—Interval arithmetic has become a popular tool for general optimization problems such as robust root finding and global maximum/minimum finding. This has been effectively applied in many computer fields, such as computer graphics. However, interval arithmetic suffers from two significant weaknesses. First, its evaluations are often very conservative, making it useless in many practical situatio...

In this paper we present a novel approach for computing the number of solutions of the linear diophantine equation of Frobenius a1·x1 + ... + aN·xN = T when the coefficients a1, ..., aN are small. The proposed algorithm has a time complexity of the order of O(N·S·log(T)), where S=a1+...+aN. The algorithm can also be implemented to run in O(S·log(S)·log(T)+N·S) time, which is more efficient when...

Fuzzy set theory is considered as a suitable setting in order to take vagueness of real world problems into considerations. Operating with fuzzy dependencies among fuzzy data is a challenging problem, because it requires special arithmetic and a powerful optimization technique. The concept of fuzzy numbers and arithmetic operation with these numbers were first introduced and investigated by Zad...

This paper presents a novel number system based on signed continuous valued digits. Arithmetic operations in this number system are performed using simple analog circuitry, in contrast to the conventional implementation of arithmetic units by Boolean or multiple-valued logic circuits. Unlike the limited precision offered by classical analog arithmetic circuits, the ensemble of continuous valued...

We investigate theories of initial segments of the standard models for arithmetics. It is easy to see that if the ordering relation is definable in the standard model then the decidability results can be transferred from the infinite model into the finite models. On the contrary we show that the Σ2–theory of multiplication is undecidable in finite models. We show that this result is optimal by ...

This paper proposes an architecture of dynamically reconfigurable arithmetic circuit. Dynamic reconfiguration is a technique to realize required functions by changing hardware construction during operations. The proposed circuit is based on a complex number multiply-accumulation circuit which is used frequently in the field of digital signal processing. In addition, the proposed circuit perform...

Galois Field arithmetic forms the basis of Reed-Solomon and other erasure coding techniques to protect storage systems from failures. Most implementations of Galois Field arithmetic rely on multiplication tables or discrete logarithms to perform this operation. However, the advent of 128-bit instructions, such as Intel’s Streaming SIMD Extensions, allows us to perform Galois Field arithmetic mu...

Floating Point (FP) arithmetic is widely used in large set of scientific and signal processing computation. Adder/subtractor is one of the common arithmetic operation in these computation. The design of FP adder/subtractor is relatively complex than other FP arithmetic operations. This paper has shown an efficient implementation of adder/subtractor module on a reconfigurable platform, which is ...