the Pentium FDIV bug
loreA 1994 flaw in the Intel Pentium that returned slightly wrong answers for certain floating-point divisions.
Mathematician Thomas Nicely spotted the error in a lookup table, and Intel's initial offer to replace chips only for those who could prove they were affected caused a public-relations disaster. Intel reversed course, took a charge of roughly 475 million dollars, and the episode reset how the industry handles hardware errata.
In 1994 a mathematician found that the Pentium's floating-point division returned slightly wrong answers for a small set of inputs, because a lookup table in the division circuit was missing a handful of entries. The error appeared around the fourth or fifth significant digit and affected roughly one division in nine billion for random inputs.
Intel's initial response is the part worth studying. The company argued, correctly, that the error was statistically negligible for ordinary users, and offered replacements only to those who could demonstrate they needed the precision. That position was mathematically defensible and completely misjudged the situation, because customers were not evaluating an error rate, they were discovering that arithmetic could be wrong at all.
The escalation forced a full recall costing around 475 million dollars, and the lasting effect was on disclosure culture rather than on chip design. Hardware errata became publicly documented rather than quietly circulated, and the incident is now the standard example of a technically correct response failing catastrophically as communication. The engineering lesson is smaller and still real: an error rate is a property of a distribution, and no user experiences a distribution.
Also known as: FDIV bug, Pentium bug, Intel FDIV
Sources
- Intel Form 8-K filed 21 December 1994, exhibit 99.1: "INTEL ADOPTS UPON-REQUEST REPLACEMENT POLICY ON PENTIUM PROCESSORS WITH FLOATING POINT FLAW; WILL TAKE Q4 CHARGE AGAINST EARNINGS", and "The flaw can produce reduced precision in floating point divide operations once every nine billion random number pairs." At that date the charge was still "as yet unspecified"
- Intel Form 8-K filed 20 January 1995, exhibit 99.2, which puts the figure on it: "Q4 Results impacted by a $475 million charge", a "one-time pretax charge of $475 million" covering "replacement and other costs associated with a divide problem in the floating point unit of the company's Pentium processor"
- Alan Edelman, 'The Mathematics of the Pentium Division Bug', SIAM Review vol. 39, no. 1 (1997), pp. 54-67, DOI 10.1137/s0036144595293959, per the Crossref record: the peer-reviewed account of the flaw
- Thomas Nicely's 1994 report of the flaw, named for precision and not linked: his page answers 404 and the Internet Archive's content host is blocked to every fetch path available here