Shor's algorithm can be sub-divided into two parts, namely, a "classical" and "quantum" part (see Algorithm 8.5.2 of Crandall & Pomerance or, unfortunately,

the Wikipedia article).

I had the following question:

Would an improvement (such as an optimized method of division, multiplication, addition, and/or subtraction) to the "classical part" of Shor's algorithm result in a somewhat significant improvement to the algorithm as a whole? Or is the "classical part" of Shor's algorithm rather insignificant compared to the "quantum part"?