# 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 eminto emax, 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

- fk is a nonnegative number less than b (f1 is also nonzero).

For x = 0, its exponent e and digits fk 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

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