Re ections on the Pentium Division Bug

Re ections on the Pentium Division

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...

Reeections 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.

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...

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...