Embedded applications integrate more and more sophisticated computations. These computations are generally a composition of elementary functions and can easily be approximated by polynomials. Indeed, polynomial approximation methods allow to find a trade-off between accuracy and computation time. Software implementation of polynomial approximation in fixed-point processors is considered. To obtain a moderate approximation error, segmentation of the interval I on which the function is computed, is necessary. This paper presents a method to compute the values of a function on I using non-uniform segmentation, and polynomial approximation. Non-uniform segmentation allows to minimize the number of segments created and is modeled by a tree-structure. The specifications of the segmentation set the balance between memory space requirement and computation time. The method is illustrated with the function (− log(x)) on the interval [2 −5 ; 2 0 ] and showed a speed-up mean of 97.7 compared to the use of the library libm on the Digital Signal Processor C55x.