ACML does not release a package that supports cygwin directly, e.g. a distribution that contains gcc linkable .a files in it.
However, I believe the windows ACML dll files should be link-able with MinGW using a few preprocessing steps documented on the MinGW site:
I've not tried this myself yet though, so your mileage may vary; I would appreciate if you let me know your experiences.
I've searched on these processes and couldn't find a way for this. I was wondering if I install Ubuntu to my Windows computer, would I have chance to install "acml for linux for gfortran"? Can it be easier than the previous steps? Can Ubuntu be accepted as Linux?
Yes, Ubuntu can most certainly be accepted as Linux, and you would use the gfortran build of ACML.