cpp_dec_float

#include <boost/multiprecision/cpp_dec_float.hpp>

namespace boost{ namespace multiprecision{

template <unsigned Digits10, class ExponentType = std::int32_t, class Allocator = void>
class cpp_dec_float;

typedef number<cpp_dec_float<50> > cpp_dec_float_50;
typedef number<cpp_dec_float<100> > cpp_dec_float_100;

}} // namespaces

The cpp_dec_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_dec_float can be used at fixed precision by specifying a non-zero Digits10 template parameter. The typedefs cpp_dec_float_50 and cpp_dec_float_100 provide arithmetic types at 50 and 100 decimal digits precision respectively. Optionally, you can specify an integer type to use for the exponent, this defaults to a 32-bit integer type which is more than large enough for the vast majority of use cases, but larger types such as long long can also be specified if you need a truly huge exponent range. In any case the ExponentType must be a fundamental (built-in) signed integer type at least 2 bytes and 16-bits wide.

Normally cpp_dec_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 the final template parameter causes cpp_dec_float to dynamically allocate the memory it needs: this significantly reduces the size of cpp_dec_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.

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

Things you should know when using this type:

Default constructed cpp_dec_floats have a value of zero.
The radix of this type is 10. As a result it can behave subtly differently from base-2 types.
The type has a number of internal guard digits over and above those specified in the template argument. Normally these should not be visible to the user.
The type supports both infinities and NaNs. An infinity is generated whenever the result would overflow, and a NaN is generated for any mathematically undefined operation.
There is a std::numeric_limits specialisation for this type.
Any number instantiated on this type, is convertible to any other number instantiated on this type - for example you can convert from number<cpp_dec_float<50> > to number<cpp_dec_float<SomeOtherValue> >. Narrowing conversions are truncating and explicit.
Conversion from a string results in a std::runtime_error being thrown if the string can not be interpreted as a valid floating-point number.
The actual precision of a cpp_dec_float is always slightly higher than the number of digits specified in the template parameter, actually how much higher is an implementation detail but is always at least 8 decimal digits.
Operations involving cpp_dec_float are always truncating. However, note that since there are guard digits in effect, in practice this has no real impact on accuracy for most use cases.

cpp_dec_float example:

#include <boost/multiprecision/cpp_dec_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_dec_float_100 b = 2;
   std::cout << std::numeric_limits<cpp_dec_float_100>::digits << std::endl;
   // Note that digits10 is the same as digits, since we're base 10! :
   std::cout << std::numeric_limits<cpp_dec_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_dec_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_dec_float_100(1000)) << std::endl;
   return 0;
}