Real Time Floating Point Computing-A Philosophy For Implementations
Charles M. Rader · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1978
The exact definition of floating point computation has always varied from one computer to another and from one implementation to another. However, three points are common to almost all systems in use today: 1) representation of numbers by a multiplier and an exponent, with fixed integer base, 2) restriction of multiplier magnitude range (l/b,l) for uniqueness, 3) unique representation of zero. To implement the four operations, addition, subtraction, multiplication and division, for floating point, whether in hardware or in software, a worst case time can be identified which, for addition and subtraction, is often much larger than the average expected execution time, and which must be provided for in a real time system. An examination of the loss in accuracy associated with approximations which reduce these worst case times has led to a re-examination of an old idea, unnormalized floating point arithmetic, in the light of availability of modern hardware. We find that a system something like unnormalized floating point arithmetic is just right for most signal processing applications.