If you want to see a real implemention of arbitrary sized integer math, mbedTLS is a great example:

https://github.com/ARMmbed/mbedtls/blob/development/library/...

All of the ECC code in that library relies on this code, which can be accelerated by dedicated hardware.

Here is multi-precision multiplication:

https://github.com/ARMmbed/mbedtls/blob/f1eb4257823ae4c3b3ac...