Me and my simple questions: Can I do this in FPGA?

When the proper units are chosen, very few caculations in the physical world cannot be done with 64 bit (or higher) integers. DSPs were for a long time strictly integer many techniques developed then are apply to FPGAs. Look into these techniques and take another look at how your problem might be solved with them.

I don't recommend using the floating point FPGA blocks that are available. They waste FPGA resources and aren't needed with some careful analysis of the problem. The same goes for floating point in OpenCL and Vivado HLS.