The SAMpler for PICosecond time (SAMPIC) chip has been designed by a collaboration including CEA/IRFU/SEDI, Saclay and CNRS/LAL/SERDI, Orsay. It benefits from both the quick response of a time to digital converter and the versatility of a waveform digitizer to perform accurate timing measurements. Thanks to the sampled signals, smart algorithms making best use of the pulse shape can be used to improve time resolution. A software framework has been developed to analyse the SAMPIC output data and extract timing information by using either a constant fraction discriminator or a fast cross-correlation algorithm. SAMPIC timing capabilities together with the software framework have been tested using pulses generated by a signal generator or by a silicon detector illuminated by a pulsed infrared laser. Under these ideal experimental conditions, the SAMPIC chip has proven to be capable of timing resolutions down to 4 ps with synthesized signals and 40 ps with silicon detector signals.