Speeding up N-body Calculations on Machines without Hardware Square Root

The most time consuming part of an N-body simulation is computing the components of the accelerations of the particles. On most machines the slowest part of computing the acceleration is in evaluating r^-3/2, which is especially true on machines that do the square root in software. This note shows how to cut the time for this part of the calculation by a factor of 3 or more using standard Fortran.