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How to read floating point numbers accurately
 Proceedings of PLDI ’90
, 1990
"... Converting decimal scientific notation into binary floating point is nontrivial, but this conversion can be performed with the best possible accuracy without sacrificing efficiency. 1. ..."
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Cited by 25 (0 self)
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Converting decimal scientific notation into binary floating point is nontrivial, but this conversion can be performed with the best possible accuracy without sacrificing efficiency. 1.
The Numerical Reliability of Econometric Software
, 1999
"... Numerical software is central to our computerized society; it is used... to analyze future options for financial markets and the economy. It is essential that it be of high ..."
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Cited by 22 (3 self)
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Numerical software is central to our computerized society; it is used... to analyze future options for financial markets and the economy. It is essential that it be of high
On the Precision Attainable with Various FloatingPoint Number Systems
 IEEE Transactions on Computers
, 1973
"... For scientific computations on a digital computer the set of real numbers is usually approximated by a finite set F of “floatingpoint ” numbers. We compare the numerical accuracy possible with different choices of F having approximately the same range and requiring the same word length. In particul ..."
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Cited by 8 (3 self)
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For scientific computations on a digital computer the set of real numbers is usually approximated by a finite set F of “floatingpoint ” numbers. We compare the numerical accuracy possible with different choices of F having approximately the same range and requiring the same word length. In particular, we compare different choices of base (or radix) in the usual floatingpoint systems. The emphasis is on the choice of F, not on the details of the number representation or the arithmetic, but both rounded and truncated arithmetic are considered. Theoretical results are given, and some simulations of typical floating pointcomputations (forming sums, solving systems of linear equations, finding eigenvalues) are described. If the leading fraction bit of a normalized base 2 number is not stored explicitly (saving a bit), and the criterion is to minimise the mean square roundoff error, then base 2 is best. If unnormalized numbers are allowed, so the first bit must be stored explicitly, then base 4 (or sometimes base 8) is the best of the usual systems. Index Terms: Base, floatingpoint arithmetic, radix, representation error, rms error, rounding error, simulation.
On the Precision Attainable with Various FloatingPoint Number Systems
"... 1 Introduction A real number x is usually approximated in a digital computer by an element fl(x) of a finite set F of "floatingpoint " numbers. We regard the elements of F as exactly representable real numbers, and take fl(x) as the floatingpoint number closest to x. The definition of &q ..."
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1 Introduction A real number x is usually approximated in a digital computer by an element fl(x) of a finite set F of "floatingpoint " numbers. We regard the elements of F as exactly representable real numbers, and take fl(x) as the floatingpoint number closest to x. The definition of "closest", rules for breaking ties, and the possibility of truncating instead of rounding are discussed later. We restrict our attention to binary computers in which floatingpoint numbers are represented in a word (or multiple word) of fixed length w bits, using some convenient (possibly redundant) code. Usually F is a set of numbers of the form
Implementing Decimal FloatingPoint Arithmetic through Binary: some Suggestions
"... Abstract—We propose algorithms and provide some related results that make it possible to implement decimal floatingpoint arithmetic on a processor that does not have decimal operators, using the available binary floatingpoint functions. In this preliminary study, we focus on roundtonearest mode o ..."
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Abstract—We propose algorithms and provide some related results that make it possible to implement decimal floatingpoint arithmetic on a processor that does not have decimal operators, using the available binary floatingpoint functions. In this preliminary study, we focus on roundtonearest mode only. We show that several functions in decimal32 and decimal64 arithmetic can be implemented using binary64 and binary128 floatingpoint arithmetic, respectively. We discuss the decimal square root and some transcendental functions. We also consider radix conversion algorithms. Keywordsdecimal floatingpoint arithmetic; square root; transcendental functions; radix conversion. I.
McCullough and Vinod: The Numerical Reliability of Econometric Software The Numerical Reliability of Econometric Software
"... Numerical software is central to our computerized society; it is used... to analyze future options for financial markets and the economy. It is essential that it be of high ..."
Abstract
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Numerical software is central to our computerized society; it is used... to analyze future options for financial markets and the economy. It is essential that it be of high