Interval arithmetic yields efficient dynamic filters for computational geometry
Discrete Applied Mathematics - Special issue 14th European workshop on computational geometry CG'98 Selected papers
Interval arithmetic: From principles to implementation
Journal of the ACM (JACM)
C++ Templates
C-XSC and Closely Related Software Packages
Numerical Validation in Current Hardware Architectures
Certification of bounds on expressions involving rounded operators
ACM Transactions on Mathematical Software (TOMS)
SIAM Journal on Optimization
How do you compute the midpoint of an interval?
ACM Transactions on Mathematical Software (TOMS)
A reformulation framework for global optimization
Journal of Global Optimization
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We present the design of the Boost interval arithmetic library, a C++ library designed to handle mathematical intervals efficiently and in a generic way. Interval computations are an essential tool for reliable computing. Increasingly a number of mathematical proofs have relied on global optimization problems solved using branch-and-bound algorithms with interval computations; it is therefore extremely important to have a mathematically correct implementation of interval arithmetic. Various implementations exist with diverse semantics. Our design is unique in that it uses policies to specify three independent variable behaviors: rounding, checking, and comparisons. As a result, with the proper policies, our interval library is able to emulate almost any of the specialized libraries available for interval arithmetic, without any loss of performance nor sacrificing the ease of use. This library is openly available at www.boost.org.