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The Pentium FDIV bug was a bug in the Intel P5 Pentium floating point unit (FPU). Because of the bug, the processor would return incorrect results for many calculations used in math and science. Intel blamed the problem on a few missing entries in the lookup table used by the company.^[1]

The error was discovered by Professor Thomas R. Nicely at Lynchburg College, Virginia, USA.^[2]

The error was rarely encountered by users (Byte magazine estimated that 1 in 9 billion floating point divides with random parameters would produce inaccurate results).^[3] However, both the flaw and Intel's initial handling of the matter were heavily criticized. Intel ultimately recalled the defective processors.

Chronology

Professor Thomas Nicely, a professor of mathematics at Lynchburg College, had written code to enumerate primes, twin primes, prime triplets, and prime quadruplets. 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.) until October 19, 1994. On October 24, 1994, he reported the issue to Intel. According to Nicely, his contact person at Intel later admitted that Intel had been aware of the problem since May 1994, when the flaw was discovered during testing of the FPU for its new P6 core, first used in the Pentium Pro.

On October 30, 1994, Nicely sent an email describing the error he had discovered in the Pentium floating point unit to various contacts, requesting reports of testing for the flaw on 486-DX4s, Pentiums and Pentium clones.^[2]

This flaw in the Pentium FPU was quickly verified by other people around the Internet, and became known as the Pentium FDIV bug (FDIV is the x86 assembly language mnemonic for floating-point division). One example was found where the division result returned by the Pentium was off by about 61 parts per million.^[2]

The story first appeared in the press on November 7, 1994, in an article in Electronic Engineering Times, "Intel fixes a Pentium FPU glitch" by Alexander Wolfe.^[4]

The story was subsequently picked up by CNN in a segment aired on November 21, 1994.^[2] This brought it into widespread public prominence.

Publicly, Intel acknowledged the floating point flaw, but claimed that it was not serious and would not affect most users. Intel offered to replace processors to users who could prove that they were affected. However, although most independent estimates found the bug to be of little importance and would have negligible effect on most users, it caused a great public outcry. Companies like IBM (whose IBM 5x86C microprocessor competed at that time with the Intel Pentium line) joined the condemnation.

On December 20, 1994, Intel offered to replace all flawed Pentium processors on the basis of request, in response to mounting public pressure.^[5] Although it turned out that only a small fraction of Pentium owners bothered to get their chips replaced, the financial impact on the company was significant. 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.^[2] Some of the defective chips were later turned into key rings by Intel.^[6]

A 1995 article in Science describes the value of number theory problems in discovering computer bugs and gives the mathematical background and history of Brun's constant, the problem Nicely was working on when he discovered the bug.^[7]

Affected models

This problem occurred only on some models of the original Pentium processor.^[8] Any Pentium family processor with a clock speed of at least 120 MHz is new enough not to have this bug.^[8]

On affected models, the Intel Processor Frequency ID Utility checks for the presence of this bug.

The ten affected processors are listed below. The 39 S-spec of those processors are not listed in the Intel processor specification finder web page.

Pentium P5 800 nm 5V
Family	Model	Stepping	Core stepping	Clock rate	FSB speed	S-spec
5	1	3	B1	60 MHz	60 MHz	Q0352, Q0412, SX753
5	1	3	B1	66 MHz	66 MHz	Q0353, Q0413, SX754
5	1	5	C1	60 MHz	60 MHz	Q0466, SX835, SZ949
5	1	5	C1	66 MHz	66 MHz	Q0467, SX837, SZ950

Pentium P54C 600 nm 3.3V
Family	Model	Stepping	Core stepping	Clock rate	FSB speed	S-spec
5	2	1	B1	75 MHz	50 MHz	Q0601
5	2	1	B1	90 MHz	60 MHz	Q0542, Q0613, Q0543, SX879, SX885, SX909, SX874
5	2	1	B1	100 MHz	66 MHz	Q0563, Q0587, Q0614, SX886, SX910
5	2	2	B3	75 MHz	50 MHz	Q0606, SX951
5	2	2	B3	90 MHz	60 MHz	Q0628, Q0611, Q0612, SX923, SX922, SX921, SX942, SX943, SX944, SZ951
5	2	2	B3	100 MHz	66 MHz	Q0677, SX960

The presence of the bug can be checked manually by performing the following calculation in any application that uses native floating point numbers, including the Windows Calculator or Microsoft Excel in Windows 95/98.

The correct value is

\textstyle {\frac {4195835}{3145727}}=1.333820449136241002

However, the value returned by the flawed Pentium is incorrect at or beyond four digits:^[9]

\textstyle {\frac {4195835}{3145727}}=1.333{\color {Red}739068902037589}

Another way of detecting the bug is using the pentnt utility included with Windows NT 3.51, Windows NT 4.0, Windows 2000, or Windows XP.^[10]

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

External links

↑ Template:Cite web
↑ ^2.0 ^2.1 ^2.2 ^2.3 ^2.4 Template:Cite web
↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang Template:Dead link
↑ Template:Cite web
↑ Template:Cite web
↑ Template:Cite web
↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
↑ ^8.0 ^8.1 Template:Cite web
↑ Template:Cite web
↑ Template:Cite web

[1] Template:Cite web

[NicelyFAQ-2] 2.0 ^2.1 ^2.2 ^2.3 ^2.4 Template:Cite web

[3] One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang Template:Dead link

[4] Template:Cite web

[5] Template:Cite web

[6] Template:Cite web

[Cipra_Pentium_Bug-7] One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

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@@ Line 1: / Line 1: @@
-Nice to meet you, my title is Refugia. North Dakota is our beginning location. He used to be unemployed but now he is a computer operator but his marketing never arrives. The preferred pastime for my children and me is to play baseball but I haven't produced a dime with it.<br><br>Here is my website - diet meal delivery ([http://2020.sc/weightlossfooddelivery24650 visit the website])
+{{lead too short|date=November 2013}}
+[[Image:KL Intel Pentium A80501.jpg|right|thumb|180px|66 MHz Intel Pentium (sSpec=SX837) with the FDIV bug]]
+The '''Pentium FDIV bug''' was a [[computer bug|bug]] in the [[Intel]] [[P5 (microarchitecture)|P5]] [[Pentium (brand)|Pentium]] [[floating point unit]] (FPU). Because of the bug, the processor would return incorrect results for many calculations used in math and science. Intel blamed the problem on a few missing entries in the lookup table used by the company.<ref>{{cite web |publisher=[[Intel]] |title=FDIV Replacement Program: Description of the Flaw |date=2004-07-09 |url=http://support.intel.com/support/processors/pentium/sb/CS-013007.htm |id=Solution ID CS-013007 |accessdate=2006-12-19 }}</ref>
+The error was discovered by [[Thomas Nicely|Professor Thomas R. Nicely]] at [[Lynchburg College]], [[Virginia]], [[USA]].<ref name="NicelyFAQ">{{cite web|title=Pentium FDIV flaw FAQ|url=http://www.trnicely.net/pentbug/pentbug.html|author=Professor Thomas Nicely}}</ref>
+The error was rarely encountered by users (''[[Byte (magazine)|Byte]]'' magazine estimated that 1 in 9 billion floating point divides with random parameters would produce inaccurate results).<ref>{{cite journal |author=Tom R. Halfhill |date=March 1995 |title=An error in a lookup table created the infamous bug in Intel's latest processor |journal=[[BYTE]] |issue=March 1995 |url=http://www.byte.com/art/9503/sec13/art1.htm |accessdate=2006-12-19 |format= – <sup>[http://scholar.google.co.uk/scholar?hl=en&lr=&q=intitle%3AAn+error+in+a+lookup+table+created+the+infamous+bug+in+Intel%27s+latest+processor&as_publication=%5B%5BBYTE%5D%5D&as_ylo=&as_yhi=&btnG=Search Scholar search]</sup>}} {{Dead link|date=March 2009}}</ref> However, both the flaw and Intel's initial handling of the matter were heavily criticized. Intel ultimately [[product recall|recalled]] the defective processors.
+==Chronology==
+Professor Thomas Nicely, a professor of mathematics at Lynchburg College, had written code to enumerate [[prime number|primes]], [[twin prime]]s, [[prime triplet]]s, and [[prime quadruplet]]s. 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.) until October 19, 1994. On October 24, 1994, he reported the issue to Intel. According to Nicely, his contact person at Intel later admitted that Intel had been aware of the problem since May 1994, when the flaw was discovered during testing of the FPU for its new [[P6 (microarchitecture)|P6]] core, first used in the [[Pentium Pro]].
+On October 30, 1994, Nicely sent an email describing the error he had discovered in the Pentium floating point unit to various contacts, requesting reports of testing for the flaw on [[Intel 80486DX4|486-DX4s]], Pentiums and [[Pentium compatible processor|Pentium clones]].<ref name="NicelyFAQ" />
+This flaw in the Pentium FPU was quickly verified by other people around the [[Internet]], and became known as the Pentium FDIV bug (FDIV is the [[x86 instruction listings|x86 assembly language mnemonic]] for '''f'''loating-point '''div'''ision). One example was found where the division result returned by the Pentium was off by about 61 parts per million.<ref name="NicelyFAQ" />
+The story first appeared in the press on November 7, 1994, in an article in ''[[Electronic Engineering Times]]'', "Intel fixes a Pentium FPU glitch" by Alexander Wolfe.<ref>{{cite web|title=Intel fixes a Pentium FPU glitch|url=http://davefaq.com/Opinions/Stupid/Pentium.html#glitch|author=Alexander Wolfe}}</ref>
+The story was subsequently picked up by [[CNN]] in a segment aired on November 21, 1994.<ref name="NicelyFAQ" /> This brought it into widespread public prominence.
+Publicly, Intel acknowledged the floating point flaw, but claimed that it was not serious and would not affect most users. Intel offered to replace processors to users who could prove that they were affected. However, although most independent estimates found the bug to be of little importance and would have negligible effect on most users, it caused a great public outcry. Companies like [[International Business Machines|IBM]] (whose [[IBM 5x86C]] [[microprocessor]] competed at that time with the Intel Pentium line) joined the condemnation.
+On December 20, 1994, Intel offered to replace all flawed Pentium processors on the basis of request, in response to mounting public pressure.<ref>{{cite web | url=http://findarticles.com/p/articles/mi_m0EIN/is_1994_Dec_20/ai_15939945 | title=Intel adopts upon-request replacement policy on Pentium processors with floating point flaw; Will take Q4 charge against earnings | accessdate=2006-12-24 | date=1994-12-20 | publisher=Business Wire}}</ref> Although it turned out that only a small fraction of Pentium owners bothered to get their chips replaced, the financial impact on the company was significant. On January&nbsp;17, 1995, Intel announced a pre-tax charge of $475 million against earnings, ostensibly the total cost associated with replacement of the flawed processors.<ref name="NicelyFAQ" />  Some of the defective chips were later turned into [[Keychain|key rings]] by Intel.<ref>{{cite web | url=http://www.boiledbeans.net/2009/04/20/how-many-engineers-does-it-take-to-change-a-lightbulb/ | title=How many engineers does it take to change a lightbulb? | work=Boiledbeans | date=20 April 2009 | accessdate=10 November 2009}}</ref>
+A 1995 article in ''[[Science (journal)|Science]]'' describes the value of number theory problems in discovering computer bugs and gives the mathematical background and history of [[Brun's constant]], the problem Nicely was working on when he discovered the bug.<ref name="Cipra Pentium Bug">{{cite journal
+ | last = Cipra
+ | first = Barry
+ | date = 1995-01-13
+ | title = How number theory got the best of the Pentium chip
+ | journal = Science
+ | volume = 267
+ | issue = 5195
+ | pages = 175
+ | doi = 10.1126/science.267.5195.175
+ | pmid = 17791336
+}}</ref>
+==Affected models==
+This problem occurred only on some models of the original Pentium processor.<ref name="IntelFaq">{{cite web |publisher=[[Intel]] |title=FDIV Replacement Program: Frequently asked questions |date=2009-03-20 |url=http://www.intel.com/support/processors/pentium/sb/CS-012748.htm |id=Solution ID CS-012748 |accessdate=2009-11-10 }}</ref> Any Pentium family processor with a clock speed of at least 120&nbsp;MHz is new enough not to have this bug.<ref name="IntelFaq"/>
+On affected models, the Intel Processor Frequency ID Utility checks for the presence of this bug.
+The ten affected processors are listed below. The 39 S-spec of those processors are not listed in the Intel processor specification finder web page.
+{| class="wikitable"
+|+ Pentium P5 800&nbsp;nm 5V
+! Family !! Model !! Stepping !! Core stepping !! Clock rate !! [[Front side bus|FSB]] speed !! S-spec
+|-
+| align="right"|5 || align="right"| 1 || align="right"| 3 || align="right"| B1 || align="right"| 60 [[Hertz|MHz]] || align="right"| 60&nbsp;MHz || Q0352, Q0412, SX753
+|-
+| align="right"|5 || align="right"| 1 || align="right"| 3 || align="right"| B1 || align="right"| 66 [[Hertz|MHz]] || align="right"| 66&nbsp;MHz || Q0353, Q0413, SX754
+|-
+| align="right"|5 || align="right"| 1 || align="right"| 5 || align="right"| C1 || align="right"| 60 [[Hertz|MHz]] || align="right"| 60&nbsp;MHz || Q0466, SX835, SZ949
+|-
+| align="right"|5 || align="right"| 1 || align="right"| 5 || align="right"| C1 || align="right"| 66 [[Hertz|MHz]] || align="right"| 66&nbsp;MHz || Q0467, SX837, SZ950
+|}
+{| class="wikitable"
+|+ Pentium P54C 600&nbsp;nm 3.3V
+! Family !! Model !! Stepping !! Core stepping !! Clock rate !! FSB speed !! S-spec
+|-
+| align="right"|5 || align="right"| 2 || align="right"| 1 || align="right"| B1 || align="right"| 75 [[Hertz|MHz]] || align="right"| 50&nbsp;MHz || Q0601
+|-
+| align="right"|5 || align="right"| 2 || align="right"| 1 || align="right"| B1 || align="right"| 90 [[Hertz|MHz]] || align="right"| 60&nbsp;MHz || Q0542, Q0613, Q0543, SX879, SX885, SX909, SX874
+|-
+| align="right"|5 || align="right"| 2 || align="right"| 1 || align="right"| B1 || align="right"| 100 [[Hertz|MHz]] || align="right"| 66&nbsp;MHz || Q0563, Q0587, Q0614, SX886, SX910
+|-
+| align="right"|5 || align="right"| 2 || align="right"| 2 || align="right"| B3 || align="right"| 75 [[Hertz|MHz]] || align="right"| 50&nbsp;MHz || Q0606, SX951
+|-
+| align="right"|5 || align="right"| 2 || align="right"| 2 || align="right"| B3 || align="right"| 90 [[Hertz|MHz]] || align="right"| 60&nbsp;MHz || Q0628, Q0611, Q0612, SX923, SX922, SX921, SX942, SX943, SX944, SZ951
+|-
+| align="right"|5 || align="right"| 2 || align="right"| 2 || align="right"| B3 || align="right"| 100 [[Hertz|MHz]] || align="right"| 66&nbsp;MHz || Q0677, SX960
+|}
+The presence of the bug can be checked manually by performing the following calculation in any application that uses native floating point numbers, including the [[Calculator (Windows)|Windows Calculator]] or [[Microsoft Excel]] in [[Windows 95]]/[[Windows 98|98]].
+The correct value is
+:<math>\textstyle \frac{4195835}{3145727} = 1.333820449136241002 </math>
+However, the value returned by the flawed Pentium is incorrect at or beyond four digits:<ref>{{cite web |publisher=Kansas University Institute for Policy and Social Research |title=Pentium FDIV bug - a Picture |date=1994-11-30 |url=http://www.ipsr.ku.edu/stafffil/hoyle/pentium_fdiv/ |accessdate=2010-11-03 }}</ref>
+:<math>\textstyle \frac{ 4195835}{3145727} = 1.333{\color{Red}739068902037589} </math>
+Another way of detecting the bug is using the pentnt utility included with [[Windows NT 3.51]], [[Windows NT 4.0]], [[Windows 2000]], or [[Windows XP]].<ref>{{cite web|url=http://technet.microsoft.com/en-us/library/bb490967.aspx|title=Pentnt}}</ref>
+==See also==
+*[[Pentium F00F bug]]
+*[[Anomaly in software]]
+*[[MOS Technology 6502#Bugs and quirks|MOS Technology 6502 bugs and quirks]]
+*[[Floating point#Accuracy problems|Accuracy problems in floating point operations]]
+*[[Division algorithm#SRT division|SRT division]]
+*[[Hardware Trojan]]
+*[[Kill switch]]
+==References==
+{{reflist|2}}
+==External links==
+*[http://www.trnicely.net/#PENT Personal website of Dr. Nicely, who discovered the bug]
+*[http://www.cs.earlham.edu/~dusko/cs63/fdiv.html A page with precise information, also about the cause]
+*[http://www.maa.org/mathland/mathland_5_12.html Ivars Peterson's Mathland on the bug]
+*[http://www.mathworks.com/company/newsletters/news_notes/pdf/win95cleve.pdf A Tale of Two Numbers], by [[Cleve Moler]] of [[MathWorks]]
+**[http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=1666&objectType=file ZIP-file containing more details] (See [[ZIP file format]] for details on the file)
+*[http://support.intel.com/support/processors/pentium/fdiv/ Intel's official site]
+*[http://www.cpucollection.se/details.php?image_id=784 Unopened Intel CPU box from the FDIV replacement program]
+{{DEFAULTSORT:Pentium Fdiv Bug}}
+[[Category:X86 architecture]]
+[[Category:Hardware bugs]]

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Revision as of 17:39, 26 January 2014

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