I find scalar_tanh_op can handle complex number, but I can't figure out which max/min function this struct use.
std::min/max or numext::min/max can't handle complex number, but there are pmax and pmin in scalar_tanh_op, I can't find any max/min operator on complex number. I know SSE2 optimization will packet complex numbers 4 by 4, but it's still complex number, so It must need max/min operator.

tanh is not vectorized for complex numbers, the packetOp() method you saw is called for float/double only.