In the past, hardware implementation of the elementary transcendental functions employ simple iterative method or CORDIC algorithm. The major drawback of this method is the accuracy. The recent VLSI technology makes it advantageous to implement the functions by the table-driven method. The analogies exist already in the mathematical software library. In this approach, various computation techniques are used for the accurate results. The function value accuracy closely depends on the interpolating polynomials. The developed algorithm is verified in the various design phases and implemented in Pilgrim microprocessor, which has instruction level compatibility with Intel Pentium processor. The control is microprogrammed with no burden to the other parts. Desired accuracy of 1 ULP error is acquired.