Generating a power of an operand by a table look-up and a multiplication

An efficient method for generating a power of an operand, i.e., X-p for an operand X and a given, fixed p, is proposed. The method is applicable to p's in the form of +/-2(k) where k is any integer and of +/-2(k1) +/- 2(-k2) where k(1) is any integer and k(2) is any non-negative integer. The reciprocal, the square root, and the reciprocal square root are included as special cases. It is a modification of the piecewise linear approximation based on the first-order Taylor expansion. The same accuracy is achieved. A power of an operand is generated through a table look-up and a multiplication with operand modification. No addition is required. The required table size is reduced, because only one coefficient instead of two has to be stored.