User's Manual

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OVERVIEW OF NUMERIC PROCESSING
Pseudo zero operands behave like unnormals, except in the following cases where they produce the
same results as true zeros:
Compare and test instructions
FRNDINT (round to integer)
Division, where the dividend
is either a true zero or a pseudo zero (the divisor is a pseudo zero)
In addition and subtraction of a pseudo zero and a true zero or another pseudo zero, the pseudo zeroes)
behaves like unnormals, except for the determination of the result's sign. The sign
is determined as
shown in table 1-10 for two true zero operands.
INFINITY
The real formats support signed representations of infinities. These values arc encoded with a biased
exponent of all ones and a significand of
I,:lOO ... OO; if the infinity is in a register, it is tagged special.
The significand distinguishes infinities from NANs, including real
indefinite.
A programmer may code an infinity, or it may be created by the NPX as its masked response to an
overflow or a zero divide exception. Note that when rounding
is up or down, the masked response may
create the largest valid value representable in the destination rather than infinity. See table
1-11 for
details.
As operands, infinities behave somewhat differently depending on how the infinity control field
in the control word
is set (see table 1-12). When the projective model of infinity is selected, the infini-
ties behave as a single unsigned representation; because of this, infinity cannot be compared with any
value except infinity. In affine mode, the signs of the infinities are observed, and comparisons are
possible.
NaN (NOT A NUMBER)
A NaN (Not a Number) is a member of a class of special values that exist in the real formats only. A
NaN has an exponent of 11..11B, may have either sign, and may have any significand except I,:lOO .. OOB,
which is assigned to the infinities. A NaN in a register is tagged special.
The
80287 will generate the special NaN, real indefinite, as its masked response to an invalid operation
exception. This
NaN is signed negative; its significand is encoded 1,:l100 .. 00. All other NaNs represent
programmer-created values.
Whenever the
NPX uses an operand that is a NaN, it signals an invalid operation exception in its
status word.
If this exception is masked in the 80287 control word, the 80287's masked exception
response
is to return the NaN as the operation result. If both operands of an instruction are NaNs, the
result
is the NaN with the larger absolute value. In this way, a NaN that enters a computation propa-
gates through the computation and will eventually be delivered as the final result. Note, however, that
the transcendental instructions
do not check their operands, and a NaN will produce an undefined
result.
By unmasking the invalid operation exception, the programmer can use NaNs to trap to the exception
handler. The generality of this approach and the large number of
NaN values that are available provide
the sophisticated programmer with a tool that can be applied to a variety of special situations.
For example, a compiler could use
NaNs as references to uninitialized (real) array elements. The
compiler could preinitialize each array element with a
NaN whose significand contained the index
(relative position) of the element.
If an application program attempted to access an element that it had
not initialized, it would use the
NaN placed there by the compiler. If the invalid operation exception
were unmaskcd, an interrupt would occur, and the exception handler would be invoked. The exception
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