Abstract
With the advances in all fields of technology, accuracy has assumed a more important role. Enhancing the level of accuracy of a computation done on a computer is becoming indispensable for a growing number of computational problem classes.Due to the fact that the computer does all computations within the limits of its own frame, accuracy may be lost since numbers have to be rounded off to a finite size.The purpose of this research is to develop software algorithms to enhance the accuracy of computations.The first approach is an unconventional but really natural way in which to represent a real number as a ratio of two integers. This format will be referred to as the rational number format.The second approach explores the possibility of enhancing the accuracy of computation using conventional floating-point representation of real numbers. This approach provides a user-defined representation for the floating-point numbers within user chosen word size (32 bits, 64 bits, etc.). The user can determine and select the number of bits allocated to the exponent and the number of bits allocated to the mantissa.Due to the emergence of super computers with FLOPS (floating-point operations per second) exceeding a billion, the time taken to run these algorithms will be within acceptable limits. The effect of these algorithms on the speed of computation has been explored.The third approach for enhancing the accuracy is the possible rearranging of the order of computation at the source level. This technique can be used with each one of the previous two approaches to obtain better accuracy.