D.2 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).
  
  
• p is the number of mantissa digits (an integer greater than 1). The number of digits differs depending on the real format, as follows:
  
  

  IEEE S_floating	24
  Compaq 1 VAX F_floating 2	24
  IEEE T_floating	53
  Compaq VAX D_floating 2	53 3
  Compaq VAX G_floating 2	53
  1 Formerly DIGITAL 2 VMS only 3 The memory format for VAX D_floating format is 56 mantissa digits, but computationally it is 53 digits. It is considered to have 53 digits by Compaq Fortran.

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

  	emin	emax
  IEEE S_floating	-125	128
  Compaq VAX F_floating 1	-127	127
  IEEE T_floating	-1021	1024
  Compaq VAX D_floating 1	-127	127
  Compaq VAX G_floating 1	-1023	1023
  1 VMS only

  
  
• 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) or REAL*4) is defined as one of the following:

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

x = 1 x 2⁵ x (1 x 2^-1 + 0 x 2^-2 + 1 x 2^-3)

x = 1 x 32 x (.5 + .125)

x = 32 x (.625)

x = 20.0