Titlebook: Elementary Functions; Algorithms and Imple Jean-Michel Muller Textbook 2016Latest edition Springer Science+Business Media New York 2016 Ele

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Table-Based MethodsAs explained in Chapter?., for evaluating a function in a large domain (possibly made up with all floating-point numbers of a given format), we first perform one or several . steps, to reduce our initial problem to the evaluation of a function in one or several (sometimes, many!) smaller intervals.

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Multiple-Precision Evaluation of FunctionsMultiple-precision arithmetic is a useful tool in many domains of contemporary science. Some numerical applications are known to sometimes require significantly more precision than provided by the usual binary32/single-precision, binary-64/double precision, and Intel extended-precision formats?[22].

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Introduction to Shift-and-Add AlgorithmsWe present the simplest shift-and-add algorithms and the notions that will be useful for designing more sophisticated algorithms.

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Some Other Shift-and-Add AlgorithmsThe shift-and-add algorithms presented in Chapters?. and?. allow us to obtain an .-bit approximation of the function being computed after about . iterations. This property makes most of these algorithms rather slow; their major interest lies in the simplicity of implementation, and in the small silicon area of designs.

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Textbook 2016Latest editionls with basic principles of multiple-precision arithmetic. ?Part II is devoted to a presentation of “shift-and-add” algorithms (hardware-oriented algorithms that use additions and shifts only). ?Issues related to accuracy, including range reduction, preservation of monotonicity, and correct rounding

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