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1 PEQUAN - Performance et Qualité des Algorithmes Numériques LIP6 - Laboratoire d-Informatique de Paris 6

Abstract : We describe the mechanisms and implementation of a library that define a decimal multiple-precision interval arithmetic. The aim of such a library is to provide guaranteed and accurate results in decimal. This library contains correctly rounded elementary operations and some transcendental functions such as sin, cos or exp. The application fields of such a library are wide from financial calculation to aeronautic engineering. In those fields, complex algorithms are generally designed in high level with decimal numbers. Thus there is a need for correctly rounded decimal arithmetic multiple-precision library. The IEEE 754-2008 2 revision introduced the definition of decimal floating-point format, with the purpose of providing a basis for a robust and correctly rounded decimal arithmetic. Apart from being IEEE 754-2008 compliant, our library holds several useful properties, such as correct rounding for decimal arbitrary precision. The correctness of some functions will be proven. Furthermore the interval arithmetic will be compliant with the new IEEE 1788-2015 Standard for Interval Arithmetic 3. Studies of implementation of decimal arithmetic libraries have shown that one of the simplest and efficient way to implement decimal functions is to use their binary counterparts 1. This method makes it possible to rely on the efficiency of the binary arithmetic and focus more effort only on some critical points. The implementation of thislibrary is based on GMP and MPFR libraries.

Keywords : interval arithmetic multi-precision IEEE 754-2008 decimal format





Author: Stef Graillat - Clothilde Jeangoudoux - Christoph Lauter -

Source: https://hal.archives-ouvertes.fr/



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