Partial double precision with residue retention: a new approach to solving differential equations on microprocessors

Abstract

This paper proposes the use of partial double and triple precision with residue retention as a new arithmetic structure for solving differential equations on microprocessors. It is shown that a residue register, which is the distinguishing feature of the digital differential analyser, improves solution accuracy considerably by suppressing the accumulation of roundoff error, which is generally a problem on short-wordlength machines. Both theory and simulation reveal that by employing partial triple precision with residue retention, better than double-precision accuracy may be achieved with only a single-precision multiplication, whereas, without residue retention, single-precision accuracy only is possible.