Elementary Functions: Algorithms and Implementation

This book provides a comprehensive treatment of the algorithms and implementation techniques for elementary functions such as exponential, logarithmic, and trigonometric functions. It covers both theoretical foundations and practical aspects, including polynomial and rational approximations, argument reduction, and correct rounding.

The third edition has been thoroughly updated to reflect the latest developments in computer arithmetic, including the IEEE 754-2008 standard and new tools like Sollya, Gappa, and FloPoCo. It also includes new research results on decimal transcendental functions, certified supremum norms, and hardware-oriented techniques for FPGA implementation.

Written by a leading expert in the field, the book is an essential resource for researchers, practitioners, and students interested in numerical computing, computer arithmetic, and the design of mathematical function libraries. It balances mathematical rigor with practical implementation details, making it accessible to a wide audience.

The book is structured to guide readers from basic concepts to advanced topics, with numerous examples and algorithms. It serves as both a reference and a textbook for courses on numerical algorithms and floating-point arithmetic.