Birkhauser Boston, dec. 2009. 572 p. 62 illus., ISBN: 978-0-8176-4704-9

BibTeX entry:

@Book{MullerEtAl2010,

title = {Handbook of Floating-Point Arithmetic},

author = {Muller, Jean-Michel and Brisebarre, Nicolas and de Dinechin, Florent and Jeannerod, Claude-Pierre and

Lef{\`e}vre, Vincent and Melquiond, Guillaume and Revol,

Nathalie and Stehl{\'e}, Damien and Torres, Serge},

publisher = {{B}irkh\"auser {B}oston },

pages = {572 },

note = {{ACM} {G}.1.0; {G}.1.2; {G}.4; {B}.2.0; {B}.2.4; {F}.2.1.,

ISBN 978-0-8176-4704-9},

year = {2010},

}

See a preliminary version of chapter 1.

Our bibliographic database (BibTeX format)

Springer/Birkhauser web site for the book

Floating-point arithmetic is by far the most widely used way of implementing real-number arithmetic on modern computers. Although the basic principles of floating-point arithmetic can be explained in a short amount of time, making such an arithmetic reliable and portable, yet fast, is a very difficult task. From the 1960s to the early 1980s, many different arithmetics were developed, but their implementation varied widely from one machine to another, making it difficult for nonexperts to design, learn, and use the required algorithms. As a result, floating-point arithmetic is far from being exploited to its full potential.

This handbook aims to provide a complete overview of modern floating-point arithmetic, including a detailed treatment of the newly revised (IEEE 754-2008) standard for floating-point arithmetic. Presented throughout are algorithms for implementing floating-point arithmetic as well as algorithms that use floating-point arithmetic. So that the techniques presented can be put directly into practice in actual coding or design, they are illustrated, whenever possible, by a corresponding program.

Key topics and features include:

- Presentation of the history and basic concepts of floating-point arithmetic and various aspects of the past and current standards
- Development of smart and nontrivial algorithms, and algorithmic possibilities induced by the availability of a fused multiply-add (fma) instruction, e.g., correctly rounded software division and square roots
- Implementation of floating-point arithmetic, either in software—on an integer processor—or hardware, and a discussion of issues related to compilers and languages
- Coverage of several recent advances related to elementary functions: correct rounding of these functions and computation of very accurate approximations under constraints
- Extensions of floating-point arithmetic such as certification, verification, and big precision

Some links related to Floating-Point Arithmetic:

Ercegovac
and Lang's book "Digital
Arithmetic"

Kornerup
and Matula's book "Finite
Precision Number Systems and Arithmetic"

Koren's book "Computer arithmetic algorithms"

Markstein's
book "IA-64
and Elementary Functions"

Cornea,
Harrison and Tang's book "Scientific
Computing on Itanium-Based Systems"

Muller's book "Elementary functions, Algorithms and Implementation" (second edition, nov. 2005)

Nick
Higham's book, Accuracy
and Stability of Numerical Algorithms(SIAM,
*Second edition*,
August 2002, xxx+680 pp.).

Bibtex
bibliography
fparith.bib, (maintained by Norbert
Juffa and Nelson H. F.
Beebe)

People and groups

Stanford architecture and arithmetic group

David G. Hough's validlab home page

Lehigh University Computer Architecture and Arithmetic Group

Nick Higham Interval computationsErrata

- page 4, line 7, "of w" should be suppressed (i.e., the sentence should end after "representation").

- page 128, line 1, the proof of Theorem 4 should start with "Without loss of generality, we assume a > 0".

- page 128, 7th line from the bottom, "If ... then s = a-b, since..." should be replaced by "If ... then s = a+b, since..."

- page 129, 4th line, "a+b" should be replaced by "|a+b|"

- page 153, 2nd line of Theorem 13, "Let sigma be x..." should be replaced by "Let sigma be sqrt(x)..."

- page 514, the complexity of Fürer's multiplication algorithm is O(n·log(n)·2^O(log*(n))), and not O(n·log(n)·log*(n))

- page 555 (reference [320]), "M. A. Overton" should be replaced by "M. L. Overton"