If you're interested in even more details you could also have a look at Tom's book about bignum arithmetics. C.f. third paragraph of https://github.com/libtom/libtommath#summary
The library evolved since then, so the algorithm documentation only exists in code nowadays.
I don't know for sure, but you can do that kind of thing pretty easily with Matplotlib in Python. Or in R base graphics, with more effort to get it looking pretty.
As a side question, does anyone the program that the author used when making that "addition" and "multiplication" performance graph? Thanks.