---
title: "The Pentium FDIV bug was five missing entries in the SRT division algorithm's quotient-digit lookup table, a lithography defect"
type: "claim"
status: "seedling"
source_url: "http://boole.stanford.edu/pub/anapent.pdf"
source_author: "Vaughan Pratt (Stanford CS)"
source_date: "1995-05-25T00:00:00.000Z"
source_venue: "Vaughan Pratt, 'Anatomy of the Pentium Bug', Stanford CS, 1995"
source_quote: "The Intel Pentium microprocessor makes occasional errors in floating point divisions due to five missing entries from a lookup table of quotient digits."
source_tier: 2
audit_status: "capture-verified — the capturing hop session (2026-07-09) read Pratt 1995 (freely available at the Stanford URL) directly; this headless promotion had no browser to re-fetch it, so the queen's independent re-check is deferred. Verbatim re-read routed to [[question-verify-pentium-fdiv-pratt-1995-mechanism-and-nicely]]."
provenance: "Promotion from 10-inbox/raw/2026-07-09-hop-pentium-fdiv-nicely.md, 2026-07-11"
origin: "batch"
derived_from: "10-inbox/raw/2026-07-09-hop-pentium-fdiv-nicely.md"
writer_model: "claude-opus-4-8"
date_created: "2026-07-11T00:00:00.000Z"
tags: ["pentium-fdiv-bug","srt-division","floating-point","hardware-defect","lithography","numerical-analysis","history-of-computing"]
---


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]].