The precision of the long double output is not correct. What might be wrong?

Question

I have a long double constant that I am setting either as const or not-const. It is longer (40 digits) than the precision of a long double on my test workstation (19 digits).

When I print it out, it no longer is displayed at 19 digits of precision, but at 16.

Here is the code I am testing:

#include <iostream>
#include <iomanip>
#include <limits>
#include <cstdio>

int main ()
{
    const long double constLog2 = 0.6931471805599453094172321214581765680755;
    long double log2 = 0.6931471805599453094172321214581765680755;    

    std::cout << std::numeric_limits<long double>::digits10 + 1 << std::endl;
    std::cout << "const via cout: " << std::setprecision(19) << constLog2 << std::endl;
    std::cout << "non-const via cout: " << std::setprecision(19) << log2 << std::endl;
    std::fprintf(stdout, "const via printf: %.19Lf\n", constLog2);
    std::fprintf(stdout, "non-const via printf: %.19Lf\n", log2);

    return 0;
}

Compile:

$ g++ -Wall precisionTest.cpp

Output:

$ ./a.out
19
const via cout: 0.6931471805599452862
non-const via cout: 0.6931471805599452862
const via printf: 0.6931471805599452862
non-const via printf: 0.6931471805599452862

I would expect 0.6931471805599453094 but instead get 0.6931471805599452862.

Is there a reason that the 19 digits of precision are cut to 16 digits?

Here is my environment:

$ gcc --version
i686-apple-darwin9-g++-4.0.1 (GCC) 4.0.1 (Apple Inc. build 5490)

I am seeing the same problem with other versions of gcc, e.g.:

$ gcc --version
g++ (GCC) 3.4.6 20060404 (Red Hat 3.4.6-10)

I can look into NTL or other libraries but I'm curious what is causing this. Thanks for your insight.

Answer 1

I get this output:

19
const via cout: 0.6931471805599453094
non-const via cout: 0.6931471805599453094
const via printf: 0.6931471805599453094
non-const via printf: 0.6931471805599453094

But i'm using long double literals instead of double literals:

const long double constLog2 = 0.6931471805599453094172321214581765680755L;
long double log2 = 0.6931471805599453094172321214581765680755L;