Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical integration in arbitrary-precision ball arithmetic   We present an implementation of arbitrary-precision numerical integration
with rigorous error bounds in the Arb library. Rapid convergence is ensured for
piecewise complex analytic integrals by use of the Petras algorithm, which
combines adaptive bisection with adaptive Gaussian quadrature where error
bounds are determined via complex magnitudes without evaluating derivatives.
The code is general, easy to use, and efficient, often outperforming existing
non-rigorous software.

29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom