ULTRA-HIGH PRECISION COMPUTATIONS

We describe a machine independent Fortran subroutine which performs the four basic arithmetic operations with a degree of accuracy prescribed by the user. Tables of Chebyshev expansions of orders 48 and 50 for some basic mathematical functions are obtained as a result of applying this subroutine in conjunction with the recursive formulation of the Tau Method. A recently devised technique for the sharp determination of upper and lower error bounds for Tau Method approximations (see [1]) enables us to find the degree n required to achieve a prescribed accuracy epsilon over a given interval [a,b]. A number of practical illustrations are given.