This time, I was finding that the intrinsic function exp(x) returned zero for x less than around -0.1E3. After some bashing, my compiler was sweet enough to tell me:

Result of EXP underflows its kind

Apparently, Fortran is not content with just "exp". It also has "dexp" and "cexp" for double-precision and complex floating point numbers respectively. So, dexp(x) it is then. But be careful how you define x, or you will get a shouty like this:Type of argument 'x' in call to 'dexp' at (1) should be REAL(8), not REAL(4)

So one should try dexp(-0.1D3) (note the letter D!) rather than exp(-0.1E3), which will return zero, possibly grumbling in the process.