Arbitrary-precision arithmetic Explanation

Question

I\'m trying to learn C and have come across the inability to work with REALLY big numbers (i.e., 100 digits, 1000 digits, etc.). I am aware that there exist libraries to do

Answer 1

You can do it with high school level of mathematics. Though more advanced algorithms are used in reality. So for example to add two 1024-byte numbers :

unsigned char first[1024], second[1024], result[1025];
unsigned char carry = 0;
unsigned int  sum   = 0;

for(size_t i = 0; i < 1024; i++)
{
    sum = first[i] + second[i] + carry;
    carry = sum - 255;
}

result will have to be bigger by one place in case of addition to take care of maximum values. Look at this :

9
   +
9
----
18

TTMath is a great library if you want to learn. It is built using C++. The above example was silly one, but this is how addition and subtraction is done in general!

A good reference about the subject is Computational complexity of mathematical operations. It tells you how much space is required for each operation you want to implement. For example, If you have two N-digit numbers, then you need 2N digits to store the result of multiplication.

As Mitch said, it is by far not an easy task to implement! I recommend you take a look at TTMath if you know C++.