de implementacion portable para aplicaciones de CFD. La idea principal es sustituir las estructuras de datos de los stencils y kernels por formatos de almacenamiento algebraicos y operadores. La estrategia de implementación consistió en la creación de una capa algebraica de bajo nivel para los cálculos de CPU y GPU, y una capa de discretización fácil de usar de alto nivel para las CPU. Como resultado, la fase de integración temporal del código se basa sólo en tres funciones algebraicas: producto de una matriz dispersa con un vector (SPMV), combinación lineal de dos vectores (AXPY) y producto escalar (DOT). Además, se prestó especial atención en el desarrollo de estructuras de datos compatibles con el modelo stream processing. Un análisis detallado de rendimiento se ha estudiado tanto en ejecución secuencial y paralela utilizando hasta 128 GPUs en un superordenador híbrido CPU / GPU. Por otra parte, hemos probado el nuevo modelo de TermoFluids en el superordenador Mont-Blanc basado en tecnología móvil. El rediseño de las funciones explota un modelo de ejecución heterogénea utilizando tanto la CPU y la GPU de los nodos basados en arquitectura ARM. El equilibrio de carga entre las dos unidades de cálculo aprovecha una estrategia de búsqueda tabú que sintoniza la distribución de carga de trabajo durante la etapa de preprocesamiento. Una comparación de los prototipos Mont-Blanc con superordenadores de alta gama en términos de rendimiento y consumo de energía nos proporcionó algunas pautas del comportamiento de las aplicaciones CFD en arquitecturas basadas en ARM. Por último, se presenta una estructura de datos auto-sintonizada para el solver de Poisson en problemas con una dirección diagonalizable mediante una descomposicion de Fourier. Este trabajo fue desarrollado y probado en la superordenador BlueGene / Q Vesta, y tiene por objeto demostrar la relevancia de vectorización y las estructuras de datos para aprovechar plenamente las CPUs de los superodenadores modernos