Intel 80287, 80286 manual Special Computational Situations, Special Numeric Values

OVERVIEW OF NUMERIC PROCESSING

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PROJECTIVE CLOSURE

- 00+ +00

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AFFINE CLOSURE

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Figure 1-10. Projective versus Affine Closure

means of closure is projective, and this is recommended for most computations. When projective closure is selected, the NPX treats the special values +00 and - 00 as a single unsigned infinity (similar to its treatment of signed zeros). In the affine mode the NPX respects the signs of +00 and - 00 .

While affine mode may provide more information than projective, there are occasions when the sign may in fact represent misinformation. For example, consider an algorithm that yields an intermediate result x of +0 and -0 (the same numeric value) in different executions.· If llx were then computed in affine mode, two entirely different values (+ 00 and - (0) would result from numerically identical values of x. Projective mode, on the other hand, provides less information but never returns misinfor- mation. In general, then, projective mode should be used globally, with affine mode reserved for local computations where the programmer can take advantage of the sign and knows for certain that the nature of the computations will not produce a misleading result.

SPECIAL COMPUTATIONAL SITUATIONS

Besides being able to represent positive and negative numbers, the 80287 data formats may be used to describe other entities. These special values provide extra flexibility, but most users will not need to understand them in order to use the 80287 successfully. This section describes the special values that may occur in certain cases and the significance of each. The 80286 exceptions are also described, for writers of exception handlers and for those interested in probing the limits of computation using the 80287.

Th ... m~teriHl presented in this section is mainly of interest to programmers concerned with writing exception handlers. For many readers, this section can be browsed lightly.

Special Numeric Values

The 80287 data formats encompass encodings for a variety of special values in addition to the typical real or integer data values that result from normal calculations. These special values have significance

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