NaN, +Inf, -Inf, horrid things...

This is the answer.
Based on such, I have a sample function to detect a +Inf:

function ispinf(x)
! function to detect if x is +Inf
integer :: ispinf
double precision :: x

!local variables
integer :: IPInf
real :: PInf
data IPInf/B'01111111100000000000000000000000'/ ! +Infinity
PInf = transfer(IPinf,Pinf)

if (x.eq.PInf) then
ispinf = 1
else
ispinf = 0
endif

end function ispinf