Fpu Error
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Pentium processors. Because of the bug, the processor could return incorrect decimal results when dividing a number. Discovered in 1994 by Professor Thomas R. Nicely intel floating point bug at Lynchburg College,[1] Intel attributed the error to missing entries in the
Pentium F00f Bug
lookup table used by the floating-point division circuitry.[2] The severity of the FDIV bug is debated. Intel, producer of the
Pentium Microprocessor Flaw
affected chip, claims that the common user would experience it once every 27,000 years while IBM, manufacturer of a chip competing with Intel's Pentium, claims that the common user would experience
Thomas Nicely
it once every 24 days. 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. The man who found the bug points out that since it went unnoticed for a year in a floating point rounding error popular product, that likely indicates that the bug was less harmful than IBM suggested. Intel ultimately recalled the defective processors. Contents 1 Chronology 2 Affected models 3 Example symptoms 4 See also 5 References 6 External links Chronology[edit] 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 by Tom Kraljevic, a Purdue co-op student working for Intel in Hillsboro, Oregon, 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 re
here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the floating point arithmetic examples company Business Learn more about hiring developers or posting ads with us Stack Overflow intel pentium chip flaw of 1994 case study Questions Jobs Documentation Tags Users Badges Ask Question x Dismiss Join the Stack Overflow Community Stack Overflow is a community of 4.7 floating point calculator million programmers, just like you, helping each other. Join them; it only takes a minute: Sign up Real life example fo Floating Point error up vote 4 down vote favorite 2 Is there any examples of https://en.wikipedia.org/wiki/Pentium_FDIV_bug a company that was burned by floating point data that caused a rounding issue? We're implementing a new system and all the monetary values are stored in floats. I think if i can show actual examples of why this has failed it'll have more weight than the theory of why the values can't be stored properly. floating-point share|improve this question asked Apr 28 '10 at 20:21 Rob 83221237 add a comment| 6 Answers http://stackoverflow.com/questions/2732845/real-life-example-fo-floating-point-error 6 active oldest votes up vote 3 down vote accepted These examples are from the embedded world (Ariane 5, Patriot) but are not floating-point rounding errors stricto sensu. The Ariane 5 bug is a bug in a conversion. The Patriot bug was introduced during adaptations of the software. It involves computations in different precisions with an inherently unrepresentable constant (which happens to be the innocuous-looking 0.10). There are two problems I foresee with binary floats for monetary values: decimal values as common as 0.10 cannot be represented exactly. If the precision is too small, what could have been a clean overflow raising an exception becomes a hard-to-track loss of precision. Note that base-10 floating-point formats have been standardized precisely for monetary values: some currencies are worth 1/1000000 of a dollar, are never exchanged in less than thousands, and the maximum amount you may want to be able to represent is proportionally big, so a scalable representation makes sense. The intent is that the mantissa is large enough for the largest sums with the official resolution. share|improve this answer edited Jan 22 '13 at 12:10 answered Apr 28 '10 at 20:26 Pascal Cuoq 58.5k5101194 Nice, though the second shows why floats would be a good thing - if consistant. –Michael Dorgan Apr 28 '10 at 20:28
mathematics involved. The Pentium microprocessor is the CPU (central processing unit) for what are now possibly the http://www.willamette.edu/~mjaneba/pentprob.html widest-selling personal computers. Unlike previous CPUs that Intel made, the 486DX and Pentium chips included a floating-point unit (FPU) also know as a math coprocessor. Previous Intel CPUs did https://support.microsoft.com/en-us/kb/78113 all their arithmetic using integers; programs that used floating-point numbers (non-integers like 2.5 or 3.14) needed to tell the chip how (for example) to divide them using integer arithmetic. floating point The 486DX and Pentium chips have these instructions built into the chip, in their FPUs. This makes them much faster for intense numerical calculations, more complex, and more expensive. The problem for Intel is that all Pentiums manufactured until sometime this fall had errors in the on-chip FPU instructions for division. This caused the Pentium's FPU to incorrectly divide intel floating point certain floating-point numbers. Many software packages, including many that do use floating-point numbers, don't actually use a computer's FPU. These packages don't show the error. Also, only certain numbers (whose binary representation show specific bit patterns) divide incorrectly. Consequently many users may never encounter the division error. The most famous example and the worst well-known case is 4195835/3145727, discovered by Tim Coe of Vitesse Semiconductors. The correct value is 1.33382 to 6 sig. figs, while the flawed Pentium's floating-point unit computed 1.33374 to 6 sig figs, a relative error of 0.006%. One can easily test a Pentium using Microsoft's Windows and this example: Use the Windows calculator in scientific mode to divide Coe's numbers and compare to the numbers above. How did all this get into the news? Thomas Nicely is a math professor at Lynchburg College, a school about Willamette's size in Virginia. In summer/fall 1994, he was computing the sum of the reciprocals of a large collection of prime numbers on his Pentium-based computer. Checking his computation, he found the result differed signif
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