We present an algorithm based on arithmetic coding that allows decompression to start at any point in the compressed le. This random access requirement poses some restrictions on the implementation of arithmetic coding and on the model used. Our main application area is executable code compression for computer systems where machine instructions are decompressed on-they before execution. We focu...

I now want to apply the basic notions of computational representations and abstract algebra that I have developed so far to concrete algorithms, and briefly to consider their complexity. As I explained earlier, underlying all of computer algebra are the integers, so I will begin by considering algorithms for performing arithmetic on integers of unlimited magnitude, which I will call long intege...

Two essential problems in computer algebra, namely polynomial factorization and greatest common divisor computation, can be efficiently solved thanks to multiple evaluations two variables using modular arithmetic. In this article, we focus on the efficient computation of such one single CPU core. We first show how leverage SIMD (single instruction, data) computing for arithmetic AVX2 AVX-512 un...

We investigate the phenomenon of depth-reduction in commutative and non-commutative arithmetic circuits. We prove that in the commutative setting, uniform semi-unbounded arithmetic circuits of logarithmic depth are as powerful as uniform arithmetic circuits of polynomial degree; earlier proofs did not work in the uniform setting. This also provides a uni ed proof of the circuit characterization...

On August 7-8, 1996, the second Workshop on Computer Arithmetic, Interval and Symbolic Computation was held in Recife, Brazil. The main purpose of the workshop was to bring together researchers interested in scientific computation and related topics and to present and discuss recent advances in this branch of computer science and its applications. Total about 27 talks and 10 posters were presen...

This report documents the program and the results of Dagstuhl Seminar 11371 “Uncertainty modeling and analysis with intervals – Foundations, tools, applications”, taking place September 11-16, 2011. The major emphasis of the seminar lies on modeling and analyzing uncertainties and propagating them through application systems by using, for example, interval arithmetic. Seminar 11.–16. September,...

INTRODUCTION ...................................................................................................................... 1 ARITHMETIC ........................................................................................................................... 2 Integer and Polynomial Addition, Multiplication, and Division with Remainder ............. 2 Integer and Polynomial Greatest C...

This paper is devoted to the analysis of the behaviour, in nite precision arithmetic, of the simplest linear iterative scheme one can think of, that is the successive iteration method (SI) x 0 ; x k+1 = Ax k + b; k 0 where A is a real or complex matrix of order n and x is a real or complex vector of size n. In exact arithmetic, the behaviour of (1) is completely understood ; there is convergenc...

This paper describes a test of a computer's floating-point arithmetic unit. The test has two goals. The first goal deals with the needs of users of computers, and the second goal deals with manufacturers of computers. The first and major goal is to determine if the machine supports a particular mathematical model of computer arithmetic. This model was developed as an aid in the design, analysis...