4.2.1 Special values

Certain bit patterns of a floating number are special, and they do not represent the values that they normally should. This is necessary to represent special values for floating point related computations.

For this discussion, let us assume the exponent has x bits, e be the unsigned raw value of the exponent (e ∈ [0…2^x − 1]). Furthermore, assume the mantissa has n bits, and m be the unsigned raw value of the mantissa bit pattern (m ∈ [0…2ⁿ − 1). The exponent bias is 2^x−1 − 1.

• e = 0 ∧ m = 0: the value is zero. Note that without this special interpretation, the bit pattern represents the least absolute value that can be represented, which is 1 ⋅ 2^{0−(2x−1−1} ).
• e = 2^x − 1 ∧ m = 0: the bit pattern represents the absolute value of infinity. If the sign bit is one, then the bit pattern represents −∞. If the sign bit is zero, then the bit pattern represents ∞.
• e = 2^x − 1 ∧ m0: the bit pattern represents the “NAN” (Not A Number).