How Can I Efficiently Square Large Integers in C Using Integer Arithmetic?

Fast bignum square computation

Problem:

How do I compute y = x^2 as fast as possible without precision loss using C and integer arithmetics (32bit with Carry)?

Solution:

The problem can be solved using Karatsuba multiplication, which has a complexity of O(N^(log2(3))), where N is the number of digits.

Implementation:

Here is an implementation of Karatsuba multiplication in C :

void karatsuba(int *a, int *b, int n, int *c) {
  if (n <p>This implementation has a complexity of O(N^(log2(3))), which is significantly faster than the naive O(N^2) algorithm.</p><p><strong>Conclusion:</strong></p><p>Using Karatsuba multiplication, it is possible to compute y = x^2 much faster than using the naive O(N^2) algorithm.</p>

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