1. A method of programming an antifuse memory, comprising, for a cell to be programmed, the steps of: counting a number of control pulses of a charge pump circuit; generating from the counted number of control pulses a signal having a value that changes over time to indicate consumed current of the antifuse memory in a memory programming mode; comparing the changing value of the signal with a threshold; and stopping the programming of the cell when said comparing indicates that the threshold has been reached.