Is there a standard way to check for Infinite and NaN in Fortran 90/95?

The simple way without using the ieee_arithmatic is to do the following.

Infinity: Define your variable infinity = HUGE(dbl_prec_var) (or, if you have it, a quad precision variable). Then you can simply check to see if your variable is infinity by if(my_var > infinity).

NAN: This is even easier. By definition, NAN is not equal to anything, even itself. Simply compare the variable to itself: if(my_var /= my_var).

I don't have enough rep to comment so I'll "answer" regarding Rick Thompson's suggestion for testing infinity.

if (A-1 .eq. A) 

This will also be true if A is a very large floating point number, and 1 is below the precision of A.

A simple test:

subroutine test_inf_1(A)
    real, intent(in) :: A
    print*, "Test (A-1 == A)"
    if (A-1 .eq. A) then
        print*, "    INFINITY!!!"
    else
        print*, "    NOT infinite"
    endif
end subroutine

subroutine test_inf_2(A)
    real, intent(in) :: A
    print*, "Test (A > HUGE(A))"
    if (A > HUGE(A)) then
        print*, "    INFINITY!!!"
    else
        print*, "    NOT infinite"
    endif
end subroutine


program test
    real :: A,B

    A=10
    print*, "A = ",A
    call test_inf_1(A)
    call test_inf_2(A)
    print*, ""

    A=1e20
    print*, "A = ",A
    call test_inf_1(A)
    call test_inf_2(A)
    print*, ""

    B=0.0 ! B is necessary to trick gfortran into compiling this
    A=1/B
    print*, "A = ",A
    call test_inf_1(A)
    call test_inf_2(A)
    print*, ""

end program test

outputs:

A =    10.0000000    
Test (A-1 == A)
    NOT infinite
Test (A > HUGE(A))
    NOT infinite

A =    1.00000002E+20
Test (A-1 == A)
    INFINITY!!!
Test (A > HUGE(A))
    NOT infinite

A =          Infinity
Test (A-1 == A)
    INFINITY!!!
Test (A > HUGE(A))
    INFINITY!!!