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Intel Math CoProcessor Technical Overview
Contents:
INTRODUCTION TO SOFTWARE: DOC. # 3000
As computer application programs get more sophisticated, they also get
larger and slower. Even if your application does not involve math
explicitly, it may use math behind the scenes to do its work. For
example, graphics and font manipulation, spreadsheet calculations, even
chart creation, all involve mathematical operations.
HOW THE INTEL MATH COPROCESSOR WORKS
Your computer's CPU - Intel's 8086(TM), 8088(TM), 286(TM), i386(TM)
SX(TM), i386(TM) SL, i386(TM) DX or i486(TM) SX microprocessors - can,
of course, do basic integer arithmetic (addition, subtraction,
multiplication, division of whole numbers). However, mathematical
operations involving very large numbers, floating point numbers (numbers
with decimals), or more complex calculations put a substantial drag on
the CPU.
The CPU tackles such complex mathematical operations by using software
subroutines. Depending on the complexity of the operation, one of these
subroutines can take hundreds of times longer than a basic arithmetic
function.
The Intel Math CoProcessor (i8087(TM), 287(TM), i387(TM), i487(TM) Math
coprocessor) takes math-intensive operations from the CPU and handles in
one instruction what would take hundreds of instructions on the
general-purpose CPU. For example, a floating point division takes 24.4
microseconds for an 8086/8087 combination and 2,000 microseconds with
the 8086 alone.
FLOATING POINT EXPERT
Specifically, the Intel Math CoProcessor is an expert at floating point
calculations. Its instruction set includes 68 numeric functions for
extended precision, floating point, trigonometric, logarithmic, and
exponential functions.
While a program is running, the CPU continues to control overall program
execution. But when it encounters a floating point operation, it
generates an ESCAPE instruction to the math coprocessor which tells it
to perform the calculation. The math coprocessor operates independently
from the time it receives the instruction to the time it is ready to
pass the result back to the CPU. While the math coprocessor is working,
the CPU can either be waiting for the result, or processing other tasks.
In addition to performing many calculations considerably faster than the
CPU, the Intel Math CoProcessor can often provide much more accurate
answers than software subroutines. The math coprocessor can perform
arithmetic on integers with 64-bit precision in the range of +/- 10E18,
and can process decimal numbers up to 18 digits without round-off
errors. It holds and manipulates all numbers in a format called
"temporary real," which has a precision of 64 bits and a range of +/-
10E4932.
THE INTEL MATH COPROCESSOR AND YOUR APPLICATIONS
The Intel Math CoProcessor can speed up all kinds of business
application software -- probably a program you're using now. The
following examples give you a good idea of how the Intel Math
CoProcessor works with a wide variety of application software to get
work done faster.
GRAPHICS AND DESKTOP PUBLISHING
There are two types of graphics software: bit-mapped and
vector-oriented. Bit-mapped graphics use patterns of dots to make up
lines, letters, boxes, and other shapes and does not take advantage of
Intel Math CoProcessors. Z-SOFT's PC Paintbrush is an example of a
bit-mapped graphics package.
Vector-oriented graphics, however, uses formulas to represent what the
user draws or writes and can benefit from the Intel Math CoProcessor.
For example, when the user draws a circle, the software actually calls
up the formula for a circle. When the user saves the circle to disk, the
formula gets stored. And when the user changes the size or location of
the circle, the software simply changes the parameters of its formula
and recalculates. The Intel Math CoProcessor makes these recalculations
considerably faster, speeding up changes and other redraws.
CHARTS & DIAGRAMS
Picture Perfect and Diagraph/2000 are menu-driven business graphics
programs from Computer Support Corporation. Picture Perfect is designed
to turn data into presentation-quality charts and graphs. Diagraph/2000
creates charts, diagrams, maps, symbols, forms, and much more.
Both programs have been optimized for speed with the Intel Math
CoProcessor. They are vector-oriented and use floating point data and
operations. The math coprocessor helps most on diagrams with bold
lines, shading, and shadowing. Tests show a time savings of 65 to 80
percent for previewing a chart, and 63 to 75 percent for previewing text
when the 287-10 Intel Math CoProcessor was added to a 286 PC.
FONT GENERATION
Font generation is an excellent example of using math behind the scenes.
Users define the typefaces they want with a font package such as
Bitstream's Fontware or SoftCraft, Inc.'s Spinfont or WYSIfonts! The
software applies a formula to produce the size and typeface requested.
The Bitstream Fontware benchmarks show, on average, a 75 percent time
savings with an Intel Math CoProcessor.
POSTSCRIPT EMULATION
POSTSCRIPT EMULATION
Freedom of Press from Custom Applications, Inc., allows you to print
PostScript files on several non-postscript laser and 24-pin dot matrix
printers. The program uses the computer's memory to interpret the
PostScript code and makes a customized bit map for your printer. The
customized bit map is generated using formulas. Intel Math CoProcessors
speed up these formulas considerably.
Tests show that the 287 math coprocessor yielded a 44 percent time
savings for an Epson LQ-850, and a 57 percent time savings for a
Hewlett-Packard LaserJet Series II.
COMPUTER-AIDED DESIGN
Computer-aided design (CAD) is a classic graphics application for Intel
Math CoProcessors. Many CAD drawings are created by specifying
coefficients for formulas. Math coprocessors are used to generate and
change drawings and are essential for image rotations and 3D diagrams.
Many CAD packages today would be so slow without a math coprocessor that
they require one. Benchmarks were done with an older version (2.5) of
Autodesk's AutoCAD to show the dramatic performance increases with Intel
Math CoProcessors (newer releases of AutoCAD will not run without an
Intel Math CoProcessor). They show a 50 percent time savings for hidden
line removal and a 77 percent time savings for drawing regeneration.
SPREADSHEETS AND STATISTICS
Intel Math CoProcessors speed up many common spreadsheet functions,
though some operations are not accelerated at all. Since basic integer
arithmetic (addition, subtraction, multiplication, division of whole
numbers) is performed easily by the main CPU, the math coprocessor will
not accelerate those functions. However, floating point operations are
laborious for the CPU and run considerably faster with an Intel Math
CoProcessor.
Floating point math includes basic arithmetic of numbers with decimals,
trigonometric and exponential functions, and any operations that build
on trigonometry or exponentiation. Many common financial and statistical
functions are based on exponents and work much faster with an Intel Math
CoProcessor.
Consider the net present value formula, the function for the periodic
interest rate, and the formula for standard deviation. Because these
functions contain exponents, they take advantage of the Intel Math
CoProcessor's specialties. The Intel Math CoProcessor can speed up
recalculation time for these and many other common financial and
statistical operations.
SPREADSHEETS
The Lotus 1-2-3 Release 2.01 benchmarks show a sample of different
functions. Each function was tested for math coprocessor sensitivity by
filling all of the cells in a large spreadsheet (200K to 400K) with that
formula. While this does not represent a realistic spreadsheet, it does
give a precise indication of the Intel Math CoProcessor's effect on each
function.
Tests show a range of time savings from 16 percent for multiplication
and division to 80 percent for periodic interest rate (@rate). This
could add up to a savings of several hours a week for many spreadsheet
users.
STATISTICS
Statistical analysis programs take advantage of Intel Math CoProcessors
primarily when working with several data sets and doing floating point
math. The many statistical formulas which are based on exponents run
much faster with an Intel Math CoProcessor installed.
The benchmarks show statistical operations with STSC, Inc.'s
STATGRAPHICS, a fully integrated statistical graphics system for PCs.
The time savings with the Intel Math CoProcessor range from 8 percent
for forecasting to 50 percent for correlation analysis.
DATABASES
Most database applications, including Ashton-Tate's dBASE IV, Fox
Software's FoxBASE +, Borland's Paradox, and Nantucket's Clipper, make
use of Intel's Math CoProcessors for math calculations included in the
database program. The DBASE IV benchmarks show a 65 percent savings for
doing square root and logarithmic calculations. This translates into
similar time savings for any function that uses exponents or logarithms
(net present value, standard deviation, variance, square root).
WE MEAN BUSINESS
So you see, math coprocessors are good for more than just speeding up
engineering and math software. They'll speed up your spreadsheets,
graphics and font packages, chart programs, CAD software, and over other
business programs.
Installation is easy; on most systems it's as easy as plugging it in and
turning your system on. You don't have to worry about compatibility,
because virtually every IBM PC and compatible on the market provides a
socket for an Intel Math CoProcessor. And you don't have to worry about
reliability, because we back every Intel Math CoProcessor with an
industry-leading limited-lifetime warranty.
Visit your PC dealer today, or contact us at one of the numbers below
for information. You may have an application (or two or three) that an
Intel Math CoProcessor could really send screaming.
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