Freescale Semiconductor MC68881 - Not-A-Numbers; Format of Zero; Format of Infinity

NOTE
Since the extended precision data format has an explicit integer part bit, a number
can be formatted with a nonzero exponent (less than the maximum value) and a
zero integer bit, which is not defined by the IEEE standard. Such a number is
called an unnormalized number. The MC68881 never generates an unnormalized
number as the result of any operation. Unnormalized inputs are always converted
to normalized or denormalized numbers or zero before being used. Thus, as
required by the IEEE standard, the FPCP does not distinguish between redundant
encodings of extended precision values.
3.2.3 Zeros
Zeros are signed (positive or negative) and represent the real values +0.0 and -0.0. See
Figure 3-5.
I
EXPONENT = 0 I MANTISSA = 0
SIGN OF MANTISSA, 0 OR 1
Figure 3-5. Format of Zero
3.2.4 Infinities
Infinities are signed (positive or negative) and represent real values that exceed the overflow
threshold. Overflow is detected for a given data format and operation when the result
exponent is greater than or equal to the maximum exponent value. (This overflow description
ignores the effects of rounding and the user selectable rounding modes.) See Figure 3-6.
For extended precision infinities, the most significant bit of the mantissa (the integer bit)
can be either one or zero.
I
I EXPONENT = MAXIMUM I MANTISSA = O*
I
SIGN OF MANTISSA. 0 OR I
*For the
extended precision format, the most significant bit of the mantissa (the integer bit) is a don't care.
Figure 3-6. Format of Infinity
3.2.5 Not-A-Numbers
When created by the FPCP, not-a-numbers (NANs) represent the results of operations that
have no mathematical interpretation, such as infinity divided by infinity. All operations
involving a NAN operand as an input return a NAN result. When created by the user, NANs
can protect against uninitialized variables and arrays, or represent user-defined special
MC68881/MC68882 USER'S MANUAL FREESCALE
3-5