Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Space-Efficient Karatsuba Multiplication for Multi-Precision Integers   The traditional Karatsuba algorithm for the multiplication of polynomials and
multi-precision integers has a time complexity of $O(n^{1.59})$ and a space
complexity of $O(n)$. Roche proposed an improved algorithm with the same
$O(n^{1.59})$ time complexity but with a much reduced $O(\log n)$ space
complexity. In Roche's paper details were provided for multiplication of
polynomials, but not for multi-precision integers. Multi-precision integers
differ from polynomials by the presence of carries, which poses difficulties in
implementing Roche's scheme in multi-precision integers. This paper provides a
detailed solution to these difficulties. Finally, numerical comparisons between
the schoolbook, traditional Karatsuba, and space-efficient Karatsuba algorithms
are provided.

4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an