For implementing it yourself from scratch for learning it is a good idea to first step back and ask how much precision do you need and how fast does it need to

For implementing it yourself from scratch for learning it is a good idea to first step back and ask how much precision do you need and how fast does it need to be. Also are we talking about just integers, or do you also want fixed point and/or floating point? If you don't need really huge numbers and you don't need it to be very fast and just need the add, subtract, multiply, and divide (with remainder) on integers there's a decent chance you can write something by just implementing the same algorithms you would use to do it by hand on paper. You To make is easy to debug you could represent an arbitrary integer as an array of base 10 digits, least significant digit first. E.g., the number 123456 would be represented as [6, 5, 4, 3, 2, 1]. Addition and subtraction are pretty straightforward in that representation. Multiplication is more complicated by just follow what you do when you hand multiply and you'll get it. Division is harder but for a project you are doing for learning purposes it is doable. Once you've got those operations you can improve them by changing to a higher base. For example you might switch to base 1000. Then 123456 would be [456, 123]. Assuming the base is small enough that each digit fits in one machine word addition and subtraction are O(n) and multiplication and division as described above are O(n^2) where n is the number of digits in your operands (let's assume equal sized operands). Switching from base 10 to base 1000 cuts the number of digits in your numbers by a factor of 3, speeding up addition and subtraction by a factor of 3 and multiplication and division by a factor of 9. It usually is easy to go up to base whatever fits in half a machine word. For example on a 32-bit processor that would be base 65536. Digits then range from 0 through 65535 and and adding or multiplying a pair of digits will not overflow. You can also go up to the full machine word for your base but that can be more work. So for a 32-bit machine that would be base 4294967295. You then have to deal with overflow which adds a small amount of extra logic for addition/subtraction. For multiplication you need a 32-bit x 32-bit => 64-bit operation. Many 32-bit processors do have that but it might not be exposed in whatever language you are using. The above is all stuff you can probably do without any more theory than you can remember from elementary school. Taking it farther you probably want to do some reading. You can get a decent speedup on multiplication by using the Karatsuba algorithm, which speeds up multiplication from O(n^2) to O(n^1.58). Karatsuba is pretty easy and Wikipedia explains it adequately. An extensive treatment of all of this is in Knuth volume 2. He covers everything from the "do it like you do by hand" up to whatever was state of the art at the time the book was written. I wouldn't necessarily say you should go out and buy Knuth volume 2, but if you can borrow it from a library or someone you know take a look.