Efficient implementation of bit-vector operation in Common Lisp

Abstract

In this paper we show various techniques for the efficient implementation of the various functions of Common Lisp involving bit-vectors and bit-arrays. Bit-vectors are extremely useful for computing everything from the Sieve of Eratosthenes for finding prime numbers, to the representation of sets and relations, to the implementation of natural language parsers, to the performance of flow analysis in an optimizing compiler, to the manipulation of complex communication codes like those used in facsimile machines. However, the efficient manipulation of bit-vectors on modern computers represents a curious point on the spectrum of data processing tasks. On the one hand, the possibility of packing many bits within a single computer word and operating on all of them in parallel offers a potential for speedup not usually available for other types of tasks. On the other hand, the lack of the ability to efficiently manipulate single bits because of addressing schemes tuned for larger objects can actually reduce the speed of operating on bits. As a result of these observations, it should be obvious that no simple, automatic techniques such as "in-lining" (procedure integration) or "loop unrolling" of the obvious serial algorithms will produce the kinds of efficiency we are seeking. For these reasons, the efficient implementation of bit-vector operations requires special-case code, and is an interesting challenge in ingenuity and engineering.