1. A network interface controller communication apparatus, comprising: a host interface for connection, via a host bus, to a host processor and a host memory, which is mapped to an address space of the host bus; a network interface, configured to transmit and receive packets over a network; a local memory, which is configured to hold data in a memory space that is not mapped to the address space of the host bus; and packet processing circuitry, which is connected between the host interface and the network interface and is connected to the local memory, through a path not including the host bus, and which is configured to receive from the network interface a packet carrying a remote direct memory access (RDMA) request that is directed to an address in the local memory, and to service the RDMA request by accessing data addressed by the RDMA request, in the local memory, without invoking a transmission of data over the host bus, wherein the packet processing circuitry is configured to determine an address modifier of received RDMA requests, to service RDMA requests for which the address modifier indicates local service, by accessing the local memory and to service RDMA requests for which the address modifier does not indicate the local service, by accessing the host memory via the host bus.