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PARSIFAL (PARametrized SImulation by Farinelli And Lavezzi) is a fast and reliable software tool that reproduces the complete response of a triple-GEM detector to the passage of a charged particle, taking into account the main physical effects. Starting from the detector configuration and the particle information, PARSIFAL reproduces ionization, spatial and temporal diffusion, effect of magnetic field, if present, and GEM amplification to provide the dependable triple-GEM detector response. In the design and optimization stages of this kind of detectors, simulations play an important role. Accurate and robust software programs, such as GARFIELD++, can simulate the transport of electrons and ions in a gas medium and their interaction with the electric field, but they are CPU-time consuming. The necessity to reduce the processing time while maintaining the precision of a full simulation is the main driver of this work. For a given set of geometrical and electrical settings, GARFIELD++ is run once-and-for-all to provide the input parameters for PARSIFAL. Once PARSIFAL is initialized and run, it produces the detector output, including the signal induction and the output of the electronics. The results of the analysis of the simulated data obtained with PARSIFAL are compared with the results of the experimental data collected during a testbeam: some tuning factors are applied to the simulation to improve the agreement. This paper describes the structure of the code and the methodology used to match the output to the experimental data.