ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º º º TECH NOTES PART 1: INTEL MATH COPROCESSOR BASICS º º º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ THE INTEL MATH COPROCESSOR GETS DOWN TO BUSINESS ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ 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 ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ 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 ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ 1/90 Intel FaxBack # 3000 Page 1 ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º º º TECH NOTES PART 1: INTEL MATH COPROCESSOR BASICS º º º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ(continued)ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ 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 ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ 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 ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ 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 ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ 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 ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ 1/90 Intel FaxBack # 3000 Page 2 ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º º º TECH NOTES PART 1: INTEL MATH COPROCESSOR BASICS º º º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ(continued)ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ 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 ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ 1/90 Intel FaxBack # 3000 Page 3 ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º º º TECH NOTES PART 1: INTEL MATH COPROCESSOR BASICS º º º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ(continued)ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ 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 ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ 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. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ PRODUCT ³ RATED ³ INTEL ³ ³ NUMBER ³ SPEED ³ MODEL # ³ ÆÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍØÍÍÍÍÍÍÍÍÍÍÍÍÍÍØÍÍÍÍÍÍÍÍÍÍÍÍÍ͵ ³ 8087 (-3) ³ 4.77 MHz ³ BOX8087 ³ ³ 8087-8 (-2) ³ 8 MHz ³ BOX8087-2 ³ ³ 8087-10 (-1) ³ 10 MHz ³ BOX8087-1 ³ ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´ ³ 80287 (-6 or -3) ³ 6 MHz ³ BOX287 ³ ³ 80287-8 ³ 8 MHz ³ BOX287-8 ³ ³ 80287-10 ³ 10 MHz ³ BOX287-10 ³ ³ 80C287A ³ 12 MHz ³ DBOXC287A-12 ³ ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´ ³ 387DX-16 ³ 16 MHz ³ BOX387DX-16 ³ ³ 387DX-20 ³ 20 MHz ³ BOX387DX-20 ³ ³ 387DX-25 ³ 25 MHz ³ BOX387DX-25 ³ ³ 387DX-33 ³ 33 MHz ³ BOX387DX-33 ³ ³ 387SX ³ 16 MHz ³ BOX387SX-16 ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ 1/90 Intel FaxBack # 3000 Page 4 ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º º º TECH NOTES PART 1: INTEL MATH COPROCESSOR BASICS º º º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ(continued)ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ 80C287A GENERAL INFORMATION ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ 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. ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ 1/90 Intel FaxBack # 3000 Page 5