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.
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© 1997 Springer Science+Business Media New York
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Muller, JM. (1997). Introduction. In: Elementary Functions. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4757-2646-6_1
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DOI: https://doi.org/10.1007/978-1-4757-2646-6_1
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4757-2648-0
Online ISBN: 978-1-4757-2646-6
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