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Basic Floating-Point Operators

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Application-Specific Arithmetic

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Abstract

This chapter shows how to build the operators for the basic operations (addition and subtraction, multiplication, division, and square root) in floating point. Specialized floating-point operators (such as squarers and constant multipliers) and fused floating-point operators (such as fused multiply-add, combined sum and difference, or sum of squares) will be reviewed in Chap. 15. For each operation, we start with the construction of simple but non-standard operators suitable for hidden application-specific datapaths. Then, refinements for improved standard compliance or improved performance are presented.

It makes me nervous to fly on airplanes since I know they are designed using floating-point arithmetic.Alston Householder

Relax. Today’s planes are piloted using floating-point arithmetic. The authors

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Notes

  1. 1.

    The IEEE 754 standard [754-19] defines five exceptions (Invalid, Overflow, Underflow, DivideByZero, and Inexact) that can be trapped by software to manage the respective situations. Software may also ignore these exceptions, because the hardware returns a value in each of these situations (a NaN for Invalid, an infinity for Overflow and DivideByZero, a subnormal result for Underflow). In this book we assume that application-specific hardware will do without raising these exceptions. Our reader having a need for any of them should be aware that they have been well thought out in the IEEE 754 standard.

  2. 2.

    It may be the subtraction of two numbers with the same sign or the addition of numbers with different signs.

  3. 3.

    Mathematically, the equality of two infinities could be endlessly debated. At least this choice is consistent with a comparison of the concatenation of fraction and exponent field (when using IEEE 754 encoding).

References

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Authors and Affiliations

  1. CITI laboratory, INSA-Lyon, Villeurbanne, France

    Florent de Dinechin

  2. Fulda University of Applied Sciences, Fulda, Germany

    Martin Kumm

Authors
  1. Florent de Dinechin
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  2. Martin Kumm
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de Dinechin, F., Kumm, M. (2024). Basic Floating-Point Operators. In: Application-Specific Arithmetic. Springer, Cham. https://doi.org/10.1007/978-3-031-42808-1_11

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  • DOI: https://doi.org/10.1007/978-3-031-42808-1_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-42807-4

  • Online ISBN: 978-3-031-42808-1

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