Double Precision - 2024.2 English

An IEEE 754 double precision floating point number is composed of the following three fields:

1. 1-bit sign
2. 11-bit biased exponent
3. 52-bit fraction (a.k.a. mantissa or significand)

The fields are stored in a 64 bit long as defined in the following figure:

The value of a floating point number v in MicroBlaze has the following interpretation:

1. If exponent = 2047 and fraction <> 0, then v = NaN, regardless of the sign bit
2. If exponent = 2047 and fraction = 0, then v = (-1)^sign * ∞
3. If 0 < exponent < 2047, then v = (-1)^sign * 2^{( exponent -1023)} * (1.fraction)
4. If exponent = 0 and fraction <> 0, then v = (-1)^sign * 2^-1022 * (0.fraction)
5. If exponent = 0 and fraction = 0, then v = (-1)^sign * 0

For practical purposes only 3 and 5 are useful, while the others all represent either an error or numbers that can no longer be represented with full precision in a 64 bit format.