So? Why are you assuming you have to carry the bitwise operation through the multiplication? You don’t have to. You can if you want, but it would be academic and impractical. Using a multiply inside of the bitwise div operation makes the divide much faster. Deconstructing a multiply into bitwise operations makes the multiply much slower, so there’s no reason to do that, and there is no such requirement that we do before we can call the div trick a bitwise algorithm.

That said, if you want a bitwise multiply algorithm, I have written one. It’s slow, but enables 64 and 128 bit multiplies in glsl, which has no 64 or 128 bit multiply or add intrinsic. See add() and mult() in the “common” buffer. https://www.shadertoy.com/view/7dfyRM