In many digital signal processing applications, we often need some special function units that can compute complicated arithmetic functions such as reciprocal, logarithm, power of 2, trigonometric functions, etc. The most popular designs are based on look-up tables with polynomial approximation. However, the table size will increase significantly in accordance with precision. In this thesis, we propose a method called remapping to reduce the table size by using non-uniform segmentation. When we obtain the coefficients for all segments, we do not store them in order. By sorting the coefficients in the ROM ,we design a efficient hardware mapping. The method can reduce the ROM size with lower extra cost spent in address mapping for non-uniform segmentation.