Intel 80286, 80287 manual Applications, ± Vb2 4ac

OVERVIEW OF NUMERIC PROCESSING

The 80287 delivers the correctly rounded result. Other typical examples of undesirable machine behav- ior in straightforward calculations occur when solving for the roots. of a quadratic equation:

-b ± Vb2 - 4ac

2a

or computing financial rate of return, which involves the expression: (1 +i)n. On most machlnes, straightforward algorithms will not deliver consistently correct results (and will not indicate when they are incorrect). To obtain correct results on traditional machines under all conditions usually requires sophisticated numerical techniques that are foreign to most programmers. General application programmers using straightforward algorithms will produce much more reliable programs using the 80287. This simple fact greatly reduces the software investment required to develop safe, accurate computation-based products.

Beyond traditional numerics support for scientific applications, the 80287 has built-in facilities for commercial computing. It can process decimal numbers of up to 18 digits without round-off errors, performing exact arithmetic on integers as large as 264 or 1018• Exact arithmetic is vital in accounting applications where rounding errors may introduce monetary losses that cannot be reconciled.

The NPX contains a number of optional facilities that can be invoked by sophisticated users. These advanced features include two models of infinity, directed rounding, gradual underflow, and either automatic or programmed exception-handling facilities.

These automatic exception-handling facilities permit a high degree of flexibility in numeric processing software, without burdening the programmer. While performing numeric calculations, the NPX automatically detects exception conditions that can potentially damage a calculation. By default, on- chip exception handlers may be invoked to field these exceptions so that a reasonable result is produced, and execution may proceed without program interruption. Alternatively, the NPX can signal the CPU, invoking a software exception handler whenever various types of exceptions are detected.

Applications

The NPX's versatility and performance make it appropriate to a broad array of numeric applications. In general, applications that exhibit any of the following characteristics can benefit by implementing numeric processing on the 80287:

•Numeric data vary over a wide range of values, or include nonintegral values.

•Algorithms produce very large or very small intermediate results.

•Computations must be very precise; i.e., a large number of significant digits must be maintained.

•Performance requirements exceed the capacity of traditional microprocessors.

•Consistently safe, reliable results must be delivered using a programming staff that is not expert in numerical techniques.

Note also that the 80287 can reduce software development costs and improve the performance of systems that use not only real numbers, but operate on multiprecision binary or decimal integer values as well.

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