Haven't read it, but isn't this just logarithmic tables in some form?
I am asking not to dismiss it, I genuinely feel I don't understand logarithms on a fundamental level (of logic gates etc.). If multiplication can be replaced with table lookup and addition, then there has to be a circuit that gives you difficult addition and easy multiplication, or any combination of those tradeoffs.
Log space is nice, multiplication can be replaced by addition.
This part is easy and anyone can implement hardware to do this. The tricky bit is always the staying in log space while doing accumulations, especially ones across a large range.
I am asking not to dismiss it, I genuinely feel I don't understand logarithms on a fundamental level (of logic gates etc.). If multiplication can be replaced with table lookup and addition, then there has to be a circuit that gives you difficult addition and easy multiplication, or any combination of those tradeoffs.