BIT 39(3), pp. 539–560, 1999 FAST AND PARALLEL INTERVAL ARITHMETIC
نویسندگان
چکیده
Infimum-supremum interval arithmetic is widely used because of ease of implementation and narrow results. In this note we show that the overestimation of midpoint-radius interval arithmetic compared to power set operations is uniformly bounded by a factor 1.5 in radius. This is true for the four basic operations as well as for vector and matrix operations, over real and over complex numbers. Moreover, we describe an implementation of midpoint-radius interval arithmetic entirely using BLAS. Therefore, in particular, matrix operations are very fast on almost any computer, with minimal effort for the implementation. Especially, with the new definition it is seemingly the first time that full advantage can be taken of the speed of vector and parallel architectures. The algorithms have been implemented in the Matlab interval toolbox INTLAB. AMS subject classifications. 65G10.
منابع مشابه
Fast Arithmetic for Public-Key Algorithms in Galois Fields with Composite Exponents
This contribution describes a new class of arithmetic architectures for Galois fields GF (2k). The main applications of the architecture are public-key systems which are based on the discrete logarithm problem for elliptic curves. The architectures use a representation of the field GF (2k) as GF ((2n)m), where k = n · m. The approach explores bit parallel arithmetic in the subfield GF (2n), and...
متن کاملEfficient implementation of low time complexity and pipelined bit-parallel polynomial basis multiplier over binary finite fields
This paper presents two efficient implementations of fast and pipelined bit-parallel polynomial basis multipliers over GF (2m) by irreducible pentanomials and trinomials. The architecture of the first multiplier is based on a parallel and independent computation of powers of the polynomial variable. In the second structure only even powers of the polynomial variable are used. The par...
متن کاملMaximally Fast Scheduling of Bit-serial Lattice Wave Digital Filters Using Three-port Adaptor Allpass Sections
In this paper we show how to achieve a maximally fast lattice wave digital filter using three-port adaptor allpass sections. Using three-port adaptors may increase the maximal sampling rate with approximately 50% compared to using second-order Richards’ allpass sections. Only bitserial arithmetics is discussed in the paper, but the same ideas can be utilized for digit-serial and bit-parallel ar...
متن کاملFast Multiprecision Evaluation of Series of Rational Numbers
We describe two techniques for fast multiple-precision evaluation of linearly convergent series, including power series and Ramanujan series. The computation time for N bits is O((logN)M(N)), whereM(N) is the time needed to multiply twoN -bit numbers. Applications include fast algorithms for elementary functions, π, hypergeometric functions at rational points, ζ(3), Euler’s, Catalan’s and Apéry...
متن کامل