revolution wrote: 
Thanks for the link. They say "practical", but there are lots of places to accidentally introduce bugs into that. But still not the n lg n that l4m2 is intimating. 

I did not finish my thought there. The paper shows that the complexity of integer division with remainder can be in fact reduced to the complexity of the multiplication algorithm you use. So you could theoretically use Fürer's multiplication there and obtain the same complexity for division (not practical, though).
l4m2 wrote: 
The algorithm is well known and have no too much diff. 

Good bignum libraries use many algorithms because the ones with lower complexity are only profitable for the large inputs. So it not unusual to use long multiplication for small inputs, switch to Karatsuba for slighly larger ones, for even larger ones use ToomCook and then SchönhageStrasse for really huge numbers. This should not really concern fasmg, since operations on such large numbers are not really what this tool is for  just like its multipass resolving is not the right tool for solving equations, even though it occasionally is able to solve one. So the main aim was to keep it simple. Look at the size of bigint routines in HeavyThing library  they are almost as long as fasmg in its entirety, while are they are still a relatively simple ones.