Interval arithmetic is widely used in numerical algorithms requiring reliability. Ray tracing of implicit surface is one of these applications that use interval arithmetic to increase the quality of a produced image. However these applications are computationally demanding. One solution is to use graphics processing unit (GPU) in order to take advantage of its computational power. We describe i...

Graphics processing relies on executing similar instructions repeatedly on a large data set. This parallelism in the data gives rise to the Single-Instruction Multiple-Data (SIMD) paradigm which is used in modern processors. This paper explores several techniques that exploit the parallelism in the SIMD execution functional units and proposes several new SIMD methods. The methods discussed in t...

Since their introduction in constructive cryptographic applications, pairings over (hyper)elliptic curves are at the heart of an ever increasing number of protocols. Software implementations being rather slow, the study of hardware architectures became an active research area. In this paper, we first study an accelerator for the ηT pairing over F3[x]/(x + x + 2). Our architecture is based on a ...

A fuzzy number intuitionistic fuzzy set (FNIFS) is a generalization of intuitionistic fuzzy set. The fundamental characteristic of FNIFS is that the values of its membership function and non-membership function are trigonometric fuzzy numbers rather than exact numbers. In this paper, we define some operational laws of fuzzy number intuitionistic fuzzy numbers, and, based on these operational la...

In a recent paper by Hirzallah et al. [O. Hirzallah, F. Kittaneh, M. Krnić, N. Lovričević, and J. Pečarić. Eigenvalue inequalities for differences of means of Hilbert space operators. Linear Algebra and its Applications, 436:1516–1527, 2012.], several eigenvalue inequalities are obtained for the difference of weighted arithmetic and weighted geometric means of two positive invertible operators ...

We introduce implementations of arithmetic operators based on the binary stored-carry-or-borrow (BSCB) representation. Several BSCB arithmetic elements, including full-adder, ripple-carry adder, and carry-lookahead adder are presented, followed by detailed design of an array multiplier. In the latter design, the conventional initial AND matrix is transformed and expressed with a redundant radix...

The cloud model, which can implement uncertain transformation between a qualitative concept and its quantitative instantiations, has attracted great attentions in multi-criteria decision-making problems with linguistic information. This paper proposes some operations and a possibility degree of trapezium clouds as well as several new aggregation operators: the trapezium cloud weighted arithmeti...

In recent work authors have proposed four new aggregation operators for triangular and trapezoidal fuzzy numbers based on means of apex angles [1][2][3][4]. Subsequently authors have proposed [5] a new aggregation operator for TFNs based on the arithmetic mean of slopes of the Land Rmembership lines. In this paper the work is extended and a new aggregation operator for TFNs is proposed in which...

We are concerned with interval constraints: solving constraints among real unknowns in such a way that soundness is not aaected by rounding errors. The contraction operator for the constraint x + y = z can simply be expressed in terms of interval arithmetic. An attempt to use the analogous deenition for x y = z fails if the usual deenitions of interval arithmetic are used. We propose an alterna...