On Parsing and Compiling Arithmetic Expressions on Vector Computers

Abstract

The problem of parsing and compiling arithmetic expressions on vector computers is considered. Methods are developed which allow encodings of one or more arithmetic expressions to be transformed directly into encodings of their corresponding derivation trees. The algorithm which performs this transformation is compact, efficient, and able to make extensive use of concurrent vector operations. Routines which concurrently transverse encoded derivation trees in a top-down or bottom-up manner are presented. These routines can be used to structure efficient, compact, and highly concurrent algorithms which complete the process of compiling arithmetic expressions.