The Algorithms discussed in this book deal directly with numbers; yet I believe they are properly called seminumerical, because they lie on the borderline between numeric and symbolic calculation. Each algorithm not only computes the desired answers to a problem, it also is intended to blend well with the internal operations of a digital computer. In many cases a person will not be able to appreciate the beauty of such an algorithm unless he or she also has some knowledge of a computer's machine language; the efficiency of the corresponding machine program is a vital factor that cannot be divorced from the algorithm itself.