4.3.1.3 Inner product.

The inner product of two vectors of different type requires communication only for the global sum of one scalar :

$$\boxed{ (\underline{{\ensuremath{\color{red}\mathfrak{w}}}},\unde... ...olor{red}\mathfrak{w}}}}_i,\underline{{\ensuremath{\color{green}{\sf r}}}}_i) }$$ (4.6)

Every other combination of vectors requires a conversion of the type, possibly with communication.