Funny, I did this myself 10 years ago. Shit, it's been that long..?
For my undergrad project I wrote a computer algebra system to do symbolic integration. The supervisor was a hardcore, old school C guy, so naturally I was going to just use C and no libraries. He told me I'd need bignums first, so I got to work (this is because many algorithms like polynomial GCD create massive numbers as they go, even if the inputs and final outputs are generally very small).
I just couldn't figure out how to do better than the largest power of 10 per digit at the time. Working with non base 10 arithmetic was a mind fuck for me at the time. So I did it with digits holding 10^9 and the classical algorithms from Knuth. Division is the hardest!
At some point I discovered the GNU multiple precision library (GMP) and made my program work with that instead of mine. I was shocked at how much faster GMP was! I finished my project with my own code, but I knew I had to come back to do it better.
The breakthrough came when I got a copy of Hacker's Delight. It has stuff like how to detect overflow after it's happened (in C). Something twigged and then I just understood how to fill each word completely rather than use a power of 10. I don't know what confused me before.
But, of course, the real way to do it is to use assembly. You can't get close to high performance in C alone. In assembly you get the overflow bit. It's actually easier in a way! So you write tiny platform specific bits for the digits and build on that in C. My add and subtract were then as fast as GMP. I lost interest when it came to implement faster multiplication algorithms.
For my undergrad project I wrote a computer algebra system to do symbolic integration. The supervisor was a hardcore, old school C guy, so naturally I was going to just use C and no libraries. He told me I'd need bignums first, so I got to work (this is because many algorithms like polynomial GCD create massive numbers as they go, even if the inputs and final outputs are generally very small).
I just couldn't figure out how to do better than the largest power of 10 per digit at the time. Working with non base 10 arithmetic was a mind fuck for me at the time. So I did it with digits holding 10^9 and the classical algorithms from Knuth. Division is the hardest!
At some point I discovered the GNU multiple precision library (GMP) and made my program work with that instead of mine. I was shocked at how much faster GMP was! I finished my project with my own code, but I knew I had to come back to do it better.
The breakthrough came when I got a copy of Hacker's Delight. It has stuff like how to detect overflow after it's happened (in C). Something twigged and then I just understood how to fill each word completely rather than use a power of 10. I don't know what confused me before.
But, of course, the real way to do it is to use assembly. You can't get close to high performance in C alone. In assembly you get the overflow bit. It's actually easier in a way! So you write tiny platform specific bits for the digits and build on that in C. My add and subtract were then as fast as GMP. I lost interest when it came to implement faster multiplication algorithms.
Code in case anyone is interested: https://github.com/georgek/bignums