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

Effective data parallel computing on multicore processors

The rise of chip multiprocessing or the integration of multiple general purpose processing cores on a single chip (multicores), has impacted all computing platforms including high performance, servers, desktops, mobile, and embedded processors. Programmers can no longer expect continued increases in software performance without developing parallel, memory hierarchy friendly software that can effectively exploit the chip level multiprocessing paradigm of multicores. The goal of this dissertation is to demonstrate a design process for data parallel problems that starts with a sequential algorithm and ends with a high performance implementation on a multicore platform. Our design process combines theoretical algorithm analysis with practical optimization techniques. Our target multicores are quad-core processors from Intel and the eight-SPE IBM Cell B.E. Target applications include Matrix Multiplications (MM), Finite Difference Time Domain (FDTD), LU Decomposition (LUD), and Power Flow Solver based on Gauss-Seidel (PFS-GS) algorithms. These applications are popular computation methods in science and engineering problems and are characterized by unit-stride (MM, LUD, and PFS-GS) or 2-point stencil (FDTD) memory access pattern. The main contributions of this dissertation include a cache- and space-efficient algorithm model, integrated data pre-fetching and caching strategies, and in-core optimization techniques. Our multicore efficient implementations of the above described applications outperform nai¨ve parallel implementations by at least 2x and scales well with problem size and with the number of processing cores

Dynamically controlled resource allocation in SMT processors

SMT processors increase performance by executing instructions from several threads simultaneously. These threads use the resources of the processor better by sharing them but, at the same time, threads are competing for these resources. The way critical resources are distributed among threads determines the final performance. Currently, processor resources are distributed among threads as determined by the fetch policy that decides which threads enter the processor to compete for resources. However, current fetch policies only use indirect indicators of resource usage in their decision, which can lead to resource monopolization by a single thread or to resource waste when no thread can use them. Both situations can harm performance and happen, for example, after an L2 cache miss. In this paper, we introduce the concept of dynamic resource control in SMT processors. Using this concept, we propose a novel resource allocation policy for SMT processors. This policy directly monitors the usage of resources by each thread and guarantees that all threads get their fair share of the critical shared resources, avoiding monopolization. We also define a mechanism to allow a thread to borrow resources from another thread if that thread does not require them, thereby reducing resource under-use. Simulation results show that our dynamic resource allocation policy outperforms a static resource allocation policy by 8%, on average. It also improves the best dynamic resource-conscious fetch policies like FLUSH++ by 4%, on average, using the harmonic mean as a metric. This indicates that our policy does not obtain the ILP boost by unfairly running high ILP threads over slow memory-bounded threads. Instead, it achieves a better throughput-fairness balance.Peer ReviewedPostprint (published version

Indexed dependence metadata and its applications in software performance optimisation

To achieve continued performance improvements, modern microprocessor design is tending to concentrate an increasing proportion of hardware on computation units with less automatic management of data movement and extraction of parallelism. As a result, architectures increasingly include multiple computation cores and complicated, software-managed memory hierarchies. Compilers have difficulty characterizing the behaviour of a kernel in a general enough manner to enable automatic generation of efficient code in any but the most straightforward of cases. We propose the concept of indexed dependence metadata to improve application development and mapping onto such architectures. The metadata represent both the iteration space of a kernel and the mapping of that iteration space from a given index to the set of data elements that iteration might use: thus the dependence metadata is indexed by the kernel’s iteration space. This explicit mapping allows the compiler or runtime to optimise the program more efficiently, and improves the program structure for the developer. We argue that this form of explicit interface specification reduces the need for premature, architecture-specific optimisation. It improves program portability, supports intercomponent optimisation and enables generation of efficient data movement code. We offer the following contributions: an introduction to the concept of indexed dependence metadata as a generalisation of stream programming, a demonstration of its advantages in a component programming system, the decoupled access/execute model for C++ programs, and how indexed dependence metadata might be used to improve the programming model for GPU-based designs. Our experimental results with prototype implementations show that indexed dependence metadata supports automatic synthesis of double-buffered data movement for the Cell processor and enables aggressive loop fusion optimisations in image processing, linear algebra and multigrid application case studies

Heterogeneity-awareness in multithreaded multicore processors

During the last decades, Computer Architecture has experienced a great series of revolutionary changes. The increasing transistor count on a single chip has led to some of the main milestones in the field, from the release of the first Superscalar (1965) to the state-of-the-art Multithreaded Multicore Architectures, like the Intel Core i7 (2009).Moore's Law has continued for almost half of a century and is not expected to stop for at least another decade, and perhaps much longer. Moore observed a trend in the process technology advances. So, the number of transistors that can be placed inexpensively on an integrated circuit has increased exponentially, doubling approximately every two years. Nevertheless, having more available transistors can not be always directly translated into having more performance.The complexity of state-of-the-art software has reached heights unthinkable in prior ages, both in terms of the amount of computation and the complexity involved. If we deeply analyze this complexity in software we would realize that software is comprised of smaller execution processes that, although maintaining certain spatial/temporal locality, imply an inherently heterogeneous behavior. That is, during execution time the hardware executes very different portions of software, with huge differences in terms of behavior and hardware requirements. This heterogeneity in the behaviour of the software is not specific of the latest videogame, but it is inherent to software programming itself, since the very beginning of Algorithmics.In this PhD dissertation we deeply analyze the inherent heterogeneity present in software behavior. We identify the main issues and sources of this heterogeneity, that hamper most of the state-of-the-art processor designs from obtaining their maximum potential. Hence, the heterogeneity in software turns most of the current processors, commonly called general-purpose processors, into overdesigned. That is, they have much more hardware resources than really needed to execute the software running on them. This fact would not represent a main problem if we were not concerned on the additional power consumption involved in software computation.The final goal of this PhD dissertation consists in assigning each portion of software exactly the amount of hardware resources really needed to fully exploit its maximal potential; without consuming more energy than the strictly needed. That is, obtaining complexity-effective executions using the inherent heterogeneity in software behavior as steering indicator. Thus, we start deeply analyzing the heterogenous behaviour of the software run on top of general-purpose processors and then matching it on top of a heterogeneously distributed hardware, which explicitly exploit heterogeneous hardware requirements. Only by being heterogeneity-aware in software, and appropriately matching this software heterogeneity on top of hardware heterogeneity, may we effectively obtain better processor designs.The PhD dissertation is comprised of four main contributions that cover both multithreaded single-core (hdSMT) and multicore (TCA Algorithm, hTCA Framework and MFLUSH) scenarios, deeply explained in their corresponding chapters in the PhD dissertation memory. Overall, these contributions cover a significant range of the Heterogeneity-Aware Processors' design space. Within this design space, we have focused on the state-of-the-art trend in processor design: Multithreaded Multicore (CMP+SMT) Processors.We make special emphasis on the MPsim simulation tool, specifically designed and developed for this PhD dissertation. This tool has already gone beyond this PhD dissertation, becoming a reference tool by an important group of researchers spread over the Computer Architecture Department (DAC) at the Polytechnic University of Catalonia (UPC), the Barcelona Supercomputing Center (BSC) and the University of Las Palmas de Gran Canaria (ULPGC)

A configurable vector processor for accelerating speech coding algorithms

The growing demand for voice-over-packer (VoIP) services and multimedia-rich applications has made increasingly important the efficient, real-time implementation of low-bit rates speech coders on embedded VLSI platforms. Such speech coders are designed to substantially reduce the bandwidth requirements thus enabling dense multichannel gateways in small form factor. This however comes at a high computational cost which mandates the use of very high performance embedded processors. This thesis investigates the potential acceleration of two major ITU-T speech coding algorithms, namely G.729A and G.723.1, through their efficient implementation on a configurable extensible vector embedded CPU architecture. New scalar and vector ISAs were introduced which resulted in up to 80% reduction in the dynamic instruction count of both workloads. These instructions were subsequently encapsulated into a parametric, hybrid SISD (scalar processor)–SIMD (vector) processor. This work presents the research and implementation of the vector datapath of this vector coprocessor which is tightly-coupled to a Sparc-V8 compliant CPU, the optimization and simulation methodologies employed and the use of Electronic System Level (ESL) techniques to rapidly design SIMD datapaths