In the past period of time, Intel has been the world’s largest and most influential processor chip manufacturer.
But back in the 1990s, Intel actually lost billions of dollars due to floating point failures.
A mathematician discovered an equation that threatened Intel’s entire processor thread, and this was just before computing became mainstream.
Next, let us review the floating point failure, which makes the Pentium a laughingstock.
1919
The Norwegian mathematician Viggo Brun proved that the sum of the reciprocal values of double prime numbers (two prime numbers with a difference of 2, such as 3 and 5) converges to a finite value, which is called the Brun’s constant. According to Thomas Nicely, a former professor of mathematics at Lynchburg University, by calculating all double prime numbers to the 14th power of 10, the constant is about 1.902160578. Nicely played an important role in our story.
Intel’s Pentium processor problem seems to be caused by the wrong person looking for a needle in the sea
In order to find the root of this story, let’s play a logic exercise:
There is somethIng wrong with this sentence.
Did you make any mistakes when typing the sentence above? Is it obvious? Will it affect your understanding?
You may have noticed: the capital letter “I” in “somethIng”. This may be a mistake we will make in our lives. Now, imagine if this is the only spelling or grammatical error on this entire website (although this is not the case). Maybe, you copied this website several times and corrected the “I”, so it was not capitalized on the word. But on the original website version, the error still exists. Now imagine that if millions of people search for every phrase I share on the website, more people find this mistake, and one of these people is an influential editor.
Although this error is very small, it is enough to threaten the reputation of a writer. This is the same situation as the error that Nicely found unknowingly after getting the new Pentium processor in October 1994. When looking for the Brun’s constant, he used Intel processors and their floating-point functions, and realized that the answers given by the processors were a bit off.
THOMAS NICELY, as shown in the picture in 1984. Image: Lynchburg University
For most people, this small error will not be noticed. After all, this mistake of Pentium is not the end of the world. But it is an exception for Nicely, because it undermines his research and creates many problems in his equations . In a 1994 CNN interview on Usenet, Nicely told the legendary story:
I have been engaged in pure mathematics research; this involves the operation of double prime numbers, and a long time division operation is performed during the calculation. I found an unusual point and spent months tracking it. Facts have proved that the source is the least suspected object: the chip.
The 60 MHz Pentium chip in Nicely’s hands was the culprit. It took him several months to correctly diagnose the problem and it was due to the CPU. For Nicely and other mathematicians, solving such problems is a very headache. But even a simple mistake like this is enough to damage the high-profile Pentium chip’s reputation in the extremely technical field of mathematics.
After Nicely reported this error on CompuServe on October 30, 1994, it became one of the first stories to be spread over the Internet. Only a few days later, someone posted a message about the problem on the comp.sys.intel group in Usenet, confirming the floating point error. Since then, after this report was reported in the news by the engineering industry publication EE Times, the story spread everywhere. Terje Mathisen, a Norwegian programmer, wrote: “In my opinion, the Pentium in the 60~90MHz model only performs floating point division to single precision.”
From then on, this story began to attract the attention of the engineering and mathematical space. But the real problem may be that Intel made a bigger mistake in dealing with this problem, a commercial mistake.
By the end of November and early December, this story began to attract everyone’s attention and explosively became one of the biggest technical stories of 1994. This year, the Internet began to enter the mainstream for the first time, albeit in a slightly awkward manner. But it is worth noting that although this problem lies in chip design errors, the real problem lies in Intel’s handling. To put it simply, Intel’s best users have not received the respect they deserve.
1913
The year the mathematician Émile Borel first proposed the infinite monkey theorem-this famous theory holds that if a million monkeys typed on a million typewriters for 10 hours a day, they would eventually write a great literary work. In many senses, the problem Nicely stumbled upon was the same thing in the academic field.
Intel Pentium chip. Picture: KRZYSZTOF BURGHARDT /Wi-Ki shared
The real cause of this story’s impact on Intel is due to Intel’s reaction
For Intel, the problem is not the problem itself, but how to deal with the emergence of this problem. Going back to the case mentioned earlier, if you receive an email from a very good editor telling you that you accidentally wrote a capital letter in the entire website, how would you react?
Maybe you will find this error quietly and fix it. But Intel did not do this. Like the correction in the newspaper, the error in the chip is basically decisive. (Well, unless you use something like a programmable array.) The best they can do is to eliminate this error in a future version. Although software can alleviate this problem to a certain extent, if there is a problem with the chip, it cannot be completely corrected unless the chip is replaced. To put it bluntly, although the floating-point error is terrible, it is very small at a macro level.
It’s like you own a calculator, and it will give you an incorrect answer during the entire time you use the calculator. According to the comparison of modern processors, recent processors are troubled by Meltdown and Spectre (most Intel, Power Architecture and ARM chips released in the past 20 years have included the former in their designs), and these defects generally destroy Sex is very big.
They are not theoretical issues, they are basic security risks. The solutions to fix the problems found by these two flaws mean that hardware and software manufacturers must turn off some of the processor’s functions, causing people’s computers to slow down. In some applications (such as cloud computing), such a change actually means that using the same processor will cost you more money and time to perform the same work. In addition to repetitive damage, Intel is still trying to repair these defects.
So how do you treat floating-point errors? Thomas Nicely, the scholar who discovered it, believes that although this was indeed a problem for him, the computer processors at the time were very complicated. This means that if he does not deliberately explore, the problem may not be discovered. “The current generation of microprocessors has become very complicated, it is no longer possible to debug a processor completely.” He told PC Magazine in early 1995. But Intel can certainly handle things better. As the mathematician and MATLAB developer Cleve Moler recalled in 2013, Intel’s initial response to customers had many areas for improvement.
According to Moler, the following is what the customer support organization sends to customers:
There have been many discussions on the Internet about floating-point defects in the Pentium processor. For most users, this is not a problem.
The thing is, Intel has detected a subtle flaw in the division accuracy of the Pentium processor. In rare cases (one in nine billion times), the accuracy of the result will be reduced. In the process of continuous testing of the Pentium processor, Intel discovered this subtle flaw after several trillion floating-point operations. Intel immediately tested the most rigorous technology applications using floating-point units, and after several months, we have not found any errors. In fact, after extensive testing and shipments of millions of Pentium processor-based systems, as far as we know, there is only one report instance affecting users. In this case, when a mathematician was doing theoretical analysis of prime numbers and reciprocals, he saw that the accuracy of the 9th digit to the right of the decimal point was reduced.
In fact, extensive engineering tests have shown that an ordinary spreadsheet user may encounter subtle defects that reduce accuracy once every 27,000 years of use. Based on these empirical observations and our extensive testing, users of conventional software will not be affected. If you have problems with the accuracy of this type of prime number generation or other complicated mathematical problems, please call 1 800 628-8686 (International) or 916 356-3551. If not, your Pentium processor-based system will not encounter any problems. In the use of the computer, if such a situation occurs, Intel will resolve it together with the customer.
As I pointed out above, Intel is very prone to the million monkey problem. The problem highlighted in this passage is that Intel knew about this before Nicely reached out and was a little laissez-faire. This is problematic, partly because the focus has shifted from the technical community who cares about this problem to the ordinary consumers who don’t care about it. Intel tried to put all the pressure on consumers, and launched the Intel Inside brand campaign that year, as well as the consumer-friendly (and trademark-friendly) brand of Pentium chips. But in trying to win the general audience, Intel seems to hint that it no longer takes the existing user base seriously.
For those focusing on technical applications, the floating-point division situation created uncertainty, and Intel’s response was not satisfactory. In a 1994 article in the Wall Street Journal, Dave Bell, a researcher at the Jet Propulsion Laboratory, made it clear that the scientific community may stop using Pentium because of the trouble with chips.
“There are many people who do research and must publish results based on computer simulations,” Bell said. “Perhaps a question now is,’Is it made on the chip in question’?”
The late Intel CEO Andy Grove (Andy Grove), who died in 2016. Image: Intel Free Media
Finally, at the end of 1994, Intel CEO Andy Grove (Andy Grove) posted a response on social media comp.sys.intel. This is not going well, especially for so-called technical figures like Grove. At first, Intel’s Richard Wirt (Richard Wirt) published this post, which led to accusations that the response was fake. Then, Grove posted it in his own name, emphasizing that he attaches great importance to this issue, and pointed out that this issue only appeared on their side more than a year after the initial release of the processor. “We postponed the launch of the chip for a few months to allow more time to check the chip and the system,” he wrote, while emphasizing that no chip is perfect. “For this, we have also worked with many software companies. Extensive cooperation.” In response, it took a better posture than customer service messages that angered many technology users. But if you look at this post, you will find that Grove still has a lot of angry posts to deal with.
“This really makes me very angry. I spent a lot of money on this chip,” one respondent wrote. “But, because I don’t do a lot of complicated math work for some large companies that may wholesale Pentium products, I It’s nothing.” This dynamic may be similar to the bad things you saw on Twitter today. After Thanksgiving in 1994, the Grove news was posted on the Internet, and mainstream media began to report the incident, and the company’s stock was also greatly affected.
This timing is terrible in many ways: 1994 was the first year many families brought home multimedia and Internet-enabled home computers, and many families adopted Pentium chips. These products have been clearly marked as things that ordinary consumers can buy. On the second day of Black Friday, Grove had to try to alleviate the concerns of technology users and scholars. The mainstream media actually played down the legendary color of this chip to the public. Some people took advantage of this situation. For example, IBM was releasing the first PowerPC machines to the public at the time. It removed the Pentium chip from its devices and publicly declared that ordinary consumers would encounter errors every 24 days, not 27,000 years. Maybe the truth is sometime in the middle? This is not a good time for Intel. The public relations crisis finally saw its inevitable ending. On Christmas Eve, Intel saw the signs of failure and recalled these chips. Bren’s constant pulled the trigger.
$475 million
Intel recalls the Pentium chip and must recalculate the relevant cancellation fees. After all, any consumer who wants to replace the new processor can get the new version of the processor. Although this expense was incurred, during the 1994 holiday season, Intel saw sales of its 486 and Pentium processors increase rapidly in demand. Maybe the extra news is a good thing. “Bad companies are destroyed by crises; good companies survive in crises; great companies improve because of crises.”
How would you evaluate the legendary time of Pentium floating-point division defect? Intel found a good way to turn this crisis into an important learning moment. This is highlighted in the company’s decision to convert the notoriously broken chip into a key link. Among them, a sentence of Grove is quoted, which is to remind employees that they are not perfect and they need to learn from their mistakes.
Even if it is flawed, the Pentium processor has become one of the most important technologies released in the 1990s. It has successfully achieved the goal by upgrading the CPU from a simple component hidden in a box to a household name. And it can be said that although there are definitely some more technical users who are unhappy, this legendary incident has improved the company’s image among ordinary computing users, which is also the purpose of the company’s emphasis on brand building. It is worth mentioning that this legendary event actually made a mathematician famous, which is not usually done.
Before that deadly equation that cost Intel 500 million dollars, Thomas Nicely’s fame was a chess and card game predicting football fantasy. He admitted that he didn’t foresee this. “Mathematicians generally have a very private life,” he said in an interview with the Associated Press at the height of the scandal. “I think it’s a bit embarrassing to see my name on the print.”
Nicely, who passed away last year, is regarded as a legend by his peers. Before retiring in 2000, he worked at Lynchburg University for about 30 years.
Perhaps one of the side effects of the scandal was that it once changed his life. He increased the accuracy of Bren’s constant a little more.
For more such interesting article like this, app/softwares, games, Gadget Reviews, comparisons, troubleshooting guides, listicles, and tips & tricks related to Windows, Android, iOS, and macOS, follow us on Google News, Facebook, Instagram, Twitter, YouTube, and Pinterest.