Microprogrammed interval arithmetic

Abstract

Computational methods using interval arithmetic allow the computer to provide rigorous error bounds along with approximate solutions for a wide and growing class of computational problems. A recent survey [1] lists over 700 references. The implementation of interval arithmetic using subroutine calls is inefficient - typically 10 to 100 times slower than floating-point arithmetic [2]. By microprogramming interval arithmetic, we can reduce this factor to around 2. This can be done by a user who has a machine with a writable control store or, better still, by a manufacturer into the read-only control store.