Table 2.

Impact of individual optimizations

Algorithm	Total runtime (%)
New	100.0
New without GCD heuristic	$+$ 1.2
New without reciprocal polynomials	$+$ 3.3
New without dynamic selection of $\mathrm{GF}(p)$ implementation	$+$ 15.5
New without balanced multifactor Hensel lifting	$+$ 16.7
New without Karatsuba’s multiplication algorithm	$+$ 26.7