Alternative Split Functions and Dekker's Product
Résumé
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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SplitDirectedRoundings.pdf (115.07 Ko)
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arith2020-code.tar.gz (6.96 Ko)
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