Model for Real Data

The model set for reals, in general, is defined as one of the following:

The following values apply to this model set:

• x is the real value.

• s is the sign (either +1 or -1).

• b is the base (real radix; an integer greater than 1; b = 2 in Intel® Fortran).

• p is the number of mantissa digits (an integer greater than 1). The number of digits differs depending on the real format, as follows:

  REAL(4)	IEEE binary32	24
  REAL(8)	IEEE binary64	53
  REAL(16)	IEEE binary128	113

• e is an integer in the range e_min to e_max inclusive. This range differs depending on the real format, as follows:

  		emin	emax
  REAL(4)	IEEE binary32	-125	128
  REAL(8)	IEEE binary64	-1021	1024
  REAL(16)	IEEE binary128	-16381	16384

• f_k is a nonnegative number less than b (f₁ is also nonzero).

For x = 0, its exponent e and digits f_k are defined to be zero.

The model set for single-precision real (REAL(4)) is defined as one of the following:

The following example shows the general real model for x = 20.0 using a base (b) of 2: