AFAICT, all modern CPUs are equipped with both original "x86" 32-bit registers AND "x86_64" 64-bit registers.
Under 64-bit, the processor is running in what's known as "long mode". CPUs automatically switch registers depending on the code they encounter at power-on.....and are fully capable of flipping back-and-forth between the two, "on-the-fly", as & when needed.
"x86" is a family of instruction set architectures initially developed by Intel based on the Intel 8086 microprocessor and its 8088 variant......according to Wikipedia. However, it was AMD who developed the first commercially-viable set of 64-bit extensions to this architecture, later adopted by Intel and called "x86_64". The entire computer world, however, marks the AMD achievement by usually referring to it as "amd64".
Until the recent rise of "Ryzen", this was pretty much the last time that AMD were collectively able to thumb their nose at Intel.
------------------------------------------
Bionicpup32 should just run on a 64-bit processor. You, as the user, need do nothing at all except to install it, and enable a suitable boot-loader.....
(*shrug...*)
Mike. 