Useful applications of correctly-rounded operators of the form ab + cd + e
Abstract
We show that the availability of fused arithmetic operators that evaluate expressions of the form $ab + cd$ (FD2 instruction) or $ab + cd + e$ (FD2A instruction) in floating-point arithmetic with one final rounding only would significantly facilitate many calculations that are hard to perform with high accuracy at small cost using only the traditional operations $+$, $-$, $\times$, $\div$, $\surd{}$, and fused multiply-add (FMA).
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