Introduction and background: The basic integer arithmetic operations of addition=subtraction, multiplication and division are implemented typically in hardware using k bits of precision with k usually 16, 32, or 64, and up to 1024 in the case of cryptography. Having a precision limited to k bits makes the arithmetic operations equivalent to their corresponding residue arithmetic modulo 2 operat...

There are several areas in computer arithmetic which are fertile for new discoveries. This paper will introduce some of these fields of research with the expectation that there will be tremendous advances in the next decade. Some of these fields are already matured with key problems still unsolved while others are nebulous at this time in history. I will address three arithmetic fields: the mul...

In data processing processors, adder is a basic digital circuit. To perform any arithmetic operation, addition is the basic operation to perform. To compute fast arithmetic operations adder must be fastest. CSLA is the fastest adder when compare to RCA and CLA. From the structure of CSLA it is observed that there is a scope to reduce area further so that power can be lowered [3-4]. This paper p...

We present efficient parallel algorithms for multiple-precision arithmetic operations of more than several million decimal digits on distributed-memory parallel computers. A parallel implementation of floating-point real FFT-based multiplication is used because a key operation in fast multiple-precision arithmetic is multiplication. We also parallelized an operation of releasing propagated carr...

Adult's simple-arithmetic strategy use depends on problem-related characteristics, such as problem size and operation, and on individual-difference variables, such as working-memory span. The current study investigates (a) whether the effects of problem size, operation, and working-memory span on children's simple-arithmetic strategy use are equal to those observed in adults, and (b) how these ...

In many practical situations, we know only the intervals which contain the actual (unknown) values of physical quantities. If we know the intervals x for a quantity x and y for another quantity y, then, for every arithmetic operation , the set of possible values of x y also forms an interval; the operations leading from x and y to this new interval are called interval arithmetic operations. For...

Shape analyses are often imprecise in their numerical reasoning, whereas numerical static analyses are often largely unaware of the shape of a program’s heap. In this paper we propose a lazy method of combining a shape analysis based on separation logic with an arbitrary arithmetic analysis. When potentially spurious counterexamples are reported by our shape analysis, the method constructs a pu...

The traditional approach to fault tolerant computing involves replicating computation units and applying a majority vote operation on individual result bits. This approach, however, has several limitations; the most severe is the resource requirement. This paper presents a new method for fault tolerant computing where for a given error rate, , the hamming distance between correct inputs and fau...