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- ¬ Intel Pentium(TM) Processor: Floating Point Unit Information ¬
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- FLOATING POINT FLAW IN THE PENTIUM PROCESSOR
-
- 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 10e5).
- 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.
-
-
- ------------------------------------------------------------------------------
-
- INTEL CORPORATION INTRODUCES 90 AND 100 MHz PENTIUM(TM) PROCESSORS
-
-
- SANTA CLARA, Calif., March 7, 1994 -- Intel Corporation today
- introduced new Pentium(TM) processors running at frequencies of
- 90 and 100 MHz. The 100-MHz version of the Pentium processor
- runs today's PC software faster than any other processor
- available. It is 50 percent faster than the original version
- announced one year ago and has an iCOMP(TM) index rating of 815
- with a SPECint92 rating of 100.0.
- These new Pentium processors will be manufactured in
- volume at Intel's most advanced microprocessor production
- factories in Ireland and Santa Clara. With the 3.3 volt,
- 0.6 micron, 4-layer metal advanced process technology, the chip
- is approximately half the size of other members of the Pentium
- processor family. This announcement comes on the heels of
- demonstrating a 150-MHz Pentium processor at the IEEE International
- Solid State Circuits Conference (ISSCC) in San Francisco
- approximately two weeks ago.
- "These new products arrive as Pentium processor-based PC's
- are moving rapidly through all channels, including retail, with
- aggressive price points for today's performance-oriented
- applications," said Paul Otellini, senior vice president and
- general manager of Intel's microprocessor product group. "PC
- purchasers can now buy Intel's fastest processor for today's and
- tomorrow's application at very affordable prices. This will
- accelerate Pentium processors entering all market segments,
- including the home, at a rate faster than any previous processor."
-
-
- The New Pentium Processors
- The 90-MHz version of the Pentium processor has an iCOMP
- index of 735 and a SPECint92 rating of 90.0. Both the 90- and
- 100-MHz versions achieve SPECint92 ratings higher than any other
- mass market processor selling today or promised for delivery this
- year.
- The new 90- and 100-MHz processors have a typical power
- dissipation of 4.0 watts or less. Extra features for easier system
- design and multiprocessing have been added such as the Intel advanced
- programmable interrupt controller (APIC), enabling dual processing
- systems at PC price points.
- PCs and servers based on the new chips are expected to be
- announced within the next 60 days from many manufacturers.
- Integrated SL technology will enable Pentium processor-based
- notebook computers with robust power management to be on the market
- later this year.
-
- World's Fastest 486
- A 100 MHz IntelDX4(TM) processor, with an iCOMP index rating of
- 435, also was announced today. A 75-MHz version is also available
- (iCOMP index rating of 319). The 100-MHz version has a SPECint92
- rating of 51.4. The IntelDX4 processor offers up to 50 percent
- more performance than the IntelDX2TM processor.
- "The world's best performing notebooks are based on the
- IntelDX4 processor," said Otellini. "Mobile computer users can get
- the same level of performance as desktop users without compromising
- battery life."
- System manufacturers can use current Intel486(TM) processor
- system designs with minor modifications to benefit from the IntelDX4
- processor's additional performance. Besides the benefits of 3.3 volt
- design for low-power operation, the processor is enhanced with SL
- technology for long battery life notebooks and energy-efficient
- desktops. The IntelDX4 processor has twice the amount of on-chip
- cache (16 kilobytes) as the IntelDX2(TM) microprocessor.
-
- PCI Local Bus
- Intel also introduced the PCI chip set for local bus support for
- the 90- and 100- MHz Pentium processors. The 82430NX PCIset allows
- system manufacturers to build the highest performance desktop
- systems based on the Pentium processor and PCI. The architecture
- of the 82430NX PCIset provides options for multiple system
- configurations to target different price points. The PCIset also
- takes advantage of the fast performance and plug-and-play
- capabilities of the PCI local bus to support high-performance
- graphics, networking, disk drives and multimedia.
-
- Pricing and Availability
- The new versions of the Pentium and the IntelDX4 processors are
- available now. The 90-MHz version of the Pentium processor is
- priced at $849 each in 1,000-piece quantities. The 100-MHz
- version is $995 each in 1,000-piece quantities and is available
- now in limited volumes and moving to high volumes in Q4 1994.
- The 75-MHz IntelDX4 processor is $475 while the 100-MHz IntelDX4
- processor is $580 each in 1,000-piece quantities (Q2 pricing).
- For pricing and availability outside the United States, contact
- the regional Intel sales office.
- For additional information about these new processors or
- other Intel products, contact an Intel sales representative or
- call (800) 628-8686. For literature, contact the Literature Center
- at (800) 548-4725 in the U.S. and Canada, or write to: Intel
- Literature, P.O. Box 7620, Mt. Prospect, IL 60056-7620.
- Intel, the world's largest chip maker, is also a leading
- manufacturer of personal computer networking and communications
- products.
-