Adding upstream version 14.2.21.upstream/14.2.21upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 3020 insertions, 0 deletions

diff --git a/src/boost/libs/multiprecision/test/test_arithmetic.hpp b/src/boost/libs/multiprecision/test/test_arithmetic.hpp
new file mode 100644
index 00000000..58699fde
--- /dev/null
+++ b/src/boost/libs/multiprecision/test/test_arithmetic.hpp
@@ -0,0 +1,3020 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2012 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at https://www.boost.org/LICENSE_1_0.txt
+
+#ifdef TEST_VLD
+#include <vld.h>
+#endif
+
+#include <boost/math/special_functions/pow.hpp>
+#include <boost/integer/common_factor_rt.hpp>
+#include <boost/functional/hash.hpp>
+#include <functional>
+#include "test.hpp"
+
+template <class T>
+struct is_boost_rational : public boost::mpl::false_
+{};
+template <class T>
+struct is_checked_cpp_int : public boost::mpl::false_
+{};
+
+#ifdef BOOST_MSVC
+// warning C4127: conditional expression is constant
+#pragma warning(disable : 4127)
+#endif
+
+template <class Target, class Source>
+Target checked_lexical_cast(const Source& val)
+{
+#ifndef BOOST_NO_EXCEPTIONS
+   try
+   {
+#endif
+      return boost::lexical_cast<Target>(val);
+#ifndef BOOST_NO_EXCEPTIONS
+   }
+   catch (...)
+   {
+      std::cerr << "Error in lexical cast\nSource type = " << typeid(Source).name() << " \"" << val << "\"\n";
+      std::cerr << "Target type = " << typeid(Target).name() << std::endl;
+      throw;
+   }
+#endif
+}
+
+bool isfloat(float) { return true; }
+bool isfloat(double) { return true; }
+bool isfloat(long double) { return true; }
+template <class T>
+bool isfloat(T) { return false; }
+
+namespace detail {
+
+template <class tag, class Arg1, class Arg2, class Arg3, class Arg4>
+typename boost::multiprecision::detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type
+abs(boost::multiprecision::detail::expression<tag, Arg1, Arg2, Arg3, Arg4> const& v)
+{
+   typedef typename boost::multiprecision::detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type result_type;
+   return v < 0 ? result_type(-v) : result_type(v);
+}
+
+} // namespace detail
+
+template <class T>
+struct is_twos_complement_integer : public boost::mpl::true_
+{};
+
+template <class T>
+struct related_type
+{
+   typedef T type;
+};
+
+template <class Real, class Val>
+void test_comparisons(Val, Val, const boost::mpl::false_)
+{}
+
+int normalize_compare_result(int r)
+{
+   return r > 0 ? 1 : r < 0 ? -1 : 0;
+}
+
+template <class Real, class Val>
+typename boost::disable_if_c<boost::multiprecision::number_category<Real>::value == boost::multiprecision::number_kind_complex>::type
+test_comparisons(Val a, Val b, const boost::mpl::true_)
+{
+   Real r1(a);
+   Real r2(b);
+   Real z(1);
+
+   int cr = a < b ? -1 : a > b ? 1 : 0;
+
+   BOOST_CHECK_EQUAL(r1 == r2, a == b);
+   BOOST_CHECK_EQUAL(r1 != r2, a != b);
+   BOOST_CHECK_EQUAL(r1 <= r2, a <= b);
+   BOOST_CHECK_EQUAL(r1 < r2, a < b);
+   BOOST_CHECK_EQUAL(r1 >= r2, a >= b);
+   BOOST_CHECK_EQUAL(r1 > r2, a > b);
+
+   BOOST_CHECK_EQUAL(r1 == b, a == b);
+   BOOST_CHECK_EQUAL(r1 != b, a != b);
+   BOOST_CHECK_EQUAL(r1 <= b, a <= b);
+   BOOST_CHECK_EQUAL(r1 < b, a < b);
+   BOOST_CHECK_EQUAL(r1 >= b, a >= b);
+   BOOST_CHECK_EQUAL(r1 > b, a > b);
+
+   BOOST_CHECK_EQUAL(a == r2, a == b);
+   BOOST_CHECK_EQUAL(a != r2, a != b);
+   BOOST_CHECK_EQUAL(a <= r2, a <= b);
+   BOOST_CHECK_EQUAL(a < r2, a < b);
+   BOOST_CHECK_EQUAL(a >= r2, a >= b);
+   BOOST_CHECK_EQUAL(a > r2, a > b);
+
+   BOOST_CHECK_EQUAL(r1 * z == r2, a == b);
+   BOOST_CHECK_EQUAL(r1 * z != r2, a != b);
+   BOOST_CHECK_EQUAL(r1 * z <= r2, a <= b);
+   BOOST_CHECK_EQUAL(r1 * z < r2, a < b);
+   BOOST_CHECK_EQUAL(r1 * z >= r2, a >= b);
+   BOOST_CHECK_EQUAL(r1 * z > r2, a > b);
+
+   BOOST_CHECK_EQUAL(r1 == r2 * z, a == b);
+   BOOST_CHECK_EQUAL(r1 != r2 * z, a != b);
+   BOOST_CHECK_EQUAL(r1 <= r2 * z, a <= b);
+   BOOST_CHECK_EQUAL(r1 < r2 * z, a < b);
+   BOOST_CHECK_EQUAL(r1 >= r2 * z, a >= b);
+   BOOST_CHECK_EQUAL(r1 > r2 * z, a > b);
+
+   BOOST_CHECK_EQUAL(r1 * z == r2 * z, a == b);
+   BOOST_CHECK_EQUAL(r1 * z != r2 * z, a != b);
+   BOOST_CHECK_EQUAL(r1 * z <= r2 * z, a <= b);
+   BOOST_CHECK_EQUAL(r1 * z < r2 * z, a < b);
+   BOOST_CHECK_EQUAL(r1 * z >= r2 * z, a >= b);
+   BOOST_CHECK_EQUAL(r1 * z > r2 * z, a > b);
+
+   BOOST_CHECK_EQUAL(r1 * z == b, a == b);
+   BOOST_CHECK_EQUAL(r1 * z != b, a != b);
+   BOOST_CHECK_EQUAL(r1 * z <= b, a <= b);
+   BOOST_CHECK_EQUAL(r1 * z < b, a < b);
+   BOOST_CHECK_EQUAL(r1 * z >= b, a >= b);
+   BOOST_CHECK_EQUAL(r1 * z > b, a > b);
+
+   BOOST_CHECK_EQUAL(a == r2 * z, a == b);
+   BOOST_CHECK_EQUAL(a != r2 * z, a != b);
+   BOOST_CHECK_EQUAL(a <= r2 * z, a <= b);
+   BOOST_CHECK_EQUAL(a < r2 * z, a < b);
+   BOOST_CHECK_EQUAL(a >= r2 * z, a >= b);
+   BOOST_CHECK_EQUAL(a > r2 * z, a > b);
+
+   BOOST_CHECK_EQUAL(normalize_compare_result(r1.compare(r2)), cr);
+   BOOST_CHECK_EQUAL(normalize_compare_result(r2.compare(r1)), -cr);
+   BOOST_CHECK_EQUAL(normalize_compare_result(r1.compare(b)), cr);
+   BOOST_CHECK_EQUAL(normalize_compare_result(r2.compare(a)), -cr);
+}
+
+template <class Real, class Val>
+typename boost::enable_if_c<boost::multiprecision::number_category<Real>::value == boost::multiprecision::number_kind_complex>::type
+test_comparisons(Val a, Val b, const boost::mpl::true_)
+{
+   Real r1(a);
+   Real r2(b);
+   Real z(1);
+
+   int cr = a < b ? -1 : a > b ? 1 : 0;
+   (void)cr;
+
+   BOOST_CHECK_EQUAL(r1 == r2, a == b);
+   BOOST_CHECK_EQUAL(r1 != r2, a != b);
+
+   BOOST_CHECK_EQUAL(r1 == b, a == b);
+   BOOST_CHECK_EQUAL(r1 != b, a != b);
+
+   BOOST_CHECK_EQUAL(a == r2, a == b);
+   BOOST_CHECK_EQUAL(a != r2, a != b);
+
+   BOOST_CHECK_EQUAL(r1 * z == r2, a == b);
+   BOOST_CHECK_EQUAL(r1 * z != r2, a != b);
+
+   BOOST_CHECK_EQUAL(r1 == r2 * z, a == b);
+   BOOST_CHECK_EQUAL(r1 != r2 * z, a != b);
+
+   BOOST_CHECK_EQUAL(r1 * z == r2 * z, a == b);
+   BOOST_CHECK_EQUAL(r1 * z != r2 * z, a != b);
+
+   BOOST_CHECK_EQUAL(r1 * z == b, a == b);
+   BOOST_CHECK_EQUAL(r1 * z != b, a != b);
+
+   BOOST_CHECK_EQUAL(a == r2 * z, a == b);
+   BOOST_CHECK_EQUAL(a != r2 * z, a != b);
+
+   if (r1 == r2)
+   {
+      BOOST_CHECK_EQUAL(normalize_compare_result(r1.compare(r2)), 0);
+      BOOST_CHECK_EQUAL(normalize_compare_result(r2.compare(r1)), 0);
+      BOOST_CHECK_EQUAL(normalize_compare_result(r1.compare(b)), 0);
+      BOOST_CHECK_EQUAL(normalize_compare_result(r2.compare(a)), 0);
+   }
+   else
+   {
+      BOOST_CHECK_NE(normalize_compare_result(r1.compare(r2)), 0);
+      BOOST_CHECK_NE(normalize_compare_result(r2.compare(r1)), 0);
+      BOOST_CHECK_NE(normalize_compare_result(r1.compare(b)), 0);
+      BOOST_CHECK_NE(normalize_compare_result(r2.compare(a)), 0);
+   }
+}
+
+template <class Real, class Exp>
+void test_conditional(Real v, Exp e)
+{
+   //
+   // Verify that Exp is usable in Boolean contexts, and has the same value as v:
+   //
+   if (e)
+   {
+      BOOST_CHECK(v);
+   }
+   else
+   {
+      BOOST_CHECK(!v);
+   }
+   if (!e)
+   {
+      BOOST_CHECK(!v);
+   }
+   else
+   {
+      BOOST_CHECK(v);
+   }
+}
+
+template <class Real>
+void test_complement(Real a, Real b, Real c, const boost::mpl::true_&)
+{
+   int i         = 1020304;
+   int j         = 56789123;
+   int sign_mask = ~0;
+   if (std::numeric_limits<Real>::is_signed)
+   {
+      BOOST_CHECK_EQUAL(~a, (~i & sign_mask));
+      c = a & ~b;
+      BOOST_CHECK_EQUAL(c, (i & (~j & sign_mask)));
+      c = ~(a | b);
+      BOOST_CHECK_EQUAL(c, (~(i | j) & sign_mask));
+   }
+   else
+   {
+      BOOST_CHECK_EQUAL((~a & a), 0);
+   }
+}
+
+template <class Real>
+void test_complement(Real, Real, Real, const boost::mpl::false_&)
+{
+}
+
+template <class Real, class T>
+void test_integer_ops(const T&) {}
+
+template <class Real>
+void test_rational(const boost::mpl::true_&)
+{
+   Real a(2);
+   a /= 3;
+   BOOST_CHECK_EQUAL(numerator(a), 2);
+   BOOST_CHECK_EQUAL(denominator(a), 3);
+   Real b(4);
+   b /= 6;
+   BOOST_CHECK_EQUAL(a, b);
+
+   //
+   // Check IO code:
+   //
+   std::stringstream ss;
+   ss << a;
+   ss >> b;
+   BOOST_CHECK_EQUAL(a, b);
+}
+
+template <class Real>
+void test_rational(const boost::mpl::false_&)
+{
+   Real a(2);
+   a /= 3;
+   BOOST_CHECK_EQUAL(numerator(a), 2);
+   BOOST_CHECK_EQUAL(denominator(a), 3);
+   Real b(4);
+   b /= 6;
+   BOOST_CHECK_EQUAL(a, b);
+
+#ifndef BOOST_NO_EXCEPTIONS
+   BOOST_CHECK_THROW(Real(a / 0), std::overflow_error);
+   BOOST_CHECK_THROW(Real("3.14"), std::runtime_error);
+#endif
+   b = Real("2/3");
+   BOOST_CHECK_EQUAL(a, b);
+   //
+   // Check IO code:
+   //
+   std::stringstream ss;
+   ss << a;
+   ss >> b;
+   BOOST_CHECK_EQUAL(a, b);
+}
+
+template <class Real>
+void test_integer_ops(const boost::mpl::int_<boost::multiprecision::number_kind_rational>&)
+{
+   test_rational<Real>(is_boost_rational<Real>());
+}
+
+template <class Real>
+void test_signed_integer_ops(const boost::mpl::true_&)
+{
+   Real a(20);
+   Real b(7);
+   Real c(5);
+   BOOST_CHECK_EQUAL(-a % c, 0);
+   BOOST_CHECK_EQUAL(-a % b, -20 % 7);
+   BOOST_CHECK_EQUAL(-a % -b, -20 % -7);
+   BOOST_CHECK_EQUAL(a % -b, 20 % -7);
+   BOOST_CHECK_EQUAL(-a % 7, -20 % 7);
+   BOOST_CHECK_EQUAL(-a % -7, -20 % -7);
+   BOOST_CHECK_EQUAL(a % -7, 20 % -7);
+   BOOST_CHECK_EQUAL(-a % 7u, -20 % 7);
+   BOOST_CHECK_EQUAL(-a % a, 0);
+   BOOST_CHECK_EQUAL(-a % 5, 0);
+   BOOST_CHECK_EQUAL(-a % -5, 0);
+   BOOST_CHECK_EQUAL(a % -5, 0);
+
+   b = -b;
+   BOOST_CHECK_EQUAL(a % b, 20 % -7);
+   a = -a;
+   BOOST_CHECK_EQUAL(a % b, -20 % -7);
+   BOOST_CHECK_EQUAL(a % -7, -20 % -7);
+   b = 7;
+   BOOST_CHECK_EQUAL(a % b, -20 % 7);
+   BOOST_CHECK_EQUAL(a % 7, -20 % 7);
+   BOOST_CHECK_EQUAL(a % 7u, -20 % 7);
+
+   a = 20;
+   a %= b;
+   BOOST_CHECK_EQUAL(a, 20 % 7);
+   a = -20;
+   a %= b;
+   BOOST_CHECK_EQUAL(a, -20 % 7);
+   a = 20;
+   a %= -b;
+   BOOST_CHECK_EQUAL(a, 20 % -7);
+   a = -20;
+   a %= -b;
+   BOOST_CHECK_EQUAL(a, -20 % -7);
+   a = 5;
+   a %= b - a;
+   BOOST_CHECK_EQUAL(a, 5 % (7 - 5));
+   a = -20;
+   a %= 7;
+   BOOST_CHECK_EQUAL(a, -20 % 7);
+   a = 20;
+   a %= -7;
+   BOOST_CHECK_EQUAL(a, 20 % -7);
+   a = -20;
+   a %= -7;
+   BOOST_CHECK_EQUAL(a, -20 % -7);
+#ifndef BOOST_NO_LONG_LONG
+   a = -20;
+   a %= 7uLL;
+   BOOST_CHECK_EQUAL(a, -20 % 7);
+   a = 20;
+   a %= -7LL;
+   BOOST_CHECK_EQUAL(a, 20 % -7);
+   a = -20;
+   a %= -7LL;
+   BOOST_CHECK_EQUAL(a, -20 % -7);
+#endif
+   a = 400;
+   b = 45;
+   BOOST_CHECK_EQUAL(gcd(a, -45), boost::integer::gcd(400, 45));
+   BOOST_CHECK_EQUAL(lcm(a, -45), boost::integer::lcm(400, 45));
+   BOOST_CHECK_EQUAL(gcd(-400, b), boost::integer::gcd(400, 45));
+   BOOST_CHECK_EQUAL(lcm(-400, b), boost::integer::lcm(400, 45));
+   a = -20;
+   BOOST_CHECK_EQUAL(abs(a), 20);
+   BOOST_CHECK_EQUAL(abs(-a), 20);
+   BOOST_CHECK_EQUAL(abs(+a), 20);
+   a = 20;
+   BOOST_CHECK_EQUAL(abs(a), 20);
+   BOOST_CHECK_EQUAL(abs(-a), 20);
+   BOOST_CHECK_EQUAL(abs(+a), 20);
+   a = -400;
+   b = 45;
+   BOOST_CHECK_EQUAL(gcd(a, b), boost::integer::gcd(-400, 45));
+   BOOST_CHECK_EQUAL(lcm(a, b), boost::integer::lcm(-400, 45));
+   BOOST_CHECK_EQUAL(gcd(a, 45), boost::integer::gcd(-400, 45));
+   BOOST_CHECK_EQUAL(lcm(a, 45), boost::integer::lcm(-400, 45));
+   BOOST_CHECK_EQUAL(gcd(-400, b), boost::integer::gcd(-400, 45));
+   BOOST_CHECK_EQUAL(lcm(-400, b), boost::integer::lcm(-400, 45));
+   Real r;
+   divide_qr(a, b, c, r);
+   BOOST_CHECK_EQUAL(c, a / b);
+   BOOST_CHECK_EQUAL(r, a % b);
+   BOOST_CHECK_EQUAL(integer_modulus(a, 57), abs(a % 57));
+   b = -57;
+   divide_qr(a, b, c, r);
+   BOOST_CHECK_EQUAL(c, a / b);
+   BOOST_CHECK_EQUAL(r, a % b);
+   BOOST_CHECK_EQUAL(integer_modulus(a, -57), abs(a % -57));
+   a = 458;
+   divide_qr(a, b, c, r);
+   BOOST_CHECK_EQUAL(c, a / b);
+   BOOST_CHECK_EQUAL(r, a % b);
+   BOOST_CHECK_EQUAL(integer_modulus(a, -57), abs(a % -57));
+#ifndef TEST_CHECKED_INT
+   if (is_checked_cpp_int<Real>::value)
+   {
+      a = -1;
+#ifndef BOOST_NO_EXCEPTIONS
+      BOOST_CHECK_THROW(a << 2, std::range_error);
+      BOOST_CHECK_THROW(a >> 2, std::range_error);
+      BOOST_CHECK_THROW(a <<= 2, std::range_error);
+      BOOST_CHECK_THROW(a >>= 2, std::range_error);
+#endif
+   }
+   else
+   {
+      a = -1;
+      BOOST_CHECK_EQUAL(a << 10, -1024);
+      a = -23;
+      BOOST_CHECK_EQUAL(a << 10, -23552);
+      a = -23456;
+      BOOST_CHECK_EQUAL(a >> 10, -23);
+      a = -3;
+      BOOST_CHECK_EQUAL(a >> 10, -1);
+   }
+#endif
+}
+template <class Real>
+void test_signed_integer_ops(const boost::mpl::false_&)
+{
+}
+
+template <class Real>
+inline Real negate_if_signed(Real r, const boost::mpl::bool_<true>&)
+{
+   return -r;
+}
+template <class Real>
+inline Real negate_if_signed(Real r, const boost::mpl::bool_<false>&)
+{
+   return r;
+}
+
+template <class Real, class Int>
+void test_integer_overflow()
+{
+   if (std::numeric_limits<Real>::digits > std::numeric_limits<Int>::digits)
+   {
+      Real m((std::numeric_limits<Int>::max)());
+      Int  r;
+      ++m;
+      if (is_checked_cpp_int<Real>::value)
+      {
+         BOOST_CHECK_THROW(m.template convert_to<Int>(), std::overflow_error);
+      }
+      else if (boost::is_signed<Int>::value)
+      {
+         r = m.template convert_to<Int>();
+         BOOST_CHECK_EQUAL(r, (std::numeric_limits<Int>::max)());
+      }
+      else
+      {
+         r = m.template convert_to<Int>();
+         BOOST_CHECK_EQUAL(r, 0);
+      }
+      // Again with much larger value:
+      m = 1u;
+      m <<= (std::min)(std::numeric_limits<Real>::digits - 1, 1000);
+      if (is_checked_cpp_int<Real>::value)
+      {
+         BOOST_CHECK_THROW(m.template convert_to<Int>(), std::overflow_error);
+      }
+      else if (boost::is_signed<Int>::value)
+      {
+         r = m.template convert_to<Int>();
+         BOOST_CHECK_EQUAL(r, (std::numeric_limits<Int>::max)());
+      }
+      else
+      {
+         r = m.template convert_to<Int>();
+         BOOST_CHECK_EQUAL(r, 0);
+      }
+
+      if (std::numeric_limits<Real>::is_signed && (boost::is_signed<Int>::value))
+      {
+         m = (std::numeric_limits<Int>::min)();
+         --m;
+         if (is_checked_cpp_int<Real>::value)
+         {
+            BOOST_CHECK_THROW(m.template convert_to<Int>(), std::overflow_error);
+         }
+         else
+         {
+            r = m.template convert_to<Int>();
+            BOOST_CHECK_EQUAL(r, (std::numeric_limits<Int>::min)());
+         }
+         // Again with much larger value:
+         m = 2u;
+         m = pow(m, (std::min)(std::numeric_limits<Real>::digits - 1, 1000));
+         ++m;
+         m = negate_if_signed(m, boost::mpl::bool_<std::numeric_limits<Real>::is_signed>());
+         if (is_checked_cpp_int<Real>::value)
+         {
+            BOOST_CHECK_THROW(m.template convert_to<Int>(), std::overflow_error);
+         }
+         else
+         {
+            r = m.template convert_to<Int>();
+            BOOST_CHECK_EQUAL(r, (std::numeric_limits<Int>::min)());
+         }
+      }
+      else if (std::numeric_limits<Real>::is_signed && !boost::is_signed<Int>::value)
+      {
+         // signed to unsigned converison with overflow, it's really not clear what should happen here!
+         m = (std::numeric_limits<Int>::max)();
+         ++m;
+         m = negate_if_signed(m, boost::mpl::bool_<std::numeric_limits<Real>::is_signed>());
+         BOOST_CHECK_THROW(m.template convert_to<Int>(), std::range_error);
+         // Again with much larger value:
+         m = 2u;
+         m = pow(m, (std::min)(std::numeric_limits<Real>::digits - 1, 1000));
+         m = negate_if_signed(m, boost::mpl::bool_<std::numeric_limits<Real>::is_signed>());
+         BOOST_CHECK_THROW(m.template convert_to<Int>(), std::range_error);
+      }
+   }
+}
+
+template <class Real, class Int>
+void test_integer_round_trip()
+{
+   if (std::numeric_limits<Real>::digits >= std::numeric_limits<Int>::digits)
+   {
+      Real m((std::numeric_limits<Int>::max)());
+      Int  r = m.template convert_to<Int>();
+      BOOST_CHECK_EQUAL(m, r);
+      if (std::numeric_limits<Real>::is_signed && (std::numeric_limits<Real>::digits > std::numeric_limits<Int>::digits))
+      {
+         m = (std::numeric_limits<Int>::min)();
+         r = m.template convert_to<Int>();
+         BOOST_CHECK_EQUAL(m, r);
+      }
+   }
+   test_integer_overflow<Real, Int>();
+}
+
+template <class Real>
+void test_integer_ops(const boost::mpl::int_<boost::multiprecision::number_kind_integer>&)
+{
+   test_signed_integer_ops<Real>(boost::mpl::bool_<std::numeric_limits<Real>::is_signed>());
+
+   Real a(20);
+   Real b(7);
+   Real c(5);
+   BOOST_CHECK_EQUAL(a % b, 20 % 7);
+   BOOST_CHECK_EQUAL(a % 7, 20 % 7);
+   BOOST_CHECK_EQUAL(a % 7u, 20 % 7);
+   BOOST_CHECK_EQUAL(a % a, 0);
+   BOOST_CHECK_EQUAL(a % c, 0);
+   BOOST_CHECK_EQUAL(a % 5, 0);
+   a = a % (b + 0);
+   BOOST_CHECK_EQUAL(a, 20 % 7);
+   a = 20;
+   c = (a + 2) % (a - 1);
+   BOOST_CHECK_EQUAL(c, 22 % 19);
+   c = 5;
+   a = b % (a - 15);
+   BOOST_CHECK_EQUAL(a, 7 % 5);
+   a = 20;
+
+   a = 20;
+   a %= 7;
+   BOOST_CHECK_EQUAL(a, 20 % 7);
+#ifndef BOOST_NO_LONG_LONG
+   a = 20;
+   a %= 7uLL;
+   BOOST_CHECK_EQUAL(a, 20 % 7);
+#endif
+   a = 20;
+   ++a;
+   BOOST_CHECK_EQUAL(a, 21);
+   --a;
+   BOOST_CHECK_EQUAL(a, 20);
+   BOOST_CHECK_EQUAL(a++, 20);
+   BOOST_CHECK_EQUAL(a, 21);
+   BOOST_CHECK_EQUAL(a--, 21);
+   BOOST_CHECK_EQUAL(a, 20);
+   a = 2000;
+   a <<= 20;
+   BOOST_CHECK_EQUAL(a, 2000L << 20);
+   a >>= 20;
+   BOOST_CHECK_EQUAL(a, 2000);
+   a <<= 20u;
+   BOOST_CHECK_EQUAL(a, 2000L << 20);
+   a >>= 20u;
+   BOOST_CHECK_EQUAL(a, 2000);
+#ifndef BOOST_NO_EXCEPTIONS
+   BOOST_CHECK_THROW(a <<= -20, std::out_of_range);
+   BOOST_CHECK_THROW(a >>= -20, std::out_of_range);
+   BOOST_CHECK_THROW(Real(a << -20), std::out_of_range);
+   BOOST_CHECK_THROW(Real(a >> -20), std::out_of_range);
+#endif
+#ifndef BOOST_NO_LONG_LONG
+   if (sizeof(long long) > sizeof(std::size_t))
+   {
+      // extreme values should trigger an exception:
+#ifndef BOOST_NO_EXCEPTIONS
+      BOOST_CHECK_THROW(a >>= (1uLL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range);
+      BOOST_CHECK_THROW(a <<= (1uLL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range);
+      BOOST_CHECK_THROW(a >>= -(1LL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range);
+      BOOST_CHECK_THROW(a <<= -(1LL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range);
+      BOOST_CHECK_THROW(a >>= (1LL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range);
+      BOOST_CHECK_THROW(a <<= (1LL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range);
+#endif
+      // Unless they fit within range:
+      a = 2000L;
+      a <<= 20uLL;
+      BOOST_CHECK_EQUAL(a, (2000L << 20));
+      a = 2000;
+      a <<= 20LL;
+      BOOST_CHECK_EQUAL(a, (2000L << 20));
+
+#ifndef BOOST_NO_EXCEPTIONS
+      BOOST_CHECK_THROW(Real(a >> (1uLL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range);
+      BOOST_CHECK_THROW(Real(a <<= (1uLL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range);
+      BOOST_CHECK_THROW(Real(a >>= -(1LL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range);
+      BOOST_CHECK_THROW(Real(a <<= -(1LL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range);
+      BOOST_CHECK_THROW(Real(a >>= (1LL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range);
+      BOOST_CHECK_THROW(Real(a <<= (1LL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range);
+#endif
+      // Unless they fit within range:
+      a = 2000L;
+      BOOST_CHECK_EQUAL(Real(a << 20uLL), (2000L << 20));
+      a = 2000;
+      BOOST_CHECK_EQUAL(Real(a << 20LL), (2000L << 20));
+   }
+#endif
+   a = 20;
+   b = a << 20;
+   BOOST_CHECK_EQUAL(b, (20 << 20));
+   b = a >> 2;
+   BOOST_CHECK_EQUAL(b, (20 >> 2));
+   b = (a + 2) << 10;
+   BOOST_CHECK_EQUAL(b, (22 << 10));
+   b = (a + 3) >> 3;
+   BOOST_CHECK_EQUAL(b, (23 >> 3));
+   //
+   // Bit fiddling:
+   //
+   int i = 1020304;
+   int j = 56789123;
+   int k = 4523187;
+   a     = i;
+   b     = j;
+   c     = a;
+   c &= b;
+   BOOST_CHECK_EQUAL(c, (i & j));
+   c = a;
+   c &= j;
+   BOOST_CHECK_EQUAL(c, (i & j));
+   c = a;
+   c &= a + b;
+   BOOST_CHECK_EQUAL(c, (i & (i + j)));
+   BOOST_CHECK_EQUAL((a & b), (i & j));
+   c = k;
+   a = a & (b + k);
+   BOOST_CHECK_EQUAL(a, (i & (j + k)));
+   a = i;
+   a = (b + k) & a;
+   BOOST_CHECK_EQUAL(a, (i & (j + k)));
+   a = i;
+   c = a & b & k;
+   BOOST_CHECK_EQUAL(c, (i & j & k));
+   c = a;
+   c &= (c + b);
+   BOOST_CHECK_EQUAL(c, (i & (i + j)));
+   c = a & (b | 1);
+   BOOST_CHECK_EQUAL(c, (i & (j | 1)));
+
+   test_complement<Real>(a, b, c, typename is_twos_complement_integer<Real>::type());
+
+   a = i;
+   b = j;
+   c = a;
+   c |= b;
+   BOOST_CHECK_EQUAL(c, (i | j));
+   c = a;
+   c |= j;
+   BOOST_CHECK_EQUAL(c, (i | j));
+   c = a;
+   c |= a + b;
+   BOOST_CHECK_EQUAL(c, (i | (i + j)));
+   BOOST_CHECK_EQUAL((a | b), (i | j));
+   c = k;
+   a = a | (b + k);
+   BOOST_CHECK_EQUAL(a, (i | (j + k)));
+   a = i;
+   a = (b + k) | a;
+   BOOST_CHECK_EQUAL(a, (i | (j + k)));
+   a = i;
+   c = a | b | k;
+   BOOST_CHECK_EQUAL(c, (i | j | k));
+   c = a;
+   c |= (c + b);
+   BOOST_CHECK_EQUAL(c, (i | (i + j)));
+   c = a | (b | 1);
+   BOOST_CHECK_EQUAL(c, (i | (j | 1)));
+
+   a = i;
+   b = j;
+   c = a;
+   c ^= b;
+   BOOST_CHECK_EQUAL(c, (i ^ j));
+   c = a;
+   c ^= j;
+   BOOST_CHECK_EQUAL(c, (i ^ j));
+   c = a;
+   c ^= a + b;
+   BOOST_CHECK_EQUAL(c, (i ^ (i + j)));
+   BOOST_CHECK_EQUAL((a ^ b), (i ^ j));
+   c = k;
+   a = a ^ (b + k);
+   BOOST_CHECK_EQUAL(a, (i ^ (j + k)));
+   a = i;
+   a = (b + k) ^ a;
+   BOOST_CHECK_EQUAL(a, (i ^ (j + k)));
+   a = i;
+   c = a ^ b ^ k;
+   BOOST_CHECK_EQUAL(c, (i ^ j ^ k));
+   c = a;
+   c ^= (c + b);
+   BOOST_CHECK_EQUAL(c, (i ^ (i + j)));
+   c = a ^ (b | 1);
+   BOOST_CHECK_EQUAL(c, (i ^ (j | 1)));
+
+   a = i;
+   b = j;
+   c = k;
+   //
+   // Non-member functions:
+   //
+   a = 400;
+   b = 45;
+   BOOST_CHECK_EQUAL(gcd(a, b), boost::integer::gcd(400, 45));
+   BOOST_CHECK_EQUAL(lcm(a, b), boost::integer::lcm(400, 45));
+   BOOST_CHECK_EQUAL(gcd(a, 45), boost::integer::gcd(400, 45));
+   BOOST_CHECK_EQUAL(lcm(a, 45), boost::integer::lcm(400, 45));
+   BOOST_CHECK_EQUAL(gcd(a, 45u), boost::integer::gcd(400, 45));
+   BOOST_CHECK_EQUAL(lcm(a, 45u), boost::integer::lcm(400, 45));
+   BOOST_CHECK_EQUAL(gcd(400, b), boost::integer::gcd(400, 45));
+   BOOST_CHECK_EQUAL(lcm(400, b), boost::integer::lcm(400, 45));
+   BOOST_CHECK_EQUAL(gcd(400u, b), boost::integer::gcd(400, 45));
+   BOOST_CHECK_EQUAL(lcm(400u, b), boost::integer::lcm(400, 45));
+
+   //
+   // Conditionals involving 2 arg functions:
+   //
+   test_conditional(Real(gcd(a, b)), gcd(a, b));
+
+   Real r;
+   divide_qr(a, b, c, r);
+   BOOST_CHECK_EQUAL(c, a / b);
+   BOOST_CHECK_EQUAL(r, a % b);
+   divide_qr(a + 0, b, c, r);
+   BOOST_CHECK_EQUAL(c, a / b);
+   BOOST_CHECK_EQUAL(r, a % b);
+   divide_qr(a, b + 0, c, r);
+   BOOST_CHECK_EQUAL(c, a / b);
+   BOOST_CHECK_EQUAL(r, a % b);
+   divide_qr(a + 0, b + 0, c, r);
+   BOOST_CHECK_EQUAL(c, a / b);
+   BOOST_CHECK_EQUAL(r, a % b);
+   BOOST_CHECK_EQUAL(integer_modulus(a, 57), a % 57);
+   for (i = 0; i < 20; ++i)
+   {
+      if (std::numeric_limits<Real>::is_specialized && (!std::numeric_limits<Real>::is_bounded || ((int)i * 17 < std::numeric_limits<Real>::digits)))
+      {
+         BOOST_CHECK_EQUAL(lsb(Real(1) << (i * 17)), static_cast<unsigned>(i * 17));
+         BOOST_CHECK_EQUAL(msb(Real(1) << (i * 17)), static_cast<unsigned>(i * 17));
+         BOOST_CHECK(bit_test(Real(1) << (i * 17), i * 17));
+         BOOST_CHECK(!bit_test(Real(1) << (i * 17), i * 17 + 1));
+         if (i)
+         {
+            BOOST_CHECK(!bit_test(Real(1) << (i * 17), i * 17 - 1));
+         }
+         Real zero(0);
+         BOOST_CHECK(bit_test(bit_set(zero, i * 17), i * 17));
+         zero = 0;
+         BOOST_CHECK_EQUAL(bit_flip(zero, i * 17), Real(1) << i * 17);
+         zero = Real(1) << i * 17;
+         BOOST_CHECK_EQUAL(bit_flip(zero, i * 17), 0);
+         zero = Real(1) << i * 17;
+         BOOST_CHECK_EQUAL(bit_unset(zero, i * 17), 0);
+      }
+   }
+   //
+   // pow, powm:
+   //
+   BOOST_CHECK_EQUAL(pow(Real(3), 4u), 81);
+   BOOST_CHECK_EQUAL(pow(Real(3) + Real(0), 4u), 81);
+   BOOST_CHECK_EQUAL(powm(Real(3), Real(4), Real(13)), 81 % 13);
+   BOOST_CHECK_EQUAL(powm(Real(3), Real(4), 13), 81 % 13);
+   BOOST_CHECK_EQUAL(powm(Real(3), Real(4), Real(13) + 0), 81 % 13);
+   BOOST_CHECK_EQUAL(powm(Real(3), Real(4) + 0, Real(13)), 81 % 13);
+   BOOST_CHECK_EQUAL(powm(Real(3), Real(4) + 0, 13), 81 % 13);
+   BOOST_CHECK_EQUAL(powm(Real(3), Real(4) + 0, Real(13) + 0), 81 % 13);
+   BOOST_CHECK_EQUAL(powm(Real(3), 4 + 0, Real(13)), 81 % 13);
+   BOOST_CHECK_EQUAL(powm(Real(3), 4 + 0, 13), 81 % 13);
+   BOOST_CHECK_EQUAL(powm(Real(3), 4 + 0, Real(13) + 0), 81 % 13);
+   BOOST_CHECK_EQUAL(powm(Real(3) + 0, Real(4), Real(13)), 81 % 13);
+   BOOST_CHECK_EQUAL(powm(Real(3) + 0, Real(4), 13), 81 % 13);
+   BOOST_CHECK_EQUAL(powm(Real(3) + 0, Real(4), Real(13) + 0), 81 % 13);
+   BOOST_CHECK_EQUAL(powm(Real(3) + 0, Real(4) + 0, Real(13)), 81 % 13);
+   BOOST_CHECK_EQUAL(powm(Real(3) + 0, Real(4) + 0, 13), 81 % 13);
+   BOOST_CHECK_EQUAL(powm(Real(3) + 0, Real(4) + 0, Real(13) + 0), 81 % 13);
+   BOOST_CHECK_EQUAL(powm(Real(3) + 0, 4 + 0, Real(13)), 81 % 13);
+   BOOST_CHECK_EQUAL(powm(Real(3) + 0, 4 + 0, 13), 81 % 13);
+   BOOST_CHECK_EQUAL(powm(Real(3) + 0, 4 + 0, Real(13) + 0), 81 % 13);
+   //
+   // Conditionals involving 3 arg functions:
+   //
+   test_conditional(Real(powm(Real(3), Real(4), Real(13))), powm(Real(3), Real(4), Real(13)));
+
+#ifndef BOOST_NO_EXCEPTIONS
+   //
+   // Things that are expected errors:
+   //
+   BOOST_CHECK_THROW(Real("3.14"), std::runtime_error);
+   BOOST_CHECK_THROW(Real("3L"), std::runtime_error);
+   BOOST_CHECK_THROW(Real(Real(20) / 0u), std::overflow_error);
+#endif
+   //
+   // Extra tests added for full coverage:
+   //
+   a = 20;
+   b = 7;
+   c = 20 % b;
+   BOOST_CHECK_EQUAL(c, (20 % 7));
+   c = 20 % (b + 0);
+   BOOST_CHECK_EQUAL(c, (20 % 7));
+   c = a & 10;
+   BOOST_CHECK_EQUAL(c, (20 & 10));
+   c = 10 & a;
+   BOOST_CHECK_EQUAL(c, (20 & 10));
+   c = (a + 0) & (b + 0);
+   BOOST_CHECK_EQUAL(c, (20 & 7));
+   c = 10 & (a + 0);
+   BOOST_CHECK_EQUAL(c, (20 & 10));
+   c = 10 | a;
+   BOOST_CHECK_EQUAL(c, (20 | 10));
+   c = (a + 0) | (b + 0);
+   BOOST_CHECK(c == (20 | 7))
+   c = 20 | (b + 0);
+   BOOST_CHECK_EQUAL(c, (20 | 7));
+   c = a ^ 7;
+   BOOST_CHECK_EQUAL(c, (20 ^ 7));
+   c = 20 ^ b;
+   BOOST_CHECK_EQUAL(c, (20 ^ 7));
+   c = (a + 0) ^ (b + 0);
+   BOOST_CHECK_EQUAL(c, (20 ^ 7));
+   c = 20 ^ (b + 0);
+   BOOST_CHECK_EQUAL(c, (20 ^ 7));
+
+   //
+   // Round tripping of built in integers:
+   //
+   test_integer_round_trip<Real, short>();
+   test_integer_round_trip<Real, unsigned short>();
+   test_integer_round_trip<Real, int>();
+   test_integer_round_trip<Real, unsigned int>();
+   test_integer_round_trip<Real, long>();
+   test_integer_round_trip<Real, unsigned long>();
+#ifndef BOOST_NO_CXX11_LONG_LONG
+   test_integer_round_trip<Real, long long>();
+   test_integer_round_trip<Real, unsigned long long>();
+#endif
+}
+
+template <class Real, class T>
+void test_float_funcs(const T&) {}
+
+template <class Real>
+void test_float_funcs(const boost::mpl::true_&)
+{
+   if (boost::multiprecision::is_interval_number<Real>::value)
+      return;
+   //
+   // Test variable reuse in function calls, see https://svn.boost.org/trac/boost/ticket/8326
+   //
+   Real a(2), b(10), c, d;
+   a = pow(a, b);
+   BOOST_CHECK_EQUAL(a, 1024);
+   a = 2;
+   b = pow(a, b);
+   BOOST_CHECK_EQUAL(b, 1024);
+   b = 10;
+   a = pow(a, 10);
+   BOOST_CHECK_EQUAL(a, 1024);
+   a = -2;
+   a = abs(a);
+   BOOST_CHECK_EQUAL(a, 2);
+   a = -2;
+   a = fabs(a);
+   BOOST_CHECK_EQUAL(a, 2);
+   a = 2.5;
+   a = floor(a);
+   BOOST_CHECK_EQUAL(a, 2);
+   a = 2.5;
+   a = ceil(a);
+   BOOST_CHECK_EQUAL(a, 3);
+   a = 2.5;
+   a = trunc(a);
+   BOOST_CHECK_EQUAL(a, 2);
+   a = 2.25;
+   a = round(a);
+   BOOST_CHECK_EQUAL(a, 2);
+   a = 2;
+   a = ldexp(a, 1);
+   BOOST_CHECK_EQUAL(a, 4);
+   int i;
+   a = frexp(a, &i);
+   BOOST_CHECK_EQUAL(a, 0.5);
+
+   Real tol = std::numeric_limits<Real>::epsilon() * 3;
+   a        = 4;
+   a        = sqrt(a);
+   BOOST_CHECK_CLOSE_FRACTION(a, 2, tol);
+   a = 3;
+   a = exp(a);
+   BOOST_CHECK_CLOSE_FRACTION(a, Real(exp(Real(3))), tol);
+   a = 3;
+   a = log(a);
+   BOOST_CHECK_CLOSE_FRACTION(a, Real(log(Real(3))), tol);
+   a = 3;
+   a = log10(a);
+   BOOST_CHECK_CLOSE_FRACTION(a, Real(log10(Real(3))), tol);
+
+   a = 0.5;
+   a = sin(a);
+   BOOST_CHECK_CLOSE_FRACTION(a, Real(sin(Real(0.5))), tol);
+   a = 0.5;
+   a = cos(a);
+   BOOST_CHECK_CLOSE_FRACTION(a, Real(cos(Real(0.5))), tol);
+   a = 0.5;
+   a = tan(a);
+   BOOST_CHECK_CLOSE_FRACTION(a, Real(tan(Real(0.5))), tol);
+   a = 0.5;
+   a = asin(a);
+   BOOST_CHECK_CLOSE_FRACTION(a, Real(asin(Real(0.5))), tol);
+   a = 0.5;
+   a = acos(a);
+   BOOST_CHECK_CLOSE_FRACTION(a, Real(acos(Real(0.5))), tol);
+   a = 0.5;
+   a = atan(a);
+   BOOST_CHECK_CLOSE_FRACTION(a, Real(atan(Real(0.5))), tol);
+   a = 0.5;
+   a = sinh(a);
+   BOOST_CHECK_CLOSE_FRACTION(a, Real(sinh(Real(0.5))), tol);
+   a = 0.5;
+   a = cosh(a);
+   BOOST_CHECK_CLOSE_FRACTION(a, Real(cosh(Real(0.5))), tol);
+   a = 0.5;
+   a = tanh(a);
+   BOOST_CHECK_CLOSE_FRACTION(a, Real(tanh(Real(0.5))), tol);
+   // fmod, need to check all the sign permutations:
+   a = 4;
+   b = 2;
+   a = fmod(a, b);
+   BOOST_CHECK_CLOSE_FRACTION(a, Real(fmod(Real(4), Real(2))), tol);
+   a = 4;
+   b = fmod(a, b);
+   BOOST_CHECK_CLOSE_FRACTION(b, Real(fmod(Real(4), Real(2))), tol);
+   a = 4;
+   b = 2;
+   a = fmod(-a, b);
+   BOOST_CHECK_CLOSE_FRACTION(a, Real(fmod(-Real(4), Real(2))), tol);
+   a = 4;
+   b = fmod(-a, b);
+   BOOST_CHECK_CLOSE_FRACTION(b, Real(-fmod(Real(4), Real(2))), tol);
+   a = 4;
+   b = 2;
+   a = fmod(a, -b);
+   BOOST_CHECK_CLOSE_FRACTION(a, Real(fmod(Real(4), -Real(2))), tol);
+   a = 4;
+   b = fmod(a, -b);
+   BOOST_CHECK_CLOSE_FRACTION(b, Real(fmod(Real(4), -Real(2))), tol);
+   a = 4;
+   b = 2;
+   a = fmod(-a, -b);
+   BOOST_CHECK_CLOSE_FRACTION(a, Real(fmod(-Real(4), -Real(2))), tol);
+   a = 4;
+   b = fmod(-a, -b);
+   BOOST_CHECK_CLOSE_FRACTION(b, Real(fmod(-Real(4), -Real(2))), tol);
+   // modf:
+   a = 5;
+   a /= 2;
+   b = modf(a, &c);
+   BOOST_CHECK_EQUAL(b + c, a);
+   BOOST_CHECK_EQUAL(b > 0, a > 0);
+   BOOST_CHECK_EQUAL(c > 0, a > 0);
+   a = -a;
+   b = modf(a, &c);
+   BOOST_CHECK_EQUAL(b + c, a);
+   BOOST_CHECK_EQUAL(b > 0, a > 0);
+   BOOST_CHECK_EQUAL(c > 0, a > 0);
+   b = modf(a, &c);
+   c = 0;
+   modf(a, &c);
+   BOOST_CHECK_EQUAL(b + c, a);
+   BOOST_CHECK_EQUAL(b > 0, a > 0);
+   BOOST_CHECK_EQUAL(c > 0, a > 0);
+   a = -a;
+   b = modf(a, &c);
+   c = 0;
+   modf(a, &c);
+   BOOST_CHECK_EQUAL(b + c, a);
+   BOOST_CHECK_EQUAL(b > 0, a > 0);
+   BOOST_CHECK_EQUAL(c > 0, a > 0);
+
+   if (std::numeric_limits<Real>::has_infinity)
+   {
+      a = std::numeric_limits<Real>::infinity();
+      b = modf(a, &c);
+      BOOST_CHECK_EQUAL(a, c);
+      BOOST_CHECK_EQUAL(b, 0);
+      a = -std::numeric_limits<Real>::infinity();
+      b = modf(a, &c);
+      BOOST_CHECK_EQUAL(a, c);
+      BOOST_CHECK_EQUAL(b, 0);
+   }
+   if (std::numeric_limits<Real>::has_quiet_NaN)
+   {
+      a = std::numeric_limits<Real>::quiet_NaN();
+      b = modf(a, &c);
+      BOOST_CHECK((boost::math::isnan)(b));
+      BOOST_CHECK((boost::math::isnan)(c));
+   }
+
+   a = 4;
+   b = 2;
+   a = atan2(a, b);
+   BOOST_CHECK_CLOSE_FRACTION(a, Real(atan2(Real(4), Real(2))), tol);
+   a = 4;
+   b = atan2(a, b);
+   BOOST_CHECK_CLOSE_FRACTION(b, Real(atan2(Real(4), Real(2))), tol);
+
+   // fma:
+   a = 2;
+   b = 4;
+   c = 6;
+   BOOST_CHECK_EQUAL(fma(a, b, c), 14);
+   BOOST_CHECK_EQUAL(fma(a, 4, c), 14);
+   BOOST_CHECK_EQUAL(fma(a, b, 6), 14);
+   BOOST_CHECK_EQUAL(fma(a, 4, 6), 14);
+   BOOST_CHECK_EQUAL(fma(a + 0, b, c), 14);
+   BOOST_CHECK_EQUAL(fma(a - 0, 4, c), 14);
+   BOOST_CHECK_EQUAL(fma(a * 1, b, 6), 14);
+   BOOST_CHECK_EQUAL(fma(a / 1, 4, 6), 14);
+   BOOST_CHECK_EQUAL(fma(2, b, c), 14);
+   BOOST_CHECK_EQUAL(fma(2, b, 6), 14);
+   BOOST_CHECK_EQUAL(fma(2, b * 1, c), 14);
+   BOOST_CHECK_EQUAL(fma(2, b + 0, 6), 14);
+   BOOST_CHECK_EQUAL(fma(2, 4, c), 14);
+   BOOST_CHECK_EQUAL(fma(2, 4, c + 0), 14);
+
+   // Default construct, for consistency with native floats, default constructed values are zero:
+   Real zero;
+   BOOST_CHECK_EQUAL(zero, 0);
+
+   //
+   // Complex number functions on scalars:
+   //
+   a = 40;
+   BOOST_CHECK_EQUAL(Real(arg(a)), 0);
+   BOOST_CHECK_EQUAL(Real(arg(a + 0)), 0);
+   a - 20;
+   BOOST_CHECK_EQUAL(Real(arg(a)), 0);
+   BOOST_CHECK_EQUAL(Real(arg(a - 20)), 0);
+}
+
+template <class T, class U>
+void compare_NaNs(const T& a, const U& b)
+{
+   BOOST_CHECK_EQUAL(a == b, false);
+   BOOST_CHECK_EQUAL(a != b, true);
+   BOOST_CHECK_EQUAL(a <= b, false);
+   BOOST_CHECK_EQUAL(a >= b, false);
+   BOOST_CHECK_EQUAL(a > b, false);
+   BOOST_CHECK_EQUAL(a < b, false);
+   //
+   // Again where LHS may be an expression template:
+   //
+   BOOST_CHECK_EQUAL(1 * a == b, false);
+   BOOST_CHECK_EQUAL(1 * a != b, true);
+   BOOST_CHECK_EQUAL(1 * a <= b, false);
+   BOOST_CHECK_EQUAL(1 * a >= b, false);
+   BOOST_CHECK_EQUAL(1 * a > b, false);
+   BOOST_CHECK_EQUAL(1 * a < b, false);
+   //
+   // Again where RHS may be an expression template:
+   //
+   BOOST_CHECK_EQUAL(a == b * 1, false);
+   BOOST_CHECK_EQUAL(a != b * 1, true);
+   BOOST_CHECK_EQUAL(a <= b * 1, false);
+   BOOST_CHECK_EQUAL(a >= b * 1, false);
+   BOOST_CHECK_EQUAL(a > b * 1, false);
+   BOOST_CHECK_EQUAL(a < b * 1, false);
+   //
+   // Again where LHS and RHS may be an expression templates:
+   //
+   BOOST_CHECK_EQUAL(1 * a == b * 1, false);
+   BOOST_CHECK_EQUAL(1 * a != b * 1, true);
+   BOOST_CHECK_EQUAL(1 * a <= b * 1, false);
+   BOOST_CHECK_EQUAL(1 * a >= b * 1, false);
+   BOOST_CHECK_EQUAL(1 * a > b * 1, false);
+   BOOST_CHECK_EQUAL(1 * a < b * 1, false);
+}
+
+template <class Real, class T>
+void test_float_ops(const T&) {}
+
+template <class Real>
+void test_float_ops(const boost::mpl::int_<boost::multiprecision::number_kind_floating_point>&)
+{
+   BOOST_CHECK_EQUAL(abs(Real(2)), 2);
+   BOOST_CHECK_EQUAL(abs(Real(-2)), 2);
+   BOOST_CHECK_EQUAL(fabs(Real(2)), 2);
+   BOOST_CHECK_EQUAL(fabs(Real(-2)), 2);
+   BOOST_CHECK_EQUAL(floor(Real(5) / 2), 2);
+   BOOST_CHECK_EQUAL(ceil(Real(5) / 2), 3);
+   BOOST_CHECK_EQUAL(floor(Real(-5) / 2), -3);
+   BOOST_CHECK_EQUAL(ceil(Real(-5) / 2), -2);
+   BOOST_CHECK_EQUAL(trunc(Real(5) / 2), 2);
+   BOOST_CHECK_EQUAL(trunc(Real(-5) / 2), -2);
+   //
+   // ldexp and frexp, these pretty much have to be implemented by each backend:
+   //
+   typedef typename Real::backend_type::exponent_type e_type;
+   BOOST_CHECK_EQUAL(ldexp(Real(2), 5), 64);
+   BOOST_CHECK_EQUAL(ldexp(Real(2), -5), Real(2) / 32);
+   Real   v(512);
+   e_type exponent;
+   Real   r = frexp(v, &exponent);
+   BOOST_CHECK_EQUAL(r, 0.5);
+   BOOST_CHECK_EQUAL(exponent, 10);
+   BOOST_CHECK_EQUAL(v, 512);
+   v = 1 / v;
+   r = frexp(v, &exponent);
+   BOOST_CHECK_EQUAL(r, 0.5);
+   BOOST_CHECK_EQUAL(exponent, -8);
+   BOOST_CHECK_EQUAL(ldexp(Real(2), e_type(5)), 64);
+   BOOST_CHECK_EQUAL(ldexp(Real(2), e_type(-5)), Real(2) / 32);
+   v = 512;
+   e_type exp2;
+   r = frexp(v, &exp2);
+   BOOST_CHECK_EQUAL(r, 0.5);
+   BOOST_CHECK_EQUAL(exp2, 10);
+   BOOST_CHECK_EQUAL(v, 512);
+   v = 1 / v;
+   r = frexp(v, &exp2);
+   BOOST_CHECK_EQUAL(r, 0.5);
+   BOOST_CHECK_EQUAL(exp2, -8);
+   //
+   // scalbn and logb, these are the same as ldexp and frexp unless the radix is
+   // something other than 2:
+   //
+   if (std::numeric_limits<Real>::is_specialized && std::numeric_limits<Real>::radix)
+   {
+      BOOST_CHECK_EQUAL(scalbn(Real(2), 5), 2 * pow(double(std::numeric_limits<Real>::radix), 5));
+      BOOST_CHECK_EQUAL(scalbn(Real(2), -5), Real(2) / pow(double(std::numeric_limits<Real>::radix), 5));
+      v        = 512;
+      exponent = ilogb(v);
+      r        = scalbn(v, -exponent);
+      BOOST_CHECK(r >= 1);
+      BOOST_CHECK(r < std::numeric_limits<Real>::radix);
+      BOOST_CHECK_EQUAL(exponent, logb(v));
+      BOOST_CHECK_EQUAL(v, scalbn(r, exponent));
+      v        = 1 / v;
+      exponent = ilogb(v);
+      r        = scalbn(v, -exponent);
+      BOOST_CHECK(r >= 1);
+      BOOST_CHECK(r < std::numeric_limits<Real>::radix);
+      BOOST_CHECK_EQUAL(exponent, logb(v));
+      BOOST_CHECK_EQUAL(v, scalbn(r, exponent));
+   }
+   //
+   // pow and exponent:
+   //
+   v = 3.25;
+   r = pow(v, 0);
+   BOOST_CHECK_EQUAL(r, 1);
+   r = pow(v, 1);
+   BOOST_CHECK_EQUAL(r, 3.25);
+   r = pow(v, 2);
+   BOOST_CHECK_EQUAL(r, boost::math::pow<2>(3.25));
+   r = pow(v, 3);
+   BOOST_CHECK_EQUAL(r, boost::math::pow<3>(3.25));
+   r = pow(v, 4);
+   BOOST_CHECK_EQUAL(r, boost::math::pow<4>(3.25));
+   r = pow(v, 5);
+   BOOST_CHECK_EQUAL(r, boost::math::pow<5>(3.25));
+   r = pow(v, 6);
+   BOOST_CHECK_EQUAL(r, boost::math::pow<6>(3.25));
+   r = pow(v, 25);
+   BOOST_CHECK_EQUAL(r, boost::math::pow<25>(Real(3.25)));
+
+#ifndef BOOST_NO_EXCEPTIONS
+   //
+   // Things that are expected errors:
+   //
+   BOOST_CHECK_THROW(Real("3.14L"), std::runtime_error);
+   if (std::numeric_limits<Real>::is_specialized)
+   {
+      if (std::numeric_limits<Real>::has_infinity)
+      {
+         BOOST_CHECK((boost::math::isinf)(Real(20) / 0u));
+      }
+      else
+      {
+         BOOST_CHECK_THROW(r = Real(Real(20) / 0u), std::overflow_error);
+      }
+   }
+#endif
+   //
+   // Comparisons of NaN's should always fail:
+   //
+   if (std::numeric_limits<Real>::has_quiet_NaN)
+   {
+      r = v = std::numeric_limits<Real>::quiet_NaN();
+      compare_NaNs(r, v);
+      v = 0;
+      compare_NaNs(r, v);
+      r.swap(v);
+      compare_NaNs(r, v);
+      //
+      // Conmpare NaN to int:
+      //
+      compare_NaNs(v, 0);
+      compare_NaNs(0, v);
+      //
+      // Compare to floats:
+      //
+      compare_NaNs(v, 0.5);
+      compare_NaNs(0.5, v);
+      if (std::numeric_limits<double>::has_quiet_NaN)
+      {
+         compare_NaNs(r, std::numeric_limits<double>::quiet_NaN());
+         compare_NaNs(std::numeric_limits<double>::quiet_NaN(), r);
+      }
+   }
+
+   //
+   // Operations involving NaN's as one argument:
+   //
+   if (std::numeric_limits<Real>::has_quiet_NaN)
+   {
+      v = 20.25;
+      r = std::numeric_limits<Real>::quiet_NaN();
+      BOOST_CHECK((boost::math::isnan)(v + r));
+      BOOST_CHECK((boost::math::isnan)(r + v));
+      BOOST_CHECK((boost::math::isnan)(r - v));
+      BOOST_CHECK((boost::math::isnan)(v - r));
+      BOOST_CHECK((boost::math::isnan)(r * v));
+      BOOST_CHECK((boost::math::isnan)(v * r));
+      BOOST_CHECK((boost::math::isnan)(r / v));
+      BOOST_CHECK((boost::math::isnan)(v / r));
+      Real t = v;
+      BOOST_CHECK((boost::math::isnan)(t += r));
+      t = r;
+      BOOST_CHECK((boost::math::isnan)(t += v));
+      t = r;
+      BOOST_CHECK((boost::math::isnan)(t -= v));
+      t = v;
+      BOOST_CHECK((boost::math::isnan)(t -= r));
+      t = r;
+      BOOST_CHECK((boost::math::isnan)(t *= v));
+      t = v;
+      BOOST_CHECK((boost::math::isnan)(t *= r));
+      t = r;
+      BOOST_CHECK((boost::math::isnan)(t /= v));
+      t = v;
+      BOOST_CHECK((boost::math::isnan)(t /= r));
+   }
+   //
+   // Operations involving infinities as one argument:
+   //
+   if (std::numeric_limits<Real>::has_infinity)
+   {
+      v = 20.25;
+      r = std::numeric_limits<Real>::infinity();
+      BOOST_CHECK((boost::math::isinf)(v + r));
+      BOOST_CHECK((boost::math::isinf)(r + v));
+      BOOST_CHECK((boost::math::isinf)(r - v));
+      BOOST_CHECK((boost::math::isinf)(v - r));
+      BOOST_CHECK_LT(v - r, 0);
+      BOOST_CHECK((boost::math::isinf)(r * v));
+      BOOST_CHECK((boost::math::isinf)(v * r));
+      BOOST_CHECK((boost::math::isinf)(r / v));
+      BOOST_CHECK_EQUAL(v / r, 0);
+      Real t = v;
+      BOOST_CHECK((boost::math::isinf)(t += r));
+      t = r;
+      BOOST_CHECK((boost::math::isinf)(t += v));
+      t = r;
+      BOOST_CHECK((boost::math::isinf)(t -= v));
+      t = v;
+      BOOST_CHECK((boost::math::isinf)(t -= r));
+      t = v;
+      BOOST_CHECK(t -= r < 0);
+      t = r;
+      BOOST_CHECK((boost::math::isinf)(t *= v));
+      t = v;
+      BOOST_CHECK((boost::math::isinf)(t *= r));
+      t = r;
+      BOOST_CHECK((boost::math::isinf)(t /= v));
+      t = v;
+      BOOST_CHECK((t /= r) == 0);
+   }
+   //
+   // Operations that should produce NaN as a result:
+   //
+   if (std::numeric_limits<Real>::has_quiet_NaN)
+   {
+      v = r  = 0;
+      Real t = v / r;
+      BOOST_CHECK((boost::math::isnan)(t));
+      v /= r;
+      BOOST_CHECK((boost::math::isnan)(v));
+      t = v / 0;
+      BOOST_CHECK((boost::math::isnan)(v));
+      if (std::numeric_limits<Real>::has_infinity)
+      {
+         v = 0;
+         r = std::numeric_limits<Real>::infinity();
+         t = v * r;
+         if (!boost::multiprecision::is_interval_number<Real>::value)
+         {
+            BOOST_CHECK((boost::math::isnan)(t));
+            t = r * 0;
+            BOOST_CHECK((boost::math::isnan)(t));
+         }
+         v = r;
+         t = r / v;
+         BOOST_CHECK((boost::math::isnan)(t));
+      }
+   }
+
+   test_float_funcs<Real>(boost::mpl::bool_<std::numeric_limits<Real>::is_specialized>());
+}
+
+template <class T>
+struct lexical_cast_target_type
+{
+   typedef typename boost::mpl::if_<
+       boost::is_signed<T>,
+       boost::intmax_t,
+       typename boost::mpl::if_<
+           boost::is_unsigned<T>,
+           boost::uintmax_t,
+           T>::type>::type type;
+};
+
+template <class Real, class Num>
+void test_negative_mixed_minmax(boost::mpl::true_ const&)
+{
+   if (!std::numeric_limits<Real>::is_bounded || (std::numeric_limits<Real>::digits >= std::numeric_limits<Num>::digits))
+   {
+      Real mx1((std::numeric_limits<Num>::max)() - 1);
+      ++mx1;
+      Real mx2((std::numeric_limits<Num>::max)());
+      BOOST_CHECK_EQUAL(mx1, mx2);
+      mx1 = (std::numeric_limits<Num>::max)() - 1;
+      ++mx1;
+      mx2 = (std::numeric_limits<Num>::max)();
+      BOOST_CHECK_EQUAL(mx1, mx2);
+
+      if (!std::numeric_limits<Real>::is_bounded || (std::numeric_limits<Real>::digits > std::numeric_limits<Num>::digits))
+      {
+         Real mx3((std::numeric_limits<Num>::min)() + 1);
+         --mx3;
+         Real mx4((std::numeric_limits<Num>::min)());
+         BOOST_CHECK_EQUAL(mx3, mx4);
+         mx3 = (std::numeric_limits<Num>::min)() + 1;
+         --mx3;
+         mx4 = (std::numeric_limits<Num>::min)();
+         BOOST_CHECK_EQUAL(mx3, mx4);
+      }
+   }
+}
+template <class Real, class Num>
+void test_negative_mixed_minmax(boost::mpl::false_ const&)
+{
+}
+
+template <class Real, class Num>
+void test_negative_mixed_numeric_limits(boost::mpl::true_ const&)
+{
+   typedef typename lexical_cast_target_type<Num>::type target_type;
+#if defined(TEST_MPFR)
+   Num tol = 10 * std::numeric_limits<Num>::epsilon();
+#else
+   Num tol = 0;
+#endif
+   static const int        left_shift      = std::numeric_limits<Num>::digits - 1;
+   Num                     n1              = -static_cast<Num>(1uLL << ((left_shift < 63) && (left_shift > 0) ? left_shift : 10));
+   Num                     n2              = -1;
+   Num                     n3              = 0;
+   Num                     n4              = -20;
+   std::ios_base::fmtflags f               = boost::is_floating_point<Num>::value ? std::ios_base::scientific : std::ios_base::fmtflags(0);
+   int                     digits_to_print = boost::is_floating_point<Num>::value && std::numeric_limits<Num>::is_specialized
+                             ? std::numeric_limits<Num>::digits10 + 5
+                             : 0;
+   if (std::numeric_limits<target_type>::digits <= std::numeric_limits<Real>::digits)
+   {
+      BOOST_CHECK_CLOSE(n1, checked_lexical_cast<target_type>(Real(n1).str(digits_to_print, f)), tol);
+   }
+   BOOST_CHECK_CLOSE(n2, checked_lexical_cast<target_type>(Real(n2).str(digits_to_print, f)), 0);
+   BOOST_CHECK_CLOSE(n3, checked_lexical_cast<target_type>(Real(n3).str(digits_to_print, f)), 0);
+   BOOST_CHECK_CLOSE(n4, checked_lexical_cast<target_type>(Real(n4).str(digits_to_print, f)), 0);
+}
+
+template <class Real, class Num>
+void test_negative_mixed_numeric_limits(boost::mpl::false_ const&) {}
+
+template <class Real, class Num>
+void test_negative_mixed(boost::mpl::true_ const&)
+{
+   typedef typename boost::mpl::if_<
+       boost::is_convertible<Num, Real>,
+       typename boost::mpl::if_c<boost::is_integral<Num>::value && (sizeof(Num) < sizeof(int)), int, Num>::type,
+       Real>::type cast_type;
+   typedef typename boost::mpl::if_<
+       boost::is_convertible<Num, Real>,
+       Num,
+       Real>::type simple_cast_type;
+   std::cout << "Testing mixed arithmetic with type: " << typeid(Real).name() << " and " << typeid(Num).name() << std::endl;
+   static const int left_shift = std::numeric_limits<Num>::digits - 1;
+   Num              n1         = -static_cast<Num>(1uLL << ((left_shift < 63) && (left_shift > 0) ? left_shift : 10));
+   Num              n2         = -1;
+   Num              n3         = 0;
+   Num              n4         = -20;
+   Num              n5         = -8;
+
+   test_comparisons<Real>(n1, n2, boost::is_convertible<Num, Real>());
+   test_comparisons<Real>(n1, n3, boost::is_convertible<Num, Real>());
+   test_comparisons<Real>(n3, n1, boost::is_convertible<Num, Real>());
+   test_comparisons<Real>(n2, n1, boost::is_convertible<Num, Real>());
+   test_comparisons<Real>(n1, n1, boost::is_convertible<Num, Real>());
+   test_comparisons<Real>(n3, n3, boost::is_convertible<Num, Real>());
+
+   // Default construct:
+   BOOST_CHECK_EQUAL(Real(n1), static_cast<cast_type>(n1));
+   BOOST_CHECK_EQUAL(Real(n2), static_cast<cast_type>(n2));
+   BOOST_CHECK_EQUAL(Real(n3), static_cast<cast_type>(n3));
+   BOOST_CHECK_EQUAL(Real(n4), static_cast<cast_type>(n4));
+   BOOST_CHECK_EQUAL(static_cast<cast_type>(n1), Real(n1));
+   BOOST_CHECK_EQUAL(static_cast<cast_type>(n2), Real(n2));
+   BOOST_CHECK_EQUAL(static_cast<cast_type>(n3), Real(n3));
+   BOOST_CHECK_EQUAL(static_cast<cast_type>(n4), Real(n4));
+   BOOST_CHECK_EQUAL(Real(n1).template convert_to<Num>(), n1);
+   BOOST_CHECK_EQUAL(Real(n2).template convert_to<Num>(), n2);
+   BOOST_CHECK_EQUAL(Real(n3).template convert_to<Num>(), n3);
+   BOOST_CHECK_EQUAL(Real(n4).template convert_to<Num>(), n4);
+#ifndef BOOST_MP_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
+   BOOST_CHECK_EQUAL(static_cast<Num>(Real(n1)), n1);
+   BOOST_CHECK_EQUAL(static_cast<Num>(Real(n2)), n2);
+   BOOST_CHECK_EQUAL(static_cast<Num>(Real(n3)), n3);
+   BOOST_CHECK_EQUAL(static_cast<Num>(Real(n4)), n4);
+#endif
+   // Conversions when source is an expression template:
+   BOOST_CHECK_EQUAL((Real(n1) + 0).template convert_to<Num>(), n1);
+   BOOST_CHECK_EQUAL((Real(n2) + 0).template convert_to<Num>(), n2);
+   BOOST_CHECK_EQUAL((Real(n3) + 0).template convert_to<Num>(), n3);
+   BOOST_CHECK_EQUAL((Real(n4) + 0).template convert_to<Num>(), n4);
+#ifndef BOOST_MP_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
+   BOOST_CHECK_EQUAL(static_cast<Num>((Real(n1) + 0)), n1);
+   BOOST_CHECK_EQUAL(static_cast<Num>((Real(n2) + 0)), n2);
+   BOOST_CHECK_EQUAL(static_cast<Num>((Real(n3) + 0)), n3);
+   BOOST_CHECK_EQUAL(static_cast<Num>((Real(n4) + 0)), n4);
+#endif
+   test_negative_mixed_numeric_limits<Real, Num>(boost::mpl::bool_<std::numeric_limits<Real>::is_specialized>());
+   // Assignment:
+   Real r(0);
+   BOOST_CHECK(r != static_cast<cast_type>(n1));
+   r = static_cast<simple_cast_type>(n1);
+   BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n1));
+   r = static_cast<simple_cast_type>(n2);
+   BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n2));
+   r = static_cast<simple_cast_type>(n3);
+   BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n3));
+   r = static_cast<simple_cast_type>(n4);
+   BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n4));
+   // Addition:
+   r = static_cast<simple_cast_type>(n2);
+   BOOST_CHECK_EQUAL(r + static_cast<simple_cast_type>(n4), static_cast<cast_type>(n2 + n4));
+   BOOST_CHECK_EQUAL(Real(r + static_cast<simple_cast_type>(n4)), static_cast<cast_type>(n2 + n4));
+   r += static_cast<simple_cast_type>(n4);
+   BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n2 + n4));
+   // subtraction:
+   r = static_cast<simple_cast_type>(n4);
+   BOOST_CHECK_EQUAL(r - static_cast<simple_cast_type>(n5), static_cast<cast_type>(n4 - n5));
+   BOOST_CHECK_EQUAL(Real(r - static_cast<simple_cast_type>(n5)), static_cast<cast_type>(n4 - n5));
+   r -= static_cast<simple_cast_type>(n5);
+   BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n4 - n5));
+   // Multiplication:
+   r = static_cast<simple_cast_type>(n2);
+   BOOST_CHECK_EQUAL(r * static_cast<simple_cast_type>(n4), static_cast<cast_type>(n2 * n4));
+   BOOST_CHECK_EQUAL(Real(r * static_cast<simple_cast_type>(n4)), static_cast<cast_type>(n2 * n4));
+   r *= static_cast<simple_cast_type>(n4);
+   BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n2 * n4));
+   // Division:
+   r = static_cast<simple_cast_type>(n1);
+   BOOST_CHECK_EQUAL(r / static_cast<simple_cast_type>(n5), static_cast<cast_type>(n1 / n5));
+   BOOST_CHECK_EQUAL(Real(r / static_cast<simple_cast_type>(n5)), static_cast<cast_type>(n1 / n5));
+   r /= static_cast<simple_cast_type>(n5);
+   BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n1 / n5));
+   //
+   // Extra cases for full coverage:
+   //
+   r = Real(n4) + static_cast<simple_cast_type>(n5);
+   BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n4 + n5));
+   r = static_cast<simple_cast_type>(n4) + Real(n5);
+   BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n4 + n5));
+   r = Real(n4) - static_cast<simple_cast_type>(n5);
+   BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n4 - n5));
+   r = static_cast<simple_cast_type>(n4) - Real(n5);
+   BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n4 - n5));
+   r = static_cast<simple_cast_type>(n4) * Real(n5);
+   BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n4 * n5));
+   r = static_cast<cast_type>(Num(4) * n4) / Real(4);
+   BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n4));
+
+   Real a, b, c;
+   a = 20;
+   b = 30;
+   c = -a + b;
+   BOOST_CHECK_EQUAL(c, 10);
+   c = b + -a;
+   BOOST_CHECK_EQUAL(c, 10);
+   n4 = 30;
+   c  = -a + static_cast<cast_type>(n4);
+   BOOST_CHECK_EQUAL(c, 10);
+   c = static_cast<cast_type>(n4) + -a;
+   BOOST_CHECK_EQUAL(c, 10);
+   c = -a + -b;
+   BOOST_CHECK_EQUAL(c, -50);
+   n4 = 4;
+   c  = -(a + b) + static_cast<cast_type>(n4);
+   BOOST_CHECK_EQUAL(c, -50 + 4);
+   n4 = 50;
+   c  = (a + b) - static_cast<cast_type>(n4);
+   BOOST_CHECK_EQUAL(c, 0);
+   c = (a + b) - static_cast<cast_type>(n4);
+   BOOST_CHECK_EQUAL(c, 0);
+   c = a - -(b + static_cast<cast_type>(n4));
+   BOOST_CHECK_EQUAL(c, 20 - -(30 + 50));
+   c = -(b + static_cast<cast_type>(n4)) - a;
+   BOOST_CHECK_EQUAL(c, -(30 + 50) - 20);
+   c = a - -b;
+   BOOST_CHECK_EQUAL(c, 50);
+   c = -a - b;
+   BOOST_CHECK_EQUAL(c, -50);
+   c = -a - static_cast<cast_type>(n4);
+   BOOST_CHECK_EQUAL(c, -20 - 50);
+   c = static_cast<cast_type>(n4) - -a;
+   BOOST_CHECK_EQUAL(c, 50 + 20);
+   c = -(a + b) - Real(n4);
+   BOOST_CHECK_EQUAL(c, -(20 + 30) - 50);
+   c = static_cast<cast_type>(n4) - (a + b);
+   BOOST_CHECK_EQUAL(c, 0);
+   c = (a + b) * static_cast<cast_type>(n4);
+   BOOST_CHECK_EQUAL(c, 50 * 50);
+   c = static_cast<cast_type>(n4) * (a + b);
+   BOOST_CHECK_EQUAL(c, 50 * 50);
+   c = a * -(b + static_cast<cast_type>(n4));
+   BOOST_CHECK_EQUAL(c, 20 * -(30 + 50));
+   c = -(b + static_cast<cast_type>(n4)) * a;
+   BOOST_CHECK_EQUAL(c, 20 * -(30 + 50));
+   c = a * -b;
+   BOOST_CHECK_EQUAL(c, 20 * -30);
+   c = -a * b;
+   BOOST_CHECK_EQUAL(c, 20 * -30);
+   c = -a * static_cast<cast_type>(n4);
+   BOOST_CHECK_EQUAL(c, -20 * 50);
+   c = static_cast<cast_type>(n4) * -a;
+   BOOST_CHECK_EQUAL(c, -20 * 50);
+   c = -(a + b) + a;
+   BOOST_CHECK(-50 + 20);
+   c = static_cast<cast_type>(n4) - (a + b);
+   BOOST_CHECK_EQUAL(c, 0);
+   Real d = 10;
+   c      = (a + b) / d;
+   BOOST_CHECK_EQUAL(c, 5);
+   c = (a + b) / (d + 0);
+   BOOST_CHECK_EQUAL(c, 5);
+   c = (a + b) / static_cast<cast_type>(n4);
+   BOOST_CHECK_EQUAL(c, 1);
+   c = static_cast<cast_type>(n4) / (a + b);
+   BOOST_CHECK_EQUAL(c, 1);
+   d = 50;
+   c = d / -(a + b);
+   BOOST_CHECK_EQUAL(c, -1);
+   c = -(a + b) / d;
+   BOOST_CHECK_EQUAL(c, -1);
+   d = 2;
+   c = a / -d;
+   BOOST_CHECK_EQUAL(c, 20 / -2);
+   c = -a / d;
+   BOOST_CHECK_EQUAL(c, 20 / -2);
+   d = 50;
+   c = -d / static_cast<cast_type>(n4);
+   BOOST_CHECK_EQUAL(c, -1);
+   c = static_cast<cast_type>(n4) / -d;
+   BOOST_CHECK_EQUAL(c, -1);
+   c = static_cast<cast_type>(n4) + a;
+   BOOST_CHECK_EQUAL(c, 70);
+   c = static_cast<cast_type>(n4) - a;
+   BOOST_CHECK_EQUAL(c, 30);
+   c = static_cast<cast_type>(n4) * a;
+   BOOST_CHECK_EQUAL(c, 50 * 20);
+
+   n1 = -2;
+   n2 = -3;
+   n3 = -4;
+   a  = static_cast<cast_type>(n1);
+   b  = static_cast<cast_type>(n2);
+   c  = static_cast<cast_type>(n3);
+   d  = a + b * c;
+   BOOST_CHECK_EQUAL(d, -2 + -3 * -4);
+   d = static_cast<cast_type>(n1) + b * c;
+   BOOST_CHECK_EQUAL(d, -2 + -3 * -4);
+   d = a + static_cast<cast_type>(n2) * c;
+   BOOST_CHECK_EQUAL(d, -2 + -3 * -4);
+   d = a + b * static_cast<cast_type>(n3);
+   BOOST_CHECK_EQUAL(d, -2 + -3 * -4);
+   d = static_cast<cast_type>(n1) + static_cast<cast_type>(n2) * c;
+   BOOST_CHECK_EQUAL(d, -2 + -3 * -4);
+   d = static_cast<cast_type>(n1) + b * static_cast<cast_type>(n3);
+   BOOST_CHECK_EQUAL(d, -2 + -3 * -4);
+   a += static_cast<cast_type>(n2) * c;
+   BOOST_CHECK_EQUAL(a, -2 + -3 * -4);
+   a = static_cast<cast_type>(n1);
+   a += b * static_cast<cast_type>(n3);
+   BOOST_CHECK_EQUAL(a, -2 + -3 * -4);
+   a = static_cast<cast_type>(n1);
+
+   d = b * c + a;
+   BOOST_CHECK_EQUAL(d, -2 + -3 * -4);
+   d = b * c + static_cast<cast_type>(n1);
+   BOOST_CHECK_EQUAL(d, -2 + -3 * -4);
+   d = static_cast<cast_type>(n2) * c + a;
+   BOOST_CHECK_EQUAL(d, -2 + -3 * -4);
+   d = b * static_cast<cast_type>(n3) + a;
+   BOOST_CHECK_EQUAL(d, -2 + -3 * -4);
+   d = static_cast<cast_type>(n2) * c + static_cast<cast_type>(n1);
+   BOOST_CHECK_EQUAL(d, -2 + -3 * -4);
+   d = b * static_cast<cast_type>(n3) + static_cast<cast_type>(n1);
+   BOOST_CHECK_EQUAL(d, -2 + -3 * -4);
+
+   a = -20;
+   d = a - b * c;
+   BOOST_CHECK_EQUAL(d, -20 - -3 * -4);
+   n1 = -20;
+   d  = static_cast<cast_type>(n1) - b * c;
+   BOOST_CHECK_EQUAL(d, -20 - -3 * -4);
+   d = a - static_cast<cast_type>(n2) * c;
+   BOOST_CHECK_EQUAL(d, -20 - -3 * -4);
+   d = a - b * static_cast<cast_type>(n3);
+   BOOST_CHECK_EQUAL(d, -20 - -3 * -4);
+   d = static_cast<cast_type>(n1) - static_cast<cast_type>(n2) * c;
+   BOOST_CHECK_EQUAL(d, -20 - -3 * -4);
+   d = static_cast<cast_type>(n1) - b * static_cast<cast_type>(n3);
+   BOOST_CHECK_EQUAL(d, -20 - -3 * -4);
+   a -= static_cast<cast_type>(n2) * c;
+   BOOST_CHECK_EQUAL(a, -20 - -3 * -4);
+   a = static_cast<cast_type>(n1);
+   a -= b * static_cast<cast_type>(n3);
+   BOOST_CHECK_EQUAL(a, -20 - -3 * -4);
+
+   a = -2;
+   d = b * c - a;
+   BOOST_CHECK_EQUAL(d, -3 * -4 - -2);
+   n1 = -2;
+   d  = b * c - static_cast<cast_type>(n1);
+   BOOST_CHECK_EQUAL(d, -3 * -4 - -2);
+   d = static_cast<cast_type>(n2) * c - a;
+   BOOST_CHECK_EQUAL(d, -3 * -4 - -2);
+   d = b * static_cast<cast_type>(n3) - a;
+   BOOST_CHECK_EQUAL(d, -3 * -4 - -2);
+   d = static_cast<cast_type>(n2) * c - static_cast<cast_type>(n1);
+   BOOST_CHECK_EQUAL(d, -3 * -4 - -2);
+   d = b * static_cast<cast_type>(n3) - static_cast<cast_type>(n1);
+   BOOST_CHECK_EQUAL(d, -3 * -4 - -2);
+   //
+   // Conversion from min and max values:
+   //
+   test_negative_mixed_minmax<Real, Num>(boost::mpl::bool_ < std::numeric_limits<Real>::is_integer && std::numeric_limits<Num>::is_integer > ());
+}
+
+template <class Real, class Num>
+void test_negative_mixed(boost::mpl::false_ const&)
+{
+}
+
+template <class Real, class Num>
+void test_mixed(const boost::mpl::false_&)
+{
+}
+
+template <class Real>
+inline bool check_is_nan(const Real& val, const boost::mpl::true_&)
+{
+   return (boost::math::isnan)(val);
+}
+template <class Real>
+inline bool check_is_nan(const Real&, const boost::mpl::false_&)
+{
+   return false;
+}
+template <class Real>
+inline Real negate_value(const Real& val, const boost::mpl::true_&)
+{
+   return -val;
+}
+template <class Real>
+inline Real negate_value(const Real& val, const boost::mpl::false_&)
+{
+   return val;
+}
+
+template <class Real, class Num>
+void test_mixed_numeric_limits(const boost::mpl::true_&)
+{
+   typedef typename lexical_cast_target_type<Num>::type target_type;
+#if defined(TEST_MPFR)
+   Num tol = 10 * std::numeric_limits<Num>::epsilon();
+#else
+   Num tol = 0;
+#endif
+
+   Real d;
+   if (std::numeric_limits<Real>::has_infinity && std::numeric_limits<Num>::has_infinity)
+   {
+      d = static_cast<Real>(std::numeric_limits<Num>::infinity());
+      BOOST_CHECK_GT(d, (std::numeric_limits<Real>::max)());
+      d = static_cast<Real>(negate_value(std::numeric_limits<Num>::infinity(), boost::mpl::bool_<std::numeric_limits<Num>::is_signed>()));
+      BOOST_CHECK_LT(d, negate_value((std::numeric_limits<Real>::max)(), boost::mpl::bool_<std::numeric_limits<Real>::is_signed>()));
+   }
+   if (std::numeric_limits<Real>::has_quiet_NaN && std::numeric_limits<Num>::has_quiet_NaN)
+   {
+      d = static_cast<Real>(std::numeric_limits<Num>::quiet_NaN());
+      BOOST_CHECK(check_is_nan(d, boost::mpl::bool_<std::numeric_limits<Real>::has_quiet_NaN>()));
+      d = static_cast<Real>(negate_value(std::numeric_limits<Num>::quiet_NaN(), boost::mpl::bool_<std::numeric_limits<Num>::is_signed>()));
+      BOOST_CHECK(check_is_nan(d, boost::mpl::bool_<std::numeric_limits<Real>::has_quiet_NaN>()));
+   }
+
+   static const int left_shift = std::numeric_limits<Num>::digits - 1;
+   Num              n1         = static_cast<Num>(1uLL << ((left_shift < 63) && (left_shift > 0) ? left_shift : 10));
+   Num              n2         = 1;
+   Num              n3         = 0;
+   Num              n4         = 20;
+
+   std::ios_base::fmtflags f               = boost::is_floating_point<Num>::value ? std::ios_base::scientific : std::ios_base::fmtflags(0);
+   int                     digits_to_print = boost::is_floating_point<Num>::value && std::numeric_limits<Num>::is_specialized
+                             ? std::numeric_limits<Num>::digits10 + 5
+                             : 0;
+   if (std::numeric_limits<target_type>::digits <= std::numeric_limits<Real>::digits)
+   {
+      BOOST_CHECK_CLOSE(n1, checked_lexical_cast<target_type>(Real(n1).str(digits_to_print, f)), tol);
+   }
+   BOOST_CHECK_CLOSE(n2, checked_lexical_cast<target_type>(Real(n2).str(digits_to_print, f)), 0);
+   BOOST_CHECK_CLOSE(n3, checked_lexical_cast<target_type>(Real(n3).str(digits_to_print, f)), 0);
+   BOOST_CHECK_CLOSE(n4, checked_lexical_cast<target_type>(Real(n4).str(digits_to_print, f)), 0);
+}
+template <class Real, class Num>
+void test_mixed_numeric_limits(const boost::mpl::false_&)
+{
+}
+
+template <class Real, class Num>
+void test_mixed(const boost::mpl::true_&)
+{
+   typedef typename boost::mpl::if_<
+       boost::is_convertible<Num, Real>,
+       typename boost::mpl::if_c<boost::is_integral<Num>::value && (sizeof(Num) < sizeof(int)), int, Num>::type,
+       Real>::type cast_type;
+   typedef typename boost::mpl::if_<
+       boost::is_convertible<Num, Real>,
+       Num,
+       Real>::type simple_cast_type;
+
+   if (std::numeric_limits<Real>::is_specialized && std::numeric_limits<Real>::is_bounded && std::numeric_limits<Real>::digits < std::numeric_limits<Num>::digits)
+      return;
+
+   std::cout << "Testing mixed arithmetic with type: " << typeid(Real).name() << " and " << typeid(Num).name() << std::endl;
+   static const int left_shift = std::numeric_limits<Num>::digits - 1;
+   Num              n1         = static_cast<Num>(1uLL << ((left_shift < 63) && (left_shift > 0) ? left_shift : 10));
+   Num              n2         = 1;
+   Num              n3         = 0;
+   Num              n4         = 20;
+   Num              n5         = 8;
+
+   test_comparisons<Real>(n1, n2, boost::is_convertible<Num, Real>());
+   test_comparisons<Real>(n1, n3, boost::is_convertible<Num, Real>());
+   test_comparisons<Real>(n1, n1, boost::is_convertible<Num, Real>());
+   test_comparisons<Real>(n3, n1, boost::is_convertible<Num, Real>());
+   test_comparisons<Real>(n2, n1, boost::is_convertible<Num, Real>());
+   test_comparisons<Real>(n3, n3, boost::is_convertible<Num, Real>());
+
+   // Default construct:
+   BOOST_CHECK_EQUAL(Real(n1), static_cast<cast_type>(n1));
+   BOOST_CHECK_EQUAL(Real(n2), static_cast<cast_type>(n2));
+   BOOST_CHECK_EQUAL(Real(n3), static_cast<cast_type>(n3));
+   BOOST_CHECK_EQUAL(Real(n4), static_cast<cast_type>(n4));
+   BOOST_CHECK_EQUAL(Real(n1).template convert_to<Num>(), n1);
+   BOOST_CHECK_EQUAL(Real(n2).template convert_to<Num>(), n2);
+   BOOST_CHECK_EQUAL(Real(n3).template convert_to<Num>(), n3);
+   BOOST_CHECK_EQUAL(Real(n4).template convert_to<Num>(), n4);
+#ifndef BOOST_MP_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
+   BOOST_CHECK_EQUAL(static_cast<Num>(Real(n1)), n1);
+   BOOST_CHECK_EQUAL(static_cast<Num>(Real(n2)), n2);
+   BOOST_CHECK_EQUAL(static_cast<Num>(Real(n3)), n3);
+   BOOST_CHECK_EQUAL(static_cast<Num>(Real(n4)), n4);
+#endif
+   // Again with expression templates:
+   BOOST_CHECK_EQUAL((Real(n1) + 0).template convert_to<Num>(), n1);
+   BOOST_CHECK_EQUAL((Real(n2) + 0).template convert_to<Num>(), n2);
+   BOOST_CHECK_EQUAL((Real(n3) + 0).template convert_to<Num>(), n3);
+   BOOST_CHECK_EQUAL((Real(n4) + 0).template convert_to<Num>(), n4);
+#ifndef BOOST_MP_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
+   BOOST_CHECK_EQUAL(static_cast<Num>(Real(n1) + 0), n1);
+   BOOST_CHECK_EQUAL(static_cast<Num>(Real(n2) + 0), n2);
+   BOOST_CHECK_EQUAL(static_cast<Num>(Real(n3) + 0), n3);
+   BOOST_CHECK_EQUAL(static_cast<Num>(Real(n4) + 0), n4);
+#endif
+   BOOST_CHECK_EQUAL(static_cast<cast_type>(n1), Real(n1));
+   BOOST_CHECK_EQUAL(static_cast<cast_type>(n2), Real(n2));
+   BOOST_CHECK_EQUAL(static_cast<cast_type>(n3), Real(n3));
+   BOOST_CHECK_EQUAL(static_cast<cast_type>(n4), Real(n4));
+   // Assignment:
+   Real r(0);
+   BOOST_CHECK(r != static_cast<cast_type>(n1));
+   r = static_cast<simple_cast_type>(n1);
+   BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n1));
+   r = static_cast<simple_cast_type>(n2);
+   BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n2));
+   r = static_cast<simple_cast_type>(n3);
+   BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n3));
+   r = static_cast<simple_cast_type>(n4);
+   BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n4));
+   // Addition:
+   r = static_cast<simple_cast_type>(n2);
+   BOOST_CHECK_EQUAL(r + static_cast<simple_cast_type>(n4), static_cast<cast_type>(n2 + n4));
+   BOOST_CHECK_EQUAL(Real(r + static_cast<simple_cast_type>(n4)), static_cast<cast_type>(n2 + n4));
+   r += static_cast<simple_cast_type>(n4);
+   BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n2 + n4));
+   // subtraction:
+   r = static_cast<simple_cast_type>(n4);
+   BOOST_CHECK_EQUAL(r - static_cast<simple_cast_type>(n5), static_cast<cast_type>(n4 - n5));
+   BOOST_CHECK_EQUAL(Real(r - static_cast<simple_cast_type>(n5)), static_cast<cast_type>(n4 - n5));
+   r -= static_cast<simple_cast_type>(n5);
+   BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n4 - n5));
+   // Multiplication:
+   r = static_cast<simple_cast_type>(n2);
+   BOOST_CHECK_EQUAL(r * static_cast<simple_cast_type>(n4), static_cast<cast_type>(n2 * n4));
+   BOOST_CHECK_EQUAL(Real(r * static_cast<simple_cast_type>(n4)), static_cast<cast_type>(n2 * n4));
+   r *= static_cast<simple_cast_type>(n4);
+   BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n2 * n4));
+   // Division:
+   r = static_cast<simple_cast_type>(n1);
+   BOOST_CHECK_EQUAL(r / static_cast<simple_cast_type>(n5), static_cast<cast_type>(n1 / n5));
+   BOOST_CHECK_EQUAL(Real(r / static_cast<simple_cast_type>(n5)), static_cast<cast_type>(n1 / n5));
+   r /= static_cast<simple_cast_type>(n5);
+   BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n1 / n5));
+   //
+   // special cases for full coverage:
+   //
+   r = static_cast<simple_cast_type>(n5) + Real(n4);
+   BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n4 + n5));
+   r = static_cast<simple_cast_type>(n4) - Real(n5);
+   BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n4 - n5));
+   r = static_cast<simple_cast_type>(n4) * Real(n5);
+   BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n4 * n5));
+   r = static_cast<cast_type>(Num(4) * n4) / Real(4);
+   BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n4));
+
+   typedef boost::mpl::bool_<
+       (!std::numeric_limits<Num>::is_specialized || std::numeric_limits<Num>::is_signed) && (!std::numeric_limits<Real>::is_specialized || std::numeric_limits<Real>::is_signed)>
+       signed_tag;
+
+   test_negative_mixed<Real, Num>(signed_tag());
+
+   n1 = 2;
+   n2 = 3;
+   n3 = 4;
+   Real a(n1), b(n2), c(n3), d;
+   d = a + b * c;
+   BOOST_CHECK_EQUAL(d, 2 + 3 * 4);
+   d = static_cast<cast_type>(n1) + b * c;
+   BOOST_CHECK_EQUAL(d, 2 + 3 * 4);
+   d = a + static_cast<cast_type>(n2) * c;
+   BOOST_CHECK_EQUAL(d, 2 + 3 * 4);
+   d = a + b * static_cast<cast_type>(n3);
+   BOOST_CHECK_EQUAL(d, 2 + 3 * 4);
+   d = static_cast<cast_type>(n1) + static_cast<cast_type>(n2) * c;
+   BOOST_CHECK_EQUAL(d, 2 + 3 * 4);
+   d = static_cast<cast_type>(n1) + b * static_cast<cast_type>(n3);
+   BOOST_CHECK_EQUAL(d, 2 + 3 * 4);
+   a += static_cast<cast_type>(n2) * c;
+   BOOST_CHECK_EQUAL(a, 2 + 3 * 4);
+   a = static_cast<cast_type>(n1);
+   a += b * static_cast<cast_type>(n3);
+   BOOST_CHECK_EQUAL(a, 2 + 3 * 4);
+   a = static_cast<cast_type>(n1);
+
+   d = b * c + a;
+   BOOST_CHECK_EQUAL(d, 2 + 3 * 4);
+   d = b * c + static_cast<cast_type>(n1);
+   BOOST_CHECK_EQUAL(d, 2 + 3 * 4);
+   d = static_cast<cast_type>(n2) * c + a;
+   BOOST_CHECK_EQUAL(d, 2 + 3 * 4);
+   d = b * static_cast<cast_type>(n3) + a;
+   BOOST_CHECK_EQUAL(d, 2 + 3 * 4);
+   d = static_cast<cast_type>(n2) * c + static_cast<cast_type>(n1);
+   BOOST_CHECK_EQUAL(d, 2 + 3 * 4);
+   d = b * static_cast<cast_type>(n3) + static_cast<cast_type>(n1);
+   BOOST_CHECK_EQUAL(d, 2 + 3 * 4);
+
+   a = 20;
+   d = a - b * c;
+   BOOST_CHECK_EQUAL(d, 20 - 3 * 4);
+   n1 = 20;
+   d  = static_cast<cast_type>(n1) - b * c;
+   BOOST_CHECK_EQUAL(d, 20 - 3 * 4);
+   d = a - static_cast<cast_type>(n2) * c;
+   BOOST_CHECK_EQUAL(d, 20 - 3 * 4);
+   d = a - b * static_cast<cast_type>(n3);
+   BOOST_CHECK_EQUAL(d, 20 - 3 * 4);
+   d = static_cast<cast_type>(n1) - static_cast<cast_type>(n2) * c;
+   BOOST_CHECK_EQUAL(d, 20 - 3 * 4);
+   d = static_cast<cast_type>(n1) - b * static_cast<cast_type>(n3);
+   BOOST_CHECK_EQUAL(d, 20 - 3 * 4);
+   a -= static_cast<cast_type>(n2) * c;
+   BOOST_CHECK_EQUAL(a, 20 - 3 * 4);
+   a = static_cast<cast_type>(n1);
+   a -= b * static_cast<cast_type>(n3);
+   BOOST_CHECK_EQUAL(a, 20 - 3 * 4);
+
+   a = 2;
+   d = b * c - a;
+   BOOST_CHECK_EQUAL(d, 3 * 4 - 2);
+   n1 = 2;
+   d  = b * c - static_cast<cast_type>(n1);
+   BOOST_CHECK_EQUAL(d, 3 * 4 - 2);
+   d = static_cast<cast_type>(n2) * c - a;
+   BOOST_CHECK_EQUAL(d, 3 * 4 - 2);
+   d = b * static_cast<cast_type>(n3) - a;
+   BOOST_CHECK_EQUAL(d, 3 * 4 - a);
+   d = static_cast<cast_type>(n2) * c - static_cast<cast_type>(n1);
+   BOOST_CHECK_EQUAL(d, 3 * 4 - 2);
+   d = b * static_cast<cast_type>(n3) - static_cast<cast_type>(n1);
+   BOOST_CHECK_EQUAL(d, 3 * 4 - 2);
+
+   test_mixed_numeric_limits<Real, Num>(boost::mpl::bool_<std::numeric_limits<Real>::is_specialized>());
+}
+
+template <class Real>
+typename boost::enable_if_c<boost::multiprecision::number_category<Real>::value == boost::multiprecision::number_kind_complex>::type test_members(Real)
+{
+   //
+   // Test sign and zero functions:
+   //
+   Real a = 20;
+   Real b = 30;
+   BOOST_CHECK(!a.is_zero());
+   a = -20;
+   BOOST_CHECK(!a.is_zero());
+   a = 0;
+   BOOST_CHECK(a.is_zero());
+
+   a = 20;
+   b = 30;
+   a.swap(b);
+   BOOST_CHECK_EQUAL(a, 30);
+   BOOST_CHECK_EQUAL(b, 20);
+
+   Real c(2, 3);
+
+   BOOST_CHECK_EQUAL(a.real(), 30);
+   BOOST_CHECK_EQUAL(a.imag(), 0);
+   BOOST_CHECK_EQUAL(c.real(), 2);
+   BOOST_CHECK_EQUAL(c.imag(), 3);
+
+   //
+   // try some more 2-argument constructors:
+   //
+   {
+      Real d(40.5, 2);
+      BOOST_CHECK_EQUAL(d.real(), 40.5);
+      BOOST_CHECK_EQUAL(d.imag(), 2);
+   }
+   {
+      Real d("40.5", "2");
+      BOOST_CHECK_EQUAL(d.real(), 40.5);
+      BOOST_CHECK_EQUAL(d.imag(), 2);
+   }
+   {
+      Real d("40.5", std::string("2"));
+      BOOST_CHECK_EQUAL(d.real(), 40.5);
+      BOOST_CHECK_EQUAL(d.imag(), 2);
+   }
+#ifndef BOOST_NO_CXX17_HDR_STRING_VIEW
+   {
+      std::string      sx("40.550"), sy("222");
+      std::string_view vx(sx.c_str(), 4), vy(sy.c_str(), 1);
+      Real             d(vx, vy);
+      BOOST_CHECK_EQUAL(d.real(), 40.5);
+      BOOST_CHECK_EQUAL(d.imag(), 2);
+   }
+#endif
+   {
+      typename Real::value_type x(40.5), y(2);
+      Real                      d(x, y);
+      BOOST_CHECK_EQUAL(d.real(), 40.5);
+      BOOST_CHECK_EQUAL(d.imag(), 2);
+   }
+#ifdef TEST_MPC
+   {
+      typename Real::value_type x(40.5), y(2);
+      Real                      d(x.backend().data(), y.backend().data());
+      BOOST_CHECK_EQUAL(d.real(), 40.5);
+      BOOST_CHECK_EQUAL(d.imag(), 2);
+   }
+#endif
+   {
+      typename Real::value_type x(40.5);
+      Real                      d(x, 2);
+      BOOST_CHECK_EQUAL(d.real(), 40.5);
+      BOOST_CHECK_EQUAL(d.imag(), 2);
+   }
+   {
+      typename Real::value_type x(40.5);
+      Real                      d(2, x);
+      BOOST_CHECK_EQUAL(d.imag(), 40.5);
+      BOOST_CHECK_EQUAL(d.real(), 2);
+   }
+   {
+      typename Real::value_type x(real(a) * real(b) + imag(a) * imag(b)), y(imag(a) * real(b) - real(a) * imag(b));
+      Real                      d(real(a) * real(b) + imag(a) * imag(b), imag(a) * real(b) - real(a) * imag(b));
+      Real                      e(x, y);
+      BOOST_CHECK_EQUAL(d, e);
+   }
+   //
+   // real and imag setters:
+   //
+   c.real(4);
+   BOOST_CHECK_EQUAL(real(c), 4);
+   c.imag(-55);
+   BOOST_CHECK_EQUAL(imag(c), -55);
+   typename Real::value_type z(20);
+   c.real(z);
+   BOOST_CHECK_EQUAL(real(c), 20);
+   c.real(21L);
+   BOOST_CHECK_EQUAL(real(c), 21);
+   c.real(22L);
+   BOOST_CHECK_EQUAL(real(c), 22);
+   c.real(23UL);
+   BOOST_CHECK_EQUAL(real(c), 23);
+   c.real(24U);
+   BOOST_CHECK_EQUAL(real(c), 24);
+   c.real(25.0f);
+   BOOST_CHECK_EQUAL(real(c), 25);
+   c.real(26.0);
+   BOOST_CHECK_EQUAL(real(c), 26);
+   c.real(27.0L);
+   BOOST_CHECK_EQUAL(real(c), 27);
+#if defined(BOOST_HAS_LONG_LONG)
+   c.real(28LL);
+   BOOST_CHECK_EQUAL(real(c), 28);
+   c.real(29ULL);
+   BOOST_CHECK_EQUAL(real(c), 29);
+#endif
+   c.imag(z);
+   BOOST_CHECK_EQUAL(imag(c), 20);
+   c.imag(21L);
+   BOOST_CHECK_EQUAL(imag(c), 21);
+   c.imag(22L);
+   BOOST_CHECK_EQUAL(imag(c), 22);
+   c.imag(23UL);
+   BOOST_CHECK_EQUAL(imag(c), 23);
+   c.imag(24U);
+   BOOST_CHECK_EQUAL(imag(c), 24);
+   c.imag(25.0f);
+   BOOST_CHECK_EQUAL(imag(c), 25);
+   c.imag(26.0);
+   BOOST_CHECK_EQUAL(imag(c), 26);
+   c.imag(27.0L);
+   BOOST_CHECK_EQUAL(imag(c), 27);
+#if defined(BOOST_HAS_LONG_LONG)
+   c.imag(28LL);
+   BOOST_CHECK_EQUAL(imag(c), 28);
+   c.imag(29ULL);
+   BOOST_CHECK_EQUAL(imag(c), 29);
+#endif
+
+   c.real(2).imag(3);
+
+   BOOST_CHECK_EQUAL(real(a), 30);
+   BOOST_CHECK_EQUAL(imag(a), 0);
+   BOOST_CHECK_EQUAL(real(c), 2);
+   BOOST_CHECK_EQUAL(imag(c), 3);
+   BOOST_CHECK_EQUAL(real(a + 0), 30);
+   BOOST_CHECK_EQUAL(imag(a + 0), 0);
+   BOOST_CHECK_EQUAL(real(c + 0), 2);
+   BOOST_CHECK_EQUAL(imag(c + 0), 3);
+
+   // string construction:
+   a = Real("2");
+   BOOST_CHECK_EQUAL(real(a), 2);
+   BOOST_CHECK_EQUAL(imag(a), 0);
+   a = Real("(2)");
+   BOOST_CHECK_EQUAL(real(a), 2);
+   BOOST_CHECK_EQUAL(imag(a), 0);
+   a = Real("(,2)");
+   BOOST_CHECK_EQUAL(real(a), 0);
+   BOOST_CHECK_EQUAL(imag(a), 2);
+   a = Real("(2,3)");
+   BOOST_CHECK_EQUAL(real(a), 2);
+   BOOST_CHECK_EQUAL(imag(a), 3);
+
+   typedef typename boost::multiprecision::component_type<Real>::type real_type;
+
+   real_type r(3);
+   real_type tol = std::numeric_limits<real_type>::epsilon() * 30;
+
+   a = r;
+   BOOST_CHECK_EQUAL(real(a), 3);
+   BOOST_CHECK_EQUAL(imag(a), 0);
+
+   a += r;
+   BOOST_CHECK_EQUAL(real(a), 6);
+   BOOST_CHECK_EQUAL(imag(a), 0);
+
+   a *= r;
+   BOOST_CHECK_EQUAL(real(a), 18);
+   BOOST_CHECK_EQUAL(imag(a), 0);
+
+   a = a / r;
+   BOOST_CHECK_EQUAL(real(a), 6);
+   BOOST_CHECK_EQUAL(imag(a), 0);
+   a = a - r;
+   BOOST_CHECK_EQUAL(real(a), 3);
+   BOOST_CHECK_EQUAL(imag(a), 0);
+   a = r + a;
+   BOOST_CHECK_EQUAL(real(a), 6);
+   BOOST_CHECK_EQUAL(imag(a), 0);
+
+   r = abs(c);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("3.60555127546398929311922126747049594625129657384524621271045305622716694829301044520461908201849071767351418202406"), r, tol);
+   r = arg(c);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("0.98279372324732906798571061101466601449687745363162855676142508831798807154979603538970653437281731110816513970201"), r, tol);
+   r = norm(c);
+   BOOST_CHECK_CLOSE_FRACTION(real_type(13), r, tol);
+   a = conj(c);
+   BOOST_CHECK_EQUAL(real(a), 2);
+   BOOST_CHECK_EQUAL(imag(a), -3);
+   a = proj(c);
+   BOOST_CHECK_EQUAL(real(a), 2);
+   BOOST_CHECK_EQUAL(imag(a), 3);
+   a = polar(real_type(3), real_type(-10));
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-2.517214587229357356776591843472194503559790495399505640507861193146377760598812305202801138281266416782353163216"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("1.63206333266810944021424298555413184505092903874867167472255203785027162892148027712122702168494964847488147271478"), imag(a), tol);
+   a = polar(real_type(3) + 0, real_type(-10));
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-2.517214587229357356776591843472194503559790495399505640507861193146377760598812305202801138281266416782353163216"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("1.63206333266810944021424298555413184505092903874867167472255203785027162892148027712122702168494964847488147271478"), imag(a), tol);
+   a = polar(real_type(3), real_type(-10) + 0);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-2.517214587229357356776591843472194503559790495399505640507861193146377760598812305202801138281266416782353163216"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("1.63206333266810944021424298555413184505092903874867167472255203785027162892148027712122702168494964847488147271478"), imag(a), tol);
+   a = polar(real_type(3) + 0, real_type(-10) + 0);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-2.517214587229357356776591843472194503559790495399505640507861193146377760598812305202801138281266416782353163216"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("1.63206333266810944021424298555413184505092903874867167472255203785027162892148027712122702168494964847488147271478"), imag(a), tol);
+   a = polar(3, real_type(-10));
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-2.517214587229357356776591843472194503559790495399505640507861193146377760598812305202801138281266416782353163216"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("1.63206333266810944021424298555413184505092903874867167472255203785027162892148027712122702168494964847488147271478"), imag(a), tol);
+   a = polar(3.0, real_type(-10) + 0);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-2.517214587229357356776591843472194503559790495399505640507861193146377760598812305202801138281266416782353163216"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("1.63206333266810944021424298555413184505092903874867167472255203785027162892148027712122702168494964847488147271478"), imag(a), tol);
+
+   a = polar(real_type(3));
+   BOOST_CHECK_EQUAL(3, real(a));
+   BOOST_CHECK_EQUAL(0, imag(a));
+   a = polar(real_type(3) + 0);
+   BOOST_CHECK_EQUAL(3, real(a));
+   BOOST_CHECK_EQUAL(0, imag(a));
+
+   r = abs(c + 0);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("3.60555127546398929311922126747049594625129657384524621271045305622716694829301044520461908201849071767351418202406"), r, tol);
+   r = arg(c + 0);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("0.98279372324732906798571061101466601449687745363162855676142508831798807154979603538970653437281731110816513970201"), r, tol);
+   r = norm(c + 0);
+   BOOST_CHECK_CLOSE_FRACTION(real_type(13), r, tol);
+   a = conj(c + 0);
+   BOOST_CHECK_EQUAL(real(a), 2);
+   BOOST_CHECK_EQUAL(imag(a), -3);
+   a = proj(c + 0);
+   BOOST_CHECK_EQUAL(real(a), 2);
+   BOOST_CHECK_EQUAL(imag(a), 3);
+
+   a = exp(c);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-7.3151100949011025174865361510507893218698794489446322367845159660828327860599907104337742108443234172141249777"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("1.0427436562359044141015039404625521939183300604422348975424523449538886779880818796291971422701951470533151185"), imag(a), tol);
+
+   a = log(c);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("1.282474678730768368026743720782659302402633972380103558209522755331732333662205089699787331720244744384629096046"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("0.9827937232473290679857106110146660144968774536316285567614250883179880715497960353897065343728173111081651397020"), imag(a), tol);
+
+   a = log10(c);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("0.556971676153418384603252578971164215414864594193534135900595487498776545815097120403823727129449829836488977743"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("0.426821890855466638944275673291166123449562356934437957244904971730668088711719757900679614536803436424488603794"), imag(a), tol);
+
+   a = exp(c + 0);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-7.3151100949011025174865361510507893218698794489446322367845159660828327860599907104337742108443234172141249777"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("1.0427436562359044141015039404625521939183300604422348975424523449538886779880818796291971422701951470533151185"), imag(a), tol);
+
+   a = log(c + 0);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("1.282474678730768368026743720782659302402633972380103558209522755331732333662205089699787331720244744384629096046"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("0.9827937232473290679857106110146660144968774536316285567614250883179880715497960353897065343728173111081651397020"), imag(a), tol);
+
+   a = log10(c + 0);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("0.556971676153418384603252578971164215414864594193534135900595487498776545815097120403823727129449829836488977743"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("0.426821890855466638944275673291166123449562356934437957244904971730668088711719757900679614536803436424488603794"), imag(a), tol);
+
+   // Powers where one arg is an integer.
+   b = Real(5, -2);
+   a = pow(c, b);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-3053.8558566606567369633610140423321260211388217942246293871310470377722279440084474789529228008638668934381183"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("3097.9975862915005132449772136982559285192410496951232473245540634244845290672745578327467396750607773968246915"), imag(a), tol);
+   a = pow(c, 3);
+   BOOST_CHECK_CLOSE_FRACTION(real_type(-46), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type(9), imag(a), tol);
+   a = pow(3, c);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-8.8931513442797186948734782808862447235385767991868219480917324534839621090167050538805196124711247247992169338"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-1.3826999557878897572499699021550296885662132089951379549068064961882821777067532977546360861176011175070188118"), imag(a), tol * 3);
+   a = pow(c + 0, b);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-3053.8558566606567369633610140423321260211388217942246293871310470377722279440084474789529228008638668934381183"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("3097.9975862915005132449772136982559285192410496951232473245540634244845290672745578327467396750607773968246915"), imag(a), tol);
+   a = pow(c + 0, 3);
+   BOOST_CHECK_CLOSE_FRACTION(real_type(-46), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type(9), imag(a), tol);
+   a = pow(3, c + 0);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-8.8931513442797186948734782808862447235385767991868219480917324534839621090167050538805196124711247247992169338"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-1.3826999557878897572499699021550296885662132089951379549068064961882821777067532977546360861176011175070188118"), imag(a), tol * 3);
+
+   r = 3;
+   // Powers where one arg is a real_type.
+   a = pow(c, r);
+   BOOST_CHECK_CLOSE_FRACTION(real_type(-46), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type(9), imag(a), tol);
+   a = pow(r, c);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-8.8931513442797186948734782808862447235385767991868219480917324534839621090167050538805196124711247247992169338"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-1.3826999557878897572499699021550296885662132089951379549068064961882821777067532977546360861176011175070188118"), imag(a), tol * 3);
+   a = pow(c + 0, r);
+   BOOST_CHECK_CLOSE_FRACTION(real_type(-46), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type(9), imag(a), tol);
+   a = pow(r, c + 0);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-8.8931513442797186948734782808862447235385767991868219480917324534839621090167050538805196124711247247992169338"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-1.3826999557878897572499699021550296885662132089951379549068064961882821777067532977546360861176011175070188118"), imag(a), tol * 3);
+   a = pow(c, r + 0);
+   BOOST_CHECK_CLOSE_FRACTION(real_type(-46), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type(9), imag(a), tol);
+   a = pow(r + 0, c);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-8.8931513442797186948734782808862447235385767991868219480917324534839621090167050538805196124711247247992169338"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-1.3826999557878897572499699021550296885662132089951379549068064961882821777067532977546360861176011175070188118"), imag(a), tol * 3);
+
+   // Powers where one arg is an float.
+   a = pow(c, 3.0);
+   BOOST_CHECK_CLOSE_FRACTION(real_type(-46), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type(9), imag(a), tol);
+   a = pow(3.0, c);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-8.8931513442797186948734782808862447235385767991868219480917324534839621090167050538805196124711247247992169338"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-1.3826999557878897572499699021550296885662132089951379549068064961882821777067532977546360861176011175070188118"), imag(a), tol * 3);
+   a = pow(c + 0, 3.0);
+   BOOST_CHECK_CLOSE_FRACTION(real_type(-46), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type(9), imag(a), tol);
+   a = pow(3.0, c + 0);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-8.8931513442797186948734782808862447235385767991868219480917324534839621090167050538805196124711247247992169338"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-1.3826999557878897572499699021550296885662132089951379549068064961882821777067532977546360861176011175070188118"), imag(a), tol * 3);
+
+   a = sqrt(c);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("1.674149228035540040448039300849051821674708677883920366727287836003399240343274891876712629708287692163156802065"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("0.8959774761298381247157337552900434410433241995549314932449006989874470582160955817053273057885402621549320588976"), imag(a), tol);
+   a = sin(c);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("9.154499146911429573467299544609832559158860568765182977899828142590020335321896403936690014669532606510294425039"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-4.168906959966564350754813058853754843573565604758055889965478710592666260138453299795649308385497563475115931624"), imag(a), tol);
+   a = cos(c);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-4.1896256909688072301325550196159737286219454041279210357407905058369727912162626993926269783331491034500484583"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-9.1092278937553365979791972627788621213326202389201695649104967309554222940748568716960841549279996556547993373"), imag(a), tol);
+   a = tan(c);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-0.0037640256415042482927512211303226908396306202016580864328644932511249097100916559688254811519914564480500042311"), real(a), tol * 5);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("1.0032386273536098014463585978219272598077897241071003399272426939850671219193120708438426543945017427085738411"), imag(a), tol);
+   a = asin(c);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("0.5706527843210994007102838796856696501828032450960401365302732598209740064262509342420347149436326252483895113827"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("1.983387029916535432347076902894039565014248302909345356125267430944752731616095111727103650117987412058949254132"), imag(a), tol);
+   a = acos(c);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("1.000143542473797218521037811954081791915781454591512773957199036332934196716853565071982697727425908742684531873"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-1.983387029916535432347076902894039565014248302909345356125267430944752731616095111727103650117987412058949254132"), imag(a), tol);
+   a = atan(c);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("1.409921049596575522530619384460420782588207051908724814771070766475530084440199227135813201495737846771570458568"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("0.2290726829685387662958818029420027678625253049770656169479919704951963414344907622560676377741902308144912055002"), imag(a), tol);
+   a = sqrt(c + 0);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("1.674149228035540040448039300849051821674708677883920366727287836003399240343274891876712629708287692163156802065"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("0.8959774761298381247157337552900434410433241995549314932449006989874470582160955817053273057885402621549320588976"), imag(a), tol);
+   a = sin(c + 0);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("9.154499146911429573467299544609832559158860568765182977899828142590020335321896403936690014669532606510294425039"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-4.168906959966564350754813058853754843573565604758055889965478710592666260138453299795649308385497563475115931624"), imag(a), tol);
+   a = cos(c + 0);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-4.1896256909688072301325550196159737286219454041279210357407905058369727912162626993926269783331491034500484583"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-9.1092278937553365979791972627788621213326202389201695649104967309554222940748568716960841549279996556547993373"), imag(a), tol);
+   a = tan(c + 0);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-0.0037640256415042482927512211303226908396306202016580864328644932511249097100916559688254811519914564480500042311"), real(a), tol * 5);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("1.0032386273536098014463585978219272598077897241071003399272426939850671219193120708438426543945017427085738411"), imag(a), tol);
+   a = asin(c + 0);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("0.5706527843210994007102838796856696501828032450960401365302732598209740064262509342420347149436326252483895113827"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("1.983387029916535432347076902894039565014248302909345356125267430944752731616095111727103650117987412058949254132"), imag(a), tol);
+   a = acos(c + 0);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("1.000143542473797218521037811954081791915781454591512773957199036332934196716853565071982697727425908742684531873"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-1.983387029916535432347076902894039565014248302909345356125267430944752731616095111727103650117987412058949254132"), imag(a), tol);
+   a = atan(c + 0);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("1.409921049596575522530619384460420782588207051908724814771070766475530084440199227135813201495737846771570458568"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("0.2290726829685387662958818029420027678625253049770656169479919704951963414344907622560676377741902308144912055002"), imag(a), tol);
+
+   a = sinh(c);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-3.5905645899857799520125654477948167931949136757293015099986213974178826801534614215227593814301490087307920223"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("0.53092108624851980526704009066067655967277345095149103008706855371803528753067068552935673000832252607835087747"), imag(a), tol);
+   a = cosh(c);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-3.7245455049153225654739707032559725286749657732153307267858945686649501059065292889110148294141744084833329553"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("0.51182256998738460883446384980187563424555660949074386745538379123585339045741119409984041226187262097496424111"), imag(a), tol);
+   a = tanh(c);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("0.965385879022133124278480269394560685879729650005757773636908240066639772853967550095754361348005358178253777920"), real(a), tol * 5);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-0.00988437503832249372031403430350121097961813353467039031861010606115560355679254344335582852193041894874685555114"), imag(a), tol);
+   a = asinh(c);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("1.968637925793096291788665095245498189520731012682010573842811017352748255492485345887875752070076230641308014923"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("0.9646585044076027920454110594995323555197773725073316527132580297155508786089335572049608301897631767195194427315"), imag(a), tol);
+   a = acosh(c);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("1.983387029916535432347076902894039565014248302909345356125267430944752731616095111727103650117987412058949254132"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("1.000143542473797218521037811954081791915781454591512773957199036332934196716853565071982697727425908742684531873"), imag(a), tol);
+   a = atanh(c);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("0.1469466662255297520474327851547159424423449403442452953891851939502023996823900422792744078835711416939934387775"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("1.338972522294493561124193575909144241084316172544492778582005751793809271060233646663717270678614587712809117131"), imag(a), tol);
+   a = sinh(c + 0);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-3.5905645899857799520125654477948167931949136757293015099986213974178826801534614215227593814301490087307920223"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("0.53092108624851980526704009066067655967277345095149103008706855371803528753067068552935673000832252607835087747"), imag(a), tol);
+   a = cosh(c + 0);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-3.7245455049153225654739707032559725286749657732153307267858945686649501059065292889110148294141744084833329553"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("0.51182256998738460883446384980187563424555660949074386745538379123585339045741119409984041226187262097496424111"), imag(a), tol);
+   a = tanh(c + 0);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("0.965385879022133124278480269394560685879729650005757773636908240066639772853967550095754361348005358178253777920"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("-0.00988437503832249372031403430350121097961813353467039031861010606115560355679254344335582852193041894874685555114"), imag(a), tol);
+   a = asinh(c + 0);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("1.968637925793096291788665095245498189520731012682010573842811017352748255492485345887875752070076230641308014923"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("0.9646585044076027920454110594995323555197773725073316527132580297155508786089335572049608301897631767195194427315"), imag(a), tol);
+   a = acosh(c + 0);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("1.983387029916535432347076902894039565014248302909345356125267430944752731616095111727103650117987412058949254132"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("1.000143542473797218521037811954081791915781454591512773957199036332934196716853565071982697727425908742684531873"), imag(a), tol);
+   a = atanh(c + 0);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("0.1469466662255297520474327851547159424423449403442452953891851939502023996823900422792744078835711416939934387775"), real(a), tol);
+   BOOST_CHECK_CLOSE_FRACTION(real_type("1.338972522294493561124193575909144241084316172544492778582005751793809271060233646663717270678614587712809117131"), imag(a), tol);
+}
+
+template <class Real>
+typename boost::enable_if_c<boost::multiprecision::number_category<Real>::value != boost::multiprecision::number_kind_complex>::type test_members(Real)
+{
+   //
+   // Test sign and zero functions:
+   //
+   Real a = 20;
+   Real b = 30;
+   BOOST_CHECK(a.sign() > 0);
+   BOOST_CHECK(!a.is_zero());
+   if (std::numeric_limits<Real>::is_signed)
+   {
+      a = -20;
+      BOOST_CHECK(a.sign() < 0);
+      BOOST_CHECK(!a.is_zero());
+   }
+   a = 0;
+   BOOST_CHECK_EQUAL(a.sign(), 0);
+   BOOST_CHECK(a.is_zero());
+
+   a = 20;
+   b = 30;
+   a.swap(b);
+   BOOST_CHECK_EQUAL(a, 30);
+   BOOST_CHECK_EQUAL(b, 20);
+   //
+   // Test complex number functions which are also overloaded for scalar type:
+   //
+   BOOST_CHECK_EQUAL(real(a), a);
+   BOOST_CHECK_EQUAL(imag(a), 0);
+   BOOST_CHECK_EQUAL(real(a + 0), a);
+   BOOST_CHECK_EQUAL(imag(a + 2), 0);
+   BOOST_CHECK_EQUAL(norm(a), a * a);
+   BOOST_CHECK_EQUAL(norm(a * 1), a * a);
+   BOOST_CHECK_EQUAL(conj(a), a);
+   BOOST_CHECK_EQUAL(conj(a * 1), a);
+   BOOST_CHECK_EQUAL(proj(a), a);
+   BOOST_CHECK_EQUAL(proj(a * 1), a);
+   BOOST_CHECK_EQUAL(a.real(), a);
+   BOOST_CHECK_EQUAL(a.imag(), 0);
+   a.real(55);
+   BOOST_CHECK_EQUAL(a, 55);
+}
+
+template <class Real>
+void test_members(boost::rational<Real>)
+{
+}
+
+template <class Real>
+void test_signed_ops(const boost::mpl::true_&)
+{
+   Real a(8);
+   Real b(64);
+   Real c(500);
+   Real d(1024);
+   Real ac;
+   BOOST_CHECK_EQUAL(-a, -8);
+   ac = a;
+   ac = ac - b;
+   BOOST_CHECK_EQUAL(ac, 8 - 64);
+   ac = a;
+   ac -= a + b;
+   BOOST_CHECK_EQUAL(ac, -64);
+   ac = a;
+   ac -= b - a;
+   BOOST_CHECK_EQUAL(ac, 16 - 64);
+   ac = -a;
+   BOOST_CHECK_EQUAL(ac, -8);
+   ac = a;
+   ac -= -a;
+   BOOST_CHECK_EQUAL(ac, 16);
+   ac = a;
+   ac += -a;
+   BOOST_CHECK_EQUAL(ac, 0);
+   ac = b;
+   ac /= -a;
+   BOOST_CHECK_EQUAL(ac, -8);
+   ac = a;
+   ac *= -a;
+   BOOST_CHECK_EQUAL(ac, -64);
+   ac = a + -b;
+   BOOST_CHECK_EQUAL(ac, 8 - 64);
+   ac = -a + b;
+   BOOST_CHECK_EQUAL(ac, -8 + 64);
+   ac = -a + -b;
+   BOOST_CHECK_EQUAL(ac, -72);
+   ac = a + -+-b; // lots of unary operators!!
+   BOOST_CHECK_EQUAL(ac, 72);
+   test_conditional(Real(-a), -a);
+}
+template <class Real>
+void test_signed_ops(const boost::mpl::false_&)
+{
+}
+
+template <class Real>
+void test_basic_conditionals(Real a, Real b)
+{
+   if (a)
+   {
+      BOOST_ERROR("Unexpected non-zero result");
+   }
+   if (!a)
+   {
+   }
+   else
+   {
+      BOOST_ERROR("Unexpected zero result");
+   }
+   b = 2;
+   if (!b)
+   {
+      BOOST_ERROR("Unexpected zero result");
+   }
+   if (b)
+   {
+   }
+   else
+   {
+      BOOST_ERROR("Unexpected non-zero result");
+   }
+   if (a && b)
+   {
+      BOOST_ERROR("Unexpected zero result");
+   }
+   if (!(a || b))
+   {
+      BOOST_ERROR("Unexpected zero result");
+   }
+   if (a + b)
+   {
+   }
+   else
+   {
+      BOOST_ERROR("Unexpected zero result");
+   }
+   if (b - 2)
+   {
+      BOOST_ERROR("Unexpected non-zero result");
+   }
+}
+
+template <class T>
+typename boost::enable_if_c<boost::multiprecision::number_category<T>::value == boost::multiprecision::number_kind_complex>::type
+test_relationals(T a, T b)
+{
+   BOOST_CHECK_EQUAL((a == b), false);
+   BOOST_CHECK_EQUAL((a != b), true);
+
+   BOOST_CHECK_EQUAL((a + b == b), false);
+   BOOST_CHECK_EQUAL((a + b != b), true);
+
+   BOOST_CHECK_EQUAL((a == b + a), false);
+   BOOST_CHECK_EQUAL((a != b + a), true);
+
+   BOOST_CHECK_EQUAL((a + b == b + a), true);
+   BOOST_CHECK_EQUAL((a + b != b + a), false);
+
+   BOOST_CHECK_EQUAL((8 == b + a), false);
+   BOOST_CHECK_EQUAL((8 != b + a), true);
+   BOOST_CHECK_EQUAL((800 == b + a), false);
+   BOOST_CHECK_EQUAL((800 != b + a), true);
+   BOOST_CHECK_EQUAL((72 == b + a), true);
+   BOOST_CHECK_EQUAL((72 != b + a), false);
+
+   BOOST_CHECK_EQUAL((b + a == 8), false);
+   BOOST_CHECK_EQUAL((b + a != 8), true);
+   BOOST_CHECK_EQUAL((b + a == 800), false);
+   BOOST_CHECK_EQUAL((b + a != 800), true);
+   BOOST_CHECK_EQUAL((b + a == 72), true);
+   BOOST_CHECK_EQUAL((b + a != 72), false);
+}
+
+template <class T>
+typename boost::disable_if_c<boost::multiprecision::number_category<T>::value == boost::multiprecision::number_kind_complex>::type
+test_relationals(T a, T b)
+{
+   BOOST_CHECK_EQUAL((a == b), false);
+   BOOST_CHECK_EQUAL((a != b), true);
+   BOOST_CHECK_EQUAL((a <= b), true);
+   BOOST_CHECK_EQUAL((a < b), true);
+   BOOST_CHECK_EQUAL((a >= b), false);
+   BOOST_CHECK_EQUAL((a > b), false);
+
+   BOOST_CHECK_EQUAL((a + b == b), false);
+   BOOST_CHECK_EQUAL((a + b != b), true);
+   BOOST_CHECK_EQUAL((a + b >= b), true);
+   BOOST_CHECK_EQUAL((a + b > b), true);
+   BOOST_CHECK_EQUAL((a + b <= b), false);
+   BOOST_CHECK_EQUAL((a + b < b), false);
+
+   BOOST_CHECK_EQUAL((a == b + a), false);
+   BOOST_CHECK_EQUAL((a != b + a), true);
+   BOOST_CHECK_EQUAL((a <= b + a), true);
+   BOOST_CHECK_EQUAL((a < b + a), true);
+   BOOST_CHECK_EQUAL((a >= b + a), false);
+   BOOST_CHECK_EQUAL((a > b + a), false);
+
+   BOOST_CHECK_EQUAL((a + b == b + a), true);
+   BOOST_CHECK_EQUAL((a + b != b + a), false);
+   BOOST_CHECK_EQUAL((a + b <= b + a), true);
+   BOOST_CHECK_EQUAL((a + b < b + a), false);
+   BOOST_CHECK_EQUAL((a + b >= b + a), true);
+   BOOST_CHECK_EQUAL((a + b > b + a), false);
+
+   BOOST_CHECK_EQUAL((8 == b + a), false);
+   BOOST_CHECK_EQUAL((8 != b + a), true);
+   BOOST_CHECK_EQUAL((8 <= b + a), true);
+   BOOST_CHECK_EQUAL((8 < b + a), true);
+   BOOST_CHECK_EQUAL((8 >= b + a), false);
+   BOOST_CHECK_EQUAL((8 > b + a), false);
+   BOOST_CHECK_EQUAL((800 == b + a), false);
+   BOOST_CHECK_EQUAL((800 != b + a), true);
+   BOOST_CHECK_EQUAL((800 >= b + a), true);
+   BOOST_CHECK_EQUAL((800 > b + a), true);
+   BOOST_CHECK_EQUAL((800 <= b + a), false);
+   BOOST_CHECK_EQUAL((800 < b + a), false);
+   BOOST_CHECK_EQUAL((72 == b + a), true);
+   BOOST_CHECK_EQUAL((72 != b + a), false);
+   BOOST_CHECK_EQUAL((72 <= b + a), true);
+   BOOST_CHECK_EQUAL((72 < b + a), false);
+   BOOST_CHECK_EQUAL((72 >= b + a), true);
+   BOOST_CHECK_EQUAL((72 > b + a), false);
+
+   BOOST_CHECK_EQUAL((b + a == 8), false);
+   BOOST_CHECK_EQUAL((b + a != 8), true);
+   BOOST_CHECK_EQUAL((b + a >= 8), true);
+   BOOST_CHECK_EQUAL((b + a > 8), true);
+   BOOST_CHECK_EQUAL((b + a <= 8), false);
+   BOOST_CHECK_EQUAL((b + a < 8), false);
+   BOOST_CHECK_EQUAL((b + a == 800), false);
+   BOOST_CHECK_EQUAL((b + a != 800), true);
+   BOOST_CHECK_EQUAL((b + a <= 800), true);
+   BOOST_CHECK_EQUAL((b + a < 800), true);
+   BOOST_CHECK_EQUAL((b + a >= 800), false);
+   BOOST_CHECK_EQUAL((b + a > 800), false);
+   BOOST_CHECK_EQUAL((b + a == 72), true);
+   BOOST_CHECK_EQUAL((b + a != 72), false);
+   BOOST_CHECK_EQUAL((b + a >= 72), true);
+   BOOST_CHECK_EQUAL((b + a > 72), false);
+   BOOST_CHECK_EQUAL((b + a <= 72), true);
+   BOOST_CHECK_EQUAL((b + a < 72), false);
+
+   T c;
+   //
+   // min and max overloads:
+   //
+#if !defined(min) && !defined(max)
+//   using std::max;
+//   using std::min;
+// This works, but still causes complaints from inspect.exe, so use brackets to prevent macrosubstitution,
+// and to explicitly specify type T seems necessary, for reasons unclear.
+   a = 2;
+   b = 5;
+   c = 6;
+   BOOST_CHECK_EQUAL( (std::min<T>)(a, b),  a);
+   BOOST_CHECK_EQUAL( (std::min<T>)(b, a), a);
+   BOOST_CHECK_EQUAL( (std::max<T>)(a, b), b);
+   BOOST_CHECK_EQUAL( (std::max<T>)(b, a), b);
+   BOOST_CHECK_EQUAL( (std::min<T>)(a, b + c), a);
+   BOOST_CHECK_EQUAL( (std::min<T>)(b + c, a), a);
+   BOOST_CHECK_EQUAL( (std::min<T>)(a, c - b), 1);
+   BOOST_CHECK_EQUAL( (std::min<T>)(c - b, a), 1);
+   BOOST_CHECK_EQUAL( (std::max<T>)(a, b + c), 11);
+   BOOST_CHECK_EQUAL( (std::max<T>)(b + c, a), 11);
+   BOOST_CHECK_EQUAL( (std::max<T>)(a, c - b), a);
+   BOOST_CHECK_EQUAL( (std::max<T>)(c - b, a), a);
+   BOOST_CHECK_EQUAL( (std::min<T>)(a + b, b + c), 7);
+   BOOST_CHECK_EQUAL( (std::min<T>)(b + c, a + b), 7);
+   BOOST_CHECK_EQUAL( (std::max<T>)(a + b, b + c), 11);
+   BOOST_CHECK_EQUAL( (std::max<T>)(b + c, a + b), 11);
+   BOOST_CHECK_EQUAL( (std::min<T>)(a + b, c - a), 4);
+   BOOST_CHECK_EQUAL( (std::min<T>)(c - a, a + b), 4);
+   BOOST_CHECK_EQUAL( (std::max<T>)(a + b, c - a), 7);
+   BOOST_CHECK_EQUAL( (std::max<T>)(c - a, a + b), 7);
+
+   long l1(2), l2(3), l3;
+   l3 = (std::min)(l1, l2) + (std::max)(l1, l2) + (std::max<long>)(l1, l2) + (std::min<long>)(l1, l2);
+   BOOST_CHECK_EQUAL(l3, 10);
+
+#endif
+}
+
+template <class T>
+const T& self(const T& a) { return a; }
+
+template <class Real>
+void test()
+{
+#if !defined(NO_MIXED_OPS) && !defined(SLOW_COMPILER)
+   boost::multiprecision::is_number<Real> tag;
+   test_mixed<Real, unsigned char>(tag);
+   test_mixed<Real, signed char>(tag);
+   test_mixed<Real, char>(tag);
+   test_mixed<Real, short>(tag);
+   test_mixed<Real, unsigned short>(tag);
+   test_mixed<Real, int>(tag);
+   test_mixed<Real, unsigned int>(tag);
+   test_mixed<Real, long>(tag);
+   test_mixed<Real, unsigned long>(tag);
+#ifdef BOOST_HAS_LONG_LONG
+   test_mixed<Real, long long>(tag);
+   test_mixed<Real, unsigned long long>(tag);
+#endif
+   test_mixed<Real, float>(tag);
+   test_mixed<Real, double>(tag);
+   test_mixed<Real, long double>(tag);
+
+   typedef typename related_type<Real>::type                                                                      related_type;
+   boost::mpl::bool_<boost::multiprecision::is_number<Real>::value && !boost::is_same<related_type, Real>::value> tag2;
+
+   test_mixed<Real, related_type>(tag2);
+
+   boost::mpl::bool_<boost::multiprecision::is_number<Real>::value && (boost::multiprecision::number_category<Real>::value == boost::multiprecision::number_kind_complex)> complex_tag;
+   test_mixed<Real, std::complex<float> >(complex_tag);
+   test_mixed<Real, std::complex<double> >(complex_tag);
+   test_mixed<Real, std::complex<long double> >(complex_tag);
+
+#endif
+#ifndef MIXED_OPS_ONLY
+   //
+   // Integer only functions:
+   //
+   test_integer_ops<Real>(typename boost::multiprecision::number_category<Real>::type());
+   //
+   // Real number only functions:
+   //
+   test_float_ops<Real>(typename boost::multiprecision::number_category<Real>::type());
+   //
+   // Test basic arithmetic:
+   //
+   Real a(8);
+   Real b(64);
+   Real c(500);
+   Real d(1024);
+   BOOST_CHECK_EQUAL(a + b, 72);
+   a += b;
+   BOOST_CHECK_EQUAL(a, 72);
+   BOOST_CHECK_EQUAL(a - b, 8);
+   a -= b;
+   BOOST_CHECK_EQUAL(a, 8);
+   BOOST_CHECK_EQUAL(a * b, 8 * 64L);
+   a *= b;
+   BOOST_CHECK_EQUAL(a, 8 * 64L);
+   BOOST_CHECK_EQUAL(a / b, 8);
+   a /= b;
+   BOOST_CHECK_EQUAL(a, 8);
+   Real ac(a);
+   BOOST_CHECK_EQUAL(ac, a);
+   ac = a * c;
+   BOOST_CHECK_EQUAL(ac, 8 * 500L);
+   ac = 8 * 500L;
+   ac = ac + b + c;
+   BOOST_CHECK_EQUAL(ac, 8 * 500L + 64 + 500);
+   ac = a;
+   ac = b + c + ac;
+   BOOST_CHECK_EQUAL(ac, 8 + 64 + 500);
+   ac = ac - b + c;
+   BOOST_CHECK_EQUAL(ac, 8 + 64 + 500 - 64 + 500);
+   ac = a;
+   ac = b + c - ac;
+   BOOST_CHECK_EQUAL(ac, -8 + 64 + 500);
+   ac = a;
+   ac = ac * b;
+   BOOST_CHECK_EQUAL(ac, 8 * 64);
+   ac = a;
+   ac *= b * ac;
+   BOOST_CHECK_EQUAL(ac, 8 * 8 * 64);
+   ac = b;
+   ac = ac / a;
+   BOOST_CHECK_EQUAL(ac, 64 / 8);
+   ac = b;
+   ac /= ac / a;
+   BOOST_CHECK_EQUAL(ac, 64 / (64 / 8));
+   ac = a;
+   ac = b + ac * a;
+   BOOST_CHECK_EQUAL(ac, 64 * 2);
+   ac = a;
+   ac = b - ac * a;
+   BOOST_CHECK_EQUAL(ac, 0);
+   ac = a;
+   ac = b * (ac + a);
+   BOOST_CHECK_EQUAL(ac, 64 * (16));
+   ac = a;
+   ac = b / (ac * 1);
+   BOOST_CHECK_EQUAL(ac, 64 / 8);
+   ac = a;
+   ac = ac + b;
+   BOOST_CHECK_EQUAL(ac, 8 + 64);
+   ac = a;
+   ac = a + ac;
+   BOOST_CHECK_EQUAL(ac, 16);
+   ac = a;
+   ac = a - ac;
+   BOOST_CHECK_EQUAL(ac, 0);
+   ac = a;
+   ac += a + b;
+   BOOST_CHECK_EQUAL(ac, 80);
+   ac = a;
+   ac += b + a;
+   BOOST_CHECK_EQUAL(ac, 80);
+   ac = +a;
+   BOOST_CHECK_EQUAL(ac, 8);
+   ac = 8;
+   ac = a * ac;
+   BOOST_CHECK_EQUAL(ac, 8 * 8);
+   ac = a;
+   ac = a;
+   ac += +a;
+   BOOST_CHECK_EQUAL(ac, 16);
+   ac = a;
+   ac += b - a;
+   BOOST_CHECK_EQUAL(ac, 8 + 64 - 8);
+   ac = a;
+   ac += b * c;
+   BOOST_CHECK_EQUAL(ac, 8 + 64 * 500);
+   ac = a;
+   ac = a;
+   ac -= +a;
+   BOOST_CHECK_EQUAL(ac, 0);
+   ac = a;
+   if (std::numeric_limits<Real>::is_signed || is_twos_complement_integer<Real>::value)
+   {
+      ac = a;
+      ac -= c - b;
+      BOOST_CHECK_EQUAL(ac, 8 - (500 - 64));
+      ac = a;
+      ac -= b * c;
+      BOOST_CHECK_EQUAL(ac, 8 - 500 * 64);
+   }
+   ac = a;
+   ac += ac * b;
+   BOOST_CHECK_EQUAL(ac, 8 + 8 * 64);
+   if (std::numeric_limits<Real>::is_signed || is_twos_complement_integer<Real>::value)
+   {
+      ac = a;
+      ac -= ac * b;
+      BOOST_CHECK_EQUAL(ac, 8 - 8 * 64);
+   }
+   ac = a * 8;
+   ac *= +a;
+   BOOST_CHECK_EQUAL(ac, 64 * 8);
+   ac = a;
+   ac *= b * c;
+   BOOST_CHECK_EQUAL(ac, 8 * 64 * 500);
+   ac = a;
+   ac *= b / a;
+   BOOST_CHECK_EQUAL(ac, 8 * 64 / 8);
+   ac = a;
+   ac *= b + c;
+   BOOST_CHECK_EQUAL(ac, 8 * (64 + 500));
+   ac = b;
+   ac /= +a;
+   BOOST_CHECK_EQUAL(ac, 8);
+   ac = b;
+   ac /= b / a;
+   BOOST_CHECK_EQUAL(ac, 64 / (64 / 8));
+   ac = b;
+   ac /= a + Real(0);
+   BOOST_CHECK_EQUAL(ac, 8);
+   //
+   // simple tests with immediate values, these calls can be optimised in many backends:
+   //
+   ac = a + b;
+   BOOST_CHECK_EQUAL(ac, 72);
+   ac = a + +b;
+   BOOST_CHECK_EQUAL(ac, 72);
+   ac = +a + b;
+   BOOST_CHECK_EQUAL(ac, 72);
+   ac = +a + +b;
+   BOOST_CHECK_EQUAL(ac, 72);
+   ac = a;
+   ac = b / ac;
+   BOOST_CHECK_EQUAL(ac, b / a);
+   //
+   // Comparisons:
+   //
+   test_relationals(a, b);
+   test_members(a);
+   //
+   // Use in Boolean context:
+   //
+   a = 0;
+   b = 2;
+   test_basic_conditionals(a, b);
+   //
+   // Test iostreams:
+   //
+   std::stringstream ss;
+   a = 20;
+   b = 2;
+   ss << a;
+   ss >> c;
+   BOOST_CHECK_EQUAL(a, c);
+   ss.clear();
+   ss << a + b;
+   ss >> c;
+   BOOST_CHECK_EQUAL(c, 22);
+   BOOST_CHECK_EQUAL(c, a + b);
+   //
+   // More cases for complete code coverage:
+   //
+   a = 20;
+   b = 30;
+   swap(a, b);
+   BOOST_CHECK_EQUAL(a, 30);
+   BOOST_CHECK_EQUAL(b, 20);
+   a = 20;
+   b = 30;
+   std::swap(a, b);
+   BOOST_CHECK_EQUAL(a, 30);
+   BOOST_CHECK_EQUAL(b, 20);
+   a = 20;
+   b = 30;
+   a = a + b * 2;
+   BOOST_CHECK_EQUAL(a, 20 + 30 * 2);
+   a = 100;
+   a = a - b * 2;
+   BOOST_CHECK_EQUAL(a, 100 - 30 * 2);
+   a = 20;
+   a = a * (b + 2);
+   BOOST_CHECK_EQUAL(a, 20 * (32));
+   a = 20;
+   a = (b + 2) * a;
+   BOOST_CHECK_EQUAL(a, 20 * (32));
+   a = 90;
+   b = 2;
+   a = a / (b + 0);
+   BOOST_CHECK_EQUAL(a, 45);
+   a = 20;
+   b = 30;
+   c = (a * b) + 22;
+   BOOST_CHECK_EQUAL(c, 20 * 30 + 22);
+   c = 22 + (a * b);
+   BOOST_CHECK_EQUAL(c, 20 * 30 + 22);
+   c  = 10;
+   ac = a + b * c;
+   BOOST_CHECK_EQUAL(ac, 20 + 30 * 10);
+   ac = b * c + a;
+   BOOST_CHECK_EQUAL(ac, 20 + 30 * 10);
+   a = a + b * c;
+   BOOST_CHECK_EQUAL(a, 20 + 30 * 10);
+   a = 20;
+   b = a + b * c;
+   BOOST_CHECK_EQUAL(b, 20 + 30 * 10);
+   b = 30;
+   c = a + b * c;
+   BOOST_CHECK_EQUAL(c, 20 + 30 * 10);
+   c = 10;
+   c = a + b / c;
+   BOOST_CHECK_EQUAL(c, 20 + 30 / 10);
+
+   //
+   // Test conditionals:
+   //
+   a = 20;
+   test_conditional(a, +a);
+   test_conditional(a, (a + 0));
+
+   test_signed_ops<Real>(boost::mpl::bool_<std::numeric_limits<Real>::is_signed>());
+   //
+   // Test hashing:
+   //
+   boost::hash<Real> hasher;
+   std::size_t       s = hasher(a);
+   BOOST_CHECK_NE(s, 0);
+#ifndef BOOST_NO_CXX11_HDR_FUNCTIONAL
+   std::hash<Real> hasher2;
+   s = hasher2(a);
+   BOOST_CHECK_NE(s, 0);
+#endif
+
+   //
+   // Test move:
+   //
+#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
+   Real m(static_cast<Real&&>(a));
+   BOOST_CHECK_EQUAL(m, 20);
+   // Move from already moved from object:
+   Real m2(static_cast<Real&&>(a));
+   // assign from moved from object
+   // (may result in "a" being left in valid state as implementation artifact):
+   c = static_cast<Real&&>(a);
+   // assignment to moved-from objects:
+   c = static_cast<Real&&>(m);
+   BOOST_CHECK_EQUAL(c, 20);
+   m2 = c;
+   BOOST_CHECK_EQUAL(c, 20);
+   // Destructor of "a" checks destruction of moved-from-object...
+   Real m3(static_cast<Real&&>(a));
+#endif
+#ifndef BOOST_MP_NOT_TESTING_NUMBER
+   //
+   // string and string_view:
+   //
+   {
+      std::string s1("2");
+      Real        x(s1);
+      BOOST_CHECK_EQUAL(x, 2);
+      s1 = "3";
+      x.assign(s1);
+      BOOST_CHECK_EQUAL(x, 3);
+#ifndef BOOST_NO_CXX17_HDR_STRING_VIEW
+      s1 = "20";
+      std::string_view v(s1.c_str(), 1);
+      Real             y(v);
+      BOOST_CHECK_EQUAL(y, 2);
+      std::string_view v2(s1.c_str(), 2);
+      y.assign(v2);
+      BOOST_CHECK_EQUAL(y, 20);
+#endif
+   }
+#endif
+   //
+   // Bug cases, self assignment first:
+   //
+   a = 20;
+   a = self(a);
+   BOOST_CHECK_EQUAL(a, 20);
+
+   a = 2;
+   a = a * a * a;
+   BOOST_CHECK_EQUAL(a, 8);
+   a = 2;
+   a = a + a + a;
+   BOOST_CHECK_EQUAL(a, 6);
+   a = 2;
+   a = a - a + a;
+   BOOST_CHECK_EQUAL(a, 2);
+   a = 2;
+   a = a + a - a;
+   BOOST_CHECK_EQUAL(a, 2);
+   a = 2;
+   a = a * a - a;
+   BOOST_CHECK_EQUAL(a, 2);
+   a = 2;
+   a = a + a * a;
+   BOOST_CHECK_EQUAL(a, 6);
+   a = 2;
+   a = (a + a) * a;
+   BOOST_CHECK_EQUAL(a, 8);
+#endif
+}