Introduction

Abstract

This book is devoted to the computation of the elementary functions. We call elementary functions the most commonly used mathematical functions: sin, cos, tan, sin^-1, cos^-1, tan^-1, sinh, cosh, tanh, sinh^-1, cosh^-1, tanh^-1, exponentials, and logarithms. From a purely theoretical point of view, these functions are not much harder to compute than quotients: it was shown by Alt [3] that elementary functions are equivalent to division with respect to Boolean circuit depth. This means that, roughly speaking, a circuit can output n digits of a sine, cosine, or logarithm in a time proportional to log n (see also Okabe et al. [147], and Beame et al. [14]). For practical implementations, however, it is quite different, and much care is necessary if we want fast and accurate elementary functions.