Interrupts are handled using the Interrupt Disable bit in the PCI command register and Interrupt Status bit in the PCI status register. All devices compliant to PCI 2.3 (circa 2002) and all compliant PCI Express devices should support these bits. uio_pci_generic detects this support, and won't bind to devices which do not support the Interrupt Disable Bit in the command register.
On each interrupt, uio_pci_generic sets the Interrupt Disable bit. This prevents the device from generating further interrupts until the bit is cleared. The userspace driver should clear this bit before blocking and waiting for more interrupts.