I have two very short questions:
1 - I just read that DEXP() is the archaic form of EXP(). Does it mean that it should not be used anymore? I always thought that DEXP() was the double precision equivalent to EXP().
2 - What is the range of the exponential function? Is it compiler dependent?
In modern Fortran it is always better to use the generic functions, such as EXP(), in preference to the outdated type specific equivalents, such as DEXP().
In the old (really old) versions of Fortran (before FORTRAN 77), a different function was required for each data type. So if you wanted the exponential function would need: EXP() for single precision numbers, DEXP() for double precision numbers, or CEXP() for complex numbers. Fortran now has function overloading, so a single function will work for any standard type.
In principle the possible range of the exponent can be processor and compiler dependent. However, most modern processors and compilers will use the IEEE standard.
If needed, it is possible to specify the required range of a variable when declaring it. The function to use is SELECTED_REAL_KIND([P,R]).
For example, suppose you to make sure that x is of a type with decimal precision of at least 10 digits and a decimal exponent range of at least 100.
INTEGER, PARAMETER :: mytype = SELECTED_REAL_KIND(10, 100)
REAL(KIND=mytype) :: x
For more information: SELECTED_REAL_KIND
In practice, if you are writing a program that requires a given accuracy, and which may be run on exotic or old systems, it is a very good idea to define your types in this way. Some common definitions are shown here: Real Precision