By sheer fluke I stumbled on an article that may be of interest here; apparently the 'ultimate multiplication' technique has now been found, building on the work of Karatsuba, Schönhage and Strassen, and lately Harvey & Van Der Hoeven.

Strange stuff but apparently achieving n log(n) steps for n digit multiplies.
https://www.quantamagazine.org/mathematicians-discover-the-perfect-way-to-multiply-20190411/
and the original paper at https://hal.archives-ouvertes.fr/hal-02070778/document

tim
--
tim Rowledge; tim@rowledge.org; http://www.rowledge.org/tim
"bOtHeR" said Pooh, mistaking the LSD tablet for aspirin