Intel® Fortran Compiler Classic and Intel® Fortran Compiler Developer Guide and Reference

ID 767251
Date 3/22/2024
Public

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Document Table of Contents

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: