How To Deal With Floating Point Processor Errors?
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If you are facing a floating point processor error, this guide can help. The Pentium bug is how a part of a part of a chip comes into being that is supposedly a floating point device, which in turn is used for extremely precise data. In rare cases, the error appears as a result of another division of the operation. Intel stated that all of the errors were due to an omission that appears in the instant transfer formula for computer hardware.
1440If the result of the new floating point calculation of 3.12 is × 10-2, but the answer to the uncountable precision calculation is also 0.0314, then it is nice and clear that with 2 units in the last property, this is a real error. Similarly, if the actual choice of 0.0314159 is represented as ×3.The problem of floating point separation in the processor chip was caused by the fact that in 1994 a subtle but specific flaw in the design of the circuit was easily corrected by changing the masks during another planned production rebuild of part of the larger chip.1410
Is there a floating point flaw on the Pentium processor?
Recently, there has been a lot of talk on the Internet about the floating point error of the Pentium processor, for almost all users it is not dangerous. Here are the facts. Intel small found a flaw in the consistency of the split operation for conventional Pentium processors.
The Pentium FDIV error is a hardware error that usually affects the floatingcomma point (FPU) of early Intel Pentium processors. Due to our own error, the absolute value processor returns incorrect binary floating point results when dividing some numbers of high precision pairs. The error was discovered in 1994 by R. Thomas. Professor Nicely, Mathematics Lynchburg College, am. The amount missing from the lookup table used by the FPU’s floating point division algorithm is approximately equal to the amount used to calculate small errors in “data collection”. While these errors rarely occur in some applications and result in correct performance even with small deviations, slips can occur more frequently and result in large deviations.
A frequently discussed FDIV bug. Although most users rarely encountered this (Byte Interested 1 estimates that in the 9th division, a floating point number of 000 would give inaccurate results with random rules),  was both a real-world error and the original solution to the Intel problem. .was sharply criticized by technicalWhich community.
In December 1994, Intel recalled defective processors, the first major recall of a computer chip. In  January 1995, Intel announced “a pre-tax write-off of $475 million in excess of the profit margin, presumably the total cost associated with defective processor replacements.”[ 5]
Why was the Intel Pentium floating-point bug such a big issue?
-2, then in the last place it will be rejected by 0.1 nine fifty units.14401430Pentium, brainchild of Intel Corp. Featured in 1In 993, as the winner of the Intel 80486 microprocessor, the Pentium contained two processors on a personal chip and about 3.3 1000 transistors.14301420Intel’s plan was to release the microprocessor simply and fix the bug before future processors. This action could bring Intel a lot of profit, no one would know right away, once and after the CPUs run out, there will be fixed CPUs and everything will be fine.1420
In order to improve the speed of floating point division on the Pentium processor compared to the 486DX processor, Intel decided to replace the shift and subtract division algorithm with the Sweeney, Robertson and Tocher (SRT) algorithm. The SRT algorithm can provide two initial division bits per clock, while the 486 algorithm can only generate one. It is implemented using a basic programmable array of 2048 cells, referring to 1066, which were supposed to be tempting cells with one of five -2 values: 0, -1, +1, +2. original When the main board was compiled for the Pentium, five values were not securely loaded into the device, which according to the tables were burned to pieces – thus, five from the material of the boardyou contained zero, whereas “they should have contained +2”. < soup>[ 6]
What causes the Intel Pentium processor to divide some floating points incorrectly?
The Pentium FDIV bug is a hardware bug that affects the first floating point unit (FPU) of Intel Pentium processors. Because the bug will cause the processor to produce some incorrect binary floating point results when pairs of high precision statistics are used together. The bug was made by 94′ Thomas R.
As a result, calculations based on these five cells accumulate errors; These errors can accumulate due to the recursive algorithm nature of SRT. case In pathologically, the error can reach the last significant digit of the result, although this rarely happens. The error is probably usually limited to the 9th 10th or significant digit. Some 
only combinations of numerator and denominator cause irritation. The commonly cited division example is actually 195 4 by 835 3 145 727. If you perform this in any software that uses our floating point coprocessor, such as the Windows calculator, you can determine if that particular Pentium chip is affected. sup>[ 7]
The converted hexadecimal value used by the CPU is 4195835 = 0x4005fb AND means 3145727 0x2FFFFF. Live “5” 0x4005FB in initiates access to “empty” array cells. Therefore, this value returned by the failed Pentium processor is incorrect and consists of four or more digits:
Thomas Nicely, professor of mathematics at Lynchburg College, wrote code to enumerate primes, two primes, prime triples, and best fours. Nett noticed some inconsistencies in the calculations on June 13, in the early 1990s, shortly after he added the Pentium to his group of computers, and was therefore unable to resolve other clues (such as programming errors, motherboard chipsets, etc.). ) who reported it to Intel on October 19, 1994 . October 24, 1994. Intel appears to have become aware of the problem it wasn’t until June 1994 that a patch was started at that time, but the non-workers decided to publish the details and not recall the affected processors. 
October 30, 1994 A kindly sent out a digital bug report to various smart contacts, requesting test reports of numerous Pentium and Pentium clone bugs on the 486-DX4.[ 9]< /sup> The bug has been verified and others in record time, word of mouth quickly spread across the Internet. Acquired bug contains information about “Pentium FDIV error” x86 setup mnemonic language for float divisioncomma, each of our most commonly used commands has been affected.
This message first appeared in print on November 7, 1994, in an Engineering article in Times Electronic, “Intel Repairs a Pentium FPU Bug” by Wolfe, Alexander. CNN editing in the segment that aired November 22. Too much has been covered in The New York and Times The Boston Globe, which headlined all of these articles.
At this point, he acknowledged the Intel-specific floating point bug and stated that it was not fatal and would not change most users. Intel offered replacement processors to customers who could document that they were affected. However, most independent evaluations indicated that the nature of the bug would have very little impact on users, resulting in significant negative press for the contractor. IBM stopped selling Intel processors and PCs, and the prices of core Intel products dropped significantly. IBM’s rationale for the decision was questioned by industry representatives; At that time, IBM produced several PowerPC processors, which may have wonalmost all of the reputational damage done by Pentium, and it could have been Intel as a company. The major decision, however, resulted in corporate buyers asking to replace Pentium processors as well as PC hardware, and shortly thereafter, other PC manufacturers began offering “no-hassle” replacements for mediocre Pentium processors.