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Scaling Newton-Raphson division iterations to avoid double rounding

Jean-Michel Muller 1
1 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : When performing divisions using Newton-Raphson (or similar) iterations on a processor with a floating-point fused multiply-add instruction, one must sometimes scale the iterations, to avoid over/underflow and/or loss of accuracy. This may lead to double-roundings, resulting in output values that may not be correctly rounded when the quotient is in the subnormal range. We show how to avoid this problem.
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Submitted on : Wednesday, June 30, 2010 - 2:25:22 PM
Last modification on : Friday, February 4, 2022 - 3:19:05 AM
Long-term archiving on: : Tuesday, October 23, 2012 - 9:40:44 AM

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Jean-Michel Muller. Scaling Newton-Raphson division iterations to avoid double rounding. 2010. ⟨ensl-00496368⟩

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