J.M. Muller
Elementary Functions. Algorithms and Implementation.

An important topic, which is on the boundary between numerical analysis and computer science, is the computation of special functions. Indeed, one has first to derive theoretical methods for that purpose and to be able to give bounds on the error.
Then, these methods have to be turned into efficient, fast and reliable algorithms. Thus, a knowledge of the computer's arithmetic is mandatory, since roundings errors have to be taken into consideration. Speed is also essential and shift-and-add algorithms have to be used. This feature also requires that one is a computer scientist.
This book is devoted to the computation of elementary functions (such as sine, cosine, tan, exponentials and logarithms) and it is intended for specialists and inquiring minds as the author says in his preface. I also think that the book will be very valuable to students both in numerical analysis and in computer science.
The author is well known among people working on computer arithmetic. I found the book well written and containing much interesting material, most of the time disseminated in specialized papers published in specialized journals difficult to find.
Moreover, there are very few books on these topics and they are not recent.

Claude Brezinski, Numerical Algorithms 15 (1997), pp 385-386

This fascinating book describes the techniques used by high level compilers and by pocket book calculators to generate values of the common elementary mathematical functions. Both the theory and the implementation details of the algorithms are explained in sufficient detail to satisfy the curious or to inform the professional.

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