Gyrokinetic tokamak plasmas can exhibit intrinsic toroidal rotation driven by the residual stress. While most studies have attributed the residual stress to the parallel-momentum flux from the turbulent E×B motion, the parallel-momentum flux from the drift-orbit motion (denoted Π_{∥}^{D}) and the E×B-momentum flux from the E×B motion (denoted Π_{E×B}) are often neglected. Here, we use the global total-f gyrokinetic code XGC to study the residual stress in the core and the edge of a DIII-D H-mode plasma. Numerical results show that both Π_{∥}^{D} and Π_{E×B} make up a significant portion of the residual stress. In particular, Π_{∥}^{D} in the core is higher than the collisional neoclassical level in the presence of turbulence, while in the edge it represents an outflux of countercurrent momentum even without turbulence. Using a recently developed "orbit-flux" formulation, we show that the higher-than-neoclassical-level Π_{∥}^{D} in the core is driven by turbulence, while the outflux of countercurrent momentum from the edge is mainly due to collisional ion orbit loss. These results suggest that Π_{∥}^{D} and Π_{E×B} can be important for the study of intrinsic toroidal rotation.