Alternative Split Functions and Dekker's Product
1 : Université Pierre et Marie Curie - LIP6
(UPMC - LIP6)
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Site web
Université Pierre et Marie Curie [UPMC] - Paris VI
4 place Jussieu 75252 Paris -
France
2 : Inria / LIP
Inria, ENS de Lyon, CNRS, UCB Lyon 1, LIP UMR 5668, Lyon
3 : CNRS/LIP
Univ Lyon, Cnrs, ENS de Lyon, Inria, UCB Lyon 1, LIP UMR 5668, Lyon, FRANCE
We introduce algorithms for splitting a positive binary floating-point number into two numbers of around half the system precision, using arithmetic operations all rounded either toward −∞ or toward +∞. We use these algorithms to compute "exact" products (i.e., to express the product of two floating-point numbers as the unevaluated sum of two floating-point numbers, the rounded product and an error term). This is similar to the classical Dekker product, adapted here to directed roundings.
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