Suddenly found, that fixed point logarithm could be an alternative to floating point. Multiplication and division are just addition and subtraction of logarithms. Addition and subtraction are not that easy, but \[\log\left(\exp a \pm \exp b\right) = a + f\left(b - a\right)\], where \[f(x) = \log\left(1 \pm \exp x\right)\] could be implemented as a lookup table (one for addition an one for subtraction). Of course, zero and negative values should be treated specially, but this is true for floating point too. (For negative values negative base logarithm should do the trick, if it is ok to have inexact negation). #floatingpoint #weirdcomputing
P.s.Edited toot due to error in math