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╔═════════════════════════════════════════════════════════════════════════╗
║ ║
║ TECH NOTES PART 1: INTEL MATH COPROCESSOR BASICS ║
║ ║
╚═════════════════════════════════════════════════════════════════════════╝
THE INTEL MATH COPROCESSOR GETS DOWN TO BUSINESS
────────────────────────────────────────────────
If you thought math coprocessor chips were only for scientists,
engineers and programmers doing lots of mathematical calculations,
think again. The Intel Math CoProcessor can be a big help to business
users, by speeding up business and graphics applications -- software
like Lotus 1-2-3, dBASE IV, Freelance Plus, and AutoCAD. In fact, the
Intel Math CoProcessor makes over 160 popular software programs run up
to five times faster.
HOW THE INTEL MATH COPROCESSOR WORKS
────────────────────────────────────
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.
Your computer's central processing unit (Intel's 8086, 8088, 286 or
386) 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 standard CPU
instruction.
The Intel Math CoProcessor (8087, 287, 387(TM)) 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.
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.
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. The math coprocessor operates
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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 be either 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
examples in Tech Notes part 2 (FaxBack document number 3106) give you a
good idea of how the Intel Math CoProcessor works with a wide variety
of application software to get work done faster.
DEVELOPMENT SUPPORT FOR THE INTEL MATH COPROCESSOR
──────────────────────────────────────────────────
Developers do not have to be concerned with whether or not a math
coprocessor is present. Unless the programmer specifies otherwise, the
compiler inserts code to check for an Intel Math CoProcessor. Each
time the program runs, it tests for math coprocessor presence. If the
chip is installed, it will automatically be used for floating point
operations. Otherwise, the program will use the software subroutines
that emulate the math coprocessor.
Of course, many business applications can run either with or without
math coprocessor, because the program includes both the software
emulator and the math coprocessor instruction set. The software
emulation is much slower than the Intel Math CoProcessor, but it gives
programs more flexibility.
SELECTING THE RIGHT INTEL MATH COPROCESSOR
──────────────────────────────────────────
Before purchasing a math coprocessor, make sure that you know which
math coprocessor is recommended for your computer. You can usually
find this information in your computer's User Guide. Intel's FaxBack
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║ TECH NOTES PART 1: INTEL MATH COPROCESSOR BASICS ║
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System also contains Math CoProcessor Compatibility Lists for many
widely used computers. If your computer is not listed, you'll need to
ask the computer manufacturer or their representatives which Intel Math
CoProcessor is right for your computer.
If these sources don't provide the necessary information there are some
general guide lines you can follow to determine which Intel Math
CoProcessor may be right for your computer. Due to the variety of ways
computers can access math coprocessors, these rules may not apply to
all computers.
Every computer contains a crystal which sets the system speed. Many
computers run the microprocessor and the math coprocessor at the same
speed, but some computers divide the crystal frequency differently for
the microprocessor than for the math coprocessor. The following
sections describe the relationships between crystal speed,
microprocessor speed and math coprocessor speed.
8088/8086 BASED COMPUTERS
In 8088/8086 computers, the microprocessor and math coprocessor run at
the same speed (1/2 crystal speed). For example, a 10-MHz 8088
computer would generally require a 10-MHz Intel Math CoProcessor. An
8-MHz 8088-based computer would require an 8-MHz Intel Math
CoProcessor. If at all possible though, find out which speed Intel
Math CoProcessor is recommended by the manufacturer.
80286 BASED COMPUTERS
In 80286-based computers, the microprocessor runs at 1/2 the crystal
speed but the math coprocessor can run at either 1/2 or 1/3 the crystal
speed depending on the design of the system board. For example, in a
computer with a 16 (MHz) crystal, the 80286 microprocessor runs at 8
MHz but the 80287 math coprocessor may run at either 8 MHz or 5.33 MHz.
In a computer with a 24 MHz crystal, the microprocessor runs at 12
MHz; the math coprocessor may run at either 12 MHz or 8 MHz.
Each system board manufacturer decides which method to use for
accessing the math coprocessor in their computers. This makes it
especially important with 80286-based computers to know which Intel
Math CoProcessor the manufacturer recommends for your model of
computer. Read your computer's User's Guide to find this information
or contact your computer dealer or manufacturer.
386(TM) DX BASED COMPUTERS
In 386-based computers, the microprocessor and math coprocessor run at
the same speed (1/2 the crystal speed). For example, a 20 MHz 386DX
computer will require a 20 MHz Intel Math CoProcessor. Also, you must
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know if your 386-based computer uses either a DX or SX microprocessor.
You must use a 387DX math coprocessor with a 386DX microprocessor and
an 387SX math coprocessor with an 386SX microprocessor. The DX or SX
designation will appear as part of the 386 chip number similar to the
387 examples in the chart which follows this section. Check with your
computers manufacturer or authorized dealer if you are uncertain which
Intel Math CoProcessor is compatible with your computer.
486 BASED COMPUTERS
Intel does not manufacture a separate math coprocessor chip for 486-
based computers. The math coprocessor is built right into to 486.
INTEL MATH COPROCESSOR IDENTIFICATION SYSTEM
────────────────────────────────────────────
Every Intel Math CoProcessor is marked to indicate its product number
and maximum operating speed. Currently, Intel marks the top of each
chip with the math coprocessor product number, a dash, then a number
representing the maximum speed of the chip. Usually this number
represents the speed in megahertz (MHz), but Intel's previous marking
scheme was slightly different. The numbers in parentheses in the
following chart are from this previous marking scheme.
┌──────────────────┬──────────────┬──────────────┐
│ PRODUCT │ RATED │ INTEL │
│ NUMBER │ SPEED │ MODEL # │
╞══════════════════╪══════════════╪══════════════╡
│ 8087 (-3) │ 4.77 MHz │ BOX8087 │
│ 8087-8 (-2) │ 8 MHz │ BOX8087-2 │
│ 8087-10 (-1) │ 10 MHz │ BOX8087-1 │
├──────────────────┼──────────────┼──────────────┤
│ 80287 (-6 or -3) │ 6 MHz │ BOX287 │
│ 80287-8 │ 8 MHz │ BOX287-8 │
│ 80287-10 │ 10 MHz │ BOX287-10 │
│ 80C287A │ 12 MHz │ DBOXC287A-12 │
├──────────────────┼──────────────┼──────────────┤
│ 387DX-16 │ 16 MHz │ BOX387DX-16 │
│ 387DX-20 │ 20 MHz │ BOX387DX-20 │
│ 387DX-25 │ 25 MHz │ BOX387DX-25 │
│ 387DX-33 │ 33 MHz │ BOX387DX-33 │
│ 387SX │ 16 MHz │ BOX387SX-16 │
└──────────────────┴──────────────┴──────────────┘
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║ TECH NOTES PART 1: INTEL MATH COPROCESSOR BASICS ║
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╚════════════════════════════════(continued)══════════════════════════════╝
80C287A GENERAL INFORMATION
───────────────────────────
This is a CHMOS version of the 80287. The advantage of the 80C287A is
that it consumes 70% less power than a 287, yet runs at speeds up to
12.5 MHz. With its low power consumption, this chip is ideal for
laptop computers.
The 80C287A chip is the same size as existing 287's, but it will work
only in computers specifically designed to use it. Examples of
computers that are compatible with 80C287A are the Toshiba T1600,
Zenith Supersport 286, Compaq SLT/286, Compaq 286e, and the Hewlett
Packard LS-12. Do not install this chip in your computer without the
manufacturers recommendation! Read your computer's User Guide or call
the manufacturer or dealer to find this information.
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