We have also explored the advantages of IEEE arithmetic in implementing linear algebra routines. For example, the accurate rounding properties of IEEE arithmetic permit high precision arithmetic to be simulated economically in short stretches of code, thereby replacing possibly much more complicated low precision algorithms. Second, the ``friendly'' exception handling capabilities of IEEE arithmetic, such as being able to continue computing past an overflow and to ask later whether an overflow occurred, permit us to use simple, fast algorithms which work almost all the time, and revert to slower, safer algorithms only if the fast algorithm fails. See [23] for more details.
However, the continuing importance of machines implementing Cray arithmetic, the existence of some machines that only implement full IEEE exception handling by slowing down all floating point operations significantly, and the lack of portable ways to refer to exceptions in Fortran or C, has led us not to include these improved algorithms in this release of LAPACK. Since Cray has announced plans to convert to IEEE arithmetic, and some progress is being made on standardizing exception handling[65] we do expect to make these routines available in a future release.