Titlebook: Handbook of Floating-Point Arithmetic; Jean-Michel Muller,Nicolas Brisebarre,Serge Torres Book 20101st edition Birkh?user Boston 2010 Algo

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https://doi.org/10.1007/978-3-658-32173-4ns arise in many fields of numerical computing. Computing sums is required, e.g., in numerical integration and the computation of means and variances. Dot products appear everywhere in numerical linear algebra. Polynomials are used to approximate many functions (see Chapter 11).

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https://doi.org/10.1007/978-3-663-07617-9ion, subtraction, multiplication, division, and square root. We will also study the fused multiply-add (FMA) operator. We review here some of the known properties and algorithms used to implement each of those operators. Chapter 9 and Chapter 10 will detail some examples of actual implementations in

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https://doi.org/10.1007/978-3-658-38348-0appear everywhere in scientific computing; thus being able to evaluate them quickly and accurately is important for many applications. Various very different methods have been used for evaluating them: polynomial or rational approximations, shift-and-add algorithms, table-based methods, etc. The cho

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https://doi.org/10.1007/978-3-658-37731-1ndeed, floating-point arithmetic introduces numerous special cases, and examining all the details would be tedious. As a consequence, the certification process tends to focus on the main parts of the correctness proof, so that it does not grow out of reach.

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https://doi.org/10.1007/978-3-658-40592-2fficient. There are reasonably rare cases when the binary64/decimal64 or binary128/decimal128 floating-point numbers of the IEEE 754 standard are too crude as approximations of the real numbers. This may occur for example when dealing with ill-conditioned numerical problems: internal computations wi

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Definitions and Basic Notions. is the significand of ., and . is its .. And yet, portability, accuracy, and the ability to prove interesting and useful properties as well as to design smart algorithms require more rigorous definitions, and much care in the specifications. This is the first purpose of this chapter. The second on

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Floating-Point Formats and Environments the rather messy situation of floating-point arithmetic before the 1980s. Anybody who estimates that the current standards are too constraining and that circuit and system manufacturers could build much more efficient machines without them should read that paper and think about it. Even if there w