Anatomy of the Pentium Bug

Reeections on the Pentium Division Bug

Re ections on the Pentium Division Bug

The Mathematics of the Pentium Division Bug

Despite all of the publicity surrounding the Pentium bug of 1994, the mathematical details of the bug are poorly understood. We discuss these details and supply a new proof of the Coe–Tang result that the at-risk divisors have six consecutive ones in positions 5 through 10. Also, we prove that the worst-case absolute error for arguments in [1, 2) is on the order of 1e–5.

Reflections on the Pentium Division Bug

We review the eld of result-checking and suggest that it be extended to a methodology for enforcing hardware/software reliability. We thereby formulate a vision for \self-monitoring" hardware/software whose reliability is augmented through embedded suites of run-time correctness checkers. In particular, we suggest that embedded checkers and correctors may be employed to safeguard against arithm...

Round-o induced instabilities and some unusual arithmetics

We consider some unusual phenomena that appear in long consecutive calculations due to a new sort of round-oo errors of Pentium oating point division bug type. Mathematical model of these round-oo errors is proposed and new phenomena in numerical simulations of dynamical systems (diierential equations) and other numerical procedures are discussed. It is shown also that these new phenomena could...