Microprogrammed significance arithmetic with tapered floating point representation

Abstract

To automatically indicate a bound for the propagated and generated errors due to finite representation of numeric values on a computer using floating point representations, two methods are used, the “normalized method” and the “unnormalized method”. The normalized method uses a normalized representation and an index to indicate the number of significant digits. The unnormalized method retains only the significant digits.This paper reports a micro-implementation of binary significance arithmetic using the normalized method with a new floating point representation. The normalized method is chosen for two reasons: (1) as indicated by Carr [2 ] , a normalized floating point procedure always gives a better result than an unnormalized procedure, and (2) this floating point representation takes advantage of a special property of normalization to afford increased exponent range and to retain potentially an extra binary digit (bit) for values between 0 and 1 as compared against conventional floating point format.