Generalizing BIAS Speci cations

This paper generalizes the speci cation of Basic Interval Arithmetic Subroutines (BIAS) to support interval arithmetic on directed (i.e. proper and improper) intervals. This is due to our understanding that the arithmetic involving improper intervals will be increasingly used in future applications and the corresponding interval arithmetic implementations require no additional cost. We extend BIAS speci cation to be su ciently precise and complete, to include everything a user needs, such as subroutine's purpose, name, method of invocation and details of its behaviour and communication with the environment. The speci ed interval arithmetic subroutines for directed intervals are consistent with conventional interval arithmetic and IEEE oating-point arithmetic.