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 early Intel Pentium processors. Because of the bug, the processor would return incorrect binary floating point results when dividing certain pairs of high-precision numbers. The bug was discovered in 1994 by Thomas R. Nicely, a professor of mathematics at Lynchburg College.[1] Missing values in a lookup table used by the FPU's floating-point division algorithm led to calculations acquiring small errors. While these errors would in most use-cases only occur rarely and result in small deviations from the correct output values, in certain circumstances the errors can occur frequently and lead to more significant deviations.[2]
The severity of the FDIV bug is debated. 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.
In December 1994, Intel recalled the defective processors in what was the first full recall of a computer chip.[4] In its 1994 annual report, Intel said it incurred "a $475 million pre-tax charge ... to recover replacement and write-off of these microprocessors."[5]
^Edelman, Alan (January 1, 1997). "The Mathematics of the Pentium Division Bug" (PDF). SIAM Review. 39 (1): 54–67. Bibcode:1997SIAMR..39...54E. doi:10.1137/S0036144595293959. Retrieved April 11, 2021.
^"'A Discussion of and Fix for the Pentium FDIV Bug' from the Notebook Archive (2002)". notebookarchive.org. Wolfram Research, Inc. Retrieved April 11, 2021.
^Tom R. Halfhill (March 1995). "An error in a lookup table created the infamous bug in Intel's latest processor". BYTE. No. March 1995. Archived from the original on February 9, 2006. Retrieved December 19, 2006.
^Carlton, Jim; Yoder, Stephen K. (December 21, 1994). "Computers: Humble Pie: Intel to Replace its Pentium Chips". The Wall Street Journal (Eastern ed.). p. B1.
^"1994 - Annual Report". Intel. June 20, 2020. Archived from the original on February 26, 2017. Retrieved June 20, 2020.
The PentiumFDIVbug is a hardware bug affecting the floating-point unit (FPU) of the early Intel Pentium processors. Because of the bug, the processor...
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Intel Pentium processors Intel Inside PentiumFDIVbug, a well-publicized flaw in the original processor Performance Rating, informally termed Pentium Rating...
processors do not have FDIVbug) Based on P5 microarchitecture Steppings: B1, B3, B5, C2, E0 (Note: D1 stepping processors do not have FDIVbug) Based on P5 microarchitecture...
debugging under its design for testing (DFT) initiative. Following the PentiumFDIVbug, the patchable microcode function took on a wider purpose to allow...
"FDIV" erratum in early Pentium processors, known as the PentiumFDIVbug. This gave incorrect answers to a floating-point division instruction (FDIV)...
Retrieved December 13, 2023. PentiumFDIVbug#Affected models Nicely, Dr. Thomas R. (October 30, 1994). "Dr. Thomas Nicely's Pentium email". Vince Emery Productions...
division operation of the AMD K5 microprocessor in the wake of the PentiumFDIVbug. The interesting applications page of the ACL2 documentation has a...
produces unexpected results in certain situations. For instance, the PentiumFDIVbug caused some Intel microprocessors in the early 1990s to produce inaccurate...
vulnerability. The Intel Pentium series of CPUs had two well-known bugs discovered after it was brought to market, the FDIVbug affecting floating point...
concentrated in integrated circuit design and verification. Since the PentiumFDIVbug, the complicated floating point units of modern microprocessors have...
division operations of the AMD K5 microprocessor in the wake of the PentiumFDIVbug. For his contributions to automated deduction, Moore received the 1999...
tiny error here can make the whole chip useless, or worse. The famous PentiumFDIVbug caused the results of a division to be wrong by at most 61 parts per...
non-BCD data is undefined. On early Intel Pentium processors, floating-point divide was subject to the PentiumFDIVbug. This also affected instructions that...
due to limited precision. Galley division Multiplication algorithm PentiumFDIVbug Despite how "little" problem the optimization causes, this reciprocal...
for example, the PentiumFDIVbug became an expensive fiasco for Intel as it required a product recall because the original Pentium processor's defective...
computations related to the distribution of prime numbers and discovered the PentiumFDIVbug. Nicely left Lynchburg College in 2000. In July 2018, the university...
prison. Worldwide (1994): Intel recalled the original Pentium processors due to the PentiumFDIVbug. USA (October 1994): Over 500,000 Santa Barney Pom-Pom...
was credited in a 1995 Byte magazine article for proposing that the PentiumFDIVbug might have worse consequences than either Intel or IBM was predicting...
Thomas Ray Nicely [de] (1943—2019), US mathematician, discoverer of the PentiumFDIVbug This page lists people with the surname Nicely. If an internal link...
present in the high-level code already, such as for the PentiumFDIV floating-point unit bug, or it can be inserted all the way down to physical synthesis...
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