The Pentium FDIV bug was five missing entries in the SRT division algorithm's quotient-digit lookup table, a lithography defect

The Pentium performed floating-point division using the SRT algorithm (Sweeney, Robertson, Tocher), which generates several quotient bits per iteration by consulting a lookup table that maps a partial remainder and divisor to the next quotient digit. On the affected Pentiums, this table was implemented as a programmable logic array, and five of its cells were empty when they should have held a quotient digit. Per Vaughan Pratt's 1995 analysis, "the Intel Pentium microprocessor makes occasional errors in floating point divisions due to five missing entries from a lookup table of quotient digits" — the omission traced to a lithography error in fabricating the array rather than to a flaw in the algorithm itself.

Because the five bad cells were reached only by particular combinations of operands, the average error rate was extremely low — on the order of one wrong result in roughly nine billion random double-precision divisions. But the error rate was highly non-uniform. Certain "bruised" operands — small integers and values falling near the threshold conditions that steer the algorithm into a missing cell — could produce wrong quotients far more often than the random-operand average, which is why a systematic computation like a reciprocal sum surfaced the defect (see claim-nicely-twin-prime-project-surfaced-pentium-fdiv-bug) while ordinary use rarely did.

The defect is a hardware realization of the abstraction in claim-linnainmaa-rounding-error-problem: a single local arithmetic error propagating into an accumulated result. It sat beneath the arithmetic layer standardized by claim-kahan-8087-spec-became-ieee-754 — the divide instruction was IEEE-754-conformant in specification but not in silicon — and, like the fabrication know-how in claim-euv-mirror-advantage-is-tacit-know-how-not-patent, it locates the failure in the physical process of building the chip rather than in its design. The commercial fallout is treated in claim-intel-475m-charge-pentium-fdiv-recall.