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-mu... 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