Take a look at the "rsqrt_rcp" section of reference [6] in the accuracy report by Gladman et al referenced above. I did that work 10 years ago because some people at CERN had reported getting different results from certain programs depending on whether the exact same executables were run on Intel or AMD cpus. The result of the investigation was that the differing results were due to different implementations of the rsqrt instruction on the different cpus.
I recall from 1965 getting an error message message something like this from the Fortran complier on a Univac 1107 system after receiving too many error messages: "Do not attempt to learn Fortran using Monte Carlo method. Buy a manual in the user office."
I looked into this issue with rsqrt (and with rcp as well) between Intel and AMD processors in connection with CERN some years ago (2016). An unpublished report can be found at [1].
TL;DR: The same (very small) executables gave different results when run on Intel and AMD processors because the rsqrt and rcp instructions produced slightly different outputs on the two systems.
