Rounding errors in random number generators Original Research Article

The deviations of the cumulative distribution function from the uniform one for the pseudorandom floating point values produced by integer arithmetics are discussed. It is shown that the converion from fixed point values into floating point values introduces specific artefacts even when the integer arithmetics guarantees ideal uniformity. Two type of defects are considered: the appearance of the value 1.0 among pseudorandom values, and the sharp jumps of uniformity at the level of discreteness which corresponds to the computer representation of the floating point values. The non-uniformity at small level of discreteness can be neglected in most cases, but the appearance of the parasitic value 1.0 where nobody expects it can be very dangerous if special precautions are not taken by the user. Both defects are demonstrated using the random number generator from the system library of the Microsoft Power Station Fortran 1.0.