Also is there any way to make the computation faster
Frustrating that we can't actually compute all those huge numbers because of annoying practical problems such as running out of atoms in the universe.
Atleast we can assure that if the universe lasted for infinite time, it would compute. But the problem is that it will show as just Infinity because anything beyond 1e308 (or 1e100,000 probably in bignum) will say Infinity. For Bignum it will say bad digits for radix 10. At least ExpantaNum will do it.
Even BigNum can compute 2^^5, but even 2^^6 takes forever and even returns bad digit for radix 10!
2^^6 = 2^(2^^5) = 2^1e19728
how about energy amount instead of atom amount
That too.
Actaully, ExpantaNum's limit is {10,9e12,1,2} which is 10{{1}}9e12, not 10{{9e12}}2, meaning that not even ExpantaNum can compute this even though i managed to recreate the function!
This seems like a truly austere hobby -- you can code the functions, but you can't actually generate any but the smallest values, and it's not the sort of limitation that will get better if you just wait a year or two for the computers to get bigger and faster.
If I were you I'd build a fusion reactor in the garage instead. That's the latest super-cool hobby; there have been, I think, three of them made by teenagers. (Joking. I mean, this is true, but messing with radioactivity is dangerous and I wouldn't really recommend it. Just that, wildly impractical as it is, your hobby seems even more so.)
(Re-reading what I wrote: I didn't intend "super-cool" as a pun!)