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Toshiba Address The Intel Pentium™ Processor Flaw (46835)
Based on Intels recent acknowledgment and analysis of the Pentium processors floating point flaw which may result in reduced precision in exceedingly rare circumstances, Toshiba America Information Systems, Inc. concludes that it represents a minimal user risk and will continue shipping its new T4900CT Pentium-based notebook computer.
According to Intels extensive analysis, the slightly reduced precision occurs for certain rare floating point divisions. The precision of the result ranges from the 4th to the 19th significant digit. Based on Intels studies, the chance of encountering such an error has been calculated to be once in every 27,000 years of average spreadsheet calculations or 1-in-9 billion random divisions. Based on these facts, the typical applications for the Toshiba T4900CT notebook computer -- high-end multimedia, field force automation, computer-based training and communications -- are not likely to be affected.
Toshiba fully supports its products, including third-party components, and is committed to providing total customer satisfaction through its service and support programs. As a result of this anomaly in todays Pentium processors, Toshiba and Intel have implemented a joint program to address customer concerns and issues. Since the 3.3-volt 75MHz Pentium processor is a non-socketed, tab-bonded processor, it requires a full motherboard replacement. If a replacement is required, Toshiba will replace the motherboard through its Toshiba Authorized Service Providers.
To obtain additional information on the floating point flaw in the Pentium processor, customers may request document #7999 from the Intel FaxBACK hotline by calling
1-800-628-2283. Intel may also be contacted directly at 1-800-628-8686 to discuss their specific application impact and replacement policy. Toshiba continues to stand behind its products and we encourage you to contact your local sales representative for assistance.
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12/20/94 - 1.0
Overview
Earlier this year, as a part of Intel's ongoing testing and product development work, a flaw was discovered in the floating point unit (FPU) of the Pentium processor. This flaw affects the accuracy of the floating point divide instruction for certain combinations of input operands (i.e. certain combinations of specific numbers). The impact of the flaw is that for one in nine billion possible independent divides, the precision of the result is reduced. The flaw can occur in all three (single, double, and extended) precisions, and is independent of rounding mode. The flaw was detected during the course of over seven trillion divisions of testing that have been performed on the Pentium processor, and a detailed investigation has determined the cause.
Description
For certain rare divisions (approximately one in nine billion divide pairs), the result of a floating point divide is returned with reduced precision. The flaw is due to a problem with the lookup table used by the iterative algorithm that performs the divide instruction. There is no simple characterization of the values for which this flaw occurs. However, Intel has run trillions of different random divides to validate that the occurrence is less than one in nine billion: the precision of the result ranges from the 4th to the 19th significant digit (or the 4th to the 19th place after the decimal point in numbers expressed in scientific notation, an example of which is 0.12345 x 105). Statistically, for these values, the 4th significant digit is the least likely position for an error. Importantly, intensive testing has shown that no known physical constant causes the reduced precision.
Types of Applications Analyzed
The impact of the flaw varies by the rate of use of floating point instructions, the input data fed to them, the use of the results in further computations, and the needed accuracy of the application. Intel has assessed the likely impact of the flaw on three types of applications that might be run on a Pentium processor-based system. These include: (i) commercial PC applications on desktop and mobile platforms running MS-DOS*, Windows*, and OS/2*. This class includes basic spreadsheets and accounting applications and personal finance; (ii) technical and workstation applications, such as engineering and scientific, advanced multimedia, educational and financial applications (thus this class includes power users of spreadsheets such as financial analysts and financial engineers); and (iii) server and transaction processing applications.
Commercial PC Applications
These applications were addressed by extensive internal validation and surveying external experts. A large majority of these applications do not invoke the floating point unit at all, much less floating point divides. This includes applications such as word processing, text editing and e-mail. In the commercial PC domain, the majority of applications that do use floating point do not invoke an appreciable number of different divides and hence do not introduce meaningful failures that will pose a data integrity problem during the useful life of the part. For applications such as corporate financial analysis and forecasting, marketing analysis, planning and so forth, the likelihood of encountering reduced precision divides is low. This is because typical calculations here are dominated by comparisons and additions. The input-output operations and the time for human conception of the results consume orders of magnitude more time than the processor spends performing arithmetic operations. This effect limits the number of divisions that are computed per day to well below what is necessary to have any appreciable probability of experiencing a meaningful inaccuracy. As an example, consider a large budget calculation implemented as a 700x700 cell spreadsheet, which is run an average of a few times a day. This will produce fewer than 10,000 divisions a day (on average): so few divisions that no reduced precision is likely to be seen for thousands of years. A more typical spreadsheet user doing 1000 divides per day will encounter this reduced precision once in every 27,000 years of use.
Technical/Workstation Applications
The second class of applications studied were workstation applications, broken down further: scientific/engineering and financial. Scientific and engineering applications were studied extensively using leading vendors' analysis and simulation packages. These applications, such as structural mechanics, fluid mechanics, computational biology, chemistry, and mathematics, were studied to determine the numerical effects of the reduced precision. For structural mechanics -- among the worst problems for numerical convergence -- an error in the fourth significant digit would appear no more often than once every thousand years. Many other applications that iterate to convergence, such as circuit simulation, are even less susceptible to reduced precision due to the algorithms they employ. The average over a large range of applications was an expected meaningful error rate of less than one per thousand years. Particular technical applications employing unusually large numbers of divides and requiring extra precision need to be evaluated individually.
Many workstation financial applications perform a significant number of divides, but the impact of the reduced precision is likely to be low, varying with the likelihood of its propagation. The typical financial user will not likely see a meaningful error in the usable life of the machine. In fact, the likelihood is less than one error per 270 years of use.
However, as the most intensive floating point use is in this category and these are the applications which could possibly suffer meaningful error, users of these applications should contact Intel for more information.
Server Applications
Database and file server applications typically do essentially no floating point computations and thus are unffected by the flaw.
Conclusions
There is a flaw in the precision of the floating point divide operation of the Pentium processor. The impact of the flaw varies by the rate of use of floating point instructions, the input data fed to them, the use of the results in further computations, and the needed accuracy of the application. The flaw is not meaningful for the vast majority of commercial PC applications. The flaw is not likely to be meaningful over the usable life of the processor for the remainder of these commercial applications and most workstation applications. Some workstation applications may see occasional reduced precision results from the flaw. The flaw has no effect on server applications.
Intel will work with users of applications involving intensive floating point calculations and resolve their concerns in the appropriate fashion, including, if necessary, replacing their chips. Please call Intel at 1-800-628-8686 (international: 916-356-3551) if you have concerns or need more information relating to this issue.