I had good fun writing my own bignum library many years ago. I initially did it because I was writing a computer algebra system to do symbolic integration and didn't want to include (or maybe didn't know about) libraries like GMP.

On my first attempt I just couldn't figure out how to use the full word for each "big digit". So I ended up using the highest power of ten I could fit in a word as my big digit radix. It took me a while to free myself from decimal notation of numbers. I remember being absolutely blown away by the performance of GMP compared to my implementation.

I revisited it later and that time I could figure out how to use full words (the key I think is knowing how to check for overflows without having access to the overflow flag). I actually started to get closer to GMP performance for addition and subtraction. I then did the core routines in x86-64 assembly which got me so close I was just a constant time off. As this article mentions, though, you need to change the algorithms to get close for multiplication and division, though.