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Floating-point arithmetic is the most widely used way of
implementing real-number arithmetic on modern computers. However,
making such an arithmetic reliable and portable, yet fast, is a
very difficult task. 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. 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. The handbook is designed for
programmers of numerical applications, compiler designers,
programmers of floating-point algorithms, designers of arithmetic
operators, and more generally, students and researchers in
numerical analysis who wish to better understand a tool used in
their daily work and research.
Floating-point arithmetic is the most widely used way of
implementing real-number arithmetic on modern computers. However,
making such an arithmetic reliable and portable, yet fast, is a
very difficult task. 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. 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. The handbook is designed for
programmers of numerical applications, compiler designers,
programmers of floating-point algorithms, designers of arithmetic
operators, and more generally, students and researchers in
numerical analysis who wish to better understand a tool used in
their daily work and research.
Floating-point arithmetic is ubiquitous in modern computing, as it
is the tool of choice to approximate real numbers. Due to its
limited range and precision, its use can become quite involved and
potentially lead to numerous failures. One way to greatly increase
confidence in floating-point software is by computer-assisted
verification of its correctness proofs. This book provides a
comprehensive view of how to formally specify and verify tricky
floating-point algorithms with the Coq proof assistant. It
describes the Flocq formalization of floating-point arithmetic and
some methods to automate theorem proofs. It then presents the
specification and verification of various algorithms, from
error-free transformations to a numerical scheme for a partial
differential equation. The examples cover not only mathematical
algorithms but also C programs as well as issues related to
compilation.
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