Titlebook: Elementary Functions:; Algorithms and Imple Jean-Michel Muller Book 19971st edition Birkhäuser Boston 1997 algorithms.computer.computer sci

Debrief

诗集

Introduction., tan., sinh, cosh, tanh, sinh., cosh., tanh., 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. Th

伪书

Some Basic Things About Computer Arithmeticut the book. For further information, the reader is referred to Goldberg’s paper [88], which gives a good survey of the topic, and Kahan’s lecture notes [106], which offer interesting and useful information. Further information can be found in [19, 39, 35, 40, 96, 111, 116, 148, 193, 197]. Here we m

obscurity

Polynomial or Rational Approximationswe add division to the set of available operations, the only functions one can compute are .. Therefore it is natural to try to approximate the elementary functions by polynomials or rational functions. Throughout this chapter we denote by .. the set of the polynomials of degree less than or equal t

interrupt

Table-Based Methodsg delays of computation, and this may also make the numerical error control difficult. A natural way to deal with this problem is to split the interval where the function is to be approximated into several smaller subintervals. It suffices to store in a table, for each subinterval, the coefficients

caldron

Introduction to Shift-and-Add algorithmsx would be proportional to the exponential of the weight of the bread! Bakers and mathematicians had the same question in mind: how could they quickly compute the price of bread? An old mathematician, called Briggs, found a convenient solution. He said to the King,

commensurate

The CORDIC Algorithmute sine, cosine, and arctangent functions) and to multiply or divide numbers using only shift-and-add elementary steps. In 1971, Walther [194] generalized this algorithm to compute logarithms, exponentials, and square roots. CORDIC is not the fastest way to perform multiplications or to compute log

Obstacle

Miscellaneousthan with the basic operations +, -, ×, ÷, and the square root. This is due to the high . of the elementary functions: when one obtains +∞ as the result. of a calculation that only contains the four basic operations and the square root, this does not necessarily mean that the exact result is infinit

acquisition

Introductionis means that, roughly speaking, a circuit can output . digits of a sine, cosine, or logarithm in a time proportional to log . (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.

sed-rate