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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: