#include <boost/multiprecision/cpp_bin_float.hpp>

namespace boost{ namespace multiprecision{

enum digit_base_type
{
   digit_base_2 = 2,
   digit_base_10 = 10
};

template <unsigned Digits, digit_base_type base = digit_base_10, class Allocator = void, class Exponent = int, ExponentMin = 0, ExponentMax = 0>
class cpp_bin_float;

typedef number<cpp_bin_float<50> > cpp_bin_float_50;
typedef number<cpp_bin_float<100> > cpp_bin_float_100;

typedef number<backends::cpp_bin_float<24, backends::digit_base_2, void, std::int16_t, -126, 127>, et_off>         cpp_bin_float_single;
typedef number<backends::cpp_bin_float<53, backends::digit_base_2, void, std::int16_t, -1022, 1023>, et_off>       cpp_bin_float_double;
typedef number<backends::cpp_bin_float<64, backends::digit_base_2, void, std::int16_t, -16382, 16383>, et_off>     cpp_bin_float_double_extended;
typedef number<backends::cpp_bin_float<113, backends::digit_base_2, void, std::int16_t, -16382, 16383>, et_off>    cpp_bin_float_quad;
typedef number<backends::cpp_bin_float<237, backends::digit_base_2, void, std::int32_t, -262142, 262143>, et_off>  cpp_bin_float_oct;

}} // namespaces

The cpp_bin_float back-end is used in conjunction with number: It acts as an entirely C++ (header only and dependency free) floating-point number type that is a drop-in replacement for the native C++ floating-point types, but with much greater precision.

Type cpp_bin_float can be used at fixed precision by specifying a non-zero Digits template parameter. The typedefs cpp_bin_float_50 and cpp_bin_float_100 provide arithmetic types at 50 and 100 decimal digits precision respectively.

Optionally, you can specify whether the precision is specified in decimal digits or binary bits - for example to declare a cpp_bin_float with exactly the same precision as double one would use number<cpp_bin_float<53, digit_base_2> >. The typedefs cpp_bin_float_single, cpp_bin_float_double, cpp_bin_float_quad, cpp_bin_float_oct and cpp_bin_float_double_extended provide software analogues of the IEEE single, double, quad and octuple float data types, plus the Intel-extended-double type respectively. Note that while these types are functionally equivalent to the native IEEE types, but they do not have the same size or bit-layout as true IEEE compatible types.

Normally cpp_bin_float allocates no memory: all of the space required for its digits are allocated directly within the class. As a result care should be taken not to use the class with too high a digit count as stack space requirements can grow out of control. If that represents a problem then providing an allocator as a template parameter causes cpp_bin_float to dynamically allocate the memory it needs: this significantly reduces the size of cpp_bin_float and increases the viable upper limit on the number of digits at the expense of performance. However, please bear in mind that arithmetic operations rapidly become very expensive as the digit count grows: the current implementation really isn't optimized or designed for large digit counts. Note that since the actual type of the objects allocated is completely opaque, the suggestion would be to use an allocator with void value_type, for example: number<cpp_bin_float<1000, digit_base_10, std::allocator<void> > >.

The final template parameters determine the type and range of the exponent: parameter Exponent can be any signed integer type, but note that MinExponent and MaxExponent can not go right up to the limits of the Exponent type as there has to be a little extra headroom for internal calculations. You will get a compile time error if this is the case. In addition if MinExponent or MaxExponent are zero, then the library will choose suitable values that are as large as possible given the constraints of the type and need for extra headroom for internal calculations.

There is full standard library and numeric_limits support available for this type.

Things you should know when using this type:

cpp_bin_float example:

#include <boost/multiprecision/cpp_bin_float.hpp>
#include <boost/math/special_functions/gamma.hpp>

#include <iostream>

int main()
{
   using namespace boost::multiprecision;

   // Operations at fixed precision and full numeric_limits support:
   cpp_bin_float_100 b = 2;
   std::cout << std::numeric_limits<cpp_bin_float_100>::digits << std::endl;
   std::cout << std::numeric_limits<cpp_bin_float_100>::digits10 << std::endl;

   // We can use any C++ std lib function, lets print all the digits as well:
   std::cout << std::setprecision(std::numeric_limits<cpp_bin_float_100>::max_digits10)
      << log(b) << std::endl; // print log(2)

   // We can also use any function from Boost.Math:
   std::cout << boost::math::tgamma(b) << std::endl;
   // These even work when the argument is an expression template:
   std::cout << boost::math::tgamma(b * b) << std::endl;

   // And since we have an extended exponent range we can generate some really large
   // numbers here (4.0238726007709377354370243e+2564):
   std::cout << boost::math::tgamma(cpp_bin_float_100(1000)) << std::endl;
   return 0;
}