ALBERT

Description: The existence of simple polynomial equations (integer relations) for the constants e/pi, e + pi, log pi, gamma (Euler's constant), e exp gamma, gamma/e, gamma/pi, and log gamma is investigated by means of numerical computations. The recursive form of the Ferguson-Fourcade algorithm (Ferguson and Fourcade, 1979; Ferguson, 1986 and 1987) is implemented on the Cray-2 supercomputer at NASA Ames, applying multiprecision techniques similar to those described by Bailey (1988) except that FFTs are used instead of dual-prime-modulus transforms for multiplication. It is shown that none of the constants has an integer relation of degree eight or less with coefficients of Euclidean norm 10 to the 9th or less.

Description: An efficient algorithm is described for finding whether or not certain fundamental mathematical constants satisfy simple algebraic polynomials. The algorithm, which finds whether an integer relation exists for a vector of real numbers, or else establishes bounds within which no relation can exist. The algorithm is implemented on high-speed computers, using multiprecision arithmetic. Numerical results are summarized, and other possible applications for the algorithm are discussed.

Description: The quartically convergent numerical algorithm developed by Borwein and Borwein (1987) for 1/pi is implemented via a prime-modulus-transform multiprecision technique on the NASA Ames Cray-2 supercomputer to compute the first 2.936 x 10 to the 7th digits of the decimal expansion of pi. The history of pi computations is briefly recalled; the most recent algorithms are characterized; the implementation procedures are described; and samples of the output listing are presented. Statistical analyses show that the present decimal expansion is completely random, with only acceptable numbers of long repeating strings and single-digit runs.

Description: In this paper we define the parameterized integer relation construction algorithm PSLQ(tau), where the parameter tau can be freely chosen in a certain interval.

Description: In this paper we report on features added to a parallel debugger to simplify the debugging of parallel message passing programs. These features include replay, setting consistent breakpoints based on interprocess event causality, a parallel undo operation, and communication supervision. These features all use trace information collected during the execution of the program being debugged. We used a number of different instrumentation techniques to collect traces. We also implemented trace displays using two different trace visualization systems. The implementation was tested on an SGI Power Challenge cluster and a network of SGI workstations.

Description: Mesh adaption is a powerful tool for efficient unstructured-grid computations but causes load imbalance among processors on a parallel machine. We describe a novel method to dynamically balance the processor workloads with a global view. Mesh question, repartitioning, processor assignment, and remapping are critical components of the framework that must be accomplished rapidly and efficiently so as not to cause a significant overhead to the numerical simulation. A data redistribution model will also be presented that predicts the remapping cost. This model is required to determine whether the gain from a balanced workload distribution offsets the cost of data movement. Results presented will demonstrate that this is an effective dynamic load balancing strategy which remains viable on a large number of processors.

Description: High Performance Fortran (HPF), the high-level language for parallel Fortran programming, is based on Fortran 90. HALF was defined by an informal standards committee known as the High Performance Fortran Forum (HPFF) in 1993, and modeled on TMC's CM Fortran language. Several HPF features have since been incorporated into the draft ANSI/ISO Fortran 95, the next formal revision of the Fortran standard. HPF allows users to write a single parallel program that can execute on a serial machine, a shared-memory parallel machine, or a distributed-memory parallel machine. HPF eliminates the complex, error-prone task of explicitly specifying how, where, and when to pass messages between processors on distributed-memory machines, or when to synchronize processors on shared-memory machines. HPF is designed in a way that allows the programmer to code an application at a high level, and then selectively optimize portions of the code by dropping into message-passing or calling tuned library routines as 'extrinsics'. Compilers supporting High Performance Fortran features first appeared in late 1994 and early 1995 from Applied Parallel Research (APR) Digital Equipment Corporation, and The Portland Group (PGI). IBM introduced an HPF compiler for the IBM RS/6000 SP/2 in April of 1996. Over the past two years, these implementations have shown steady improvement in terms of both features and performance. The performance of various hardware/ programming model (HPF and MPI (message passing interface)) combinations will be compared, based on latest NAS (NASA Advanced Supercomputing) Parallel Benchmark (NPB) results, thus providing a cross-machine and cross-model comparison. Specifically, HPF based NPB results will be compared with MPI based NPB results to provide perspective on performance currently obtainable using HPF versus MPI or versus hand-tuned implementations such as those supplied by the hardware vendors. In addition we would also present NPB (Version 1.0) performance results for the following systems: DEC Alpha Server 8400 5/440, Fujitsu VPP Series (VX, VPP300, and VPP700), HP/Convex Exemplar SPP2000, IBM RS/6000 SP P2SC node (120 MHz) NEC SX-4/32, SGI/CRAY T3E, SGI Origin2000.

Description: This paper examines the applications most commonly run on the supercomputers at the Numerical Aerospace Simulation (NAS) facility. It analyzes the extent to which such applications are fundamentally oriented to vector computers, and whether or not they can be efficiently implemented on hierarchical memory machines, such as systems with cache memories and highly parallel, distributed memory systems.

Description: The speaker will give an overview of high performance computing in the U.S. in general and within NASA in particular, including a description of the recently signed NASA-IBM cooperative agreement. The latest performance figures of various parallel systems on the NAS Parallel Benchmarks will be presented. The speaker was one of the authors of the NAS (National Aerospace Standards) Parallel Benchmarks, which are now widely cited in the industry as a measure of sustained performance on realistic high-end scientific applications. It will be shown that significant progress has been made by the highly parallel supercomputer industry during the past year or so, with several new systems, based on high-performance RISC processors, that now deliver superior performance per dollar compared to conventional supercomputers. Various pitfalls in reporting performance will be discussed. The speaker will then conclude by assessing the general state of the high performance computing field.

Description: The Gorden Bell Prizes given out at Supercomputing every year includes at least two catergories: performance (highest GFLOP count) and price-performance (GFLOP/million $$) for real applications. In the past five years, the winners of the price-performance categories all came from networks of work-stations. This reflects three important facts: 1. supercomputers are still too expensive for the masses; 2. achieving high performance for real applications takes real work; and, most importantly; 3. it is possible to obtain acceptable performance for certain real applications on network of work stations. With the continued advance of network technology as well as increased performance of "desktop" workstation, the "Swarm of Ants vs. Herd of Elephants" debate, which began with vector multiprocessors (VPPs) against SIMD type multiprocessors (e.g. CM2), is now recast as VPPs against Symetric Multiprocessors (SMPs, e.g. SGI PowerChallenge). This paper reports on performance studies we performed solving a large scale (2-million grid pt.s) CFD problem involving a Boeing 747 based on a parallel version of OVERFLOW that utilizes message passing on PVM. A performance monitoring tool developed under NASA HPCC, called AIMS, was used to instrument and analyze the the performance data thus obtained. We plan to compare its performance data obtained across a wide spectrum of architectures including: the Cray C90, IBM/SP2, SGI/Power Challenge Cluster, to a group of workstations connected over a simple network. The metrics of comparison includes speed-up, price-performance, throughput, and turn-around time. We also plan to present a plan of attack for various issues that will make the execution of Grand Challenge Applications across the Global Information Infrastructure a reality.