Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userParFORM: Parallel Version of the Symbolic Manipulation Program FORM
121
0
0.0
(
0
)
Added by
Tentyukov Mikhail
Publication date
2004
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
After an introduction to the sequential version of FORM and the mechanisms behind, we report on the status of our project of parallelization. We have now a parallel version of FORM running on Cluster- and SMP-architectures. This version can be used to run arbitrary FORM programs in parallel.
rate research
Read More
We report on the status of our project of parallelization of the symbolic manipulation program FORM. We have now parall
We give a brief introduction to FORM, a symbolic programming language for massive batch operations, designed by J.A.M. Vermaseren. In particular, we stress various methods to efficiently use FORM under the UNIX operating system. Several scripts and examples are given, and suggestions on how to use the vim editor as development platform.
We propose efficient parallel algorithms and implementations on shared memory architectures of LU factorization over a finite field. Compared to the corresponding numerical routines, we have identified three main difficulties specific to linear algebra over finite fields. First, the arithmetic complexity could be dominated by modular reductions. Therefore, it is mandatory to delay as much as possible these reductions while mixing fine-grain parallelizations of tiled iterative and recursive algorithms. Second, fast linear algebra variants, e.g., using Strassen-Winograd algorithm, never suffer from instability and can thus be widely used in cascade with the classical algorithms. There, trade-offs are to be made between size of blocks well suited to those fast variants or to load and communication balancing. Third, many applications over finite fields require the rank profile of the matrix (quite often rank deficient) rather than the solution to a linear system. It is thus important to design parallel algorithms that preserve and compute this rank profile. Moreover, as the rank profile is only discovered during the algorithm, block size has then to be dynamic. We propose and compare several block decomposition: tile iterative with left-looking, right-looking and Crout variants, slab and tile recursive. Experiments demonstrate that the tile recursive variant performs better and matches the performance of reference numerical software when no rank deficiency occur. Furthermore, even in the most heterogeneous case, namely when all pivot blocks are rank deficient, we show that it is possbile to maintain a high efficiency.
To interpolate a supersparse polynomial with integer coefficients, two alternative approaches are the Prony-based big prime technique, which acts over a single large finite field, or the more recently-proposed small primes technique, which reduces the unknown sparse polynomial to many low-degree dense polynomials. While the latter technique has not yet reached the same theoretical efficiency as Prony-based methods, it has an obvious potential for parallelization. We present a heuristic small primes interpolation algorithm and report on a low-level C implementation using FLINT and MPI.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
