The ZM package is a collection of Fortran subroutines that performs floating point multiple precision evaluation of complex arithmetic and elementary functions. These routines use the FM package [7] for real multiple precision arithmetic, constants, and elementary functions. Brent’s MP package [4] did not support complex arithmetic, and Bailey’s more recent MP package [2,3] provides complex ari...

In this paper, the implementation of residue number system reverse converters based on hybrid parallelprefix adders is analyzed. The parallel prefix adder provides high speed and reduced delay arithmetic operations but it is not widely used since it suffers from high power consumption. Hence, a hybrid parallel prefix adder component is presented to perform fast modulo addition in Residue Number...

In this chapter, we present a high performance sorting function on GPUs that is able to exploit the parallel processing power and memory bandwidth of modern GPUs to sort large quantities of data at a very high speed. We revisit the traditional radix sorting framework, analyze the weaknesses, and then propose a solution based on the implicit counting data presentation and its associated operatio...

The aim of this paper is designing of pipelined architecture of arithmetic core and analysis of area and timing performance of that arithmetic core consisting of fixed point as well as floating point arithmetic cores. The basic concept behind designing such a core is to optimally utilize the algorithms of fixed point as well as floating point arithmetic operations, i.e., addition, subtraction d...

Background: At present scenario, the frequent and the most fundamental component in low power processor design is Arithmetic and Logic Unit (ALU). Further Power utilization due to clock gated ALU can be noteworthy in high performance systems. In general functionality of the ALU's is a mixture of arithmetic and logic operations which are realized by means of combinational circuits. In attendance...

Vedic mathematics or ancient mathematics is a unique technique of calculations based on 16 sutras. It provides an innovative way of computation of almost all the mathematical operations. In this era of digitization, engineers are working on increase speed of the digital circuits while reducing the size and power consumed. Arithmetic operations are the basic units of all the digital circuitry an...

We consider the prospect of a processor that can perform interval arithmetic at the same speed as conventional floating-point arithmetic. This makes it possible for all arithmetic to be performed with the superior security of interval methods without any penalty in speed. In such a situation the IEEE floating-point standard needs to be compared with a version of floating-point arithmetic that i...

Residue number systems have gained significant importance in the field of high-speed digital signal processing due to their carry-free nature and speed-up provided by parallelism. The cynical aspect in the application of RNS is the selection of the moduli set and the design of the conversion units. In the residue number system, a set of moduli which are independent of each other is given. An in...

Elliptic curve cryptography provides a methodology for obtaining high-speed, efficient, and scalable implementations of network security protocols. In this paper, we describe in detail three protocols based on elliptic curve cryptographic techniques, and the results of our implementation of the elliptic curve cryptography over the Galois field GF (2k), where k is a composite number. 1 Elliptic ...