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 interprocess communication (IPC) in a real-time transputer network

The thesis describes the design and implementation of an interprocess communication (IPC) mechanism within a real-time distributed operating system kernel (RT-DOS) which is designed for a transputer-based network. The requirements of real-time operating systems are examined and existing design and implementation strategies are described. Particular attention is paid to one of the object-oriented techniques although it is concluded that these techniques are not feasible for the chosen implementation platform. Studies of a number of existing operating systems are reported. The choices for various aspects of operating system design and their influence on the IPC mechanism to be used are elucidated. The actual design choices are related to the real-time requirements and the implementation that has been adopted is described. [Continues.

Compiling Programs for Nonshared Memory Machines

Nonshared-memory parallel computers promise scalable performance for scientific computing needs. Unfortunately, these machines are now difficult to program because the message-passing languages available for them do not reflect the computational models used in designing algorithms. This introduces a semantic gap in the programming process which is difficult for the programmer to fill. The purpose of this research is to show how nonshared-memory machines can be programmed at a higher level than is currently possible. We do this by developing techniques for compiling shared-memory programs for execution on those architectures. The heart of the compilation process is translating references to shared memory into explicit messages between processors. To do this, we first define a formal model for distribution data structures across processor memories. Several abstract results describing the messages needed to execute a program are immediately derived from this formalism. We then develop two distinct forms of analysis to translate these formulas into actual programs. Compile-time analysis is used when enough information is available to the compiler to completely characterize the data sent in the messages. This allows excellent code to be generated for a program. Run-time analysis produces code to examine data references while the program is running. This allows dynamic generation of messages and a correct implementation of the program. While the over-head of the run-time approach is higher than the compile-time approach, run-time analysis is applicable to any program. Performance data from an initial implementation show that both approaches are practical and produce code with acceptable efficiency

X10 for high-performance scientific computing

High performance computing is a key technology that enables large-scale physical simulation in modern science. While great advances have been made in methods and algorithms for scientific computing, the most commonly used programming models encourage a fragmented view of computation that maps poorly to the underlying computer architecture. Scientific applications typically manifest physical locality, which means that interactions between entities or events that are nearby in space or time are stronger than more distant interactions. Linear-scaling methods exploit physical locality by approximating distant interactions, to reduce computational complexity so that cost is proportional to system size. In these methods, the computation required for each portion of the system is different depending on that portion’s contribution to the overall result. To support productive development, application programmers need programming models that cleanly map aspects of the physical system being simulated to the underlying computer architecture while also supporting the irregular workloads that arise from the fragmentation of a physical system. X10 is a new programming language for high-performance computing that uses the asynchronous partitioned global address space (APGAS) model, which combines explicit representation of locality with asynchronous task parallelism. This thesis argues that the X10 language is well suited to expressing the algorithmic properties of locality and irregular parallelism that are common to many methods for physical simulation. The work reported in this thesis was part of a co-design effort involving researchers at IBM and ANU in which two significant computational chemistry codes were developed in X10, with an aim to improve the expressiveness and performance of the language. The first is a Hartree–Fock electronic structure code, implemented using the novel Resolution of the Coulomb Operator approach. The second evaluates electrostatic interactions between point charges, using either the smooth particle mesh Ewald method or the fast multipole method, with the latter used to simulate ion interactions in a Fourier Transform Ion Cyclotron Resonance mass spectrometer. We compare the performance of both X10 applications to state-of-the-art software packages written in other languages. This thesis presents improvements to the X10 language and runtime libraries for managing and visualizing the data locality of parallel tasks, communication using active messages, and efficient implementation of distributed arrays. We evaluate these improvements in the context of computational chemistry application examples. This work demonstrates that X10 can achieve performance comparable to established programming languages when running on a single core. More importantly, X10 programs can achieve high parallel efficiency on a multithreaded architecture, given a divide-and-conquer pattern parallel tasks and appropriate use of worker-local data. For distributed memory architectures, X10 supports the use of active messages to construct local, asynchronous communication patterns which outperform global, synchronous patterns. Although point-to-point active messages may be implemented efficiently, productive application development also requires collective communications; more work is required to integrate both forms of communication in the X10 language. The exploitation of locality is the key insight in both linear-scaling methods and the APGAS programming model; their combination represents an attractive opportunity for future co-design efforts

Scientific Grand Challenges: Crosscutting Technologies for Computing at the Exascale - February 2-4, 2010, Washington, D.C.

The goal of the "Scientific Grand Challenges - Crosscutting Technologies for Computing at the Exascale" workshop in February 2010, jointly sponsored by the U.S. Department of Energy’s Office of Advanced Scientific Computing Research and the National Nuclear Security Administration, was to identify the elements of a research and development agenda that will address these challenges and create a comprehensive exascale computing environment. This exascale computing environment will enable the science applications identified in the eight previously held Scientific Grand Challenges Workshop Series

On expressing different concurrency paradigms on virtual execution environment

Virtual execution environments (VEE) such as the Java Virtual Machine (JVM) and the Microsoft Common Language Runtime (CLR) have been designed when the dominant computer architecture featured a Von-Neumann interface to programs: a single processor hiding all the complexity of parallel computations inside its design. Programs are expressed in an intermediate form that is executed by the VEE that defines an abstract computational model in which the concurrency model has been influenced by these design choices and it basically exposes the multi-threading model of the underlying operating system. Recently computer systems have introduced computational units in which concurrency is explicit and under program control. Relevant examples are the Graphical Processing Units (GPU such as Nvidia or AMD) and the Cell BE architecture which allow for explicit control of single processing unit, local memories and communication channels. Unfortunately programs designed for Virtual Machines cannot access to these resources since are not available through the abstractions provided by the VEE. A major redesign of VEEs seems to be necessary in order to bridge this gap. In this thesis we study the problem of exposing non-von Neumann computing resources within the Virtual Machine without need for a redesign of the whole execution infrastructure. In this work we express parallel computations relying on extensible meta-data and reflection to encode information. Meta-programming techniques are then used to rewrite the program into an equivalent one using the special purpose underlying architecture. We provide a case study in which this approach is applied to compiling Common Intermediate Language (CIL) methods to multi-core GPUs; we show that it is possible to access these non-standard computing resources without any change to the virtual machine design

Domain Specific Memory Management for Large Scale Data Analytics

Hardware trends over the last several decades have lead to shifting priorities with respect to performance bottlenecks in the implementations of dataflows typically present in large-scale data analytics applications. In particular, efficient use of main memory has emerged as a critical aspect of dataflow implementation, due to the proliferation of multi-core architectures, as well as the rapid development of faster-than-disk storage media. At the same time, the wealth of static domain-specific information about applications remains an untapped resource when it comes to optimizing the use of memory in a dataflow application. We propose a compilation-based approach to the synthesis of memory-efficient dataflow implementations, using static analysis to extract and leverage domain-specific information about the application. Our program transformations use the combined results of type, effect, and provenance analyses to infer time- and space- effective placement of primitive memory operations, precluding the need for dynamic memory management and its attendant costs. The experimental evaluation of implementations synthesized with our framework shows both the importance of optimizing for memory performance, as well as significant benefits of our approach, along multiple dimensions. Finally, we also demonstrate a framework for formally verifying the soundness of these transformations, laying the foundation for their use as a component of a more general implementation synthesis ecosystem

木を用いた構造化並列プログラミング

High-level abstractions for parallel programming are still immature. Computations on complicated data structures such as pointer structures are considered as irregular algorithms. General graph structures, which irregular algorithms generally deal with, are difficult to divide and conquer. Because the divide-and-conquer paradigm is essential for load balancing in parallel algorithms and a key to parallel programming, general graphs are reasonably difficult. However, trees lead to divide-and-conquer computations by definition and are sufficiently general and powerful as a tool of programming. We therefore deal with abstractions of tree-based computations. Our study has started from Matsuzaki’s work on tree skeletons. We have improved the usability of tree skeletons by enriching their implementation aspect. Specifically, we have dealt with two issues. We first have implemented the loose coupling between skeletons and data structures and developed a flexible tree skeleton library. We secondly have implemented a parallelizer that transforms sequential recursive functions in C into parallel programs that use tree skeletons implicitly. This parallelizer hides the complicated API of tree skeletons and makes programmers to use tree skeletons with no burden. Unfortunately, the practicality of tree skeletons, however, has not been improved. On the basis of the observations from the practice of tree skeletons, we deal with two application domains: program analysis and neighborhood computation. In the domain of program analysis, compilers treat input programs as control-flow graphs (CFGs) and perform analysis on CFGs. Program analysis is therefore difficult to divide and conquer. To resolve this problem, we have developed divide-and-conquer methods for program analysis in a syntax-directed manner on the basis of Rosen’s high-level approach. Specifically, we have dealt with data-flow analysis based on Tarjan’s formalization and value-graph construction based on a functional formalization. In the domain of neighborhood computations, a primary issue is locality. A naive parallel neighborhood computation without locality enhancement causes a lot of cache misses. The divide-and-conquer paradigm is known to be useful also for locality enhancement. We therefore have applied algebraic formalizations and a tree-segmenting technique derived from tree skeletons to the locality enhancement of neighborhood computations.電気通信大学201