An axiomatic treatment ofSIMD assignment

Abstract

Abstract.The aims of this article are to provide (i) an abstract characterisation of SIMD computation and (ii) a simple proof theory for SIMD programs. A soundness result is stated and the consequences of the result are analysed. The use of the axiomatic theory is illustrated by a proof of a parallel implementation of Euclid's GCD algorithm.

An Axiomatic Semantics for Data-Parallel Computation

“…An array a is a function which for each possible argument gives the value of the array at that point. Rule DPD is sound and relatively complete [13]. Rule DPD assumes that:…”

Proving Data-Parallel Programs: A Unifying Approach

“…The originality of our approach lies in the treatment of the extent of parallelism, that is, the subset of currently active indices at which a vector instruction is to be applied. Previous approaches led to manipulate lists of indices explicitly 7,12], or to consider context expressions as assertions modi ers 8]. In contrast, our proof system for L described the activity context by a vector boolean expression distinct from the usual predicates on program variables.…”

Laws of data parallel assignment

“…One means of exploiting the potential of supercomputers for the efficient execution of scientific programs is to specie' a set of ~'fine grained" order independent operations which may be applied to a data structure. 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.…”

“…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.…”