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Construction from Specific Values Without Precision Loss

Construction of multiprecision types from built-in floating-point types can lead to potentially unexpected, yet correct, results. Consider, for instance constructing an instance of cpp_dec_float_50 from the literal built-in floating-point double value 11.1.

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

#include <boost/multiprecision/cpp_dec_float.hpp>

int main()
  using my_dec_100 = boost::multiprecision::cpp_dec_float_50;

  const my_dec_100 f11(11.1);

  // On a system with 64-bit double:
  // 11.09999999999999964472863211994990706443786621093750
  std::cout << std::setprecision(std::numeric_limits<my_dec_100>::digits10)
            << std::fixed
            << f11
            << std::endl;

In this example, the system has a 64-bit built in double representation. The variable f11 is initialized with the literal double value 11.1. Recall that built-in floating-point representations are based on successive binary fractional approximations. These are, in fact, very close approximations. But they are approximations nonetheless, having their built-in finite precision.

For this reason, the full multiple precision value of the double approximation of 11.1 is given by the large value shown above. Observations show us that the value is reliable up to the approximate 15 decimal digit precision of built-in 64-bit double on this system.

If the exact value of 11.1 is desired (within the wider precision of the multiprecision type), then construction from literal string or from a rational integral construction/division sequence should be used.

const my_dec_100 f11_str("11.1");
const my_dec_100 f11_n  (my_dec_100(111) / 10);