Laurent Fousse
Abstract
This article presents a multiple-precision binary floating-point library, written in the ISO C language, and based on the GNU MP library. Its particularity is to extend to arbitrary-precision, ideas from the IEEE 754 standard, by providing correct rounding and exceptions. We demonstrate how these strong semantics are achieved---with no significant slowdown with respect to other arbitrary-precision tools---and discuss a few applications where such a library can be useful.
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Index Terms
MPFR
Reviews
Wolfgang Schreiner
Many computer programs in science and engineering depend on the accurate and efficient computation of continuous quantities represented as floating-point numbers. These numbers are stored as bit strings of fixed length that allow their implementation in hardware, and also put a limit to their precision. In 1985, the standard IEEE Standard for Binary Floating-Point Arithmetic (IEEE 754) specified two such floating-point representations together with the corresponding operations, paying special attention to critical issues such as correct rounding. This universally accepted standard has put an end to the compatibility problems caused by previous implementations. The software library MPFR presented in this paper generalizes IEEE 754 by providing floating-point numbers with arbitrary precision on the basis of the widely used GNU MP library. Each number has its own precision, and for each operation the expected target precision may be specified; the software pays attention to correct rounding, and handles exceptional situations in the spirit of IEEE 754. MPFR is freely available in open source, and is widely used by other mathematical applications and packages. The paper provides insight into the overall design principles of MPFR: its data representation and its implementation of the arithmetic operations. It also discusses the testing of the software and presents experimental results that demonstrate its superiority with respect to efficiency and accuracy over other similar packages. Although the correctness of MPFR is of major importance, a discussion of its formal specification and verification is lacking; this might be a subject for future work. Online Computing Reviews Service
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