In wireless networks, energy consumed for communication includes both the transmission and the processing energy. In this paper, point-to-point communication over a fading channel with an energy harvesting transmitter is studied considering jointly the energy costs of transmission and processing. Under the assumption of known energy arrival and fading profiles, optimal transmission policy for throughput maximization is investigated. Assuming that the transmitter has sufficient amount of data in its buffer at the beginning of the transmission period, the average throughput by a given deadline is maximized. Furthermore, a 'directional glue pouring algorithm' that computes the optimal transmission policy is described.