June 21, 2024

Pentium Error: Primes Reveal Errors

Pentium Error: Primes Reveal Errors

For PR reasons, Intel had no choice but to replace the failed chips with new ones. This is mainly because the company has been aware of the error for months without telling users. Although the officials had fixed the newly produced hardware, they hoped the error would not be noticeable in the processors sold so far.

Ordinary users hardly feel the effects

Hope was not at all baseless. In the worst case, the error can lead to an inaccuracy from the fourth decimal place of the number. However, the error usually only appears – if it is present – from the tenth or eleventh decimal place of the number. Also, not all calculations are wrong. Only dividing very specific values ​​leads to problems: from 2.28 x 1047 The different combinations of numerator and denominator that a computer can make are only 3 * 1037 affected. So Intel assumed that standard user error would only occur every 27,000 years on average. On the other hand, scientific studies such as those by Nicely often lead to contradictions. Experts challenged Intel’s assessment, but agreed that most users are unlikely to suffer from the error.

Kindly share this opinion: “Software bugs are likely to cause incorrect results on a Pentium 1,000 to a million times more – more than the processor itself. For the average user, I don’t think the error has any significant impact.” The mathematician explained that he got the feeling, many people overestimate the error. “Retrieval is a waste of resources”, locksmith.

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Segmentation as a source of error

But how did the error happen in the first place? The main difference between the Pentium 486 chips and their predecessors was the algorithm they used to divide numbers. Instead of using the usual method we learn in school, the developers chose the SRT approach, named after the three inventors, Dura Sweeney, James Robertson, and Keith Tocher. In fact, they came up with the idea independently and at about the same time in 1958. Even if the method seems more complicated at first glance, it allows to perform calculations much faster than traditional division.

© Spectrum of Science / Manon Bischoff (Details)

Written division

It is not necessary to know all the details of the SRT method to understand what went wrong with the Pentium. The deciding factor is one aspect common to all division methods: clever guessing as many as possible You must multiply the divisor to get a value smaller than the divisor. For example, if you want to divide 7739 by 39, you first have to check how many times 39 “fit” into 77. One might initially assume 2, but then realize that this is wrong (39 * 2 = 78 > 77). That’s why you start from the beginning with the factor 1.

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In order to adapt the SRT process to Pentium processors as efficiently as possible, the developers used what is known as a transformation table: you select the relevant parts of the divisor (77 in the example above) in the row and the divisor (39) in the column – this then leads to the factorial Desired (1). The 1066 entries contained the possible factors -2, -1, 0, 1 and 2 (there were no more numbers because the decimal system was not used). But when the Intel employees moved the table to the machines, they made a mistake: five entries that were supposed to contain 2 remained empty – and were interpreted as 0 by the processors.

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