User's Manual
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
± V b
2
-
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
2
64
or
10
18
•
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
multi precision binary or decimal integer values
as
well.
1-3