[lugao]

Exactly! If you didn't strictly limit the operator's complexity, you could just smuggle a Turing machine in via bitwise logic and turn the whole thing into a parlor trick. The beauty here is that eml(x,y) is a pure, continuous analytical function with no hidden branching whatsoever.

To clarify my earlier point: the author isn't trying to build a practical calculator or generate human-readable algebra. Using exp and ln isn't a cheat code because the goal is purely topological. The paper just proves that this massive, diverse family of continuous math can be mapped perfectly onto a uniform binary tree, without secretly burying a state machine inside the operator.

[gus_massa]

> The beauty here is that eml(x,y) is a pure, continuous analytical function with no hidden branching whatsoever.

They use the complex version of logarithm, that has a lot of branching problems.

[lugao]

Well, the paper explicitly takes the principal branch to solve this.

So it isn't exploiting the branching for computation.

[gus_massa]

I agree, as the sibling comment there are two different things that are named "branches". Anyway, to get the principal branch in the microprocessor it's necessary to implement "atan2" that has a lot of special cases.

For example, IIRC ln( -inf.0 + y * i ) = ´+inf.0 + pi * sign(y)

[drdeca]

Different sense of “branching”

[gus_massa]

Yep.