Accuracy loss when calculating magnitudes <1 with magnitudes >1

Question

I'm testing string constructed gmp_float.

This code

#include <boost/multiprecision/number.hpp>
#include <boost/multiprecision/gmp.hpp>
#include <iostream>

using namespace boost::multiprecision;

typedef number<gmp_float<15>> mp_type;

int main()
{
    mp_type total("1.01");
    cout << total.str(0) << endl;
    mp_type first_addition(".01");
    cout << first_addition.str(0) << endl;
    total += first_addition;
    cout << total.str(0) << endl;
}

prints

1.01
0.01
1.01999999999999999998

Why? I ran more tests, and in this particular case, it doesn't matter what the operation is so long as the magnitude of one number is >0 and <1 while the other's is >1.

From the link above

It is not possible to round-trip objects of this type to and from a string and get back exactly the same value. This appears to be a limitation of GMP.

Are there any other zones where accuracy is lost?

Answer 1

Boost Multiprecision has decimal floating point numbers too:

See it Live On Coliru prints:

clang++ -std=c++11 -Os -Wall -pedantic main.cpp && ./a.out
1.01
0.01
1.02

---

#include <boost/multiprecision/cpp_dec_float.hpp>
#include <iostream>

using namespace boost::multiprecision;
using std::cout;
using std::endl;

typedef cpp_dec_float_50 mp_type;

int main()
{
    mp_type total("1.01");
    cout << total.str(0)          << endl;

    mp_type first_addition(".01");
    cout << first_addition.str(0) << endl;

    total += first_addition;
    cout << total.str(0)          << endl;
}