Download e-book for iPad: Elementary Functions: Algorithms and Implementation by Jean-Michel Muller

By Jean-Michel Muller

This textbook offers the techniques and instruments essential to comprehend, construct, and enforce algorithms for computing uncomplicated capabilities (e.g., logarithms, exponentials, and the trigonometric functions). either undefined- and software-oriented algorithms are integrated, in addition to concerns concerning actual floating-point implementation. This 3rd version has been up to date and extended to include the latest advances within the box, new ordinary functionality algorithms, and serve as software.
After a initial bankruptcy that in short introduces a few primary techniques of machine mathematics, equivalent to floating-point mathematics and redundant quantity platforms, the textual content is split into 3 major components. half I considers the computation of common capabilities utilizing algorithms according to polynomial or rational approximations and utilizing table-based equipment; the ultimate bankruptcy during this part bargains with uncomplicated ideas of multiple-precision mathematics. half II is dedicated to a presentation of “shift-and-add” algorithms (hardware-oriented algorithms that use additions and shifts only). matters concerning accuracy, together with diversity aid, upkeep of monotonicity, and proper rounding, in addition to a few examples of implementation are explored partly III. quite a few examples of command traces and whole courses are supplied all through for varied software program programs, together with Maple, Sollya, and Gappa. New to this variation are an in-depth review of the IEEE-754-2008 usual for floating-point mathematics; a bit on utilizing double- and triple-word numbers; a presentation of latest instruments for designing actual functionality software program; and a bit at the Toom-Cook kinfolk of multiplication algorithms.
The ideas provided during this publication might be of curiosity to implementers of ordinary functionality libraries or circuits and programmers of numerical purposes. also, graduate and complex undergraduate scholars, execs, and researchers in clinical computing, numerical research, software program engineering, and computing device engineering will locate this an invaluable reference and resource.
“[T]his e-book appears like a vital reference for the specialists (which i am not). extra importantly, this is often an engaging e-book for the curious (which I am). subsequently, you will likely examine many attention-grabbing issues from this publication. for those who train numerical research or approximation thought, then this e-book offers you a few solid examples to debate in class.' — MAA reports (Review of moment Edition)
'The wealthy content material of rules sketched or provided in a few element during this e-book is supplemented via an inventory of over 300 references, so much of them of 1980 or more moderen. The e-book additionally includes a few proper common programs.' — Zentralblatt MATH (Review of moment Edition)
“I imagine that the e-book could be very useful to scholars either in numerical research and in computing device technology. i discovered [it to be] good written and containing a lot fascinating fabric, as a rule disseminated in really good papers released in really expert journals tricky to find.' — Numerical Algorithms (Review of First Edition)

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Elementary Functions: Algorithms and Implementation by Jean-Michel Muller

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