Let f be a degree D univariate polynomial with real coefficients and exactly m monomial terms. We show that in the special case m 1⁄4 3 we can approximate within e all the roots of f in the interval 1⁄20;R using just OðlogðDÞlogðD log Re ÞÞ arithmetic operations. In particular, we can count the number of roots in any bounded interval using just Oðlog DÞ arithmetic operations. Our speed-ups are ...

In processors that do not support floating-point instructions, using fixed-point arithmetic instead of floating-point emulation trades off computation accuracy for execution speed. This trade-off is often profitable. In many cases, like embedded systems, low-cost and speed bounds make it the only acceptable option. We present an environment supporting fixed-point code generation from C programs...

Processor speed and available computing power constantly increases, enabling computation of more and more complex problems such as numerical simulations of physical processes. In this domain, however, the problem of accuracy arises due to rounding of intermediate results. One solution is to avoid intermediate rounding by using exact arithmetic. The use of FPGAs as application-specific accelerat...

Concepts of interval arithmetic like arithmetic operations, comparison relations, distances, convergence, etc. are clearly defined terms of pure mathematics. The development of a standard for interval arithmetic should be based on these concepts. This paper considers the definition of the arithmetic operations and of comparison relations for an interval arithmetic computation standard. For deri...

Interval arithmetic is arithmetic for continuous sets. Floating-point intervals are intervals of real numbers with floating-point bounds. Operations for intervals can be efficiently implemented. Hence, the time is ripe for standardization. In this paper we present an interval model that is mathematically sound and closed for the 4 basic operations. The model allows for exception free interval a...

In a typical processor, Multiplication is one of the basic arithmetic operations and it requires substantially more hardware resources and processing time. In computers S-MB, a typical central processing unit devotes a considerable amount of processing time in implementing arithmetic operations, particularly multiplication operations. In this paper, multiplier is done for low power requirement ...