The Mathematics of the Pentium Division Bug

Reeections on the Pentium Division Bug

Re ections on the Pentium Division Bug

Anatomy of the Pentium Bug

The Pentium computer chip’s division algorithm relies on a table from which five entries were inadvertently omitted, with the result that 1738 single precision dividenddivisor pairs yield relative errors whose most significant bit is uniformly distributed from the 14th to the 23rd (least significant) bit. This corresponds to a rate of one error every 40 billion random single precision divisions...

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...

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...