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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Basic Properties and Algorithms, such as the ones given in the various successive IEEE standards. Thanks to these standards, we now have an accurate definition of floating-point formats and operations. The behavior of a sequence of operations becomes at least partially. predictable (see Chapter 7) for more details on this). We th

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Enhanced Floating-Point Sums, Dot Products, and Polynomial Valuesns 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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Algorithms for the Five Basic Operationsion, 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