Pentium FDIV bug

The Pentium FDIV bug was a bug in Intel's original Pentium floating point unit. Certain floating point division operations performed with these processors would produce incorrect results. According to Intel, there were a few missing entries in the lookup table used by the divide operation algorithm.

The flaw was publicly disclosed by Professor Thomas Nicely, then at Lynchburg College, in 1994.

Although encountering the flaw was extremely rare in practice (Byte magazine estimated that 1 in 9 billion floating point divides with random parameters would produce inaccurate results), both the flaw and Intel's handling of the matter were heavily criticized. Intel ultimately recalled the defective processors.

Chronology

Professor Thomas Nicely, then 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 would later admit that Intel had been aware of the problem since May 1994, when the flaw had been discovered when testing the FPU for its new Intel P6 core, first used in the Pentium Pro.

On October 30, 1994, Nicely sent an email out 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.

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 instruction for floating-point division). Other people found division problems where the result returned by the Pentium was off by up to 61 parts per million.

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.

The story was subsequently picked up by CNN in a segment which aired on November 21 1994. 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. This had a huge potential cost to the company, although it turned out that only a small fraction of Pentium owners bothered to get their chips replaced. Some of the defective chips were later turned into key rings by Intel.

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.

Affected models

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

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

The following tables list the 10 affected processors. The 39 S-spec of those 10 processors are not listed in the intel processor spec finder web page.

Pentium P5 800nm 5V

Family	Model	Stepping	Manufacturing Stepping	Clock rate	FSB speed	S-spec
5	1	3	B1	60 MHz	60 MHz	Q0352
5	1	3	B1	60 MHz	60 MHz	Q0412
5	1	3	B1	60 MHz	60 MHz	SX753
5	1	3	B1	66 MHz	66 MHz	Q0353
5	1	3	B1	66 MHz	66 MHz	Q0413
5	1	3	B1	66 MHz	66 MHz	SX754
5	1	5	C1	60 MHz	60 MHz	Q0466
5	1	5	C1	60 MHz	60 MHz	SX835
5	1	5	C1	60 MHz	60 MHz	SZ949
5	1	5	C1	66 MHz	66 MHz	Q0467
5	1	5	C1	66 MHz	66 MHz	SX837
5	1	5	C1	66 MHz	66 MHz	SZ950

Pentium P54C 600nm 3,3V

Family	Model	Stepping	Manufacturing 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
5	2	1	B1	90 MHz	60 MHz	Q0613
5	2	1	B1	90 MHz	60 MHz	Q0543
5	2	1	B1	90 MHz	60 MHz	SX879
5	2	1	B1	90 MHz	60 MHz	SX885
5	2	1	B1	90 MHz	60 MHz	SX909
5	2	1	B1	90 MHz	60 MHz	SX874
5	2	1	B1	100 MHz	66 MHz	Q0563
5	2	1	B1	100 MHz	66 MHz	Q0587
5	2	1	B1	100 MHz	66 MHz	Q0614
5	2	1	B1	100 MHz	66 MHz	SX886
5	2	1	B1	100 MHz	66 MHz	SX910
5	2	2	B3	75 MHz	50 MHz	Q0606
5	2	2	B3	75 MHz	50 MHz	SX951
5	2	2	B3	90 MHz	60 MHz	Q0628
5	2	2	B3	90 MHz	60 MHz	Q0611
5	2	2	B3	90 MHz	60 MHz	Q0612
5	2	2	B3	90 MHz	60 MHz	SX923
5	2	2	B3	90 MHz	60 MHz	SX922
5	2	2	B3	90 MHz	60 MHz	SX921
5	2	2	B3	90 MHz	60 MHz	SX942
5	2	2	B3	90 MHz	60 MHz	SX943
5	2	2	B3	90 MHz	60 MHz	SX944
5	2	2	B3	90 MHz	60 MHz	SZ951
5	2	2	B3	100 MHz	66 MHz	Q0677
5	2	2	B3	100 MHz	66 MHz	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 in Windows 95/98:

4195835.0/3145727.0 = 1.333 820 449 136 241 002 (Correct value)

4195835.0/3145727.0 = 1.333 739 068 902 037 589 (Value returned by flawed Pentium)

References

See also

• f00f
• Intel
• Anomaly in software
• MOS Technology 6502#Dubious_features

External links

• Personal website of Dr. Nicely, who discovered the bug
• A page with precise information, also about the cause
• Ivars Peterson's Mathland on the bug
• A Tale of Two Numbers, by Cleve Moler of The MathWorks
• ZIP-file containing more details (See ZIP file format for details on the file)
• Intel's official site
• Pentium bug jokes
• Unopened Intel CPU box from the FDIV replacement program
• Intel key chain with Andy Grove quote regarding the FDIV bug