In this example we'll show how individual bits within an integer may be manipulated, we'll start with an often needed calculation of 2ⁿ - 1, which we could obviously implement like this:

using boost::multiprecision::cpp_int;

cpp_int b1(unsigned n)
{
   cpp_int r(1);
   return (r << n) - 1;
}

Calling:

std::cout << std::hex << std::showbase << b1(200) << std::endl;

Yields as expected:

0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF

However, we could equally just set the n'th bit in the result, like this:

cpp_int b2(unsigned n)
{
   cpp_int r(0);
   return --bit_set(r, n);
}

Note how the bit_set function sets the specified bit in its argument and then returns a reference to the result - which we can then simply decrement. The result from a call to b2 is the same as that to b1.

We can equally test bits, so for example the n'th bit of the result returned from b2 shouldn't be set unless we increment it first:

BOOST_ASSERT(!bit_test(b1(200), 200));     // OK
BOOST_ASSERT(bit_test(++b1(200), 200));    // OK

And of course if we flip the n'th bit after increment, then we should get back to zero:

BOOST_ASSERT(!bit_flip(++b1(200), 200));   // OK