Big numbers library in c++

The GNU Multiple Precision Arithmetic Library does what you want http://gmplib.org/

Gnu MP is a C library but it has a C++ class Interface and if you are interested only in big integers, you may just deal with mpz_class. Look at the sample below which I took from the page C++ Interface General

 int main (void)
 {
   mpz_class a, b, c;

   a = 1234;
   b = "-5678";
   c = a+b;
   cout << "sum is " << c << "\n";
   cout << "absolute value is " << abs(c) << "\n";

   return 0;
 }

You said you want a simple interface/implementation, here's one http://www.di-mgt.com.au/bigdigits.html. Personally I'd still go for GMP however.

Unfortunately, there is no standard library for big numbers. You said you are looking for a "simple" library, the simplest library I know of is InfInt. It consists of just one header file. Its usage is fairly simple. Here is a sample code:

InfInt myint1 = "15432154865413186646848435184100510168404641560358";
InfInt myint2 = 156341300544608LL;

myint1 *= --myint2 - 3;
std::cout << myint1 << std::endl;