Pentium FDIV bug
[1] Missing values in a lookup table used by the FPU's floating-point division algorithm led to calculations acquiring small errors.
Though rarely encountered by most users (Byte magazine estimated that 1 in 9 billion floating point divides with random parameters would produce inaccurate results),[3] both the flaw and Intel's initial handling of the matter were heavily criticized by the tech community.
Nicely noticed some inconsistencies in the calculations on June 13, 1994, shortly after adding a Pentium system to his group of computers, but was unable to eliminate other factors (such as programming errors, motherboard chipsets, etc.)
[9] Intel had reportedly become aware of the issue independently by June 1994, and had begun fixing it at this point, but chose not to publicly disclose any details or recall affected CPUs.
During a 2019 talk, while reflecting on development of Quake, John Romero described how frequently and persistently this bug could be reproduced by Michael Abrash.
Abrash spent hours tracking down exact conditions needed to produce the bug, which would result in parts of a game level appearing unexpectedly when viewed from certain camera angles.
[4] The growing dissatisfaction with Intel's response led to the company offering to replace all flawed Pentium processors on request on December 20.
[15] On January 17, 1995, Intel announced a pre-tax charge of $475 million against earnings, ostensibly the total cost associated with replacement of the flawed processors.
Intel's justification for this, posted on its support web page, was that "it is the individual decision of the end user to determine if the flaw is affecting their application accuracy".
[18] While most users were unlikely to encounter the flaw in their day-to-day computing, the company's initial reaction to not replace chips unless customers could guarantee they were affected caused pushback from a vocal minority of industry experts.
The subsequent publicity generated shook consumer confidence in the CPUs, and led to a demand for action even from people unlikely to be affected by the issue.
[4] In the aftermath of the bug and subsequent recall, there was a marked increase in the use of formal verification of hardware floating point operations across the semiconductor industry.
In the development of the Pentium 4, symbolic trajectory evaluation and theorem proving were used to find a number of bugs that could have led to a similar recall incident had they gone undetected.
One specific algorithm, outlined in a paper in IEEE Computational Science & Engineering, is to check for divisors that can trigger the access to the programmable logic array cells that erroneously contain zero, and if found, multiply both numerator and denominator by 15/16.
Some companies, such as Wolfram Research, opted to directly patch the machine code of existing executables to replace the FDIV opcode with an illegal instruction.
