Highly accurate tables for elementary functions

In this article we describe a fast method to obtain highly accurate tables for all elementary functions by using Bresenham's algorithm. For nearly equally spaced table-points {x _i } we construct pairs {f(x _i ),g(x _i )} such thatf(x _i ) is a machine number andg(x _i ) is very close to an exactly representable number. By a random sampling in an interval centered onx _i we can even find a triplet of nearly machine numbers. The table method together with a polynomial approximation of the function near a table value provides last bit accuracy for more than 99.8% of the argument values without using extended precision calculations 3, 4, 10, 11].