Correct translation of data parallel assignment onto array processors

Abstract

Two models of computation which are suitable for the description of parallel scientific calculations on large data structures are presented. Data parallel assignment is a construct which may be used to specify the application of a set of order independent fine grained operations to a regular data structure. It is formulated in a machine independent way and, consequently, is suitable for implementation on a range of novel parallel architectures. An operational model of data parallel computation is provided by specifying a model array processor. The specification captures the essential features of the class of array processors and it may be instantiated in order to define a particular machine. A formal operational semantics of data parallel assignment is given for the model array processor. The translation mechanism is shown to be correct. The exercise clarifies some of the issues in deciding whether or not it is feasible to translate data parallel assignment directly onto array processor architectures.

Laws of data parallel assignment

“…Data parallel assignment is interpreted on a model distributed array" processor in [15]. To this end, the structural normal form ensures that each "atomic" assignment involves at most one "non-local" data element (that which occurs in the sub-expressions NL).…”

“…These definitions exhibit mathematical regularity and facilitate the development and verification of correct data parallel programs. In further work a formal array processor based operational semantics of the construct has been specified [15] aaqd data parallel a~signment has been compared with apparently similar constructs in Fortran 90 and High Performance Fortran [11].…”