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Steps To Troubleshoot Intel Math Coprocessor Errors

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    Over the past few days, some of our readers have come across a known error code related to an intel math coprocessor bug. This issue occurs due to a number of factors. Let’s look at them now. The Pentium FDIV bug is the most famous (or known) due to Intel microprocessor bugs. This was caused by a bug in the whole table of who is looking for, which was a perfect part of the Intel SRT algorithm, which, according to experts, is faster and more accurate.

    1401The product’s floating-point separation problem was subtle, but caused by a specific flaw in the circuit design – the flaw was easily remedied by changing the masks during another manufacturing overhaul from which the chip originated in 1994.one401

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  • The Pentium FDIV bug is a hardware error that affects the floating point unit (FPU), and early Intel Pentium processors. Due to a bug, the processor may incorrectly return floating point binary precedence when dividing certain pairs of all high-precision numbers. The error, for example, was discovered in 1994 by R. Thomas. Nicely, a good professor of mathematics at Lynchburg College.[1] Missing values ​​in the lookup table used by the FPU floating point group results in minor errors in the calculations. Although these errors rarely occur in most applications and also cause small deviations from a certain correct output value, errors can occur frequently and also cause large deviations.[2]

    intel math coprocessor error

    The extent of the FDIV error is inconsistent. Although most Internet users rarely encountered it (Byte magazine calculated that 1 in 9 billion floating-point numbers with random parameters would lead to erroneous results), the [3] bug and Intel’s core processing were heavily criticized . . technical s society.

    intel math coprocessor error

    In December 1994, Intel announced a defective processor recall, our first complete workstation chip recall.[4] $000, estimated total cost associated with complex processor replacement.”[5]


    What causes the Intel Pentium processor to divide some floating points incorrectly?

    The Pentium FDIV bug is a PC bug affecting the floating point (FPU) model of early Intel Pentium processors. Due to a bug, the brand was returning incorrect floating binary reference results when splitting related pairs with high precision numbers. An error discovered in 1994. Thomas.

    In order to improve the floating point division calculation on the Pentium chip compared to the 486DX, Intel decided to replace the shift split and subtract algorithms with Sweeney, Robertson in addition to the Tocher ( srt ) algorithm. .The SRT protocol can generate two of my bits of the result of the division cycle, in contrast to the 486 algorithm, which could only generate one. were filled with one of the following nine values: 1, ≤ ≤ 2, 0, +1, +2. When compiling the original array for each of our Pentiums, the five values ​​were not properly loaded into the array-to-chip burners—so five cells in the new array contained zeros when they were expected to contain +2.< soup> [6]

    Calculations based on these 4 cells lead to errors; errors these potentialsThe values ​​can accumulate many times over due to the recursive integer nature of the SRT algorithm. In pathological cases, the error may be on the order of the fourth digit, although this is rare. The error is usually limited to the ninth of this or the tenth significant digit.[3]

    Only certain combinations of numerator and denominator cause errors. A typical example would probably be a division of 4,195,835 3,145,727. If you perform calculations here in software with a floating point coprocessor selected, such as the Windows Calculator, users can choose whether their Pentium processor will be affected.[ 7]

    What was Intel’s original proposal on the flawed chips?

    Intel’s plan was to release this chip and only fix the lack of future processors. This would make Intel’s promotions a winning bid that no one would believe, and once the processors were available, those that came out would remain fixed and everything would be back to normal.

    When converting hexadecimal to processor second hand format, 4195835 and 0x4005fb = 3145727 = 0x2FFFFF. “5” in 0x4005FB triggers access to “blank” table cells. So the value returned by a good, reliable, buggy Pentium processor is wrong here Four or more digits: with [8]

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    Thomas Nicely, Professor of Mathematics at Lynchburg University, has written a code to enumerate primes, twin primes perfect t Beds and quadruple primes. Others noticed inconsistencies in the calculations on June 13, 1994, shortly after adding their own Pentium system to their computer group, but could not get rid of other factors (such as programming failures, motherboard chipsets, etc.) until October. 15, 1994. [1] On October 24, 1994, no one reported the issue to Intel.[9] that Intel reportedly became aware of each issue in June 1994. that someone started repairing it at such a time but chose not to divulge details and not recall damaged processors. October 30, 1994, [10]

    An email has been sent to various scientific contacts describing the bug and requesting bug testing reports on 486-DX4, Pentium and Pentium clone processors.[9] The pest was quickly checked by others, resulting in news spread over the Internet. The bug has been given the arbitrary name “Pentium FDIV Bug”, which is an x86 assembly language abbreviation of many for the most commonly used classes that affect floating point operations. history [9]

    This first appeared in printon November 7, 1994 in the Electronic Engineering Times In “Intel Fixes a Pentium FPU Bug” by Alexander Wolf[11] CNN in phase A and aired on November 22. It was also reported by The New York Times and The Globe boston and made headlines, the latter.[10][12]

    At the time, Intel paid for the floating point bug, but said it was not serious and might not affect most users. Intel made replacements available to CPU users who could really show what they were hurt. While most independent evaluations suggested that the bug would have a very limited impact on most people, it nevertheless generated significant negative press for the company. IBM ended the sale of Intel-based PCs, causing Intel’s share price to drop significantly. Some [13] industry representatives dismissed IBM’s rationale for the decision; IBM made PowerPC processors most of the time and potentially helped damage the reputation of Pentium or Intel as an industry. However, this decision led PC hardware buyers to demand existing alternatives to Pentium processors, and soonOther PC manufacturers have begun offering “no questions asked” replacements for the troubled Pentium processors.

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