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1994-12-14
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+--------------------------------------------------------------------------+
¬ ¬
¬ Intel Pentium(TM) Processor: Floating Point Unit Information ¬
¬ ¬
+--------------------------------------------------------------------------+
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.
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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.