ΙΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝ» Ί Ί Ί INTEL MATH COPROCESSOR TECHNICAL OVERVIEW Ί Ί Ί ΘΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΌ INTRODUCTION TO SOFTWARE 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 central processing unit (Intel's 8086, 8088, 286, 386(TM) SX(TM) or 386 DX(TM)) 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 (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. 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. 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 be either waiting for the result or processing other tasks. ΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝ February 25, 1991 Intel FaxBack # 3000 Page 1 ΙΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝ» Ί Ί Ί INTEL MATH COPROCESSOR TECHNICAL OVERVIEW Ί Ί Ί ΘΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝ (continued) ΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΌ 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 a 287-10 Intel Math CoProcessor was added to a 286 PC. ΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝ February 25, 1991 Intel FaxBack # 3000 Page 2 ΙΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝ» Ί Ί Ί INTEL MATH COPROCESSOR TECHNICAL OVERVIEW Ί Ί Ί ΘΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝ (continued) ΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΌ 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 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. ΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝ February 25, 1991 Intel FaxBack # 3000 Page 3 ΙΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝ» Ί Ί Ί INTEL MATH COPROCESSOR TECHNICAL OVERVIEW Ί Ί Ί ΘΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝ (continued) ΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΌ 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). ΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝ February 25, 1991 Intel FaxBack # 3000 Page 4 ΙΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝ» Ί Ί Ί INTEL MATH COPROCESSOR TECHNICAL OVERVIEW Ί Ί Ί ΘΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝ (continued) ΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΌ 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; just plug it in and go. 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 5 year 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. Other ways to contact Intel for information: U.S. and Canada (800) 538-3373 International (503) 629-7354 Fax Machine (800) 458-6231 Compuserve "GO INTEL" MCI MAIL "INTEL SUPPORT" Intel BBS (503) 645-6275 (9600bps, 8 bits, NO parity, 1 stop) Intel is a registered trademark of Intel Corporation. Other brand and product names are trademarks of their respective owners. ΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝΝ February 25, 1991 Intel FaxBack # 3000 Page 5