This paper presents a new functional parallel language: Minimally Synchronous Parallel ML. The execution time can then be estimated and dead-locks and indeterminism are avoided. It shares with Bulk Synchronous Parallel ML its syntax and high-level semantics but it has a minimally synchronous distributed semantics. Programs are written as usual ML programs but using a small set of additional functions. Provided functions are used to access the parameters of the parallel machine and to create and operate on a parallel data structure. It follows the cost model of the Message Passing Machine model (MPM). 1.

Skeleton programming enables programmers to build parallel programs easier by providing efficient ready-made parallel algorithms. The diffusion skeleton was proposed (associated with a method for program derivation) to abstract a good combination of primitive skeletons, such as map, parallel reduction and parallel prefix sum (scan).

An e#cient parallel interval narrowing algorithm for solving numerical problems is designed, implemented and tested. Di#erences with the corresponding sequential algorithm are clearly stated. The algorithm's performance is analyzed in the Bulk-Synchronous Parallel (BSP) cost model which suggests speed-ups on highbandwidth architectures. Experimental results on a massively parallel machine Cray T3E-1200 validate the model and show the parallel algorithm's e#ciency as well as its limitations. Key words: parallel algorithms, numerical algorithms, interval narrowing, constraint propagation, BSP model. Appears in: Information Processing Letters, 74(3-4):141--146, 2000. Elsevier Science. 1 Introduction Parallel processing of numerical problems via interval constraints has been proposed as a general framework for high-performance numerical computation in [5]. Its two potential advantages over classical methods are 1. the guarantee of numerically correct answers through interval arithme...

The BSML (Bulk Synchronous ML) language is a data-parallel functional language for programming BSP (Bulk Synchronous algorithms) algorithms in so-called direct mode. In a direct mode BSP algorithm, the physical structure of processes is made explicit. The execution time can then be estimated and dead-locks and indeterminism are avoided. The BSMLlib library, the current implementation of the BSML language, permits, as an extension of Objective Caml, the use of the exceptions handling mechanism that comes with this language. However, the interaction of Objective Caml exceptions with the BS#-calculus (the theoretical model underlying the BSML language) has not yet been studied and yields some safety issues. In particular, the use of collective synchronization operations needs the participation of all processes during the call to one of these operation, should the opposite occur, processes involved in this call are locked. The BSML language, without exceptions, ensures that all processes participate to such a call and thus that dead-locks are avoided (except for process failure). When one introduces Objective Caml exceptions, this safety property does not hold any more. Thus it is needed to study a new semantics, suitable to exceptions handling, to recover this property. The present work introduces such a semantics in which the participation of all processes is ensured and dead-lock issues are avoided. We will also introduce a semantics allowing the pattern-matching of BSML parallel vectors. This semantics has been studied in the framework of a previous work on exceptions handling which has not been retained here but its functionalities will be nethertheless add to the BSML language.