Normal numbers
Most of the representable values in an IEEE standard floating-point number system are normal numbers (as their name might suggest). The normal numbers have direct counterparts in the real number system. Most of your calculations should involve normal numbers and zero. Signed zeroes
An artifact of the signed-magnitude representation of floating-point numbers, in which each value has either a positive or negative sign, is that zero also has a sign. The IEEE standards assign a meaning to the zero's sign, as discussed in examples "Continued fractions with infinities" on page 195 and "Interpreting the sign of zero" on page 197. Mathematically, both 
and 
can be thought of as corresponding to the real number zero. The value zero results from the subtraction of identical finite values, the division of a finite value by infinity, and the underflow of a value beyond the smallest subnormal number. In the last case, the sign of the zero result indicates the sign of the underflowed value. The sign of the floating-point value zero matters only outside the realm of real number arithmetic; for example, when division by signed zero produces signed infinity. Subnormal numbers
The previous section illustrated how a set of tiny unnormalized numbers can span the gap between zero and the smallest normal numbers. These subnormal numbers have counterparts in the real number system. Infinities
A floating-point number system, having finite extent, cannot accommodate arbitrarily large values. To cope with results larger than the largest representable number, and to cope also with division by zero, the IEEE standards define values 
and 
. NaNs
To represent missing or uninitialized data and to provide some result for operations such as 
and 
(whose result defies mathematical definition, even as a limit), the IEEE standards specify NaNs (not-a-number entities). NaNs have algebraic sign, but the standards specify neither the determination nor the meaning of a NaN's sign.
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