multiprecision/doc/tutorial_float_builtin_ctor.qbk

[/
  Copyright 2021 John Maddock.
  Copyright 2021 Paul A. Bristow.
  Copyright 2021 Christopher Kormanyos.

  Distributed under the Boost Software License, Version 1.0.
  (See accompanying file LICENSE_1_0.txt or copy at
  http://www.boost.org/LICENSE_1_0.txt).
]

[section:floatbuiltinctor 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);

[endsect] [/section:floatbuiltinctor Construction from Built-In Floats]