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Alternative Split Functions and Dekker's Product

Abstract : 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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Contributor : Jean-Michel Muller <>
Submitted on : Thursday, May 14, 2020 - 8:44:06 AM
Last modification on : Thursday, June 11, 2020 - 3:46:33 AM


  • HAL Id : hal-02470782, version 2


Stef Graillat, Vincent Lefèvre, Jean-Michel Muller. Alternative Split Functions and Dekker's Product. ARITH-2020 - IEEE 27th Symposium on Computer Arithmetic, Jun 2020, Portland, United States. pp.1-7. ⟨hal-02470782v2⟩



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