Handbook of Floating-Point Arithmetic , 2nd edition

Jean-Michel Muller (coordinator), Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre, Guillaume Melquiond, Nathalie Revol, Serge Torres.

Birkhäuser Boston, 2018. 632 p., ISBN 978-3-319-76525-9, ISBN 978-3-319-76526-6 (eBook)

BibTeX entry:

  title        = {Handbook of Floating-Point Arithmetic, 2nd edition},
  author    = {Muller, Jean-Michel and Brunie, Nicolas and de Dinechin, Florent and Jeannerod, Claude-Pierre and Joldes, Mioara and
          Lef{\`e}vre, Vincent and Melquiond, Guillaume and Revol,
          Nathalie and  Torres, Serge},
  publisher    = {{B}irkh\"auser {B}oston },
  pages    = {632},
  note        = {{ACM} {G}.1.0; {G}.1.2; {G}.4; {B}.2.0; {B}.2.4; {F}.2.1.,
                  ISBN 978-3-319-76525-9},
  year        = {2018},

See a preliminary version of chapter 1.

Our bibliographic database (BibTeX format)

Springer/Birkhauser web site for the book

This handbook is a definitive guide to the effective use of modern floating-point arithmetic, which has considerably evolved, from the frequently inconsistent floating-point number systems of early computing to the recent IEEE 754-2008 standard. Most of computational mathematics depends on floating-point numbers, and understanding their various implementations will allow readers to develop programs specifically tailored for the standard’s technical features. Algorithms for floating-point arithmetic are presented throughout the book and illustrated where possible by example programs which show how these techniques appear in actual coding and design.
The volume itself breaks its core topic into four parts: the basic concepts and history of floating-point arithmetic; methods of analyzing floating-point algorithms and optimizing them; implementations of IEEE 754-2008 in hardware and software; and useful extensions to the standard floating-point system, such as interval arithmetic, double- and triple-word arithmetic, operations on complex numbers, and formal verification of floating-point algorithms. This new edition updates chapters to reflect recent changes to programming languages and compilers and the new prevalence of GPUs in recent years. The revisions also add material on fused multiply-add instruction, and methods of extending the floating-point precision. 
As supercomputing becomes more common, more numerical engineers will need to use number representation to account for trade-offs between various parameters, such as speed, accuracy, and energy consumption. The Handbook of Floating-Point Arithmetic is designed for students and researchers in numerical analysis, programmers of numerical algorithms, compiler designers, and designers of arithmetic operators.

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"

Muller's book "Elementary functions, Algorithms and Implementation" (third edition, 2016)

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

Beebe's book "The Mathematical-Function Computation Handbook" (Springer, 2017)

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

John Harrison

William Kahan's home page

David Matula

Paul Zimmerman
Nick Higham

Interval computations