Scaling Newton-Raphson division iterations to avoid double rounding

Jean-Michel Muller (1)

1 ARENAIRE - Computer arithmetic

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.

Mots clés: Floating-point arithmetic; Division; Newton-raphson iteration; Underflow; Subnormal numbers; Double rounding

Domaines: Autre [cs.OH]

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