Half-precision floating-point number format

The half-precision floating-point formats available are ieee and alternative. In both formats, the basic layout of the 16-bit number is the same. See Figure 1.

Figure 1. Half-precision floating-point format

Where:

   S (bit[15]):      Sign bit
   E (bits[14:10]):  Biased exponent
   T (bits[9:0]):    Mantissa.

The meanings of these fields depend on the format that is selected.

IEEE half-precision format is as follows:

IF E==31:
   IF T==0: Value = Signed infinity
   IF T!=0: Value = Nan
             T[9] determines Quiet or Signalling:
                  0: Quiet NaN
                  1: Signalling NaN
IF 0<E<31:
   Value = (-1)Sx2(E-15)x(1+2-10T)

IF E==0:
   IF T==0: Value = Signed zero
   IF T!=0: Value = (-1)Sx2(-14)x(0+2-10T)

Alternative half-precision format is as follows:

IF 0<E<32:
   Value = (-1)Sx2(E-15)x(1+2-10T)

IF E==0:
   IF T==0: Value = Signed zero
   IF T!=0: Value = (-1)Sx2(-14)x(0+2-10T)