Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fast Compensated Algorithms for the Reciprocal Square Root, the
  Reciprocal Hypotenuse, and Givens Rotations   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 paper we develop a simple differential
compensation (much like those developed in \cite{borges}) that can be used to
improve the accuracy of a naive calculation. The approach relies on the use of
the fused multiply-add (FMA) which is widely available in hardware on a variety
of modern computer architectures. We then demonstrate how to combine this
approach with a somewhat inaccurate but fast square root free method for
estimating the reciprocal square root to get a method that is both fast (in
computing environments with a slow square root) and, experimentally, highly
accurate. Finally, we show how this same approach can be extended to the
reciprocal hypotenuse calculation and, most importantly, to the construction of
Givens rotations.

8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat