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#### gmp_rational

`#include <boost/multiprecision/gmp.hpp>`

    namespace boost{ namespace multiprecision{

    class gmp_rational;

    typedef number<gmp_rational >         mpq_rational;

    }} // namespaces

The `gmp_rational` back-end is used via the typedef `boost::multiprecision::mpq_rational`. It acts as a thin wrapper around the GMP `mpq_t` to provide a rational number type that is a drop-in replacement for the native C++ number types, but with unlimited precision.

As well as the usual conversions from arithmetic and string types, instances of `number<gmp_rational>` are copy constructible and assignable from:

- The GMP native types: `mpz_t`, `mpq_t`.
- `number<gmp_int>`.

There is also a two-argument constructor that accepts a numerator and denominator (both of type `number<gmp_int>`).

There are also non-member functions:

    mpz_int numerator(const mpq_rational&);
    mpz_int denominator(const mpq_rational&);

which return the numerator and denominator of the number.

It's also possible to access the underlying `mpq_t` via the `data()` member function of `mpq_rational`.

Things you should know when using this type:

- Default constructed `mpq_rational`s have the value zero (this is the GMP default behavior).
- Division by zero results in a `std::overflow_error` being thrown.
- Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted as a valid rational number.
- No changes are made to the GMP library's global settings, so this type can coexist with existing GMP code.
- The code can equally be used with MPIR as the underlying library - indeed that is the preferred option on Win32.

###### Example:

    #include <boost/multiprecision/gmp.hpp>

    using namespace boost::multiprecision;

    mpq_rational v = 1;

    // Do some arithmetic:
    for(unsigned i = 1; i <= 1000; ++i)
       v *= i;
    v /= 10;

    std::cout << v << std::endl; // prints 1000! / 10
    std::cout << numerator(v) << std::endl;
    std::cout << denominator(v) << std::endl;

    mpq_rational w(2, 3);  // component wise constructor
    std::cout << w << std::endl; // prints 2/3

    // Access the underlying data:
    mpq_t q;
    mpq_init(q);
    mpq_set(q, v.backend().data());