A math problem cost the chip giant $500million

1993 year ,CPU giant Intel Launched Pentium processor .

The new brand got rid of AMD Wait for the company to 286,386,486 And other digital series brands “ Plagiarism ”, Set up a new image as a leader .

Plus 90 In the early s, it was successfully promoted with a huge amount of money Intel Inside plan , Intel Successfully from a company that mainly supplies computer manufacturers , Turn into a brand that directly faces consumers .

I don't know which genius put Pentium Translated into domineering “ Galloping ”, It's really a brilliant stroke that amazes the audience .

New products , New brand ,Intel It can be said that he is in high spirits , Prepare to rule the world .

But what no one thought was , The one who has high hopes CPU There is a hidden one inside Bug！

1、

Bug The process of being discovered is also quite legendary , We have to start with a mathematical concept .

Back in Greek times , Euclid has proved that there are infinite primes , And the larger the number , The more sparsely primes are distributed .

The magic is , Although the distribution is very sparse , But as long as there is a prime number , You can find another one nearby , for example 41 and 43、101 and 103、10007 and 10009, The difference between them is 2.

Mathematicians give these differences as 2 The continuous prime of has a name ： twin primes .

1919 year , Mathematician of Norway Viggo Brun Proved an interesting thing , Even if there are infinite twin prime numbers , Their reciprocal sum converges to a constant , This constant is called “ Brownian constant ”.

But what bothers mathematicians is ： They don't know whether this Brownian constant is irrational .

With the advent of computers , Some people think of a trick ： With the powerful computing power of computers , Violent solution .

The United States Lynchburg College Professor of Mathematics Thomas Nicely It's one of them , His laboratory happens to be equipped with a new Pentium computer .

compact Nicely To prevent miscalculation , Two algorithms are used to make double insurance , If the answer is different , There must be something wrong somewhere .

Nicely He began to calculate with hope , But the result disappointed him ： The results of the two algorithms are really different ！

After in-depth study ,Nicely Find out ：824 633 702 441 and 824 633 702 443 These two twin prime numbers , They're the last decimal place of their number 10 Bit is miscalculated ！

Nicely Replaced with an old one 486 Computer to calculate , The answer is right .

He uses Pentium computer to recalculate , Error recurrence .

What is wrong with your own program ？ Or the computer ？

Nicely Start eliminating , Eliminate errors in your own code ,Borland Compiler error , Chipset error , It took a whole 4 months , Finally found Bug The origin of ： Galloping CPU.

2、

1994 year 10 month 24 Number ,Nicely Phoning Intel Technical support department , Tell them the problem ,Intel Say there will be a reply in a few days , But I haven't heard from you since .

The reason is simple ,Intel As early as 1994 year 6 Month knew this problem ： Floating point division （FDIV） error .

Galloping CPU Of FDIV Introduced a new 、 Fast implementation method , Used a 2048 Hardware lookup table for item , But because of an accident , Yes 5 Values are not set correctly , They should have been 2, But it was set to 0.

This Bug It will be triggered only when it is calculated with high accuracy , It's hard for ordinary users ,Byte The magazine estimated that , The probability of error is 90 1/100000000 .

Since the impact is small ,Intel The choice is ： hide , Quietly repair , No details will be released .

After all, millions of pieces have been sold CPU 了 , Large scale recall costs too much .

It's not useless ！

3、

There is no reply Nicely I'm upset ,10 month 30 Number , He began to give some IT Famous people and magazines send emails , Include Byte The magazine ,PC Week,InfoWorld,PC Magazine.

This matter quickly ferments on the Internet , A large number of people started the relay race of problem orientation ：

The first player is the one mentioned above Nicely.

The second is Norway Terje Mathis, He quickly confirmed Nicely The problem of , And wrote a simple assembly test program , Sent to comp.sys.intel In newsgroups （ you 're right , Don't talk about social networks at that time , Even BBS Is not popular ）

The third is Germany Andreas Kaiser , He found it. 24 A digital , Their countdown is surging CPU Only single precision results can be obtained .

The fourth is a designer FPU(floating-point-unit) The professionals , California Vitesse Semiconductor designer Tim Coe.

According to 24 Clues of numbers , Speculate that Pentium CPU The cardinality adopted is 4 Of SRT Algorithm , Each clock cycle can generate a two digit quotient , Make the speed twice as fast as before .

It's true , Internal professionals are really good .

To the fifth bar , A super bull appeared ,MATLAB The father of ：Cleve Moler

Moler Summarize the previous data , eureka Bug Laws .

It can be seen that after making a mistake , If you want to cover it, you can't cover it , The more you want to cover , The more people in this world want to pick you up .

But so far ,Intel Pentium hardware Bug Also mainly in the science and technology circle , Breaking the circle still needs to wait for an important moment .

4、

1994 year 11 month 24 Number ,JPL（ Jet Propulsion Laboratory , Qian Xuesen is an important founder ） Two engineers learned about this Bug, It is suggested that the laboratory stop buying Pentium computers .

CNN Reporter Steve · Yang heard JPL Things about , With a good sense of smell, he immediately contacted Moler, Do an interview , In the evening JPL News and Moler The interview was broadcast on TV , The New York times 、 The Boston Globe and others have made a lot of reports , Articles are overwhelming .

Galloping CPU This is originally difficult to appear Bug It suddenly became a hot topic in the streets .

Under the heavy pressure of the media ,Intel Finally admitted the vulnerability of floating-point calculation , But still hard spoken , It claims not to be serious , And only for those users who can prove that they are affected CPU.

This attitude of trying to muddle through caused public anger , Shaken consumers' awareness of Intel CPU The confidence of the .

Other manufacturers also move with the times ,IBM Suspension of sales with Intel CPU PC of , Lead to Intel Stocks fell sharply .

1994 year 12 month , It won't hold Intel Finally announced ： Recall all defective processors .

This is also the first full recall of computer chips in history .

Intel The price to pay for this is ：4.75 Billion dollars , The loss of reputation is even more incalculable .

5、

This is not the end of the story .

Logically, there is something wrong with the hardware , Can't modify , Can only replace .

But don't forget the genius we just mentioned ,MATLAB The father of Cleve Moler ,Tim Coe, Argonne National Laboratory Peter Tang And several engineers from Intel , They worked together , stay 12 month 5 No. 1 actually developed a very clever software repair method .

I won't go into details here , Probably ： In certain circumstances , Multiply both the divisor and the divisor by 15/16, You can enter a safe state .

This fix was posted to the newsgroup , Let everyone use it for free .

Smart Cleve Moler Let the company release a that can detect and correct division errors MATLAB edition , And immediately sent a press release 《MathWorks Repair the Intel Pentium floating point number Bug》.

Just in the Pentium Bug Make a scene , When it is known all over the country , The press release appeared on the fax machines of major American media .

Cleve Moler Successfully implemented a perfect marketing , This year , His company MathWorks Just less than one family 250 People's small company , Then he walked on the fast lane , Become a giant in this field .

Reference material

https://dl.acm.org/doi/pdf/10.1145/3386331《A History of MATLAB》
https://buzzorange.com/techorange/2019/11/08/intel-pentium-bug/
https://faculty.lynchburg.edu/~nicely/pentbug/pentbug.html
https://en.wikipedia.org/wiki/Pentium
https://en.wikipedia.org/wiki/Pentium_FDIV_bug
https://en.wikipedia.org/wiki/Intel#Intel_Inside