multiprecision/detail/default_ops.hpp

///////////////////////////////////////////////////////////////////////////////
//  Copyright 2011 John Maddock. 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)

#ifndef BOOST_MATH_BIG_NUM_DEF_OPS
#define BOOST_MATH_BIG_NUM_DEF_OPS

#include <boost/math/policies/error_handling.hpp>
#include <boost/multiprecision/detail/number_base.hpp>
#include <boost/math/special_functions/fpclassify.hpp>
#include <boost/math/special_functions/next.hpp>
#include <boost/math/special_functions/hypot.hpp>
#include <boost/utility/enable_if.hpp>
#include <boost/mpl/front.hpp>
#include <boost/mpl/fold.hpp>
#include <boost/cstdint.hpp>
#include <boost/type_traits/make_unsigned.hpp>
#ifndef BOOST_NO_CXX17_HDR_STRING_VIEW
#include <string_view>
#endif

#ifndef INSTRUMENT_BACKEND
#ifndef BOOST_MP_INSTRUMENT
#define INSTRUMENT_BACKEND(x)
#else
#define INSTRUMENT_BACKEND(x)\
   std::cout << BOOST_STRINGIZE(x) << " = " << x.str(0, std::ios_base::scientific) << std::endl;
#endif
#endif


namespace boost{ namespace multiprecision{

   namespace detail {

      template <class T>
      struct is_backend;

      template <class To, class From>
      void generic_interconvert(To& to, const From& from, const mpl::int_<number_kind_floating_point>& /*to_type*/, const mpl::int_<number_kind_integer>& /*from_type*/);
      template <class To, class From>
      void generic_interconvert(To& to, const From& from, const mpl::int_<number_kind_integer>& /*to_type*/, const mpl::int_<number_kind_integer>& /*from_type*/);
      template <class To, class From>
      void generic_interconvert(To& to, const From& from, const mpl::int_<number_kind_floating_point>& /*to_type*/, const mpl::int_<number_kind_floating_point>& /*from_type*/);
      template <class To, class From>
      void generic_interconvert(To& to, const From& from, const mpl::int_<number_kind_rational>& /*to_type*/, const mpl::int_<number_kind_rational>& /*from_type*/);
      template <class To, class From>
      void generic_interconvert(To& to, const From& from, const mpl::int_<number_kind_rational>& /*to_type*/, const mpl::int_<number_kind_integer>& /*from_type*/);

}

namespace default_ops{

#ifdef BOOST_MSVC
// warning C4127: conditional expression is constant
// warning C4146: unary minus operator applied to unsigned type, result still unsigned
#pragma warning(push)
#pragma warning(disable:4127 4146)
#endif
//
// Default versions of mixed arithmetic, these just construct a temporary
// from the arithmetic value and then do the arithmetic on that, two versions
// of each depending on whether the backend can be directly constructed from type V.
//
// Note that we have to provide *all* the template parameters to class number when used in
// enable_if as MSVC-10 won't compile the code if we rely on a computed-default parameter.
// Since the result of the test doesn't depend on whether expression templates are on or off
// we just use et_on everywhere.  We could use a BOOST_WORKAROUND but that just obfuscates the
// code even more....
//
template <class T, class V>
inline typename disable_if_c<is_convertible<V, T>::value >::type
   eval_add(T& result, V const& v)
{
   T t;
   t = v;
   eval_add(result, t);
}
template <class T, class V>
inline typename enable_if_c<is_convertible<V, T>::value >::type
   eval_add(T& result, V const& v)
{
   T t(v);
   eval_add(result, t);
}
template <class T, class V>
inline typename disable_if_c<is_convertible<V, T>::value>::type
   eval_subtract(T& result, V const& v)
{
   T t;
   t = v;
   eval_subtract(result, t);
}
template <class T, class V>
inline typename enable_if_c<is_convertible<V, T>::value>::type
   eval_subtract(T& result, V const& v)
{
   T t(v);
   eval_subtract(result, t);
}
template <class T, class V>
inline typename disable_if_c<is_convertible<V, T>::value>::type
   eval_multiply(T& result, V const& v)
{
   T t;
   t = v;
   eval_multiply(result, t);
}
template <class T, class V>
inline typename enable_if_c<is_convertible<V, T>::value>::type
   eval_multiply(T& result, V const& v)
{
   T t(v);
   eval_multiply(result, t);
}

template <class T, class U, class V>
void eval_multiply(T& t, const U& u, const V& v);

template <class T, class U, class V>
inline typename disable_if_c<!is_same<T, U>::value && is_same<T, V>::value>::type eval_multiply_add(T& t, const U& u, const V& v)
{
   T z;
   eval_multiply(z, u, v);
   eval_add(t, z);
}
template <class T, class U, class V>
inline typename enable_if_c<!is_same<T, U>::value && is_same<T, V>::value>::type eval_multiply_add(T& t, const U& u, const V& v)
{
   eval_multiply_add(t, v, u);
}
template <class T, class U, class V>
inline typename disable_if_c<!is_same<T, U>::value && is_same<T, V>::value>::type eval_multiply_subtract(T& t, const U& u, const V& v)
{
   T z;
   eval_multiply(z, u, v);
   eval_subtract(t, z);
}
template <class T, class U, class V>
inline typename enable_if_c<!is_same<T, U>::value && is_same<T, V>::value>::type eval_multiply_subtract(T& t, const U& u, const V& v)
{
   eval_multiply_subtract(t, v, u);
}
template <class T, class V>
inline typename enable_if_c<is_convertible<V, number<T, et_on> >::value && !is_convertible<V, T>::value>::type
   eval_divide(T& result, V const& v)
{
   T t;
   t = v;
   eval_divide(result, t);
}
template <class T, class V>
inline typename enable_if_c<is_convertible<V, number<T, et_on> >::value && is_convertible<V, T>::value>::type
   eval_divide(T& result, V const& v)
{
   T t(v);
   eval_divide(result, t);
}
template <class T, class V>
inline typename enable_if_c<is_convertible<V, number<T, et_on> >::value && !is_convertible<V, T>::value>::type
   eval_modulus(T& result, V const& v)
{
   T t;
   t = v;
   eval_modulus(result, t);
}
template <class T, class V>
inline typename enable_if_c<is_convertible<V, number<T, et_on> >::value&& is_convertible<V, T>::value>::type
   eval_modulus(T& result, V const& v)
{
   T t(v);
   eval_modulus(result, t);
}
template <class T, class V>
inline typename enable_if_c<is_convertible<V, number<T, et_on> >::value && !is_convertible<V, T>::value>::type
   eval_bitwise_and(T& result, V const& v)
{
   T t;
   t = v;
   eval_bitwise_and(result, t);
}
template <class T, class V>
inline typename enable_if_c<is_convertible<V, number<T, et_on> >::value && is_convertible<V, T>::value>::type
   eval_bitwise_and(T& result, V const& v)
{
   T t(v);
   eval_bitwise_and(result, t);
}
template <class T, class V>
inline typename enable_if_c<is_convertible<V, number<T, et_on> >::value && !is_convertible<V, T>::value>::type
   eval_bitwise_or(T& result, V const& v)
{
   T t;
   t = v;
   eval_bitwise_or(result, t);
}
template <class T, class V>
inline typename enable_if_c<is_convertible<V, number<T, et_on> >::value && is_convertible<V, T>::value>::type
   eval_bitwise_or(T& result, V const& v)
{
   T t(v);
   eval_bitwise_or(result, t);
}
template <class T, class V>
inline typename enable_if_c<is_convertible<V, number<T, et_on> >::value && !is_convertible<V, T>::value>::type
   eval_bitwise_xor(T& result, V const& v)
{
   T t;
   t = v;
   eval_bitwise_xor(result, t);
}
template <class T, class V>
inline typename enable_if_c<is_convertible<V, number<T, et_on> >::value && is_convertible<V, T>::value>::type
   eval_bitwise_xor(T& result, V const& v)
{
   T t(v);
   eval_bitwise_xor(result, t);
}

template <class T, class V>
inline typename enable_if_c<is_convertible<V, number<T, et_on> >::value && !is_convertible<V, T>::value>::type
   eval_complement(T& result, V const& v)
{
   T t;
   t = v;
   eval_complement(result, t);
}
template <class T, class V>
inline typename enable_if_c<is_convertible<V, number<T, et_on> >::value && is_convertible<V, T>::value>::type
   eval_complement(T& result, V const& v)
{
   T t(v);
   eval_complement(result, t);
}

//
// Default versions of 3-arg arithmetic functions, these mostly just forward to the 2 arg versions:
//
template <class T, class U, class V>
void eval_add(T& t, const U& u, const V& v);

template <class T>
inline void eval_add_default(T& t, const T& u, const T& v)
{
   if(&t == &v)
   {
      eval_add(t, u);
   }
   else if(&t == &u)
   {
      eval_add(t, v);
   }
   else
   {
      t = u;
      eval_add(t, v);
   }
}
template <class T, class U>
inline typename enable_if_c<is_convertible<U, number<T, et_on> >::value && !is_convertible<U, T>::value>::type eval_add_default(T& t, const T& u, const U& v)
{
   T vv;
   vv = v;
   eval_add(t, u, vv);
}
template <class T, class U>
inline typename enable_if_c<is_convertible<U, number<T, et_on> >::value && is_convertible<U, T>::value>::type eval_add_default(T& t, const T& u, const U& v)
{
   T vv(v);
   eval_add(t, u, vv);
}
template <class T, class U>
inline typename enable_if_c<is_convertible<U, number<T, et_on> >::value>::type eval_add_default(T& t, const U& u, const T& v)
{
   eval_add(t, v, u);
}
template <class T, class U, class V>
inline void eval_add_default(T& t, const U& u, const V& v)
{
   if(is_same<T, V>::value && ((void*)&t == (void*)&v))
   {
      eval_add(t, u);
   }
   else
   {
      t = u;
      eval_add(t, v);
   }
}
template <class T, class U, class V>
inline void eval_add(T& t, const U& u, const V& v)
{
   eval_add_default(t, u, v);
}

template <class T, class U, class V>
void eval_subtract(T& t, const U& u, const V& v);

template <class T>
inline void eval_subtract_default(T& t, const T& u, const T& v)
{
   if((&t == &v) && is_signed_number<T>::value)
   {
      eval_subtract(t, u);
      t.negate();
   }
   else if(&t == &u)
   {
      eval_subtract(t, v);
   }
   else
   {
      t = u;
      eval_subtract(t, v);
   }
}
template <class T, class U>
inline typename enable_if_c<is_convertible<U, number<T, et_on> >::value && !is_convertible<U, T>::value>::type eval_subtract_default(T& t, const T& u, const U& v)
{
   T vv;
   vv = v;
   eval_subtract(t, u, vv);
}
template <class T, class U>
inline typename enable_if_c<is_convertible<U, number<T, et_on> >::value && is_convertible<U, T>::value>::type eval_subtract_default(T& t, const T& u, const U& v)
{
   T vv(v);
   eval_subtract(t, u, vv);
}
template <class T, class U>
inline typename enable_if_c<is_convertible<U, number<T, et_on> >::value && is_signed_number<T>::value>::type eval_subtract_default(T& t, const U& u, const T& v)
{
   eval_subtract(t, v, u);
   t.negate();
}
template <class T, class U>
inline typename enable_if_c<is_convertible<U, number<T, et_on> >::value && !is_convertible<U, T>::value && is_unsigned_number<T>::value>::type eval_subtract_default(T& t, const U& u, const T& v)
{
   T temp;
   temp = u;
   eval_subtract(t, temp, v);
}
template <class T, class U>
inline typename enable_if_c<is_convertible<U, number<T, et_on> >::value && is_convertible<U, T>::value && is_unsigned_number<T>::value>::type eval_subtract_default(T& t, const U& u, const T& v)
{
   T temp(u);
   eval_subtract(t, temp, v);
}
template <class T, class U, class V>
inline void eval_subtract_default(T& t, const U& u, const V& v)
{
   if(is_same<T, V>::value && ((void*)&t == (void*)&v))
   {
      eval_subtract(t, u);
      t.negate();
   }
   else
   {
      t = u;
      eval_subtract(t, v);
   }
}
template <class T, class U, class V>
inline void eval_subtract(T& t, const U& u, const V& v)
{
   eval_subtract_default(t, u, v);
}

template <class T>
inline void eval_multiply_default(T& t, const T& u, const T& v)
{
   if(&t == &v)
   {
      eval_multiply(t, u);
   }
   else if(&t == &u)
   {
      eval_multiply(t, v);
   }
   else
   {
      t = u;
      eval_multiply(t, v);
   }
}
#if !BOOST_WORKAROUND(BOOST_MSVC, < 1900)
template <class T, class U>
inline typename enable_if_c<is_convertible<U, number<T, et_on> >::value && !is_convertible<U, T>::value>::type eval_multiply_default(T& t, const T& u, const U& v)
{
   T vv;
   vv = v;
   eval_multiply(t, u, vv);
}
template <class T, class U>
inline typename enable_if_c<is_convertible<U, number<T, et_on> >::value && is_convertible<U, T>::value>::type eval_multiply_default(T& t, const T& u, const U& v)
{
   T vv(v);
   eval_multiply(t, u, vv);
}
template <class T, class U>
inline typename enable_if_c<is_convertible<U, number<T, et_on> >::value>::type eval_multiply_default(T& t, const U& u, const T& v)
{
   eval_multiply(t, v, u);
}
#endif
template <class T, class U, class V>
inline void eval_multiply_default(T& t, const U& u, const V& v)
{
   if(is_same<T, V>::value && ((void*)&t == (void*)&v))
   {
      eval_multiply(t, u);
   }
   else
   {
      t = number<T>::canonical_value(u);
      eval_multiply(t, v);
   }
}
template <class T, class U, class V>
inline void eval_multiply(T& t, const U& u, const V& v)
{
   eval_multiply_default(t, u, v);
}

template <class T>
inline void eval_multiply_add(T& t, const T& u, const T& v, const T& x)
{
   if((void*)&x == (void*)&t)
   {
      T z;
      z = number<T>::canonical_value(x);
      eval_multiply_add(t, u, v, z);
   }
   else
   {
      eval_multiply(t, u, v);
      eval_add(t, x);
   }
}

template <class T, class U>
inline typename boost::disable_if_c<boost::is_same<T, U>::value, T>::type make_T(const U& u)
{
   T t;
   t = number<T>::canonical_value(u);
   return BOOST_MP_MOVE(t);
}
template <class T>
inline const T& make_T(const T& t)
{
   return t;
}

template <class T, class U, class V, class X>
inline typename disable_if_c<!is_same<T, U>::value && is_same<T, V>::value>::type eval_multiply_add(T& t, const U& u, const V& v, const X& x)
{
   eval_multiply_add(t, make_T<T>(u), make_T<T>(v), make_T<T>(x));
}
template <class T, class U, class V, class X>
inline typename enable_if_c<!is_same<T, U>::value && is_same<T, V>::value>::type eval_multiply_add(T& t, const U& u, const V& v, const X& x)
{
   eval_multiply_add(t, v, u, x);
}
template <class T, class U, class V, class X>
inline typename disable_if_c<!is_same<T, U>::value && is_same<T, V>::value>::type eval_multiply_subtract(T& t, const U& u, const V& v, const X& x)
{
   if((void*)&x == (void*)&t)
   {
      T z;
      z = x;
      eval_multiply_subtract(t, u, v, z);
   }
   else
   {
      eval_multiply(t, u, v);
      eval_subtract(t, x);
   }
}
template <class T, class U, class V, class X>
inline typename enable_if_c<!is_same<T, U>::value && is_same<T, V>::value>::type eval_multiply_subtract(T& t, const U& u, const V& v, const X& x)
{
   eval_multiply_subtract(t, v, u, x);
}

template <class T, class U, class V>
void eval_divide(T& t, const U& u, const V& v);

template <class T>
inline void eval_divide_default(T& t, const T& u, const T& v)
{
   if(&t == &u)
      eval_divide(t, v);
   else if(&t == &v)
   {
      T temp;
      eval_divide(temp, u, v);
      temp.swap(t);
   }
   else
   {
      t = u;
      eval_divide(t, v);
   }
}
#if !BOOST_WORKAROUND(BOOST_MSVC, < 1900)
template <class T, class U>
inline typename enable_if_c<is_convertible<U, number<T, et_on> >::value && !is_convertible<U, T>::value>::type eval_divide_default(T& t, const T& u, const U& v)
{
   T vv;
   vv = v;
   eval_divide(t, u, vv);
}
template <class T, class U>
inline typename enable_if_c<is_convertible<U, number<T, et_on> >::value && is_convertible<U, T>::value>::type eval_divide_default(T& t, const T& u, const U& v)
{
   T vv(v);
   eval_divide(t, u, vv);
}
template <class T, class U>
inline typename enable_if_c<is_convertible<U, number<T, et_on> >::value && !is_convertible<U, T>::value>::type eval_divide_default(T& t, const U& u, const T& v)
{
   T uu;
   uu = u;
   eval_divide(t, uu, v);
}
template <class T, class U>
inline typename enable_if_c<is_convertible<U, number<T, et_on> >::value && is_convertible<U, T>::value>::type eval_divide_default(T& t, const U& u, const T& v)
{
   T uu(u);
   eval_divide(t, uu, v);
}
#endif
template <class T, class U, class V>
inline void eval_divide_default(T& t, const U& u, const V& v)
{
   if(is_same<T, V>::value && ((void*)&t == (void*)&v))
   {
      T temp;
      temp = u;
      eval_divide(temp, v);
      t = temp;
   }
   else
   {
      t = u;
      eval_divide(t, v);
   }
}
template <class T, class U, class V>
inline void eval_divide(T& t, const U& u, const V& v)
{
   eval_divide_default(t, u, v);
}

template <class T, class U, class V>
void eval_modulus(T& t, const U& u, const V& v);

template <class T>
inline void eval_modulus_default(T& t, const T& u, const T& v)
{
   if(&t == &u)
      eval_modulus(t, v);
   else if(&t == &v)
   {
      T temp;
      eval_modulus(temp, u, v);
      temp.swap(t);
   }
   else
   {
      t = u;
      eval_modulus(t, v);
   }
}
template <class T, class U>
inline typename enable_if_c<is_convertible<U, number<T, et_on> >::value && !is_convertible<U, T>::value>::type eval_modulus_default(T& t, const T& u, const U& v)
{
   T vv;
   vv = v;
   eval_modulus(t, u, vv);
}
template <class T, class U>
inline typename enable_if_c<is_convertible<U, number<T, et_on> >::value && is_convertible<U, T>::value>::type eval_modulus_default(T& t, const T& u, const U& v)
{
   T vv(v);
   eval_modulus(t, u, vv);
}
template <class T, class U>
inline typename enable_if_c<is_convertible<U, number<T, et_on> >::value && !is_convertible<U, T>::value>::type eval_modulus_default(T& t, const U& u, const T& v)
{
   T uu;
   uu = u;
   eval_modulus(t, uu, v);
}
template <class T, class U>
inline typename enable_if_c<is_convertible<U, number<T, et_on> >::value && is_convertible<U, T>::value>::type eval_modulus_default(T& t, const U& u, const T& v)
{
   T uu(u);
   eval_modulus(t, uu, v);
}
template <class T, class U, class V>
inline void eval_modulus_default(T& t, const U& u, const V& v)
{
   if(is_same<T, V>::value && ((void*)&t == (void*)&v))
   {
      T temp(u);
      eval_modulus(temp, v);
      t = temp;
   }
   else
   {
      t = u;
      eval_modulus(t, v);
   }
}
template <class T, class U, class V>
inline void eval_modulus(T& t, const U& u, const V& v)
{
   eval_modulus_default(t, u, v);
}

template <class T, class U, class V>
void eval_bitwise_and(T& t, const U& u, const V& v);

template <class T>
inline void eval_bitwise_and_default(T& t, const T& u, const T& v)
{
   if(&t == &v)
   {
      eval_bitwise_and(t, u);
   }
   else if(&t == &u)
   {
      eval_bitwise_and(t, v);
   }
   else
   {
      t = u;
      eval_bitwise_and(t, v);
   }
}
template <class T, class U>
inline typename disable_if_c<is_convertible<U, T>::value>::type eval_bitwise_and_default(T& t, const T& u, const U& v)
{
   T vv;
   vv = v;
   eval_bitwise_and(t, u, vv);
}
template <class T, class U>
inline typename enable_if_c<is_convertible<U, T>::value>::type eval_bitwise_and_default(T& t, const T& u, const U& v)
{
   T vv(v);
   eval_bitwise_and(t, u, vv);
}
template <class T, class U>
inline typename enable_if_c<is_convertible<U, number<T, et_on> >::value>::type eval_bitwise_and_default(T& t, const U& u, const T& v)
{
   eval_bitwise_and(t, v, u);
}
template <class T, class U, class V>
inline typename disable_if_c<is_same<T, U>::value || is_same<T, V>::value>::type eval_bitwise_and_default(T& t, const U& u, const V& v)
{
   t = u;
   eval_bitwise_and(t, v);
}
template <class T, class U, class V>
inline void eval_bitwise_and(T& t, const U& u, const V& v)
{
   eval_bitwise_and_default(t, u, v);
}

template <class T, class U, class V>
void eval_bitwise_or(T& t, const U& u, const V& v);

template <class T>
inline void eval_bitwise_or_default(T& t, const T& u, const T& v)
{
   if(&t == &v)
   {
      eval_bitwise_or(t, u);
   }
   else if(&t == &u)
   {
      eval_bitwise_or(t, v);
   }
   else
   {
      t = u;
      eval_bitwise_or(t, v);
   }
}
template <class T, class U>
inline typename enable_if_c<is_convertible<U, number<T, et_on> >::value && !is_convertible<U, T>::value>::type eval_bitwise_or_default(T& t, const T& u, const U& v)
{
   T vv;
   vv = v;
   eval_bitwise_or(t, u, vv);
}
template <class T, class U>
inline typename enable_if_c<is_convertible<U, number<T, et_on> >::value && is_convertible<U, T>::value>::type eval_bitwise_or_default(T& t, const T& u, const U& v)
{
   T vv(v);
   eval_bitwise_or(t, u, vv);
}
template <class T, class U>
inline typename enable_if_c<is_convertible<U, number<T, et_on> >::value>::type eval_bitwise_or_default(T& t, const U& u, const T& v)
{
   eval_bitwise_or(t, v, u);
}
template <class T, class U, class V>
inline void eval_bitwise_or_default(T& t, const U& u, const V& v)
{
   if(is_same<T, V>::value && ((void*)&t == (void*)&v))
   {
      eval_bitwise_or(t, u);
   }
   else
   {
      t = u;
      eval_bitwise_or(t, v);
   }
}
template <class T, class U, class V>
inline void eval_bitwise_or(T& t, const U& u, const V& v)
{
   eval_bitwise_or_default(t, u, v);
}

template <class T, class U, class V>
void eval_bitwise_xor(T& t, const U& u, const V& v);

template <class T>
inline void eval_bitwise_xor_default(T& t, const T& u, const T& v)
{
   if(&t == &v)
   {
      eval_bitwise_xor(t, u);
   }
   else if(&t == &u)
   {
      eval_bitwise_xor(t, v);
   }
   else
   {
      t = u;
      eval_bitwise_xor(t, v);
   }
}
template <class T, class U>
inline typename enable_if_c<is_convertible<U, number<T, et_on> >::value && !is_convertible<U, T>::value>::type eval_bitwise_xor_default(T& t, const T& u, const U& v)
{
   T vv;
   vv = v;
   eval_bitwise_xor(t, u, vv);
}
template <class T, class U>
inline typename enable_if_c<is_convertible<U, number<T, et_on> >::value && is_convertible<U, T>::value>::type eval_bitwise_xor_default(T& t, const T& u, const U& v)
{
   T vv(v);
   eval_bitwise_xor(t, u, vv);
}
template <class T, class U>
inline typename enable_if_c<is_convertible<U, number<T, et_on> >::value>::type eval_bitwise_xor_default(T& t, const U& u, const T& v)
{
   eval_bitwise_xor(t, v, u);
}
template <class T, class U, class V>
inline void eval_bitwise_xor_default(T& t, const U& u, const V& v)
{
   if(is_same<T, V>::value && ((void*)&t == (void*)&v))
   {
      eval_bitwise_xor(t, u);
   }
   else
   {
      t = u;
      eval_bitwise_xor(t, v);
   }
}
template <class T, class U, class V>
inline void eval_bitwise_xor(T& t, const U& u, const V& v)
{
   eval_bitwise_xor_default(t, u, v);
}

template <class T>
inline void eval_increment(T& val)
{
   typedef typename mpl::front<typename T::unsigned_types>::type ui_type;
   eval_add(val, static_cast<ui_type>(1u));
}
template <class T>
inline void eval_decrement(T& val)
{
   typedef typename mpl::front<typename T::unsigned_types>::type ui_type;
   eval_subtract(val, static_cast<ui_type>(1u));
}

template <class T, class V>
inline void eval_left_shift(T& result, const T& arg, const V val)
{
   result = arg;
   eval_left_shift(result, val);
}

template <class T, class V>
inline void eval_right_shift(T& result, const T& arg, const V val)
{
   result = arg;
   eval_right_shift(result, val);
}

template <class T>
inline bool eval_is_zero(const T& val)
{
   typedef typename mpl::front<typename T::unsigned_types>::type ui_type;
   return val.compare(static_cast<ui_type>(0)) == 0;
}
template <class T>
inline int eval_get_sign(const T& val)
{
   typedef typename mpl::front<typename T::unsigned_types>::type ui_type;
   return val.compare(static_cast<ui_type>(0));
}

template <class T, class V, class U>
inline void assign_components_imp(T& result, const V& v1, const U& v2, const mpl::int_<number_kind_rational>&)
{
   result = v1;
   T t;
   t = v2;
   eval_divide(result, t);
}

template <class T, class V, class U, int N>
inline void assign_components_imp(T& result, const V& v1, const U& v2, const mpl::int_<N>&)
{
   typedef typename component_type<number<T> >::type component_number_type;

   component_number_type x(v1), y(v2);
   assign_components(result, x.backend(), y.backend());
}

template <class T, class V, class U>
inline void assign_components(T& result, const V& v1, const U& v2)
{
   return assign_components_imp(result, v1, v2, typename number_category<T>::type());
}
#ifndef BOOST_NO_CXX17_HDR_STRING_VIEW
template <class Result, class Traits>
inline void assign_from_string_view(Result& result, const std::basic_string_view<char, Traits>& view)
{
   // since most (all?) backends require a const char* to construct from, we just
   // convert to that:
   std::string s(view);
   result = s.c_str();
}
template <class Result, class Traits>
inline void assign_from_string_view(Result& result, const std::basic_string_view<char, Traits>& view_x, const std::basic_string_view<char, Traits>& view_y)
{
   // since most (all?) backends require a const char* to construct from, we just
   // convert to that:
   std::string x(view_x), y(view_y);
   assign_components(result, x.c_str(), y.c_str());
}
#endif
template <class R, int b>
struct has_enough_bits
{
   template <class T>
   struct type : public mpl::and_<mpl::not_<is_same<R, T> >, mpl::bool_<std::numeric_limits<T>::digits >= b> >{};
};

template <class R>
struct terminal
{
   terminal(const R& v) : value(v){}
   terminal(){}
   terminal& operator = (R val) { value = val;  return *this; }
   R value;
   operator R()const {  return value;  }
};

template<class R, class B>
struct calculate_next_larger_type
{
   // Find which list we're looking through:
   typedef typename mpl::if_<
      is_signed<R>,
      typename B::signed_types,
      typename mpl::if_<
         is_unsigned<R>,
         typename B::unsigned_types,
         typename B::float_types
      >::type
   >::type list_type;
   // A predicate to find a type with enough bits:
   typedef typename has_enough_bits<R, std::numeric_limits<R>::digits>::template type<mpl::_> pred_type;
   // See if the last type is in the list, if so we have to start after this:
   typedef typename mpl::find_if<
      list_type,
      is_same<R, mpl::_>
   >::type start_last;
   // Where we're starting from, either the start of the sequence or the last type found:
   typedef typename mpl::if_<is_same<start_last, typename mpl::end<list_type>::type>, typename mpl::begin<list_type>::type, start_last>::type start_seq;
   // The range we're searching:
   typedef mpl::iterator_range<start_seq, typename mpl::end<list_type>::type> range;
   // Find the next type:
   typedef typename mpl::find_if<
      range,
      pred_type
   >::type iter_type;
   // Either the next type, or a "terminal" to indicate we've run out of types to search:
   typedef typename mpl::eval_if<
      is_same<typename mpl::end<list_type>::type, iter_type>,
      mpl::identity<terminal<R> >,
      mpl::deref<iter_type>
      >::type type;
};

template <class R, class T>
inline typename boost::enable_if_c<boost::is_integral<R>::value, bool>::type check_in_range(const T& t)
{
   // Can t fit in an R?
   if((t > 0) && std::numeric_limits<R>::is_specialized && std::numeric_limits<R>::is_bounded && (t > (std::numeric_limits<R>::max)()))
      return true;
   else
   return false;
}

template <class R, class B>
inline typename boost::enable_if_c<boost::is_integral<R>::value>::type eval_convert_to(R* result, const B& backend)
{
   typedef typename calculate_next_larger_type<R, B>::type next_type;
   next_type n;
   eval_convert_to(&n, backend);
   if(!boost::is_unsigned<R>::value && std::numeric_limits<R>::is_specialized && std::numeric_limits<R>::is_bounded && (n > (next_type)(std::numeric_limits<R>::max)()))
   {
      *result = (std::numeric_limits<R>::max)();
   }
   else if (std::numeric_limits<R>::is_specialized && std::numeric_limits<R>::is_bounded && (n < (next_type)(std::numeric_limits<R>::min)()))
   {
      *result = (std::numeric_limits<R>::min)();
   }
   else
      *result = static_cast<R>(n);
}

template <class R, class B>
inline typename boost::disable_if_c<boost::is_integral<R>::value>::type eval_convert_to(R* result, const B& backend)
{
   typedef typename calculate_next_larger_type<R, B>::type next_type;
   next_type n;
   eval_convert_to(&n, backend);
   if(std::numeric_limits<R>::is_specialized && std::numeric_limits<R>::is_bounded && ((n > (next_type)(std::numeric_limits<R>::max)() || (n < (next_type)-(std::numeric_limits<R>::max)()) )))
   {
      *result = n > 0 ? (std::numeric_limits<R>::max)() : -(std::numeric_limits<R>::max)();
   }
   else
      *result = static_cast<R>(n);
}

template <class R, class B>
inline void last_chance_eval_convert_to(terminal<R>* result, const B& backend, const mpl::false_&)
{
   //
   // We ran out of types to try for the conversion, try
   // a lexical_cast and hope for the best:
   //
   if (std::numeric_limits<R>::is_integer && !std::numeric_limits<R>::is_signed && (eval_get_sign(backend) < 0))
      BOOST_THROW_EXCEPTION(std::range_error("Attempt to convert negative value to an unsigned integer results in undefined behaviour"));
   try
   {
      result->value = boost::lexical_cast<R>(backend.str(0, std::ios_base::fmtflags(0)));
   }
   catch (const bad_lexical_cast&)
   {
      if (eval_get_sign(backend) < 0)
      {
         *result = std::numeric_limits<R>::is_integer && std::numeric_limits<R>::is_signed ? (std::numeric_limits<R>::min)() : -(std::numeric_limits<R>::max)();
      }
      else
         *result = (std::numeric_limits<R>::max)();
   }
}

template <class R, class B>
inline void last_chance_eval_convert_to(terminal<R>* result, const B& backend, const mpl::true_&)
{
   //
   // We ran out of types to try for the conversion, try
   // a lexical_cast and hope for the best:
   //
   if (std::numeric_limits<R>::is_integer && !std::numeric_limits<R>::is_signed && (eval_get_sign(backend) < 0))
      BOOST_THROW_EXCEPTION(std::range_error("Attempt to convert negative value to an unsigned integer results in undefined behaviour"));
   try
   {
      B t(backend);
      R mask = ~static_cast<R>(0u);
      eval_bitwise_and(t, mask);
      result->value = boost::lexical_cast<R>(t.str(0, std::ios_base::fmtflags(0)));
   }
   catch (const bad_lexical_cast&)
   {
      if (eval_get_sign(backend) < 0)
      {
         *result = std::numeric_limits<R>::is_integer && std::numeric_limits<R>::is_signed ? (std::numeric_limits<R>::min)() : -(std::numeric_limits<R>::max)();
      }
      else
         *result = (std::numeric_limits<R>::max)();
   }
}

template <class R, class B>
inline void eval_convert_to(terminal<R>* result, const B& backend)
{
   typedef mpl::bool_<boost::is_unsigned<R>::value && number_category<B>::value == number_kind_integer> tag_type;
   last_chance_eval_convert_to(result, backend, tag_type());
}

template <class B1, class B2, expression_template_option et>
inline void eval_convert_to(terminal<number<B1, et> >* result, const B2& backend)
{
   //
   // We ran out of types to try for the conversion, try
   // a generic conversion and hope for the best:
   //
   boost::multiprecision::detail::generic_interconvert(result->value.backend(), backend, number_category<B1>(), number_category<B2>());
}

template <class B>
inline void eval_convert_to(std::string* result, const B& backend)
{
   *result = backend.str(0, std::ios_base::fmtflags(0));
}

template <class B>
inline void eval_convert_to(std::complex<float>* result, const B& backend)
{
   typedef typename scalar_result_from_possible_complex<multiprecision::number<B> >::type scalar_type;
   scalar_type re, im;
   eval_real(re.backend(), backend);
   eval_imag(im.backend(), backend);

   *result = std::complex<float>(re.template convert_to<float>(), im.template convert_to<float>());
}

template <class B>
inline void eval_convert_to(std::complex<double>* result, const B& backend)
{
   typedef typename scalar_result_from_possible_complex<multiprecision::number<B> >::type scalar_type;
   scalar_type re, im;
   eval_real(re.backend(), backend);
   eval_imag(im.backend(), backend);

   *result = std::complex<double>(re.template convert_to<double>(), im.template convert_to<double>());
}

template <class B>
inline void eval_convert_to(std::complex<long double>* result, const B& backend)
{
   typedef typename scalar_result_from_possible_complex<multiprecision::number<B> >::type scalar_type;
   scalar_type re, im;
   eval_real(re.backend(), backend);
   eval_imag(im.backend(), backend);

   *result = std::complex<long double>(re.template convert_to<long double>(), im.template convert_to<long double>());
}

//
// Functions:
//
template <class T>
void eval_abs(T& result, const T& arg)
{
   typedef typename T::signed_types type_list;
   typedef typename mpl::front<type_list>::type front;
   result = arg;
   if(arg.compare(front(0)) < 0)
      result.negate();
}
template <class T>
void eval_fabs(T& result, const T& arg)
{
   BOOST_STATIC_ASSERT_MSG(number_category<T>::value == number_kind_floating_point, "The fabs function is only valid for floating point types.");
   typedef typename T::signed_types type_list;
   typedef typename mpl::front<type_list>::type front;
   result = arg;
   if(arg.compare(front(0)) < 0)
      result.negate();
}

template <class Backend>
inline int eval_fpclassify(const Backend& arg)
{
   BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_floating_point, "The fpclassify function is only valid for floating point types.");
   return eval_is_zero(arg) ? FP_ZERO : FP_NORMAL;
}

template <class T>
inline void eval_fmod(T& result, const T& a, const T& b)
{
   BOOST_STATIC_ASSERT_MSG(number_category<T>::value == number_kind_floating_point, "The fmod function is only valid for floating point types.");
   if((&result == &a) || (&result == &b))
   {
      T temp;
      eval_fmod(temp, a, b);
      result = temp;
      return;
   }
   switch(eval_fpclassify(a))
   {
   case FP_ZERO:
      result = a;
      return;
   case FP_INFINITE:
   case FP_NAN:
      result = std::numeric_limits<number<T> >::quiet_NaN().backend();
      errno = EDOM;
      return;
   }
   switch(eval_fpclassify(b))
   {
   case FP_ZERO:
   case FP_NAN:
      result = std::numeric_limits<number<T> >::quiet_NaN().backend();
      errno = EDOM;
      return;
   }
   T n;
   eval_divide(result, a, b);
   if(eval_get_sign(result) < 0)
      eval_ceil(n, result);
   else
      eval_floor(n, result);
   eval_multiply(n, b);
   eval_subtract(result, a, n);
}
template<class T, class A>
inline typename enable_if<is_arithmetic<A>, void>::type eval_fmod(T& result, const T& x, const A& a)
{
   typedef typename boost::multiprecision::detail::canonical<A, T>::type canonical_type;
   typedef typename mpl::if_<is_same<A, canonical_type>, T, canonical_type>::type cast_type;
   cast_type c;
   c = a;
   eval_fmod(result, x, c);
}

template<class T, class A>
inline typename enable_if<is_arithmetic<A>, void>::type eval_fmod(T& result, const A& x, const T& a)
{
   typedef typename boost::multiprecision::detail::canonical<A, T>::type canonical_type;
   typedef typename mpl::if_<is_same<A, canonical_type>, T, canonical_type>::type cast_type;
   cast_type c;
   c = x;
   eval_fmod(result, c, a);
}

template <class T>
void eval_round(T& result, const T& a);

template <class T>
inline void eval_remquo(T& result, const T& a, const T& b, int* pi)
{
   BOOST_STATIC_ASSERT_MSG(number_category<T>::value == number_kind_floating_point, "The remquo function is only valid for floating point types.");
   if((&result == &a) || (&result == &b))
   {
      T temp;
      eval_remquo(temp, a, b, pi);
      result = temp;
      return;
   }
   T n;
   eval_divide(result, a, b);
   eval_round(n, result);
   eval_convert_to(pi, n);
   eval_multiply(n, b);
   eval_subtract(result, a, n);
}
template<class T, class A>
inline typename enable_if<is_arithmetic<A>, void>::type eval_remquo(T& result, const T& x, const A& a, int* pi)
{
   typedef typename boost::multiprecision::detail::canonical<A, T>::type canonical_type;
   typedef typename mpl::if_<is_same<A, canonical_type>, T, canonical_type>::type cast_type;
   cast_type c;
   c = a;
   eval_remquo(result, x, c, pi);
}
template<class T, class A>
inline typename enable_if<is_arithmetic<A>, void>::type eval_remquo(T& result, const A& x, const T& a, int* pi)
{
   typedef typename boost::multiprecision::detail::canonical<A, T>::type canonical_type;
   typedef typename mpl::if_<is_same<A, canonical_type>, T, canonical_type>::type cast_type;
   cast_type c;
   c = x;
   eval_remquo(result, c, a, pi);
}
template <class T, class U, class V>
inline void eval_remainder(T& result, const U& a, const V& b)
{
   int i;
   eval_remquo(result, a, b, &i);
}

template <class B>
bool eval_gt(const B& a, const B& b);
template <class T, class U>
bool eval_gt(const T& a, const U& b);
template <class B>
bool eval_lt(const B& a, const B& b);
template <class T, class U>
bool eval_lt(const T& a, const U& b);

template<class T>
inline void eval_fdim(T& result, const T& a, const T& b)
{
   typedef typename boost::multiprecision::detail::canonical<unsigned, T>::type ui_type;
   static const ui_type zero = 0u;
   switch(eval_fpclassify(b))
   {
   case FP_NAN:
   case FP_INFINITE:
      result = zero;
      return;
   }
   switch(eval_fpclassify(a))
   {
   case FP_NAN:
      result = zero;
      return;
   case FP_INFINITE:
      result = a;
      return;
   }
   if(eval_gt(a, b))
   {
      eval_subtract(result, a, b);
   }
   else
      result = zero;
}

template<class T, class A>
inline typename boost::enable_if_c<boost::is_arithmetic<A>::value>::type eval_fdim(T& result, const T& a, const A& b)
{
   typedef typename boost::multiprecision::detail::canonical<unsigned, T>::type ui_type;
   typedef typename boost::multiprecision::detail::canonical<A, T>::type arithmetic_type;
   static const ui_type zero = 0u;
   arithmetic_type canonical_b = b;
   switch((::boost::math::fpclassify)(b))
   {
   case FP_NAN:
   case FP_INFINITE:
      result = zero;
      return;
   }
   switch(eval_fpclassify(a))
   {
   case FP_NAN:
      result = zero;
      return;
   case FP_INFINITE:
      result = a;
      return;
   }
   if(eval_gt(a, canonical_b))
   {
      eval_subtract(result, a, canonical_b);
   }
   else
      result = zero;
}

template<class T, class A>
inline typename boost::enable_if_c<boost::is_arithmetic<A>::value>::type eval_fdim(T& result, const A& a, const T& b)
{
   typedef typename boost::multiprecision::detail::canonical<unsigned, T>::type ui_type;
   typedef typename boost::multiprecision::detail::canonical<A, T>::type arithmetic_type;
   static const ui_type zero = 0u;
   arithmetic_type canonical_a = a;
   switch(eval_fpclassify(b))
   {
   case FP_NAN:
   case FP_INFINITE:
      result = zero;
      return;
   }
   switch((::boost::math::fpclassify)(a))
   {
   case FP_NAN:
      result = zero;
      return;
   case FP_INFINITE:
      result = std::numeric_limits<number<T> >::infinity().backend();
      return;
   }
   if(eval_gt(canonical_a, b))
   {
      eval_subtract(result, canonical_a, b);
   }
   else
      result = zero;
}

template <class T>
inline void eval_trunc(T& result, const T& a)
{
   BOOST_STATIC_ASSERT_MSG(number_category<T>::value == number_kind_floating_point, "The trunc function is only valid for floating point types.");
   switch(eval_fpclassify(a))
   {
   case FP_NAN:
      errno = EDOM;
      // fallthrough...
   case FP_ZERO:
   case FP_INFINITE:
      result = a;
      return;
   }
   if(eval_get_sign(a) < 0)
      eval_ceil(result, a);
   else
      eval_floor(result, a);
}

template <class T>
inline void eval_modf(T& result, T const& arg, T* pipart)
{
   typedef typename boost::multiprecision::detail::canonical<unsigned, T>::type ui_type;
   int c = eval_fpclassify(arg);
   if(c == (int)FP_NAN)
   {
      if(pipart)
         *pipart = arg;
      result = arg;
      return;
   }
   else if(c == (int)FP_INFINITE)
   {
      if(pipart)
         *pipart = arg;
      result = ui_type(0u);
      return;
   }
   if(pipart)
   {
      eval_trunc(*pipart, arg);
      eval_subtract(result, arg, *pipart);
   }
   else
   {
      T ipart;
      eval_trunc(ipart, arg);
      eval_subtract(result, arg, ipart);
   }
}

template <class T>
inline void eval_round(T& result, const T& a)
{
   BOOST_STATIC_ASSERT_MSG(number_category<T>::value == number_kind_floating_point, "The round function is only valid for floating point types.");
   typedef typename boost::multiprecision::detail::canonical<float, T>::type fp_type;
   int c = eval_fpclassify(a);
   if(c == (int)FP_NAN)
   {
      result = a;
      errno = EDOM;
      return;
   }
   if((c == FP_ZERO) || (c == (int)FP_INFINITE))
   {
      result = a;
   }
   else if(eval_get_sign(a) < 0)
   {
      eval_subtract(result, a, fp_type(0.5f));
      eval_ceil(result, result);
   }
   else
   {
      eval_add(result, a, fp_type(0.5f));
      eval_floor(result, result);
   }
}

template <class B>
void eval_lcm(B& result, const B& a, const B& b);
template <class B>
void eval_gcd(B& result, const B& a, const B& b);

template <class T, class Arithmetic>
inline typename enable_if<is_integral<Arithmetic> >::type eval_gcd(T& result, const T& a, const Arithmetic& b)
{
   typedef typename boost::multiprecision::detail::canonical<Arithmetic, T>::type si_type;
   using default_ops::eval_gcd;
   T t;
   t = static_cast<si_type>(b);
   eval_gcd(result, a, t);
}
template <class T, class Arithmetic>
inline typename enable_if<is_integral<Arithmetic> >::type eval_gcd(T& result, const Arithmetic& a, const T& b)
{
   eval_gcd(result, b, a);
}
template <class T, class Arithmetic>
inline typename enable_if<is_integral<Arithmetic> >::type eval_lcm(T& result, const T& a, const Arithmetic& b)
{
   typedef typename boost::multiprecision::detail::canonical<Arithmetic, T>::type si_type;
   using default_ops::eval_lcm;
   T t;
   t = static_cast<si_type>(b);
   eval_lcm(result, a, t);
}
template <class T, class Arithmetic>
inline typename enable_if<is_integral<Arithmetic> >::type eval_lcm(T& result, const Arithmetic& a, const T& b)
{
   eval_lcm(result, b, a);
}

template <class T>
inline unsigned eval_lsb(const T& val)
{
   typedef typename boost::multiprecision::detail::canonical<unsigned, T>::type ui_type;
   int c = eval_get_sign(val);
   if(c == 0)
   {
      BOOST_THROW_EXCEPTION(std::range_error("No bits were set in the operand."));
   }
   if(c < 0)
   {
      BOOST_THROW_EXCEPTION(std::range_error("Testing individual bits in negative values is not supported - results are undefined."));
   }
   unsigned result = 0;
   T mask, t;
   mask = ui_type(1);
   do
   {
      eval_bitwise_and(t, mask, val);
      ++result;
      eval_left_shift(mask, 1);
   }
   while(eval_is_zero(t));

   return --result;
}

template <class T>
inline int eval_msb(const T& val)
{
   int c = eval_get_sign(val);
   if(c == 0)
   {
      BOOST_THROW_EXCEPTION(std::range_error("No bits were set in the operand."));
   }
   if(c < 0)
   {
      BOOST_THROW_EXCEPTION(std::range_error("Testing individual bits in negative values is not supported - results are undefined."));
   }
   //
   // This implementation is really really rubbish - it does
   // a linear scan for the most-significant-bit.  We should really
   // do a binary search, but as none of our backends actually needs
   // this implementation, we'll leave it for now.  In fact for most
   // backends it's likely that there will always be a more efficient
   // native implementation possible.
   //
   unsigned result = 0;
   T t(val);
   while(!eval_is_zero(t))
   {
      eval_right_shift(t, 1);
      ++result;
   }
   return --result;
}

template <class T>
inline bool eval_bit_test(const T& val, unsigned index)
{
   typedef typename boost::multiprecision::detail::canonical<unsigned, T>::type ui_type;
   T mask, t;
   mask = ui_type(1);
   eval_left_shift(mask, index);
   eval_bitwise_and(t, mask, val);
   return !eval_is_zero(t);
}

template <class T>
inline void eval_bit_set(T& val, unsigned index)
{
   typedef typename boost::multiprecision::detail::canonical<unsigned, T>::type ui_type;
   T mask;
   mask = ui_type(1);
   eval_left_shift(mask, index);
   eval_bitwise_or(val, mask);
}

template <class T>
inline void eval_bit_flip(T& val, unsigned index)
{
   typedef typename boost::multiprecision::detail::canonical<unsigned, T>::type ui_type;
   T mask;
   mask = ui_type(1);
   eval_left_shift(mask, index);
   eval_bitwise_xor(val, mask);
}

template <class T>
inline void eval_bit_unset(T& val, unsigned index)
{
   typedef typename boost::multiprecision::detail::canonical<unsigned, T>::type ui_type;
   T mask, t;
   mask = ui_type(1);
   eval_left_shift(mask, index);
   eval_bitwise_and(t, mask, val);
   if(!eval_is_zero(t))
      eval_bitwise_xor(val, mask);
}

template <class B>
void eval_integer_sqrt(B& s, B& r, const B& x)
{
   //
   // This is slow bit-by-bit integer square root, see for example
   // http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Binary_numeral_system_.28base_2.29
   // There are better methods such as http://hal.inria.fr/docs/00/07/28/54/PDF/RR-3805.pdf
   // and http://hal.inria.fr/docs/00/07/21/13/PDF/RR-4475.pdf which should be implemented
   // at some point.
   //
   typedef typename boost::multiprecision::detail::canonical<unsigned char, B>::type ui_type;

   s = ui_type(0u);
   if(eval_get_sign(x) == 0)
   {
      r = ui_type(0u);
      return;
   }
   int g = eval_msb(x);
   if(g <= 1)
   {
      s = ui_type(1);
      eval_subtract(r, x, s);
      return;
   }

   B t;
   r = x;
   g /= 2;
   int org_g = g;
   eval_bit_set(s, g);
   eval_bit_set(t, 2 * g);
   eval_subtract(r, x, t);
   --g;
   if(eval_get_sign(r) == 0)
      return;
   int msbr = eval_msb(r);
   do
   {
      if(msbr >= org_g + g + 1)
      {
         t = s;
         eval_left_shift(t, g + 1);
         eval_bit_set(t, 2 * g);
         if(t.compare(r) <= 0)
         {
            BOOST_ASSERT(g >= 0);
            eval_bit_set(s, g);
            eval_subtract(r, t);
            if(eval_get_sign(r) == 0)
               return;
            msbr = eval_msb(r);
         }
      }
      --g;
   }
   while(g >= 0);
}

template <class B>
inline void eval_conj(B& result, const B& val)
{
   result = val;  // assume non-complex result.
}
template <class B>
inline void eval_proj(B& result, const B& val)
{
   result = val;  // assume non-complex result.
}

//
// These have to implemented by the backend, declared here so that our macro generated code compiles OK.
//
template <class T>
typename enable_if_c<sizeof(T) == 0>::type eval_floor();
template <class T>
typename enable_if_c<sizeof(T) == 0>::type eval_ceil();
template <class T>
typename enable_if_c<sizeof(T) == 0>::type eval_trunc();
template <class T>
typename enable_if_c<sizeof(T) == 0>::type eval_sqrt();
template <class T>
typename enable_if_c<sizeof(T) == 0>::type eval_ldexp();
template <class T>
typename enable_if_c<sizeof(T) == 0>::type eval_frexp();
// TODO implement default versions of these:
template <class T>
typename enable_if_c<sizeof(T) == 0>::type eval_asinh();
template <class T>
typename enable_if_c<sizeof(T) == 0>::type eval_acosh();
template <class T>
typename enable_if_c<sizeof(T) == 0>::type eval_atanh();

//
// eval_logb and eval_scalbn simply assume base 2 and forward to
// eval_ldexp and eval_frexp:
//
template <class B>
inline typename B::exponent_type eval_ilogb(const B& val)
{
   BOOST_STATIC_ASSERT_MSG(!std::numeric_limits<number<B> >::is_specialized || (std::numeric_limits<number<B> >::radix == 2), "The default implementation of ilogb requires a base 2 number type");
   typename B::exponent_type e;
   switch(eval_fpclassify(val))
   {
   case FP_NAN:
#ifdef FP_ILOGBNAN
      return FP_ILOGBNAN > 0 ? (std::numeric_limits<typename B::exponent_type>::max)() : (std::numeric_limits<typename B::exponent_type>::min)();
#else
      return (std::numeric_limits<typename B::exponent_type>::max)();
#endif
   case FP_INFINITE:
      return (std::numeric_limits<typename B::exponent_type>::max)();
   case FP_ZERO:
      return (std::numeric_limits<typename B::exponent_type>::min)();
   }
   B result;
   eval_frexp(result, val, &e);
   return e - 1;
}

template <class T>
int eval_signbit(const T& val);

template <class B>
inline void eval_logb(B& result, const B& val)
{
   switch(eval_fpclassify(val))
   {
   case FP_NAN:
      result = val;
      errno = EDOM;
      return;
   case FP_ZERO:
      result = std::numeric_limits<number<B> >::infinity().backend();
      result.negate();
      errno = ERANGE;
      return;
   case FP_INFINITE:
      result = val;
      if(eval_signbit(val))
         result.negate();
      return;
   }
   typedef typename boost::mpl::if_c<boost::is_same<boost::intmax_t, long>::value, boost::long_long_type, boost::intmax_t>::type max_t;
   result = static_cast<max_t>(eval_ilogb(val));
}
template <class B, class A>
inline void eval_scalbn(B& result, const B& val, A e)
{
   BOOST_STATIC_ASSERT_MSG(!std::numeric_limits<number<B> >::is_specialized || (std::numeric_limits<number<B> >::radix == 2), "The default implementation of scalbn requires a base 2 number type");
   eval_ldexp(result, val, static_cast<typename B::exponent_type>(e));
}
template <class B, class A>
inline void eval_scalbln(B& result, const B& val, A e)
{
   eval_scalbn(result, val, e);
}

template <class T>
inline bool is_arg_nan(const T& val, mpl::true_ const&, const mpl::false_&)
{
   return eval_fpclassify(val) == FP_NAN;
}
template <class T>
inline bool is_arg_nan(const T& val, mpl::false_ const&, const mpl::true_&)
{
   return (boost::math::isnan)(val);
}
template <class T>
inline bool is_arg_nan(const T&, mpl::false_ const&, const mpl::false_&)
{
   return false;
}

template <class T>
inline bool is_arg_nan(const T& val)
{
   return is_arg_nan(val, mpl::bool_<boost::multiprecision::detail::is_backend<T>::value>(), is_floating_point<T>());
}

template <class T, class U, class V>
inline void eval_fmax(T& result, const U& a, const V& b)
{
   if(is_arg_nan(a))
      result = number<T>::canonical_value(b);
   else if(is_arg_nan(b))
      result = number<T>::canonical_value(a);
   else if(eval_lt(number<T>::canonical_value(a), number<T>::canonical_value(b)))
      result = number<T>::canonical_value(b);
   else
      result = number<T>::canonical_value(a);
}
template <class T, class U, class V>
inline void eval_fmin(T& result, const U& a, const V& b)
{
   if(is_arg_nan(a))
      result = number<T>::canonical_value(b);
   else if(is_arg_nan(b))
      result = number<T>::canonical_value(a);
   else if(eval_lt(number<T>::canonical_value(a), number<T>::canonical_value(b)))
      result = number<T>::canonical_value(a);
   else
      result = number<T>::canonical_value(b);
}

template <class R, class T, class U>
inline void eval_hypot(R& result, const T& a, const U& b)
{
   //
   // Normalize x and y, so that both are positive and x >= y:
   //
   R x, y;
   x = number<R>::canonical_value(a);
   y = number<R>::canonical_value(b);
   if(eval_get_sign(x) < 0)
      x.negate();
   if(eval_get_sign(y) < 0)
      y.negate();

   // Special case, see C99 Annex F.
   // The order of the if's is important: do not change!
   int c1 = eval_fpclassify(x);
   int c2 = eval_fpclassify(y);

   if(c1 == FP_ZERO)
   {
      result = y;
      return;
   }
   if(c2 == FP_ZERO)
   {
      result = x;
      return;
   }
   if(c1 == FP_INFINITE)
   {
      result = x;
      return;
   }
   if((c2 == FP_INFINITE) || (c2 == FP_NAN))
   {
      result = y;
      return;
   }
   if(c1 == FP_NAN)
   {
      result = x;
      return;
   }

   if(eval_gt(y, x))
      x.swap(y);

   eval_multiply(result, x, std::numeric_limits<number<R> >::epsilon().backend());

   if(eval_gt(result, y))
   {
      result = x;
      return;
   }

   R rat;
   eval_divide(rat, y, x);
   eval_multiply(result, rat, rat);
   eval_increment(result);
   eval_sqrt(rat, result);
   eval_multiply(result, rat, x);
}

template <class R, class T>
inline void eval_nearbyint(R& result, const T& a)
{
   eval_round(result, a);
}
template <class R, class T>
inline void eval_rint(R& result, const T& a)
{
   eval_nearbyint(result, a);
}

template <class T>
inline int eval_signbit(const T& val)
{
   return eval_get_sign(val) < 0 ? 1 : 0;
}

//
// Real and imaginary parts:
//
template <class To, class From>
inline void eval_real(To& to, const From& from)
{
   to = from;
}
template <class To, class From>
inline void eval_imag(To& to, const From& )
{
   typedef typename mpl::front<typename To::unsigned_types>::type ui_type;
   to = ui_type(0);
}

} namespace default_ops_adl {

template <class To, class From>
inline void eval_set_real_imp(To& to, const From& from)
{
   typedef typename component_type<number<To> >::type to_component_type;
   typename to_component_type::backend_type to_component;
   to_component = from;
   eval_set_real(to, to_component);
}
template <class To, class From>
inline void eval_set_imag_imp(To& to, const From& from)
{
   typedef typename component_type<number<To> >::type to_component_type;
   typename to_component_type::backend_type to_component;
   to_component = from;
   eval_set_imag(to, to_component);
}

} namespace default_ops{

template <class To, class From>
inline typename enable_if_c<number_category<To>::value == number_kind_complex>::type eval_set_real(To& to, const From& from)
{
   default_ops_adl::eval_set_real_imp(to, from);
}
template <class To, class From>
inline typename disable_if_c<number_category<To>::value == number_kind_complex>::type eval_set_real(To& to, const From& from)
{
   to = from;
}

template <class To, class From>
inline void eval_set_imag(To& to, const From& from)
{
   default_ops_adl::eval_set_imag_imp(to, from);
}

template <class T>
inline void eval_set_real(T& to, const T& from)
{
   to = from;
}
template <class T>
void eval_set_imag(T&, const T&)
{
   BOOST_STATIC_ASSERT_MSG(sizeof(T) == INT_MAX, "eval_set_imag needs to be specialised for each specific backend");
}

//
// These functions are implemented in separate files, but expanded inline here,
// DO NOT CHANGE THE ORDER OF THESE INCLUDES:
//
#include <boost/multiprecision/detail/functions/constants.hpp>
#include <boost/multiprecision/detail/functions/pow.hpp>
#include <boost/multiprecision/detail/functions/trig.hpp>

}

//
// Default versions of floating point classification routines:
//
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
{
   using multiprecision::default_ops::eval_fpclassify;
   return eval_fpclassify(arg.backend());
}
template <class tag, class A1, class A2, class A3, class A4>
inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
   typedef typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type value_type;
   return fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(value_type(arg));
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
{
   int v = fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(arg);
   return (v != (int)FP_INFINITE) && (v != (int)FP_NAN);
}
template <class tag, class A1, class A2, class A3, class A4>
inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
   typedef typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type value_type;
   return isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(value_type(arg));
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
{
   return fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(arg) == (int)FP_NAN;
}
template <class tag, class A1, class A2, class A3, class A4>
inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
   typedef typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type value_type;
   return isnan BOOST_PREVENT_MACRO_SUBSTITUTION(value_type(arg));
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
{
   return fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(arg) == (int)FP_INFINITE;
}
template <class tag, class A1, class A2, class A3, class A4>
inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
   typedef typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type value_type;
   return isinf BOOST_PREVENT_MACRO_SUBSTITUTION(value_type(arg));
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
{
   return fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(arg) == (int)FP_NORMAL;
}
template <class tag, class A1, class A2, class A3, class A4>
inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
   typedef typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type value_type;
   return isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(value_type(arg));
}

// Default versions of sign manipulation functions, if individual backends can do better than this
// (for example with signed zero), then they should overload these functions further:

template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline int sign BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
{
   return arg.sign();
}
template <class tag, class A1, class A2, class A3, class A4>
inline int sign BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
   typedef typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type value_type;
   return sign BOOST_PREVENT_MACRO_SUBSTITUTION(value_type(arg));
}

template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline int signbit BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
{
   using default_ops::eval_signbit;
   return eval_signbit(arg.backend());
}
template <class tag, class A1, class A2, class A3, class A4>
inline int signbit BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
   typedef typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type value_type;
   return signbit BOOST_PREVENT_MACRO_SUBSTITUTION(value_type(arg));
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline multiprecision::number<Backend, ExpressionTemplates> changesign BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
{
   return -arg;
}
template <class tag, class A1, class A2, class A3, class A4>
inline typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type changesign BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
   typedef typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type value_type;
   return changesign BOOST_PREVENT_MACRO_SUBSTITUTION(value_type(arg));
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline multiprecision::number<Backend, ExpressionTemplates> copysign BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& a, const multiprecision::number<Backend, ExpressionTemplates>& b)
{
   return (boost::multiprecision::signbit)(a) != (boost::multiprecision::signbit)(b) ? (boost::multiprecision::changesign)(a) : a;
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates, class tag, class A1, class A2, class A3, class A4>
inline multiprecision::number<Backend, ExpressionTemplates> copysign BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& a, const multiprecision::detail::expression<tag, A1, A2, A3, A4>& b)
{
   return copysign BOOST_PREVENT_MACRO_SUBSTITUTION(a, multiprecision::number<Backend, ExpressionTemplates>(b));
}
template <class tag, class A1, class A2, class A3, class A4, class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline multiprecision::number<Backend, ExpressionTemplates> copysign BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& a, const multiprecision::number<Backend, ExpressionTemplates>& b)
{
   return copysign BOOST_PREVENT_MACRO_SUBSTITUTION(multiprecision::number<Backend, ExpressionTemplates>(a), b);
}
template <class tag, class A1, class A2, class A3, class A4, class tagb, class A1b, class A2b, class A3b, class A4b>
inline typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type copysign BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& a, const multiprecision::detail::expression<tagb, A1b, A2b, A3b, A4b>& b)
{
   typedef typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type value_type;
   return copysign BOOST_PREVENT_MACRO_SUBSTITUTION(value_type(a), value_type(b));
}
//
// real and imag:
//
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline typename scalar_result_from_possible_complex<multiprecision::number<Backend, ExpressionTemplates> >::type
   real(const multiprecision::number<Backend, ExpressionTemplates>& a)
{
   using default_ops::eval_real;
   typedef typename scalar_result_from_possible_complex<multiprecision::number<Backend, ExpressionTemplates> >::type result_type;
   boost::multiprecision::detail::scoped_default_precision<result_type> precision_guard(a);
   result_type result;
   eval_real(result.backend(), a.backend());
   return result;
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline typename scalar_result_from_possible_complex<multiprecision::number<Backend, ExpressionTemplates> >::type
   imag(const multiprecision::number<Backend, ExpressionTemplates>& a)
{
   using default_ops::eval_imag;
   typedef typename scalar_result_from_possible_complex<multiprecision::number<Backend, ExpressionTemplates> >::type result_type;
   boost::multiprecision::detail::scoped_default_precision<result_type> precision_guard(a);
   result_type result;
   eval_imag(result.backend(), a.backend());
   return result;
}

template <class tag, class A1, class A2, class A3, class A4>
inline typename scalar_result_from_possible_complex<typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type>::type
   real(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
   typedef typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type value_type;
   detail::scoped_default_precision<value_type> precision_guard(arg);
   return real(value_type(arg));
}

template <class tag, class A1, class A2, class A3, class A4>
inline typename scalar_result_from_possible_complex<typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type>::type
   imag(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
   typedef typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type value_type;
   detail::scoped_default_precision<value_type> precision_guard(arg);
   return imag(value_type(arg));
}

//
// Complex number functions, these are overloaded at the Backend level, we just provide the
// expression template versions here, plus overloads for non-complex types:
//
template <class T, expression_template_option ExpressionTemplates>
inline typename boost::lazy_enable_if_c<number_category<T>::value == number_kind_complex, component_type<number<T, ExpressionTemplates> > >::type
   abs(const number<T, ExpressionTemplates>& v)
{
   return BOOST_MP_MOVE(boost::math::hypot(real(v), imag(v)));
}
template <class tag, class A1, class A2, class A3, class A4>
inline typename boost::lazy_enable_if_c<number_category<typename detail::expression<tag, A1, A2, A3, A4>::result_type>::value == number_kind_complex, component_type<typename detail::expression<tag, A1, A2, A3, A4>::result_type> >::type
   abs(const detail::expression<tag, A1, A2, A3, A4>& v)
{
   typedef typename detail::expression<tag, A1, A2, A3, A4>::result_type number_type;
   return BOOST_MP_MOVE(abs(static_cast<number_type>(v)));
}

template <class T, expression_template_option ExpressionTemplates>
inline typename enable_if_c<number_category<T>::value == number_kind_complex, typename scalar_result_from_possible_complex<number<T, ExpressionTemplates> >::type>::type
arg(const number<T, ExpressionTemplates>& v)
{
   return BOOST_MP_MOVE(atan2(imag(v), real(v)));
}
template <class T, expression_template_option ExpressionTemplates>
inline typename enable_if_c<number_category<T>::value == number_kind_floating_point, typename scalar_result_from_possible_complex<number<T, ExpressionTemplates> >::type>::type
arg(const number<T, ExpressionTemplates>&)
{
   return 0;
}
template <class tag, class A1, class A2, class A3, class A4>
inline typename enable_if_c<number_category<typename detail::expression<tag, A1, A2, A3, A4>::result_type>::value == number_kind_complex || number_category<typename detail::expression<tag, A1, A2, A3, A4>::result_type>::value == number_kind_floating_point, typename scalar_result_from_possible_complex<typename detail::expression<tag, A1, A2, A3, A4>::result_type>::type>::type
arg(const detail::expression<tag, A1, A2, A3, A4>& v)
{
   typedef typename detail::expression<tag, A1, A2, A3, A4>::result_type number_type;
   return BOOST_MP_MOVE(arg(static_cast<number_type>(v)));
}

template <class T, expression_template_option ExpressionTemplates>
inline typename boost::lazy_enable_if_c<number_category<T>::value == number_kind_complex, component_type<number<T, ExpressionTemplates> > >::type
norm(const number<T, ExpressionTemplates>& v)
{
   typename component_type<number<T, ExpressionTemplates> >::type a(real(v)), b(imag(v));
   return BOOST_MP_MOVE(a * a + b * b);
}
template <class T, expression_template_option ExpressionTemplates>
inline typename boost::enable_if_c<number_category<T>::value != number_kind_complex, typename scalar_result_from_possible_complex<number<T, ExpressionTemplates> >::type >::type
norm(const number<T, ExpressionTemplates>& v)
{
   return v * v;
}
template <class tag, class A1, class A2, class A3, class A4>
inline typename scalar_result_from_possible_complex<typename detail::expression<tag, A1, A2, A3, A4>::result_type>::type
norm(const detail::expression<tag, A1, A2, A3, A4>& v)
{
   typedef typename detail::expression<tag, A1, A2, A3, A4>::result_type number_type;
   return BOOST_MP_MOVE(norm(static_cast<number_type>(v)));
}

template <class Backend, expression_template_option ExpressionTemplates>
typename complex_result_from_scalar<number<Backend, ExpressionTemplates> >::type polar(number<Backend, ExpressionTemplates> const& r, number<Backend, ExpressionTemplates> const& theta)
{
   return typename complex_result_from_scalar<number<Backend, ExpressionTemplates> >::type(number<Backend, ExpressionTemplates>(r * cos(theta)), number<Backend, ExpressionTemplates>(r * sin(theta)));
}

template <class tag, class A1, class A2, class A3, class A4, class Backend, expression_template_option ExpressionTemplates>
typename enable_if_c<boost::is_same<typename detail::expression<tag, A1, A2, A3, A4>::result_type, number<Backend, ExpressionTemplates> >::value,
   typename complex_result_from_scalar<number<Backend, ExpressionTemplates> >::type>::type
      polar(detail::expression<tag, A1, A2, A3, A4> const& r, number<Backend, ExpressionTemplates> const& theta)
{
   return typename complex_result_from_scalar<number<Backend, ExpressionTemplates> >::type(number<Backend, ExpressionTemplates>(r * cos(theta)), number<Backend, ExpressionTemplates>(r * sin(theta)));
}

template <class Backend, expression_template_option ExpressionTemplates, class tag, class A1, class A2, class A3, class A4>
typename enable_if_c<boost::is_same<typename detail::expression<tag, A1, A2, A3, A4>::result_type, number<Backend, ExpressionTemplates> >::value,
   typename complex_result_from_scalar<number<Backend, ExpressionTemplates> >::type>::type
      polar(number<Backend, ExpressionTemplates> const& r, detail::expression<tag, A1, A2, A3, A4> const& theta)
{
   return typename complex_result_from_scalar<number<Backend, ExpressionTemplates> >::type(number<Backend, ExpressionTemplates>(r * cos(theta)), number<Backend, ExpressionTemplates>(r * sin(theta)));
}

template <class tag, class A1, class A2, class A3, class A4, class tagb, class A1b, class A2b, class A3b, class A4b>
typename enable_if_c<boost::is_same<typename detail::expression<tag, A1, A2, A3, A4>::result_type, typename detail::expression<tagb, A1b, A2b, A3b, A4b>::result_type >::value,
   typename complex_result_from_scalar<typename detail::expression<tag, A1, A2, A3, A4>::result_type >::type>::type
      polar(detail::expression<tag, A1, A2, A3, A4> const& r, detail::expression<tagb, A1b, A2b, A3b, A4b> const& theta)
{
   typedef typename detail::expression<tag, A1, A2, A3, A4>::result_type scalar_type;
   return typename complex_result_from_scalar<scalar_type>::type(scalar_type(r * cos(theta)), scalar_type(r * sin(theta)));
}
//
// We also allow the first argument to polar to be an arithmetic type (probably a literal):
//
template <class Scalar, class Backend, expression_template_option ExpressionTemplates>
typename boost::enable_if_c<boost::is_arithmetic<Scalar>::value, typename complex_result_from_scalar<number<Backend, ExpressionTemplates> >::type>::type
   polar(Scalar const& r, number<Backend, ExpressionTemplates> const& theta)
{
   return typename complex_result_from_scalar<number<Backend, ExpressionTemplates> >::type(number<Backend, ExpressionTemplates>(r * cos(theta)), number<Backend, ExpressionTemplates>(r * sin(theta)));
}

template <class tag, class A1, class A2, class A3, class A4, class Scalar>
typename enable_if_c<boost::is_arithmetic<Scalar>::value,
   typename complex_result_from_scalar<typename detail::expression<tag, A1, A2, A3, A4>::result_type>::type>::type
   polar(Scalar const& r, detail::expression<tag, A1, A2, A3, A4> const& theta)
{
   typedef typename detail::expression<tag, A1, A2, A3, A4>::result_type scalar_type;
   return typename complex_result_from_scalar<scalar_type>::type(scalar_type(r * cos(theta)), scalar_type(r * sin(theta)));
}
//
// Single argument overloads:
//
template <class Backend, expression_template_option ExpressionTemplates>
typename complex_result_from_scalar<number<Backend, ExpressionTemplates> >::type polar(number<Backend, ExpressionTemplates> const& r)
{
   return typename complex_result_from_scalar<number<Backend, ExpressionTemplates> >::type(r);
}

template <class tag, class A1, class A2, class A3, class A4>
typename complex_result_from_scalar<typename detail::expression<tag, A1, A2, A3, A4>::result_type>::type
   polar(detail::expression<tag, A1, A2, A3, A4> const& r)
{
   return typename complex_result_from_scalar<typename detail::expression<tag, A1, A2, A3, A4>::result_type>::type(r);
}


} // namespace multiprecision

namespace math {

   //
   // Import Math functions here, so they can be found by Boost.Math:
   //
   using boost::multiprecision::signbit;
   using boost::multiprecision::sign;
   using boost::multiprecision::copysign;
   using boost::multiprecision::changesign;
   using boost::multiprecision::fpclassify;
   using boost::multiprecision::isinf;
   using boost::multiprecision::isnan;
   using boost::multiprecision::isnormal;
   using boost::multiprecision::isfinite;

}

namespace multiprecision{

   typedef ::boost::math::policies::policy<
      ::boost::math::policies::domain_error< ::boost::math::policies::errno_on_error>,
      ::boost::math::policies::pole_error< ::boost::math::policies::errno_on_error>,
      ::boost::math::policies::overflow_error< ::boost::math::policies::errno_on_error>,
      ::boost::math::policies::evaluation_error< ::boost::math::policies::errno_on_error>,
      ::boost::math::policies::rounding_error< ::boost::math::policies::errno_on_error>
   > c99_error_policy;

   template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
   inline typename boost::enable_if_c<number_category<Backend>::value != number_kind_complex, multiprecision::number<Backend, ExpressionTemplates> >::type
      asinh BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
   {
      detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(arg);
      return boost::math::asinh(arg, c99_error_policy());
   }
   template <class tag, class A1, class A2, class A3, class A4>
   inline typename boost::enable_if_c<number_category<typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type>::value != number_kind_complex, typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type>::type
         asinh BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
   {
      typedef typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type value_type;
      detail::scoped_default_precision<value_type > precision_guard(arg);
      return asinh(value_type(arg));
   }
   template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
   inline typename boost::enable_if_c<number_category<Backend>::value != number_kind_complex, multiprecision::number<Backend, ExpressionTemplates> >::type
      acosh BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
   {
      detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(arg);
      return boost::math::acosh(arg, c99_error_policy());
   }
   template <class tag, class A1, class A2, class A3, class A4>
   inline typename boost::enable_if_c<number_category<typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type>::value != number_kind_complex, typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type>::type
      acosh BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
   {
      typedef typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type value_type;
      detail::scoped_default_precision<value_type > precision_guard(arg);
      return acosh(value_type(arg));
   }
   template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
   inline typename boost::enable_if_c<number_category<Backend>::value != number_kind_complex, multiprecision::number<Backend, ExpressionTemplates> >::type
      atanh BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
   {
      detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(arg);
      return boost::math::atanh(arg, c99_error_policy());
   }
   template <class tag, class A1, class A2, class A3, class A4>
   inline typename boost::enable_if_c<number_category<typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type>::value != number_kind_complex, typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type>::type
      atanh BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
   {
      typedef typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type value_type;
      detail::scoped_default_precision<value_type > precision_guard(arg);
      return atanh(value_type(arg));
   }
   template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
   inline multiprecision::number<Backend, ExpressionTemplates> cbrt BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
   {
      detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(arg);
      return boost::math::cbrt(arg, c99_error_policy());
   }
   template <class tag, class A1, class A2, class A3, class A4>
   inline typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type cbrt BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
   {
      typedef typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type value_type;
      detail::scoped_default_precision<value_type> precision_guard(arg);
      return cbrt(value_type(arg));
   }
   template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
   inline multiprecision::number<Backend, ExpressionTemplates> erf BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
   {
      detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(arg);
      return boost::math::erf(arg, c99_error_policy());
   }
   template <class tag, class A1, class A2, class A3, class A4>
   inline typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type erf BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
   {
      typedef typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type value_type;
      detail::scoped_default_precision<value_type> precision_guard(arg);
      return erf(value_type(arg));
   }
   template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
   inline multiprecision::number<Backend, ExpressionTemplates> erfc BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
   {
      detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(arg);
      return boost::math::erfc(arg, c99_error_policy());
   }
   template <class tag, class A1, class A2, class A3, class A4>
   inline typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type erfc BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
   {
      typedef typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type value_type;
      detail::scoped_default_precision<value_type> precision_guard(arg);
      return erfc(value_type(arg));
   }
   template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
   inline multiprecision::number<Backend, ExpressionTemplates> expm1 BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
   {
      detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(arg);
      return boost::math::expm1(arg, c99_error_policy());
   }
   template <class tag, class A1, class A2, class A3, class A4>
   inline typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type expm1 BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
   {
      typedef typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type value_type;
      detail::scoped_default_precision<value_type> precision_guard(arg);
      return expm1(value_type(arg));
   }
   template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
   inline multiprecision::number<Backend, ExpressionTemplates> lgamma BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
   {
      detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(arg);
      multiprecision::number<Backend, ExpressionTemplates> result;
      result = boost::math::lgamma(arg, c99_error_policy());
      if((boost::multiprecision::isnan)(result) && !(boost::multiprecision::isnan)(arg))
      {
         result = std::numeric_limits<multiprecision::number<Backend, ExpressionTemplates> >::infinity();
         errno = ERANGE;
      }
      return result;
   }
   template <class tag, class A1, class A2, class A3, class A4>
   inline typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type lgamma BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
   {
      typedef typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type value_type;
      detail::scoped_default_precision<value_type> precision_guard(arg);
      return lgamma(value_type(arg));
   }
   template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
   inline multiprecision::number<Backend, ExpressionTemplates> tgamma BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
   {
      detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(arg);
      if((arg == 0) && std::numeric_limits<multiprecision::number<Backend, ExpressionTemplates> >::has_infinity)
      {
         errno = ERANGE;
         return 1 / arg;
      }
      return boost::math::tgamma(arg, c99_error_policy());
   }
   template <class tag, class A1, class A2, class A3, class A4>
   inline typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type tgamma BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
   {
      typedef typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type value_type;
      detail::scoped_default_precision<value_type> precision_guard(arg);
      return tgamma(value_type(arg));
   }

   template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
   inline long lrint BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
   {
      return lround(arg);
   }
   template <class tag, class A1, class A2, class A3, class A4>
   inline long lrint BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
   {
      return lround(arg);
   }
#ifndef BOOST_NO_LONG_LONG
   template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
   inline boost::long_long_type llrint BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
   {
      return llround(arg);
   }
   template <class tag, class A1, class A2, class A3, class A4>
   inline boost::long_long_type llrint BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
   {
      return llround(arg);
   }
#endif
   template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
   inline multiprecision::number<Backend, ExpressionTemplates> log1p BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
   {
      detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(arg);
      return boost::math::log1p(arg, c99_error_policy());
   }
   template <class tag, class A1, class A2, class A3, class A4>
   inline typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type log1p BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
   {
      typedef typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type value_type;
      detail::scoped_default_precision<value_type> precision_guard(arg);
      return log1p(value_type(arg));
   }

   template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
   inline multiprecision::number<Backend, ExpressionTemplates> nextafter BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& a, const multiprecision::number<Backend, ExpressionTemplates>& b)
   {
      detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(a, b);
      return boost::math::nextafter(a, b, c99_error_policy());
   }
   template <class Backend, multiprecision::expression_template_option ExpressionTemplates, class tag, class A1, class A2, class A3, class A4>
   inline multiprecision::number<Backend, ExpressionTemplates> nextafter BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& a, const multiprecision::detail::expression<tag, A1, A2, A3, A4>& b)
   {
      detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(a, b);
      return nextafter BOOST_PREVENT_MACRO_SUBSTITUTION(a, multiprecision::number<Backend, ExpressionTemplates>(b));
   }
   template <class tag, class A1, class A2, class A3, class A4, class Backend, multiprecision::expression_template_option ExpressionTemplates>
   inline multiprecision::number<Backend, ExpressionTemplates> nextafter BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& a, const multiprecision::number<Backend, ExpressionTemplates>& b)
   {
      detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(a, b);
      return nextafter BOOST_PREVENT_MACRO_SUBSTITUTION(multiprecision::number<Backend, ExpressionTemplates>(a), b);
   }
   template <class tag, class A1, class A2, class A3, class A4, class tagb, class A1b, class A2b, class A3b, class A4b>
   inline typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type nextafter BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& a, const multiprecision::detail::expression<tagb, A1b, A2b, A3b, A4b>& b)
   {
      typedef typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type value_type;
      detail::scoped_default_precision<value_type> precision_guard(a, b);
      return nextafter BOOST_PREVENT_MACRO_SUBSTITUTION(value_type(a), value_type(b));
   }
   template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
   inline multiprecision::number<Backend, ExpressionTemplates> nexttoward BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& a, const multiprecision::number<Backend, ExpressionTemplates>& b)
   {
      detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(a, b);
      return boost::math::nextafter(a, b, c99_error_policy());
   }
   template <class Backend, multiprecision::expression_template_option ExpressionTemplates, class tag, class A1, class A2, class A3, class A4>
   inline multiprecision::number<Backend, ExpressionTemplates> nexttoward BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& a, const multiprecision::detail::expression<tag, A1, A2, A3, A4>& b)
   {
      detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(a, b);
      return nexttoward BOOST_PREVENT_MACRO_SUBSTITUTION(a, multiprecision::number<Backend, ExpressionTemplates>(b));
   }
   template <class tag, class A1, class A2, class A3, class A4, class Backend, multiprecision::expression_template_option ExpressionTemplates>
   inline multiprecision::number<Backend, ExpressionTemplates> nexttoward BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& a, const multiprecision::number<Backend, ExpressionTemplates>& b)
   {
      detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(a, b);
      return nexttoward BOOST_PREVENT_MACRO_SUBSTITUTION(multiprecision::number<Backend, ExpressionTemplates>(a), b);
   }
   template <class tag, class A1, class A2, class A3, class A4, class tagb, class A1b, class A2b, class A3b, class A4b>
   inline typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type nexttoward BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& a, const multiprecision::detail::expression<tagb, A1b, A2b, A3b, A4b>& b)
   {
      typedef typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type value_type;
      detail::scoped_default_precision<value_type> precision_guard(a, b);
      return nexttoward BOOST_PREVENT_MACRO_SUBSTITUTION(value_type(a), value_type(b));
   }

template <class B1, class B2, class B3, expression_template_option ET1, expression_template_option ET2, expression_template_option ET3>
inline number<B1, ET1>& add(number<B1, ET1>& result, const number<B2, ET2>& a, const number<B3, ET3>& b)
{
   BOOST_STATIC_ASSERT_MSG((is_convertible<B2, B1>::value), "No conversion to the target of a mixed precision addition exists");
   BOOST_STATIC_ASSERT_MSG((is_convertible<B3, B1>::value), "No conversion to the target of a mixed precision addition exists");
   using default_ops::eval_add;
   eval_add(result.backend(), a.backend(), b.backend());
   return result;
}

template <class B1, class B2, class B3, expression_template_option ET1, expression_template_option ET2, expression_template_option ET3>
inline number<B1, ET1>& subtract(number<B1, ET1>& result, const number<B2, ET2>& a, const number<B3, ET3>& b)
{
   BOOST_STATIC_ASSERT_MSG((is_convertible<B2, B1>::value), "No conversion to the target of a mixed precision addition exists");
   BOOST_STATIC_ASSERT_MSG((is_convertible<B3, B1>::value), "No conversion to the target of a mixed precision addition exists");
   using default_ops::eval_subtract;
   eval_subtract(result.backend(), a.backend(), b.backend());
   return result;
}

template <class B1, class B2, class B3, expression_template_option ET1, expression_template_option ET2, expression_template_option ET3>
inline number<B1, ET1>& multiply(number<B1, ET1>& result, const number<B2, ET2>& a, const number<B3, ET3>& b)
{
   BOOST_STATIC_ASSERT_MSG((is_convertible<B2, B1>::value), "No conversion to the target of a mixed precision addition exists");
   BOOST_STATIC_ASSERT_MSG((is_convertible<B3, B1>::value), "No conversion to the target of a mixed precision addition exists");
   using default_ops::eval_multiply;
   eval_multiply(result.backend(), a.backend(), b.backend());
   return result;
}

template <class B, expression_template_option ET, class I>
inline typename enable_if_c<is_integral<I>::value, number<B, ET>&>::type
   add(number<B, ET>& result, const I& a, const I& b)
{
   using default_ops::eval_add;
   typedef typename detail::canonical<I, B>::type canonical_type;
   eval_add(result.backend(), static_cast<canonical_type>(a), static_cast<canonical_type>(b));
   return result;
}

template <class B, expression_template_option ET, class I>
inline typename enable_if_c<is_integral<I>::value, number<B, ET>&>::type
   subtract(number<B, ET>& result, const I& a, const I& b)
{
   using default_ops::eval_subtract;
   typedef typename detail::canonical<I, B>::type canonical_type;
   eval_subtract(result.backend(), static_cast<canonical_type>(a), static_cast<canonical_type>(b));
   return result;
}

template <class B, expression_template_option ET, class I>
inline typename enable_if_c<is_integral<I>::value, number<B, ET>&>::type
   multiply(number<B, ET>& result, const I& a, const I& b)
{
   using default_ops::eval_multiply;
   typedef typename detail::canonical<I, B>::type canonical_type;
   eval_multiply(result.backend(), static_cast<canonical_type>(a), static_cast<canonical_type>(b));
   return result;
}

template <class tag, class A1, class A2, class A3, class A4, class Policy>
inline typename detail::expression<tag, A1, A2, A3, A4>::result_type trunc(const detail::expression<tag, A1, A2, A3, A4>& v, const Policy& pol)
{
   typedef typename detail::expression<tag, A1, A2, A3, A4>::result_type number_type;
   return BOOST_MP_MOVE(trunc(number_type(v), pol));
}

template <class Backend, expression_template_option ExpressionTemplates, class Policy>
inline number<Backend, ExpressionTemplates> trunc(const number<Backend, ExpressionTemplates>& v, const Policy&)
{
   using default_ops::eval_trunc;
   detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(v);
   number<Backend, ExpressionTemplates> result;
   eval_trunc(result.backend(), v.backend());
   return BOOST_MP_MOVE(result);
}

template <class tag, class A1, class A2, class A3, class A4, class Policy>
inline int itrunc(const detail::expression<tag, A1, A2, A3, A4>& v, const Policy& pol)
{
   typedef typename detail::expression<tag, A1, A2, A3, A4>::result_type number_type;
   number_type r(trunc(v, pol));
   if((r > (std::numeric_limits<int>::max)()) || r < (std::numeric_limits<int>::min)() || !(boost::math::isfinite)(v))
      return boost::math::policies::raise_rounding_error("boost::multiprecision::itrunc<%1%>(%1%)", 0, number_type(v), 0, pol);
   return r.template convert_to<int>();
}
template <class tag, class A1, class A2, class A3, class A4>
inline int itrunc(const detail::expression<tag, A1, A2, A3, A4>& v)
{
   return itrunc(v, boost::math::policies::policy<>());
}
template <class Backend, expression_template_option ExpressionTemplates, class Policy>
inline int itrunc(const number<Backend, ExpressionTemplates>& v, const Policy& pol)
{
   number<Backend, ExpressionTemplates> r(trunc(v, pol));
   if((r > (std::numeric_limits<int>::max)()) || r < (std::numeric_limits<int>::min)() || !(boost::math::isfinite)(v))
      return boost::math::policies::raise_rounding_error("boost::multiprecision::itrunc<%1%>(%1%)", 0, v, 0, pol);
   return r.template convert_to<int>();
}
template <class Backend, expression_template_option ExpressionTemplates>
inline int itrunc(const number<Backend, ExpressionTemplates>& v)
{
   return itrunc(v, boost::math::policies::policy<>());
}
template <class tag, class A1, class A2, class A3, class A4, class Policy>
inline long ltrunc(const detail::expression<tag, A1, A2, A3, A4>& v, const Policy& pol)
{
   typedef typename detail::expression<tag, A1, A2, A3, A4>::result_type number_type;
   number_type r(trunc(v, pol));
   if((r > (std::numeric_limits<long>::max)()) || r < (std::numeric_limits<long>::min)() || !(boost::math::isfinite)(v))
      return boost::math::policies::raise_rounding_error("boost::multiprecision::ltrunc<%1%>(%1%)", 0, number_type(v), 0L, pol);
   return r.template convert_to<long>();
}
template <class tag, class A1, class A2, class A3, class A4>
inline long ltrunc(const detail::expression<tag, A1, A2, A3, A4>& v)
{
   return ltrunc(v, boost::math::policies::policy<>());
}
template <class T, expression_template_option ExpressionTemplates, class Policy>
inline long ltrunc(const number<T, ExpressionTemplates>& v, const Policy& pol)
{
   number<T, ExpressionTemplates> r(trunc(v, pol));
   if((r > (std::numeric_limits<long>::max)()) || r < (std::numeric_limits<long>::min)() || !(boost::math::isfinite)(v))
      return boost::math::policies::raise_rounding_error("boost::multiprecision::ltrunc<%1%>(%1%)", 0, v, 0L, pol);
   return r.template convert_to<long>();
}
template <class T, expression_template_option ExpressionTemplates>
inline long ltrunc(const number<T, ExpressionTemplates>& v)
{
   return ltrunc(v, boost::math::policies::policy<>());
}
#ifndef BOOST_NO_LONG_LONG
template <class tag, class A1, class A2, class A3, class A4, class Policy>
inline boost::long_long_type lltrunc(const detail::expression<tag, A1, A2, A3, A4>& v, const Policy& pol)
{
   typedef typename detail::expression<tag, A1, A2, A3, A4>::result_type number_type;
   number_type r(trunc(v, pol));
   if((r > (std::numeric_limits<boost::long_long_type>::max)()) || r < (std::numeric_limits<boost::long_long_type>::min)() || !(boost::math::isfinite)(v))
      return boost::math::policies::raise_rounding_error("boost::multiprecision::lltrunc<%1%>(%1%)", 0, number_type(v), 0LL, pol);
   return r.template convert_to<boost::long_long_type>();
}
template <class tag, class A1, class A2, class A3, class A4>
inline boost::long_long_type lltrunc(const detail::expression<tag, A1, A2, A3, A4>& v)
{
   return lltrunc(v, boost::math::policies::policy<>());
}
template <class T, expression_template_option ExpressionTemplates, class Policy>
inline boost::long_long_type lltrunc(const number<T, ExpressionTemplates>& v, const Policy& pol)
{
   number<T, ExpressionTemplates> r(trunc(v, pol));
   if((r > (std::numeric_limits<boost::long_long_type>::max)()) || r < (std::numeric_limits<boost::long_long_type>::min)() || !(boost::math::isfinite)(v))
      return boost::math::policies::raise_rounding_error("boost::multiprecision::lltrunc<%1%>(%1%)", 0, v, 0LL, pol);
   return r.template convert_to<boost::long_long_type>();
}
template <class T, expression_template_option ExpressionTemplates>
inline boost::long_long_type lltrunc(const number<T, ExpressionTemplates>& v)
{
   return lltrunc(v, boost::math::policies::policy<>());
}
#endif
template <class tag, class A1, class A2, class A3, class A4, class Policy>
inline typename detail::expression<tag, A1, A2, A3, A4>::result_type round(const detail::expression<tag, A1, A2, A3, A4>& v, const Policy& pol)
{
   typedef typename detail::expression<tag, A1, A2, A3, A4>::result_type number_type;
   return BOOST_MP_MOVE(round(static_cast<number_type>(v), pol));
}
template <class T, expression_template_option ExpressionTemplates, class Policy>
inline number<T, ExpressionTemplates> round(const number<T, ExpressionTemplates>& v, const Policy&)
{
   using default_ops::eval_round;
   detail::scoped_default_precision<multiprecision::number<T, ExpressionTemplates> > precision_guard(v);
   number<T, ExpressionTemplates> result;
   eval_round(result.backend(), v.backend());
   return BOOST_MP_MOVE(result);
}

template <class tag, class A1, class A2, class A3, class A4, class Policy>
inline int iround(const detail::expression<tag, A1, A2, A3, A4>& v, const Policy& pol)
{
   typedef typename detail::expression<tag, A1, A2, A3, A4>::result_type number_type;
   number_type r(round(v, pol));
   if((r > (std::numeric_limits<int>::max)()) || r < (std::numeric_limits<int>::min)() || !(boost::math::isfinite)(v))
      return boost::math::policies::raise_rounding_error("boost::multiprecision::iround<%1%>(%1%)", 0, number_type(v), 0, pol);
   return r.template convert_to<int>();
}
template <class tag, class A1, class A2, class A3, class A4>
inline int iround(const detail::expression<tag, A1, A2, A3, A4>& v)
{
   return iround(v, boost::math::policies::policy<>());
}
template <class T, expression_template_option ExpressionTemplates, class Policy>
inline int iround(const number<T, ExpressionTemplates>& v, const Policy& pol)
{
   number<T, ExpressionTemplates> r(round(v, pol));
   if((r > (std::numeric_limits<int>::max)()) || r < (std::numeric_limits<int>::min)() || !(boost::math::isfinite)(v))
      return boost::math::policies::raise_rounding_error("boost::multiprecision::iround<%1%>(%1%)", 0, v, 0, pol);
   return r.template convert_to<int>();
}
template <class T, expression_template_option ExpressionTemplates>
inline int iround(const number<T, ExpressionTemplates>& v)
{
   return iround(v, boost::math::policies::policy<>());
}
template <class tag, class A1, class A2, class A3, class A4, class Policy>
inline long lround(const detail::expression<tag, A1, A2, A3, A4>& v, const Policy& pol)
{
   typedef typename detail::expression<tag, A1, A2, A3, A4>::result_type number_type;
   number_type r(round(v, pol));
   if((r > (std::numeric_limits<long>::max)()) || r < (std::numeric_limits<long>::min)() || !(boost::math::isfinite)(v))
      return boost::math::policies::raise_rounding_error("boost::multiprecision::lround<%1%>(%1%)", 0, number_type(v), 0L, pol);
   return r.template convert_to<long>();
}
template <class tag, class A1, class A2, class A3, class A4>
inline long lround(const detail::expression<tag, A1, A2, A3, A4>& v)
{
   return lround(v, boost::math::policies::policy<>());
}
template <class T, expression_template_option ExpressionTemplates, class Policy>
inline long lround(const number<T, ExpressionTemplates>& v, const Policy& pol)
{
   number<T, ExpressionTemplates> r(round(v, pol));
   if((r > (std::numeric_limits<long>::max)()) || r < (std::numeric_limits<long>::min)() || !(boost::math::isfinite)(v))
      return boost::math::policies::raise_rounding_error("boost::multiprecision::lround<%1%>(%1%)", 0, v, 0L, pol);
   return r.template convert_to<long>();
}
template <class T, expression_template_option ExpressionTemplates>
inline long lround(const number<T, ExpressionTemplates>& v)
{
   return lround(v, boost::math::policies::policy<>());
}
#ifndef BOOST_NO_LONG_LONG
template <class tag, class A1, class A2, class A3, class A4, class Policy>
inline boost::long_long_type llround(const detail::expression<tag, A1, A2, A3, A4>& v, const Policy& pol)
{
   typedef typename detail::expression<tag, A1, A2, A3, A4>::result_type number_type;
   number_type r(round(v, pol));
   if((r > (std::numeric_limits<boost::long_long_type>::max)()) || r < (std::numeric_limits<boost::long_long_type>::min)() || !(boost::math::isfinite)(v))
      return boost::math::policies::raise_rounding_error("boost::multiprecision::iround<%1%>(%1%)", 0, number_type(v), 0LL, pol);
   return r.template convert_to<boost::long_long_type>();
}
template <class tag, class A1, class A2, class A3, class A4>
inline boost::long_long_type llround(const detail::expression<tag, A1, A2, A3, A4>& v)
{
   return llround(v, boost::math::policies::policy<>());
}
template <class T, expression_template_option ExpressionTemplates, class Policy>
inline boost::long_long_type llround(const number<T, ExpressionTemplates>& v, const Policy& pol)
{
   number<T, ExpressionTemplates> r(round(v, pol));
   if((r > (std::numeric_limits<boost::long_long_type>::max)()) || r < (std::numeric_limits<boost::long_long_type>::min)() || !(boost::math::isfinite)(v))
      return boost::math::policies::raise_rounding_error("boost::multiprecision::iround<%1%>(%1%)", 0, v, 0LL, pol);
   return r.template convert_to<boost::long_long_type>();
}
template <class T, expression_template_option ExpressionTemplates>
inline boost::long_long_type llround(const number<T, ExpressionTemplates>& v)
{
   return llround(v, boost::math::policies::policy<>());
}
#endif
//
// frexp does not return an expression template since we require the
// integer argument to be evaluated even if the returned value is
// not assigned to anything...
//
template <class T, expression_template_option ExpressionTemplates>
inline typename enable_if_c<number_category<T>::value == number_kind_floating_point, number<T, ExpressionTemplates> >::type frexp(const number<T, ExpressionTemplates>& v, short* pint)
{
   using default_ops::eval_frexp;
   detail::scoped_default_precision<multiprecision::number<T, ExpressionTemplates> > precision_guard(v);
   number<T, ExpressionTemplates> result;
   eval_frexp(result.backend(), v.backend(), pint);
   return BOOST_MP_MOVE(result);
}
template <class tag, class A1, class A2, class A3, class A4>
inline typename enable_if_c<number_category<typename detail::expression<tag, A1, A2, A3, A4>::result_type>::value == number_kind_floating_point, typename detail::expression<tag, A1, A2, A3, A4>::result_type>::type
   frexp(const detail::expression<tag, A1, A2, A3, A4>& v, short* pint)
{
   typedef typename detail::expression<tag, A1, A2, A3, A4>::result_type number_type;
   return BOOST_MP_MOVE(frexp(static_cast<number_type>(v), pint));
}
template <class T, expression_template_option ExpressionTemplates>
inline typename enable_if_c<number_category<T>::value == number_kind_floating_point, number<T, ExpressionTemplates> >::type frexp(const number<T, ExpressionTemplates>& v, int* pint)
{
   using default_ops::eval_frexp;
   detail::scoped_default_precision<multiprecision::number<T, ExpressionTemplates> > precision_guard(v);
   number<T, ExpressionTemplates> result;
   eval_frexp(result.backend(), v.backend(), pint);
   return BOOST_MP_MOVE(result);
}
template <class tag, class A1, class A2, class A3, class A4>
inline typename enable_if_c<number_category<typename detail::expression<tag, A1, A2, A3, A4>::result_type>::value == number_kind_floating_point, typename detail::expression<tag, A1, A2, A3, A4>::result_type>::type
frexp(const detail::expression<tag, A1, A2, A3, A4>& v, int* pint)
{
   typedef typename detail::expression<tag, A1, A2, A3, A4>::result_type number_type;
   return BOOST_MP_MOVE(frexp(static_cast<number_type>(v), pint));
}
template <class T, expression_template_option ExpressionTemplates>
inline typename enable_if_c<number_category<T>::value == number_kind_floating_point, number<T, ExpressionTemplates> >::type frexp(const number<T, ExpressionTemplates>& v, long* pint)
{
   using default_ops::eval_frexp;
   detail::scoped_default_precision<multiprecision::number<T, ExpressionTemplates> > precision_guard(v);
   number<T, ExpressionTemplates> result;
   eval_frexp(result.backend(), v.backend(), pint);
   return BOOST_MP_MOVE(result);
}
template <class tag, class A1, class A2, class A3, class A4>
inline typename enable_if_c<number_category<typename detail::expression<tag, A1, A2, A3, A4>::result_type>::value == number_kind_floating_point, typename detail::expression<tag, A1, A2, A3, A4>::result_type>::type
frexp(const detail::expression<tag, A1, A2, A3, A4>& v, long* pint)
{
   typedef typename detail::expression<tag, A1, A2, A3, A4>::result_type number_type;
   return BOOST_MP_MOVE(frexp(static_cast<number_type>(v), pint));
}
template <class T, expression_template_option ExpressionTemplates>
inline typename enable_if_c<number_category<T>::value == number_kind_floating_point, number<T, ExpressionTemplates> >::type frexp(const number<T, ExpressionTemplates>& v, boost::long_long_type* pint)
{
   using default_ops::eval_frexp;
   detail::scoped_default_precision<multiprecision::number<T, ExpressionTemplates> > precision_guard(v);
   number<T, ExpressionTemplates> result;
   eval_frexp(result.backend(), v.backend(), pint);
   return BOOST_MP_MOVE(result);
}
template <class tag, class A1, class A2, class A3, class A4>
inline typename enable_if_c<number_category<typename detail::expression<tag, A1, A2, A3, A4>::result_type>::value == number_kind_floating_point, typename detail::expression<tag, A1, A2, A3, A4>::result_type>::type
frexp(const detail::expression<tag, A1, A2, A3, A4>& v, boost::long_long_type* pint)
{
   typedef typename detail::expression<tag, A1, A2, A3, A4>::result_type number_type;
   return BOOST_MP_MOVE(frexp(static_cast<number_type>(v), pint));
}
//
// modf does not return an expression template since we require the
// second argument to be evaluated even if the returned value is
// not assigned to anything...
//
template <class T, expression_template_option ExpressionTemplates>
inline typename enable_if_c<number_category<T>::value == number_kind_floating_point, number<T, ExpressionTemplates> >::type modf(const number<T, ExpressionTemplates>& v, number<T, ExpressionTemplates>* pipart)
{
   using default_ops::eval_modf;
   detail::scoped_default_precision<multiprecision::number<T, ExpressionTemplates> > precision_guard(v);
   number<T, ExpressionTemplates> result;
   eval_modf(result.backend(), v.backend(), pipart ? &pipart->backend() : 0);
   return BOOST_MP_MOVE(result);
}
template <class T, expression_template_option ExpressionTemplates, class tag, class A1, class A2, class A3, class A4>
inline typename enable_if_c<number_category<T>::value == number_kind_floating_point, number<T, ExpressionTemplates> >::type modf(const detail::expression<tag, A1, A2, A3, A4>& v, number<T, ExpressionTemplates>* pipart)
{
   using default_ops::eval_modf;
   detail::scoped_default_precision<multiprecision::number<T, ExpressionTemplates> > precision_guard(v);
   number<T, ExpressionTemplates> result, arg(v);
   eval_modf(result.backend(), arg.backend(), pipart ? &pipart->backend() : 0);
   return BOOST_MP_MOVE(result);
}

//
// Integer square root:
//
template <class B, expression_template_option ExpressionTemplates>
inline typename enable_if_c<number_category<B>::value == number_kind_integer, number<B, ExpressionTemplates> >::type
   sqrt(const number<B, ExpressionTemplates>& x)
{
   using default_ops::eval_integer_sqrt;
   number<B, ExpressionTemplates> s, r;
   eval_integer_sqrt(s.backend(), r.backend(), x.backend());
   return s;
}
//
// fma:
//

namespace default_ops {

   struct fma_func
   {
      template <class B, class T, class U, class V>
      void operator()(B& result, const T& a, const U& b, const V& c)const
      {
         eval_multiply_add(result, a, b, c);
      }
   };


}

template <class Backend, class U, class V>
inline typename enable_if<
   mpl::and_<
      mpl::bool_<number_category<number<Backend, et_on> >::value == number_kind_floating_point>,
      mpl::or_<
         is_number<U>,
         is_number_expression<U>,
         is_arithmetic<U>
      >,
      mpl::or_<
         is_number<V>,
         is_number_expression<V>,
         is_arithmetic<V>
      >
   >,
   detail::expression<detail::function, default_ops::fma_func, number<Backend, et_on>, U, V>
>::type
fma(const number<Backend, et_on>& a, const U& b, const V& c)
{
   return detail::expression<detail::function, default_ops::fma_func, number<Backend, et_on>, U, V>(
      default_ops::fma_func(), a, b, c);
}

template <class tag, class Arg1, class Arg2, class Arg3, class Arg4, class U, class V>
inline typename enable_if<
   mpl::and_<
   mpl::bool_<number_category<typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type >::value == number_kind_floating_point>,
   mpl::or_<
   is_number<U>,
   is_number_expression<U>,
   is_arithmetic<U>
   >,
   mpl::or_<
   is_number<V>,
   is_number_expression<V>,
   is_arithmetic<V>
   >
   >,
   detail::expression<detail::function, default_ops::fma_func, detail::expression<tag, Arg1, Arg2, Arg3, Arg4>, U, V>
>::type
fma(const detail::expression<tag, Arg1, Arg2, Arg3, Arg4>& a, const U& b, const V& c)
{
   return detail::expression<detail::function, default_ops::fma_func, detail::expression<tag, Arg1, Arg2, Arg3, Arg4>, U, V>(
      default_ops::fma_func(), a, b, c);
}

template <class Backend, class U, class V>
inline typename enable_if<
   mpl::and_<
   mpl::bool_<number_category<number<Backend, et_off> >::value == number_kind_floating_point>,
   mpl::or_<
   is_number<U>,
   is_number_expression<U>,
   is_arithmetic<U>
   >,
   mpl::or_<
   is_number<V>,
   is_number_expression<V>,
   is_arithmetic<V>
   >
   >,
   number<Backend, et_off>
>::type
fma(const number<Backend, et_off>& a, const U& b, const V& c)
{
   using default_ops::eval_multiply_add;
   detail::scoped_default_precision<multiprecision::number<Backend, et_off> > precision_guard(a, b, c);
   number<Backend, et_off> result;
   eval_multiply_add(result.backend(), number<Backend, et_off>::canonical_value(a), number<Backend, et_off>::canonical_value(b), number<Backend, et_off>::canonical_value(c));
   return BOOST_MP_MOVE(result);
}

template <class U, class Backend, class V>
inline typename enable_if<
   mpl::and_<
      mpl::bool_<number_category<number<Backend, et_on> >::value == number_kind_floating_point>,
      is_arithmetic<U>,
      mpl::or_<
         is_number<V>,
         is_number_expression<V>,
         is_arithmetic<V>
      >
   >,
   detail::expression<detail::function, default_ops::fma_func, U, number<Backend, et_on>, V>
>::type
fma(const U& a, const number<Backend, et_on>& b, const V& c)
{
   return detail::expression<detail::function, default_ops::fma_func, U, number<Backend, et_on>, V>(
      default_ops::fma_func(), a, b, c);
}

template <class U, class tag, class Arg1, class Arg2, class Arg3, class Arg4, class V>
inline typename enable_if<
   mpl::and_<
      mpl::bool_<number_category<typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type >::value == number_kind_floating_point>,
      is_arithmetic<U>,
      mpl::or_<
         is_number<V>,
         is_number_expression<V>,
         is_arithmetic<V>
      >
   >,
   detail::expression<detail::function, default_ops::fma_func, U, detail::expression<tag, Arg1, Arg2, Arg3, Arg4>, V>
>::type
fma(const U& a, const detail::expression<tag, Arg1, Arg2, Arg3, Arg4>& b, const V& c)
{
   return detail::expression<detail::function, default_ops::fma_func, U, detail::expression<tag, Arg1, Arg2, Arg3, Arg4>, V>(
      default_ops::fma_func(), a, b, c);
}

template <class U, class Backend, class V>
inline typename enable_if<
   mpl::and_<
      mpl::bool_<number_category<number<Backend, et_off> >::value == number_kind_floating_point>,
      is_arithmetic<U>,
      mpl::or_<
         is_number<V>,
         is_number_expression<V>,
         is_arithmetic<V>
      >
   >,
   number<Backend, et_off>
>::type
fma(const U& a, const number<Backend, et_off>& b, const V& c)
{
   using default_ops::eval_multiply_add;
   detail::scoped_default_precision<multiprecision::number<Backend, et_off> > precision_guard(a, b, c);
   number<Backend, et_off> result;
   eval_multiply_add(result.backend(), number<Backend, et_off>::canonical_value(a), number<Backend, et_off>::canonical_value(b), number<Backend, et_off>::canonical_value(c));
   return BOOST_MP_MOVE(result);
}

template <class U, class V, class Backend>
inline typename enable_if<
   mpl::and_<
   mpl::bool_<number_category<number<Backend, et_on> >::value == number_kind_floating_point>,
      is_arithmetic<U>,
      is_arithmetic<V>
   >,
   detail::expression<detail::function, default_ops::fma_func, U, V, number<Backend, et_on> >
>::type
fma(const U& a, const V& b, const number<Backend, et_on>& c)
{
   return detail::expression<detail::function, default_ops::fma_func, U, V, number<Backend, et_on> >(
      default_ops::fma_func(), a, b, c);
}

template <class U, class V, class tag, class Arg1, class Arg2, class Arg3, class Arg4>
inline typename enable_if<
   mpl::and_<
   mpl::bool_<number_category<typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type >::value == number_kind_floating_point>,
      is_arithmetic<U>,
      is_arithmetic<V>
   >,
   detail::expression<detail::function, default_ops::fma_func, U, V, detail::expression<tag, Arg1, Arg2, Arg3, Arg4> >
>::type
fma(const U& a, const V& b, const detail::expression<tag, Arg1, Arg2, Arg3, Arg4>& c)
{
   return detail::expression<detail::function, default_ops::fma_func, U, V, detail::expression<tag, Arg1, Arg2, Arg3, Arg4> >(
      default_ops::fma_func(), a, b, c);
}

template <class U, class V, class Backend>
inline typename enable_if<
   mpl::and_<
   mpl::bool_<number_category<number<Backend, et_off> >::value == number_kind_floating_point>,
      is_arithmetic<U>,
      is_arithmetic<V>
   >,
   number<Backend, et_off>
>::type
fma(const U& a, const V& b, const number<Backend, et_off>& c)
{
   using default_ops::eval_multiply_add;
   detail::scoped_default_precision<multiprecision::number<Backend, et_off> > precision_guard(a, b, c);
   number<Backend, et_off> result;
   eval_multiply_add(result.backend(), number<Backend, et_off>::canonical_value(a), number<Backend, et_off>::canonical_value(b), number<Backend, et_off>::canonical_value(c));
   return BOOST_MP_MOVE(result);
}

namespace default_ops {

   struct remquo_func
   {
      template <class B, class T, class U>
      void operator()(B& result, const T& a, const U& b, int* pi)const
      {
         eval_remquo(result, a, b, pi);
      }
   };

}

template <class Backend, class U>
inline typename enable_if_c<
   number_category<number<Backend, et_on> >::value == number_kind_floating_point,
   detail::expression<detail::function, default_ops::remquo_func, number<Backend, et_on>, U, int*>
>::type
remquo(const number<Backend, et_on>& a, const U& b, int* pi)
{
   return detail::expression<detail::function, default_ops::remquo_func, number<Backend, et_on>, U, int*>(
      default_ops::remquo_func(), a, b, pi);
}

template <class tag, class Arg1, class Arg2, class Arg3, class Arg4, class U>
inline typename enable_if_c<
   number_category<typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type >::value == number_kind_floating_point,
   detail::expression<detail::function, default_ops::remquo_func, detail::expression<tag, Arg1, Arg2, Arg3, Arg4>, U, int*>
>::type
remquo(const detail::expression<tag, Arg1, Arg2, Arg3, Arg4>& a, const U& b, int* pi)
{
   return detail::expression<detail::function, default_ops::remquo_func, detail::expression<tag, Arg1, Arg2, Arg3, Arg4>, U, int*>(
      default_ops::remquo_func(), a, b, pi);
}

template <class U, class Backend>
inline typename enable_if_c<
   (number_category<number<Backend, et_on> >::value == number_kind_floating_point)
   && !is_number<U>::value && !is_number_expression<U>::value,
   detail::expression<detail::function, default_ops::remquo_func, U, number<Backend, et_on>, int*>
>::type
remquo(const U& a, const number<Backend, et_on>& b, int* pi)
{
   return detail::expression<detail::function, default_ops::remquo_func, U, number<Backend, et_on>, int*>(
      default_ops::remquo_func(), a, b, pi);
}

template <class U, class tag, class Arg1, class Arg2, class Arg3, class Arg4>
inline typename enable_if_c<
   (number_category<typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type >::value == number_kind_floating_point)
   && !is_number<U>::value && !is_number_expression<U>::value,
   detail::expression<detail::function, default_ops::remquo_func, U, detail::expression<tag, Arg1, Arg2, Arg3, Arg4>, int*>
>::type
remquo(const U& a, const detail::expression<tag, Arg1, Arg2, Arg3, Arg4>& b, int* pi)
{
   return detail::expression<detail::function, default_ops::remquo_func, U, detail::expression<tag, Arg1, Arg2, Arg3, Arg4>, int*>(
      default_ops::remquo_func(), a, b, pi);
}

template <class Backend, class U>
inline typename enable_if_c<
   number_category<number<Backend, et_on> >::value == number_kind_floating_point,
   number<Backend, et_off>
>::type
remquo(const number<Backend, et_off>& a, const U& b, int* pi)
{
   using default_ops::eval_remquo;
   detail::scoped_default_precision<multiprecision::number<Backend, et_off> > precision_guard(a, b);
   number<Backend, et_off> result;
   eval_remquo(result.backend(), a.backend(), number<Backend, et_off>::canonical_value(b), pi);
   return BOOST_MP_MOVE(result);
}
template <class U, class Backend>
inline typename enable_if_c<
(number_category<number<Backend, et_on> >::value == number_kind_floating_point)
&& !is_number<U>::value && !is_number_expression<U>::value,
number<Backend, et_off>
>::type
remquo(const U& a, const number<Backend, et_off>& b, int* pi)
{
   using default_ops::eval_remquo;
   detail::scoped_default_precision<multiprecision::number<Backend, et_off> > precision_guard(a, b);
   number<Backend, et_off> result;
   eval_remquo(result.backend(), number<Backend, et_off>::canonical_value(a), b.backend(), pi);
   return BOOST_MP_MOVE(result);
}


template <class B, expression_template_option ExpressionTemplates>
inline typename enable_if_c<number_category<B>::value == number_kind_integer, number<B, ExpressionTemplates> >::type
   sqrt(const number<B, ExpressionTemplates>& x, number<B, ExpressionTemplates>& r)
{
   using default_ops::eval_integer_sqrt;
   detail::scoped_default_precision<multiprecision::number<B, ExpressionTemplates> > precision_guard(x, r);
   number<B, ExpressionTemplates> s;
   eval_integer_sqrt(s.backend(), r.backend(), x.backend());
   return s;
}

#define UNARY_OP_FUNCTOR(func, category)\
namespace detail{\
template <class Backend> \
struct BOOST_JOIN(category, BOOST_JOIN(func, _funct))\
{\
   void operator()(Backend& result, const Backend& arg)const\
   {\
      using default_ops::BOOST_JOIN(eval_,func);\
      BOOST_JOIN(eval_,func)(result, arg);\
   }\
   template <class U>\
   void operator()(U& result, const Backend& arg)const\
   {\
      using default_ops::BOOST_JOIN(eval_,func);\
      Backend temp;\
      BOOST_JOIN(eval_,func)(temp, arg);\
      result = temp;\
   }\
};\
\
}\
\
template <class tag, class A1, class A2, class A3, class A4> \
inline typename enable_if_c<number_category<detail::expression<tag, A1, A2, A3, A4> >::value == category,\
   detail::expression<\
    detail::function\
  , detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type> \
  , detail::expression<tag, A1, A2, A3, A4> > \
>::type \
func(const detail::expression<tag, A1, A2, A3, A4>& arg)\
{\
    return detail::expression<\
    detail::function\
  , detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type> \
  , detail::expression<tag, A1, A2, A3, A4> \
> (\
        detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>() \
      , arg   \
    );\
}\
template <class Backend> \
inline typename enable_if_c<number_category<Backend>::value == category,\
   detail::expression<\
    detail::function\
  , detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend> \
  , number<Backend, et_on> > \
>::type \
func(const number<Backend, et_on>& arg)\
{\
    return detail::expression<\
    detail::function\
  , detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend> \
  , number<Backend, et_on> \
  >(\
        detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend>() \
      , arg   \
    );\
}\
template <class Backend> \
inline typename boost::enable_if_c<\
   boost::multiprecision::number_category<Backend>::value == category,\
   number<Backend, et_off> >::type \
func(const number<Backend, et_off>& arg)\
{\
   detail::scoped_default_precision<multiprecision::number<Backend, et_off> > precision_guard(arg);\
   number<Backend, et_off> result;\
   using default_ops::BOOST_JOIN(eval_,func);\
   BOOST_JOIN(eval_,func)(result.backend(), arg.backend());\
   return BOOST_MP_MOVE(result);\
}

#define BINARY_OP_FUNCTOR(func, category)\
namespace detail{\
template <class Backend> \
struct BOOST_JOIN(category, BOOST_JOIN(func, _funct))\
{\
   void operator()(Backend& result, const Backend& arg, const Backend& a)const\
   {\
      using default_ops:: BOOST_JOIN(eval_,func);\
      BOOST_JOIN(eval_,func)(result, arg, a);\
   }\
   template <class Arithmetic> \
   void operator()(Backend& result, const Backend& arg, const Arithmetic& a)const\
   {\
      using default_ops:: BOOST_JOIN(eval_,func);\
      BOOST_JOIN(eval_,func)(result, arg, number<Backend>::canonical_value(a));\
   }\
   template <class Arithmetic> \
   void operator()(Backend& result, const Arithmetic& arg, const Backend& a)const\
   {\
      using default_ops:: BOOST_JOIN(eval_,func);\
      BOOST_JOIN(eval_,func)(result, number<Backend>::canonical_value(arg), a);\
   }\
   template <class U>\
   void operator()(U& result, const Backend& arg, const Backend& a)const\
   {\
      using default_ops:: BOOST_JOIN(eval_,func);\
      Backend r;\
      BOOST_JOIN(eval_,func)(r, arg, a);\
      result = r;\
   }\
   template <class U, class Arithmetic> \
   void operator()(U& result, const Backend& arg, const Arithmetic& a)const\
   {\
      using default_ops:: BOOST_JOIN(eval_,func);\
      Backend r;\
      BOOST_JOIN(eval_,func)(r, arg, number<Backend>::canonical_value(a));\
      result = r;\
   }\
   template <class U, class Arithmetic> \
   void operator()(U& result, const Arithmetic& arg, const Backend& a)const\
   {\
      using default_ops:: BOOST_JOIN(eval_,func);\
      Backend r;\
      BOOST_JOIN(eval_,func)(r, number<Backend>::canonical_value(arg), a);\
      result = r;\
   }\
};\
\
}\
template <class Backend> \
inline typename enable_if_c<number_category<Backend>::value == category,\
   detail::expression<\
    detail::function\
  , detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend> \
  , number<Backend, et_on> \
  , number<Backend, et_on> > \
>::type \
func(const number<Backend, et_on>& arg, const number<Backend, et_on>& a)\
{\
    return detail::expression<\
    detail::function\
  , detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend> \
  , number<Backend, et_on> \
  , number<Backend, et_on> \
  >(\
        detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend>() \
      , arg,\
      a\
    );\
}\
template <class Backend, class tag, class A1, class A2, class A3, class A4> \
inline typename enable_if_c<\
   (number_category<Backend>::value == category) && (boost::is_convertible<typename detail::expression<tag, A1, A2, A3, A4>::result_type, number<Backend, et_on> >::value),\
   detail::expression<\
    detail::function\
  , detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend> \
  , number<Backend, et_on> \
  , detail::expression<tag, A1, A2, A3, A4> > \
>::type \
func(const number<Backend, et_on>& arg, const detail::expression<tag, A1, A2, A3, A4>& a)\
{\
    return detail::expression<\
    detail::function\
  , detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend> \
  , number<Backend, et_on> \
  , detail::expression<tag, A1, A2, A3, A4> \
  >(\
        detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend>() \
      , arg,\
      a\
    );\
}\
template <class tag, class A1, class A2, class A3, class A4, class Backend> \
inline typename enable_if_c<\
   (number_category<Backend>::value == category) && (boost::is_convertible<typename detail::expression<tag, A1, A2, A3, A4>::result_type, number<Backend, et_on> >::value),\
   detail::expression<\
    detail::function\
  , detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend> \
  , detail::expression<tag, A1, A2, A3, A4> \
  , number<Backend, et_on> > \
>::type \
func(const detail::expression<tag, A1, A2, A3, A4>& arg, const number<Backend, et_on>& a)\
{\
    return detail::expression<\
    detail::function\
  , detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend> \
  , detail::expression<tag, A1, A2, A3, A4> \
  , number<Backend, et_on> \
  >(\
        detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend>() \
      , arg,\
      a\
    );\
}\
template <class tag, class A1, class A2, class A3, class A4, class tagb, class A1b, class A2b, class A3b, class A4b> \
inline typename enable_if_c<\
      (number_category<detail::expression<tag, A1, A2, A3, A4> >::value == category) && (number_category<detail::expression<tagb, A1b, A2b, A3b, A4b> >::value == category),\
   detail::expression<\
    detail::function\
  , detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type> \
  , detail::expression<tag, A1, A2, A3, A4> \
  , detail::expression<tagb, A1b, A2b, A3b, A4b> > \
>::type \
func(const detail::expression<tag, A1, A2, A3, A4>& arg, const detail::expression<tagb, A1b, A2b, A3b, A4b>& a)\
{\
    return detail::expression<\
    detail::function\
  , detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type> \
  , detail::expression<tag, A1, A2, A3, A4> \
  , detail::expression<tagb, A1b, A2b, A3b, A4b> \
  >(\
        detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>() \
      , arg,\
      a\
    );\
}\
template <class Backend, class Arithmetic> \
inline typename enable_if_c<\
   is_compatible_arithmetic_type<Arithmetic, number<Backend, et_on> >::value && (number_category<Backend>::value == category),\
   detail::expression<\
    detail::function\
  , detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend> \
  , number<Backend, et_on> \
  , Arithmetic\
  > \
>::type \
func(const number<Backend, et_on>& arg, const Arithmetic& a)\
{\
    return detail::expression<\
    detail::function\
  , detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend> \
  , number<Backend, et_on> \
  , Arithmetic\
  >(\
        detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend>() \
      , arg,\
      a\
    );\
}\
template <class tag, class A1, class A2, class A3, class A4, class Arithmetic> \
inline typename enable_if_c<\
   is_compatible_arithmetic_type<Arithmetic, typename detail::expression<tag, A1, A2, A3, A4>::result_type>::value && (number_category<detail::expression<tag, A1, A2, A3, A4> >::value == category),\
   detail::expression<\
    detail::function\
  , detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type> \
  , detail::expression<tag, A1, A2, A3, A4> \
  , Arithmetic\
  > \
>::type \
func(const detail::expression<tag, A1, A2, A3, A4>& arg, const Arithmetic& a)\
{\
    return detail::expression<\
    detail::function\
  , detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type> \
  , detail::expression<tag, A1, A2, A3, A4> \
  , Arithmetic\
   >(\
        detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>() \
      , arg,\
      a\
    );\
}\
template <class Backend, class Arithmetic> \
inline typename enable_if_c<\
   is_compatible_arithmetic_type<Arithmetic, number<Backend, et_on> >::value && (number_category<Backend>::value == category),\
   detail::expression<\
    detail::function\
  , detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend> \
  , Arithmetic \
  , number<Backend, et_on> \
  > \
>::type \
func(const Arithmetic& arg, const number<Backend, et_on>& a)\
{\
    return detail::expression<\
    detail::function\
  , detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend> \
  , Arithmetic \
  , number<Backend, et_on> \
  >(\
        detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend>() \
      , arg,\
      a\
    );\
}\
template <class tag, class A1, class A2, class A3, class A4, class Arithmetic> \
inline typename enable_if_c<\
   is_compatible_arithmetic_type<Arithmetic, typename detail::expression<tag, A1, A2, A3, A4>::result_type>::value && (number_category<detail::expression<tag, A1, A2, A3, A4> >::value == category),\
   detail::expression<\
    detail::function\
  , detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type> \
  , Arithmetic \
  , detail::expression<tag, A1, A2, A3, A4> \
  > \
>::type \
func(const Arithmetic& arg, const detail::expression<tag, A1, A2, A3, A4>& a)\
{\
    return detail::expression<\
    detail::function\
  , detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type> \
  , Arithmetic \
  , detail::expression<tag, A1, A2, A3, A4> \
   >(\
        detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>() \
      , arg,\
      a\
    );\
}\
template <class Backend> \
inline typename enable_if_c<(number_category<Backend>::value == category),\
   number<Backend, et_off> >::type \
func(const number<Backend, et_off>& arg, const number<Backend, et_off>& a)\
{\
   detail::scoped_default_precision<multiprecision::number<Backend, et_off> > precision_guard(arg, a);\
   number<Backend, et_off> result;\
   using default_ops:: BOOST_JOIN(eval_,func);\
   BOOST_JOIN(eval_,func)(result.backend(), arg.backend(), a.backend());\
   return BOOST_MP_MOVE(result);\
}\
template <class Backend, class Arithmetic> \
inline typename enable_if_c<\
   is_compatible_arithmetic_type<Arithmetic, number<Backend, et_off> >::value && (number_category<Backend>::value == category),\
   number<Backend, et_off> \
>::type \
func(const number<Backend, et_off>& arg, const Arithmetic& a)\
{\
   detail::scoped_default_precision<multiprecision::number<Backend, et_off> > precision_guard(arg);\
   number<Backend, et_off> result;\
   using default_ops:: BOOST_JOIN(eval_,func);\
   BOOST_JOIN(eval_,func)(result.backend(), arg.backend(), number<Backend, et_off>::canonical_value(a));\
   return BOOST_MP_MOVE(result);\
}\
template <class Backend, class Arithmetic> \
inline typename enable_if_c<\
   is_compatible_arithmetic_type<Arithmetic, number<Backend, et_off> >::value && (number_category<Backend>::value == category),\
   number<Backend, et_off> \
>::type \
func(const Arithmetic& a, const number<Backend, et_off>& arg)\
{\
   detail::scoped_default_precision<multiprecision::number<Backend, et_off> > precision_guard(arg);\
   number<Backend, et_off> result;\
   using default_ops:: BOOST_JOIN(eval_,func);\
   BOOST_JOIN(eval_,func)(result.backend(), number<Backend, et_off>::canonical_value(a), arg.backend());\
   return BOOST_MP_MOVE(result);\
}\


#define HETERO_BINARY_OP_FUNCTOR_B(func, Arg2, category)\
template <class tag, class A1, class A2, class A3, class A4> \
inline typename enable_if_c<\
   (number_category<detail::expression<tag, A1, A2, A3, A4> >::value == category),\
   detail::expression<\
    detail::function\
  , detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type> \
  , detail::expression<tag, A1, A2, A3, A4> \
  , Arg2> \
>::type \
func(const detail::expression<tag, A1, A2, A3, A4>& arg, Arg2 const& a)\
{\
    return detail::expression<\
    detail::function\
  , detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type> \
  , detail::expression<tag, A1, A2, A3, A4> \
  , Arg2\
   >(\
        detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>() \
      , arg, a   \
    );\
}\
template <class Backend> \
inline typename enable_if_c<\
   (number_category<Backend>::value == category),\
  detail::expression<\
    detail::function\
  , detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend> \
  , number<Backend, et_on> \
  , Arg2> \
>::type \
func(const number<Backend, et_on>& arg, Arg2 const& a)\
{\
    return detail::expression<\
    detail::function\
  , detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend> \
  , number<Backend, et_on> \
  , Arg2\
  >(\
        detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend>() \
      , arg,\
      a\
    );\
}\
template <class Backend> \
inline typename enable_if_c<\
  (number_category<Backend>::value == category),\
  number<Backend, et_off> >::type \
func(const number<Backend, et_off>& arg, Arg2 const& a)\
{\
   detail::scoped_default_precision<multiprecision::number<Backend, et_off> > precision_guard(arg, a);\
   number<Backend, et_off> result;\
   using default_ops:: BOOST_JOIN(eval_,func);\
   BOOST_JOIN(eval_,func)(result.backend(), arg.backend(), a);\
   return BOOST_MP_MOVE(result);\
}\

#define HETERO_BINARY_OP_FUNCTOR(func, Arg2, category)\
namespace detail{\
template <class Backend> \
struct BOOST_JOIN(category, BOOST_JOIN(func, _funct))\
{\
   template <class Arg>\
   void operator()(Backend& result, Backend const& arg, Arg a)const\
   {\
      using default_ops:: BOOST_JOIN(eval_,func);\
      BOOST_JOIN(eval_,func)(result, arg, a);\
   }\
};\
\
}\
\
HETERO_BINARY_OP_FUNCTOR_B(func, Arg2, category)

namespace detail{
template <class Backend>
struct abs_funct
{
   void operator()(Backend& result, const Backend& arg)const
   {
      using default_ops::eval_abs;
      eval_abs(result, arg);
   }
};
template <class Backend>
struct conj_funct
{
   void operator()(Backend& result, const Backend& arg)const
   {
      using default_ops::eval_conj;
      eval_conj(result, arg);
   }
};
template <class Backend>
struct proj_funct
{
   void operator()(Backend& result, const Backend& arg)const
   {
      using default_ops::eval_proj;
      eval_proj(result, arg);
   }
};

}

template <class tag, class A1, class A2, class A3, class A4>
inline typename boost::disable_if_c<number_category<typename detail::expression<tag, A1, A2, A3, A4>::result_type>::value == number_kind_complex,
   detail::expression<
    detail::function
  , detail::abs_funct<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>
  , detail::expression<tag, A1, A2, A3, A4> > >::type
abs(const detail::expression<tag, A1, A2, A3, A4>& arg)
{
    return detail::expression<
    detail::function
  , detail::abs_funct<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>
  , detail::expression<tag, A1, A2, A3, A4>
> (
        detail::abs_funct<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>()
      , arg
    );
}
template <class Backend>
inline typename disable_if_c<number_category<Backend>::value == number_kind_complex,
   detail::expression<
    detail::function
  , detail::abs_funct<Backend>
  , number<Backend, et_on> > >::type
abs(const number<Backend, et_on>& arg)
{
    return detail::expression<
    detail::function
  , detail::abs_funct<Backend>
  , number<Backend, et_on>
  >(
        detail::abs_funct<Backend>()
      , arg
    );
}
template <class Backend>
inline typename disable_if_c<number_category<Backend>::value == number_kind_complex, number<Backend, et_off> >::type
abs(const number<Backend, et_off>& arg)
{
   detail::scoped_default_precision<multiprecision::number<Backend, et_off> > precision_guard(arg);
   number<Backend, et_off> result;
   using default_ops::eval_abs;
   eval_abs(result.backend(), arg.backend());
   return BOOST_MP_MOVE(result);
}

template <class tag, class A1, class A2, class A3, class A4>
inline detail::expression<
    detail::function
  , detail::conj_funct<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>
  , detail::expression<tag, A1, A2, A3, A4> >
conj(const detail::expression<tag, A1, A2, A3, A4>& arg)
{
    return detail::expression<
    detail::function
  , detail::conj_funct<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>
  , detail::expression<tag, A1, A2, A3, A4>
> (
        detail::conj_funct<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>()
      , arg
    );
}
template <class Backend>
inline detail::expression<
    detail::function
  , detail::conj_funct<Backend>
  , number<Backend, et_on> >
conj(const number<Backend, et_on>& arg)
{
    return detail::expression<
    detail::function
  , detail::conj_funct<Backend>
  , number<Backend, et_on>
  >(
        detail::conj_funct<Backend>()
      , arg
    );
}
template <class Backend>
inline number<Backend, et_off>
conj(const number<Backend, et_off>& arg)
{
   detail::scoped_default_precision<multiprecision::number<Backend, et_off> > precision_guard(arg);
   number<Backend, et_off> result;
   using default_ops::eval_conj;
   eval_conj(result.backend(), arg.backend());
   return BOOST_MP_MOVE(result);
}

template <class tag, class A1, class A2, class A3, class A4>
inline detail::expression<
    detail::function
  , detail::proj_funct<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>
  , detail::expression<tag, A1, A2, A3, A4> >
proj(const detail::expression<tag, A1, A2, A3, A4>& arg)
{
    return detail::expression<
    detail::function
  , detail::proj_funct<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>
  , detail::expression<tag, A1, A2, A3, A4>
> (
        detail::proj_funct<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>()
      , arg
    );
}
template <class Backend>
inline detail::expression<
    detail::function
  , detail::proj_funct<Backend>
  , number<Backend, et_on> >
proj(const number<Backend, et_on>& arg)
{
    return detail::expression<
    detail::function
  , detail::proj_funct<Backend>
  , number<Backend, et_on>
  >(
        detail::proj_funct<Backend>()
      , arg
    );
}
template <class Backend>
inline number<Backend, et_off>
proj(const number<Backend, et_off>& arg)
{
   detail::scoped_default_precision<multiprecision::number<Backend, et_off> > precision_guard(arg);
   number<Backend, et_off> result;
   using default_ops::eval_proj;
   eval_proj(result.backend(), arg.backend());
   return BOOST_MP_MOVE(result);
}

UNARY_OP_FUNCTOR(fabs, number_kind_floating_point)
UNARY_OP_FUNCTOR(sqrt, number_kind_floating_point)
UNARY_OP_FUNCTOR(floor, number_kind_floating_point)
UNARY_OP_FUNCTOR(ceil, number_kind_floating_point)
UNARY_OP_FUNCTOR(trunc, number_kind_floating_point)
UNARY_OP_FUNCTOR(round, number_kind_floating_point)
UNARY_OP_FUNCTOR(exp, number_kind_floating_point)
UNARY_OP_FUNCTOR(exp2, number_kind_floating_point)
UNARY_OP_FUNCTOR(log, number_kind_floating_point)
UNARY_OP_FUNCTOR(log10, number_kind_floating_point)
UNARY_OP_FUNCTOR(cos, number_kind_floating_point)
UNARY_OP_FUNCTOR(sin, number_kind_floating_point)
UNARY_OP_FUNCTOR(tan, number_kind_floating_point)
UNARY_OP_FUNCTOR(asin, number_kind_floating_point)
UNARY_OP_FUNCTOR(acos, number_kind_floating_point)
UNARY_OP_FUNCTOR(atan, number_kind_floating_point)
UNARY_OP_FUNCTOR(cosh, number_kind_floating_point)
UNARY_OP_FUNCTOR(sinh, number_kind_floating_point)
UNARY_OP_FUNCTOR(tanh, number_kind_floating_point)
UNARY_OP_FUNCTOR(log2, number_kind_floating_point)
UNARY_OP_FUNCTOR(nearbyint, number_kind_floating_point)
UNARY_OP_FUNCTOR(rint, number_kind_floating_point)

HETERO_BINARY_OP_FUNCTOR(ldexp, short, number_kind_floating_point)
//HETERO_BINARY_OP_FUNCTOR(frexp, short*, number_kind_floating_point)
HETERO_BINARY_OP_FUNCTOR_B(ldexp, int, number_kind_floating_point)
//HETERO_BINARY_OP_FUNCTOR_B(frexp, int*, number_kind_floating_point)
HETERO_BINARY_OP_FUNCTOR_B(ldexp, long, number_kind_floating_point)
//HETERO_BINARY_OP_FUNCTOR_B(frexp, long*, number_kind_floating_point)
HETERO_BINARY_OP_FUNCTOR_B(ldexp, boost::long_long_type, number_kind_floating_point)
//HETERO_BINARY_OP_FUNCTOR_B(frexp, boost::long_long_type*, number_kind_floating_point)
BINARY_OP_FUNCTOR(pow, number_kind_floating_point)
BINARY_OP_FUNCTOR(fmod, number_kind_floating_point)
BINARY_OP_FUNCTOR(fmax, number_kind_floating_point)
BINARY_OP_FUNCTOR(fmin, number_kind_floating_point)
BINARY_OP_FUNCTOR(atan2, number_kind_floating_point)
BINARY_OP_FUNCTOR(fdim, number_kind_floating_point)
BINARY_OP_FUNCTOR(hypot, number_kind_floating_point)
BINARY_OP_FUNCTOR(remainder, number_kind_floating_point)

UNARY_OP_FUNCTOR(logb, number_kind_floating_point)
HETERO_BINARY_OP_FUNCTOR(scalbn, short, number_kind_floating_point)
HETERO_BINARY_OP_FUNCTOR(scalbln, short, number_kind_floating_point)
HETERO_BINARY_OP_FUNCTOR_B(scalbn, int, number_kind_floating_point)
HETERO_BINARY_OP_FUNCTOR_B(scalbln, int, number_kind_floating_point)
HETERO_BINARY_OP_FUNCTOR_B(scalbn, long, number_kind_floating_point)
HETERO_BINARY_OP_FUNCTOR_B(scalbln, long, number_kind_floating_point)
HETERO_BINARY_OP_FUNCTOR_B(scalbn, boost::long_long_type, number_kind_floating_point)
HETERO_BINARY_OP_FUNCTOR_B(scalbln, boost::long_long_type, number_kind_floating_point)

//
// Complex functions:
//
UNARY_OP_FUNCTOR(exp, number_kind_complex)
UNARY_OP_FUNCTOR(log, number_kind_complex)
UNARY_OP_FUNCTOR(log10, number_kind_complex)
BINARY_OP_FUNCTOR(pow, number_kind_complex)
UNARY_OP_FUNCTOR(sqrt, number_kind_complex)
UNARY_OP_FUNCTOR(sin, number_kind_complex)
UNARY_OP_FUNCTOR(cos, number_kind_complex)
UNARY_OP_FUNCTOR(tan, number_kind_complex)
UNARY_OP_FUNCTOR(asin, number_kind_complex)
UNARY_OP_FUNCTOR(acos, number_kind_complex)
UNARY_OP_FUNCTOR(atan, number_kind_complex)
UNARY_OP_FUNCTOR(sinh, number_kind_complex)
UNARY_OP_FUNCTOR(cosh, number_kind_complex)
UNARY_OP_FUNCTOR(tanh, number_kind_complex)
UNARY_OP_FUNCTOR(asinh, number_kind_complex)
UNARY_OP_FUNCTOR(acosh, number_kind_complex)
UNARY_OP_FUNCTOR(atanh, number_kind_complex)

//
// Integer functions:
//
BINARY_OP_FUNCTOR(gcd, number_kind_integer)
BINARY_OP_FUNCTOR(lcm, number_kind_integer)
HETERO_BINARY_OP_FUNCTOR(pow, unsigned, number_kind_integer)

#undef BINARY_OP_FUNCTOR
#undef UNARY_OP_FUNCTOR

//
// ilogb:
//
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline typename enable_if_c<number_category<Backend>::value == number_kind_floating_point, typename Backend::exponent_type>::type
   ilogb(const multiprecision::number<Backend, ExpressionTemplates>& val)
{
   using default_ops::eval_ilogb;
   return eval_ilogb(val.backend());
}

template <class tag, class A1, class A2, class A3, class A4>
inline typename enable_if_c<number_category<detail::expression<tag, A1, A2, A3, A4> >::value == number_kind_floating_point, typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type::backend_type::exponent_type>::type
ilogb(const detail::expression<tag, A1, A2, A3, A4>& val)
{
   using default_ops::eval_ilogb;
   typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type arg(val);
   return eval_ilogb(arg.backend());
}

} //namespace multiprecision

namespace math{
//
// Overload of Boost.Math functions that find the wrong overload when used with number:
//
namespace detail{
   template <class T> T sinc_pi_imp(T);
   template <class T> T sinhc_pi_imp(T);
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline multiprecision::number<Backend, ExpressionTemplates> sinc_pi(const multiprecision::number<Backend, ExpressionTemplates>& x)
{
   boost::multiprecision::detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(x);
   return BOOST_MP_MOVE(detail::sinc_pi_imp(x));
}

template <class Backend, multiprecision::expression_template_option ExpressionTemplates, class Policy>
inline multiprecision::number<Backend, ExpressionTemplates> sinc_pi(const multiprecision::number<Backend, ExpressionTemplates>& x, const Policy&)
{
   boost::multiprecision::detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(x);
   return BOOST_MP_MOVE(detail::sinc_pi_imp(x));
}

template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline multiprecision::number<Backend, ExpressionTemplates> sinhc_pi(const multiprecision::number<Backend, ExpressionTemplates>& x)
{
   boost::multiprecision::detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(x);
   return BOOST_MP_MOVE(detail::sinhc_pi_imp(x));
}

template <class Backend, multiprecision::expression_template_option ExpressionTemplates, class Policy>
inline multiprecision::number<Backend, ExpressionTemplates> sinhc_pi(const multiprecision::number<Backend, ExpressionTemplates>& x, const Policy&)
{
   boost::multiprecision::detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(x);
   return BOOST_MP_MOVE(boost::math::sinhc_pi(x));
}

using boost::multiprecision::gcd;
using boost::multiprecision::lcm;

#ifdef BOOST_MSVC
#pragma warning(pop)
#endif
} // namespace math

namespace integer {

using boost::multiprecision::gcd;
using boost::multiprecision::lcm;

}

} // namespace boost

//
// This has to come last of all:
//
#include <boost/multiprecision/detail/no_et_ops.hpp>
#include <boost/multiprecision/detail/et_ops.hpp>
//
// min/max overloads:
//
#include <boost/multiprecision/detail/min_max.hpp>

#endif