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Performance of BLAS 3, FFTs and NAS Parallel Benchmarks on Cray T3D

Recently, a Cray T3D Emulator has been made available on the Cray Y-MP and C90 computers. The Pittsburgh Supercomputer Center has acquired a CRAY T3D system and many other centers like Jet Propulsion Laboratory (JPL) will have it by the end of 1994. The Cray T3D system is the firstphase system in Cray Research, Inc.'s (CRI) three-phase massively parallel processing (MPP) program. This system features a heterogeneous architecture that closely couples DEC's ALPHA microprocessors and CRI's parallel-vector technology, i.e. the Cray Y-MP and Cray C90. The Cray T3D Emulator will give prospective users a valuable experience in developing high performance applications on the MPP system. This emulator runs programs written in CRI's MPP Fortran programming model (data sharing and work sharing) or Parallel Virtual Machine (PVM) programming model. It will help the users to study data layout, data locality, and data reference patterns thereby providing feedback which will enable one to write more efficient parallel codes. An overview of the Cray T3D hardware, software, and three of its available programming models is presented.The Cray Fortran Programming Model comprising (a) Data Sharing, (b) Worksharing and (c) Message Passing, will be discussed with examples. We have also implemented distributed BLAS 3 (matrix-matrix multiplication) in data parallel model (using only CSHIFT); worksharing model using block distribution and collapsed distribution; and message passing model using PVM. We have also implemented 2D and 3D FFTs for radix-2 using PVM. The performance of NAS Parallel 'Benchmarks (NPB) on CRAY T3D will be compared with other highly parallel systems such as CM-5, Paragon, C90 etc.

Saini, Subhash↗

Linear-Algebra Programs

The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.

Lawson, C. L.↗

Applications Performance on NAS Intel Paragon XP/S - 15#

The Numerical Aerodynamic Simulation (NAS) Systems Division received an Intel Touchstone Sigma prototype model Paragon XP/S- 15 in February, 1993. The i860 XP microprocessor with an integrated floating point unit and operating in dual -instruction mode gives peak performance of 75 million floating point operations (NIFLOPS) per second for 64 bit floating point arithmetic. It is used in the Paragon XP/S-15 which has been installed at NAS, NASA Ames Research Center. The NAS Paragon has 208 nodes and its peak performance is 15.6 GFLOPS. Here, we will report on early experience using the Paragon XP/S- 15. We have tested its performance using both kernels and applications of interest to NAS. We have measured the performance of BLAS 1, 2 and 3 both assembly-coded and Fortran coded on NAS Paragon XP/S- 15. Furthermore, we have investigated the performance of a single node one-dimensional FFT, a distributed two-dimensional FFT and a distributed three-dimensional FFT Finally, we measured the performance of NAS Parallel Benchmarks (NPB) on the Paragon and compare it with the performance obtained on other highly parallel machines, such as CM-5, CRAY T3D, IBM SP I, etc. In particular, we investigated the following issues, which can strongly affect the performance of the Paragon: a. Impact of the operating system: Intel currently uses as a default an operating system OSF/1 AD from the Open Software Foundation. The paging of Open Software Foundation (OSF) server at 22 MB to make more memory available for the application degrades the performance. We found that when the limit of 26 NIB per node out of 32 MB available is reached, the application is paged out of main memory using virtual memory. When the application starts paging, the performance is considerably reduced. We found that dynamic memory allocation can help applications performance under certain circumstances. b. Impact of data cache on the i860/XP: We measured the performance of the BLAS both assembly coded and Fortran coded. We found that the measured performance of assembly-coded BLAS is much less than what memory bandwidth limitation would predict. The influence of data cache on different sizes of vectors is also investigated using one-dimensional FFTs. c. Impact of processor layout: There are several different ways processors can be laid out within the two-dimensional grid of processors on the Paragon. We have used the FFT example to investigate performance differences based on processors layout.

Saini, Subhash↗

Applications Performance Under MPL and MPI on NAS IBM SP2

On July 5, 1994, an IBM Scalable POWER parallel System (IBM SP2) with 64 nodes, was installed at the Numerical Aerodynamic Simulation (NAS) Facility Each node of NAS IBM SP2 is a "wide node" consisting of a RISC 6000/590 workstation module with a clock of 66.5 MHz which can perform four floating point operations per clock with a peak performance of 266 Mflop/s. By the end of 1994, 64 nodes of IBM SP2 will be upgraded to 160 nodes with a peak performance of 42.5 Gflop/s. An overview of the IBM SP2 hardware is presented. The basic understanding of architectural details of RS 6000/590 will help application scientists the porting, optimizing, and tuning of codes from other machines such as the CRAY C90 and the Paragon to the NAS SP2. Optimization techniques such as quad-word loading, effective utilization of two floating point units, and data cache optimization of RS 6000/590 is illustrated, with examples giving performance gains at each optimization step. The conversion of codes using Intel's message passing library NX to codes using native Message Passing Library (MPL) and the Message Passing Interface (NMI) library available on the IBM SP2 is illustrated. In particular, we will present the performance of Fast Fourier Transform (FFT) kernel from NAS Parallel Benchmarks (NPB) under MPL and MPI. We have also optimized some of Fortran BLAS 2 and BLAS 3 routines, e.g., the optimized Fortran DAXPY runs at 175 Mflop/s and optimized Fortran DGEMM runs at 230 Mflop/s per node. The performance of the NPB (Class B) on the IBM SP2 is compared with the CRAY C90, Intel Paragon, TMC CM-5E, and the CRAY T3D.

Saini, Subhash↗

An Optimized Multicolor Point-Implicit Solver for Unstructured Grid Applications on Graphics Processing Units

In the field of computational fluid dynamics, the Navier-Stokes equations are often solved using an unstructuredgrid approach to accommodate geometric complexity. Implicit solution methodologies for such spatial discretizations generally require frequent solution of large tightly-coupled systems of block-sparse linear equations. The multicolor point-implicit solver used in the current work typically requires a significant fraction of the overall application run time. In this work, an efficient implementation of the solver for graphics processing units is proposed. Several factors present unique challenges to achieving an efficient implementation in this environment. These include the variable amount of parallelism available in different kernel calls, indirect memory access patterns, low arithmetic intensity, and the requirement to support variable block sizes. In this work, the solver is reformulated to use standard sparse and dense Basic Linear Algebra Subprograms (BLAS) functions. However, numerical experiments show that the performance of the BLAS functions available in existing CUDA libraries is suboptimal for matrices representative of those encountered in actual simulations. Instead, optimized versions of these functions are developed. Depending on block size, the new implementations show performance gains of up to 7x over the existing CUDA library functions.

Zubair, Mohammad↗

Adding GPU Support to the Markov Chain Monte Carlo Code Catmip

In geophysics, we are confronted with many under-determined inverse problems. For example, all of our observations of earthquakes are made at the Earth’s surface. So, when we try to infer how slip during an earthquake evolves in space and time, we find that there are many potential slip histories that are consistent with our limited observations and our understanding of earthquake physics. One way to approach these problems is with Bayesian analysis which allows us to infer the ensemble of all potential slip models that satisfy the observations and our prior knowledge of earthquake physics. In Bayesian analysis, our prior knowledge is known as the prior probability density function or prior PDF, the fit to the data is known as the data likelihood, and the target PDF that satisfies both the prior PDF and data likelihood is known as the posterior PDF. However, simulating the posterior PDF typically requires using Markov Chain Monte Carlo (MCMC) to draw tens of billions of random realizations of earthquake slip models, which may not be computationally feasible. To make this and similar geophysical inversions computationally tractable, we developed the Cascading Adaptive Transitional Metropolis In Parallel (CATMIP) algorithm. CATMIP is an efficient parallel Markov Chain Monte Carlo (MCMC) sampler that is used for model fitting and uncertainty quantification in geophysics. Example use cases are earthquake rupture modeling, determining mineral composition on Mars, reconstructing the history of ocean salinity, and historical earthquake relocation. CATMIP employs many parallel instances of the Metropolis algorithm for sampling in a transitioning framework. Transitioning is a process in which a set of random samples at equilibrium with a known probability density function (PDF) are used as seeds for the Markov chains to sample successive target PDFs that incrementally move the distribution from the starting seeds to the final desired PDF that describes the relative plausibility of potential values for the model parameters. The algorithm is implemented as a Master-Worker model employing MPI for communication. The worker processes are loosely coupled with global parameters periodically optimized by the master process. This provides a very high amount of parallelism with little communication between updates. During the presentation we will discuss the history of the algorithm and elaborate the earthquake rupture modeling use case for the CATMIP package. Our first step toward GPU optimization was to optimize the code for the CPU. CPU profiling revealed that most of the compute time is spent in calls to level 2 BLAS routines and calls to GSL random number generators. We revised the algorithm to employ level 3 BLAS routines instead. In our presentation we will describe how this was accomplished. Adding GPU support to CATMIP consisted mostly of replacing the calls to GSL with calls to GPU vendor-provided library routines. A small number of loops were directly implemented in CUDA. In the presentation will provide implementation details. Finally, we will discuss methods for profiling and opportunities for further optimizing GPU execution. By creating a code with the flexibility to run on either a CPU or GPU architecture, CATMIP can be used on systems ranging from large CPU-based HPC environments to single servers with GPU acceleration and everything in between.

HECC↗

Computer Program For Linear Algebra

Collection of routines provided for basic vector operations. Basic Linear Algebra Subprogram (BLAS) library is collection from FORTRAN-callable routines for employing standard techniques to perform basic operations of numerical linear algebra.

Krogh, F. T.↗

Spaceport Florida Authority

The topics are covered in viewgraph form and include the following: objectives; current initiatives; the Space Research Initiative Program; the Cape San Blas Launch Program; and Spaceport Florida Laboratories.

Source record↗

Particle astrophysics

The following scientific areas are reviewed: (1) cosmology and particle physics (particle physics and the early universe, dark matter, and other relics); (2) stellar physics and particles (solar neutrinos, supernovae, and unconventional particle physics); (3) high energy gamma ray and neutrino astronomy; (4) cosmic rays (space and ground observations). Highest scientific priorities for the next decade include implementation of the current program, new initiatives, and longer-term programs. Essential technological developments, such as cryogenic detectors of particles, new solar neutrino techniques, and new extensive air shower detectors, are discussed. Also a certain number of institutional issues (the funding of particle astrophysics, recommended funding mechanisms, recommended facilities, international collaborations, and education and technology) which will become critical in the coming decade are presented.

Sadoulet, Bernard↗