How do I print a double value with full precision using cout?

You can set the precision directly on std::cout and use the std::fixed format specifier.

double d = 3.14159265358979;
cout.precision(17);
cout << "Pi: " << fixed << d << endl;

You can #include <limits> to get the maximum precision of a float or double.

#include <limits>

typedef std::numeric_limits< double > dbl;

double d = 3.14159265358979;
cout.precision(dbl::max_digits10);
cout << "Pi: " << d << endl;

Use std::setprecision:

#include <iomanip>
std::cout << std::setprecision (15) << 3.14159265358979 << std::endl;

Here is what I would use:

std::cout << std::setprecision (std::numeric_limits<double>::digits10 + 1)
          << 3.14159265358979
          << std::endl;

Basically the limits package has traits for all the build in types.
One of the traits for floating point numbers (float/double/long double) is the digits10 attribute. This defines the accuracy (I forget the exact terminology) of a floating point number in base 10.

See: http://www.cplusplus.com/reference/std/limits/numeric_limits.html
For details about other attributes.