Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Floating point numbers are real numbers   Floating point arithmetic allows us to use a finite machine, the digital
computer, to reach conclusions about models based on continuous mathematics. In
this article we work in the other direction, that is, we present examples in
which continuous mathematics leads to sharp, simple and new results about the
evaluation of sums, square roots and dot products in floating point arithmetic.

23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph