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                TECH NOTES PART 1: INTEL MATH COPROCESSOR BASICS            
                                                                            
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   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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       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.

       Ŀ
        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    
       Ĵ
        80287 (-6 or -3)  6 MHz         BOX287       
        80287-8           8 MHz         BOX287-8     
        80287-10          10 MHz        BOX287-10    
        80C287A           12 MHz        DBOXC287A-12 
       Ĵ
        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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   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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