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A Correctly Rounded Newton Step for the Reciprocal Square Root
Carlos F. Borges
The reciprocal square root is an important computation for which many sophisticated algorithms exist (see for example \cite{Moroz,863046,863031} and the references therein). A comm…
Fast Compensated Algorithms for the Reciprocal Square Root, the Reciprocal Hypotenuse, and Givens Rotations
Carlos F. Borges
The reciprocal square root is an important computation for which many very sophisticated algorithms exist (see for example \cite{863046,863031} and the references therein). In this…
An Improved Algorithm for hypot(a,b)
Carlos F. Borges
We develop a fast and accurate algorithm for evaluating for two floating point numbers and . Library functions that perform this computation are generally n…
An Improved Formula for Jacobi Rotations
Carlos F. Borges
We present an improved form of the algorithm for constructing Jacobi rotations. This is simultaneously a more accurate code for finding the eigenvalues and eigenvectors of a real s…