Simd language design using prescriptive semantics

Abstract

Abstract.The goal of this article is to isolate a set of primitives necessary for the construction of SIMD programs and to give a denotational semantics for these primitives. The intent is to devise a language with a simple semantics rather than to propose a language which may be conveniently implemented. The approach taken results in the addition of a synchronous parallel assignment statement and a synchronous communication statement to the familiar sequential programming language control structures of composition, projection and iteration.

An axiomatic treatment ofSIMD assignment

“…The reason for not doing so is to simplify the denotational definitions by ensuring that the notational constructs of the programming language closely resemble the notational constructs of the meta-language (in this case sets and functions [9]). …”

“…The effect of the simple SIMD assignment command is to assign the values of the expression E for all indices in S to the corresponding components of the structure denoted by the program variable v. The order in which the individual assignments are performed over the components in the set S is unimportant -that is the assignments are mutually independent [9].…”

“…Typically, a soundness proof is carried out by simultaneous induction over the notational structures of a particular language; see, for example, Theorems 2.21 and 4.6 in [3]. In order to avoid defining a formal syntax and semantics for the SIMD language (as in [9]) the soundness of the axiom of SIMD assignment is simply stated. It can be additionally shown that the axiom defines the weakest pre-condition.…”

Laws of data parallel assignment

“…The concept of applying order independent updates to data structures [1,8,7,12,10] may be viewed as an extension of multiple assigmnent [3,4]. Data parallel assignment [9,10] captures the concept of independence of a set of operations; it may be executed using any combination (parallel or sequential) of its atomic constituents (individual updates) and, consequently; is suitable for implementation on a wide range of parallel architectures.…”