Compiler Library/XL Reference Manual (32650-90029)

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Representation:
For real numbers stored in normalized form, the exponent portion has a
range of [1,254] and the fraction portion has a range of [0,223 -1]. The
sign bit indicates the sign of the fraction portion (0 indicates a
positive value and 1 indicates a negative value).
Real numbers in normalized form have an implied value of 1.0 to the left
of the fraction's most significant bit. Thus, a normalized decimal value
equals
(-1)Sign * 2Exponent-127 * (1.0+ Fraction * 2-23 )
and has a range of
(-1)Sign * [1.175494 x 10-38 ,3.402823 x 1038 ]
However, the IEEE Standard P754 allows decimal numbers whose absolute
values are smaller than 1.175494 x 10-38 . This so-called denormalized
number with Exponent equal to zero has the value
(-1)Sign * 2-126 * (0.0 + Fraction * 2-23 )
and has a range of
(-1)Sign * [1.401298 x 10-45 ,1.175494 x 10-38 )
When the significant bit, the exponent, and the fraction are zero, the
decimal value is equal to 0.0.
NaN (not a number) can be encoded in the real number format as follows:
When all the exponent bits are set to 1 and at least one of the
fraction bits is non-zero, there is a NaN regardless of the sign bit.
For example:
Exponent = 255; fraction <> 0