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  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. , and Beame et al. ). For practical implementations, however, it is quite different, and much care is necessary if we want fast and accurate elementary functions.
KeywordsElementary Function Polynomial Approximation Computer Arithmetic Range Reduction CORDIC Algorithm
Unable to display preview. Download preview PDF.