Nash - Scientific Computing with PCs, страница 10

For such applications, we note that there are alsoautomatic differentiation programs (Griewank, 1992; Fournier, 1991) which "differentiate program code"rather than produce analytic derivatives. A different task occurs in some statistical calculations (Baglivo,Olivier and Pagano, 1992) where symbolic "computation" of expressions may permit exact rather thanapproximate statistical tests to be performed. One can even prove theorems in some situations.Combined symbolic and computational tools for problem solving are becoming more widely available andeasy to use.

Their application to user problems remains a challenge.3.5Getting things to workThe message of this chapter is threefold:•PCs may have physical or logical limitations to the solutions of a particular sub-task that prevent usfrom solving our problem;•Such obstacles should be identified before we do all the programming and related work;•Finding appropriate software we can use without many hours of programming and testing is the mainobstacle to use of a PC.This message is primarily not just for PCs — it applies to any situation where we want to change fromone computing environment to another.Whereas two decades ago, almost all scientific computing involved some form of programming, manyusers now accomplish their work without ever working with FORTRAN or Pascal or C.

"Programming"is still going on, sometimes almost explicitly in high level languages such as GAMS or MATLAB, but moreoften in such tools as spreadsheets, statistical packages or optimization systems.As an early example of such uses, we note the investment analysis of Kahl and Rentz (1982) who discussa complicated depreciation analysis problem (called Capital Cost Allowance in Canadian tax law) underconditions prevailing before and after the November 1980 Federal Government of Canada budget. Theproblem was quickly and easily solved without requiring any knowledge of programming.Previous24Copyright © 1984, 1994 J C & M M NashNash Information Services Inc., 1975 Bel Air Drive, Ottawa, ON K2C 0X1 CanadaHomeSCIENTIFIC COMPUTING WITH PCsCopy for:Dr.

Dobb’s JournalPART II: Computing environmentsThe next eight chapters are concerned with the computer facing the user. This is as mucha function of the software as the hardware, but the current marketplace offers so manyplug-in options that the familiar boxes which house well-known PC systems may holdentire replacement computers. With this caution, we now turn to the study of thecomputing environment that presents itself to a user. Users who are familiar withcomputer hardware and software may wish to skim this material, which provides a baseof information about PCs so that implications for scientific problem solving can beaddressed in later chapters.Chapter 4Will a PC suffice?4.14.24.34.44.54.64.74.84.84.94.104.114.124.13HardwareSoftwareInterfacing, communications and data sharingPeripheralsOperational considerationsIssues to be addressedProgramming effectivelyThe software development environmentInput/output problems — bugs and glitchesDebugging and troubleshootingPrecision problemsSize problemsUtilities and supportSummaryEvery computing device has its own strengths and weaknesses.

For purposes of calculation in particular,some machines are clearly more attractive as tools in that they provide greater speed, better precision,more memory capacity, more data storage or better software support. This chapter attempts to providea comparison between PCs and other computers based on the above criteria.Next4: WILL A PC SUFFICE?4.125HardwareThe actual electronic components of PCs are quite similar to and sometimes the same as those used inlarger machines. There are simply fewer pieces — less memory, fewer processor parts, fewer powersupplies, fewer input/output channels.

Higher performance of mainframes and workstations comes fromparallelism in the processes — winning the race by being able to do many things at once. PCs are rapidlyclosing this gap. Most microprocessors, until recently, handled 8 or 16 bits at a time, but 32-bit processorsare now common.There are many factors that contribute to the time required to execute a given program. The word sizeand cycle time, while important basic measures for theoretical speed, have little to do with the measuredtime for a particular job. Computer purchasers should remember that price and performance are the mainconsiderations for any piece of equipment.

How a given performance level is achieved should beimmaterial, be it PC, workstation or mainframe.A more serious matter related to the word size has been the address space of the machine. Mostcomputers work with Random Access Memories (RAMs), meaning that any single element of data canbe retrieved or stored equally quickly. To do this, memory is arranged as an array of pigeonholes or cells,each of which has a location number or address. Of course, each cell can only store a certain amount ofdata. Since addresses are data when used within programs, there is a relationship between the word size(memory cell capacity) and the maximum address allowed. Many 8- and 16-bit processors use a 16-bitaddress.

That is, the 8-bit machines must use two memory cells for each address. The 16-bit address spacemeans memory cells can be numbered from zero (0) to 216-1 This is the 64K limit common to many earlyPC systems. At any one time, such computers can access only 65536 = 216-1 memory cells. This means thatprogram, data and operating system functions must all be fitted into this maximum space. Whenever anew function is added to the system software, the amount of memory available to the user’s program anddata is correspondingly reduced.For example, in a machine that stores a floating-point number in only 32 bits or 4 bytes, a matrix 100 by100 requires 40K bytes of memory, leaving very little room for the program to work with it.

Clearly userswho must have such arrays in memory in order to solve their problems are going to be hard pressed tomake them fit. On typical PCs of the late 1970s, the Intel 8080, Zilog Z80, Motorola 6800 and Mostek 6502processors all imposed limits of this type. Some imaginative solutions were invented to overcome theproblem. For example, clever use of special input/output or other instructions allowed the processor tolook at different banks of memory, one at a time. This is like the movable stacks in some libraries.

Apatron can move the wheeled shelves to select one set of books at a time. The Intel 8086 and 8088microprocessors used a similar mechanism to expand a 16-bit processor bus to a 20-bit memory address,to access 220 = 1,048,576 bytes (or 1 Megabyte) of memory. The "640K limit" of 8088 based PCs was dueto design choices related to display and other devices mentioned below.Processors allowing for larger address spaces are better suited to the matrix problems of the previousparagraph.

The Motorola 68000 family of processors and the more recent members of the Intel 80x86family can address large amounts of memory directly without special tricks. For Intel-based machines,however, backward compatibility with existing software, especially operating systems, may mean thatusers cannot use this capability easily.Another address space limitation of many PC systems is the use of memory mapped input/output orsimilar functions. As a historical example, the Intel 8080 and Zilog Z80 computers have OUT instructionsthat allow data currently in the accumulator of the CPU to be directed to a given I/O channel.

Othersystems, notably the Mostek 6502 of early Apple, Commodore and Atari computers, simply "write" thedata to a specified memory address that contains an output channel instead of a memory device. Memorymapped I/O is common, especially for displays. Of course, each address used for I/O is unavailable forprograms or data.

Worse, we generally lose address locations in blocks simplify the design of theaddressing circuitry. Other hardware functions that may use memory addresses for either control orbuffering functions are disk controllers, network adapters, some floating-point processors, and ROMs(read-only-memories) that hold the startup software of the computer or provide special control functions,26Copyright © 1984, 1994 J C & M M NashNash Information Services Inc., 1975 Bel Air Drive, Ottawa, ON K2C 0X1 CanadaSCIENTIFIC COMPUTING WITH PCsCopy for:Dr. Dobb’s Journalsuch as our own SnoopGuard security access device for MS-DOS computers.

The startup software iscommonly called the BIOS (Basic Input Output System).Certain essential software also takes memory away from problem-solving. The operating system, of course,must occupy some space to control all processes and manage the machine resources. Any program thatwe want resident or always ready to work must have interrupt handlers to activate the working parts ofthe program. Sometimes the whole program remains in memory. On MS-DOS PCs, such "terminate andstay resident" or TSR programs are very common for handling screen savers, keyboard buffers, and otheruseful functions.

Device drivers use memory to operate RAM-disks (see 8.5), provide special keyboardemulations or display characters, or allow access to such peripherals as optical scanners, nonstandardtapes, disks or CD-ROMs. In the case of RAM-disks, disk caches or print buffers, memory space is neededto store data if this is taken from the main system memory.Integrated program development environments and debuggers may use up a lot of memory, since muchof the code stays resident.

Trends to different operating system principles, as in the Microsoft Windowsapproach, while having a high overhead cost in terms of system resources, offer a certain freedom fromthe memory squeeze.A different limitation for PCs concerns the ways in which devices are connected. Even if there aresufficient physical connectors, we may find that there are not enough circuits to run all our devices atonce. In particular, the IBM PC design is notoriously limited in terms of interrupt request (IRQ) lines.These carry signals to tell the processor that it should pay attention to something happening with respectto a device.