# 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 emin to emax 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

- 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)) 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:

Parent topic: Data Representation Models