Editing Pentium FDIV bug (section)

{{redirect|Pentium bug|the 1997 bug affecting Pentium processors|Pentium F00F bug}}
{{Use mdy dates|date=May 2021}}
{{good article}}
{{Short description|Bug in the Intel P5 Pentium floating-point unit}}
[[Image:KL Intel Pentium A80501.jpg|right|thumb|66 MHz Intel Pentium (sSpec=SX837) with the FDIV bug]]
The '''Pentium FDIV bug''' is a [[hardware bug]] affecting the [[floating-point unit]] (FPU) of the [[P5 (microarchitecture)|early Intel Pentium processors]]. Because of the bug, the processor would return incorrect binary [[floating point]] results when dividing certain pairs of [[Significant_figures|high-precision]] numbers. The bug was discovered in 1994 by Thomas R. Nicely, a professor of mathematics at [[Lynchburg College]].<ref name="siam">{{cite journal |last1=Edelman |first1=Alan |title=The Mathematics of the Pentium Division Bug |journal=SIAM Review |date=January 1, 1997 |volume=39 |issue=1 |pages=54–67 |doi=10.1137/S0036144595293959 |bibcode=1997SIAMR..39...54E |access-date=April 11, 2021 |url=http://www-math.mit.edu/~edelman/homepage/papers/pentiumbug.pdf |archive-date=August 14, 2024 |archive-url=https://web.archive.org/web/20240814062858/http://www-math.mit.edu/~edelman/homepage/papers/pentiumbug.pdf |url-status=live }}</ref> Missing values in a lookup table used by the FPU's floating-point division algorithm led to calculations acquiring small errors. In certain circumstances the errors can occur frequently and lead to significant deviations.<ref name="wolfram">{{cite web |title='A Discussion of and Fix for the Pentium FDIV Bug' from the Notebook Archive (2002) |url=https://notebookarchive.org/a-discussion-of-and-fix-for-the-pentium-fdiv-bug--2018-10-10r833w/ |website=notebookarchive.org |publisher=Wolfram Research, Inc. |access-date=April 11, 2021 |language=en}}</ref>

The severity of the FDIV bug is debated. Though rarely encountered by most users (''[[Byte (magazine)|Byte]]'' magazine estimated that 1 in 9 billion floating point divides with random parameters would produce inaccurate results),<ref name="halfhill-199503">{{cite magazine |author=Tom R. Halfhill |date=March 1995 |title=An error in a lookup table created the infamous bug in Intel's latest processor |magazine=[[BYTE]] |issue=March 1995 |url=http://www.byte.com/art/9503/sec13/art1.htm |access-date=December 19, 2006 |url-status=dead |archive-url=https://web.archive.org/web/20060209005434/http://www.byte.com/art/9503/sec13/art1.htm |archive-date=February 9, 2006 }}</ref> both the flaw and Intel's initial handling of the matter were heavily criticized by the tech community.  

In December 1994, Intel [[product recall|recalled]] the defective processors in what was the first full recall of a computer chip.<ref name="wsjhumblepie">{{cite news |last1=Carlton |first1=Jim |last2=Yoder |first2=Stephen K. |title=Computers: Humble Pie: Intel to Replace its Pentium Chips. |work=The Wall Street Journal |edition=Eastern |date=December 21, 1994 |page=B1}}</ref> In its 1994 annual report, Intel said it incurred "a $475 million pre-tax charge&nbsp;... to recover replacement and write-off of these microprocessors."<ref>{{Cite web |date=June 20, 2020 |title=1994 - Annual Report |publisher=Intel |url=https://www.intel.com/content/www/us/en/history/history-1994-annual-report.html|url-status=live|archive-url=https://web.archive.org/web/20170226113353/https://www.intel.com/content/www/us/en/history/history-1994-annual-report.html|archive-date=February 26, 2017|access-date=June 20, 2020}}</ref>