Yukio Umetani

Compiling techniques for first-order linear recurrences on a vector computer

Linear recurrences are the most important class of nonvectorizable problems in typical scientific/engineering calculations. This work discusses high-performance methods for solving first-order linear recurrences on a vector computer, investigates automatic transformations, and develops compiling techniques for first-order linear recurrence problems. The results show that the improved vector code generated by the vectorizing compiler on the HITAC S-820 supercomputer runs at the rate of 150 MFLOPS (million floating operations per second) for moderate loop lengths (>1000) and over 200 MFLOPS for long loop lengths (> 10000). Also, overall performance improvements of 69% in the 14 Lawrence Livermore Loops and 25 % in the 24 Lawrence Livermore Loops, as measured by the harmonic mean, are attained.

Interactive/visual DEQSOL: interactive creation, debugging, diagnosis and visualization of numerical simulation

DEQSOL is a very high level language specially designed to describe PDE problems in a way quite natural for numerical analyses. The DEQSOL translator automatically generates highly vectorizable FORTRAN simulation codes from the mathematical-level DEQSOL descriptions. DEQSOL requires only one tenth source lines of code by FORTRAN to describe simulation program and reduces the time needed to implement a simulation procedure to less than one sixth that of FORTRAN. DEQSOL possesses both finite difference method (FDM) and finite element method (FEM) as discretization facilities and its functional enhancement has been continued for years. DEQSOL has been becoming a considerably powerful system for numerical analysis specialists. However, the present DEQSOL is a batch-type language system and there is still something to brush up DEQSOL to be a more intelligent PSE (Problem Solving Environment) for PDE problems. Through the study of applying the present DEQSOL to practical problems, the time consuming process and its problems are analyzed and the future DEQSOL system is proposed. That is the interactive⧸visual DEQSOL which consists of eight subsystems, where the present DEQSOL acts just as the code generator subsystem. From our evaluation, the new DEQSOL will be able to shorten the above-mentioned simulation procedure time by one more order of magnitude of the present DEQSOL, and make the system will become a more user-oriented PSE as well.

Paragram: A high-level programming language for parallel processors

This paper presents the design principle of PARAGRAM, which is being developed for the parallel processing description for numerical simulation. The specification for the language is outlined, and the result of applying the language to the description of the actual problem is presented. The proposed language aims primarily at the following. The programmer is asked to indicate the parallelism inherent to the problems in the lumped system such as structural analysis and network analysis, and the particle problems such as neutron transport. This facilitates the mapping to the parallel computer architecture to be employed. The productivity and the maintainability of the program are improved by the simplicity of the description. Usually, different types of parallel processings are required for the lumped system and the particle system. In the former, the array-oriented parallelism often is observed, for example, the calculation of elements in the sparse matrix and the linear calculation using the sparse matrix. In the latter, the procedure-oriented parallelism often is observed based on the processing for each particle. The declaration function for the structure of various sparse matrices as well as the operation description based on the logical structure are employed for the former. The definition function for the particle density and probability distribution for the Monte Carlo particle system, as well as the parallel execution control block function for the simulation, are provided for the latter. As a result of applying the proposed language to the parallel processing description of the actual problem, it was verified that the description lines can be reduced by 23 to 62 percent from the traditional serial processing FORTRAN, indicating that the language is useful in the clear description, thereby improving the descriptive power.

The visual diagnosis on numerical calculation of PDE problems and experiments

A systematic method to diagnose the causes of symptoms found in the PDE solving process by visual means is proposed and tested. This method diagnoses the causes of the symptoms by reducing them to the attribute of dominant eigenvectors or to the column vectors of the matrix of the discretized equation. This method uses the shape-preserving nature of eigenvectors in linear transformations. A contour map representation of vector values is utilized also to aid this reduction process by human cognitive capability. This method was incorporated into the high level PDE solver PDEQSOL. The results of its application to several PDE problems show the feasibility of this method. Incorporating this kind of method will enhance the ease-of-use of interactive PDE systems, and also will give a good testbed to judge their quality in various application environments.