Unfortunately the performance would be poor. This is not a reflection on Julia. Even compiled C is between 4 and 12 times slower than assembly for some bignum operations.
Also, LLVM handles carries and certain loop optimisations poorly, so even using LLVM bytecode you can't do much better than compiled C. It would be a massive project to improve this in LLVM (I thought about giving it a go sone time ago but decided it was overwhelming). And that use case is probably too specialised for the improvements to help with much else. Obviously the LLVM backend is fantastic for 99% of use cases and improving all the time.
N.B. I am not implying that a good assembly programmer is generically faster than a C compiler. Bignums are a very special case.
That makes a whole lot of sense. For myself, I wouldn't even attempt this because it's so much harder and more time-consuming to try to reimplement something like bignums efficiently than it is to just use a stable, mature and fast external library like GMP or CLN — or something like your project if BSD/MIT licensing is a must.
It's been done. I think it was Gambit Scheme that had its own bignum library. And for a while, very large integer arithmetic was reportedly faster than GMP, which if you know anything about GMP is quite an achievement. However, the GMP guys subsequently fixed this problem.
Also, LLVM handles carries and certain loop optimisations poorly, so even using LLVM bytecode you can't do much better than compiled C. It would be a massive project to improve this in LLVM (I thought about giving it a go sone time ago but decided it was overwhelming). And that use case is probably too specialised for the improvements to help with much else. Obviously the LLVM backend is fantastic for 99% of use cases and improving all the time.
N.B. I am not implying that a good assembly programmer is generically faster than a C compiler. Bignums are a very special case.