Method and apparatus for implementing adaptive forward differencing using integer arithmetic.

摘要

A method and apparatus for implementing adaptive forward differencing technique in integer arithmetic resulting in an increase in precision while minimizing the number of mathematical operations to be performed is disclosed. The method and apparatus of the present invention provides for using a floating binary point adaptive forward differencing technique in which the binary point of the forward difference register, containing the value of the parametric function, is not shifted during parameter adjust- up and adjust-down operations. The binary point of the succeeding forward difference registers each containing a value corresponding to succeeding higher order derivatives of the parametric functions, are initially shifted a number of bits equal to a predetermined number of bits `N` multipled by a multiplication factor (referred to as guard bits) and the binary point is shifted to the right by one bit when an adjust-up operation is performed and to the left by one bit when an adjust-down operation is performed respectively reflecting the removal of a guard bit when an adjust-up operation is performed and the addition of a guard bit when an adjust-down operation is performed.