In a previous study we developed an elegant technique to compute the signal travel time delay due to the neutral atmosphere, also known as slant total delay (STD), between a Global Positioning System (GPS) satellite and a ground-based receiver utilizing data from a numerical weather model (NWM). Currently, we make use of NWM data from the Global Forecast System (GFS) because short-range forecasts are easily accessible. In this study we introduce some modifications which double the speed of our algorithm without altering its precision; on an ordinary PC (using a single core) we compute about 2000 STDs per second with a precision of about 1 mm. The data throughput and precision are independent of the vacuum elevation (azimuth) angle of the receiver satellite link. Hence, the algorithm allows the computation of STDs in a mesobeta-scale NWM with an unprecedented speed and precision. A practical by-product of the algorithm is introduced as well; the Potsdam Mapping Factors (PMFs), which are generated by fast direct mapping utilizing short-range GFS forecasts. In fact, it appears that the PMFs make the application of parameterized mapping in GPS processing obsolete.